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Index of Subjects in all Volumes

Vol. II, 2008

From: Berj Ensanian
Date: Wed, 02 Jan 2008 16:39:53 -0500 (EST)

Subject: J.VS: Thank you

For the record, the J.VS Committee of Moderators, CM, herewith declares its appreciation to Yahoo! Inc., and in particular its GeoCities web hosting operation, for providing the mechanism that has been presenting the J.VS Archive to the online community since the founding of the Journal of Voynich Studies:



J.VS Formal Rules page

List of Subjects in all Volumes page

Vol. I (2007) Archive page

Vol. II (2008) Archive page

And once more, CM declares its appreciation to the Mt. Suhora Observatory for hosting the J.VS Library:

Index page to the Library of J.VS

On behalf of J.VS CM,

Berj N. Ensanian / KI3U

From: Berj Ensanian
Date: Thu, 03 Jan 2008 23:35:00 -0500 (EST)

Subject: J.VS: conyio vs congio and Conye etc. and the elusive Baresch

Redacted off-J discussions 30 DEC 2007 - 1 JAN 2008

Berj Ensanian says:
The thing about the [f24v] Schnazbrothers is this: it is an analysis of primary VMS material. With things like the Moretus letter we are hoping it is relevant, even if only circumstantially, but we can't be sure. Same with the hidden gallows letter in Baresch's sine. But the Schnazbrothers are, arguably, right there in the world's most mysterious manuscript, and it is a wonder that in a hundred years nobody ever noticed them before. It's the power of negative suggestion: the VMS illustrations have traditionally been deemed crude and lacking in sophistication.

Jan Hurych says:
Berj, you wrote [J.VS comm. #133]:

" But it is not entirely satisfactory - for one thing, would Moretus really get involved, twice, in such an affair? "

Well, I think he just happened to travel to Italy and he might not have known what was in the package. As for second delivery, we do not know who was the messenger, probably same as per Kinner's letter. As for Marci, his package was most likely delivered by Pater Provincial as per Kinner's letter. Strangely, Marci's letter was written on 19th of August 1666 and Kinner's letter was dated 5 January 1667. So he did not get any confirmation by Kircher that he got the book, not even after five months? But if it was sent by messenger, wasn't he back by that time to tell Marci he delivered the package? Marci died on 10th of April 1667 and in January 1667 he was apparently completely blind ( the record says he was blind when he was dying) so he asked Kinner for favor. (I quote from Kinner's letter the part: "Dominus Marcus qui omnium rerum poene oblitus, Tui tamen adhuc memor, Te suo nomine officiosissime salutari iussit, ac per me scire desiderat, num iamiam Oedypum egeri! s in enodando libro, quem per Patrem Prouincialem anno superiore transmiserat et quaenam ibidem mysteria contineri existimet: magno solatio eidem erit si in hoc puncto placuerit illius curiositati fauere." Maybe Greg could give us exact meaning?

" Of course you've conjectured that Moretus motivated Kircher to ignore Baresch. "

Only if the person he was ridiculing in his letter was Baresch and of that I am not sure. If he was the one, that would mean they talked or wrote about him already before since he is not mentioned by name - and M[oretus] might not be so nice about him as Marci was. It would be natural for mistrusting person like Kircher to ask Moretus while he was still in Rome if he knew Baresch well. There is another indication for that in the letter: Moretus was apparently not too happy in Bohemia and he might have extended that feeling to some particular persons - the feeling might have been mutual after all, he was the stranger there.

" But then we still have Marci in his book and letters defending Baresch as a good guy. Either way, the older thought that Baresch was a tool to make contact with Kircher still seems very attractive. Possibly Kircher were introduced to the Prague ms via Baresch, and then quickly dumped Baresch as an economics-driven conehead:), while nevertheless taking his ms seriously. "

Right. The samples of the script must have looked too interesting and surely would excited Kircher since he was asking for references on Baresch. And yes, he might have carried on secretly the research already. Since his letters to Marci were lost, there might have been one letter asking about Baresch or even asking for more samples. Marci knew about his craving so he finally sent him the whole book. Kircher of course did not solve it, otherwise he would brag about it, after all he was a showman, he made living by doing research and writing books.

" But just how real a person is Baresch? Again I ask: is there independent evidence at La Sapienza that a Georgius Baresch studied there? "

Well, somebody in the VML (Rene?) claimed there is a paper written by Baresch in Sapienza. Only listed, nobody really saw it.

" We have to get all the evidence for Baresch's existence together, ............ "

Right, most importantly to discover who was the first to mention his name in relation with the VM. As for B's existence, there are several proofs he did exist (his letter, his name in Marci's book. Marci's letter and maybe more, some records in Clementinum, as per Rene. That we cannot find too much about him is really not surprising - he was apparently a modest scientist, alchemists always worked for somebody and he apparently did not making too much money (neither did Horczicky as a chemist) and spending most of them them on books, probably not even married. Apparently he never published anything nor was lecturing and Marci might have been his only friend. So he was soon forgotten.

Berj says:
M25DEC1638, Moretus-to-Kircher letter:

APUG 567, 7r = 25 DEC 1638 ltr fm Theodorus Moretus to AK; Magnetismos; Archimede; Praga; verso adr

has what looks like "conyio" as the last word in line 28 (the 2nd paragraph starts with line 16):

27: Si laminar Villalpandianurum figurum Roma' in Collegio existant, quod opr-
28: nor, desiderarem ex ipsa Carmina accipi circino longitudinem pedis conyio
29: Farnesiano adscriptam. deinde optarem, si per otium R.V.a' esset integrum,

Here's a first shot at it:

27: If the Villalpandus sheet (map?) of the layout of Rome exists in the Collegio, the definitive work>
28: >work, need from it Carmina receiving the peripheral measurement conyio
29: written to Farnese. ........

Here conyio, like Conye in M22FEB1642, again seems to be something essentially mathematical. I'm wondering if these terms, conyio and Conye, that Moretus is discussing with Kircher, refer to conic projections mapping.

[ end of year 2007, start of year 2008 ]

Greg Stachowski says:
Well that would be what I understand Apollonius' text to be largely about. Conic sections. But then one would expect "conica"or some variation thereof. I haven't looked at the new Moretus yet, but I was leaning towards Jan's 'longas' for the 22 Feb.

Jan says:
Berj, letter "y" does not exist in Latin, it would be used in foreign name or latinized name (local or one of the foreign person). Your word "conyo" is quite clearly "congio" from "congius", a liquid measure of 3.25 litres (0.86 gallons) - as per Wiki, which consists of six sextarii, etc. Compare your "y" with "g" in the same letter, one line above in "collegio".

One more thing: Wiki says:
There is a congius in existence, called the "congius of Vespasian", or the "Farnese congius", ...

and if you look on next line in the letter, it says "Farnesiano", so it is really "congio Farnesiano" or as they say in mathematics: q.e.d. (quod erat demonstrandum = which was to be demonstrated)

Berj says:
I don't think it is absolute that there is no "y" in Latin - what about:

ymber : rain shower, rain storm, pelting rain.
ymo (immo): on the contrary, by no means/ by all means

This all reinforces the idea of transliteration vs transcription, and the need to be extra careful. However, I'd say the Farnese congius sure seems to clinch the q.e.d. but of course it must fit the rest of the sentence. Assuming I have isolated the sentence ok from the punctuations, then what do you guys translate lines 27-28 ?

[ end J.VS comm. #135 ]

From: Berj Ensanian
Date: Sat, 05 Jan 2008 12:14:20 -0500 (EST)

Subject: J.VS: The New Year brings a new member

Dear Colleagues

Journal of Voynich Studies welcomes aboard Dana Scott, well familiar to us as a fellow Voynich researcher.

Berj / KI3U

From: Berj Ensanian
Date: Sun, 06 Jan 2008 21:20:56 -0500 (EST)

Subject: J.VS: Inscriptions of specimens of Congius Farnesianus

Redaction of off-J discussions 5 - 6 JAN 2008:

Dana Scott says:
Dear Colleagues, I am honored to be a member of this esteemed group of Voynich reasearchers. Happy New Year to all.

Robert Teague says:
Hey, Dana, welcome aboard!

Jan Hurych says:
Welcome Dana and feel like home here!

Dennis Fedak says:
A hearty welcome to the J.VS forum. Your participation and insights are eagerly anticipated.

Greg Stachowski says:
Hello, Dana, and welcome.

Greg continues: Berj wrote [J.VS comm. #135]:

" Moretus-to-Kircher M25DEC1638 (APUG 576, 7r) has what looks like "conyio" as the last word in line 28 (the 2nd paragraph starts with line 16):

27: Si laminar Villalpandianurum figurum Roma' in Collegio existant, quod opr-
28: nor, desiderarem ex ipsa Carmina accipi circino longitudinem pedis conyio
29: Farnesiano adscriptam. deinde optarem, si per otium R.V.a' esset integrum, "

After a look at the original + Jan's comments, I make the transcription:

27: Si laminae V. figurum Romae in Collegio existant, quod ope-
28: ror, desiderarem ex ipsa lamina [??a]ccipi circino longitudinem pedis congio
29: Farnesiano adscriptam.

There is something before the "accipi": it is a longer word: can anyone make it out?

The first part is, roughly,

" If the plates* of V's drawings exist in the Collegio in Rome, which I am working on [finding out?], I wished/asked for [??accipi] ... from those particular** plates ... "

*perhaps sheets, but that would usually be say charta; he may mean plates as in prints, as used in older books for example.

** self-same; very.

Beyond that I am still unclear; I understand the words and have a vague idea, but have not finalised it yet. It would be enormously helpful if I could see a decent photo of this Farnese congius.

Berj says:
I can't understand how a liquid measure (congio Farnesiano) relates to the earlier parts of the sentence. But as I've admitted before, my Latin is simply inadequate.

Greg says:
While congius in general is a unit, the Farnese congius is a physical object, a measuring jug, as it were. I'm thinking that Moretus is referring to either the dimensions of the object itself or to an inscription on it. I now have a German-language description from 1798 of the Farnese congius, as seen in a collection in Dresden, where it is described as being 13 inches high and an inscription (referring to Vespasian) is given, as are comparisons with two other documented congii. I haven't gone over this new data thoroughly and put it all together yet, though. The German is attached:

Johann Gottfried Lipsius
{& Johann Friedrich Wacker)

Beschreibung der Churfuerstlichen Antiken-Galerie in Dresden. zum Theil nach hinterlassenen Papieren Herrn Johann Friedrich Wacker's, ehemaligen Inspector's dieser Galerie


Dritte Abtheilung.

In der Mitte steht ein roemisches Maas zu fluidis, das ohngefehr, nach unserm Maas, drei Kannen, oder sechs Noesel, fasst. Dieses Stueck ist unter dem Namen Congius Farnesianus bekannt, und hat folgende Auffschrift: IMP CAESARI VESPAS VI. cos I. CAES AVG F IIII MENSVRAE EXACTAE IN CAPITOLIO P (ondo). X

Es ist von gelbem Bronze, und wuerde, wenn man Aechtheit und Alterthum ganz gewiss beweisen koennte, unter die vorzueglich seltenen Stuecke dieser Sammlung gehoeren. S. [] LE PLAT Tab. 184, 4. Ist 13 Zoll hoch.

In den Recherches sur l`Origine, l`Esprit et les Progres des Arts de la Grece etc. (a Londres. 1785. Voll. III. 4.) T. II. Pl. XXXIV. findet man einen aehnlichen Congium, auch unter dem namen Congius Farnesianus, aber mit einer correctern Auffschrift, wie folgt: IMPER CAESARE VESP VI COS T CAES AVG F IIII MENSVRAE EXACTAE IN CAPITOLIO P. X.

Noch ein Congius, von eben der Art, aber ein wenig duenner und hoeher, finden wie in MONTFAUCON`S ant. expl. Vol. VI. (oder Tome III. P. I.) Pl. LXXXVII. Mit einer Aufschrift, die eben dieses sagt, aber in Nebendingen etwas abweicht, wie folgt: IMP CAESARE VESPAS VI COS CAES AVG. F IIII MENSVRAE EXACTAE IN CAPITOLIO P. X.

Vielleicht sind alles dieses Kopien, von einem Originale, es mag nun das Farnesische, oder irgend ein anderes seyn, bei welchem die verschiedenen Kuenstler die Woerter nach Belieben abkuerzten oder verlaengerten, je nachdem es die Symmetrie, nach der einmal angelegten Schrift, verlangte.

Berj says:
I'm wondering about the exact transcription (typos?) of the 1798 German, but anyway it seems to say this:


Johann Gottfried Lipsius

Description of the Crownprince-ian antiquities gallery in Dresden. In part after left-behind papers of Mr. Johann Friedrich Wacker, former inspector of this gallery.


Third Section/Department/Unit

In the middle stands a Roman measure for fluids, that approximately, after our measure, holds three Kannen (pots/cans), or six Noesel. This piece is known by the name Congius Farnesianus, and has the following inscription: IMP CAESARI VESPAS VI. cos I. CAES AVG F IIII MENSVRAE EXACTAE IN CAPITOLIO P (ondo). X

It is of yellow bronze, and would belong, if one could very surely prove genuine-ness and age, among the excellent rare pieces of this collection. LE PLAT Tab. 184, 4. Is 13 Zoll in height.

In the Recherches sur l`Origine, l`Esprit et les Progres des Arts de la Grece etc. (a Londres. 1785. Voll. III. 4.) T. II. Pl. XXXIV. one finds a similar Congium, also under the name Congius Farnesianus, but with a more correct inscription, which is as follows: IMPER CAESARE VESP VI COS T CAES AVG F IIII MENSVRAE EXACTAE IN CAPITOLIO P. X.

Yet another Congius, of the same art, but a little thinner and taller, is found as in MONTFAUCON`S ant. expl. Vol. VI. (oder Tome III. P. I.) Pl. LXXXVII. With an inscription, that says the same, but differs some in side-matters, as follows: IMP CAESARE VESPAS VI COS CAES AVG. F IIII MENSVRAE EXACTAE IN CAPITOLIO P. X.

Perhaps these are all copies, of an original, It may be only the Farnese-ian, or some other, on which the different artists according to their inclinations, abbreviated or expanded the words, as the symmetry, and again the once applied script, demanded it.

Greg says:
Great! Thanks Berj, that saves me a lot of work. The errors may be the usual minor spelling and style differences one would expect from an 18th century text. 'Zoll' is 'inch', so 13 inches high.

I wonder if Moretus was also aware of the other congius' inscriptions and that is what he was after?

Berj says:
Interesting thought, that Moretus was after the inscriptions, rather than some measurement unit.

Dana [commenting on Voynich studies sources] says:
There is some (unsubstantiated) evidence that Wilfrid Voynich was at the Villa Mondragone in 1911 (ref. ELV's closed letter concerning these events), and that the actual purchase of the VMS occurred in 1912. As part of the purchase, it seems that Wilfrid may have included some of his own books/manuscripts in exchange. I don't have the actual references on hand at the moment. These items are still in boxes following my family's move to a new house this past November. It also may be that Wilfrid first showed the VMS to scholars in France and England, though I imagine this was most likely done privately.

Berj says:
That's an important point and should be included in the Overview-Outline. There is always the possibility that a tenuous lead, even a rumor, points to some long dormant documentation somewhere in some dusty old desk, and it contains a major piece of actual evidence. I'm thinking this for this item in Section II: Unsubstantiated and possibly important evidence.

[ end J.VS comm. #137 ]

From: Berj Ensanian
Date: Tue, 08 Jan 2008 21:07:12 -0500 (EST)

Subject: J.VS: Comments on the Voynich f68r3 PM-curve question

Dear Colleagues

Below I make some general comments on the "PM-curve" of Voynich panel f68r3. I hope my comments are helpful to newcomers interested in an overview of this. Mostly I will confine myself to my own perspective of the subject, based on my 2006-2007 PM-curve work. [1]

1.) The PM-curve question divides into two versions that are somewhat subtly differentiated according to:

1-1.) The curve on Voynich panel f68r3 linking the "moon" and a distinct group of 7 stars, is meant to link the moon and the Pleiades star cluster to present some kind of astronomy-information.
1-2.) The curve on Voynich panel f68r3 linking the "moon" and a distinct group of 7 stars, may or may not be meant to link the moon and the Pleiades star cluster specifically, but nevertheless it is some kind of astronomy-information curve.

My own PM-curve work has focused on 1-2.), i.e. it avoids the more comprehensive problem of the intended meaning of the 7 stars. My work did not even require that the object in the center of the f68r3 diagram be the moon.

Thus, my PM-curve work has been totally independent of whether or not the well-known little group of seven star symbols in the f68r3 diagram represents the "Pleiades" star cluster in our sky. That drawn little group has traditionally been called the Pleiades in Voynich circles because it suggests the Pleiades, the Pleiades are a handy label for that group, and no veteran of Voynich studies will be surprised if one day it is proven that the f68r3 illustrator indeed intended to portray the Pleiades star cluster.

In the meanwhile, as far as I know, no serious Voynich researcher claims that it has been proven as fact that the f68r3 star group represents the actual Pleiades. The curve in question, connecting as it does to the f68r3 stars group, was named the Pleiades-Moon curve, PM-curve, as a logical handy label following the tradition of referring to the f68r3 group as the Pleiades, and the central object as moon. But it makes not the slightest difference to my own PM-curve work to date what the f68r3 illustrator had in mind when he / she drew that group of stars. It is irrelevant. During the 2006-2007 work I wrote:

" And needless to say, the mathematical structure of the PM-curve is unaffected completely by the identification of the seven-stars-cluster in f68r3 as being Pleiades or whatever. "

2.) The relevant assumptions going into general "PM-curve" work are:

2-1.) The Voynich f68r3 panel is an astronomical panel.
2-2.) The curve drawn between the "moon" and the "Pleiades" is possibly a carefully sketched curve, and perhaps even a plotted curve. [2]

3.) The PM-curve question then, for my focus to date, has been:

IF the assumptions of 2.) are taken as valid, and given the aging / condition factors of the VMS f68r3 parchment and its illustration components, and the necessity of working from the f68r3 SID image rather than the actual manuscript, is it possible to extract an interpretation of the curve, and then further, from the interpretation deduce something about the origin of the Voynich Manuscript, or at least its f68r3 panel?

I suggest that all other factors aside, the just stated is a worthwhile question for the attention of serious Voynich students.

4.) My 2006-2007 PM-curve efforts were, arguably, extensive, and I concluded:

4-1.) It is possible to extract precision data about the curve from the available SID image of f68r3.
4-2.) The curve is indeed a carefully plotted curve, and moreover it was plotted so carefully, employing a French-curve type template, as to suggest that the plotter desired to achieve the steganographic effect of the curve appearing to the casual and non-mathematical observer, as being mere free-hand.
4-3.) The best interpretation of the curve is that it represents transformed elliptic orbits etc.
4-4.) The mathematics and astronomy represented by the curve fit more comfortably in the 17th century, rather than earlier in time.
4-5.) The nature of the overall problem is such that efforts toward resolution require judges who are mathematically competent and experienced with hand-plotted curves, preferably astronomers.

5.) Certainly the crux of the PM-curve question is 2-2.), being at its most critical the question: Is the PM-curve an intentionally plotted curve, yes or no? The simplest attack on the validity of the PM-curve question is to dismiss it with: no, it is not a plotted curve. Fine. Is such a dismissal to be taken seriously? It depends of course on who is doing the dismissing. In light of 4-5.), most people cannot rule on the matter. In my own case, being trained in physics and mostly involved with experimental laboratory work where curves are born almost as often as we breathe, I have been hand-plotting curves, and studying the hand-plotted curves of other mathematically trained people, since 1959. I presume I know something about the art, and during my work I hand-plotted the transcribed PM-curve to a resolution of 145 points on an 18.3 cm span of the graph paper. I would of course pay attention to a dismissal of the curve-as-a-plot were such a dismissal to come from someone who fits into 4-5.) and provides detailed comments explaining their dismissal, comments as extensive as my comments when I explained why I believed the curve is indeed a carefully plotted curve.

6.) Referring to 1-1.) it is entirely possible to consider the PM-curve as an intended statement about an astronomical event involving the actual moon and the actual Pleiades cluster specifically. I believe my J.VS colleague Robert Teague's work, resulting in a Table of Moon occultation dates, one of which is 29 DEC 1615, is along those lines [3].

The degree to which the PM-curve's precision needs to be suggestive of actual plottable sky-paths, for Robert's work, has been discussed now and then by him and our J.VS colleague Greg Stachowski (who is a professional astronomer), myself jumping into such discussions at every opportunity. The most recent brief comment I made about it was in J.VS comm. #122, where comes across my biased sentiment that the PM-curve was a precision plot and therefor its analysis yields what I say above. However, I concede that it is entirely valid to conclude Robert's results without the PM-curve on parchment being an actual plot, and being instead a quicker sketch done by someone who nevertheless knows the sky-path curve, and either has before, or could if desired, plot it carefully.

So in other words, as I see it, Robert recognizes the PM-curve as an intentional sky-path curve, rendered sufficiently to suggest that the f68r3 author was familiar with sky-path mathematical details and he / she included enough information in the entire f68r3 panel to enable getting out of it a date, whereas I believe that the f68r3 author actually went to the trouble to plot the curve sufficiently carefully to make a point about the kinematics, and plausibly even the dynamics of sky-paths: elliptic orbits etc. Robert suspects that the f68r3 author wanted to give a date, I suspect the author wanted to present astronomical physics. I doubt that we are both wrong, and indeed we could both be right.

Could one ask for greater beauty in the friendly debate over the meaning of the PM-curve?

7.) Finally, I would like to point out an interesting contrast beween Voynich f68r3 and the hypothetical steganographic hand-script text-art (akin to today's ASCII art) portrait in f76r. Recalling 4-5.) above, the f68r3 PM-curve question, per version 1-2.), requires technically competent judges. But the reality of the face in f76r can be decided, as I proposed in J.VS comm. #111, by the man-in-the-street. And yet, both questions, the f68r3 PM-curve, and the f76r text-art stego portrait face, are astonishingly masterful creations, if indeed they are what I suggest they are. We see in them a genius in completely contrasting fields: pure science and pure art.

I don't know if the man I see in 3D portrait, in f76r, is the man who calculated and plotted the f68r3 PM-curve. But overall, to me it all makes sense for "the world's most mysterious manuscript".

Berj / KI3U

[1] The PM-curve developments were/are complicated and highly controversial in Voynich study circles. They began with the 4:49 PM, 4 DEC 2006, old-vms-list post "Re: VMs: 3x3 matrix of f58r and the f68r3 moon-ring". The detailed record may be found in the vms-list archive, but is easier to follow as a whole in the J.VS Library, where it is preserved in deposit # 1-1-2007-05-05, 3JVSlibKI3U.htm and 4vmsKI3Ulab.htm

[2] An apparently free-hand curve, one that quite closely approximates a rotated version of the f68r3 PM-curve, is found, drawn on rectangular cross-hairs, on Voynich f87r. For more on that see J.VS comm. #105 in J.VS Vol. I:

[3] Teague's Table is available as a document-file "Moon Occultation Date Summary" in J.VS Library deposit # 1-5-2007-06-24:

From: Berj Ensanian
Date: Sat, 12 Jan 2008 22:25:33 -0500 (EST)

Subject: J.VS: off-J discussions 9 - 12 JAN 2008, various topics

Redaction of off-J discussions 9 - 12 JAN 2008:

Berj Ensanian says:
Dana's conference, as much as I would like to attend, I can't. But I was thinking that if we all had high bandwidth (and I don't) would a J.VS video conference be practical?

Say something like this: we all have those little cameras connected to our computers, pointed at us (microphones too). We fire up some software, get online, and everyone's computer screen is divided into 6 panels, each panel being the video from a colleague. And we have a conference. Is that practical? Is there GNU software for something like that?

Dana Scott says:
Off the top of my head, we could have an open Skype line over the internet. I don't know at the moment what might be good for video conferencing.

Robert Teague says:
I've got a webcam and can do a video conference (I think) , but have never used it.

Greg Stachowski says:
I have a microphone and can do audio. I do have a webcam but it's somewhat dated and newer software doesn't want to talk to it. Buying a new webcam isn't really a problem, though, I was going to do that anyway at some point.

Dana's right to mention Skype, and there are some other tools as well. I'm sure we could manage something. The biggest issue we have is bandwidth, particularly Berj's.

Berj says:
My webcam is also very dated and I never used it except to try it when I first got it. I wouldn't worry about every member having bandwidth at this stage. The first thing is to see if it can be done, and even just two or three members with a webcam and adequate bandwidth can do an experiment for a few minutes and report results. A first step might be just an audio conference. Eventually the video conferences could become periodic, say once a month or something.

Jan Hurych says:
I have Skype, it is free and it works OK, even as a conference, but only sound conference - actually I haven't tried video conference yet. Ordinary videophone shows the other party and your camera as small insert in the corner. Could be, that with conference it will show more of those inserts, but even so, how to switch to different sender's picture? Complicated, to say at least. I made calls to Europe and even with low speed modem the pictures were acceptable by very modest standards. Of course the no. of pictures per minute is rather low.

Berj says:
I've got experience with amateur radio slow-scan TV on short-wave, and with just two people going back and forth, even that low bandwidth mode (~ 2.7 kHz) can result in remarkable communications. So it seems to me that with all this internet infrastructure around, and most of us using computers that are fairly recent vintage, something workable should be possible. Maybe Greg and Dennis can try an experiment and tell us what happened.

Since we last worked on it [Overview-outline of the Voynich studies field for newcomers] (was it Version 7?) I've come around to Greg's view ..... So, it seems that the overview-outline must be phrased very generally in some of its sections.

Dennis Fedak says:
I've used a 8.6Kbps connection with acceptable voice quality using VOIP. Some of the compression protocols are truly amazing. The delay was about 1 sec, and echo suppression made it tolerable.

Greg says:
From what I've heard of Berj's download troubles, his connection seems to be singularly poor both in speed and in stability. It would probably manage an audio connection, but perhaps not the video.

Berj says:
The conferencing will undoubtedly have bumps along the way. But I'm suggesting that it is a logical development in the future - the internet etc. infrastructure is expanding and eventually it will be as routine as these emails. I'm just saying we can do some experiments and see what happens.

Jan says:
The video conference could become a disaster. How did the last conference go ( I think it was organized by Nick (?)) and due to different time zones they were chasing each other all around the globe.

Berj says:
I myself don't have skype, and actually don't even know anything about it, but will get it and take a look at it and try it.

Jan says:
Let's go for it. I will try to find more on Skype video conferencing.

Berj says:
Referring back to the discussions recorded in J.VS comm. #137, are we tentatively assuming that there is a possible VMS connection between "Congius Farnesianus", being presumably a congius specimen tracing to the Farnese family, and the Farnese family, as conjectured by Wilfrid Voynich (see D'Imperio), being in possession of the Voynich ms sometime after Kircher got it? In other words, are we thinking something along the lines that:

the Farnese family was already involved with the VMS in the 1630's, and Moretus / Kircher had latched onto that possibility, and Moretus was investigating specimens of Farnese congius in search of inscriptions. ???

Is that what's going on currently? I'd like to be clear on this.

Greg says:
Woah! Unless I missed something, we're nowhere near any such assumption. We haven't translated Moretus' letters to Kircher fully, or seen Kircher's to him, or anything to point to either of them taking an active or even passive interest in the VMS, let alone linking it to the Farnese family or congius.

As far as I was aware, the congius came up because of what turned out to be a superficial similarity to the mysterious word from the 22 Feb letter, which meantime has been plausibly identified as 'longas'. Even so, that sentence has not been fully translated yet (I'm working on it). Also, without translating a substantially longer extract from the 'congias' letter, we have no idea why Moretus was interested in it, although given his interest in measures as evidenced by one of the other letters I suspect that that is all there is to it.

Further, as far as I know there is no record of Kircher having either received or analysed the VMS. All we have is the Baresch and Marci letters to him, neither of which is unassailable; to my knowledge no one has found any record of Kircher writing anything about the VMS -- which I find surprising.

Berj says:
Ah, I knew if I asked a naive question I had a good chance of getting a synopsis of where things currently stand with the Moretus letters ;) Thanks Greg. The Farnese family is interesting nevertheless - seems they had a talent for collecting unusual antiquities, including the "Farnese Atlas", a sculpture bearing the oldest known western / Greek zodiac. Hmm. Here's a long paper about that by B.E. Schaefer of Louisiana State Univ. that I haven't yet had a chance to read (I see "Aratus" in there - were'nt we just discussing him recently?), but it has a couple of pictures also:

Greg says:
Indeed. The thing which bothers me though is the complete lack of mention of the VMS in any catalogue, which one would expect for any prince's collection, be it Rudolph or the Farneses.

Berj says:
Yes, that's one of the old really serious problems in this whole mystery. Of course it could be cataloged in some clever way so as to hide it, maybe say listing it as some mundane book, or even something else, that is just slightly intentionally mis-cataloged. Remember this?:

vocabula nova et fictitia

If I'm seeing that Kircher list properly, then that paper bearing the above as a list item was written by Kircher himself (or one of his assistants).

Greg says:
Yes, this we need to get back to. Kircher strikes be as being too thorough and extensive in his correspondence not to either:
(a) catalogue it
(b) acknowledge receipt to Baresch or Marci
(c) mention it to _someone_ ( e.g. Moretus).

I find it hard to believe that, if K. had the VMS and did not dismiss it immediately, that there should be no trace anywhere in _his_ writing.

Berj says:
Anyway, the simplest solution to the problem seems to be to assume that the VMS was, for some reason, so hot, that its existence was kept secret. And the simplest reason I can think of that it was so hot, is that there was some sort of secret society, associated maybe with Hermes, Archimedes, Apollonius, and so on, and that Kircher was the "Oedipus", i.e. the grand master of the society. And once in a while some material would accidentally leak out and cause problems that today we see as one of the mysteries: Baresch.

All just guessing of course. But it seems that an old crypto work, no matter how hot during its heyday, would eventually get cataloged. But a secret society might have its stuff kept out of standard catalog listings.

Greg says:
Either the VMS was, as you say, too hot to index[1], or, it was seen as junk[2] or didn't even exist at all (being a later creation) and the Marci letter is a red herring.

[1] But then, would we not expect some hints of such a group to have come to light, 300 years later?
[2] But then, would we not expect some hint of this, a note to Marci or Moretus?

[replying to: But it seems that an old crypto work, no matter how hot during its heyday, would eventually get cataloged. But a secret society might have its stuff kept out of standard catalog listings.] says:
At the time, yes, but for 300 years? After it became irrelevant?

Like you, I think it would eventually surface somewhere (although, I suppose one might say that it _did_: in the collection WMV found it in; but I would have expected some mention elsewhere). Well, I'm not going to give an opinion either way, like you say this is all just guesswork, but these are all good points to think about.

Berj says:
If indeed Kircher saw the same ms that we see today as MS 408, then I think he would react as we do today: it is definitely NOT junk! So that would eliminate [2] above, leaving [1], the hypothetical mystery of why there are no obviously visible traces of the secret society after all these years - we don't know if that possible VMS word that is visible in the image of the letter-draft of Kircher to Adamus Schall (J.VS comm. #13, 82, 83), is actually a "trace". Well, of course there is the remote possibility that the secret society is still operating. Less sensational an explanation is inertia: say that the first guy to catalog Kircher's papers, I forget his name at the moment, meticulously separated the VMS papers and stamped them the Jesuit or whatever equivalent of TOP SECRET. The years roll on, and the mountain of papers every new archivist has to deal with grows, and lacking any particular reason to "de-classify" the VMS papers, why bother? Of course that covers only the most massive archive, the Catholic church. It seems very difficult to explain a beautiful script like the VMS's not being utilized to the point where we'd see some papers here and there. Unless very, very few people ever saw it.

Greg says:

Berj [commenting on Greg's just released J.VS paper: "Improving legibility of manuscript letters"] says:
Super! Well done Greg.

[ end J.VS comm. #139]

From: Greg Stachowski
To: "J.VS:"
Date: Sun, 13 Jan 2008 02:02:05 +0100

Subject: J.VS: Library subcollection 0-7-2007-01-12 on Image processing

With a view to sharing knowledge and evolving standard methods, I have created a new Library subcollection for image processing resources (articles, guides, software etc.; see also J.VS communications #113-#115).

As this is one of our '0' series common resources, everyone is invited (and indeed encouraged!) to contribute. I have started off with a short guide to improving the legibility of manuscripts such as those available through APUG, which arose through my current work on the Moretus-Kircher letters.

The URL is :

Contributions should be sent to me in the usual way. Updates and comments are also welcome.

From: Greg Stachowski
To: "J.VS:"
Date: Mon, 14 Jan 2008 04:09:29 +0100

Subject: J.VS: New paper by Robert Teague: Translations of some Labels in the VM

Robert has deposited his latest paper,

"Cracks in the Ice: Translations of some Labels in the Voynich Manuscript"

in the Library as deposit # 4-5-2008-01-12. The paper is in PDF format, to preserve portability.

From the paper,

" This paper presents the results of efforts to translate star labels based on assumed identifications from star charts ... ."

The URL is: .


From: Berj Ensanian
Date: Thu, 17 Jan 2008 19:27:14 -0500 (EST)

Subject: J.VS: Robert Teague's Seven Voynich Letters

Dear Colleagues

With reference to J.VS comm. #141, I understand, to this point, the essentials in Robert Teague's J.VS Library deposit # 4-5-2008-01-12 as follows:

1.) Obtain possible star identifications in VMS astro folios by matching the VMS star illustrations with the output of a planetarium program, and when necessary run the program for dates, typically several centuries past, that are assumed to be relevant.

2.) Collect VMS-label variations for identified stars, notably ALDEBARAN.

3.) Deduce from 2.) a presumed labeling convention employed by the VMS astro-section author, notably: leaving out some star-name letters in some labels, and anagraming.

4.) Note some further peculiar details in the convention of 3.) such as progressive economy in the letters-set of the labels, as the astro folios progress by folio-number.

5.) Across astro folios f67r2, 68r1, 68r2, 68r3, and 72r2, the ALDEBARAN label-variations are condensed to result in the essential correspondences between Voynich-label-text letters and these seven Latin letters: A, B, D, E, L, N, R, (Tables 1.4 and 1.5).

6.) Building on 5.) begin work in a similar vein to obtain a complete (26 letters) alphabet correspondences chart.

7.) The analysis proceeding with 6.) entails some detailed history of star charts, for example, the choice of ALCYONE rather than ALDEBARAN.

8.) To proceed further, invoke reference to past VMS-work "allowed letters substitutions", resulting in nine assignments in the correspondences (Table 2.5). Thus at this stage, "allowed letters substitutions" is added to the presumed convention of 3.).

9.) Draw on the apparent "key-like" column of Voynich letters in VMS f49v for further correspondences clues, and employ an anagraming program.

10.) " A comparison of the letters involved in Glen Claston's Prime 17 Letters list and Philip Neal's Vertical Letter Sequence reveals there are nineteen letters of interest. " (Table 5.1).

11.) Speculate that Voynich "4" has flexible value assignments, but "8" and "9" have fixed single values.

12.) Give Tables 5.3 to 5.6 showing correspondences possibilities for "allowed substitutions", touching on complex Voynich glyphs like intruding gallows letters. Table 5.5 for "4o" is easiest to understand first on how constructed Voynich digraphs enter Teague's theory.

Now of course, above at 8.) the theory jumps significantly in scope, and accordingly it is open to that much more challenge. Here I will confine myself to the theory as developed to 5.), and have a look at the seven letters-correspondences that Robert produced:

Table 1 (Adapted from Teague's Table 1.5)

Latin letter:: D'Imperio (MD) / EVA / GC transcription-alphabet equivalents

A:: K / d / 8
B:: H / a / a
D:: I / l / e
E:: B / ch / 1
L:: D / o / o
N:: N / y / 9
R:: C / e / c

Interesting that decades ago Mary D'Imperio had chosen "N" for transcribing the VMS letter that Robert decodes as "N".

Do Robert's analytically derived 7 letters de-code anything in the Voynich manuscript, with or without his presumed conventions in 3.) above? Obviously this is a very big task to investigate. I spent just a few minutes looking at some VMS text with Table 1 above in mind; of course some tantalizing possibilities cropped up. The most interesting I chanced on is on balneology folio f84v, the last / bottom word of a stack of six words positioned at bottom right of the lower blue-water pool with its eight bathing ladies. This word on the folio is MD-DBCKN, which with Table 1 becomes "LERAN", and if it is an anagram, it can be de-anagramed immediately to:


The f84v illustration is not at all dissonant with the idea of "learn". So, scant as my investigation here is, this is interesting. This is as far as I have had time to take it. I echo those who have already encouraged Robert to continue with this work. With his basic analytic procedures there is undoubtedly much more to learn.

Berj / KI3U

From: Berj Ensanian
Date: Thu, 17 Jan 2008 22:45:41 -0500 (EST)

Subject: J.VS: Iterative translation of Latin, VMS scientific testing, and other off-J discussions 12 - 17 JAN 2008

off-J discussions from 12 JAN to 17 JAN 2008:

Robert Teague [replying to Berj Ensanian's comments (at end of J.VS comm. #139] says:
Or the cataloguer didn't know what to make of it, so just tossed it aside and didn't bother to include it. Or it intrigued him and he didn't include it so he could take it home for study without anyone knowing.

I think a secret society, while possible, is going a bit too far out.

It occurs to me that in the VML archives there is mention of evidence that folios went missing AFTER Voynich found the book. The evidence was along the lines of "in one catalog it's listed as having X number of pages, while in a later catalog only Y number".

To my knowledge, nobody has ever followed that up. I think it should be kept in mind for later investigation.

Greg Stachowski says:
Yes, here's the thread:

If I'm speed-reading correctly (too tired, 4am here), I think they're listed in Newbold but then disappear.

As an aside, I haven't seen a thorough analysis of the contents of the Grolier Club files. Am I remembering correctly that Dana has something on that?

Dana Scott says:
Yes, Newbold's book lists VMs folio numbers which we do not find in the current bound version of the VMs at Beinecke. Unfortunately, I have not yet been able to visit the Grolier Club. This I plan to do on my next trip to N.Y., though I do not know when that might be.

Berj Ensanian says:
I tried to contact the Grolier Club once. Not being a member, my friendly email was ignored - no surprise.

Jan Hurych says:
Greg, this may be little off the subject but after careful reading of the [standard] translation of Marci's letter, he wrote he sent Kircher the book as well as Baresch's attempts to solve it. Those notes were not mentioned anywhere else. OK, Baresch sent the copies of folios with the first letter that were never found either, but the first letter was not found, while the book delivered OK and notes apparently with it too.

Why would Kircher put Marci's letter in the book without those Baresch's notes? Could it be that they were there but Voynich did not bother to publicize them? And if they were not there, did Voynich ask for them? After all, they may be somewhere else with lost folios.

Greg says:
Not off topic at all, these are again good questions. Where indeed are both Baresch's notes and Baresch's folios? Again, one can wonder: given how organised Kircher's papers are, where could they be? Could it be that someone removed one or other or both? Who, and why haven't they appeared? Or, is this again the old problem of the link between the Baresch & Marci letters and the VMS being only circumstantial: if they are not, in fact, anything to do with the VMS then Baresch's notes and folios could be out there in plain sight, and we would not see them for what they are.

[j.h.: Why would Kircher put Marci's letter in the book without those Baresch's notes?] Or perhaps the letter was put there later by a librarian, who mistakenly associated the letter with the VMS.

[j.h.: Could it be that they were there but Voynich did not bother to publicize them? And if they were not there, did Voynich ask for them?] He may not have been aware of them at the time (I believe he said he looked at the Marci letter later) or he may not have wanted to draw attention to his purchase (remember our discussions about the legality of it) by asking after additional material related to it.

Again, more speculation. We assume that the Baresch and Marci letters really are about the VMS, because it seems likely and because we have nothing better to go on. I too shall continue to work on that. But I submit that a lot of problems go away if this were not the case; perhaps we should look for evidence of an alternate provenance for the VMS or an alternative document which fits the Baresch and Marci letters.

Jan says:
I agree and it would be rather difficult to look for them 300 years after Kircher and 100 years after Voynich visit. Too bad. Assuming Baresch knew more than we suspect, his notes would be a real treasure. Or maybe not, but we will never know.

Dana says:
Hello Jan and Greg, As I recall, Baresch bequeathed his library to Marci. Marci's library was passed on to his son, I believe. I would think that there might be a reasonable expectation that at least a portion of these documents may still be in existence, if not damaged by flood or fire.

Berj says:
Looks like La Sapienza, Galileo, and Benedict XVI are making some news:

Jan says:
Sapienza was lay university already when Baresch was there.

Berj says:
Here is my current comprehension of Baresch's surfacing:

1.) Wilfrid Voynich discovers Baresch as a POI (by 1921?) but does not publicize Baresch.
2.) John Edward Fletcher in his 1972 Janus paper on Marci writing to Kircher, discusses Baresch but does not conjecture Baresch as an owner of the VMS.
3.) Robert S. Brumbaugh in his 1978 book, The Most Mysterious Manuscript ... ", tells of finding Wilfrid's notes in the Beinecke MS 408 papers, where Wilfrid had noted that Marci probably had inherited the manuscript from George Barschius.

Greg [concerning his 6 JAN 2008 statements (see J.VS comm. # 137) onM25DEC1638 ] says:

27: Si laminae V. figurum Romae in Collegio existant, quod ope-
28: ror, desiderarem ex ipsa lamina accipi circino longitudinem ped[i|e]s congio
29: Farnesiano adscriptam.

Just an update to say that I have been working on this and making progress, but it is tricky to pin down the exact meaning. I am now coming to the conclusion that I will need to backtrack and work through the preceding paragraph, which mentions Villalpandus and feet (as measure) before I can commit to a firm translation. This will obviously take a bit more time. However, I can confirm that Moretus was not interested in the inscription on the Farnese congius per se.

Berj says:
Ok, sounds like progress.

Greg says:
It is. This is one if the trickier sentences I've had to do.

Berj says:
r. I'm patiently waiting for your comments when you have them. In the meantime about it all I keep thinking of the first half of the subject line of J.VS comm. #4: " Just Latin, or something more? "

Greg says:
Heh, who knows :) But with Latin, its long history combined with a relatively small vocabulary means that most words (particularly verbs) have multiple meanings, often similar but not quite the same, with the precise one being determined by context, and also much of the meaning or rather the relationships is carried by the endings. But these may also give multiple possibilities sometimes. So translation is very much iterative: do a bit, then see how that influences the other words, and revise as necessary.

In this case Moretus is saying that, if the Villalpandus plates are in Rome, he wants them looked at to see what there is written there about the length of ... and here I hit some uncertainties which I hope to resolve by looking earlier in the paragraph to see what he is discussing. Clearly I have some favoured ideas but I don't want to jump ahead of myself in case I'm wrong.

Berj says:
That's not far different from my first shot at it (comm. #135), but I expect that when you are ready we will still haggle some over the transcription.

Jan [on Marci's last letter] says:
The text in question [from Marci's last letter] is this:

"....uerum librum ipsum transmittere tum recusabat in quo discifrando posuit indefessum laborem, uti manifestum ex conatibus ejusdem hic una tibi transmissis neque prius huius spei quam uitae suae finem fecit. "

Translated (1968 Tiltman-reference in D'Imperio, pgs.1, 80, 81) as:

"...but he at that time refused to send the book itself. To its deciphering he devoted unflagging toil, [as is apparent from attempts of his which I send you herewith], and he relinquished hope only with his life. "

I have made the critical expression in brackets. I did really locate in the original text the word "attempt" = conatibus, ablative of "conatus" (attempt, effort) which of course could mean only some records made by Baresch, i.e. notes or samples of solution.

It makes perfect sense that Kircher stored those notes as well as he stored Baresch's second letter. They should be somewhere, but where? It is rather surprising nobody ever noticed this discrepancy, as far as I know.

Greg says:
Indeed. This is exactly what I was getting at in my mails a few days ago.

Berj says:
Lets check the much earlier translation in Newbold's book.

Greg says:
As far as I can tell, Newbold does not provide a translation directly, but summarises the letter, to the same effect (copies sent to Kircher earlier etc).

Berj says:
The 1968 Tiltman-referenced translation given by D'Imperio (p. 1, 80, 81) is apparently a 1921 translation prepared for Wilfrid Voynich. But prepared for Voynich by who? Does anyone recall?

Greg says:
If 1921, that would suggest it was done for the Philadelphia paper, and might be referenced there. Dana?

WMV might have translated it himself, you know, perhaps together with AMN.

Jan says:
Newbold's book ... the question is: how much of it is really Newbold? There are also 2 comments about Kent in VML:

Dana says:
I am also interested in researching Baresch's attendance at La Sapienza. I wonder if records have been kept that far back on the enrolled students?

Berj [commenting on Dana's question of what a list of objectives for scientific testing of MS 408 might have] says:
I think before a list of objectives like spectrographic analysis of the inks and pigments can be put before Beinecke, there is another question that needs an answer.

Who is going to take responsibility?

It seems to me that undertaking a scientific examination of a unique antiquity requires very serious protocols, therefore a committee or committees plugged into networks, including financial, and someone with sufficient qualifications in the preceeding must first decide to take on the responsibility of igniting the project and moving it along, and that implies taking the responsibility for the potential hazards along the way, those ranging from damage to the manuscript, to irreversible discord for one reason or another within the affected networks.

A project like the scientific examination of MS 408 involves considerations of the personalities and interests of the necessary people and organizations involved, and that is complicated. It requires first an ideal someone taking responsibility, it seems to me.

Dana says:
Berj, I agree with you whole heartedly. ..... One of the major reasons that I have lit this candle is to bring out in the open the real complexity of seeing this "wish list" to fruition.

[ end of J.VS communication #143 ]

From: Greg Stachowski
Date: Fri, 18 Jan 2008 21:37:26 +0100

Subject: J.VS: Library deposit # 11-4-2008-01-18: The Lost Notes of Georgius Baresch, by Jan Hurych

Jan's new article,


Is now in the library as deposit # 11-4-2008-01-18

To quote Jan's abstract:

" The article provides the summary history of several sets of Baresch's attachments to his letters as well as the attachement to Marci's letter and the VM. It is the last set that was surely received by Kircher, most likely stored by him as well and can be an important addition to the existing VM documentation. "

The URL is :


From: Berj Ensanian
Date: Tue, 22 Jan 2008 22:07:14 -0500 (EST)

Subject: J.VS: Alchemical Herbal Eyes, and the Steganographic Face Problem

Dear Colleagues

Our Librarian Greg has installed for me an additional two images, along with updated metadata, in the J.VS Library deposit # 12-1-2007-10-12 [1]. Althought not the only Library deposit concerned with VMS faces, that one is a growing collection of some faces and hypothetical faces including steganographic, in the Voynich ms, and browsing it makes for a quick tour of the subject. The metadata textfile tells how the two new images were obtained: no processing was applied. Discussion:

1.) "Streamface"

This image, r1vmsf84vStreamface.jpg, is a rotated crop from the upper-right of the f84v illustration saved as a jpg, and it is, I think, an excellent example for considerations of the problem:

Are some graphical details in VMS illustrations intentional steganographic faces?

This one is a really tough call. Debating the issue could bring in arguments like that the symbology of the scene supports an anthropomorphic-deity component in the "heavenly" stream that is apparently feeding the upper blue-water pool with its seven bathing VMS sisters. Interestingly, this balneology folio f84v came up just very recently in connection with Robert Teague's Seven Voynich Letters, and the possible decoding of its last right-margin word as "LEARN". [2]

2.) "Red Eyes Root"

This image, 1crf17rRedEyesRoot.jpg, is a rotated crop of the root plus some stem and leaves of the f17r plant. I personally think it is rather obvious that here the artist intended to depict eyes in the plant's root, rather fierce big eyes that are gazing up the plant's stem. It is remarkable I'd say, that these eyes are not especially obvious in the normal view of the page, but suddenly do become very obvious when the page is rotated to 90 degrees c.c.w. Jorge Stolfi described it:

' The eyes in the roots seem to be the result of "enhancing" two eye-like gaps in the roots. ' [3]

This image I thought would be good for discussions of the VMS botanical section in connection with "alchemical herbals". In her book, Mary D'Imperio suggested investigating early herbals in connection with alchemical themes. In section 3.3.1 she wrote:

" The faces attached to some plant roots (see 33r, 89r1), and the suggestion of eyes, horns, snouts, etc., on other plant parts (see 38r, 28r, and figure 9 for examples), are considerably harder to explain. ..... should receive more systematic study in comparison with similar practices in known herbal and alchemical manuscripts ... " [4]

D'Imperio comments further in her section 8.8, wherein she discusses pictures in Ashmole's 1652 "Theatrum Chemicum Britannicum", and she ends chapter 10 with:

" The alchemical drawings shown in figure 36 seem, at least to my eye, considerably closer in style and feeling to the plant drawings of the Voynich manuscript than most, if not all, of the herbal illustrations I have seen in my own admittedly limited search for parallels. It is my feeling that we should certainly include alchemy works in our investigations, even though they might not be expected to deal with plants as such, but rather as symbols for alchemical entities (the sun, moon, metals, chemicals, etc.). " [5, 6]

And, as we know, D'Imperio's book gives in Fig. 42, her table of some Alchemy Symbols, where we see the Voynich manuscript's signature gallows letter, MD-A (EVA-t; Frogguy-qp) is essentially a copy of the alchemy symbol for "Urine".

Incidentally, Voynich f17r is, as we also know, somewhat special on account of the odd tiny fading script at the top of the page, which was investigated by Brumbaugh & Brumbaugh as possibly being a notation in the hand of the alchemist we have been spending so much time on lately: George Baresch. [7]

Berj / KI3U


[2] J.VS communication #142.

[3] Version TEXT16E5 Interlinear archive of Voynich manuscript transcriptions. Derived from INTERLN.EVT file version 1.6 Created by Gabriel Landini, 27 September 1996. Split into separate files (one per textual unit) by J. Stolfi, 10 october 1997. Version 16E6 is available here:

[4] The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7, pg. 15. In figure 9 on pg. 87 D'Imperio gives drawings of eight relevant examples of VMS illustration components, including faces in plant roots.

[5] D'Imperio figure 36 reproduces from Ashmole's 1652 work two alchemical drawings, the herb Lunaria, and "Spiritus, Anima, Corpus.".

[6] Alchemy considerations in connection with the VMS have yielded other opinions; see for example the section "TORESELLA - ALCHEMICAL HERBALS" in "Historical Precedents for the Voynich Manuscript" by Dennis Stallings, July 20, 2001:

[7] The Most Mysterious Manuscript, The Voynich "Roger Bacon" Cipher Manuscript, edited by Robert S. Brumbaugh, Southern Illinois University Press, 1978, pg. 136.

From: Berj Ensanian
Date: Thu, 24 Jan 2008 01:25:53 -0500 (EST)

Subject: J.VS: vocabula nova et fictitia

Dear Colleagues

Reference J.VS communications #125 (Vol. I) and #139 (Vol. II) we have the open question of:

"vocabula nova et fictitia"

in Kircher's papers. What does it mean? Does it relate in any way to the Voynich manuscript?

I've here taken the liberty of putting this little puzzle in its own J.VS communication subject-line so as to give this problem some visible continuing emphasis.

Berj / KI3U

From: Greg Stachowski
Date: Thu, 24 Jan 2008 14:21:29 +0100

Subject: J.VS: Re: vocabula nova et fictitia

Finally devoting a moment of time to look at this, I find that both Lewis & Short and my Collins dictionaries give 'designation, appellation, name' for 'vocabulum' (the singular of 'vocabula').

'fictitia' is of course from 'ficticius/fictitius', being 'pretend, artificial, ficticious', as expected. 'nova' is obvious.

So 'vocabula nova et fictitia' would be perhaps 'new and invented names' rather than vocabulary (in fact, the Collins gives 'verborum copia' for 'vocabulary').

So this could refer to something akin to Richard SantaColoma's 'New Atlantis' text: a list of invented names of places and things. Of course this has no bearing either on his theory of the VMS or on whether 'vocabula nova et fictitia' refers to the VMS (it still might, in translation).

It is a pity the list has no context, numbers or references which could expand the listed terms. Still, this list should (as I think Berj said earier) be transcribed and looked over. (As a humous aside, I noticed that above 'incognita alia' is 'incognita ep.[?] Rabelesia'.)


From: Berj Ensanian
Date: Thu, 24 Jan 2008 16:08:24 -0500 (EST)

Subject: J.VS: Painting Art with the Script of a Language of Nouns

Dear Colleagues

In J.VS comm. #147 (J.VS: Re: vocabula nova et fictitia) Greg Stachowski wrote:

" So 'vocabula nova et fictitia' would be perhaps 'new and invented names' rather than vocabulary (in fact, the Collins gives 'verborum copia' for 'vocabulary'). "

Upon that let me conjecture the possibility that a list of names could be thought of as a "vocabulary of names" and conjecture further a "language of nouns", that is a language where the spoken and written units are all nouns, and some more expanded-into-normality interpretation of a particular stream of nouns is well understood by the speakers and writers of the language - somewhat akin to some kinds of mathematical statements.

Let me see if I can clarify this, for myself also. Consider:

y = f(x)

can, for brevity, be replaced with just:


where it is understood that if a "y" is part of the discussion, then y = f(x) is also understood. Actually the "language" here could write the statement:

y f(x)

Some nit-picking might be necessary to give f(x) the unambiguous status of a noun, but lets proceed. Suppose then, as experienced practitioners of this language of nouns, we come across this no-punctuation "sentence" of nouns:

x 5 y 25

We could reasonably infer:

y = f(x) = x^2

and expand it further into normal vocabulary and language as:

The dependent variable y is calculated as the square of the independent variable x, so that if x is 5, then y is 25.

Certainly yes, a lot more context would be needed to settle on this particular expansion from "x 5 y 25". But as we are seeing in our efforts to translate the Latin letters of Kircher's day, that's the case there too, and context-driven iterative translations are not at all a crushing objection to what I am trying to clarify here.

Now, if something even remotely like this is going on with some blocks, or even just labels of Voynich text, then undoubtedly there is some set of rules, I would think highly mathematics-grounded rules, that is governing this vocabula fictitia, and the rules may not be explicitly written in the VMS for some reason - perhaps because they are deducable.

Altogether then, and I am still trying to clarify this in my mind, the thought is of a possibility that parts of the VMS text are written as a language of nouns.

Incidentally, that possibility might be natural for a palette of "words" designed to simultaneously paint hand-script text-art per the hypothetical f76r portrait: that is, the upper-half block of text of f76r not only forms a 3D portrait of a man, but the very same text-glyphs / mosaic tiles, discuss the man in a language of nouns, perhaps biographically. In other words, the original designer of that, system of text-glyphs as simultaneous script letters and graphics tiles, might have found during his / her experimentation that a language of nouns made the art-plus-language system most satisfactory. A normal language with more than just nouns on the palette, might cause serious problems, say from inconvenient word-lengths, whereas I think it is much easier to trade a short noun as a suitable substitute for a long noun, than to do that with an article.

Now we ask of course:

Given a language of nouns, nevertheless what is new and invented about the "names" y and x and f(x) etc.?

Well, what is so special about "new and invented names"? Nothing - it happens all the time, doesn't it? Thus, even if "vocabula nova et fictitia" indeed means "new and invented names", it seems to me that if it is included by Kircher as an item in a list that he titled "Catalogus Linguas", then perhaps there is something more to it than just a list of new artificial names. Perhaps, when y = f(x) is written simply as f(x), the f(x) takes on a new and artificial character as a unit of language, especially so if it is to simultaneously serve as mosaic tiles in a graphic. The f(x) is then a new and invented name for something besides its usual "function of x".

No, for sure I'm not clear on this completely yet. And also, some research is needed into "language of nouns", since that seems an idea that must have come up before somewhere sometime.

Berj / KI3U

From: Greg Stachowski
Date: Fri, 25 Jan 2008 02:40:20 +0100

Subject: J.VS: Re: vocabula nova et fictitia

To continue from my earlier posting, I believe I can now explain "vocabula nova et fictitia".

Having processed the image of APUG 563 142r using the procedure I presented earlier for improving the legibility of the APUG manuscripts (see Library deposit # 0-7-2008-01-12 ), I find that in most, if not all, cases the list entries on the two pages are followed by a terminating full stop.

The entry "vocabula nova et fictitia" is not, suggesting that we should read on. Doing so, we find on the next line:

"Merlini Coccaji carmina."

terminated by the full stop, as expected.

Thus I submit that the full list entry is:

"vocabula nova et fictitia Merlini Coccaji carmina."

An image of the appropriate part of 142r is now in the Library as deposit # 1-2-2008-01-25, at the URL:

Now, 'Merlin Coccajo' was the pseudonym of one Teofilo (Theophilus) Folengo, a 16th century poet, whose work 'Baldo' contained various invented characters and was a model for the later work of Rabelais (who is himself referred to two lines earlier on 142r). More detail in Wikipedia:

So it seems that "vocabula nova" does not refer to the VMS; which is not to say that there is not another entry somewhere on the list which does.


From: Berj Ensanian
Date: Thu, 24 Jan 2008 22:46:42 -0500 (EST)

Subject: J.VS: Re: vocabula nova et fictitia

Greg wrote in J.VS comm. #149:

" To continue from my earlier posting, I believe I can now explain "vocabula nova et fictitia".

Having processed the image of APUG 563 142r using the procedure I presented earlier for improving the legibility of the APUG manuscripts (see Library deposit # 0-7-2008-01-12 ), I find that in most, if not all, cases the list entries on the two pages are followed by a terminating full stop.

The entry "vocabula nova et fictitia" is not, suggesting that we should read on.

... etc. "

Very good Greg. I am almost with you on this. But there seems to be one little thing I'd like explained: on this page of Catalogus Linguas it looks to me that when a list entry takes up more than one line, its continuation on the second line is indented. The "Merlini Coccaji carmina." entry is not indented from the margin.


Prior Subject-sequence: J.VS comms. #146, 147, 149.

From: Greg Stachowski
Date: Fri, 25 Jan 2008 05:09:50 +0100

Subject: J.VS: Re: vocabula nova et fictitia

Berj wrote in J.VS comm. #150:

"on this page of Catalogus Linguas it looks to me that when a list entry takes up more than one line, its continuation on the second line is indented. The "Merlini Coccaji carmina." entry is not indented from the margin."

This is true. It may be that "vocabula nova" and "Merlini Coccaji carmina" [carmina = pl. of 'carmen' -- poetry, verse] are separate entries. In fact, to support your argument, one might argue that for it to be one entry it should be 'carminibus' in the ablative: "fictitious names from the poetry of M.C.".

I'm open to both options, though it may be that the question cannot be decided without additional evidence.

A couple of other thoughts:

1) The 'incognita alia' in the line above 'vocabula' is also interesting: 'other unknowns'; particularly if it is not a continuation of the earlier Rabelais line.

2) This page (142r) seems to be more a list of odd works or even notes than the list of languages found on the other side (142v). After all, 'unknown works of Rabelais' (is that perhaps 'op.' = 'opera'?) and 'poetry of Merlin Coccajo' can hardly be described as languages. So if the VMS were to be listed anywhere (and if this list was prepared after Kircher received it) it should be here.


Prior Subject-sequence: J.VS comms. #146, 147, 149, 150.

From: Berj Ensanian
Date: Fri, 25 Jan 2008 01:21:51 -0500 (EST)

Subject: J.VS: Re: vocabula nova et fictitia

Greg wrote in comm. #151:

" After all, 'unknown works of Rabelais' (is that perhaps 'op.' = 'opera'?) and 'poetry of Merlin Coccajo' can hardly be described as languages. So if the VMS were to be listed anywhere (and if this list was prepared after Kircher received it) it should be here. "

I do agree that, the leads you gave in comm. #149, showing Coccajo / Folengo employing so-called Macaronic language in his compositions, and so inspiring Rabelais - who invented words, do well for making sense for these as "vocabula nova et fictitia" entries in APUG 563 142r. Basically my gut feel is that you've cleared it up. The indent problem is then a little nag I suppose, and as you say we can use some additional clinching evidence.


Prior Subject-sequence: J.VS comms. #146, 147, 149, 150, 151.

From: Berj Ensanian
Date: Sat, 26 Jan 2008 13:15:44 -0500 (EST)

Subject: J.VS: Baresch's lost notes become fish-wrap paper?

Redaction of some off-J discussions of 20 JAN 2008:

Berj Ensanian says:
For general reference here is some Jesuit news:

Just a thought: I wonder if there are indications of pain in the VMS, say indications that the author had pain episodes. If severe, they might become clues to the identity of the author. Similarly we already know that Marci had trouble with his eyes. Now for instance, there is the "Ghostface Terror" of f40r. Could it be a face depicting some kind of pain? Is the f40r plant identifyable as a specific pain reliever? And then, who among the POI's suffered from that kind of pain?

I've now had a chance to read Jan's new paper [The Lost Notes of Georgius Baresch; ref. comm. #144] with concentration:

" The notes should be somewhere, but where? Of course, they might not have been transported to Mondragone with the VM and could be possibly lost. It is rather surprising nobody ever noticed this discrepancy - and - as far as I know - ever searched for those notes. .... And who knows, the full story of the VM could have be written by Baresch in those notes as well, when he realized that nobody else knew it and after his death, it would be therefore lost forever. "

Thinking about this, it occurs to me to point to the odd little sub-mystery contributed by H.P. Kraus when he visited the Vatican Library in 1963 to find out more about the VMS. Could it be that the material Monsignor Ruysschaert had in his stacks was the lost Baresch notes?

Dana Scott says:
Anne Nill worked for Kraus, possibly for as long as 10 years, I don't recall exactly. Perhaps she and ELV thought it appropriate for him to own the VMS, since he was in a better position to sell it. I would have to go back and research the details. Kraus paid Anne a reasonable commission for the VMS, but was subsequently unable to sell the manuscript, as we know. It would probably be a good idea to iron out the details of this time period concering the VMS, for the record.

Greg Stachowski says:
Good points, Berj and Dana. Particularly Anne Nill has been very much ignored; the Christian Science Monitor interview [J.VS comm. #19 et al.] strongly hints at her involvement with the VMS in the early days, and of course she was its owner before Kraus. Yet we have nothing (as far as I know) of her notes or research on it.

Anyway, here's another thought: what if Kircher did a Hyvernat? That is, suppose that Kircher indeed got the additional papers from Baresch and later Marci. However, rather than trying to solve them himself (perhaps supsecting a hoax, or through lack of time) he passed the copies and notes to someone else, a student or assistant or colleague? (Like Hyvernat to Petersen).

He could plausibly have kept the original (i.e. the VMS) for himself, so that if the assistant turned up something interesting he could go back to it and complete the job. This would explain why the notes are missing while the VMS and Marci letter remain. So the question is, who did Kircher work with who could have been given the task? If we can identify such a person, then perhaps in APUG we might find something like progress reports or questions, and of course *this* person's archives could be searched (if they exist).

Berj says:
For reference on this topic, there are some comments on Kraus in J.VS comm. #60, points 6.) and 7.), and in comm. #69. Greg asked: " So the question is, who did Kircher work with ... ? "

Yes! Who?

Jan Hurych says:
Good question, Greg. It must have been some fellow mathematician. Moretus, eh? Just kidding, most likely he would be closer to Rome, geographically.

It surely looks like Baresch's notes arrived safely with the VM to Kircher, they are the most likely of all Baresch's attachments to survive, but to trace them or learn what happened afterwards we do not know. Come to think of it, Kircher must have had a lot of papers that were not letters or specific type of communications. What happened to them during Risorgimento? Apparently if it was worth to save VM, same would apply for other papers, since some were Kirchers own writings (maybe even some of his notes about the VM, who knows?) and they did not have time to sort them, just to pack them and go.

And then, what happened to them during the move to safety? Where were for instance hidden the now existing letters in Museo Kircheriano? Most likely not in Mondragone, so there must have been more places of hiding. But if that is the fact, why only VM and Marci's letter were transported to Mondragone? Besides, the very same year of Voynich sale (1912) Pope also bought some documents from Mondragone.

Father Kolacek, the Czech Jesuit and radio commentator in Rome told me by email some time ago that during Risorgimento, there was terrible waste of Jesuit documents - some papers were used for wrapping the fish, nobody cared what kind of papers. So why would only the letters survive and the rest be lost? There should be some notes surviving in Museo Kircheriano, if they were packed all together. My second best bet would be Mondragone. But of course even Voynich could have got them as a bonus with the VM sale, maybe even free of charge. Most likely however, they were separated from the VM (most likely by Kircher himself) and then nobody knew what they are about. Now, it would probably take only the VM expert to recognize them even if they survived.

Berj says:
Baresch's VMS papers used to wrap fish - what an awful thought!

From: Berj Ensanian
Date: Mon, 28 Jan 2008 23:51:32 -0500 (EST)

Subject: J.VS: Looking for cracks in the ice on the trail of Georgius Baresch

Redaction of some off-J discussions 21 - 28 JAN 2008:

Jan Hurych [on investigating Baresch] says:
To get Marci's book [Philosophia vetus restituta, in the original Latin] however would be a real asset.

Dana Scott says:
Here is what is found in Fletcher's article relating to Baresch:

Revue Internationale De L'Histoire Des Sciences, De La Medecine, De La Pharmacie Et De La Technique
Tome LIX
Annee 1972
Amsterdam 1973

Johann Marcus Marci Writes To Athanasius Kircher, By John Fletcher

p. 101
' What was perhaps the only non_horrific event of the [Thirty Years] in MARCI's eyes came when Imperial troops intercepted coded letters from the Swedish commander GUSTAV BANNER, the deciphering of which "haud dubie cladem avertissent" (Letter 4). MARCI describes their frenetic but vain attempts __ "plures alii mecum frustra insudavimus" until, on recollecting KIRCHER's cryptographical omniscience, 19) the complete copy was dispatched post_haste to Rome to secure "sensum paperorum et alphabetum". '

' 19) Similarly, when confronted by a scientific anagram from Christiaan HUYGENS, Gottfried Aloyssius KINNER lost little time in forwarding the riddle for prompt decoding by KIRCHER: "Tu ingenousissime Oedype qui Sphyngem haves, facile interpretationem elicies (v. PUG. 557 f. 248, Reichenbachii, 4. Jan. 1656), in language to be echoed some ten years later by MARCI himself when submitting for decipherment what has since been called the VOYNICH Manuscript: " quidem non nisi suo Kirchero obediunt ejusmodi Sphinges." This letter, dated Prague, 19 Aug. 1666, and now preserved with the VOYNICH Manuscript under Ms. 408 of the Beinecke Rare Book Room, Yale University Library, is reproduced in W. R. NEWBOLD, The Cipher of Roger Bacon, Philidelphia, 1928, Plate I, p. 32. A recent discussion of this enigmatic, as yet un_deciphered manuscript is that by C. A. ZIMANSKY, William F. Friedman and the Voynich Manuscript, in: Philological Quarterly, Iowa, 1970, XLIX, 433_441. '

' Marci and Science
Like most of his age, MARCI saw in KIRCHER an accessile figure, ready to absorb or equally prepared to pronounce decisively on varied and miscellaneous aspects of the natural sciences. MARCI's scientific correspondence with KIRCHER seems to have been promoted by a variety of motives. In one instance, for example, he forwards a "schaedata" drawn up by George BARSCH 51) "certe vir optimus et rerum Chymicarum peritissimus" (Letter 2, v. also Letter 3) whilst on another occasion he frankly submits for KIRCHER's scrutiny and criticism the Anatomia demon_strationis 52) with the statement "ecquidem paratus sum meas errores revocare" (Letter 25). '

p. 117
51) Georg BARSCH had already visited KIRCHER in Rome and on his return to Prague had praised KIRCHER's "opera ingeniosissima," v. PUG. 557 f. 353. Prague, 27 April, 1639.

Berj says:
What was Fletcher's source for the idea: that Baresch visited Rome, and met Kircher?

Jan says [22 JAN 2008]:
What puzzles me most is the trip by Baresch to Italy _ he surely have made one for his studies :_) but if he liked it there _ and I think he must have, he was a romantic par excellence, as we all Voynicheros are _ he might have had come back. For instance, if Rene is right about the third set of samples, Baresch could have delivered them himself. I imagine that would be very interesting, if there is any record of it, of course.

Even if Voynich knew about Baresch, the reason he was not too public about it is most likely the fact he [Baresch] did not fit in his [Voynich's] theory of Rudolph. We have to give him a benefit of doubt. As for the letter [Baresch's to Kircher], we have no proof he saw it. The other thing is of course the translation: if he SAW the letter and if he KNEW the content of that letter, he might have hidden it deliberately, but I cannot see why _ as I said, it would be more beneficial for him to make it public than not. Come to think of it: what if there is still somewhere the first letter by Baresch? Crazy as it may sound, it took 50 years before the second letter was found and identified with the VM history.

Berj says:
The BIGGEST impact Jan's latest paper [Baresch's lost notes; (J.VS comm. #144)] has had on me is this: the realization that (if indeed the Prague ms = VMS then) Marci must have sent to Kircher not just the book with some few scraps of paper, but a lifetime's worth of Baresch's research on the book. Additionally, Jan wrote this especially pertinent observation:

" And who knows, the full story of the VM could have be written by Baresch in those notes as well, when he realized that nobody else knew it and after his death, it would be therefore lost forever. "

This is entirely logical as a possibility! It would be Baresch's last shot at having accomplished something solid with the manuscript _ if, after toiling a lifetime in vain, he did not succeed in de_coding it, then at least he could be its first historian. So Jan is entirely right to motivate the idea that Marci possibly handed over to Kircher a tremendous amount of Baresch material; if Baresch had just one page of notes per page of the MS, then the amount of Baresch ms material would equal the bulk of the ms itself!

So where is this PILE of stuff??? On the depressing_possibilities side per J.VS comm. #153 it would mean a great many fish were graced. Or, if Greg's possibility is correct, and Kircher in the 17th c. did as Hyvernat in the 20th, we are again back to WHO was the Fr. Petersen equivalent in Kircher's day? Could it have been Fr. Adamus Schall (J.VS comm. #13), and so some of Baresch's work on the VMS is still today gathering dust somewhere in a Jesuit archive in China?

And this: as Robert mentioned, via Newbold's work we have the mystery that some VMS pages went missing after Wilfrid Voynich obtained the ms. Maybe those missing pages had Baresch's annotations, and Wilfrid for one reason or another kept them private; perhaps to skip over Baresch in the provenance and go straight to Tepenece, or to give himself more time in researching the manuscript's provenance.

Dana says:
r Berj: Concerning who might well have been aware of Baresch's notes on the VMs, I would study Kircher's students. For one, I would consider Gaspar Schott.

Berj says:
Now that is interesting Dana, because I have an old Schott thing I've been meaning to bring up. In a 14? APR 1657 letter to AK from Schott, a letter that would be hard to transcribe on account of Schott's hand, and also the condition of the letter, there is what looks at first glance like "barchi ouss" on line 12, the 4th & 5th words from line_start. (The "+" at the very top of the letter is line zero in our system).

I have not looked closely at this. This Schott letter is APUG 561 278r:

Greg Stachowski says:
At first glance, it looked to me like the letter is in Italian rather than Latin, and checking the metadata in Luna Insight confirms this.

The words don't feel like a name to me: Schott seems to use fairly clear initial capitals for names, but what it does say I don't know. His handwriting plus this being in Italian doesn't help.

The last stroke of first word ('barchi' or whatever it is) and the first of the next seem as if they might be truncated; as if it was one word originally, separated by damage to the parchment. However there does not appear to be any ink staining in between them. The image from the link above is badly affected here by big, blocky artifacts at the scale of Schott's lettering, Luna Insight can be used to obtain an image which is the same resolution, but without the nasty compression artifacts, so the text is clearer. Still, it is not quite good enough for me to be sure whether this was originally one word or two. I've included a crop of this fragment [barchi.tif]; the whole image is some 9MB.

Just for interest, here is a small TIFF [artifacts.tif] (I am using TIFFs for this so as not to introduce any additional artifacts) to illustrate the problem: the top one is cropped from the image linked to by Berj, the bottom from the Luna Insight 'best' image. Depending on your eyesight and monitor, you may need to adjust the contrast a bit, but once you do the difference should be clear.

Although that was not my original intent, in this image it seems there may indeed be a very faint remnant of a connection between the two words.

Berj says:
Quite interesting! Looks like it may have been a single long Italian word. Anyway, has anyone looked at an Italian dictionary to see what's there that starts with "barchi" ?

Greg says:
I think we should agree on a transcription first; for example I think that's bo_ not ba_, look at the a in 'gratia' at the beginning of the same line.

Jan says:
There is no barchi in Italian vocabulary, only Barchi is a comune (municipality) in the Province of Pesaro e Urbino in the Italian region, or a family name, both with capital B. The second word looks to me like "scusi" which means "excuse me".

Dennis Fedak says:
Hebrew dictionary:
Barchi, a city in the province of Pesaro e Urbino (Italy);
Barchi, a type of lance.

Latin dictionary:
( pronunciation as BarKey )
barki _ of barking

Berj [28 JAN 2008] says:
r, good to keep handy, even though Greg is reading "bo-" something. I think altogether it is unlikely this particular word in Schott's letter is a variation of the name Baresch that we are interested in.

Robert Teague [commenting on current VML text-statistics discussions] says:
At least those two guys are DOING something.

Berj says:
Very true, which is why they are worth spending time on. If they were weren't, I wouldn't waste a second pointing out that they happily analyze transcripts with impressive math, while ignoring an obvious question: what, quantitatively, is the effect of transcription versions? It would be like me having launched into the PM-curve work without first having done the quantitative measurements that established that the areas of interest on the imaged f68r3 are indeed flat enough to transcribe the curve meaningfully. So, instead of just giving an opinion about that, I gave measurements.

Robert [commenting on his astro section work] says:
One thing I want to do is rename it "Cracks in the Ice I", and make it first in a series. The second will be about the Zodiac section itself, the third about word links between the Astro, Zodiac, and Almanac (Recipe) sections, and the fourth the meanings of a number of Astro folios.One thing I've noticed in the letter values is a very conspicuous absence of "i" and "u". I suspect those two letters are covered by EVA i and ii. So if an ending is "ium", in EVA it's iiir. I've also seen i as a stand-alone character.

[ end J.VS comm. #154 ]

From: Berj Ensanian
Date: Thu, 31 Jan 2008 23:05:23 -0500 (EST)

Subject: J.VS: Re: Library subcollection 0-7-2007-01-12 on Image processing

Dear Colleagues

In J.VS comm. #140 Greg introduced, via J.VS Library deposit # 0-7-2007-01-12, a very effective and at the same time very simple image processing algorithm that, as we have already seen, is proving its practical value. I especially appreciate that in under half a minute total time I can, with a few mouse clicks, very often obtain an improvement in a problematic image. As you know from off-J discussions, I had to "translate" Greg's algorithm slightly for my particular computer installation and GIMP program experience, in order to get it functional. I thought it wouldn't hurt to list here Greg's procedure, translated as I do it on my equipment. [1]

Berj / KI3U

[1] Greg Stachowski's image processing algorithm per J.VS comm. #140, implemented with Windows XP hosting GIMP 2, GNU Image Manipulation Program 2.4.1, in eleven steps from GIMP 2 start-up to saving processed image-file:

TW = toolbox window
SI = source image
IW = image window
LW = layers window

1.) Start Gimp: the TW appears.

2.) In TW, load ("open") the SI: IW appears.

3.) In IW, under "File", Open as Layers the same SI: the IW appears unchanged.

4.) In IW, under Dialogs, click open LW: it shows two thumbnail copies of SI with eye-open icons, one marked filename, the other as background.

5.) In LW, keep the filename copy as the selected one - click on it if needed.

6.) In IW, under Colors, click Invert: the IW image colors invert - also seen in its LW thumbnail.

7.) In LW, change Mode to Dodge: the IW image changes.

8.) In LW, adjust Opacity to 22.0 or thereabouts: the IW image changes accordingly.

9.) In IW, under Image, Merge Visible Layers.

10.) In IW, under Image, Flatten Image.

11.) In IW, under File, Save As newfilename.

From: Berj Ensanian
Date: Mon, 04 Feb 2008 00:35:15 -0500 (EST)

Subject: J.VS: The Voynich hypothetical f76r text-art portrait: how was it done?

Dear Colleagues

Here I present the most recent results of my investigations into the hypothetical steganographic hand-script text-art portrait (akin to today's ASCII art) on Voynich folio f76r. [1]

On the assumption that the hypothesis is correct, I have been focused on attempting to understand how the artist managed to achieve what he / she did: producing on the f76r parchment a 3-dimensional-illusion steganographic portrait, presumably a self-portrait, employing the hand-scripted Voynich text as mosaic tiles.

I studied the positional distribution of some of the text glyphs and tentatively concluded that the "4o" and "9" glyphs especially may have been involved in whatever was the system for achieving the effect, perhaps as text position anchors. This led me further into guessing the artist's system:

Preliminary outline of the assumed system producing the steganographic hand-script text-art of Voynich f76r:

1.) The source picture is prepared on a grid sheet that has lines somewhat like raster lines (to become the guides for the text-lines). The essential markers for the grid are easily alignable to the final f76r parchment in some convenient manner; the traces of these markers may possibly be still discoverable on f76r.

2.) On the grid sheet, by some previously worked out and satisfactory scheme, perhaps just experience, the picture is dissected into discontinuous (floating like islands) tiles that in outline have the approximate shape of the envelopes of words. For example, the envelope for the word "outline" has roughly the shape of a horizontal rectangle with a smaller rectangular chimney atop its middle.

3.) A second sheet is prepared, bearing only the delineated and empty island envelope tiles.

4.) From a palette of "words", words are selected that will fit well into the envelope tiles, and they are scripted into them.

5.) A final copy is made, in our case it is f76r, that reproduces only the raster with its now populated islands of word-tiles, their envelope outlines omitted.

It can be seem that in this system the blank spaces between the envelope tiles, function as well as mosaics, that make up the final picture.

I have sent to our Librarian Greg as an addendum to J.VS Library deposit # 14-1-2007-10-22 (the deposit that holds f76r stego. picture materials) a digital photograph, 1VMSf76rStudyKI3U.jpg, showing some of my sketches during the process of deducing points 1-5 above. [2]

The other difficult problem is: how to process the f76r source image uniformly so that the hypothesis that its embedded steganographic picture is objective, is better investigated. On confronting the proposition that f76r may hold a steganographic hand-script text-art picture, and even more radically a picture that is so advanced as to create the illusion of three-dimensionality, there are of course to consider items such as "Rohrschach", "cloud bunnies", "apophenia", "pareidolia", "all in the mind" and so on. Those are powerful ideas that place the burden of proof on the hypothesizer, as it should be. We proceed as best we can, and I recall here the point I made about this in J.VS communication #111: the reality of the steganographic images can be decided by the man in the street. So for the man in the street I provide the best data I can.

My latest effort in this vein follows from point 2.) above: the recognition that image processing must recover, as well as possible, the originally dissected islands. The simplest way to do that is to blur the f76r source image, so that the letters of its words blend together, and so that a whole word starts to melt into an integral graphic unit: a mosaic tile island. Accordingly, I have also sent to Greg for Library-deposit the best-yet experimentally processed image:


In my view, this picture goes a long way toward providing consideration-worthy data on the problem of the hypothetical reality of the f76r stego portrait. Again, the man in the street can weigh in on this issue as well as the most seasoned Voynich expert. But certainly much more improvement is possible, in particular in bringing out the 3-dimensional illusion effect. [3]

fnGzp77C91s3b75g76rVMSblink1.tif has allowed me to form a more detailed opinion of the embedded stego picture of f76r. What I now see in it is, that the man whose face is in there, is using his right hand, and possibly also his left hand, to hold up right against his eyes, a rectangular plate that he is looking through. This plate may have a small indent for bridging his nose. But overall, to me it suggests that he is viewing something through an optical filter, and perhaps there is the suggestion that the process of creating the f76r stego picture and / or other VMS folios materials, involves the use of special illumination and optical devices; that is in tune with my already long running and periodically stated suspicion that the VMS is at least partly concerned with color optics / physics. A further thought along this vein is that the Voynich manuscript's long-so-assumed "pharmaceutical" section is possibly actually concerned with the manufacture of vegetable dyes for a set of experimental optical filters, intended both for spectral illumination and detection experiments.

What would make a suitable control image to test the image processing procedure of [3] ? To be really fair it would have to be a block of Voynich script in the f76r hand, of about the same size and formatting and sub-alphabet as the upper paragraph of f76r, which holds the proposed embedded stego portrait, while presumably having been generated in some manner that does NOT intentionally, nor inadvertently, create an objectively perceivable picture. So, this control problem is a very difficult problem also. As a step toward dealing with it, I lightly ruled 29 lines on a blank sheet of paper to about the frame of the upper paragraph frame of f76r. Then I just started writing random "words" using the Voynich alphabet I am long familiar with. I made no effort to conform, or not conform to known VMS text digraph properties, nor to avoid or emphasize actual VMS words. I just wrote using the VMS alphabet. About three quarters of the way through I noticed that unconsciously I had been spacing my words more or less evenly - this is definitely not the case in the actual Vonich folios where it is often uncertain where one word ends and the next one begins; the variable word spacing seen in the VMS, does makes perfect sense in light of a picture dissected into mosaic islands.

After completing the twenty-nine lines, and noting that the raw writing exhibited the usual apparent wavy lines running through it, but nothing else in the way of an organized pattern, I digitally photographed the paper, and then subjected the image to the same processing as in [3]. I didn't know what to expect, but as soon as I saw the result, it made perfect sense: it appears like an out-of-focus brick wall of an old building. So therefore, for the time being, it appears that the equivalent of random noise in constructed images according to the system of [3] is this old-brick-wall effect. The source writing (KI3UvmsTestScript3feb2k8.bmp) and the final brick-wall image (nGzp77C91s3b75KI3UvmsTestScript3feb2k8.bmp) have also been sent to Greg for deposit. I have left their orientation upright, so that if someone discerns a pattern that I didn't see (other than brick-wall) at a particular rotation angle, we have a reference for the angle.

Finally, point 4.) above strikes directly at the heart of considerations that the Voynich manuscript "text" is actually "text". It may well still be, but if indeed the Voynich text is, aside all else, a set of graphics elements for the rendering of pictures in a novel manner, then it seems that at the very least any rules operating that pertain to language of any type, code, cipher, shorthand, and so on, must include as well some adaptation to graphics usage of the text elements. Within this hypothesis it is at this stage too soon to guess how sophisticated the VMS author's experiments became. In J.VS comm. #148 (Vol. II, [1]), I discussed as a possibility "Painting Art with the Script of a Language of Nouns".

There is also this: even if it turns out not correct that Voynich f76r has embedded within its text a steganographic picture, the system outlined in points 1.) to 5.) above, for producing a hand-script text-art picture, plainly visible or steganographically sophisticated, may, in the hands of an accomplished artist, actually work.

Berj / KI3U

[1] For earlier information on the possibility of hand-script text-art in the Voynich manuscript, and in particular f76r, see J.VS communications #107, 108, 109, 111, 112, 113, 117, 120, 121, 122, 132, in J.VS Vol. I:

and comms. #138, 148, in Vol. II:

[2] J.VS Library deposit # 14-1-2007-10-22 is available online here:

[3] fnGzp77C91s3b75g76rVMSblink1.tif was produced with this procedure:

3-1: Load 76rVMSblink1.tif (an item already in [2]) into IrfanView Version 3.99 (for Windows XP).
3-2: Convert to Greyscale.
3-3: Execute 75 times in succession the "blur" operation.
3-4: Execute 3 times in succession the "Sharpen" operation; (sharpen and blur are not perfect inverses).
3-5: Set Contrast = 91
3-6: Set Gamma = 0.77
3-7: Execute the "Negative" operation (invert the grey values). The essential transformation is completed.
3-8: Finish up with blacking out the white borders (for less eye-strain), and adding some information text at lower left away from the f76r picture portion itself.

From: Greg Stachowski
Date: Tue, 5 Feb 2008 17:02:13 +0100

Subject: J.VS: Re: The Voynich hypothetical f76r text-art portrait: how was it done?

Dear Colleagues,

Sidestepping the issues of whether such text-art images exist in the VMS, and whether the appeal to 'the man in the street' is valid -- both points on which I disagree with Berj -- his post # 156 brings two interesting things to the table. One is a method for generating such images, which as Berj points out, is interesting in itself even if it is later shown not to apply in the VMS. The other is a first attempt at a control experiment to test the hypothesis, which again as Berj admits is incomplete since it neither reproduces the statistics of the VMS nor consists of 'meaningful' text.

In this post, I present some further suggestions for control experiments and testing, broken down into three related sections. Although certainly not exhaustive, they might give us a better handle on the likelyhood of the text-art hypothesis and a means of objectively identifying the images if such exist.

-- Greg

Suggested controls:

A. Testing the serendipitous occurrence of text-art images, or: how likely is it an apparent image will appear by chance?

1. Duplicate test described in # 156, but have a computer generate samples which match VMS statistics and copy them out by hand. (Perhap's Rugg's methodology might be useful here.)

2. Test on real texts in other languages (as I mentioned before, the APUG Latin manuscripts make a good set) to see if meaningful text behaves differently, and to get away from using your own writing.

Applicable to all these is the requirement simply for more controls: if 10, 20 or 100 tests are done without finding any images, then that is more persuasive than just one false test. Introducing a number of experimenters to independently view the test samples is also important to get a handle on how likely individuals are to see the images.

B. Quantifying the effect.

If the images are deliberate, then one might reasonably expect the frequency distribution of the sizes of inter-word spaces in an 'image' block of text to be different from that in an 'imageless' block. (One might expect the latter to be a simple random distribution around some mean). Indeed, in the 'image' block, one might expect two peaks in the distribution - one matching the 'normal' spacing exhibited by the background text and one narrower one with a larger value of the mean representing the presumably slightly wider spacing which delineates the 'islands' or 'tiles' mentioned in Berj's post.

The same analysis should be carried out on both VMS pages and artificial controls. The controls would consist of the same block of text (for example as generated in A.1 above) with and without an image added according to Berj's procedure. Since we know a priori whether an image exists or not in the control, that would allow testing of the method before we apply it to VMS pages.

If something like this were indeed found on an 'image' page and not on an 'imageless' page it would be rather persuasive. Even better if one could then use it to find other hidden images. Of course it would be a lot of work, although it might be possible to automate it somehow using the digital images and appropriate software.

C. Testing reproducibility of images, or: do we see the same thing?

In this case, have a third party prepare (as in A and B above) pages of text with and without text-art images, and submit them for analysis, both visually and by the quantitative methods described in B above. The sample size should be large, and contain a good mix of no-image pages, and hard- and easy- to spot images. The original images would be known only to the third party. The test here is to see (a) how well both the visual and numerical methods perform at correctly picking out the images and (b) whether the viewer sees the same image as the creator. Again, a number of experimenters should view the images, for the same reasons as in A.

From: Berj Ensanian
Date: Wed, 06 Feb 2008 00:40:14 -0500 (EST)

Subject: J.VS: The problem of test protocols for hypothetical steganographic hand-script text-art

Dear Colleagues

In J.VS communication #156 I presented my latest experiments in investigating the hypothesis: that the text-block of the upper half of Voynich folio f76r, exhibits a steganographic 3D portrait-picture, employing a technique of "hand-script text-art" (akin to today's ASCII art). Included in #156 I gave a first, and crude, attempt at control testing, resulting in the qualitative so-called "old-brick-wall" effect of random noise. Our colleague Greg Stachowski, and I thank him dearly for this, replied with communication #157, wherein he gave an outline for the beginnings of placing the testing on a rigorous, mathematical foundation. The problem, as Greg also indicates, is very, very difficult: are these hypothetical hand-script text-art pictures for real? Because the testing is a general concern, not just for f76r, I make the following comments, motivated in reply to Greg, under its own J.VS communication subject-line.

Greg wrote in Comm. #157:

" ..... I present some further suggestions for control experiments and testing, broken down into three related sections. Although certainly not exhaustive, ..... "

One reason that I think a set of fair testing protocols is likely to be even more complex than the outline you gave, is the possible effects of the inks on the actual parchment (which is off-white) - they may have been deliberately chosen to interact with special illuminations and color filters to achieve steganographic images with the "text". Of course I agree that we are here trying to open a path into testing territory, and starting out with nominally black print on white background for analysis is a practical first constraint, and I was conscious of that when I hand-scripted my test Voynichian, writing it on a sheet of common white paper, that later I then photographed in color.

" Applicable to all these is the requirement simply for more controls: if 10, 20 or 100 tests are done without finding any images, then that is more persuasive than just one false test. "

Agreed. And I still think the man in the street can weigh in as well as any expert on whether or not a piece of text raster projects a definite image - more on that later on here.

" If the images are deliberate, then one might reasonably expect the frequency distribution of the sizes of inter-word spaces in an 'image' block of text to be different from that in an 'imageless' block. (One might expect the latter to be a simple random distribution around some mean). Indeed, in the 'image' block, one might expect two peaks in the distribution - one matching the 'normal' spacing exhibited by the background text and one narrower one with a larger value of the mean representing the presumably slightly wider spacing which delineates the 'islands' or 'tiles' mentioned in Berj's post. "

I ought to have been clearer in #156 about the presumed technique - it appears that some tiles islands are intentionally created to make contact across raster lines. And if you go back and look at my exploratory sketch in 1VMSf76rStudyKI3U.jpg you can see that I had deduced that, and in fact the technique seems to rely significantly on bridging between raster lines here and there along them. This is quite illuminating I think, toward the mystery of why in the VMS text we so often see instances where the text symbols are distorted / modified variations of their assumed standard-ductus prototypes.

For example, in the f76r text, you can see instances (e.g. line 18, 2nd word) where the descender of the "4o" glyph has obviously been bent from its normal straight vertical. Then, in line 20, compare the examples of "9" in the 2nd, 3rd, and 4th words. In the 3rd word the last letter seems to be scripted only to the extent of bridging to the line below, and it is not even certain if it is a "9" or a "4". How subtle does it get in this (hypothetical) technique? And so, in the context of this discussion it is natural to ask: is that in fact the real reason the "9" appears there at that particular spot - in order to serve as a bridge between two island-tiles on different raster-lines?

Needless to say such a thought is of more than passing interest to the analysis of the Voynich text as text as such. The truly big thing in that is this: suppose the text-art is real, simultaneous with the text islands being text in the normal sense, but the bridge symbols serve the graphics only, and can be discarded to recover the readable text. That might call for going back for another look at old shelved text deciphering efforts that almost made it, but just didn't, because of troublesome characters - that happen to be the raster-lines bridge-characters.

So, the technique seems to be based in general on bridged raster lines, and therefore both horizontal and vertical axes, (X,Y), of the image-text-block must be analyzed in the manner of objects like circles, ellipses, and spirals etc. that in rectangular reference frames are multi-valued for the independent variable, although here we may also have (X,Y,Z) where the Z dimension takes into account optical effects. Now, your comments on the frequency distribution of inter-island spacing are fortunately general. But there is a chance for simple first analysis, and that within an individual raster line, we hopefully might see the text-art effect per your observation. This would incidentally become a welcome link to Captain Currier's observation that the normal Voynich text line is a functional entity [1]. Unfortunately, we don't yet know the magnitude of the subtlety of the text-art effect, so instead of two peaks in the distribution curve, it might show itself instead as just a flattening of the curve toward exhibiting a plateau. Of course yes, if the flattening component goes deep enough just around the mean, then two peaks will be created.

However, as I mentioned in #156, we do not know the sophistication of this hypothetical artistic technique that the VMS author attained. Your very observation, that the distribution curve for the tile spacings might betray the technique, could be artistic incentive to thwart such detection. Certainly anyone clever enough to have originated this technique might well come to think of that, at least qualitatively, in the course of his / her experimentations. We might even Fourier transform the frequency distribution curves themselves with the hope of seeing the subtlest pattern betraying the hand-script text-art technique, and still find ourselves with a problem similar to explaining the Mona Lisa's "smile" - most "men in the street" probably agree that her mouth curves are peculiar, but are they really a smile? Maybe it is her eyes that are causing us to perceive her mouth as smiling.

" Even better if one could then use it to find other hidden images. Of course it would be a lot of work, although it might be possible to automate it somehow using the digital images and appropriate software. "

I think advanced controls-based analysis would be a lot of work even with automation help - there is after all right at the beginning the artistic judgment concerning the manner in which the image is to be dissected into raster-line tiles, and even more complicatedly, into bridged lines, not to mention if ink density and so forth are also factors. If testing were totally automated, it might well lead to an effective result in many experiments, but it might miss a peculiarity of artistic skill and build up a false confidence that the automated technique is able to analyze all possible hand-script text-art scenarios.

" Again, a number of experimenters should view the images, for the same reasons as in A. "

I do not see where you show convincingly that the viewing of the images, for the purpose of making a decision on whether or not they project definite steganographic pictures, should be confined to "experimenters", who I take you mean are savvy in some way above the man in the street. I gave a scenario on this question in communication #111:

' Here is what I am getting at (contrived scenario): 20,000 [scientists and learned scholars] look at f76r and conclude it is just a block of strange hand-script text showing no particular pattern, even accidental, and certainly nothing in the way of an intentional stego picture. 450,000 "man in the street" look at it, and 389,000 of them all say there is a portrait, a fairly 3D one, of a man facing right and tilted up, and with long hair that bulbs out at the sides, and they all sketch roughly similar copies of what they see. So you've got altogether 389,000 face-seers against 81,000 nothing-special-seers. What is the "scientific" conclusion here? '

Again: what is the scientific compulsion for the idea that the decision, at least the initial decision, on whether or not a piece of hand-script text contains an embedded stego picture, is not to be trusted to healthy-eyesight men in the street? Lets note too that the man in street includes the savvy, as well as members of the text-art community, BAUDOT, ASCII, and other. The man in the street is everybody with eyesight good enough for a driver's license. Sure, if the stego images happen to be of specialized objects like an air-core goniometer (an out-of-era example just to make the point), then further narrowing down of the viewers is necessary, once the majority of the man-in-the-street have agreed that there is definitely an intentional picture of something in there. I think.

Returning to the task of specifying rigorous testing protocols, I think it is first necessary, for me anyway, to spend a little more time focused on understanding possible extents of sophistication in the technique. For example, prior to the work that I reported in comm. #156, I had not realized the major significance of the bridging. Previously I had been puzzled at the remarkable richness, even 3D, of the f76r picture, yet achieved by the artist with most of it residing in just 27 text-raster-lines spanning about 9.8 cm on the parchment. Even if the blank-lines between text-lines are counted as lines, that still comes to only 2x27 = 54 scanlines. Now, the history of facsimile transmissions is perhaps more relevant, but we have a ready benchmark from the history of early television systems engineering where 30 scan-lines in a raster frame were just enough to produce a recognizable face [2]. But here in this hand-script text-art, there is a phenomenally complicated interaction between not-always-straight horizontal raster-lines that are modulated, not by simple varying light intensity, but variously scripted symbols having a vertical dimension, and that also here and there bridge to one another both within line, and across lines. So therefore, I want to first spend some more time understanding the technique, in preparation for better, more comprehensive suggestions toward hypothesis-testing protocols, while of course trying controls also - as Greg suggested, the APUG is a ready rich source for handwritten material [3]. I shall therefore see if I can improve the image processing technique that I used on f76r, and detailed in comm. #156.

As Greg agreed in #157, even if these pictures do not exist in the Voynich manuscript, the novel art genre of steganographic hand-script text-art is nevertheless interesting. This underscores one of the founding principles of the Journal of Voynich Studies: it is a new polymathic field that, although inspired by the problem of the Voynich manuscript, will not end with the definitive solution of the VMS mystery. Voynich studies appears to have an unlimited future, with the broadest horizons.

Berj / KI3U

[1] Some Important New Statistical Findings by Captain Prescott H. Currier, (from the Proceedings of a Seminar held on 30th November 1976 in Washington D.C., edited by Mary D'Imperio, moderator).

[2] Early British Television History, The Background to Baird's 'Phonovision'.

[3] On reading Greg's APUG suggestion I had a thought I can't resist mentioning here: what if in the Kircher correspondence, say a Marci letter, we find a hand-script text-art image that closely resembles one from the VMS? Now that would be something, wouldn't it?

From: Greg Stachowski
To: "J.VS:"
Date: Wed, 6 Feb 2008 14:48:27 +0100

Subject: J.VS: Library deposit # 12-4-2008-02-04: The Research of the Voynich Manuscript, by Jan Hurych

Jan has placed another article in the library as deposit # 12-4-2008-02-04. The URL is:

The abstract follows below.

-- Greg

THE RESEARCH OF THE VOYNICH MANUSCRIPT: The new philosophy and new methods.

by Jan. B. Hurych

The article provides the discussion of general split among VM researchers for solving the text, namely into the group proclaiming the Vm is written in plain, natural language, and those who suspect that some encoding was used as well. The new philosophy should incorporate however the learning process as well. That can be achieved by using Neural Networks (NN) that could be trained for the task. Should they be found useful, they can replace the "manual" methods of one or even both groups and the solving process would be not only mechanized but optimized as well.

From: Berj Ensanian
Date: Wed, 06 Feb 2008 22:47:09 -0500 (EST)

Subject: J.VS: Neural networks and cellular automata in VMS text-attacks

Redaction of some off-J discussion of 6 FEB 2008 on neural networks and cellular automata, motivated by publication of Jan Hurych's latest paper (ref. J.VS comm. #159):

Jan Hurych says:
What is also interesting is that in the VM List, there is only one comment on NN [neural networks] and that is the statement that Gordon Rugg teaches NN.

Berj Ensanian says:
The idea of applying neural networks to the Voynich manuscript is very interesting, and makes you wonder why no-one thought of it before. I'm glad Jan seeded the idea. Well it's been years since I looked at a book on neural networks. But it seems to me that an NN analysis of page-specific blocks of VMS text might well produce some insight into methods of testing the stego hand-script text-art hypothesis with its text-raster-lines bridging feature [ref. J.VS comm. #156, 157, 158]. Curiously, Dennis was recently going to embark, subject to his having the convenience amidst moving to Illinois, on some cellular automata experiments. The NN and CA ideas might interface in VMS text analysis. Back in the nineties I did a bunch of CA experiments - I'd have to dig up my old notes, but come to think of it, I remember almost identical repetitions being easily obtained, and that might come in handy with VMS text attacks - each new cellular state might be mapped to generate a "word". Once resigned to get on with it, it takes only about a half hour's worth of reading and another half hour's worth of programming to get started with interesting CA experiments.

Greg Stachowski says:
Possibly they [someone] did [think of the idea of applying neural networks to the VMS ], but building a meaningful one and training it is a pain (as Jan said). The biggest issue will be deciding what the inputs and outputs are going to be. Without any concrete ideas of what the VMS is, it will be difficult. Of course that is all the more reason to think about it, and modern computers make it easier to do than 5 or 10 years ago. I look into NNs every few years and usually end up solving whatever problem I have by other means :)

CA is great stuff, and might be more easily applicable since it can be used to hit the text through the transcriptions. I have a vague memory of CA being brought up by someone on the [vms-] list once, but I may be wrong.

Berj says:
A quick check - I found only one mention of cellular automata in the old [vms-list] archives: a 2004 post by Steve Ekwall replying to Marke Fincher, wherein Steve recommends Wolfram's CA book, as apparently it contains statements that Steve found resonant to his difficulties in explaining his folding key theory:

Greg says:
Could be, I only had the vague memory of the phrase being mentioned.

Berj says:
So if that's it, then apparently not much if anything CA has been tried with the VMS text, and it ought to be ripe for someone to roll up their sleeves and give it a whirl.

Greg says:

[ end J.VS comm. #160 ]

From: Berj Ensanian
Date: Thu, 07 Feb 2008 18:35:44 -0500 (EST)

Subject: J.VS: Debating Johannes Marcus Marci as possible Voynich MS author

Redaction of some off-J discussions of 6 - 7 FEB 2008:

Berj Ensanian says:
Does someone have handy a url to the best English or German biography of Marci ?

Greg Stachowski says:
I think there was one on some website listing scientists? Google gives us: (yay! pictures!)

and two books both in Czech:,+Zdenek/Jan+Marek+Marci+Z+Kronlandu:+Zapomenuty+Zakladatel+Novoveke+Fyziologie+a+Mediciny/

This is less useful, but may contain some nugget:

And this is interesting even if not a bio (the paper can be downloaded):

Berj says:
Yes it is. The endnotes have a lot of info, especially 4.) gives leads to older 19th c. bios in German. And 21.) mentions Newbold's book & the VMS. Jan came up with essentially these same url's.

Greg says:
I wouldn't mind getting a look at those Czech books, particularly the first one. With Jan's help we could make a stab at them, and who knows, there might be something interesting in a couple of hundred pages. A reference to Baresch, perhaps. Or something else, some detail the author might not have associated with the VMS. I doubt they have been examined in that respect.

Berj says:
Here's another good short outline bio:

Greg says:
BTW, this was the scientist bio site I was thinking of:

Berj says:
The single most burning question about Marci I am after answering is: what was the extent of his artistic skills? Could he have done, for example, The King of f37v? We know he was complaining about his eyesight - maybe besides looking through prisms he was also hunched over a magnifying lens for years, executing steganographic miniatures.

The thing is this: Joannes Marcus Marci [1595-1667] has EVERYTHING you could ask for as the author of the VMS under the hypothesis that the VMS is a compilation of the discoveries and philosophy of a genius polymath scientist with special interest in color physics, medicine, and languages (and therefore symbols), but with just one major detail left to verify - his artistic skills versus those found in the Voynich. Moreover, if ANY of the standard Voynich history is to be believed as at least peripherally indicative of the truth, then Marci is already in the center of the drama.

The only other guy so far I've come across who has the combination of brains and skills and interests resonant with the VMS is of course Robert Hooke [1635-1703], and he definitely did have advanced artistic skills, but these days if this minute I was forced to bet the farm on who is behind the VMS, I'd say Marci. Does anyone have in mind any more likely candidate?

Or, let me ask this: What are SOLID reasons that Marci could NOT be the author of the VMS, or at least parts of the VMS?

Jan Hurych says:
All guesses aside, I see only one obstacle: the letter by Baresch to Kircher. To me, it looks most probable that Marci was "helping" Baresch to crack the VM. But since we do not know from whom Baresch got the VM, we can speculate even there.

Berj says:
Right. But it is not quite solid, and therfore not solid, that Baresch [d. before 1662] is talking about Beinecke MS 408. Furthermore, it is not even solid that Marci in his last letter to Fr. Athanasius Kircher [1601?-1680] is talking about MS 408. The Baresch and last Marci letter may be talking about the same ms, or talking about two different mss, but either way we still have no solid proof that MS 408 is being talked about. And all that impacts more or less neutrally upon the proposition, that during his lifetime Marci put together MS 408. So it appears that you agree, that it is not impossible that Marci is the author of MS 408.

Greg says:
Without the link from the letters there is nothing to associate him with the VMS. Of course it is not impossible, but it is equally not impossible for any one of a hundred other skilled people, and it is no more probable either.

Berj says:
But this: if indeed Marci composed the VMS, as a kind of compilation of his life's more secret work, it still seems very probable that his dear friend Kircher would have known about it. Who else would Marci have preferred to discuss his experiments and ideas with? So, even if Marci authored the VMS, we still have the probable problem of missing Marci-Kircher papers dealing directly with the VMS.

Greg says:
Well, quite. Which on top of what I said above makes it even less likely in my view. As ever in VMS-land, there is nothing solid. The best argument is the one Jan hinted at, that is:

If we take the Baresch and Marci letters to refer to the VMS, then it doesn't make sense that Marci would be both the author and the person who mediated in getting the VMS to Kircher. On the other hand, if we deny that the letters refer to the VMS (which can be done), then there is nothing left to link Marci to the VMS. All that's left is that he was intellectually capable of it, but then so were probably hundreds of others at the time.

That's the argument. On a personal note, Marci doesn't "feel" like the type. He strikes me as a practical man, an engineer or applied physicist type. Accomplished in many fields, sure; given to learning new skills (artistic or linguistic even); but always with a practical view: solving a problem, learning a new skill, understanding something new. I don't think he would spend time creating something like the VMS, it's too involved and abstract. Even if he wanted to experiment with methods of creating some cryptic text (as we once discussed) I think he would be satisfied after a page or two, enough for a proof of concept, but no more.

Jan says:
Greg, I agree 100 percent. Whatever Marci discovered, he preferred the public printing, after all he was an honorable professor. He does not look like a guy trying to fool somebody and besides, what secrets he would have to hide?

Mnishowsky [Dr. Rafael -, 1580-1644] of course is a different story. I was really surprised learning that his book was mainly cryptographical and not a textbook of Czech language (his introductory statement in that sense looks more like a coverup) . According to Czech cryptographers, the cipher used in his book is Trithemian Ave Maria style. Of course the VM has something much more complex.

Berj says:
Those are excellent arguements Greg. I'll address what I think are your key points. You wrote:

" On the other hand, if we deny that the letters refer to the VMS (which can be done), then there is nothing left to link Marci to the VMS. All that's left is that he was intellectually capable of it, but then so were probably hundreds of others at the time. "

There still is one way that Marci can be linked to the VMS: the effort was part of some sort of secret society (involving Kircher), or in any case of sufficient secrecy, that Marci had to disguise his authorship, and in his last letter to Kircher he (Marci) had the scribe write things like Dr. Rafael [Mnischowsky] and 600 ducats - perhaps little signals to Kircher with meanings other than their face value.

Greg says:
Anything is possible, but we have no evidence for such a society, or such a need for secrecy.

Berj says:
As to the hundreds capable - I have my doubts, because as time goes on, and with things like f76r popping up in 3D, Robert's description of a second hidden layer of the VMS is looking more and more solid, special optical filters for reading Jan's hidden numbers in f102v2 seem more and more a possibility, and so if the second layer is real in the first place, it seems to be of very advanced sophistication, right up Marci's alley.

Well anyway, the point of the exercise here is to see what mitigates against Marci being a possible author, although at the moment I admit I can't think of anyone more likely to have done the VMS - because I think it exhibits very great sophistication in fields Marci was competent in.

Greg says:
Well, perhaps not hundreds, but certainly tens of people over the likely period. And again, the 3D effect, the second layer and the colour filters are still just working hypotheses at this point, not firm evidence (interesting though they may be). The key words here are "think". :) It's an opinion. I personally would not put my money on Marci; of the period characters, Kircher himself strikes me as much more likely, and also had the right skills.

Berj says:
Let me propose a need for secrecy: ideas and techniques expressed in the VMS that potentially impacted global political power (yes this needs to be placed on a more convincing footing). Specifically, let us assume that the f68r3 PM-curve is indeed indicative of advanced astronomy. Then let us review the case of Kircher colleague Fr. Adamus Schall [1591-1666, J.VS comms. #13, 15, 82, 83, 139, 154], he being associated with the only known possible Voynich text word in a Kircher paper: Schall was at the center of one of the most sensitive episodes in Chinese astronomy history. Essentially, Jesuit astronomy proved superior to Chinese astronomy, and Schall in effect became a Mandarin. And Chinese astronomical heads rolled [as also nearly did Schall's at one point], if I remember the essentials correctly. So, if you are a society, Jesuits say, and you have powerful knowledge, say astronomy, that can greatly impact global political arrangements, say Jesuit presence and influence at the Chinese court, then it stands to reason that even if your society is heavily involved in teaching advanced knowledge, that nevertheless there is reason to keep secret, that is to keep confined to a select few, some of the most advanced knowledge you possess.

The Catholic Encyclopedia article on Schall:

is good background for the secrecy point I was trying to make. It has the Academia dei Lincei and all that good stuff in there too.

Greg says:
Let me rephrase: there is no evidence for such secrecy in the case of Marci and Kircher. In the case of Schall there is a potential reason for it, but he is not Marci and Marci was not a Jesuit (at least, not until his deathbed). In other words, this argument is plausible for someone other than Marci, but it was Marci we were discussing.

Berj says:
Can you give some possible candidates?

Greg says:
Without research, no, but you yourself mention Schall; earlier you mentioned Hooke; then there is Kircher and his associates, students and correspondents, probably a bunch of other Jesuits. I'm sure there are names from your Persons of Interest [POI] list who make the grade. Depending on how far back and how wide across Europe one wants to go, it should be possible to put together a list of a few tens of names of people who had the skills you postulate the VMS author had. That was my point; I was not putting anyone forward as the author over Marci, just pointing out that a relatively large number of people with Marci's skills and abilities existed at the time. Whether or not they wrote the VMS is a whole different question.

Berj says:
You said earlier that Marci didn't "feel" like the type to author the VMS. I take it that Kircher "feels" more like the type. But we are seeing that we have not got all that much detailed biographical data yet on Marci. In any case I question if Kircher feels more likely than Marci.

Greg says:
Well, we have discussed Kircher as the author before, and you weren't so dismissive then. Anyway, while we don't have that much biographical detail on Marci, we do know he didn't become a Jesuit, preferring to be a practicing doctor, we know he travelled on diplomatic missions, raised and commanded a force of soldiers, applied empirical and experimental methods to medicine and physics, and wrote extensively. From that I see a practical man, a man of action, a problem solver, and an outgoing, direct man. Whereas the VMS seems to be more esoteric, more fitted to someone like Kircher, who played with hieroglyphs and collected a museum-full of curiosities. Of course these are my opinions, no more. I would also see the VMS alternatively as the notebook of someone who needed to keep his knowledge secret, such as a poor student or medic whose only asset was his knowledge, but nothing in Marci's bio suggests he fits that profile; quite the reverse.

Berj says:
As you know, I always hold out for the possibility of a collaboration that included Kircher and Marci, and possibly others, including even the lowly alchemist Georgius Baresch.

Greg says:
This would be more likely, I could see Marci helping with something like this, but not creating it himself. But we still have the letters argument, which works against it.

Jan says:
Greg, I vaguely remember one of the Jesuit of that time was quoted as a member of some order (Black something, maybe it was a medal?. Was there any order within SJ? I think not, they were too disciplined at that time).

There was always a group of SJ scientists who doubted the Church doctrines, mainly because of their own scientific discoveries. My friend "in the know" was seriously claiming they already had it confirmed by their own experiments that the Earth revolves around the Sun, even some time before Galileo, but since it was dangerous for common masses, they went with the sentencing him anyway.

Bruno [Giordano, 1548-1600] was different, he talked about infinite cosmos - that was VERY dangerous: people would ask where exactly is the Heaven and where is the God Himself. So he had to go up in smoke, no pun inteded. I personally do not think anything of it is in the VM however.

[ end J.VS comm. #161 ]

From: Berj Ensanian
Date: Fri, 08 Feb 2008 23:05:58 -0500 (EST)

Subject: J.VS: A quick qualitative experiment comparing a paragraph with its boustrophedon version

Dear Colleagues

I have not seen much discussion of experimentation on the VMS text from the perspective of boustrophedon. I found just two mentions of the word in the old vms-list archives, one in 2004 by Jacques Guy, offering boustrophedon as a function in his "Monkey" text handling program, expected on account of Guy's expertise in Rongorongo, and the other a mention in passing by me in 2006. I thought I would try a quick experiment to obtain a qualitative impression of its effects, on ordinary text.

Let us begin with a source text paragraph, borrowed from a paper by Jan Hurych [1]. We remove its punctuation marks, change it to all capital letters, and place it in a reference frame of 72 columns (a convenient number), and indicate spaces with "_" and "#", the latter at the beginnings and endings of lines so as to make easier seeing some of the statistics changes after the boustrophedon and justification operations are applied. Lacking mirror letters, we can here only apply the sequencing aspect of boustrophedon, but that will suffice for the experiment:

Table 1: source sequence

00: 123456789012345678901234567890123456789012345678901234567890123456789012


Table 2: source sequence with boustrophedon appplied

00: 123456789012345678901234567890123456789012345678901234567890123456789012


Table 3: Table 1 with lines 3, 10, 11, 13, left-justified

00: 123456789012345678901234567890123456789012345678901234567890123456789012


Table 4: Table 2 with lines 3, 11, 13, left-justified

00: 123456789012345678901234567890123456789012345678901234567890123456789012


It is interesting to see that Tables 3 and 4 exhibit the identical pattern for their lines that end in spaces, whereas that is not the case with their parent tables, in this 72 columns experiment. Undoubtedly Guy would yawn at this, but I had not spent enough time on boustrophedon to appreciate how quick and easy interesting effects arise with it.

Berj / KI3U

[1] taken from: MORE ABOUT DR. RAPHAEL MNISHOWSKY. Jan. B. Hurych, 20th December, 2007. J.VS Library deposit # 10-4-2007-12-20:

From: Berj Ensanian
Date: Sat, 09 Feb 2008 23:05:22 -0500 (EST)

Subject: J.VS: Re: The Voynich hypothetical f76r text-art portrait: how was it done?

Redaction of an off-J discussion of 9 FEB 2008:

Berj Ensanian says:
I just noticed something interesting: a key component of the image processing procedure I used for f76r in comm. #156, blurring, was anticipated, with f76r, by Greg way back in comm. #111:

" I find the blurs slightly better than blinking in this case. "

This is even more interesting in light of Greg's skepticism about just what is what with f76r.

Greg Stachowski says:
In retrospect, this is not entirely surprising and is just a convergence resulting from how visual perception works. Our brains are geared towards seeing and recognising shapes primarily using contrast, and can be confused if a second pattern of a different scale and higher contrast overlies the first. This is how all those seemingly counter-intuitive modern camouflage schemes work: by using a small, higher-contrast pattern they break up the silhouette of the soldier or vehicle, rather than trying to blend in colour-wise with the background. Applying a slight blur on the scale of the small pattern reduces the contrast and smooths the hard edges, reducing the confusion and making the larger shape easier to see.

In this case the high-contrast text works as a camouflage pattern, distracting the brain from seeing a fainter, larger-scale pattern. I didn't think about it in these terms at the time: I applied a blur intuitively since the method is common in image processing to enhance visibility (although usually described in terms of smoothing noise). Anyway, both of us were trying to see the shape, so we eventually gravitated towards the same solution.

Berj says:
Yes, as I mentioned in a conversation we had a while back, I also intuitively blur, and also zoom in and out, when I'm looking for patterns.

[ Prior Subject-sequence: J.VS comms. #156, 157; related: #158. ]

From: Berj Ensanian
Date: Sun, 10 Feb 2008 10:15:18 -0500 (EST)

Subject: J.VS: Re: A quick qualitative experiment comparing a paragraph with its boustrophedon version

Redaction of some off-J discussion of 8 - 9 FEB 2008:

Greg Stachowski says:
Can you explain this pattern?

Berj Ensanian says:
Lets look at the pattern of the #'s in columns 1 and 72. Below are the bare essentials:

Table 1: source sequence installed left -> right, line-break, and reset.

03: #__E
10: #__R
11: #__#
13: #__M

Table 2: source installed boustrophedon

03: #__E
10: R__#
11: #__#
13: #__M

Table 3: Table 1 with all possible lines left-justified: 3, 10, 11, 13.

03: O__#
10: W__#
11: V_##
13: H__#

Table 4: Table 2 with all possible lines left-justified: 3, 11, 13.

03: O__#
10: R__#
11: V_##
13: H__#

Apparently the final equal #'s distribution is not entirely trivial, i.e. not entirely a yawner, because of the difference in columns 1 for lines 10, of Tables 3 and 4.

Greg says:
Ok, I follow you now.

Now to the analysis. Lines 3, 11 and 13 are odd-numbered lines, so they are not reversed in the boustrophedon. Line 10 is even-numbered and so is reversed. After justification, the leading letter is the leftmost letter ignoring any spaces or #s. Thus for any line, given knowledge of that left-most letter and whether the line is even or odd-numbered, the output is entirely predictable.

In this case, the pattern is almost the same in T.3 and T.4 since only 1 out of 4 lines with #s is even-numbered. The other lines (3, 11, 13) remain unchanged by the boustrophedon, and so come out the same after justification as well.

What interests me is whether how techniques such as boustrophedon affect the various word-order related correlations and statistics people have been doing, and whether such effects could explain any discrepancies between such statistics in the VMS and other languages. Similarly how does it affect the synthetic 'grammars' some people have calculated.

Berj says:
Agreed - excellent points, and huge in scope. It took a bit of thinking for me to conclude that the situation in the experiment Tables is not entirely trivial. I think to investigate the points you raised likely involves considerable further effort. There are so many variables, like formatting (72 columns matrix in the experiment being simply one fixed-column width example), and "magical" uses of spaces as chameleon-like entities able to be assigned visible unattached characters when in certain matrix positions, or attached to adjacents to form compounds like Voynich intruding gallows. There is also the possibility of dual final-scripting alphabets, one mapped off the boustrophedon-unaffected lines, the other mapped off the boustrophedon-affected lines and their original alphabet. And of course the choice of which line and line-terminal to start the boustrophedon at, and even switch in and out the boustrophedon every n lines. And so on and so forth - lots of possible variations. A standard, fixed specifications scenario, would seem to be the practical start toward investigating the points you bring up.

As for the VMS specifically, it seems that for text analysis a crucial set of data would be a study of the text spaces, their relative lengths, as multiples of the smallest satisfactory length identified, versus page position coordinates; it would seem the shortest space, the reference minimum space, should be no wider than the thinnest character. In other words ignore all the scripted characters and just make the spaces visible glyphs, to see what is what with them - that could work even with non-straight text lines, and even the more troublesome text non-linearities like the parts of "the second paragraph" that are to the right of the intruding plant in f9r. True, the margins would be areas of uncertainty, but between them the data ought to be good. But even if one could trust the SID images for geometrically adequate measurements, it could be even more labor intensive than transcribing all the VMS text. Perhaps a shortcut could be had via some image processing technique akin to the steps used on f76r in comm. #156.

[ Prior Subject-sequence: J.VS comms. #162. ]

From: Berj Ensanian
Date: Sun, 10 Feb 2008 18:47:02 -0500 (EST)

Subject: J.VS: Crypto-economics of boustrophedon effects; In-line boustrophedon switching

Dear Colleagues

In comm. #162 I tried a simple experiment with boustrophedon that exhibited an apparently non-trivial effect in Tables 3 and 4 at the terminals of lines 3, 10, 11, 13, here reproduced in contraction (of the original 72 matrix columns) for clarity, with asterisks denoting inter-line:

Table #162-1

03: #O*********
10: #WITH_*****
11: #V********#
13: #H*********

Table #162-2

03: #O*********
10: RM_*******#
11: #V********#
13: #H*********

Table #162-3

03: O*********#
10: WITH_*****#
11: V********##
13: H*********#

Table #162-4

03: O*********#
10: RM_*******#
11: V********##
13: H*********#

That is, in Tables 3 and 4, whereas the spaces (denoted by #'s) at the ends of the lines have become the same and thus their corresponding text-block-envelopes are the same, some of the in-line statistics though have changed, with respect to lines 10; for example, the lengths of the first words there differ by a factor of two. Of course some in-line stats also affect some text-block stats.

In the follow-up discussion, J.VS comm. #164, Greg Stachowski's comments included:

" What interests me is whether how techniques such as boustrophedon affect the various word-order related correlations and statistics people have been doing, and whether such effects could explain any discrepancies between such statistics in the VMS and other languages. Similarly how does it affect the synthetic 'grammars' some people have calculated. "

and in response to Greg I waxed at some length about the huge spectrum of possibilities for considerations of same.

But from the foregoing, we can see what Greg is getting at: that when for every N lines of text, a transcription to boustrophedon has N/2 lines contributing toward an altering of some of the text's statistics, by more or less a factor of two, while really nothing profoundly cryptic yet has been done to the source characters sequence by just the boustrophedoning of it, then it seems that one is already in a strong position to question conclusions about a block of characters (VMS text) being gibberish, or natural language, or cipher-text, or shorthand, or this or that grammar or whatever, if the comparison texts used for the analytics, Vulgate and so forth, were not also tried in their boustrophedon versions.

That seems to be the noteworthy cryptographic economics about boustrophedon: by itself it is such a mild operation upon the source sequence, but it seems to have great potential for altering the statistics of the perceived text when it is assumed to be framed left to right and top to bottom.

When then we consider probable VMS text realities, notably Currier's line=entity, from which immediately one can ponder the possibility of changing alphabet maps, ponderably introduced by the VMS text designer so as to preserve some pattern that ultimately reveals itself in digraph entropies across entire blocks of text, it all becomes so complicated that we are right back to the original question: just what is the function of the VMS "text"?

Well, here one more potentially complicating thought: inter-line boustrophedon switching.

In comm. #164 I mentioned switching boustrophedon in and out every n lines. Suppose though a step-up scheme: switching boustrophedon every m matrix slots. Lets have a quick look at a possibility - we'll take the entire line 10 from Table #162-1:


The first character, the #, is the 9x72 + 1 = 649th matrix-slot occupant. Lets say that the scheme calls for boustrophedon to be switched in at m = 673. To m = 672 we have:


It is as if there is now a line break, but we do remain on the same physical line. The remainder might then be mirror-written in from column 72 so that the entire line becomes:


where some of the line's stats have changed while others have remained the same. But here now we have a rare kind of line among its boustrophedon brethren lines: it is a boustrophedon in / out switching line with the switch occuring inter-line. And provided one knows the value of m, nothing profoundly cryptic has been done to the original line 10 sequence! Look at line 10 now: the experimental plain text, borrowed from Jan Hurych, is still easily read, despite the altered stats.

But cast it into a strange alphabet, perhaps sweetening the scheme a little more with sub-alphabets handling respectively the straight and mirror sub-sequences, those sub-alphabets set up so as to produce some apparently consistent digraph properties, and throw in different matrix sizes here and there across the folios, and we'd have a rather interesting system based on nothing very profound. And with just a few simple keys, like m, it would not be difficult to decrypt, if you know what is what. Yet, if the above crypto-economics possibility for boustrophedon proves justified, then this simple system, with some experience fine-tuning it, might well confuse statistical attacks.

Boustrophedon therefore seems to be worth some more attention in VMS text considerations: it is simple and economical to experiment with, while touching upon major statistical properties of sequences.

Berj / KI3U

From: Berj Ensanian
Date: Sat, 16 Feb 2008 13:59:59 -0500 (EST)

Subject: J.VS: Transcribing Voynich text to music

Redaction of some off-J discussions 12 - 16 FEB 2008:

Jan Hurych [commenting on Voynich Studies encompassing far more than the VMS solution, and in particular the history of Czech cryptography] says:
When reading back, I discovered the answer to my other question: Wikipedia says Mnishowsky "apparently invented a cipher which he claimed was uncrackable (ca. 1618)".

Now I found that he wrote in his book preface "Occultus occulti scribendi modus quem nemo mortalium queat penetrareo" (Method of hidden writing, which no mortal can penetrate), as per Rafal [Prinke].

So he was bragging allright, except the year is apparently 1628 (written in the book, 1618 was the Prague uprising, they had different problems :-) and no connection with the VM is apparent.

Berj Ensanian says:
r Jan. Mnischowsky's: " Occultus occulti scribendi modus quem nemo mortalium queat penetrareo " has a slight poetic tone to it I thought. I wonder if in his book Mnischowsky employs poetic devices for some purpose or other. In light of Ave Maria this might not be a dumb question?

It was news to me to learn just a moment ago that back in Dec. 2004 our very own Dana had discovered Fr. Adamus Schall:

It's really cool combing the old archives and bumping into surprises :) What a shame that all the notes of the really early researchers from D'Imperio on back to Wilfrid are not available in one huge searchable database. There are lots of good ideas just in the VML archives that apparently never saw much development, for example the idea that the VMS script might be musical notation. So it occurred to me:

Would it be all that difficult for someone good at music and also math, to map some of the VMS text to modern musical notation, and then have the computer play it MIDI ? I'd love to hear what it sounds like. Would make a great deposit for the Library - Currier A versus Currier B interpreted musically for this or that mapping. Has anyone done this yet?

Page f20r is botanical, and has three modest text paragraphs above the plant / bush. Attached is a grey-scale tif of the first paragraph [gp1f20r.tif]. It has 4 lines of text, actually three and a half. Presumably it could be transcribed directly into whatever is used by MIDI aficionados in discussing music in plain ASCII emails.

Anyway, even if one maps these glyphs to musical notes purely at random, the "composition" when played in some manner is going to make for something to listen to. If one has musical talent, then the mapping may proceed with musical insight, and the resulting composition will sound more interesting.

But most importantly, what will happen is that auditory intelligence will be brought into the analysis of the VMS text. So far, the auditory channel as an analytic tool has been neglected - we routinely visualize the VMS, but we have not "listened" to it.

One obvious goal of auditory VMS text analysis would be to find out what is what with the intruding gallows - are they really single "notes", or a group of notes, or even a little bundle of groups of notes? What will "sound" more likely when listening to different musical interpretations of the gallows?

Here is the 1st paragraph of VMS f20r from Glen Claston's voyn_101.txt transcription:


We note that in GC's transcription system:
"." period is a full space while a "," comma is a "soft" or half-space
"-" indicates end-of-line and "=" indicates end-of-paragraph

Here's a slightly different transcription, still using GC's transcription alphabet. GC's voyn_101.txt is notorious for assuming abbreviations, and transcribing groups of symbols as a single. Below are some expansions, e.g. GC-C is expanded to GC-cc, and GC-m is expanded to GC-iiN

Variation-1 of VMS f20r 1st paragraph:


I also think GC-4o should be tried as a single character / note rather than two separates. In other words, in this case, GC may be over-expanded. Unfortunately his transcription alphabet does not have a single element for GC-4o, although AGC-168 is close.

On the VMS parchment, the rare glyph GC-A and the common glyph GC-a are very close in appearance. Suppose for a particular mapping of Voynich glyphs to musical notes, that when when GC-A is replaced with GC-a the score sounds better, or sounds "right". This might be interpreted that GC-A is nothing more than an incidental variation of GC-a, rather than a distinct Voynich text element. And so on and so forth, even possibly the text author's subconscious musical leanings might be guessed. That's what I mean about the possibility of doing auditory analysis on the text using music. Comments?

I seem to recall much earlier VML mentions of the music idea (going back to discussions of Hildegard of Bingen), but I just found and read the January, 2004 VML archives on "Voynechese as musical notation". Unfortunately, as it went after the introduction and enthusiasm of a good idea by Voynich Scene newcomers Kutowski and Bjerke, the encouragement of Dana Scott and Dennis Stallings did not prevail, and the data in that thread seems of more interest to psychologists studying Voynich Scene dynamics than to Voynich music theorists. So apparently presently, there are no files you can download, that give a bit of transcription, a mapping of same to musical notes, and a MIDI or .wav file you can listen to.

Greg Stachowski says:
Google is your friend [to find the recorded "Voynich music" mentioned in the 2004 VML post]:

I'm not sure that the German symphony bases itself directly on the text as notation, just is 'inspired' by it (presumably the CD sleeve would give more info). It is therefore a pity the idea was shot down; on the other hand it would indeed be very difficult to get something meaningful, since the mapping to notes is even more arbitrary than the transcription mappings. The best approach would be to map iteratively, looking for patterns typical of music (i.e. we favour a mapping which brings up those patterns) while trying to maintain the uniqeness of symbols.

On a related and perhaps more immediately applicable note (ha, ha), have any of the statistics and grammars done so far been looked at with respect to patterns indicative of poetry, music, tables or other structures? Someone may have done something like this, but I don't recall it at the moment. If not, it would be useful.

Jan says:
Berj, I have to agree. It reminds me of the situation when my colleague criticized one young fellow and added "I was with this company for 25 years!". He got a rather cute answer: "But you don't look too rusty and dusty to me."

Berj says:
r Jan. I wonder if Suzy Bjerke is still around and if she could be motivated to pick up the idea again.

Otherwise, some replies to Greg. First, if google is my friend, then AltaVista is my girlfriend ;-)

" I'm not sure that the German symphony bases itself directly on the text as notation, just is 'inspired' by it (presumably the CD sleeve would give more info). ........ "

That was my conclusion from the amazon link, there likely is no data for analysis, especially after reading the review of "Edward Wright":

" Equally effective is The Voynich Cipher Manuscript, a setting of passages from as as yet undeciphered secret script. (Kyburz adds to this script readings of three brief poems by Velimir Chlebnikov, which appear at three structurally significant points of the work.) The music is in something of an arch form, with outer sections in which the instrumental writing here is less driven and one-dimensional than in Malstrom, with plenty of space to hear the delicate traceries of pitched percussion that are sometimes swamped in the other work. The central sections are faster and louder, with more complex counterpoint and a preference for the chorus over solo voices. "

Quoting Greg again:

" ..... on the other hand it would indeed be very difficult to get something meaningful, since the mapping to notes is even more arbitrary than the transcription mappings. "

The point I was trying to make is to involve the auditory intelligence, and then start drawing conclusions from it. Your comment seems to dismiss the point a priori.

" .... have any of the statistics and grammars done so far been looked at with respect to patterns indicative of poetry, music, tables or other structures? "

I provided the voyn_101.txt transcript of the 4 lines from the 1st paragraph of f20r - something altogether like 100-150 symbols. I chose that block because it is relatively clean - easy to transcribe. If I knew musical notation I could have already tried a first mapping and have something to start playing with, in the time we are spending intellectualizing the idea. It's like the boustrophedon - it takes only a few minutes to do an experiment, and sometimes you get lucky and hit something interesting - as we saw. Therefore, does anyone know of an elementary music learning program, a modest kilobytes one, that I can download, that allows the following:

1.) On an empty staff I can place musical notes.
2.) With a mouse-click I can play the composition in Windows XP.
3.) I can save the composition as a .wav file.
4.) The musical notes are described in plain language, say "f sharp", so that a mapping table like the following can be exhibited in plain ASCII text:

Voynich GC-k is mapped to f-sharp
Voynich GC-y is mapped to b-flat

Note that I have almost no knowledge of notes (pun intended :) and may be stating the above naively, but I believe the basic thing I am after is straightforward and do-able.

Greg says:
Berj wrote: " The point I was trying to make is to involve the auditory intelligence, and then start drawing conclusions from it. Your comment seems to dismiss the point a priori. "

Not if you read the rest of it. I did say it was a pity the original attempt was killed, and I did also offer some suggestions on how to attack the problem. I'm quite aware of the point you were making: using music to 'visualise' (audalise?) the VMS to expose the patterns within it by harnessing the brain's power of detecting patterns in sound. My point was (while not dismissing yours) is that simply assigning notes to symbols ad hoc will mask any pattern (except for repeating notes), because it does not reflect the relationships either between notes or between symbols.

" Therefore, does anyone know of an elementary music learning program, a modest kilobytes one, that I can download, that allows the following: ..... "

Or possibly write a freeebasic program which does this mapping? I'm sure freebasic has some elementary sound commands, and you could just do a transcription to pitch mapping.

Jan says:
If I would try to convert the speech to music, I would probably convert the whole words into notes - mainly because of the note duration, using letters for notes would surely give very peculiar music. Of course, there will be many words than notes, so it would be futile.

It was one of possibilities that the VM can be a "notebook" (the pun intended) however in middle ages the notation of music was already very similar to ours and the educated author should have been aware of it. Of course, he might have had deliberately used the other format.

I guess it was [Robert] Firth, who first suggested the text may be some chant, namely because of apparent repetitions. Then of course the music would be important as well.

The whole idea, 24 letters of alphabet = 24 notes may be very attractive however we do not know what sign would correspend to each note. But the music might be very interesting anyway.

Converting transcript to music should be however simple: I have seen somewhere that for midi, you just use frequency numbers for notes, numbers for durations e.t.c. Of course different assignments for different letters would give different music, so one can play with the idea until he gets something pleasurable. Now that would be one of the interesting solutions, would it not?

Greg says:
Here's a webpage which does text to music conversion (one letter -> one note). No control over what is what, but it might suffice to start with:

Jan says:
I have found freeware that converts numbers into notes. It is free, from:

You might also need the table from:

Mind you, I haven't tried it yet.

Berj says:
Greg wrote: " My point was (while not dismissing yours) is that simply assigning notes to symbols ad hoc will mask any pattern (except for repeating notes), because it does not reflect the relationships either between notes or between symbols. "

Granted, but as a first experiment it is of interest, I say, to hear the relation between repeated notes. They presumably differ between Currier A and B, and the auditory intelligence may notice something that the visual intelligence, including math analysis visual intelligence, overlooked, perhaps. In any case I am curious and want to listen, with the curiosity of a radio astronomer who, takes a moment away from the strip-charts and spectrum displays, and puts on a pair of headphones :)

Jan wrote: " If I would try to convert the speech to music, I would probably convert the whole words into notes - mainly because of the note duration, using letters for notes would surely give very peculiar music. "

I was wondering about that also - there would be several ways to do it. But again, a first simple step is to simply convert script sequence glyhs to sounds. I've been saying "music", but as Greg mentioned it could simply be different pitches. In which case one gains more physicists attentions and loses musicians attentions, and this time I'm more interested in what the latter group, being in the habit of using the auditory intelligence faculty, thinks of it all. Or alternatively, if one can take seriously the statistical analyses of transcriptions, who is to say that a blind person listening to a "musical transcription" could not detect something interesting. I will look at the programs provided at the url's that Greg and Jan gave, and see what I can make of them.

Greg says:
I installed it [musette]. If you have one (or more) notes selected (red) it only plays those; if you have none selected (all black) it plays everything. Here's another one. Supposedly converts midifiles to text and back; presumably once you have the format you can fill it with whatever you like. I have no idea if it works:

Berj says:
It [musette] seems to work - I tried a supplied sample .mus file. Two questions:

1.) Can it momentarily hilight the note being sounded? I'm assuming that I can insert the transcription as "lyrics".

Greg says:
I don't know, I didn't see an option for it. Possibly it is in the upgraded version.

Berj says:
2.) How do I get the names for the notes symbols?

Greg says:
Again, I didn't see this. I think you'll have to learn them :)

Berj says:
I just accidentally stumbled onto something I had not thought of, even though to a musically savvy Voynich researcher it might well occur. I loaded into musette one of the supplied .mus files. Then I experimented by randomly inserting notes - I was initially interested in hearing the changing S/N - at what point would the basic tune become too corrupted to recognize. One of my notes insertions caused two notes (it and the good original note) to play simutaneously. My immediate thought: intruding gallows!

I'm convinced now that this technique has merit as an investigation tool. Incidentally, the lyrics do hilight as the tune plays along. This all may just work as a starter. I'm interested: Toccata and Fugue in Voynich Major :)

Jan says:
MUSINUM does not work for XP immediately, you have to restart. I made it working and converted some samples there into midi, it plays OK. Nice program is Noteworthy player from:

it plays midi and shows graphically all channels separately and the note played turns red. Nice gadget. You were asking for red coloring of played note - "Noteworthy player" does that - it is a simple midi player, but it also shows notes in different channels (or how do they call it). It can be downloaded here:

The page says: "You can also use NoteWorthy Player as your MIDI player. It will play back *.mid files and show notation and lyrics (if present) for the song. I wonder how they pack lyrics into midi?

If you download program, pls start it and open the midi file I am sending in attachment - it is really amazing, actually you can see accords for different channels (what if VM words are really accords?)

Greg says [concerning music entries in the J.VS Timeline]:
I put Heinrich and Aurelian in; at some point when I have more time I shall also put in points for the first appearance of various notations. By the way, I noticed while reading all this that notations which write out the notes in order as numbers or letters are known as 'cipher notations'. That would bring a whole new meaning to 'Voynich cipher manuscript' :)

Berj says:
r very good. I had been thinking back again to Carmina Cantabrigiensia (J.VS comm. #84) and its odd double-loop gallows etc. notation. From the TL just now I noticed that Aurelian and the Carmina are only a couple of centuries apart.

I've been using musette to transcribe to music the f20r first paragraph. It is going very interestingly, and I would have already had some results to share, but I am greatly slowed down by my lack of technical musical knowledge - I have no idea what musical notes I am mapping, and it looks like it will be tedious learning the minimum terminology. Musette is aimed at people who already know music theory, and the freebie version has severe limitations for VMS transcription work. It did get me started though and I was quite surprised, that so far, the musical sound of VMS text is more agreeable than I had expected. However, once I've completed this round with musette I'm going back to look at Jan's suggested program which allows transcribing notes with numbers. Incidentally, I've been using Currier's transcription alphabet because one of the objectives is to play the Currier A and Currier B Voynich scripts in comparison.

Robert Teague says:
Here's a suggestion; use my letter values for note values, and see what happens.

Berj says:
That's a rather interesting idea Robert. I hope you try it - I do hope this discussion is motivating the trying out of the auditory intelligence in VMS research. I want to HEAR what various Voynich workers compose off the VMS text. It had already occurred to me that even if Voynich star labels and normal Voynich text are incompatible in the usual cipher text analytics, nevertheless the star (or other) labels might have been intended to be heard musically. Now suppose this: your interesting finding (comm. #142) of progressive economy in same labels: what if that somehow makes a lot of sense when heard as music?

Once I complete this first round with f20r using musette, I'll dig into Jan's numbers-based music programs suggestions, and try some labels also. As a warmup for musicalizing labels I thought I might start with J.VS's ISSN: 1937-9277

[ end J.VS comm. #166 ]

From: Berj Ensanian
Date: Sun, 17 Feb 2008 00:03:43 -0500 (EST)

Subject: J.VS: Voynich clefs and key signatures

Dear Colleagues

As mentioned (J.VS comm. #166) I have been proceeding experimentally to set the first paragraph of Voynich f20r to "music", proceeding intuitively but without benefit of prior music theory knowledge. As our colleague Greg Stachowski pointedly suggested to me, I should learn music theory as I go along. And that seems to be a natural part of the process of my delving into Voynich text interpreted musically. I do want to emphasize that musical investigation of the VMS, presently just its text, is distinct from the hypothesis that the VMS text was intentional musical notation: in comm. #166 I argued for the value of musical analysis as a potentially valuable analytic technique involving the auditory intelligence faculty, and gave an example or two of how so in my own investigations.

The to-me-new musical vocabularly is fascinating: I just encountered "tessitura". I don't pretend to yet have any good appreciation for its definition, but I do have the sense that the concept may well become relevant in advanced Voynich music-text experimentation. My still vague understanding of "accidental" leads me to wonder if the variously shaped and positioned apparent diacritics, notably the plumes or hooks atop the Voynich text symbol EVA-ch, are accidentals.

Nor do I venture to say at this stage how comprehensive my exposure to music theory and notation will become, but in exploring, somewhat haphazardly, music theory during my experimentations, I have now come across some items that sparked ideas that I thought worth mentioning early on. Hence this communication.

I have been looking at the concept of "clef" and how important it is in musical notation, at the beginning of the musical staff. Although in my experiments so far I have merely been mapping the symbols sequence of f20r to notes just by ear, I have now read that there are nine possible distinct clefs - how remarkable in light of the nine rosettes manuscript! And how remarkable that one of the three clef symbols, namely the F-clef, so greatly resembles that common Voynich text symbol: the "9". And the G-clef by not much of a stretch of imagination is reminiscent of some of the gallows letters too, which commonly appear as the first letter of the first word of a Voynich paragraph.

There is also the concept of the "key signature", where generally at the start of a sequence of musical notation the clef and some other symbols define relations between natural notes and semitones in the music to follow. All this reminded me of the initial word on the Voynich herbal pages, and the important 1998 study of them by Jorge Stolfi [1] where he concluded:

" However, it turns out that the first word of each page is almost always page-specific. I take this fact as a sign that, as a rule, the first word of the page is the plant's name. "

Setting aside Stolfi's conclusion about plant names, only so because here it is not needed, and keeping his conclusion of "page-specific", it then becomes possible upon it to conjecture within the hypothesis of Voynich text as music, that the first words on the herbal pages are some kind of musical key signature, and each such distinct herbal page has its own musical key signature. My musical theory knowledge being as crude as it is, I don't yet know if this is a musically preposterous idea, but upon the possibility that Voynich text alphabet mapping, whatever it is that it may be mapping, changes across blocks of text and therefore folios, and therefore the number of distinct keys might be quite a bit less than the number of herbal pages, the notion seems to me to be worthwhile to bring up early.

Presently I am thinking that the Voynich script is indeed multi-purpose: at times used to construct cipher text, plain language text of some type including socalled universal language, steganographic text-art images, magical symbols, numbers tables or mathematical equations, musical notation, and combinations of the preceeding. In other words the Voynich script symbols and their system were devised by the VMS author as an ingenious universal medium. So it is entirely conceivable that a page-initial word on an herbal folio functions both as a plant name, and a musical key signature, all the more so if the Voynich manuscript fits into the category of "alchemical herbal" as per Mary D'Imperio's conjecture. It would then not be at all surprising in that context to have some sort of tonal expressions accompany the business of a magical herb.

One way to think about it is this: if we set out to devise a universal medium for the page, what form would it take? It would not be difficult to imagine that, after a lot of experimentation, we would conclude that a special alphabet would be the most suitable core for a universal medium system: the elements of the alphabet could be pressed into service for expressing everything from music to images. One might say the system gives a practical demonstration of: In the beginning was the word.

We've been seeing it, so why not also hear it.

Berj / KI3U

[1] The names of the plants, by Stolfi, 1998-01-27, available online here:

From: Berj Ensanian
Date: Tue, 19 Feb 2008 19:07:48 -0500 (EST)

Subject: J.VS: Work and transcription decisions involved in converting Voynich text to music

Redaction of some off-J discussions 17 - 19 FEB 2008 [ related J.VS comms. are #166 and #167 ]:

Berj Ensanian says:
Attached is VMSf20rp1.mus being a musette file of my first effort to transcribe line-1 of f20r, which is deemed Currier language-A, to music. Just load it into musette and play it, with the tempo set to about 130 quarter beats per minute. You'll see the Currier transcription entered as text, so for those who know musical notation, the mapping of the Currier letters A, B, C, D, E, F, I, P, R, S, 0, 4, 8, 9, to musical notes is readable off the staff.

Note that the experimentation had me decide to transcribe the double-i in the group iiN as a single note, but definitely the whole as two notes, in other words a musical transcription contrary to both the GC and interlinear views of that text group. It just sounds better to me as done.

Obviously this is just the barest beginning. I want to finish the entire paragraph, try some boustrophedoning of its music, and of course pick a Currier language-B block for comparison to do also. Here is my Currier alphabet transcription of f20r 1st paragraph that I've been working with - note that I've made an attempt to gauge text-groups inter-spacing to a resolution of 4.

f20r 1st paragraph transcribed in Currier:

{f20rL1} F8S089////S0B9////SCC9////40PS0E///40P0CC9////8S0R//SAIID-
{f20rL2} S08/C9/QC9///S0P0E//08AIIR///40PS9//Q089///S08S9-
{f20rL3} 40PCC9////S0/S08AIID///Z0///40S9///SC9////PSC08AE//8ARAE-
{f20rL4} 0/S0E////0E/PCC9////0PAESC9=

Altogether there are 16 transcription letters appearing: A, B, C, D, E, F, I, P, Q, R, S, Z, 0, 4, 8, 9,

Robert Teague says:
I just looked up the .mus file extension, and it contains data, but not the music. It can be opened with Notepad. I did see reference to a program that converts .mus to .mid, so will have to check that out.

Berj says:
That's what I want - a conversion from mus to mid. Attached is the complete first paragraph of f20r: [2VMSf20rp1.mus]. I got screwed up with musette's text editing, so I could not insert the remaining Currier transcription. But if you have musette, you can play the whole thing - again at MM = 130 speed or so.

I'm rather amazed at how good it sounds. It sounds reminiscent of a relaxed piano player just doing some leisurely exploring.

Jan Hurych says:
It really sounds (literally) interesting.

Berj says:
That's a terrific way to put it Jan: literally interesting! :)

I just completed transcribing via Currier notation a Currier language B block of text: the first paragraph from herbal f95r2, which is of similar size to the language A herbal f20r first paragraph. Here it is:

f95r2 1st paragraph transcribed in Currier:

{f95r2L1} FZC89///0R//S89////8AEVS9////40//8AIID///SX9VS9////8ARAIID///8AE/AE-
{f95r2L2} 8AIID///Z089////SFAID//S0E///SX9///0PAID///0P9///0PCC89//FAR/0FAJ-
{f95r2L3} P08AIID///S0R/SXC9///40F0E//SFAR//0E//0PAIID//0VAR//0FAID//AR/AJ-
{f95r2L4} 8AIID///Z089//P0R///0R//0FAID//SXC9=

Altogether there are 17 transcription letters appearing:

A, C, D, E, F, I, J, P, R, S, V, X, Z, 0, 4, 8, 9,

The alphabet differences between the first paragraphs of f20r and f95r2 are these:

p1f20r_: A, B, C, D, E, F, I, P, Q, R, S, Z, 0, 4, 8, 9,
p1f95r2: A, C, D, E, F, I, J, P, R, S, V, X, Z, 0, 4, 8, 9,

My next step is to set the f95r2 paragraph to music with musette again. There will be a few new notes to define. What I am working toward is to have the two .mus files converted to MIDI (has anyone got a lead on that yet?), and compile the music transcription-alphabet-to-notes mapping table. Then we'll have a starting package for a Library deposit concerned with VMS music work.

Jan says:
Have I got a nice name for your creation: Symphony Sinapia. Come to think of it, "Simphonia Sinapia" sounds even better.

Berj says:
Though certainly catchy, it seems to give Horczicky credit that we have not yet established he deserves :) I was thinking something more technical along the lines of: Experimental piano concerto for Voynich f20rp1

Anyway, I found a couple of minor errors in the f20r score which I corrected. I also was able to get the text in there for a full transcription, so the musette screen now is in effect a mapping table. The corrected version is 3VMSf20rp1.mus and it is attached here. It should be possible to make a screenshot of this as a jpeg - that would be a minimal first way to generally present the mapping of the 16 involved VMS letters to musical notes.

But anyway, next I am doing the language-B text of f95r2. From a quick glance at the first paragraphs of f20r (language A) versus f95r2 (language B) the Currier A vs B distinction may be relatively mild - so I'm quite curious if the two scores reveal distinctly different themes (I don't yet know the music theory term for this - the dominant periodic component around which the score proceeds).

I just got line-1 of f95r2 set to music: musette file 1VMSf95r2p1.mus is attached. Two new notes appear, from Currier V and X. CR-X is an intruding gallows: a CR-F intruding upon a CR-S, so in keeping with my system I mapped CR-X to the notes for CR-F and CR-S played simultaneously. To my ear this very limited language B musical data already sounds like there is indeed a distinct difference from language A. To me it sounds like this first line of f95r2 is characterized by bursts of tone oscillations much more so than f20r. The f20r is far more pleasant I think. We'll see (or rather we'll hear) once all of f95r2 is completed.

The difference sounds so great that I wondered if it is possible that Currier A and Currier B were devised by different persons, colleagues perhaps. Or perhaps that the A and B systems were devised by the same person at widely different times in life. So, these are preliminary thoughts stimulated at the early stages of these experiments.

Has anyone come across a .mus to MIDI conversion program yet?

Robert says:
Well, nothing simple. I found there are several programs that will do it, but the process seemed complicated. I Googled ".mus format", and how to convert to other formats came up.

Berj says:
A conversion from *.mus to *.wav would be just as good.

Jan says:
There are 2 converters at:
but both work from DOS only.

Berj says:
Thanks Jan. I'll have a look at them. ........ I tried both DOS programs that Jan pointed to. Cannot get either to work. The qmus2mid program always just gives a stack fault error message. The simpler mus2midi at least tries to do the conversion, but reports that the .mus source file has a corrupted header. I checked with one of the sample .mus files that came with musette, and got the same error, so I am guessing that the freebie version of musette does this intentionally in order to force buying the full boat version of musette.

Greg Stachowski says:
Or more likely a Musette .mus is not the same as the other .mus (and indeed they probably aren't the same as each other) . Few filename extensions are unique -- which incidentally is why filename extensions are a poor way of identifying file types, but that is another story.

Berj says:
I am thinking of getting away from musette altogether, and for the already done work rigging up another computer and doing a direct speakers-to-microphone recording. Anyway, I'll solve that problem later, as I first want to complete transcribing the music of f95r2.

Greg says:
Why another computer?

Attached is a 128kbps MP3 of 1VMSf95r2p1.mus . (If you did use another computer, line-out to line-in would be better, anyway.)

Jan says:
As Greg pointed out, the formats are weird and converters as well. The program Easy recorder ... Greg suggests works OK. I tried that ( for sound not for .mus) You do not need to use microphone, just set your speaker icon at Windows bar to Options, Properties, check Recording to Stereo Mix and when you play your music on Musette, after starting Easy recorder, it will record it all as mp3 file (preferable, it is much shorter than Wav). Then you can send mp3 by mail, however it is still much larger than Midi, of course. Maybe there is one mus convertor on Musette page?

Berj says:
The free Easy MP3 Sound Recorder that Greg suggested worked immediately - thanks Greg. I didn't realize there was a freeware available that was quick and easy and actually does what I needed done. As for line-to-line, the assumption is we have the right cables within arm's reach. These are all just annoyances along the way to getting the VMS text converted to listenable music.

After installing Easy MP3 Sound Recorder, here was the procedure I used:

1.) Have musette ready to play the f20r *.mus file.
2.) Set up the Easy MP3 Sound Recorder as follows:
Input pin = Mono Mix
Output Type: Channel = Mono; 16 bits/sample; Sample per 44100; MP3; Audio bitrate = 224 bps. Specify the save filename that Easy MP3 is to use.
3.) Click "Start Recording" on Easy MP3, and then immediately click "Play" on musette.
4.) After musette finishes playing, click "Stop" on Easy MP3. The recorded file is saved automatically - just play it to test it.

The f20r first paragraph came to about one minute and weighed 1,738 Kb in *.mp3 format. In the *.wav format, as Jan anticipated, it was much heavier: 5,427 Kb. We can finesse things later - the conversion to a more or less standard audio format, and at an acceptable kilobytes weight, is now accomplished, and it is back to transcribing f95r2. I am barely able to contain my curiosity at listening to the complete paragraphs of f20r versus f95r2.

[ end J.VS comm. #168 ]

From: Berj Ensanian
Date: Wed, 20 Feb 2008 15:54:34 -0500 (EST)

Subject: J.VS: From Voynich MS music to Voynich MS speech

Redaction of some off-J discussions 19 - 20 FEB 2008 [ related J.VS comms. are #166, #167, #168 ] :

Greg Stachowski says:
You don't need to use such a high quality for the mp3s, 128 kbps is more than enough with the distinct, simple notes from musette. Probably less would be okay, in fact. It would do a lot to keep the file size down.

Dennis Fedak says:
We might be able to set up an "auto-play" feature, on one of the web sites. Below is an example:
Choose "Play Midi" from the menu for a ".mid" file
Choose "Embed" for an alternate programming example ( mostly works with IE ).
Choose "play Movie" ( with the poor quality sound ) for more complex (.wmv) presentations.

In general, all we have to do is get the browser to download the file and then invoke the preferred player on the client. I'll see what I can find for ".mp3" but I suspect most newer PC's can play them, although even at work, the convention is to change all audio to ".wav" ( remember you only need monophonic 11 kbps for most tones that are going to be played, unless your going to do full orchestration and / or use different portions of text as differecnt voices in different staves!

The ".mus" program itself, is interesting. I've played, and transposed, the folio piece, several times. ( and some of their examples ). Nice effort!

Berj Ensanian says:
r Dennis, Greg suggested the same: reducing the sampling rate to keep filesize down, while remaining adequate - I'd like it to continue to sound like piano, rather than a Hewlett-Packard pulse generator. As for a click-and-it-plays installation in the Library, that would be up to Greg of course.

Greg says:
Shouldn't be a problem, just a question of telling the server to send the correct MIME-type.

Berj says:
I imagine that after finishing f95r2 if I get a well-constructed mapping table written, one that has in addition to Currier also a couple of other transcription alphabet equivalents, like EVA and GC, then presumably there will be motivation to write programs that take existing transcripts like GC's voyn_101.txt and automatically convert to music. The drawback with that is that I have been using a resolution for space of 4, and GC's is at best 2: what he calls hard (i.e. "normal") and soft (somewhat shorter) spaces. Not to mention other-worker's transcription choices and errors.

Jan says:
Berj, it seems there are general ( or shall we say generic :-) problems with MUS files, namely the conversion.

Interesting discussion is at:

Apparently the format MUS is used for videogames so one way to play it would be through some DLL driver. If you are planning to musify ( the pun intended) something longer, MIDI or MUS formats would be still the best choice of posting , thanks to very short files.

Greg says:
That discussion illustrates the point about filename extensions very well. .mus is used for at least DOOM (a videogame) music files, Finale Notepad files, Sibelius files, Musette files. Some of these are actually MIDI files in disguise, some not. It is just a natural file extension for "MUSic". The conversion tools invariably assume one particular type which was of interest to the author.

For distribution, I would be inclined to go for the mp3 file. MIDI is good and all, but actually not that well supported in terms of default installations these days. For example, of 5 systems I use across 3 machines, only one can at this moment play MIDI files, whereas all can play wav or mp3. Of course, me being me this isn't a problem, I can install the right plugins, but you get the point. The mp3s can be made small enough for distribution by cutting the bitrate: as Jan said for this simple music the bitrate can be cut very hard before the quality deteriorates appreciably. Experiments are needed.

Jan says:
Greg, I agree, I also like MP3, because I have a MP3 cutter, merger and gain booster ( I can send the program, it even shows visually the sound versus time. That is all I need :-).

It is just I cannot imagine the length of the whole VM ( Voynich Music :-) -how much per folio? And yes, bit rate can be cut to the bone, for speech is good enough 32 kbps, some sites go as low as 10 kbps, we can go lower. After all this music is generated by mathematics, that is the main frequency only and it does not include too many higher harmonics, even if one can simulate some instruments.

As for Easy recorder, I could not find any adjustment of the volume or display of the amplitude, in conversion, to avoid saturation or too low intensity recording. I am using Megasound recorder, I am enclosing the installation program, since I could not find it any more on Net.

Berj says:
In following the discussion between Jan and Greg just now, I was struck by a comment that Jan made in passing; it sparked a new idea. Jan said:

" It is just I cannot imagine the length of the whole VM ( Voynich Music :-) -how much per folio? And yes, bit rate can be cut to the bone, for speech is good enough 32 kbps, some sites go as low as 10 kbps, we can go lower. "

My thought on reading this was: if we are successfully mapping Voynich text to music, then why can't we also map Voynich text to "speech" using a sound chip? Back in the 8-bit computer days we had the wonderful Commodore 64 with its great MOS Tech 6510 controlling an onboard revolutionary MOS 6581/8580 SID audio chip (Sound Interface Device, not to be confused with the recent SID image format) and with I-forget-the-program we could just type sentences at the keyboard and hear very impressive speech. The Texas Instruments TI-99/4 and 4A computers of that era had available an optional outboard speech synthesizer that just stunned me when I first heard it. With those computers, in effect you could map codes (letters typed in at the keyboard or from a file) to complex audio bursts that simulated speech units, phonemes if you will, and executed in sequence it really was like hearing someone speaking. And all that became commonplace so where today we are often irritated by computer voices on the telephone when we are after a live person we want to talk with.

Anyway, in the Voynich studies field there are plenty of theories of the Voynich text being this or that natural language, often uncommon or even lost dialects. So, does it not make sense for Voynich-is-natural-language theorists to experiment with some mappings in the manner of the music experiments, and produce some "speech" that can be listened to, and then judged? Conceivably, a recording might get linguists to admit: Aha, yes, this passage does indeed sound like the W dialect spoken in the X province of country Y during the Z period.

Jan says:
Excellent idea! Now I guess you can start with sample sounds for each character of the alphabet - the net is full of them - but better way would be to sound the whole syllables. Come to think of it, our linguist experts already "established" which characters in the VM are wovels :-). So you can record syllables for the same wovel but with different consonants, say ba, be, bi, bo, bu, by - provided that it was written in simple transcribable sound (not like bee, boo and others ( the long ones) where we need three characters to express one sound). By replacing those bi-letters in the VM transsound (= sound equivalent of the VM transcript), so we could be able to establish if the vowels are really wovels by judging the pronounceability of the transsound. ( I like that word :-).

Frankly, Sukhotin's theory ( how to establish which are vowels and which consonants) looks to me more like a statistical gimmick - surely it would be different statistics for different languages - e.g. Japanese and Hawaiian do not have all consonants we have. In reverse, the bonus could be that we may be able to establish that way what are the REAL wovels in the VM. Only if it is a natural language and no encoding, of course.

Berj says:
Good Jan - you've brought up several important issues from past Voynich linguistic theorizings that can be investigated with synthetic speech! To get started I was thinking of something very simple: mapping some VMS labels' letters to phonemes and then listening to the "speech" of the spoken label. Then it immediately occurred to me that we have a ready-waiting item that we can explore: Robert's observation that the hypothetical "ALDEBARAN" is progressively economized in labels in the astro section [J.VS comms. #141, #142]. Converting the ALDEBARAN variations to speech might just reinforce Robert's observation, or in any case let us hear something interesting that was not obvious with vision-based analysis.

Well, I better hurry up and finish the f95r2 music: the speech experiments are already hollering to be started!

Jan says:
Great, I can't wait to hear it.

[ end of J.VS comm. #169 ]

From: Berj Ensanian
Date: Fri, 22 Feb 2008 02:23:35 -0500 (EST)

Subject: J.VS: Experimental Piano Concertos of Voynich texts f20rp1 and f95r2p1 in C Major

Dear Colleagues

I have sent to our Librarian Greg for deposit # 16-1-2008-02-21 six files representing the completion of the first experimental effort to convert two Voynich text blocks to music. [1]

The background with pertinent further details aside those given here, and given in the Library deposit materials, is in J.VS communications #166, #167, #168, and #169. What has been done is this:

1.) The first text paragraph of Voynich manuscript herbal folio f20r has been transcribed in Currier notation: the transcript is given in J.VS comm. #168 [2]. This particular Voynich text is generally considered to be an example of "Currier language A" in the corpus of the Voynich ms text. [3]

2.) Using the musette.exe music-composing computer program [4] a mapping of the Currier transcription to music has been done, the mapping being of course a matter of subjective choices. A screen shot of the musette screen, in effect "sheet music", has been made. In the Library deposit this image file is: MusicVMSf20rp1.jpg

3.) Using the "Easy Mp3 Sound Recorder" program [5] the musette file from 2.) has been converted to an .mp3 audio file that is ready to play the music. The Easy Mp3 set-up and procedure was as detailed in J.VS comm. #168, except that an Audio bitrate = 128 bps was used. In the Library deposit this file is: MusicVMSf20rp1.mp3

4.) A grey-scale jpeg image of the 1st paragraph of VMS f20r has been made, suitable for viewing while the mp3 file from 3.) is heard playing. In the Library deposit this file is: r40gp1f20r.jpg

The same steps 1.) - 4.) have been done with the first paragraph of VMS f95r2, and in the Library deposit the corresponding files are accordingly named. The f95r2 text is considered Currier language B per [3].

So then, the two mp3 files can be played, they are about one minute long each, to hear one interpretation of what their respective Voynich texts, taken as music, sound like. The limitations attending these efforts, notably my inexperience in composing music, have been recorded in the above given J.VS communications. I'm quite sure that the results could be improved. The designation "Experimental Piano Concerto of Voynich f20rp1" and similarly for f95r2p1 is more lighthearted than serious, but at the same time it is intended to capture the attention of those Voynich ms interested persons who really do have musical skills, and to encourage them to produce musical investigations of the VMS text. As stated in the above referenced communications, music is a way to involve the auditory intelligence faculty in attacks upon the Voynich mystery, and that is entirely independent of whether or not the VMS author intended any of the folios to record music. Music is a valid attack instrument upon the mysterious VMS text.

Of course modifications of the mapping that I made are wide open. Here is the mapping I devised:

Table 1: Mapping of Voynich alphabet to musical notes in C Treble clef:

Currier symbol = musical note

A = B sixteenth note
B = G one octave up whole note
C = D one octave up half note
D = C one octave up whole note
E = A sixteenth note
F = B sixteenth note
I = middle C eighth note
J = C one octave up sixteenth note
P = B whole note
Q = E quarter note PLUS B whole note; (note that CR-Q is a Voynich intruding gallows glyph)
R = E one octave up quarter note
S = E quarter note
V = F one octave up sixteenth note
X = E quarter note PLUS B sixteenth note; (note that CR-X is a Voynich intruding gallows glyph)
Z = A eighth note
0 = F half note
4 = not mapped separately from 40
8 = G eighth note
9 = D sixteenth note
II = A eighth note
40 = tight pair of G sixteenth notes

The 16 and 17 respectively transcribed Currier letters in the f20r and f95r2 first paragraphs are:

p1f20r_: A, B, C, D, E, F, I, P, Q, R, S, Z, 0, 4, 8, 9,
p1f95r2: A, C, D, E, F, I, J, P, R, S, V, X, Z, 0, 4, 8, 9,

Note that the digraph II was transcribed as a single VMS text element, as was the common "4o".

As mentioned in comm. #169 a computer program might be written that takes as input Voynich text transcriptions and a mapping table like Table 1, and produces music output, subject to limitations noted in previous discussion. In any case such a program would make for an immediate new tool for working with existing VMS transcripts. Toward that I give here the correspondences between Currier and a few other Voynich transcription alphabets, for just the letters of Table 1:

Table 2: VMS transcription-alphabet correspondences for Table 1 (use with caution)

Currier (CR-); D'Imperio (MD-); EVA-; GC-

A; H; a; a
B; G; p; g or j
C; C; e; c
D; P; n; N
E; I; l; e
F; W; k; h
I; L; i; i
J; S; m; p
P; A; t; k
Q; J; cth; K
R; O; r; y
S; B; ch; 1
V; Z; f; f or u
X; X; ckh; H
Z; R; sh; several, typically: 2
0; D; o; o (note: problem distinguishing oh from zero in [2]; the VMS letter is the little oh)
4; F; q; 4
8; K; d; 8 or 7 or &
9; N; y; 9 or (
II; LL; ii; I
40; FD; qo; 4o

I began this work with line 1 of f20r and therefore that line had the greatest influence on the mapping shown in Table 1. That must be kept in mind when judging the different musical effects of the Currier-A f20r and the Currier-B f95r2. To my ear the f20r sounds more pleasant, but it is entirely possible that had I begun with f95r2 then it would sound more pleasant.

After completing the work, I was surprised to see in Table 1 that I had transcribed the II digraph to the same musical note as CR-Z. Also, as mentioned in comm. #168, I found myself interpreting the II as a single musical note. It is interesting that of the four transcription systems in Table 2, only GC had II available as a distinct digraph. In the VMS text we see III and if I recall correctly there might be IIII also somewhere. Anyway, there would be mapping choices to make with text groups containing say III: per Table 1 should it be transcribed to music, for example as:

I II or II I

or even transcribed as a musical trigraph?

Finally, some impressions of f20r versus f95r2. The f20r actually sounds quite good to me - I would not be surprised to hear something like it in walking in on someone relaxing at their piano. The f95r2 sounds quite different to me. Its lines seem to differ more from one another, than do the f20r lines. Perhaps the f95r2 lines are boustrophedon, and their music sounds better that way - I will explore that. But as transcribed, although not awful to listen to, the f95r2 is to me reminiscent of random bursts of data in a digital signal stream, at times almost cacophonous. Compared with f20r, the f95r2 sounds less thematic, less organized, somewhat as if a novice musician is attempting to compose a piece far more complex than his capabilities. But the Currier language-A of f20r sounds as if there is a coherent unifying theme throughout. Perhaps that motivates considerations of Currier A being closer to a natural language than Currier B.

Berj / KI3U


[2] Currier transcription alphabet as per Table Fig. 19, pg. 97, The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7.

[3] As per: Version TEXT16E5 Interlinear archive of Voynich manuscript transcriptions. Derived from INTERLN.EVT file version 1.6 Created by Gabriel Landini, 27 September 1996. Split into separate files (one per textual unit) by J. Stolfi, 10 october 1997. Version 16E6 is available here:



From: Berj Ensanian
Date: Sat, 23 Feb 2008 19:01:20 -0500 (EST)

Subject: J.VS: ALCIONE / ALCYONE on astro f68r3 and Voynich-text to speech conversion challenges

Redaction of some off-J discussions 22 - 23 FEB 2008 [related: J.VS comm. #169]:

Berj Ensanian says:
Does anyone have any recommendations for a freeware speech synthesizer that is not too huge in kilobytes that I can download and play with?

Jan Hurych says:
Berj, I guess you do not want any text voice-reader or text to speech programs, but synthesis of phonemes. I found some free progs, but did not have time to check them. You can expect however that for synthetizer, 10 meg is probably a normal length of program.
seems interesting, but java.
11 meg.
for DOS and other dinosaurs.
8 meg.

As for MUS files, I could not find any working MUS to MP3 converter, apparently the best is the way you do it, e.g. via voicecard (e.g. play), Easy recorder directly into the Mp3.

Berj says:
Thanks Jan. I like dinosaurs! :) I do intend to have a look at the DOS programs, but I first obtained the freeware version of TTS Builder Pro 1.2 weighing in at ~ 8.1 Mb from the bluechillies site you gave. It installs quickly and works right away, and is easy to use, and is limited to 30 characters sequences - that is adequate for the first focus - investigating the VMS labels, starting with Robert's ALDEBARAN ideas. As for the speech quality, it is adequate for some initial experiments I'd say.

I have to reacquaint myself with Robert's tables, but I did obtain a few preliminary mappings that I'll build on. Try these in the TTS program:


With the last two I've obtained what I was after: making "L" by itself take the place of "AL". So a first mapping table is:

Syllable = TTS string

A = -AH
L = -uL
D = -DEH
RA = -raah
N = n

Note that the N is mapped to an "n" without a leading dash.

Greg Stachowski says:
I found this:

Which is two programs, espeak and espeakedit, the latter from editing the phoneme data. 1Mb for the first and 4.5Mb for the second. I haven't tested either yet, but perhaps will later tonight.

The classic speech synthesiser where I came from was Speech! for the BBC micro:

Which was nicely phoneme based. I did a lot of playing with that. Of course that was 1986 or so :)

Berj says:
Interesting - the writer says he uses espeak regularly to listen to blogs and news, that is he uses the program to convert written matter to speech.

I just came across a small (the download is a modest 240 kb) speech engine called "SayIt", Version v2.03 from analogx:

I've had only a few seconds to try it, but it seems to have potential. Handles up to 500 characters input.

I think it is important to define an objective. With the music it was quite clear: auditorily compare approximately equal sized blocks of Currier A and B. With the speech experiments we need something equally clear to go after, but what? I have several vague ideas of course, but I'm probing for something well defined.

For example, I wondered if the text of f65r had been proposed by anyone as a comment on that plant there, in some natural language or other. That f65r is rather unusual in the manuscript on account of bearing mostly an illustration and just two or three words text. In other words, compared with the astro section label ALDEBARAN [hypothetical], the f65r might just be a phrase. I guess what I am trying to say is that I am looking for a piece of VMS source text that has high probability of being a short phrase. We can then start speech mapping it, change the mappings, and maybe at some point it will actually sound like a sensible phrase in some language we recognize. Going for a phrase seems more promising than going for just a label. Does this seem reasonable?

Jan says:
Yes, it is important to figure out what we want to achieve - turning text into speech may be very powerful tool for further investigation of the VM. It is probably the only chance to prove, in general, that natural language was not used, in plaintext, of course. It could for instance put to the rest such idea, if it is found unpronounceable.

In that case there are only few possibilities: the characters could be just letters or syllables (like Japanese katakana). The third possibility, the picture script like Chinese or hieroglyphs is eliminated automatically, since we have only 28 or so characters.

The search for the language was so far rather futile - we either did not try all of them or the language is long time forgotten or artificial. Still, IF the VM is using system of characters similar to our alphabet, we should be able to spot the similarity when synthesizing it.

As for other options, the sounding (pardon the pun) would not work if a cipher, shorthand or similar workover was used. It also would not work if the script without wovels was used - the PRONOUNCEABILITY is the key criterion here. It could however work if the codebook was used where the codes were words of some natural language.

As I said, we should take the symbols our "subotniks" told us are wovels - it would not matter too much which is which and then fill in the consonants, again arbitrarily. The text then should be pronounceable. If not, they were way out with their statistics.

Of course the word "bird" is not in fact pronounced as bee-ay-are-dee, prounced quickly and sequentially or even by braking it in twos (bi- ard) but such arrangement still gives a reasonable, pronounceable sound. On the other hand, word "prbkl" would not give pronounceable sound.

Well, I do not exactly know how the synthesizer might work for non-English language, since they seldom use two letters for one wovel sound, (English language has even 2 pronounciations for oo, as in pool or door). It would be better to use the international convention, where "o" is always o pronounced clearly as in pot). I guess at the beginning, we should ignore the double letters in the VM - are there actually any except of those characters looking like EVA's ir,iir,iiir, which Courier identifies as single T,U,O? Since we do not know for sure, we may try both options...

Berj says:
Indeed Jan, the VMS text-to-speech challenge is far more difficult than the text-to-music challenge, as you are illustrating. Perhaps we are almost brushing against the idea that it is speech which separates human intelligence from the animals (although I've heard of a parrot or two that one could seemingly "converse" with, perhaps even productively ;-). Let me raise the complexity even one more notch: abbreviations. And in the process I'll pick up on a strong but perhaps subtly-stated hint I got from Robert's latest paper [ref. J.VS comms. #141 and #142].

Lets take a quick look at the word that is directly under my favorite curve: the word underneath the f68r3 PM-curve [Pleiades - Moon curve]. At first glance, in EVA we might transcribe it:

EVA: oalcheol

and that is in fact what the 16E5 interlinear file has it as. But, as usual, a transcription compromise was made. So, lets go back to the f68r3 parchment (the SID image of it), and try to do a more "accurate" transcription. Taking some liberty with the EVA system, I'll temporarily introduce "_" to designate the space between Voynich glyphs. Then the next transcription effort becomes:

EVA: o_a_l_ch_eol

That last part, the "eol" is problematic, as we see it on the f68r3 parchment: is it 3 symbols, 2, or even a single glyph? Frankly, it suggests the possibility of an abbreviation constructed of three components. So, lets set aside EVA and transcribe anew, borrowing the manner of Frogguy, and using ordinary lower-case Latin letters symbols chosen in such a manner that they resemble as close as possible what we see on the f68r3 parchment:


The "col" we are now trying to match to an abbreviation. I didn't see anything in Capelli (perhaps it is there and I missed it), but lo and behold in D'Imperio's Table Fig. 17 on pg. 95 I see she has as a Latin abbreviation for "one" a three-component glyph that is invitingly close to the "col" above. She shows "ol" with a little diacritic "c" plume or hook floating atop the "l". If that c-hook is simply rotated and moved onto the left side of the "ol", we have our "col". Now, I'm not clear if she means that the meaning of this abbreviation is the text "one" or the numeral "1", but I'll assume it is text. The text group "one" is not especially common in Latin words as far as I know, and quite rare as a suffix - the noun "expeditione" is about all that comes to mind. However, if the "col" is an abbreviation for "one", then no matter - it can appear in script as is the convenience of the writer. So now we've got:


Once again D'Imperio's table weighs in: she has a perfect match for c~c being a Latin abbreviation for "ci". So now we have:


and since only the initial "o" is left to deal with, lets write this: o_A_L_CI_ONE

So we have o ALCIONE. Needless to say, the star ALCYONE is one of the 7 sisters among the 9 named stars of the Pleiades cluster, and she is the brightest of the lot, even brighter than her two named parents. And in tune with Robert's hint, ALCYONE may be used to designate the Pleiades.

Assuming we are correct this far, what is the initial "o" signifying? The simplest answer seems to be to reason that, since abbreviation is already being used, the initial "o" is an abbreviation. Considering the context of f68r3 and the PM-curve and moon, it might stand for "occulto" or "occultus".

And now the big question: on the assumption that the foregoing is indeed correct, how do we get to it, or even get close to it, with speech engines, when we are starting with input transcriptions like EVA-oalcheol ? Jan wrote:

" ... the PRONOUNCEABILITY is the key criterion here. "

I think he is absolutely right. Because, provided we give the speech synthesis engine accurate transcription input, it is going turn out something un-pronounceable, or at least discordant when it hits something like the above "col", and we may have a clue it is an abbreviation. Now, that will not be the case with traditional assumed abbreviation assignments as with the well-known "iiN" being transcribed "m", 8aiin being about as pronounceable or non-pronounceable as 8am, but no matter, we are after the truth in the thing.

For minimum complications initial speech testing, it seems that we need a phrase, a phrase that somehow suggests that the VMS author wanted us to spot it, and start with it as a directly speakable phrase. I have been wondering if simple anagramming might be detected with synthetic speech, but the question is just so broad, and experimentation there could well entail enormous work before any useful generalizations could be deduced.

[ end J.VS comm. #171 ]

From: Berj Ensanian
Date: Tue, 26 Feb 2008 23:49:55 -0500 (EST)

Subject: J.VS: Boustrophedon versions of the Voynich experimental f20r and f95r2 music transcriptions

Dear Colleagues

I have completed the boustrophedon versions of the Voynich f20r and f95r2 first-paragraphs musical transcriptions work of J.VS comm. #170.

VMS f20rp1 transcribed boustrophedon (original lines 1 & 3 left to right, lines 2 & 4 right to left) in Currier notation:

b{f20rL1} F8S089////S0B9////SCC9////40PS0E///40P0CC9////8S0R//SAIID-
b{f20rL2} 9S80S///980Q//9SP04///RIIA80//E0P0S///9CQ/9C/80S-
b{f20rL3} 40PCC9////S0/S08AIID///Z0///40S9///SC9////PSC08AE//8ARAE-
b{f20rL4} 9CSEAP0////9CCP/E0////E0S/0=

VMS f95r2p1 transcribed boustrophedon (original lines 1 & 3 left to right, lines 2 & 4 right to left) in Currier notation:

b{f95r2L1} FZC89///0R//S89////8AEVS9////40//8AIID///SX9VS9////8ARAIID///8AE/AE-
b{f95r2L2} JAF0/RAF//98CCP0///9P0///DIAP0///9XS///E0S//DIAFS////980Z///DIIA8-
b{f95r2L3} P08AIID///S0R/SXC9///40F0E//SFAR//0E//0PAIID//0VAR//0FAID//AR/AJ-
b{f95r2L4} 9CXS//DIAF0//R0///R0P//980Z///DIIA8=

As per the procedures detailed in comm. #170, sheet-music image files for the above have been prepared:


and also ready-to-play mp3 audio files:


From the sheet-music pictures it is seen that I transcribed musically the "4o" glyph's boustrophedon version, "o4" the same as "4o" - all factors taken into account, this seemed the thing to do. Our Libarian Greg has installed these four new files in the same Library deposit containing the previous work, deposit # 16-1-2008-02-21 for which the url is:

To my subjective musical sense, the boustrophedoning of f20rp1 (Currier language A) sounds like a severe disruption of the pleasing flow of the normal f20rp1. In contrast, the boustrophedoning of f95r2p1 (Currier language B) does not make much difference: it sounds about as random (or "bad") as the straight f95r2p1. As Greg noted when he received these files from me, this is a subjective detection of a symmetry, the f95r2p1 cases, and an assymetry: the f20rp1 cases. This is quite interesting, but lacking further data and analysis we cannot make too much of it yet. As noted in comm. #170, the line-1 of f20r had the most influence on the Voynich glyphs to musical notes mapping that rules all four compositions.

Berj / KI3U

From: Berj Ensanian
Date: Wed, 05 Mar 2008 22:47:28 -0500 (EST)

Subject: J.VS: Some hypothetical steganographic faces in the Voynich f93r Sunflower folio spill-stain

Dear Colleagues

I thought to investigate the long vertical-running irregular stain on the f93r folio. Voynich f93r is of course famous for bearing the plant illustration that botanist Hugh O'Neill in 1944 identified as an American sunflower: Helianthus annuus L. [1]. That, and his capsicum pepper identification in f101 in his same 1944 paper are the classic first items of evidence toward the hypothesis that the Voynich manuscript post-dates 1493. The dating of the VMS as post-discovery of the New World includes other items for consideration, for example the possibility that the animal drawn on the left margin in the upper half of f80v is an armadillo, rather than, say, a sheep, or a fictitious animal.

In the VMS, as stains ago, the apparent stain on f93r is quite conspicuous, on account of its size and prominence. At first glance one gets the impression of water color paint, the same that was used to fill in the head of the sunflower, having accidentally spilled onto the parchment and run down from the top margin to almost the bottom, and then simply left to dry. Examining the high-resolution SID image of f93r my impression is that this stain feature came onto the parchment after the sunflower had been rendered, but before the writing. There are complications: the color is darker in the broadest portion of the stain, and there are some indications of interaction with the green paint of the sunflower leaves.

I was curious about the stain being possibly intentional, because there do not seem to be any clear indications that any effort was made by the f93r composer to remove or mitigate any part of the stain. I wondered if perhaps the stain, on account of the impression it so gives, was meant to illustrate a system of connected bodies of water, and it crossed my mind that, given O'Neill's sunflower identification as correct, that the stain depicts some bodies of inland waters, connected by a river, in the area of the New World where the VMS author understood the sunflower to have been discovered.

Continuing to study the stain, I noticed a number of possible steganographic faces formed within it. If intentional, their existence might reinforce the notion that the stain was on purpose, although of course it could have been an accidental spill that the artist then decided to exploit further. I cropped images of altogether six faces, although there may be more, and I have sent them in five image files to our Librarian Greg for an addendum to J.VS Library deposit # 12-1-2007-10-12, the deposit which holds many of the VMS's faces, both unambiguous and hypothetical steganographic. [2]

The new image files for the Sunflower folio stain-faces are:

VMSf93rfaces1&2&3.jpg (Sunflower folio stain-faces 1, 2, and 3)
VMSf93rface4.jpg (Sunflower folio stain-face #4)
VMSf93rface5.jpg (Sunflower folio stain-face #5)
VMSf93rface6.jpg (Sunflower folio stain-face #6)
xgVMSf93rface6.jpg (Sunflower folio stain-face #6 grey and contrast enhanced)

The updated metadata text-file for 12-1-2007-10-12 explains how they were made. The faces are numbered 1 to 6, with the identifying number placed close to the mouthes of their respective faces. Stainfaces #1, 4, and 5 are approximately humanoid, the others more animal. These jpeg images are intended merely for locating guides - the SID and / or its TIF image should be examined to see the faces best.

Stainface #1 is the most vague. One can just barely entertain that there is there a right-side profile, an eye, a couple of nostrils, and a mouth, opportunely added to the stain's shaping at that location, at the end of the topmost leaf on the left side of the sunflower's stem structure. To me the general impression is similar to some of the faces of the most crudely rendered Voynich ladies in the zodiac panels.

Proceeding down, stainface #2 is quite passably a face in my opinion, resembling something feline, a three-quarter right-side profile, also facing toward the sunflower.

To the right, stainface #3 is formed from an island stain that is separate from the major stain. This island stain is on the second leaf from top, again on the left side of the plant. The face it depicts suggests an animal of some sort, perhaps a bat. If intentional, then the mouth is obviously well rendered.

Proceeding down again from stainface #2, stainface #4 is one of the more interesting ones. It is also a right-side profile, looking toward the sunflower, and to me it appears as if some care was taken rendering the face's right eye, which is just under and against the arc of ink-trace that forms the top outline of the third down from top, left-side leaf. The neck of the head of this male face may have some hidden glyphs in it, including a script capital "E".

Proceeding down along the stain, as it becomes free of all overlap with the sunflower, there is stainface #5. The jpeg has it quite vague, but the SID is much better, and a little bit of contrast enhancement should demonstrate why I thought it worth including this example. It has an interesting, highly aware contemplative expression.

At near the bottom of the folio, the very end of the stain forms stainface #6, which I see as feline but with some humanoid character. Situated at the end of the long stain, it is almost like the head of a serpent, although it does not resemble a serpent's face. It is this face which to me suggests most strongly that, assuming the stainfaces, or some of them anyway, were indeed intentional, then of the two possibilities:

a.) the stain was an accident that the artist exploited for embedding steagnographic faces.
b.) the stain was planned from the beginning to be added to f93r for one or more reasons, including steganographic faces.

that the possibility b.) is the likely one. That still leaves the problem of the remarkable artistic technique of controlling the form of the end of the stain to become a rather detailed face.

These faces are in tune with the hypothetical alchemical herbal character of portions of the Voynich manuscript as discussed in J.VS comm. #145 (Vol. II). But as always there is the general steganographic problem: are these hypothetical features what they seem to be, and even if so, were they intentionally put there by the VMS creator(s)?

I feel that that it is useful to add to the databank of faces even some very marginal cases, like stainface #1 above, to fill out the spectrum of possibilities for analysis.

Berj / KI3U

[1] Botanical Observations on the Voynich MS., Hugh O'Neill, Speculum, Vol. 19, No. 1. (Jan., 1944), p. 126.


From: Greg Stachowski
To: "J.VS:"
Date: Tue, 11 Mar 2008 02:00:05 +0100

Subject: J.VS: Library deposit # 13-4-2008-03-06: The Search for Numerical Codes in the VM, by Jan Hurych

The latest article by Jan Hurych, "The Search for Numerical Codes in the VM", is now in the Library as deposit # 13-4-2008-03-06.

The abstract of the article is given below. The URL is:

" The article describes the discovery of possible codes (or rather keys) hidden in the VM by means of masking or indirectly, by steganoraphy. Two examples are presented, one for each case, the first one with the application of forensic deconvolution filter. Even if those really are the keys, in the meantime we would not know how to use them yet. It may take further research to get more information or simply use the direct application of decrypting methods to the text alone. "


From: Berj Ensanian
Date: Sun, 16 Mar 2008 00:10:24 -0400 (EDT)

Subject: J.VS: Voynich f79v and SOL DEUS CHRISTUS

Dear Colleagues

In our discussions recorded in J.VS comm. #171 is the experiment with Latin abbreviations that I did to convert, or transform if you like, the label under the f68r3 PM-curve into: occulto / occultus ALCIONE.

That experiment was, I thought, quite interesting, especially so because it was simple, and relied on an initial contextual clue, a fairly clear one, from astronomy. And of course, it was in tune with the long established observation that many of the Voynich text elements strongly resemble traditional Latin abbreviations forms routinely found in old documents. I set out to see if that experiment's potential Voynich glyph - Latin letters correspondences, and its basic procedure, could be applied elsewhere in the VMS to obtain another interesting result. In going through the pages of the manuscript in search of a good label to attack, one with a clear context clue, my attention was caught by the upper part of folio f79v, which I have always considered one of the most dramatic sections of the manuscript, on account of its striking Christianity symbolism: a celestial "nymph" with a cross in her left hand apparently blessing the page's first paragraph. [1]

It occurred to me, that given a high possibility of a variation of the word "Christ" appearing in the f79v text, then the approach used with ALCIONE might produce its conversion readily and quickly, especially since historically there have been many abbreviations for "Christ", notably Greek and Latin, that could be considered for the experiment. I looked over the f79v text for a word that stood out in some way, especially a word incorporating a gallows glyph. Eventually I concluded that of all the words on the page, the one that stands out the most, is the very first word: actually I noticed that, whereas heretofore I had been taking the nymph to be blessing the entire first paragraph, it seems on closer examination that the drawing suggests more that the cross is aimed specifically at the first word of f79v. So I chose that word to experiment with. Being part of normal text, it is not a label; actually there don't appear to be any labels in f79v. So the experiment takes on an implied assumption that, per Currier's observation on lines, the entire first line of f79v may be subjected to the basic experimental procedure, although that need not also imply that every word in the line is the result of the identical set(s) of original synthesis procedures [2]. Here follows the experimental conversion of the beginning group of apparently eight Voynich text-letters, the apparent first "word" of f79v.

Let us begin with transcribing this first word of f79v per the method detailed in comm. #171 used with ALCYONE, where the aim is to achieve with ordinary ASCII text as close as possible a reasonably practical visual representation of what is actually seen on the f79v parchment. I shall attempt an improvement over the #171 ASCII artistry, and also here use a grid of three rows, necessitated by the glyphs as they appear on the VMS parchment, per the Beinecke online SID image [3]:

Fig. 1:


It is seen that the initial gallows letter (MD-G/ CR-B/ EVA-p/ GC-g) has been transcribed, using the numerals 1, 4, 7, and 9, like this:

Fig. 2:


and the diacritic accented c-pair symbol like this:

Fig. 3:


We have a decision to make with this particular glyph, because on the f79v parchment the 9 clearly intrudes upon the c~c. We do learn from studying the classic work on Latin abbreviations by Capelli that the intrusion of one component into another does not automatically mean the two components have lost their individual identities and that an entirely new glyph is indicated. [4]

Now let us temporarily set aside the initial gallows letter. Let us again use some letter assignments from comm. #171, and again use D'Imperio's adapted-from-Capelli Latin abbreviations in her Table Fig. 17 [5], and work row 3 as follows:

Fig. 4:


where we have used the "CRI" option rather than the "CI" for c~c, and we also have decoded c~c separately from the intruding 9. Next let us assign a modern Latin letter to the "8" glyph. Currier commented on this (and other letters and abbreviations) during the well-known 1976 VMS seminar that Mary D'Imperio beautifully recorded, while she therewith also pioneered the Voynich research dialog / discussion redaction record, a device that was revived by J.VS upon inspiration from her work. [6]

Currier is recorded as saying:

' As for '8', it is a frequent letter in Etruscan, in Lydian, and in the Lemnos alphabet, but there that letter always had the value "F", never "S." In medieval Latin on occasion it did represent "S." This symbol could have been taken from these other alphabets. '

Indeed, in the traditional f116v considerations of "oladabas" the "8" on the parchment is taken as an "s", the final letter in oladabas. That doesn't seem to help us here, and since there is to date nothing available beyond hypothesis that in the Voynich manuscript on any of its folios the "8" glyph actually means "S", we are free to conjecture differently. Returning to Capelli [4] we do find examples of scripted "d" with rather good similarity to our "8". For example: in the abbreviations for "denariis" and "demonstrandi". Lets take it: we will assign to the Voynich glyph "8" the letter d / D in this experiment. But let us take advantage of the phonic aspects of this letter and expand the assignment: let "8" be d, d', or de. Substituting into row 3 we now have:

Fig. 5


The next step is obvious: we bring the "9" from row 2 above the CRI down to its left, and substitute it as "US", and while we are at it, contract at the end of the word:

Fig. 6:


Phonetically, the "c" can be sounded "s" as in Latin "circum", and Capelli provides a good script sample similarity with the abbreviation "sacerdote". So let us write:

Fig. 7:


where the "DEUS CRISDUS" is welcome in the overall context of the experiment. Altogether we now have:

Fig. 8:


and it remains to transform the initial gallows letter and the "O_L" into something that makes sense with the rest. The simplest transformation that makes sense seems to be to assign "S" to the gallows letter so as to obtain:

Fig. 9:


The fancy "S" shown in Capelli for the abbreviation "Signum" permits pondering that an initial capital letter "S" might well be depicted by the impressive Voynich MD-G gallows symbol. So then, the experimental transformation gives us:


which we can translate:


Now, this suggests a theme relating Christianity with the Roman DEUS SOL INVICTUS. The f79v illustration shows also what appears to be in barest terms a distillation proceeding from a heavenly canopy associated with the cross-holding nymph, ultimately reaching at the bottom of the folio another nymph who is emerging from the mouth of a large fish in a dirty pool attended by some ugly animals. The fish symbol is of course associated with Christianity. It seems conceivable then that f79v is making a statement, positive, neutral, or negative, between paganism and Christianity, and that SOL DEUS CHRISTUS could be consistent with such.

Even a first glance at the rest of line 1 of f79v indicates that it would be difficult to make further sense of it with this experimental procedure, consistent with the foregoing. But there is also no guarantee that the rest of line 1 isn't simply filler. In the absence of demonstrations to the contrary, it is then possible that the first word of line 1 of f79v constitutes that line's entire literal payload.

Berj / KI3U

[1] vms-list post: VMs: Christianity symbolism in the VMS; Monday, May 1, 2006 10:11 AM. Preserved complete in J.VS Library deposit # 1-1-2007-05-05, file: 2JVSlibKI3U.htm

[2] The f79v text is judged as Currier language B in the: Version TEXT16E5 Interlinear archive of Voynich manuscript transcriptions. Derived from INTERLN.EVT file version 1.6 Created by Gabriel Landini, 27 September 1996. Split into separate files (one per textual unit) by J. Stolfi, 10 october 1997. Version 16E6 is available here:


[4] see for example the abbreviation exhibit for "frustra":

[5] The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7, pg. 95.

[6] Some Important New Statistical Findings by Captain Prescott H. Currier, (from the Proceedings of a Seminar held on 30th November 1976 in Washington D.C., edited by Mary D'Imperio, moderator). Available online here:

From: Berj Ensanian
Date: Wed, 26 Mar 2008 00:37:22 -0400 (EDT)

Subject: J.VS: A Problem concerning Eulerian Circuits in Voynich Text

Dear Colleagues

I have wondered about Eulerian circuits as a possible analytic method applied to Voynich text. We recall that Leonhard Euler (1707-1783) solved the Keonigsberg Bridges Problem, thereby laying the foundations of topology. Stated abstractly, Euler showed that a network of vertices may be traversed, beginning and ending at the same vertex, and travelling each existing vertex-to-vertex path just once, that is an Eulerian circuit may be made, if and only if all the vertices participate in an even number of paths. Lets see if we can get started applying this to Voynich text.

Let us denote by a "completely connected network" a network where each of its vertices is connected to every other vertex with exactly one direct path. If the number of vertices is Nv, then the total number of paths in the completely connected network, Np, is given by:

Np = Nv(Nv-1)/2

If Nv is an odd number, then every vertex will connect to every other with an even number of paths, (Nv-1), and from any starting vertex an Eulerian circuit may be made.

Now, let us choose an odd Nv, and let each vertex be a piece of text. Let each path be the joining of the text-pieces at the path's two ends. That is, if one vertex is "man" and another vertex is "handle", then the path between them is taken to mean "manhandle".

Traversed in the other direction we would get "handleman". For experimental flexibility let us allow the joining to be both concatenation of the text-pieces as well sequential pairing separated by a space within a line of source-text:

"manhandle" and also "man handle" within the same text-line.

For VMS work convenience we will write "man handle" as "man.handle"

We will also observe that for any pair of vertices, there are two travel directions on their mutual path, so we then also obtain:

handleman and

Now let Nv = 5, so that Np = 10, and let the following five Voynich digraphs, expressed in GC- transcription alphabet letters:

oy, oh, ae, 89, 4o,

be the vertices of the network. We will use the voyn_101.txt transcription of the Voynich manuscript by Glen Claston [1] to search for the paths generated by the Eulerian forward and reverse circuits. For this first experiment I omit the counts of occurrences in voyn_101.txt, and just indicate if any concatenations and sequential pairings are found.

Table 1: Arbitrary forward Eulerian circuit from / to VMS digraph GC-oy

1-1: oy.oh
1-2: ohae
1-3: ae89, ae.89
1-4: 89.4o
1-5: 4ooy, 4o.oy

1-6: oyae,
1-7: ae.4o
1-8: 4ooh, 4o.oh
1-9: oh89
1-10: 89oy, 89.oy

Table 2: Per Table 1, but traversed in reverse direction.

2-1: oy.4o
2-2: 4o89
2-4: aeoh, ae.oh
2-5: ohoy, oh.oy

2-6: oy89, oy.89
2-7: 89.oh
2-8: oh.4o
2-9: 4oae
2-10: aeoy, ae.oy

We see that every possible path appears in voyn_101.txt, although as for example in 1-2 we get only concatenation, and no instance where GC-oh ends a word, and the next word begins with GC-ae. The omitted counts vary greatly across the tables, from one or two, to very many occurrences. For the moment, even though I've been lazy here and have not supplied them, let Ci stand for count, where i is a suitable index covering all 40 possibilities in the tables. Obviously the Ci will change a lot depending on the chosen particular text-pieces, be they single letters, digraphs, trigraphs, entire words, or a mix, and also higher Nv will have a great effect on the Ci's.

This suggests defining some sort of gauge function. Many interesting functions could of course be defined upon Tables 1 and 2. But for discussion purposes, with an eye toward improvements, let us define a first Eulerian Text-Circuit gauge function:

E1 == Nv * { (over all forward and reverse paths i):SUM[ Ci * L(Ti)^2] }


Ti = i'th path, being either a concatenation, or a sequence pairing
L(Ti) = length of the path in total glyphs / symbols
Ci = number of found occurrences in the block of text under consideration

We might improve with defining an E2 that weighs concatenation and sequence pairing differently, rather than equally. But already with E1 we have an interesting problem-question, one that is another perspective, another way of thinking about the Voynich text:

How does E1 change with respect to its variables, and what is its absolute maximum across just the labels, Currier A text, Currier B text, and across the entire Voynich manuscript text corpus?

Berj / KI3U

[1] Glen Claston (GC) provides his transcription alphabet and transcriptions of the Voynich manuscript online here:

From Berj Ensanian
Sent Date 03-26-2008 11:20:38 AM

Subject J.VS: Re: A Problem concerning Eulerian Circuits in Voynich Text

Dear Colleagues

Looking over the choices in comm. #176 I noticed a symmetry and anti-symmetry characteristic in the text topology considerations that seems necessary to take into account if the procedure's possible full potential is to be exploited. To show what I mean, and borrowing the previously used "man" and "handle" examples, consider the forward traversals:

manhandle, man.handle

For the reverse traversal we took:


But especially in Voynich text work a reverse traversal ought also to include sequencing according to:

eldnahnam, eldnah.nam

For example a quick check of voyn_101.txt indicates that whereas for Table item 1-3, the paths 98ea and 98.ea are not found and their counts would be zero, for Table item 2-10, path eayo does exist, but ea.yo does not. The reverse traversals as they were taken in comm. #176, actually introduced an assymetric perspective, and purely mathematically it would seem that eldnahnam is more proper than handleman. However, we are interfacing network theory with text, and especially with the mysterious Voynich text we ought to retain options: study all the arrangements of the text vertices.

When in VMS work we routinely see "aeoy" and "eayo" transcriptions we tend to sound them in our minds. And so, in connection with the foregoing one could fathom this network gauging procedure carried over to speech experiments: Eulerian speech-circuits, where the vertices hold phonemes and syllables. Interestingly, the thought occurs if, from the point of view of artificial two-way communications, in the spirit of a universal language adapted for computer-to-computer conversations, experimental Eulerian speech-circuits in completely connected networks might have peculiar efficiencies.


From: Berj Ensanian
Date: Fri, 28 Mar 2008 19:13:25 -0400 (EDT)

Subject: J.VS: Some notes on Eulerian text-circuit analysis for Order Nv = 3

Dear Colleagues

I have been doing some more experimenting with the concepts sketched in J.VS communications #176 and #177, and I am finding that using Eulerian text-circuits as a gauge of patterns in text is increasingly interesting. I notice that even at this early stage into it, the simple basic procedures quickly show the Voynich text in striking light.

For example, there is an old idea in Voynich studies, a very attractive one, that about the simplest way to conceive of the structure behind the Voynich vocabulary with its many, many almost-but-not-quite identical words, is that the words are based on numbers: just for words up to nine letters in length you could have 1-999999999 possibilities that is a billion possibilities for "words" with enormous numbers of them nearly identical; for example: 123156, 123256, 123356, 123456, 124456, 125456, 126456, and so on.

With an average word-length of around 5 symbols, in a book the size of the VMS, you'd be hard pressed to run out of nearly-identical words. Just the stock of possible 5-symbols long vocabulary is a hundred thousand unique strings, and so you could have hundreds of groups of nearly-identicals, and put them together into text-lines according to some scheme that matches other VMS text characteristics, like the relative frequencies of adjacent specific symbols groups and their mirror versions. Of course, in this the-Voynich-text-is-tables-of-numbers perspective it is nevertheless entirely possible independently that the numbers encode ultimate plaintext.

This words-are-numbers possibility really jumps out at you very clearly and quickly when you use Euler text-circuits as a gauge for patterns in the VMS text. In other words, if you are a newcomer to the Voynich text, and start some simple experimenting in this vein, it is likely that the words-are-numbers suspicion will hit you very quickly, and you'll get a sort of quantum jump in your feel for the VMS text, regardless of whether or not its vocabularly was indeed constructed by scripting base-10 numbers with Voynich letters.

At this early stage I am sorting out the many complications, especially with notation. I also find that defining a single very good Eulerian text-circuit gauge function will require a lot more experimental work. In the meantime, toward that here are some really basic notes I've been making, and some VMS results.

Let us consider the simplest completely connected network, a third-order network with Nv = 3, within which there are Np = 3 paths. Let ABC, DEF, GHI, be three words of 3 letters each, a built-in symmetry right at the start.

Let us define these words, these symbols sequences, to possess polarity in terms of letters sequence in a circuit, and not merely "read left-to-right". We will say that for ABC, the A followed by B followed by C, shall be its clockwise sequence. Its c.c.w. sequence shall be: C followed by B followed by A. So, vertex-texts of length greater than 1 have a sequence polarity.

The polarity of vertex-texts is distinguished from the polarity of a particular circuit traversal, itself either clockwise or c.c.w., and the coupling of a vertext-text to a traversal is in general either or both co-polar and anti-polar.

Now, let us draw a triangle on a sheet of paper, number its vertices, and place those words at its vertices:



Considering only the vertices, aside the texts, from any vertex i there are here two possible Eulerian circuits:

{2-1} clockwise: [i]-to-[i+1]-to-[i+2]-to-[i]

{2-2} counter-clockwise: [i]-to-[i-1]-to-[i-2]-to-[i]

From the "-to-" it is seen that each circuit is comprised of 3 paths. In higher order completely connected networks where Nv is greater than 3, the circuit schematic of {2} will need to be generalized in some suitable systematic manner with something like [i+/-q]. But here, since i ranges 1-3, the total number of possible Eulerian circuits in this network is 6, three clockwise circuits, and three c.c.w. Let us identify the paths in these circuits, P, as follows:

{3} Identification of Paths, P



d = traversal direction: d=R for clockwise; d=L for c.c.w.
i = index of the beginning vertex of the path.
j = index of the ending vertex of the path.
k = index identifying the type of text-to-circuit coupling.

So for example, the path that begins at vertex 2 and proceeds clockwise to vertex 3 is identified PRk23.

Let us identify the full Eulerian text-circuits similarly: Edkv, where v is the index of the vertex at which the circuit starts and ends. If a network is identified as sustaining a complete set of circuits, let it be designated: n-th order ERLk.

Now let us couple the vertex symbols-sequences, the words in this case, to the circuit traversals. A very important point is that the index k allows specifying various couplings.

Let us for now adopt these first few coupling specifications:

{4} Network-vertex-text circuit-coupling specifications:

k=0 : text coupled arbitrarily to suit temporary experimental convenience.
k=1 : text is coupled as a sequence, its polarity same as the circuit traversal polarity.
k=2 : text is coupled as a sequence, its polarity opposite to circuit traversal polarity.
k=3 : text at vertex j is coupled as a sequence, observing oscillating polarity wrt to traversal, the text at v on starting having being taken clockwise.
k=4 : text at vertex j is coupled as a sequence, observing oscillating polarity wrt to traversal, the text at v on starting having being taken c.c.w.
k=5 : text is coupled as a sequence with its polarity clockwise, regardless of traversal polarity.
k=6 : text is coupled as a sequence with its polarity c.c.w., regardless of traversal polarity.

Here are some paths and couplings showing the effects of the k specifications, and using a period between coupled text-pieces to make for easier seeing:


v=1: PR112 = ABC.DEF
v=1: PR212 = CBA.FED
v=3: PR212 = CBA.FED
v=3: PR312 = CBA.DEF
v=1: PR312 = ABC.FED

v=2: PL213 = ABC.GHI
v=2: PL432 = IHG.DEF
v=1: PL521 = DEF.ABC
v=2: PR631 = IHG.CBA

We could specify all manner of coupling systems, including anagram coupling, and systems that specify a particular coupling as a function of d,i,j, and the characteristics of the text at a vertex, say if it includes adjacent doubled letters or not.

Let us now show the PR1ij and PL1ij for our triangle, and the six complete Eulerian text-circuits they are part of, the Ed1v written in contracted notation. In the following we are diagraming the type k=1 paths and circuits:

{5-1} ER11 = ABC.DEF.GHI

v=1: PR112 = ABC.DEF
v=1: PR123 = DEF.GHI
v=1: PR131 = GHI.ABC

{5-2} ER12 = DEF.GHI.ABC

v=2: PR123 = DEF.GHI
v=2: PR131 = GHI.ABC
v=2: PR112 = ABC.DEF

{5-3} ER13 = GHI.ABC.DEF

v=3: PR131 = GHI.ABC
v=3: PR112 = ABC.DEF
v=3: PR123 = DEF.GHI

{5-4} EL11 = CBA.IHG.FED

v=1: PL113 = CBA.IHG
v=1: PL132 = IHG.FED
v=1: PL121 = FED.CBA

{5-5} EL13 = IHG.FED.CBA

v=3: PL132 = IHG.FED
v=3: PL121 = FED.CBA
v=3: PL113 = CBA.IHG

{5-6} EL12 = FED.CBA.IHG

v=2: PL121 = FED.CBA
v=2: PL113 = CBA.IHG
v=2: PL132 = IHG.FED

Expected results are easily seen, for example v=1:PR112 and v=2:PL121 are essentially mirror versions of each other.

Now, by affixing pieces of text (or in general sequences of glyphs) to the vertices of a completely connected network we are creating a completely connected text-network. And if the Nv is an odd number, then we can proceed with the generating of text-paths and entire text-circuits per above and have Eulerian circuits and their component paths. If the vertex text-pieces were taken from a body of text being studied, then that body's text characteristics can be gauged as to its Eulerian topology by comparing the generated paths and circuits with existing sequences in the body of text that is being investigated.

In order to quantitatively gauge the topological characteristics of text we have considered, so far only very primitively in comm. #176, the desirability of an Eulerian text-circuit gauge function, being a number function:

{6} General form of an Eulerian text-circuit gauge function:

e = e(Nv,f(Pdkij),g(Edkv))

where the function f(Pdkij) will take into account the factors mentioned in comm. #176, namely the coupled text-length of the path Pdkij, and the number of its occurrences per text-block size in the text body under investigation. The function may well involve weighting coefficients, for example to distinguish assymetric length couplings, like BC coupled to DEF. The function g(Edkv) will take into account the occurrences of complete Eulerian text-circuits in the text being studied, and may involve weighting coefficients also, say according to k.

Now suppose we study the following block of 6 text-lines, taken from above:



or its text-equivalent numbers table:



The lines could be in any order. Our study would conclude that these blocks of text are characterized by a maximum of their 3rd-order (i.e. Nv = 3) e-function for k=1, at the lines level, for text-units ABC, DEF, and GHI, or equivalently 123, 456, and 789. That is, there is a high degree of text-topological invariance in these blocks of text: the lines are Eulerian text-circuits forming a complete set.

We should not neglect linguistic connections. After all, text symbols may represent phonemes and syllables, and in the present context we may consider speech topology. Consider for example the text-vertices "GOOD", "THINKING", and "OFTEN". Suppose that throughout some record of speech conversation there were the following six statements, each one arguably making sense self-standing:





We could argue that a cluster of speech, characterized by high speech-topological invariance, is dispersed in the conversation.

And so if we study enough texts with e-functions, including cipher-texts, and tables of numbers regarded as text, we will get some idea of the text topology of various texts, and there will be some distribution of corresponding e-functions values, and some types of sequences will be characteristically low in e while other types will be high. And we would like to know where Voynich text fits into that spectrum, and how e varies from text-block to text-block in the VMS. Obviously it is all quite a big task, especially for Nv = 5 and above. It isn't even easy for Nv = 3, although working without a detailed e-function, and simply generating comparison paths and circuits in tables as in {5} is straightforward and very useful for investigating bodies of text.

Analytically, a major question is: what are good choices for lengths of trial text-vertices, versus Nv, for getting high e ?

Above we had all three words the same length of 3 symbols. In systematic work of course we would begin with all lengths = 1. I did some exploring in the voyn_101.txt transcription at Nv = 3. It seemed obvious to put together some low-lengths vertices made up from among the commonest Voynich letters, and poke around in Voyn_101.txt with ordinary text searching.

It did not take long to get hints of a curious pattern: for some vertex sets consisting of two digraphs and one unigraph, the type k=5 Eulerian circuits are evident.

{10} Edkv circuits of type k=5 in Nv=3 networks, for AB, CD, E:

v=1: ER51 = ABCDE
v=2: ER52 = CDEAB
v=3: ER53 = EABCD

v=1: EL51 = ABECD
v=2: EL52 = ECDAB
v=3: EL53 = CDABE

The above patterns can be used to substitute Voynich transcription alphabet symbols.

{11} Some voyn_101.txt search hits showing Ed5v for text-vertices: GC-oh, GC-oe, GC-1

ER51: .ohoe19.
ER52: .oe.1oham.
ER53: .1ohoe.

EL51: .oh1oe.
EL52: .1oe.oh9.
EL53: .9hoe.oh19.

{12} The extracted circuits in {11} with substitutions 1=GC-o, 2=GC-h, 3=GC-e, 4=GC-1

ER51: 12134
ER52: 13412
ER53: 41213

EL51: 12413
EL52: 41312
EL53: 13124

Now of course, as always before, it is an open question how, in the VMS text, to treat adjacents, in particular inter-word spaces. They can be ignored, or treated like just another symbol. As we know, voyn_101.txt resolves spaces to just a resolution of 2, namely ordinary common "hard" spaces denoted by periods, and shorter "soft" spaces denoted by commas. Obviously as a first systematic step the transcribed Voynich text, voyn_101.txt or other, should be stripped of spaces and searched for matches with Euler text-circuit generated sequences.

Now, my quick browsing of voyn_101.txt was neither exhaustive nor systematic, and I looked only for existence of sequences and did not keep counts of their occurrences, but another pattern that came up in my searches was this:

{13} Text-vertex sets found in ER1v circuits but without any corresponding EL1v:

oh oe 1; oh oe 2; o8 oe 1; oh oy 1; oh oe 8; oh oe 9; oh o8 9; oh 1 89;

To the present my investigations have been barely scratching the surface of this text topology method of analysis, so that for example the sets in {13}, other than oh oe 1, I did not check for k other than k=1.

However, we can see from {11} that in voyn_101.txt, if spaces are ignored, there exists a dispersed, order Nv = 3, type k=5, Eulerian text-network, that is a third-order ERL5 text network, the vertices of which are the clockwise denoted digraphs GC-oh and GC-oe, together with the unigraph GC-1. And we can see from the corresponding alphabet to numbers transformation in {12} the attractiveness of the idea that the Voynich vocabulary is based on base-10 numbers.

Berj / KI3U

From Berj Ensanian
Sent Date 04-01-2008 9:02:53 PM

Subject J.VS: Cosmology in the Voynich MS and the f68v3 "Spiral Galaxy" panel

[ redaction of off-J discussion of 1 APR 2008 ]

Berj Ensanian says:
By the way Greg, do you know of any historical astronomical diagrams that are similar to the VMS f68 spiral? The f68 trio of panels truly obviously suggests cosmology. Looking at the spiral "galaxy" panel: its center is a T-O. It seems to suggest the Earth coalescing from a whirlpool of sky-matter.

Greg Stachowski says:
None occur to me, but I haven't looked very hard. I think I once saw something like 68v1, and I think someone somewhere once mentioned the 68v3 one as a representation of winds.

I'd be very careful looking for cosmology in f68, in the sense that one has to be very careful to separate not just modern knowledge from the knowledge of the time, but also modern thinking, which can be difficult. The mindset has changed a lot in the last 600 years.

Berj says:
Are you suggesting it is not cosmological? Can you list a few points contrasting the change in mindset over the last 600 years?

Greg says:
It could be cosmological. I'm not saying it isn't. I am saying that when discussing it one has to be careful not to unconsciously project modern concepts back into the mind of the person who drew it. The most obvious changes were of course due to Copernicus, Tycho, Kepler and Galileo, then also Newton etc. The universe suddenly got very much bigger, the principles on which it worked changed and our place within it changed. Very rapidly. Pick a decent book or webpage on the history of cosmology.

Berj says:
Well we are in VMS land, where quite frequently we are more or less forced to project, consciously and unconsciously, some idea or other as a plausible thought in the mind of the VMS author, who we really don't know lived 500 years ago, so as to attempt progress.

Greg says:
Well, we don't know he lived 500 years ago, but even if he lived 100 years ago, his view of cosmology would be way different from ours. No expanding universe, no big bang, no modern view of galaxies (they were still 'nebulae' then). To give but a few examples. Obviously we have to project something, but in dealing with the 'cosmology' section we have to be especially careful not to project something which is from our world view and base our interpretation on it. A plant to us is a plant to someone of 1500 or 1600, but what is a galaxy to us is an utterly alien concept to someone of that time.

Berj says:
Agreed. However, there are commonalities in thought, say archetypal, that extend from today back to the ancient mists of time. Now, nebulae or no, galaxies are collections of stars. Arguably the VMS spiral "galaxy" panel depicts a unified collection of stars.

Greg says:
But the idea that nebulae are collections of stars is what, mid 18th C. They weren't even begun to be resolved into stars until the mid 19th. The idea that the Milky Way is made up of stars is ancient Greek, but was not proved until Galileo, and even then the sheer size was not appreciated until much later. The idea that 'spiral nebulae' are galaxies, like ours but external, is early 20th century. The sheer scale of the whole thing is modern.

So if the VMS spiral panel depicts a unified collection of stars, then it is more along the lines of an asterism, constellation or at best a cluster like the Pleiades. Even then, except for close by, open clusters like the Pleiades and Hyades, clusters weren't known until roughly the 19th century either. These things need decent optics to resolve.

Without the mental apparatus of Copernicus through to Newton it is almost impossible to conceive of external galaxies in the way we know them today. The paradigm is all wrong.

Berj says:
Certainly yes, Copernicus et al forced some major changes in conceptions of the universe. Do you lean toward pre-Copernicus or post-Copernicus for the genesis of the VMS? Why?

Greg says:
The question is poorly put. Copernicus lived across the turn of the 15th and 16th centuries, which is compatible with some assessments of the VMS dating, and his ideas published in 1543 were not universally accepted for another two hundred or so years, covering the 'late' range of datings. So a document with a geocentric cosmology could have been written a hundred years 'post-Copernicus'.

My idea of the date of the VMS is nebulous: I don't subscribe to a firm dating because I have not analysed in detail all of the propositions which have been put forward. The most reasonable seem to be between perhaps mid 15th to perhaps mid 17th centuries. I would be surprised if it were outside that range.

Berj says:
I would be too, although I go from early 15th to the late 17th century. Nevertheless it is remarkable that there is there a range of 300 years and still it is so difficult to zero in more precisely.

Greg says:

Berj says:
I got something from your comments that I was vaguely fishing for: you point out that a "geocentric" cosmology could have been advanced fully a hundred years post-Copernicus. This is well worth keeping in mind.

Now, again lets consider the f68 "spiral galaxy" panel. We see it, and we wonder what it is supposed to depict, in context also with the rest of the VMS. Lets try a couple of different projections upon the thoughts of the VMS author:

1.) We might say it is a from-atop-view depiction of a washtub with a drainhole at the bottom, and water is rapidly being drained out and down onto the Earth underneath which is symbolized by the T-O map symbolism. And the serrates represent the clothing that was being washed, itself symbolic of the spirit of the aspiring adept studying the VMS philosophy. And the text is the guiding philosophy for all that. But what do the stars represent? What are they doing there? Well, we note that elsewhere in the zodiac panels we have tubs / barrels with people in them holding a tethered star. So, even though the spiral galaxy panel does not show a tub or barrel directly, we might have here some sufficiently common symbols to entertain that the overall suggestion is an aspiring adept of the VMS philosophy undergoing spiritual cleansing, purifying the celestial self by draining away the grosser material leanings to where they belong.

Greg says:
A little stretched with the wash tub, but the rest, perhaps.

Berj says:
2.) The spiral galaxy panel depicts a statement about the Creator and the Creator's Works that combines the beginning of Revelation with the beginning of Genesis. To make this work, we assume that the panel's sequential sense is from the periphery of the diagram inward toward the center. So, In the Beginning was the Word: the diagram begins with text at its periphery. In general, it looks like the message is that Earth is coalescing from a whirlpool of sky-matter: In the Beginning God created the heavens and the earth....

Greg says:

Berj says:
Now, personally, I think 2.) makes more sense for the panel than 1.). But it seems to me that both 1.) and 2.) are essentially independent of Copernicus.

Greg says:
Yes, particularly as both are more geocentric than heliocentric.

It occurs to me that at least another interpretation of the f68 spiral is possible. I don't recall anyone mentioning such an interpretation before, and I believe it is original. As follows:

The T-O represents the Earth (naturally); it is perhaps flat, surrounded by the encircling sea; either way then there is a sphere of stars, finally whatever is outside the sphere.

I must look into sphere-of-stars models and see if there are any analogues for the spiral lines, which obviously come from outside the stars and reach Earth.

[ end J.VS comm. #179 ]

From Berj Ensanian
Sent Date 04-07-2008 9:43:12 PM

Subject J.VS: The emblem-animal plant-leaves of Voynich botanical illustration f9r

Dear Colleagues

In a 2003 VMS list post about the Voynich f9r plant illustration, Dana Scott (our J.VS colleague) noted:

" .... I have been considering Botrychium as a possible match where there seem to be additional features that warrant consideration. Notice how the author of the VMS has drawn the leaves to possibly resemble some kind of animal (they seem to remind me of clowns in pajamas, though they are more likely drawings reflecting what might be seen on certain flags or banners). " [1]

I thought it might be good to place in the J.VS Library a picture cropped from f9r that shows, what I think, Dana was pointing out. I have sent to our Librarian Greg the image file: 1ArmorialGreenLionsVMSf9r.jpg, as an addendum to Library deposit # 12-1-2007-10-12, the deposit that holds many plausible VMS-illustration steganographic faces. [2]

The image shows the two lower-left leaves of the f9r plant. These two leaves strike me as the two best f9r examples depicting Dana's impression of animals drawn on flags or banners, in other words along the vein of Armorial or Heraldic emblem art.

The two "animals", colored green, are facing and walking to the right. To me, they just vaguely enough resemble stylized heraldic lions to note that "green lion" is a major alchemical symbol [3], and so to note also a plausible mixing of heraldry and alchemical herbal [4] in the f9r illustration. Perhaps the Moonwort (Botrychium) angle is also significant in the mix.

Attention to steganographic heraldry symbolism, or crypto coats-of-arms, in the VMS illustrations, has most recently and most strongly been advocated by Richard Sale on vms-list, specifically concerning alternating blue and white slanted stripes on two of the cans / barrels in f71r. Now, if we regard the above mentioned leaves as plausible symbols mixing heraldry and alchemy, then perhaps it is also worth noting that this is folio nine, and 9 is one of the numbers that is especially emphasized in the VMS, in particular in the arguable climax of the entire Voynich manuscript: the nine rosettes fold-out.

Berj / KI3U

[1] vms-list post: VMs: Re: Folio f9r, Sun, 14 Dec 2003 17:02:35 -0700, From Dana Scott.


[3] See her alchemy discussion on pg. 61: The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7.

[4] For more on alchemical herbal see J.VS comm. #167, but especially comm. #145, J.VS: Alchemical Herbal Eyes, and the Steganographic Face Problem.

From Berj Ensanian
Sent Date 04-13-2008 12:03:58 AM

Subject J.VS: Voynich steganography: The Boy Astronomer of f103v

Dear Colleagues

Toward the hypothesis that the Voynich manuscript is loaded with steganographic details of various techniques, I'd like to bring to your attention an interesting possibility in the star-page folio f103v. It appears to me that among the many steganographic details in this folio there is a scene that depicts a young boy intensely star gazing. To show this, I have sent to our Librarian Greg, and he has installed for me, the image file x1NRRc3VMSf103v.bmp as J.VS Library deposit # 17-1-2008-04-12; the metadata for this deposit details how the image was obtained. [1]

Under the steganography hypothesis I have steadily continued my steganographic survey of the VMS, and I have tentatively concluded that every page of the manuscript holds some form of steganography, and often more than one form exhibiting different techniques. In addition to the examples I have commented on in J.VS communications and their images that I have already placed in the J.VS Library, I have collected hundreds more of examples, of several different forms. I intend to present many more examples as soon as I have a more complete idea of the variety of forms.

But I can say at this stage that I believe that the presently available high-resolution SID / TIF images of the manuscript provided by Beinecke are not good enough to reveal the full scope of steganography in the Voynich manuscript: from the indications I have, I believe that the VMS author was using, in his steganographic work, in addition to special illumination and optical filtering, a magnifyer instrument of sufficient power so that his / her work is in places beyond the resolution available in the Beinecke SID images. We have already seen the amazing steganographic miniature of "The King" of f37v, which altogether measures on the order of just 1 cm. My survey indicates the possibility of steganography, or at least attempted steganography in the VMS an order of magnitude finer in detail than we see in The King, and it involves techniques for stabilizing the art upon the relatively grainy flexible parchment. If the existence of higher detail steganography proves correct, then it ought to have a bearing on the dating of the VMS in light of the known history of magnifying lenses.

If it is ever proven beyond any doubt that the VMS was brought to Rudolph II, or for that matter to any powerful person's attention, one possibility that occurs to me for explaining the vast scope of steganographic effort in the book is that the book was meant as a demonstration of the possibilities of steganography.

Now to the boy astronomer of f103v. This folio has 46 lines of text. Its only apparent illustration elements are 14 stars that run vertically along the left margin. The page has an ample bottom margin - equivalent to a group of about 7 lines.

In this bottom margin are some thin lines of ink that at casual glance appear to be just some abandoned rough sketch outlines, or perhaps even just doodling. I took a closer look, and saw that there seemed to be great care taken in the drawing of the lines, suggesting that whatever it was, it was not abandoned, and certainly not doodling. I got up and walked about the computer screen to get different perspectives, and at one perspective I got the impression of a figure standing, if the page were viewed rotated 90 degrees clockwise.

I rotated the image 90 degrees clockwise, and my initial impression was reinforced with more detail: a standing figure, clothed in something substantial, apparently facing to the right (in absolute page coordinates facing toward the top of the page). I changed magnifications repeatedly, zooming in and out, until I had an idea what I was seeing: the figure, holding something with his right arm, was looking directly at the stars in the f103v left margin.

With that impression in mind, I proceeded to do some image processing, finally deeming x1NRRc3VMSf103v.bmp good enough at this stage to present to you. Here is my current best guess on what is going on in f103v:

Upon the blank folio was first drawn, either with very faint ink, or ink that requires some specific optical sub-spectrum for strong visibility, a scene depicting a young boy beholding a meteor shower, or an auroral event, or in any case a wondrous starry night. After this scene was rendered, the text was added like an overlay, in the normal inking, and the 14 stars either were added, or more likely reinforced with normal inking.

The boy, and he does give me the impression of being a boy rather than a full grown man, may be wearing some kind of a hat or hood. He is leaning forward, gazing directly at the stars in the left margin, and he gives me the impression of walking toward them. He has on a heavy coat, and under his right arm between it and his body he is carrying a large rectangular object that resembles a big pad or book, perhaps even a chart that is unfolded open. His right hand is clearly gloved.

When I had concluded beyond doubt that his right hand is gloved, it naturally occurred to me that a clear seeing winter night-sky is suggested. But further, there is also a curious similarity of theme here with the Marci-to-Kircher APUG letter arm-star diagram, with its gloved arm and strong suggestions of optical magnification in astronomy. [2]

In tune with the hypothesis that steganographic hand-script text-art is present in some Voynich folios, notably the well investigated 3D portrait in f76r, I spent just a little time investigating f103v in that vein. As we've seen, investigating hand-script text-art possibilities is very demanding before a plausible convincing demonstration of it can be obtained. I have not done that yet with f103v, but my subjective impressions at the moment are that if f103v holds steganographic hand-script text-art, then it may be a montage of portraits, possibly of great astronomers: in some perspectives I see a montage of portraits surrounding a main portrait that on first apprehension suggested Galileo to me. This remains extremely tentative and speculative at present.

Now we ask: suppose it is really true that f103v holds a picture of a young boy astronomer gazing at the stars? If the f76r portrait is the VMS author as a grown man, is the boy of f103v perhaps him too, as a young boy starting out with his intense interest in astronomy? From the f68r3 PM-curve work on I have, as you know, been convinced that the VMS author was, whatever else, a first class mathematical and experimental astronomer. Further, I have commented extensively on optics and color physics being a major factor in the VMS. We have unification possibilities here touching on several Voynich ms themes, including the old idea that the VMS represents its author's lifetime work.

Finally, one more item I wish to bring up. The f103v page is one of a group of pages in the manuscript that has traditionally been called the "recipes section". I have never been able to warm up to that classification, and I know from private correspondence with other Voynich oldtimers that I am not alone in that. The "recipes" designation got started a long time ago and rests on nothing more, absolutely nothing more, than the assumption that the Voynich manuscript somewhat resembles an old herbal, and so the writing on those mysterious pages must be herbal recipes. Despite its entrenched old age, this classification has yielded zero toward illuminating the Voynich manuscript, and may have, and still may be falsely influencing conceptions of the manuscript, especially those of newcomers. As you know, I have consistently referred to those "recipe" pages, together with f58r and f58v, as "star-pages", for obvious reasons. I suggest that that is a reasonable alternate class-name for those pages: after all, they actually do have drawings of stars as their only obvious illustrations. And just maybe, some of those pages are concerned with serious astronomy.

Berj / KI3U


[2] see J.VS comms. #4, #85, and #121.

From: Berj Ensanian
Date: Wed, 16 Apr 2008 00:53:39 -0400 (EDT)

Subject: J.VS: Steganography: The Book-covers Binding of the Voynich Manuscript

Dear Colleagues

As I mentioned in J.VS comm. #181 I am well along in a steganographic survey of the Voynich manuscript. The survey includes checks, for example looking at period graphics works other than the VMS. Here, along the steganographic hypothesis line, I'd like to present some data on the VMS Book-covers, that is its binding, front and back faces. Depending on your general views of the VMS, the data may surprise you greatly, as it did me.

Incidentally, a quick note on the exhibit concerning f103v that was the subject of comm. #181: I ended my comments there suggesting that some of the star-pages, f103v of course, may be concerned with serious, that is advanced, astronomy. Taking my own suggestion I took another look at the x1NRRc3VMSf103v.bmp image, and I realized that indeed something far more serious than the boy astronomer just taking in a meteor shower may be being depicted.

If you look at the line of stars, you see that they are symbolically variable. Off to the far right, a smudge on the folio parchment shines like a steganographic moon or sun. It occurred to me that the boy astronomer may have been recording data on a variable star, during successive intervals, and keeping the record of his observations on the large chart under his arm. Have another look at x1NRRc3VMSf103v.bmp and see if this could make good speculative sense.

Now to the Voynich ms binding and the new data I have for you to take a look at: from my perspective the binding is rich in steganographics, but I will confine myself here to three items. As you recall, in 1946 the cryptology historian of the Army Security Agency, Dr. Albert Howard Carter, spent an hour, courtesy of Miss Nill, examining the Voynich manuscript. Afterward he wrote his very valuable impressions, which ended as follows:

" The binding is early, i. e., pre-18th century, and carefully done. The cover, also vellum, has come loose, and it is possible to examine the binding closely. It was a competent and workman-like job. " [1]

We really don't know much more about the binding, it doesn't get all that much attention, and in particular as best as I know, it has been an entirely open question whether or not the VMS author was involved with the binding, at least to the extent that he / she produced its original, and that the present VMS binding, as it exists in the Beinecke Library, is directly traceable to the VMS author, even if at some later time another person tightened, or did some other maintenance on it.

As you will see, the new data I have, suggests that indeed the present binding originated with the VMS author, and moreover, that he incorporated into it steganographic artwork of similar nature to that in the manuscript's folios, along with one plausibly very significant clue concerning the secrets of the world's most mysterious manuscript. I have sent to our Librarian Greg Stachowski four image files for new J.VS Library deposit # 18-1-2008-04-15 as follows:

Binding front-side:

1.) c1VMSOFC.tif
2.) x1c1VMSOFC.bmp

Binding back-side:

3.) c1VMSOBC.tif
4.) gNc1VMSOBC.bmp

The metadata in this Library deposit [2] gives the details on how these images were obtained. The TIF's are straightforward crops, after SID to TIF conversion, from the Beinecke high-resolution source images. The bmp's are casual enhancements for convenience, and are not necessary to see the data of interest.

It's best to view the backside image first, so as to gain an easy familiarity with steganographics on the binding. It shows a feature in the top-right quadrant of the backside of the binding. Now, we have spent a lot of discussion on the problem of ruling on the intentionality validity of a plausible steganographic face, for example in comm. #105, but I do think that here the feature is unmistakable: it is a head, plainly so, with the thought-preoccupied face so rendered that its eyes are gazing upwards. Just how the effect of embossing that image onto the leather was achieved I am not prepared to comment on here, but I do believe that it is quite difficult to argue that this face is an accidental artifact, and not the intended conscious work of an artist.

Now to the front-side. The image is of two features in the lower-right quadrant. They are problematic as to their clarity and structure, seemingly thinner or worn down, and they are quite open to arguements that they are accidental artifacts. But I don't think so. What I see is: a profile head of a man, he is facing to our left and so therefore we are seeing his left side; his left eye is gazing intensely directly downward, toward the second feature of interest that is situated where his neck would be, there at the bottom-right of the binding - an approximately rectangular object with two indentation sockets, within which are dark circles suggestive of eyes looking out through the object.

What it all suggests to me is this: this is a self-portrait of the author of the Voynich manuscript, and the rectangular object is the optical color physics goggles necessary to properly view the VMS - quite consistent with the steganographic hand-script text-art 3D portrait of f76r where he depicts himself holding the optical filter up before his eyes in actual use. [3]

I had a strange thought: the bizarre mysterious Lone Ranger Mask of Miss Anne Nill [4] came into my mind, and I wondered if perhaps Wilfrid Voynich and Ethel and Miss Nill really had figured out a lot more about their manuscript then they ever let on openly. It seems almost bizarre to contemplate that the Lone Ranger Mask picture is a crypto-signal from Wilfrid and Miss Nill that optical filter goggles are needed to see the real VMS, but then too, Wilfrid certainly was optically obsessed with at least f1r.

So, can we judge a book by its cover? Or perhaps better: can we ponder that the author of such a wondrous book, the only book to be known as the world's most mysterious manuscript, and rightfully so, would have overlooked taking advantage of a binding for his masterpiece? If that is really him on the front of the book, and also in f76r, the two pictures of him are consistent: he is squarely European, middle aged, and without a beard.

A couple of years ago I first noticed the somewhat hidden figures, including what I interpreted as "Jesus preaching", in the rosette of f86v4 (also known as f85v per Beinecke) [5]. It was those that really got me going in earnest in taking seriously the steganographic possibilities in the VMS. To this point I have to say that I think we are just lately scratching the steganographic surface of the VMS: I think there are going to be many more terrific surprises, even being as we are forced to work from the SID images, and as yet unable to get the Voynich manuscript into an optical physics laboratory.

Berj / KI3U

[1] Much of Carter's report is quoted in D'Imperio. Carter's entire report, with source information, is online at Jim Reeds' website:

[2] Index page to the online Library of Journal of Voynich Studies:

[3] Data concerning the hypothetical text-art portrait of f76r was first introduced in J.VS comm. #107 (Vol. I), 22 OCT 2007.

[4] see J.VS comm. #74 (Vol. I).

[5] vms-list post: VMs: The very Heart of the Voynich Manuscript, Friday, April 28, 2006 1:14 AM, from Berj / KI3U. This post is preserved in J.VS Library deposit # 1-1-2007-05-05, file 2JVSlibKI3U.htm.

From: Berj Ensanian
Date: Fri, 18 Apr 2008 14:19:24 -0400 (EDT)

Subject: J.VS: Similar steganographic Color Physics depictions in Voynich f76r and Binding front-cover

Dear Colleagues

In connection with the steganographic hypothesis of the Voynich manuscript [1] I presented data in J.VS communication #182 (Vol. II) indicating that the VMS's Binding book-covers hold stego images, and that one such feature in the lower-right area of the front cover is consistent with the previously hypothesized idea that the VMS author created the VMS according to optical color physics principles, requiring some kind of special optical filter goggles for proper viewing [2,3,4]. Here I present further data that I believe reinforces this idea very strongly. It was a great surprise to me finding this new data.

Beginning in J.VS comm. #107 (Vol. I) I brought attention to the hypothetical steganographic hand-script text-art portrait in f76r that I soon conjectured was a self-portrait of the VMS author [5]. And in comm. #156 (Vol. II) I opined further:

" fnGzp77C91s3b75g76rVMSblink1.tif has allowed me to form a more detailed opinion of the embedded stego picture of f76r. What I now see in it is, that the man whose face is in there, is using his right hand, and possibly also his left hand, to hold up right against his eyes, a rectangular plate that he is looking through. This plate may have a small indent for bridging his nose. But overall, to me it suggests that he is viewing something through an optical filter, and perhaps there is the suggestion that the process of creating the f76r stego picture and / or other VMS folios materials, involves the use of special illumination and optical devices; that is in tune with my already long running and periodically stated suspicion that the VMS is at least partly concerned with color optics / physics. A further thought along this vein is that the Voynich manuscript's long-so-assumed "pharmaceutical" section is possibly actually concerned with the manufacture of vegetable dyes for a set of experimental optical filters, intended both for spectral illumination and detection experiments. "

So then, to comm. #182 the hypothetical developments of this subject are summarized: the steganography of f76r shows the VMS author using an optical filter plate that he is holding up before his eyes, and the steganography at the lower-right area of the VMS binding front-cover shows the profile of the VMS author with an optical filter goggles placed underneath his portrait.

This correlation is now considerably advanced with the new data from the binding's front-cover: our Librarian Greg has installed for me four additional image files into the existing J.VS Library deposit # 18-1-2008-04-15, the deposit that holds the pictures described in comm. #182 (VMS Binding stego pictures) [6]. The pictures are two pairs, all suitable for blinking, and the deposit's metadata textfile explains how they were obtained. Two of them are of the f76r portrait, and two entirely new ones are crops of approximately 75% of the Binding front-cover:

Blink1c2VMSOFC.bmp (binding front-cover, man using optical filter)
Blink2c2VMSOFC.bmp (binding front-cover, man using optical filter, outlined)
Blink1bVMSf76r.bmp (f76r handscript text-art portrait)
Blink2bVMSf76r.bmp (f76r handscript text-art portrait, outlined)

As you will see from the pictures, I am suggesting that the Voynich MS Binding front-cover holds a steganographic picture of what is essentially the same scene depicted in f76r: a man holding an optical filter plate up to his eyes and looking through it [7]. As before in comm. #182, the enhanced image is for convenience and is not necessary once the picture has been perceived: the raw Beinecke SID image of the Binding front-cover shows it quite well enough. Assuming the man portrayed in both f76r and the Binding front-cover is the VMS author, we can see again that he has clearly European features, that he is middle-aged, and that he does not have a beard, although a thin mustache is a possibility. On first seeing this new larger view of him I thought he resembled Isaac Newton in his prime per one of the famous Newton portraits.

In the last couple of days there was a very interesting discussion initiated on vms-list by Dennis Stallings concerning the problem of the intentionality reality of the Binding stego pictures, our colleague Dana Scott added important comments based on his personal inspection of the actual Beinecke MS 408, and this vms-list thread is an important adjunct reference in these developments. [8]

As you can see from the Binding OFC pictures, there are additional details requiring interpretation. Stacked atop the optical filter plate are two more partial renderings of the eyes-viewing-through-handheld-optical-filter graphic. This could well help analyze better the f76r picture details. The stacking seems to indicate also a kind of perspective: objects receding into the distance becoming smaller. The question of symbolism of the group also arises - why are there three stacked graphics, when the major one alone seems to make the essential optical physics point? Is there here an implication of a spirit or magical "third eye" ? Or is there here a graphic statement exploring the philosophical paradox of: I know that I know I know.

However, it is possible to stick firmly with optical physics for an interpretation: the VMS author is saying that not only should the Voynich manuscript be viewed through special optical filters, but also with the book and the observer situated between facing mirrors. This would be consistent with my observation on f76r in comm. #111:

" In addition, the horizontal flipping gives me the idea that f76r was created with some kind of technique, perhaps optical, that inherently resulted in a left-right polarity reversal. "

At the top of the f82v illustration there is a suggestion of a rainbow. It may be interesting now to contemplate some of these strange Voynich pictures with optics in mind, and filtered rainbows as per at the bottom of f82v, and also "wave theory of light" being symbolically illustrated as undulating channels of fluid, with spectral sub-bands emphasized, often monochromatic, that is, filtered light. It all fits well with other indicators like the f68r3 PM-curve pointing to a 17th century genesis of the VMS, when the likes of Robert Hooke, Athanasius Kircher, and Johannes Marcus Marci were profoundly advancing optical physics.

As noted in [8] we are usually analyzing not MS 408, but limited-resolution images of it, and the steganographic hypothesis takes that very much into account. However, the stego hypothesis data, if nothing else, can serve as a checklist for those Voynich students who have the opportunity to go and personally inspect the actual Beinecke MS 408.

Berj / KI3U

[1] In J.VS comm. #115 (Vol. I) Jan Hurych commented:

" Steganography was long time suggested for the VM but never taken too seriously. But your pictures, the numbers discovered and if I may, suggest, take a look at 1006246, 7 and 8 [f99r, f99v, f100r]. The roots there are weird, but each has distinct number of sub-roots, clearly countable. Why would herbal show different roots so neatly lined-up? "

Until a far more comprehensive idea of the steganography in the VMS is known, the very nature of steganography permits, at this early stage of investigation, a statement on the "Voynich Manuscript steganography hypothesis" only to the extent that steganographic information is a major characteristic of the VMS, with indications that color physics is a prominent component in some of the steganographic techniques.

[2] Quoting myself from vms-list post: VMs: Voynich f67v prime numbers, de Molay & Knights Templar, Saturday, April 22, 2006 1:29 AM, by Berj / KI3U; preserved in file 1JVSlibKI3U.htm in J.VS Library deposit # 1-1-2007-05-05:

" First, I digress for just a moment to ask a question on the left-side diagram of f67v. At lower-left in that diagram is a circle containing four coupled balloon-heads set on a background of 3 colors. Am I seeing right - are those colors red, green, and blue, and in prominent ratio relationships? I ask because red, green, blue (RGB) are the primary colors of theoretical physiological color perception, and that theory, the Young-Helmholtz theory of color vision, has its formal start in 1807. "

[3] Quoting myself from J.VS comm. #107 (Vol. I):

" I have been finding a broad spectrum of hidden imagery and these include some different techniques by the artist. I have finally got what to me is a reasonable hint for a longtime major puzzle - why there is in f67v2 that RGB color-theory diagram - at least I cannot see any other way to think of that thing. Here's my reasonable hint (to myself - not trying to argue for it yet): I am getting the impression that the VMS artist experimented with color-painted art viewed through different color filters. As if that thing at the top of the f42v plant is a suggestion of wearing goggles. I'm getting indications, and this may be very difficult to argue for, that the VMS artist was experimenting with the production of hidden 3D effects, that become noticable only when the page is viewed through a color filter.

Some of the images are so faint that I too have doubts they are real, and I'm concerned that I am just selectively seeing patterns in random image data. Others are quite definite, but quite subtle and seem to be experimentations in a kind of abstract art: for example, I have a candidate for what seems to me to be a kind of Arcimboldo synthesis-style taken to an abstract level. "

[4] Quoting myself from J.VS comm. #109 (Vol. I):

" ..... that possibly the f67v2 color-theory diagram (as I call it) was even supposed to be some kind of calibration for that, and that the inks and paints were keyed to filtered light. "

[5] Quoting myself from J.VS comm #111 (Vol. I):

" So, I wonder if the f76r portrait, assuming it is real, is a self-portrait of the VMS author, especially I wonder this because of 76r being the very center of the VMS from the nested-shells / Slavic dolls model point of view (comm. #51). I've anyway always believed that the author must have left his / her sine in the ms somewhere. "


[7] In Blink2c2VMSOFC.bmp I may have been too conservative in outlining the bottom edge of the optical filter plate: it may be somewhat lower than I've drawn it, covering the man's nose.

[8] vms-list thread: VMs: Steganographics and the Voynich MS Binding, thread launched by Berj / KI3U beginning 04-16-2008 1:54:45 AM.

From: Berj Ensanian
Date: Tue, 22 Apr 2008 18:58:47 -0400 (EDT)

Subject: J.VS: Some possible steganographic script on the Voynich Binding Front-cover

Dear Colleagues

I have been inspecting some marks on the upper quarter of the VMS Binding front-cover that possibly suggest fairly large script letters. Our Librarian Greg has installed for me in the existing J.VS Library deposit # 18-1-2008-04-15 the additional image file c5VMSOFC.jpg, intended as a guide to the corresponding high-resolution SID image, where I have painted in outlines of what I am studying. [1]

I first brought this up yesterday in a vms-list post where I wondered if perhaps there is a mix of Greek, Phoenician, and Latin letters on the Binding. [2]

Earlier today in that same vms-list thread I expounded further my thoughts on the matter, and also mentioned the apparent clear "Phoenicia" listing in the Kircher document "Catalogus Linguas" in APUG (see discussion in J.VS comm. #125 etc.).

It may prove spurious in the end, but in the meantime it is certainly interesting to investigate if some initials or even a name, whether or not in mixed alphabets, whether steganographic or just worn and faded, and possibly associated with someone connected with the Voynich manuscript's history, are there on the book's Binding.

Berj / KI3U


[2] post: RE: VMs: Universal Ancient Language?, 04-21-2008 10:07:33 PM, by Berj.

From Berj Ensanian
Sent Date 04-29-2008 12:12:15 AM

Subject J.VS: Voynich steganography reference: f80v CATWOMAN's cat-face versus f1r Tepenece

Dear Colleagues

In connection with the very difficult problem of hypothetical steganographic imagery in the Voynich manuscript, I mentioned in J.VS comm. #109, on the f76r hand-script text-art portrait, my impression that a second face might be juxtaposed with its main face. [1]

Since then, in my steganographic survey of the VMS I am suspecting many examples of juxtaposed and merged heads and faces, an artistic device that can make the already difficult problem of ruling on the reality of a stego image, even more difficult.

Not uncommonly plausible "faces" can be perceived in more or less random patterns. For example if you take a walk on a somewhat rough asphalt-paved walkway, you occasionally spot a fairly startling "face" down there on the asphalt. It may even retain its "face-ness" as you change your perspective. And sometimes you can even find a case where it seems two or more faces are juxtaposed, either fixed with varying perspective, or one face turning into another as the perspective is changed. Likely the asphalt was laid down "randomly" and the faces resulted accidentally as unique features: a deduction from the context in this case.

One criterion I have been using for judging the intentionality reality of an apparently associated face of a graphic, is to consider the artist when known. At present we don't know who the Voynich MS illustrator was. But, in Robert Hooke's (1635-1703) seminal work Micrographia the illustrations exhibit, it seems to me, several embedded faces. For example, in Shem. 20 Hooke illustrates his microscopic image of Purslane-seeds. If you rotate his illustration 90 degrees clockwise, you can see the middle seed patently suggests a horrific face, looking directly at the observer, and it seems that Hooke has drawn it intentionally so, with carefully placed "eyes". His comments about Schem. 20 in the Micrographia text further suggest that he was well aware of this. Considering that Hooke began his career as a trained artist, altogether it is for me rather difficult to imagine that Hooke was not consciously and intentionally emphasizing, but emphasizing obliquely or subtly, what he perceived as facial suggestions in Purcelane seeds. We might further ponder that Hooke had ideas about faces being indicative of a kind of creative-force-of-nature, making itself visible here, there, and everywhere, with faces.

The illustrations, in books and online, of others in the VMS network of interest across the 15th to 17th centuries that I have looked at, that suggest to me they employed this artistic device of animating what they were illustrating with variously embedded faces, include: Albrecht Duerer (1471-1528), Giuseppe Arcimboldo (1527-1593), Heinrich Khunrath (c. 1560-1605), Cornelius Drebbel (1572-1633), and Robert Nanteuil (c. 1623-1678). As with Hooke, it is for me very hard to believe that Duerer was not aware of the faces he was embedding in, for example, his famous Praying Hands. Of course I also come across many period illustrations that seem utterly devoid of this artistic device, but again as with the apparent face-bearing pictures, one cannot be more or less sure without direct access to the originals.

Among the many VMS hypothetical stego image examples already in the J.VS Library there is one that shows a fairly plausible exhibition of merged heads / faces: the long vertical-running irregular stain on the f93r "Sunflower" folio. If we look carefully at the Library picture VMSf93rface6.jpg and its grey version xgVMSf93rface6.jpg, and then check the corresponding high-resolution SID images, we can entertain that that "stain" ends at the bottom with heads coming out of heads, and that the last head, at the end of the stain, is merely the most ovious head / face. [2,3]

The first part of a steganography problem in the VMS is the question: is this particular type of steganography plausibly present in the VMS?

As a step toward settling that, specifically with respect to merged or juxtaposed heads and faces, I have now identified what I think is a rather convincing example of the VMS illustrator employing the artistic device of merged or juxtaposed heads and faces, and employing the device steganographically. I have sent to our Librarian Greg as an addendum to J.VS Library deposit # 12-1-2007-10-12 the image file CATWOMANc10VMSf80v.tif to serve as a reference for the VMS stego merged / juxtaposed heads and faces question. I call this example "CATWOMAN" for reasons which will become clear in a moment.

By CATWOMAN I denote the naked female figure ("nymph") at the upper right of the VMS balneology section folio f80v. There is in my view quite a lot of steganography present in and around this VMS lady, but here we will focus on her head. The CATWOMANc10VMSf80v.tif shows framed together three small crops of her head from the Beinecke MS 408 f80v SID-to-TIF high-resolution source image. The left crop shows her full head, the middle is a detail of the lower part of her face, and the right crop is the middle crop again but with some contrast adjustment for viewing convenience. The contrast adjustment serves as a quick pointer, and the raw images are quite adequate for seeing the face-upon-a-face juxtaposition, as they should be if the example is to weigh in as a reference toward settling the above stego question.

From the Beinecke data for the dimensions of the VMS (16 cm wide by 22.5 cm high) I estimate CATWOMAN's vertical measure, that is her height, to be approximately 2.25 - 2.5 cm, and her head to be approximately 5x7 mm in size. For a quick comparison I open the nearest pocket dictionary, and measure the common letter "e" at about 0.9x0.9 mm. Therefore the graphic areas that the unaided observing eye must resolve for details, are approximately 35 mm^2 for CATWOMAN's head, and about 0.81 mm^2 for the e letter. On the CATWOMANc10VMSf80v.tif there is some inserted text, including "CATWOMAN". The width of the "W" letter is just about the equivalent to 0.9 mm on the crops in the tif and may be used as a gauge for estimating the size of individual details in CATWOMAN. Of course in the pocket dictionary the common periods are much smaller than the "e", still easily visible to the normal eye, but the e has more complex geometric structure that the observer must resolve.

Lets now examine CATWOMAN's face in the left, full-head crop. A casual look, especially from the mental frame of being accustomed to the normal appearance of Voynich female figures, has us peceive her with rosy cheeks and a red painted mouth. But a closer, more careful look tells us there is something odd about the lower 40% or so of her face, especially the chin, and the unusually low placement of her left rosy cheek: the lower 40% shows a second face, one that resembles a cat's face. The red mouth in the normal face now is the cat's nose, the normal rosy cheek of her left side (right side in the crops) is the cat-face's left eye, the normal face's nose-tip seems to serve as the cat-face's right eye, and the odd chin is the cat-face's mouth. In the tif frame the smaller crops show this.

I have worked routinely for many years with a 10x magnification eyeloop, of focal distance approximately 4 cm, in various tasks, including graphics. From my experience I estimate that a medium quality (by today's standards) 10x lens is quite adequate for a skilled artist to render the cat-face, with good lighting of course. I did some experiments with a 10x lens to check my estimate, attempting to duplicate some of the CATWOMAN details on paper. The 10x was indeed adequate, provided it was rigidly mounted. The distance between the lens and the work area, restricted to being less than 4 cm, was sufficient for getting a scriber in there and manipulating it. It was quite obvious to me that a very fine point scriber would be necessary, and that extensive experience and steadiness in controlling it would be critical: the CATWOMAN was likely not done when the artist was well past his / her prime. Although presently from other VMS data I believe the VMS author was, if a single individual, a man [1,4], however, admittedly a skilled woman with her smaller hands rendering some of the VMS illustrations must be considered a possibility.

I experimented with another, unmarked but evidently very good quality magnifying glass. Judging from its focal length, compared with that of the 10x eyeloop, and taking into account the somewhat imprecise meaning of the "magnification" of magnifying lenses, it was about 2x. I was able to work with it also, but despite the much greater room afforded by its substantially greater focal length, the need for very great skill in controlling the scriber was much more indicated due to the lens's significantly lower magification.

For the purpose of estimating a single likely magnifying glass available to the VMS artist in order to produce CATWOMAN's features, I think from the foregoing it is reasonable to consider a medium to good quality lens (by today's standards) of about 4x to 5x. This estimated lens might also suffice for achieving The King of f37v [5]. This estimate now motivates using it to date the Voynich manuscript, via its f80v CATWOMAN steganographics, against the known history of lenses. We would want to know when and where in Europe a 4x or 5x lens of the-then-very-best quality was available. Well, apparently serious interest in the possibilities of lenses took off dramatically in the 16th century, Italian lens makers produced the best examples to the end of the century, and in the opening years of the 17th century lenses of the above specification should have been available from lens makers in the Netherlands. [6]

Therefore, setting aside the possibility that someone very early, say Roger Bacon (c. 1214-1292), possessed and kept very secret some high quality magnifying lenses, then we can choose about 1600 when pretty much anyone with the necessary money could have bought a lens good enough to use in rendering CATWOMAN. This is just my estimate from the indicated lens requirement, but in general the dating of the Voynich manuscript, via its steganographics, against the known history of lenses, and other optical aids such as filters, seems promising field to plough. [4]

Also, concerning the often debated subject of the timespan-of-VMS-completion versus life-track of the VMS author from youth through prime of life to old age, and the eyesight and dexterity issues pertaining thereto, the optical gauging of the steganographics in the VMS should provide estimates and insight into that.

In J.VS comm. #181 I stated that I believe that the presently available high-resolution SID / TIF images of the manuscript provided by Beinecke are not good enough to reveal the full scope of steganography in the VMS.

To see an example indication of inadequate resolution in the CATWOMAN image, lets look once again at the CATWOMAN tif, zeroing in on the normal face's eyes that appear to be rendered with the usual VMS ink. Especially her right eye (left in the crop) hints at intentionally rendered detailed structure suggesting a symbol, vaguely like a scripted "H", or perhaps even a pair of ligatured symbols, resembling: Je, Jl, Jc, or J4. Per above, using the "W" as a gauge, this detail resides within an area of 1 mm^2. Without better resolution than the SID provides we cannot say much more, but with what we know already, we are justified in suspecting that better resolution might possibly reveal more intentional steganography in the manuscript.

Experimenting as per above, my attempts to draw something resembling CATWOMAN's normal right eye structure reinforced my belief that the cat-face may be intentional. And that also reinforces my belief that the Voynich manuscript is arguably an original, and not a mere copy, for the obvious reason that a faithful copy-job of so much time-consuming and high-talent-level steganography as is suggested by CATWOMAN, would make a copy an original in its own right, in the manner of illuminated medieval Bibles.

Now, as said before we are analyzing not the VMS, but the SID / TIF images of it, and without having the actual Voynich MS to examine, it is only a deduction, but from the foregoing I do believe that someone with good eyesight, able to easily read the typical pocket dictionary, would be able to perceive the f80v cat-face with the actual VMS at hand, provided they were examining the folio quite carefully in good light, and with the mind-frame that tiny details may not be accidental, but intentional.

And so then altogether, I think the CATWOMAN can serve as a VMS steganographic reference, and weigh in toward an answer to the question asked here at the beginning, with: yes, within the bounds of the steganography hypothesis, steganographic juxtaposed / merged faces, even miniature, are plausibly present in at least one Voynich manuscript drawing.

It is of course also proper here to mention that the foregoing bears upon the question of whether or not the Voynich f68r3 PM-curve is a steganographically carefully plotted curve of sufficient precision to encode complex astro-mathematical data. [7]

Although I have satisfied myself that the major SID-visible details of CATWOMAN's head can be done with a 10x lens, and even with a 2x lens by someone with exceptional and long experienced miniature-art skills, I suspect that the VMS illustrator may have used several magnification instruments, including some significantly greater than 10x. Perhaps even a microscope of some kind was used, not necessarily compound, although possibly compound - the quality of magnification is equally an important factor, as Antonie van Leeuwenhoek (1632-1723) demonstrated in the 17th century. A major consideration here is the effective focal length because it limits how much room there is between the objective lens and the work area to permit manipulation of the scribing instruments.

In comm. #181 I opined that one possibility for explaining optical physics based steganography in the VMS is that the book was meant as a demonstration of the possibilities of steganography; therefore there is the possibility that someone able to produce exceptionally high quality magnifying lenses and or microscopes (in addition to color optics instrumentation) might have produced the VMS to demonstrate them and their obvious application to secret communications: being in exclusive possession of ultra-high quality magnification instruments making possible steganographic communications, would bar those with inferior instrumentation from obtaining the communicated information. John Dee (1527-1609) may have had such thoughts. [6]

Of course all this is at least somewhat reminiscent of the VMS work of William Romaine Newbold, specifically the part of it dealing with identifying cryptographic marks in the manuscript with the aid of a reading glass or microscope. Newbold's colleague Roland Grubb Kent accepted some of the microscopic features he himself saw, but not nearly to the degree that Newbold was seeing them. And as we know, Newbold's view was severely rejected by John Manly, who explained Newbold's perceived microscopic marks as just cracking of the old ink on the old parchment. But as best as I know, Manly merely opined so, and did not demonstrate so. Moreover, a serious demonstration of the cracking ink explanation, or for that matter cracking paints, could not be a simple project it seems to me, and ought to examine also how it is that some ancient illuminated parchment manuscripts today still retain their remarkable miniature details. It is hard to believe that Prof. Newbold would not have thought about this, and had some comeback to Manly on it, had Manly, to whom Newbold was communicating his observations during his work, not waited until Newbold was dead to argue against him. So we have it that Newbold wanted to see microscopic marks and Manly did not, and Kent was somewhere in the middle.

Thus I think it is via the power of suggestion, and not scientific demonstration, that John Manly's opinion has, for most of the modern period of Voynich MS research, effectively discouraged the magnified examination of the Voynich manuscript. And Manly was not the first to strongly affect perceptions of the VMS via the power of suggestion: Wilfrid Voynich himself of course started everything by suggesting Roger Bacon as the VMS author. But far more lasting and influential was Wilfrid Voynich's peculiar accident-story suggestion that "Jacobj a Tepenece" is to be seen on f1r. Always in search of a clear exhibit of the fabled Tepenece on f1r, back in January, 2007, after seeing some f1r image processing by our Dana Scott, I thought I finally saw the "Tepenece", although I qualified myself:

" Also, the demonstration pictures must, in my opinion, include a larger area around the writing, so that it is clearly seen that the words Jacobi Tepenec are free of peripheral artifacts that mitigate against their interpretation.

The goal of the demonstration, in my opinion, should be to produce pictures that make it possible to analyze if "Jacobi Tepenec" was written as a unit, rather than was constructed from pre-existing marks on the parchment. In other words, determine it is really a signature, no matter who signed it, and not a fake signature made by modifying, and adding to, pre-existing marks on the parchment. " [8]

Since then I've swung back to not being able to convince myself that I can see Tepenece anywhere on f1r. For me, Tepenece is not there on f1r. Yet Wilfrid's suggestion continues to keep the faith in its existence going in much of Voynichland, and thereby prop up the standard VMS history theory received from Wilfrid that the VMS was once associated with Rudolph II's court - which may be true independently, anyway. And Wilfrid's suggestion is fortified with infrared and ultraviolet legends, but as best as I know no-one who claims to have seen Tepenece on f1r with infrared or ultraviolet illumination has brought back even so much as a crude sketch to hold up and say: this is what I saw.

So then, no Tepenece / Horczicky / Sinapius, then no Rudolph's court connection for the VMS, beyond the rumor in the last known letter of "Marci" to Kircher which, as best as I know, no-one has yet seriously demonstrated was even written for Marci with his knowledge, much less signed by him personally.

Back now then directly to the power of suggestion, which always unavoidably plays a role in VMS steganography hypothesis research. Now, I don't see any variation of Tepenece on f1r, but I do clearly see CATWOMAN's cat-face on f80v, and without ultraviolet illusions. And I suggest that you can too, dear reader, see CATWOMAN's cat-face, whether or not you see Tepenece. I suggest that we don't need acid accidents and faith to see CATWOMAN's cat-face.

Berj / KI3U

[1] J.VS comm. #109 (Vol. I): J.VS: New blink pics: hypothetical steganographic handscript mosaic text-art portrait in Vms f76r.

[2] The f93r stain steganography is discussed in J.VS comm. #173 (Vol. II): J.VS: Some hypothetical steganographic faces in the Voynich f93r Sunflower folio spill-stain.

[3] The VMSf93rface6.jpg and xgVMSf93rface6.jpg images are in J.VS Library deposit # 12-1-2007-10-12:

[4] For more discussion on optical physics and the VMS, and conjectures about the VMS author, see J.VS comm #183 (Vol. II): J.VS: Similar steganographic Color Physics depictions in Voynich f76r and Binding front-cover.

[5] see J.VS comm. #107 (Vol. I): J.VS: The VMS f3v Deathmask, the f76r text-mosaic portrait, The King, Rudolf, and more.

[6] The Invention of the Telescope, by Albert Van Helden, Transactions of the American Philosophical Society, Philadelphia, Vol. 67, Part 4 - 1977.

[7] See J.VS comm. #138 (Vol. II): J.VS: Comments on the Voynich f68r3 PM-curve question.

[8] vms-list thread post: Re: VMs: Tepenecz: three scenarios...?, Sunday, January 28, 2007 10:18 PM, by Berj. This post is preserved in the J.VS Library file 4vmsKI3Ulab.htm, J.VS Library deposit # 1-1-2007-05-05:

From: Berj Ensanian
Date: Sat, 03 May 2008 16:53:27 -0400 (EDT)

Subject: J.VS: Patterns within random patterns and the steganography problem

Dear Colleagues

In J.VS communication #185 (CATWOMAN), in discussing the steganographic intentionality problem, I gave the example of the random surface of an asphalt walkway as a sometimes source of apparent faces. I thought it useful to put in the J.VS Library, as a counter example to the CATWOMAN reference image, a picture of plausible merged faces arising in an almost certainly random pattern.

Looking for something handy with at least some resemblance to VMS parchment, my plan was to photograph a "face" on the surface of a cinnamon cracker. Remarkably, I could not find any passable faces on the crackers I examined. Then I had a better idea: in many of the Beinecke SID images of the Voynich manuscript there is seen also an object that is not part of the VMS - the plastic hold-down strip that kept the pages more or less flat when the SID photographs were taken.

The strip(s) appears as a rather rough semi-transparent plastic. In the SID images of f47r and f85r2 the vertical top and bottom ends of the strip are well visible beyond the edges of the VMS. I cropped those as best-resolution SID-to-TIF's and assembled the four of them together in one frame, and then did some color and contrast adjusting to achieve some plausible "looks-like-a-face" impressions. I have sent the above image, VMSsidsRandPatternsRef.tif, to our Librarian Greg for deposit as an addendum to J.VS Library deposit # 12-1-2007-10-12. [1]

Different plausibilities can be gotten with different image processings, so the particular adjustments here are not critical for the point being made: the difficulty of ruling on the intentionality of an apparently organized pattern that is perceived within an ambiguous or random pattern.

I can perceive plausible faces, including merged / juxtaposed faces as per comm. #185, in the VMSsidsRandPatternsRef.tif examples. In particular, the upper right crop, of the top-end of the strip from f85r2, in the area where the strip extends beyond the VMS's edge, there is, as I see it, a rather astonishingly well organized apparition of an animal-like face. Although faint, it seems to me so realistic that when I first perceived it I wondered if indeed that strip had had that face, along with some merged companions, intentionally embedded within it by the maker of the strip.

Rotating the picture 180 degrees and also trying a horizontal flip allows new faces to be perceived. I cannot at this point really tell if the same strip is being used in both f47r and f85r2, and even if so, if the strip's orientation is the same. In any case VMSsidsRandPatternsRef.tif points to demonstrations of the big problem: steganographic intentionality.

It is entirely conceivable that the VMS illustrator was well aware of the problem and actually worked with it, to make ruling on the question even more difficult. And all that to consider before one can even try to figure out what the overall message of hidden faces is supposed to be.

Berj / KI3U


From Berj Ensanian
Sent Date 05-04-2008 11:11:18 AM

Subject J.VS: The Spectre of Archives Splitting: Scottish Catholic Archives

Dear Colleagues

The question of the intactness, versus their archival history, of the Athanasius Kircher, S.J. papers is a critical factor in Voynich MS historical research, as we all know too well. We might therefore keep note of present developments concerning the Scottish Catholic Archives in Edinburgh: they are to be moved to Aberdeen University, but there are fears and controversy over the possibility that the archives will be split. More up-to-date information is here in a BBC news website article:

Berj / KI3U

From: Berj Ensanian
Date: Tue, 06 May 2008 11:01:04 -0400 (EDT)

Subject: J.VS: M. Fincher's Word Pair Permutation Analysis

Dear Colleagues

Yesterday well-known-to-us Voynich researcher Marke Fincher announced on VML the online availability of his new paper titled:

Word Pair Permutation Analysis of natural language samples and it's value for characterizing the 'Voynich Manuscript' [1,2]

Replying on VML in his thread, my comments to Marke included:

" I just had my first readthrough of your excellent paper and my initial impression is that its ideas provide a new platform for gauging " what the hell " is going on with the Voynich script. I need much more study before getting a thorough critical understanding of it all. I did wonder what kinds of curves would result from WPPA analysis of a series of numbers, random in lengths and magnitudes, as generated by some sort of randomizing algorithm. "

I feel that Marke's paper belongs, like Dennis Stallings' entropy work from the 1990's, among the must-be-familiar-with works in the special area of mathematical analysis of symbols and symbols-groups sequences, in particular of course the Voynich "text".

Berj / KI3U

[1] vms-list (VML) thread-launch post: VMs: Write up of wordpair permutation analysis, Sent Date 05-05-2008 1:42:47 PM, by Marke Fincher.

[2] Marke's paper is online here:

From: Berj Ensanian
Date: Wed, 07 May 2008 22:51:33 -0400 (EDT)

Subject: J.VS: Sequence Spectra of text-signals and Equal Statistics Analysis

Dear Colleagues

For future reference I would like to introduce here an elementary version of an analytic notion, that is useful in some kinds of attacks on symbols sequences. As will be seen, for self-evident reasons I call it: sequence spectra of text-signals. The essential simple idea is to focus on the various kinds of orders present within a signal sequence: the are more kinds of sequence orders in a sequence of symbols than just the first symbol at the beginning is the first, the next is the second, the next is the third, and so on. This may be old hat to you, but I think we could use something about this subject for handy reference when in the future these techniques are used in openly communicated work.

Let us view a sequence of text symbols as a serial signal stream. In the following we will take a reading of left-to-right to correspond to the start and end of a signal stream. For a source of example text, let us take text-line 11 from the Voynich biological folio f77r (conventionally deemed Currier language B) as it is seen in the Beinecke image. The Voynich "words" in this line are well defined, and except for the separation between the last (right-most) and second-last words, the inter-word spaces are about equal. For simplicity here we will take it that all inter-word spaces are equal.

By first-order appearances then, this line consists of 7 unique words, and a total of 9 words. Using "_" to indicate inter-word spaces, let us transcribe line 11 using D'Imperio's transcription alphabet:

Transcribed in MD-


And now transcribed in GC-

{2} 4ohcc89_e1c9_e2cc9_4ohcc89_4ohcc89_4ohay_4ohcc9_eaiiN_1c9

Counting the spaces as signal units in their own right, we then have line 11 as a signal consisting of a sequence of 57 signal units. If the spaces are thrown out, then we have 49. If line 11 is to be the total signal of concern, then we can assign to the total signal field 57, or 49, units of length.

Now for a moment let us pretend that {1} and {2} are independently encountered. From the point of view of the relations between line-symbols-sets, these two sequences have equal statistics we can say. For example, in {1} the relations of the occurrences of the "B" symbol are equal to the relations of the occurrences of the "1" symbol in {2}, and so on [1]. Therefore aside all else, these two signals exhibit some common signal-analytic components.

By throwing out some information we can contract the signal field so as to emphasize the identical words, and transcribe {1} and {2} like this:

{3-1} 1_2_3_1_1_4_5_6_7

{3-2} 1_2_3_1_1_4_5_6_7

We have used numbers to designate the words, assigning the numbers in order, according to a word's order of appearance. And we have contracted the signal field to a length of 17. Although {3-1} and {3-2} came from the same signal, line 11, had they originated independently, the spectral exhibits of {3} would indicate significant commonality. Likewise, this sequence:

" Always consider that always always makes sense to some "

can be transformed into the same spectrum as in {3}, and therefore its signal, and the signal of VMS f77r line 11, have a significant common spectral characteristic. Naturally, the throwing out of information in the process of contracting the signal-field, can be viewed as a filtering step in order to resolve some particular feature of the source signal.

Let us again transcribe but keep different information, this time resolving the sequences framed upon word-units and their internal structural sequences. Because all the words are less than 9 symbols in length, the notation in Arabic numerals may remain simple:

{4-1} 1234456_1234_12334_1234456_1234456_12345_123445_12334_123

{4-2} 1234456_1234_12334_1234456_1234456_12345_123445_12334_123

Again, both {1} and {2} have been transformed into {4}, exhibiting some equal statistics. The alphabetic information of the particular symbols has been discarded of course. We note that, as expected, the first, fourth, and fifth words have identical structural spectra.

And we also note that the third and eighth words now record with identical structural spectra, even though they appear as quite different alphabetically dressed words in {1} and {2}: IRCCN vs IHLLP, or e2cc9 vs eaiiN. We have discarded information there also. However, if the alphabetical aspects are merely noise, and the originally intended true signal is the super-sequence of word-framed structural spectra, then we can consider {4} to be a filtering of {1} and {2}.

It is easily seen that with the restricted-to-maximum-9-letters words, the Arabic numerals notation can identify part of the information in the words as components of vectors pointing to a look-up table of some kind, say a dictionary, vocabulary, or codebook. It is nevertheless important to keep in mind that the third and eighth words, although possessing identical structural spectra, are not identical vectors: the two identical spectra occupy different word-sequence positions, and those sequence positions must be figured as components of their total vectors, when appropriate.

So, from this perspective, we can for example say that the number 123 is a spectral invariant associated with a set of symbols-sequences that includes "and", "the", "VMS", "bug", "bit", "him", and the number 112 is an invariance associated with "eel", "BBC", "EEG". And so on and so forth.

Another thing that is easily seen from {4} is an analogy to alphabetical-based digraph and trigraph analysis. Specific to the VMS, the analogy is the identifying of Voynich digraphs and trigraphs and studying their properties throughout the text. With {4} this becomes identifying clusters of word-structural spectra and studying them. For example, we might investigate if 1234_12334 is a significant di-spectral cluster, and if 123445_12334_123 is a significant tri-spectral cluster anywhere, or throughout the Voynich text.

Now, we all know that the time-honored magnetism of the Voynich text to attract those who can "read" it in one language or another, natural or artificial, continues undiminished. And in fact that is how I too originally started with the VMS. I would like to comment here that my studies of sequence-spectrum clusters in the VMS text, and comparing them with clusters in control texts of different languages, has convinced me that it is an excellent path to follow for understanding the VMS-can-be-read-in-language-X magnetism - that is after all a very interesting phenomenon in its own right, independently of whether or not any blocks of the VMS script really are in language X. Clusters like 123_1234_123_1234 and 123_123456 seem to be common, popping up not only in the VMS, but also in, for example, Schiller's great German poem: Das Lied von der Glocke.

Further up the scale, well-chosen spectral-analytic specifications can identify super-clusters, that is sequences of clusters that may or may not repeat, and finding these both in the Voynich and in normal works, may well weigh in on such a question as the limits of creative variability in intelligence-directed sequences, and the meaning of "random".

The preceeding with {4} was a word-framed analysis that was able to take notational advantage of the Arabic numerals 1-9. That advantage could be lost for line-framed spectra. For example, {1} might be written this way for one possible line spectrum analysis:



This {5} analytic seems suitable for analysis of vertical "word columns" in collections of lines, say a paragraph. But obviously if, with a slightly different analytic specification, the inter-word spaces were treated the same as all the other symbols, then the resulting line spectrum of {1} would look quite different than {5}. It could be written like this:



If, rather than the line, an entire paragraph is to be the total signal field, then {6} would continue, and its next number would be 15, denoting the first appearance of a linebreak (on the assumption here that line 11 is the first line of the paragraph being studied). Of course by analytic choice, the distinction between inter-word space and line-break might be voided, and then the next number would not be 15, but again 7.

And it is {6} that most quickly shows that these sequence spectra can be regarded as curves and studied as such. The simple basic rule governing a symbols-sequence signal spectrum curve like {6} is that when we follow the progression of the curve, any rise in the curve reaches at most a point higher than the curve's previous highest peak by exactly the amount 1. This rule is universal regardless of the nature of the sequence of elements being transcribed as a signal, be the source signal letters on a page, telemetry coming into a recording receiver, or phonemes reaching the linguistically trained ear.

In the same way that a Fourier transform of a curve can be regarded as a new curve, be the Fourier operation concerned with a continuous function, or a set of points requiring the discreet Fourier transform (DFT), the set of numbers of {6}, originating as a characteristic of a text-signal, can be plotted as a curve, and studied as a curve, and if the curve is long enough then too with a DFT.

Berj / KI3U

[1] Recently in an interesting vms-list discussion I mentioned that in my private notes I call a particular type of analysis "equal statistics text analysis": vms-list post: Re: [RE]VMs: VMs - Word Structure - Spanish?, 03-14-2008 11:09:26 AM, by Berj.

From: Berj Ensanian
Date: Sat, 10 May 2008 10:30:26 -0400 (EDT)

Subject: J.VS: Latin language boost

Dear Colleagues

Good news: the Roman Catholic Church is boosting emphasis on communication in the Latin language:

New resources are available online:

And this website is by Fr. Reginal Foster, Benedict XVI's official Latinist:

Here are just a couple of titles found there:

11/4/06 - Accademia
Our "Latin Lover " explains how the Pontifical Academy of Sciences could possibly be connected to lynxes! All this and more.

9/14/07 - What Latin
Augustine, Jerome, Ignatius of Loyola all wrote Latin, but what were their skills in this ancient language really like?

This all looks to be very useful for VMS historical research.

Berj / KI3U

From Berj Ensanian
To Journal of Voynich Studies
Date 05-21-2008 11:18:12 PM

Subject J.VS: Possible versus Impossible Sequence Spectra, and Associated Relations

Dear Colleagues

In J.VS communication #189 I began attempts at developing an effective vocabulary and notation for sequence spectrum analysis with an elementary exploration of the concept [1]. Sequence analysis can be very tricky with its subtleties inviting mistakes, and so it takes some getting used to, but its power to give insights is well worth the effort. Here I will attempt to broaden the picture with a precise distinguishing between possible and impossible sequence spectrums, and explore some associated relations, including sequence spectrum generating algorithms. Still only the elementary ideas from the mathematics of permutations and discreet variables are needed in the following, and we use only the minimum necessary rigour to develop what we are after. If you find errors in the following I would appreciate you pointing them out to me. The vocabulary and notation are of course subject to improvement.

The over-riding attraction of studying sequence spectra is the invariances and universal rules associated with sequences that sequence spectrum analysis illuminates. Everything that can be viewed in terms of sequences, be it astronomical signals from a pulsar, DNA proteins, picture elements, voices, Eulerian text circuits, information channels, random noise etc., has some properties deriving directly from the general concept of sequence, a concept that pervades all human experience of the cosmos and its details: nature speaks to all in sequences, with and without our participation as nature's scribe. Sequences are thus bridges connecting ideas across realms of interest. And remarkably, the first universal rule governing all sequences is so simple that it might be overlooked and so its deeper significances not suspected. In comm. #189 I attempted to convey that rule in plain language: when we follow the progression of a symbols-sequence points-plot curve, any rise in the curve reaches at most a point higher than the curve's previous highest peak by exactly the amount 1. Let us now look at this a bit more comprehensively and generally. [2]

Our concern is sequences, and, mathematically, we will take sequences to mean series with certain properties. And then, whereas all sequences are series, not all series are sequences. We shall below develop the distinction precisely, as our notation is developed.

For there to be a sequence, first there must be things that can be taken to appear serially. And for there to be "things" so contemplated, the things among themselves may be distinguished, at least, as either equal or unequal, and either way they must be indexable as to their serial order, by the progression of arithmetic integers 1,2,3,4,5,....... within the sequence reference frame the things are detected or studied.

Therefore, a thing in a sequence exists with never less than two identification labels, which in their most basic form are an integer number identifying the thing's serial order, and an integer number identifying the thing as either a new thing in its initial appearance in the sequence, or a thing equal to a previous thing or things in the sequence. Graphically then, a progressive plot of the integer-pairs of the things traces a points-curve. And we ask: what does the universe, or what does "existence" allow for these sequence curves? What are the possible extremes of such curves? A good notation for sequence spectra ought to make it easy to deal with possible versus impossible sequences.

It is easily realized that one limiting extreme is the case where in the sequence every thing is equal to every other thing. In our present notation we may write this case (here illustrated with more than 4 things) as a "sequence spectrum" as follows:

{1-1} 1,1,1,1, .......,1,

where the first 1 on the left indicates the first thing in the sequence of any kind, and the subsequent 1's indicate identical things. The 1,2,3,4,5,.... etc. integer numbers indexing the serial order of the things are not shown in the notation, but are obviously implicit. And so the graph of this extreme case of all the same things is a flat horizontal line, or spectral "wall". Using ordinary mathematical notation the function for the curve in (x,y) frames is given by:

{1-2} y(x) = 1

where x is an integer indexing the serial order on the reference axis of progression, and the range of x is from x=1 to x=n where n is the number of things in the sequence under consideration. [4]

It is also easily realized what the opposite limiting extreme is - progressively, every thing in the sequence is a new thing, different from every previous thing:

{1-3} 1,2,3,4, .......,n,

The graph of the function of the curve for this extreme case of all different things is given in ordinary mathematical notation by:

{1-4} y(x) = x

where x is as before in {1-2}. It is convenient to refer to spectral sequences or sub-sequences of the type {1-3} as: sequence spectrum ramps.

Now that we have the valid extremes, we consider the possibilities for sequence spectrum curves between them. It is obvious from the outset that not all mathematically possible curves bounded by the extremes, as represented in our notation, can represent valid sequences. For example, the following curve does not violate the bounds of the extremes, but it cannot be a valid sequence:

{2} 1,1,3,

In our notation {2} states an impossibility: that a third different thing exists in a sequence that lacks a prior second different thing. We realize that it is logical to begin an investigation of the question of valid sequence curves between the extremes by considering the smallest possible sequences: those of just two things. And there are only two possibilities here:

{2-1} 1,1,

{2-2} 1,2,

That is, an elementary wall, and an elementary ramp. Every sequence analytic frame, whether it hold an even or odd number of things, that is broken up into a collection of the smallest possible frames, must consist of sub-frames that contain sequences which, when properly re-notated to their own sub-frames to make them self-standing sequence spectrum frames, are either of type {2-1} or {2-2}. Any long sequence is a concatenation of walls and ramps, and the sizes of the walls and ramps in the properly finalized concatenation depend upon observing the equalness or non-equalness of things from the contributing sub-frames. That is, as walls and ramps are concatenated, their sizes may change, and a thing that was part of a wall may become part of a ramp, and vice versa. As we will see, concatenation may affect ramps in addition as to size.

To clarify, let us illustrate this by properly concatenating four example independent elementary frames per {2-1} and {2-2}, but with additional temporary notation:

{2-3} 1(red),2(green),
{2-4} 1(green),2(blue),
{2-5} 1(blue),1(blue),
{2-6} 1(green),2(red),

{2-7} red,green,green,blue,blue,blue,green,red

{2-8} 1,2,2,3,3,3,2,1,

It is quickly seen that, as expected, the curve representing {2-8} falls between the extreme curves of {1-2} and {1-4} in a frame of span n=8. The curve represents a valid sequence. We also see something resulting from the concatenation that is not possible in elementary sequence frames of just two things: descending ramps. So in general we now have rising and descending ramps, but there is an assymetry: elementary ramps in self-standing frames always rise.

For a new example, let us take the above four elementary spectra, without the colors so that all the 1's are equal things among themselves, and all the 2's are equal things among themselves, and again concatenate them:

{2-9} 1,2,1,2,1,1,1,2,

This sequence spectrum is valid, and as shown, its third-in-order thing is a 1. For valid sequences, what possibilities other than 1 exist for the third-in-order thing? It is easy to see the possibilities are: 2 and 3:

{2-10} 1,2,2,2,1,1,1,2,

{2-11} 1,2,3,2,1,1,1,2,

The sequences {2-9}, {2-10}, and {2-11} are strikingly different overall, even though the detailed differences are just at x=3. These overall differences now provoke an interesting fundamental question: what is a logical step-wise progression in sequence spectra? That is, given a sequence spectrum, what are its logical immediate neighboring spectra?

From one viewpoint it can be taken that {2-10} is the immediate "higher" neighbor of {2-9}, and {2-11} is the immediate higher neighbor of {2-10}. But, we can see that there are many other possible valid spectra "between" {2-9} and {2-10}, and between {2-10} and {2-11}.

So it is clear from inspection of {2-9}, {2-10}, and {2-11} that in general there is no one answer, and a logical progression of sequence spectra must be identified in accordance with a particular system of sequence spectrum analysis. Although sequence spectra are intimitely involved with the natural sequence of the integers 1,2,3,4,5,..... a "series or sequence of sequence spectra" on account of involving collections of integers, introduces more possibilities for neighboring [5]. Perhaps at best we might say that the elementary wall and ramp of {2-1} and {2-2} are as close neighbors in "sequence spectrum space" as it gets. But by way of metaphor with chickens and eggs, what came first, the wall or the ramp? With sequences of sequence spectra there are ambiguities as regards their serial order, and therefore any metric between sequence spectra must be settled in the context of a particular system of analysis. Thus what may be a logical cluster of sequence spectra in one analytic system, might not be so in another system. We will however later look at one system of generating sequences in-order that may prove broadly useful for defining neighboring of sequences.

Before proceeding further it is now best to improve our understanding of a precise distinction between "sequence" and "series". Consider the valid sequence:

{2-12} 1,2,2,3,4,5,3,5,

As we committed to at the outset, a series is a more general idea than sequence, and in our considerations a sequence is a series with particular properties. Lets see this precisely via examples. The following example sub-series of {2-12} are all valid sequences, and therefore they are sub-sequences of {2-12}:

{2-13} 1,
{2-14} 1,2,
{2-15} 1,2,2,3,
{2-16} 1,2,2,3,4,5,3,

The case of {2-13} is included in the terms "sub-series" and "sub-sequence" so that we retain mathematical consistency with later requirements: a sub-series or sub-sequence may be as short as 1 element. But the following example sub-series of {2-12} are not valid sequences, and therefore they are not valid sub-sequences of {2-12}, because as does {2}, they violate our fundamental conception of sequences:

{2-17-1} 2,2,
{2-18-1} 2,3,4,5,
{2-19-1} 4,5,3,5,

These sub-series could of course easily be transformed into valid sequences:

{2-17-2} 1,1
{2-18-2} 1,2,3,4,
{2-19-2} 1,2,3,2,

The above examples emphasize that in our considerations, the things in sequences are distinguished strictly only as to their order of appearance in the series, plus whether they be equal or unequal among themselves.

The basic rules defining our system of valid / true integer sequences can now be listed:

{3-a} Sequences always start with the lowest possible sequence element y=1 at x=1.
{3-b} No sequence element y(x) may be greater than its x.

{3-c} At any serial order index position x, the lowest possible element y(x) is a 1, and the highest possible is (h+1) where h is the highest y previously appearing in the sequence among all the sequence positions 1 to (x-1). Therefore the possible integers that may appear at some index position x are: 1 to (h+1) inclusive. If h is taken to designate the highest integer anywhere in the sequence, then all integers 1 to (h-1) inclusive appear at least once in the sequence, before h.

{3-d} Any subsequence of a valid sequence, is a valid sequence. Therefore truncations of valid sequences from the right result in new valid sequences. Successive truncations generating successive new, and shorter sequences, are another example of the previously discussed ambiguity of metrics between sequences.
{3-e} Any valid sequence may be expanded into a longer valid sequence by appending to it any of its sub-series or even a copy of its entire self, introducing periodic characteristics. Of course an appended subseries may also happen to be a subsequence, but it need not be: its appending will not violate {3-c} above.
{3-f} If A and B are any two valid sequence spectra, both of their concatenations, AB and BA, result in valid spectra.

The rule {3-c} is really the heart of the matter: all the rest can be deduced from it. This rule's chief feature is the h numbers. Studying the h numbers systematically yields more insights into the question of possible versus impossible sequence spectra, and associated relations.

Let us define an integer number function h( f(x) ) of the integer number function f(x). In less specific and more general contexts we might name it the "progressive maximum function" of f(x), but so as to remain in tune with our present themes, we will here equally well also refer to it as the high-history function, or hh-function of f(x) :

{4} h(x) = h[ f(x) ] = max[ f(x) ]

where max[ f(x) ] means the maximum or highest value reached by f(x) across the range of x from its start, up to, and including the specific x under consideration. [6]

Let us illustrate the hh-function with an arbitrary f(x) over the range x=1 to x=11 :

{4-1} x; f(x); h[ f(x) ]

01; -2; -2
02; -1; -1
03; 2; 2
04; 5; 5
05; 1; 5
06; -7; 5
07; 5; 5
08; 4; 5
09; 9; 9
10; 9; 9
11; 5; 9

We can see that the hh-function progresses only with rises and plateaus, and unlike some f(x) progress, it never descends. Therefore, if f(x) after some x repeats some sub-series of its values, or even becomes entirely periodic, its hh-function merely continues accordingly as a constant amplitude plateau. Thus the curve of the hh-function traces the initial-appearance or birth history of the successive new highs of the progressing curve f(x). If f(x) happens to be such that it only exhibits constancies or births of new highs, then it follows:

{4-2} If f(x) has no descents, then: h[ f(x) ] = f(x)

Therefore for any f(x):

{4-3} h[ h[ f(x) ]] = h[ f(x) ]

That is, the high-history of any f(x), is also its own high-history.

Now let us consider the hh-functions of y(x) sequence functions. In the cases of the sequence spectrum extremes of the {1-1} wall and the {1-3} ramp, it follows from {4-2} that the high-history function is clearly identical to its corresponding y(x) sequence function.

Now let f(x) = y(x), a valid sequence spectrum function. Lets illustrate the hh-function of an example y(x), whose values for x=1 to x=8 run 1,1,2,3,1,4,2,3, :

{4-4} x; y(x); h[ y(x) ]

1; 1; 1
2; 1; 1
3; 2; 2
4; 3; 3
5; 1; 3
6; 4; 4
7; 2; 4
8; 3; 4

We note the critical difference between the {4-1} and {4-4} examples: in the latter the rises in the hh-function are always exactly as the natural sequence of the integers. From the cardinal rule {3-c} fact that the progression of y(x) is such that its next new high is always exactly its previous high value plus 1, there follows a critical characteristic of the hh-functions of valid / true sequences that most succinctly summarizes possible true sequence spectra, and that we express in conventional mathematical terminology as follows:

{4-5} (delta h[ y(x) ])/(delta x)

for y(x) a true sequence function, is such that: for (delta x) = 1 it is always either 0, or +1.

It can be quickly calculated that the hh-function for the invalid curve {2} would violate {4-5}.

Using {4-3} we can write a special case:

{4-6} h[ h[ y(x) ]] = h[ y(x) ]

and since h[ y(x) ] satisfies {4-5}, it follows that h[ h[ y(x) ]] does also.

To see the implication without confusion, let us assymetrically substitute Y(x) = h[ y(x) ] and rewrite {4-6}:

{4-7} h[ Y(x) ] = h[ y(x) ]

and since h[ y(x) ] satisfies {4-5}, it follows that h[ Y(x) ] does also. Therefore Y(x) must be a valid sequence spectrum curve. And Y(x) is nothing more nor less than the hh-function of a y(x). So then:

{4-8} For any span n, the hh-function of a valid sequence function is itself a valid sequence function.

Taking the hh-function of a valid non-extreme sequence function can thus be viewed as either a sequence generating mechanism, or an irreversible transformation of one true sequence into another. As an example, in {4-4} we can see that h[ y(x) ] is indeed a valid sequence spectrum curve in its own right.

Thus, in general, every y(x) sequence curve is paired with an h(x) sequence curve, but not uniquely: different y(x) curves may pair with the same h(x) curve - we can see this in {4-4} if we change the y(x) curve slightly, by replacing, for example, y(5)=1 with y(5)=3. Another example would be replacing y(7)=2 with y(7)=1. The hh-functions remain the same. So we see that families consisting of different y(x) sequence spectrum curves map to the same high-history curves. And so the hh-curve families become a specific subject for investigation. In a sense, the hh-functions of y(x) functions can be viewed as the "least complex nearest neighbors" of the member sequences of their families.

Because it is an equation expression of the general rule {3-c} for the possible true / valid sequence spectra, the expression of {4-5} can be used to construct algorithms and formulas for systematically generating true sequence spectra. If a trial number function f(x) taken as a potential y(x) conforms to {4-5}, then it is a valid sequence function, and so also is its hh-function. Here is one sequence generating system:

{5} A procedure for generating all possible true sequence spectra of span n, up to and including n=9 :

{5-1} Write the upper and lower extremes of the span:


{5-2} Treat the sequences as ordinary Arabic numerals; for example treat 1,1,1,1, as if it were one thousand one hundred eleven. Consider the lower extreme to have been processed by the generating procedure.

{5-3} Increment the previously processed Arabic number to obtain the current Arabic number; for example increment 1111 to become 1112. If the current number equals an Arabic numerals image of the upper extreme, then exit the procedure - it is completed for the specified span n.

{5-4} Recast the current Arabic number into element values for an f(x) curve; for example: 1,1,1,2,

{5-5} Calculate the hh-function for the f(x) and test it against {4-5}.

{5-6} If the current hh-function obeys {4-5} then keep the current f(x) as the y(x) curve of a valid / true sequence spectrum, and go to {5-3}. (Note: optionally, the current obeyant hh-function may itself be kept as a valid sequence spectrum curve.) Otherwise, discard the current f(x) and go to {5-3}.

With care, this system can be generalized to n higher than 9, but at the cost of losing the simple conveniences of Arabic numerals notation and incrementation. Implemented in a computer program we would of course want to stick to the simplest integer operations instead of using fractions and floating point arithmetic, and in so doing the steps in {5-5} can also be economized:

{5-5-a} If any f(x) element is greater than its index x, then the hh-function fails to obey {4-5}.
{5-5-b} For any f(x) element beyond the first, is there present in the range of x before it at least one occurrence of either an equal element, or an element that is less by exactly 1 ? If yes, then the hh-function obeys {4-5}.

There may well be other economizing possibilities for computations, especially as n becomes large and extensions of shorter valid sequences are calculated. Here is the output of a program written per the above, for the possible sequence spectra of n=4 with the spectra displayed in notation without commas, like ordinary Arabic numbers:

{5-7} All Possible Sequence Spectra for n=4 in Arabic numbers notation and order, with their hh-functions:

01 : 1111 : 1111
02 : 1112 : 1112
03 : 1121 : 1122
04 : 1122 : 1122
05 : 1123 : 1123
06 : 1211 : 1222
07 : 1212 : 1222
08 : 1213 : 1223
09 : 1221 : 1222
10 : 1222 : 1222
11 : 1223 : 1223
12 : 1231 : 1233
13 : 1232 : 1233
14 : 1233 : 1233
15 : 1234 : 1234

Here in {5-7} the fifteen possible n=4 spectra are ordered according to numerical hierarchy, and show patterns of evolving periodicity, for example in the recurring 2-elements sub-sequences at the ends. We have seen that the ordering of sequence spectra in a sequence of sequence spectra is an ambiguous concept that must be determined by a particular system. A system like {5-7} though makes it easy to determine: how many true spectra exist "between" two given spectra? And, what is the distribution of true spectra in this numerical hierarchy? Evidently for spectral width n=4 the clan of neighbors belonging to hh-spectrum 1222 is the biggest, with four members.

In this system we could define the spectra in table {5-7} to be each other's nearest neighbors by their numerical hiearchy order, despite sometimes belonging to different hh-families. By extension, the nearest next higher neighbor of 1234 would be 11111. And so on. Above n=9 the simple Arabic number notation and incrementation could not be used, but a suitably modified version of {5}, akin to hexadecimal numbers, would generate the bigger sequences in the same way as the shorter ones, and so an ordering / neighboring system would remain.

It is interesting that in this ordering system in the table we can can quickly find clusters of sequential sequence spectra that correspond with sensible phrases in some language. For example, the cluster made up of the series of spectra 11 through 15 dressed up in text letters like this:


11: 1223 : seen
12: 1231 : that
13: 1232 : gala
14: 1233 : bill
15: 1234 : once

which might be embedded in a statement like this:




And we note one more curiosity: if we concatenate the first two words, then the statement's line aquires a symmetry from its terminals:




Throughout the exploration of sequence spectra we've observed that becoming familiar with their clusters, as they commonly appear in various sequence scenarios, including of course text, is among the first tasks in a serious study of the subject. And that will take some time. But this last example suggests that one simple initial systematic approach to familiarization with clusters specific to text analysis, is to explore the number of sensible phrases in various languages that can quickly be matched to numerical hierarchy ordered tables as done in {5-8}, the number of matches easily found versus the span n. "Easily found" is admittedly imprecise, but we are considering initial forays into the field, where we are on the lookout for clusters of universal significance. It is a simple start down that path, considering that important clusters are of course not expected to be just comprised of spectra of all the same spans, nor even serially contiguous. Clusters can overlap with other clusters, and a cluster's member spectra can be separated by other spectra not belonging to the cluster, somewhat like various guest spectra checking in and out of a Spectral Cluster Hotel.

Let us close with a little experimental philosophy of sequences, just to partake for a moment of the philosophical pleasures that Voynich studies offer in abundance. So far we have proceeded from the perspective of mathematical idealization, with the elements of sequences being "things" distinguished among themselves as equal or unequal. With texts of serial symbols, provided the symbols are easily resolved, the "things" are the symbols, and in general also the spaces, lines, and paragraphs etc. of the text. We might allow though that even ideas coming in a serial stream can be considered "things" in a particular system of sequence spectrum analysis. Thus the following stream.

As the perspective of idealization begins to merge with physical reality, the essential idea within the Heisenberg Uncertainty Principle enters the considerations, because its fundamental generality addresses the notion of how "equal" or "unequal" two things may be established to be.

In VMS studies we have a kind of macroscopic analog to the uncertainty physics of two separately, perhaps even successively detected "free electrons", that is to say "identical charge-transporting actors", when we are transcribing for analysis the mysterious unique hand-scripted Voynich text: are two apparently similar glyphs really intended to convey the same symbol, that is are they symbolically equal in the context, or is a subtle difference a critical unequalness reflecting two different symbols? The more precisely we resolve distinct differences between the two glyphs to see them as individuals, the less precisely we can see them as representing the exact same symbol. By analogy with Heisenberg it is an inescapable cost of existence. And the VMS text is notorious for its uncertainties.

Well of course, in order to obtain a transcript at all, that is in order to proceed without ambiguity, if only experimentally, we are forced to make a decision, we are forced to react one way or another, so we can move on to the next scribble signal. Herein is a philosophical point bridging the idealization of our sequence spectrum formalism and reality's Heisenberg Uncertainty: any two "elements" in a series, if they are to be included at all in an unambiguous reaction, must, regardless of all other gaugings, at the least be either equal in the reaction, or unequal in the reaction. Uncertain or not, the reaction decides one way or another: equal, or unequal. And that, and the counted order in the series is all that we need to say that the reaction sequence exists. And from that we have the philosophical reaction that all there ever was, all that is, and all that ever shall be, is a dance among the possible sequence spectra expressed by {4-5}.

And we might add, perhaps almost humorously, that since it is popularly observed that "history repeats itself", then it stands to good reason that far and wide among all sorts of signals, including those of serially constructed text elements, there exist common clusters of sequence spectra, that is serially correlated groups of sequence spectra echoing invariances, universally significant sequence spectrum clusters, that invite familiarity with them.

Berj / KI3U

[1] J.VS comm. #189 (Vol. II): Sequence Spectra of text-signals and Equal Statistics Analysis
In that communication I employed the term "spectrum" in two different ways, one standard, and the other as developed in #189, and which is the term's use also here.

[2] While it is of course of high interest to find out if any Voynich manuscript text blocks are a cipher of some system, practical or not from one or another viewpoint, say diplomatic communications "back then", nevertheless I want to emphasize that I am more interested in analytic possibilities for sequences, than I am in identifying building blocks for practical cipher systems. This is in tune with Voynich studies being a polymathic field beyond just the solution of the VMS mystery, while at the same time acknowledging the possibility that the Voynich "text" is not necessarily ultimately solely or even at all a record of literal material, and may be something else meaningful. [3]

[3] Taking the variable spacing between "words" and other script quirks in the VMS text very seriously, I have spent considerable effort showing that, hypothetically, blocks of VMS "text" may be, aside from literal information carriers, employing the VMS alphabet elements like mosaic tiles to make pictures, a hand-script text-art akin to the less complex ASCII art of today, most notably in the hypothesized 3D portrait in the upper half of VMS f76r:
J.VS communications #156, #157, and #163 (Vol. II): The Voynich hypothetical f76r text-art portrait: how was it done?

Another Voynich researcher who has contemplated the Voynich text as graphics related material, notably maps, is David Suter (online a.k.a. MONET273) and David's ideas as expressed by him on vms-list from time to time are important reading for anyone interested in the graphical-composition view of the VMS text.

[4] At this stage the y(x) curve is a points defined curve, that is it is defined upon a discreet reference field and frame, with a number function specifying integer values of y, and there is no necessary implication that x is a continuous real variable. However, it may develop in higher analysis that it may be advantageous to let x be real and continuous, and also y(x), and do some transformations on the sequence spectrum curves with the mathematics of continuous variables, and then transform back to a discreet integer variable x, having perhaps obtained valid and interesting results.

[5] A precise distinction between "series of sequence spectra", and "sequence of sequence spectra", still needs to be made, and we must address that in due time. For the present no problems arise here with loose usage of the phrases.

[6] A logical companion function to the high-history function is a similarly defined low-history function, but presently we don't need it.

From: Greg Stachowski
To: "J.VS:"
Date: Fri 05/30/2008 04:10 AM

Subject: J.VS: Materials from Richard Santa-Coloma's visit to the Grolier Club

By kind permission from Richard, copies of the materials he uncovered during his 23 May 2008 visit to the Voynich archives at the Grolier Club, New York, have been placed in the Library as deposit # 0-8-2008-05-23. Included are letters from Newbold to Voynich, Ethel Voynich's notebook on VMS plants, and some of Anne Nill's notes.

The address is:

I anticipate that, should Richard return to the Grolier as he has suggested he might, any further materials will be deposited in the same place.

Greg Stachowski
Librarian, J.VS

From Berj Ensanian
Sent Date 05-31-2008 1:39:17 PM

Subject J.VS: Voynich Biographical Data and "Mrs Anna Mill"

Dear Colleagues

Our Dana Scott has just brought attention [1] to the 2007 English translation with notes by Seamus O'Coigligh, of the 1957 Russian language work:

Our Friend Ethel Lilian Boole/Voynich, by Evgeniya Taratuta

This material, with many pictures, available online as a pdf document, mainly concerns Ethel Voynich's history in the events leading up to the Russian Revolution, and her literary contacts and activities. It has a lot of interesting peripheral information too.

We all know the problems in getting exact information on Miss Nill, presumably never married, among which are variations in the spelling of her name. It appears that this document continues in the tradition of the mysterious Miss Nill: on pages 33-34, and page 48 of Taratuta's manuscript we get "Mrs Anna Mill" and "Anna Mill".

On page 26 is brief information on "Voynich village" in the spurs of the Carpathian mountains.

I had wondered sometime back, in a question to Dana, if Wilfrid Voynich's hand was withered [2]. An 1892 letter given on page 30 appears to clearly suggest Wilfrid had a serious problem with one of his hands.

It continues to puzzle me that we do not come across any indications of the Voynich's having crossed paths with Gurdjieff.

Berj / KI3U

[1] vms-list post: VMs: ELV and Ivan Mikhailovich, 05-31-2008 4:10:45 AM, by Dana Scott.

[2] vms-list post: Re: VMs: Re: The mysterious Miss Nill, Saturday, February 3, 2007 10:57 AM, by Berj.

From: Greg Stachowski
Date: Sat 05/31/2008 04:08 PM

Subject: J.VS: Voynich Biographical Data and "Ivan Kelchevsky"

Referring to the translation of a Russian biography of ELV [1], in J.VS #193 Berj mentioned to the letter quoted on page 30, in the context of WMV's perhaps-injured hand.

It seems to me also worth pointing out another interesting piece of peripheral information provided by this letter and the one on the previous page. That is the alias by which WMV was also known in exile: Ivan Kel'chevsky. It may be that this is why it has been hard to trace his activities in London before c. 1900: we have been looking for the wrong name. Further, it may also be worth looking to see if this alias crops up later, perhaps in the context of book deals which WMV might have wanted to dissociate himself from.


[1] vms-list post: VMs: ELV and Ivan Mikhailovich, 05-31-2008 4:10:45 AM, by Dana Scott.

From: Greg Stachowski
Date: Sun 06/01/2008 03:41 AM

Subject: J.VS: Re: Voynich Biographical Data and "Ivan Kelchevsky"

Following up on my comment yesterday, searching with Google reveals the following in the current catalogue of the second-hand/antiquarian book dealers "Any Amount of Books" of Charing Cross Road, London:

" KHASIN, E. A JEW TO JEWS. (EVREI K EVREYAM.) The Fund Of The Russia Free Press, London, 1892. First Edition. Hardback. 12mo. pp 76. Russian text. Bound in thick card with facsimile of printed cover onset to cover, original wrap bound in. Sl wear, sl tape marks to title page, old catalogue entry for book loosely inserted, original wraps sl frayed and soiled but overall a presentable near vg example of a rear piece. Catalogue of Russian books at rear from a Mr Kelchevsky of Iffley Road Hammersmith and list of contacts for the Russian Free Press in Russian and English on feps throughout world eps USA , France and Switzerland. Anderson 17470. A28338 £40 " [2]



From Berj Ensanian
Sent Date 06-01-2008 10:22:21 AM

Subject J.VS: Re: Voynich Biographical Data and "Ivan Kelchevsky"

In J.VS comm. #195 Greg quoted from the description of the for-sale book:

" Catalogue of Russian books at rear from a Mr Kelchevsky of Iffley Road Hammersmith and list of contacts for the Russian Free Press in Russian and English on feps throughout world eps USA , France and Switzerland. "

That certainly looks intriguing. Excellent find Greg - goes to show there could well be a lot of unrecognized Voynich papers scattered about on both sides of the Atlantic. I've long wondered if Wilfrid perhaps came into possession of the VMS long before 1911 or 1912, and regardless, the more we know of his earlier contacts and haunts the better: there is still the peculiar conflict between Mondragone and an Austrian castle, as the place where WMV obtained the VMS.


From: Greg Stachowski
Date: Sun, 1 Jun 2008 23:25:20 +0200

Subject: J.VS: Re: Voynich Biographical Data and "Ivan Kelchevsky"

In J.VS comm. #196 Berj wrote:

" I've long wondered if Wilfrid perhaps came into possession of the VMS long before 1911 or 1912, and regardless, the more we know of his earlier contacts and haunts the better: there is still the peculiar conflict between Mondragone and an Austrian castle, as the place where WMV obtained the VMS. "


I haven't finished reading this translation yet, but I just noticed that at the end of the PDF are a series of short bios of the major players. These seem to have been added either by the translator or the publisher. There is surprisingly little on Voynich, and no mention of the VMS (!), but his bio (p. 64) includes this:

" Achille Ratti (later Pius XI) was librarian at the Ambrosiana from 1888 to 1912 and from 1912 was vice-prefect of the Vatican Library. Voynich is reported to have made his acquaintance at some stage and to have been on friendly terms with him. "

I do not recall having seen this contact of WMV's mentioned anywhere before: do correct me if I'm wrong. If not, though, it does seem rather relevant: WMV friends with the vice-prefect of the Vatican Library? The future Pope (and, by the way, apostolic vistor to Poland after his stint at the VL)? I could well imagine this was how he got into the Mondagone!

Returning to the letters and "Kelchevsky", ELV's letter on p. 27 is datelined "The Grove, Hammersmith". What is now "Hammersmith Grove" was once "Grove Road" and is long enough to accomodate a no. 149; it does not seem too much of a stretch that this is ELV's "The Grove". It is one street away from and parallel to the Iffley Road mentioned in the book catalogue.


From: Greg Stachowski
Date: Mon, 2 Jun 2008 00:05:20 +0200

Subject: J.VS: Re: Voynich Biographical Data and "Mrs Anna Mill"

In J.VS comm. # 193, Berj wrote:

" It appears that this document continues in the tradition of the mysterious Miss Nill: on pages 33-34, and page 48 of Taratuta's manuscript we get "Mrs Anna Mill" and "Anna Mill". "

I think from context that this is definitely "our" Anne Nill, and these differences are explicable as follows:

1. Anna vs. Anne: in Central and Eastern Europe the form is Anna, and she herself was familiar with it from her German ancestry. It is likely then that either she used that form with the Russians knowing it would be familiar to them, or that they russified Anne to Anna (perhaps confusing a handwritten 'e' with the more familiar 'a' ending of the name).

2. Mill vs. Nill: again I suspect a confusion due to handwriting: in Russian cyrillic 'N' is written as something closer to 'H', and in particular the cursive upper-case 'M' looks not unlike some handwritten forms of the Latin 'N'. If Anne signed her notes by hand, a Russian not entirely familiar with the Latin script might easily have confused the two. See the picture at:

'M' and 'N' are the last two letters on the top line.

3. Mrs vs Miss: I am not really familiar with Russian honorifics, but in Polish, "Mrs" and "Miss" are "Pani" and "Panna", respectively; however one would be very unlikely to use "Panna" for a woman of around sixty regardless of her marital status. If the same holds in Russian, then it seems possible that the mistake is in the translation back from Russian to English. Since the translator seems to have been unfamiliar with WMV and the VMS it seems likely he was unfamiliar with Anne Nill as well, and translated the Russian honorific back as "Mrs" rather than the modern English usage "Ms" or the original "Miss" (at the same time missing the Mill/Nill mistake).


From Berj Ensanian
Sent Date 06-02-2008 4:38:31 PM

Subject J.VS: Re: Voynich Biographical Data and "Ivan Kelchevsky"

In J.VS comm. #197 Greg brought up Wilfrid Voynich's friend Achille Ratti (later Pius XI), who was librarian at the Ambrosiana from 1888 to 1912, and from 1912 was vice-prefect of the Vatican Library.

Greg, Ratti and the Ambrosiana have been on my radar for quite a while - didn't we discuss them off-J a while back? I had even thought we had a J.VS mention of them somewhere, but apparently not. But it would be useful to find out by what avenue they had come onto my radar - the mountain of VMS data is getting so huge it is a major chore keeping any sizeable part of it organized. Perhaps sometime a keywords list in the Library might be started - then itself another maintenance job :)

In any case then it is good that you've brought this out: Ratti has to be a prime suspect for Wilfrid's manuscript leads, if not for more.


From: Greg Stachowski
Date: Mon, 2 Jun 2008 23:15:33 +0200

Subject: J.VS: Re: Voynich Biographical Data and "Ivan Kelchevsky"

In J.VS comm. #199 Berj wrote:

" Ratti and the Ambrosiana have been on my radar for quite a while - didn't we discuss them off-J a while back? I had even thought we had a J.VS mention of them somewhere, but apparently not. "

I don't remember it, and searching my mail archive comes up with nothing. Perhaps you could indeed search at your end and try to find where you came across it.

Anyway, you're right about the mountain growing too big to handle. I shall think about how we can manage the information better.

From: Greg Stachowski
To: J.VS
Date: Sun, 15 Jun 2008 00:56:07 +0200

Subject: J.VS: Palaeography and Image-Processing online paper

Perhaps of interest:


From: Greg Stachowski
To: J.VS
Date: Thu, 26 Jun 2008 02:22:22 +0200

Subject: J.VS: Paper on VMS zodiac crowned nymphs by Robert Teague in Library

Robert's latest paper, "Zodiac Crowned Nymph Star Matches", is now in the J.VS Library as deposit # 5-5-2008-06-16.

Quoting Robert's own description:

" I have identified stars at the positions of the VMs Zodiac's Crowned Nymphs using the precession of the Equinoxes as a mechanism. The question answered was "If a star were at the Crowned Nymph position in 1400 CE, where would it be in 2000 CE?" A list of fixed star positions for the year 2000 was consulted for matches. A match was considered made if a given star was within 1° of the calculated position.

Calculations of star movements were carried out in 50-year increments, and 1° increments between the years 1400 and 1600 CE.

The only time matches were found for all three positions were between 1450 and 1500 (50 year increment) and the closest matches were in 1471 (1° increment). The three stars identified are: Alzirr in Cancer (short of the position by 11 minutes), Foramen in Libra (short by 15 minutes) and Kochab in Leo (short by 5 minutes). "

The URL is


From Berj Ensanian
To Journal of Voynich Studies
Sent Date 06-30-2008 1:27:16 AM

Subject J.VS: Reference Data for Analysis of Signal Sequence Series

Dear Colleagues

In this communication I have attempted to organize some experimental data to serve as reference material in investigations of series of signal sequences in the sense of J.VS communication #191 [1]. This long communication is divided into managable sections as follows:

I. Using hh Super-spectra to measure transformation effects on series of sequences.
II. A simple transformation of a series of sequences all belonging to the same hh-family.
III. The simplest invariance of hh-families under transformation.
IV. Reverse-direction transformation of a mixed series of ramps.
V. Reverse-direction transformation of a Latin text series.
VI. Reverse-direction transformation of the Voynich f68v3.1 text series.
VII. Reverse-direction transformation of the Voynich f68v3.1 text series with "4o" as a single element.
VIII. Reverse-direction transformation of a random numbers series.
IX. Comparative pillow ratios and hh ratios of some series.
X. The PR-function and HHR-function of unified successive series: Moretus vs Hooke. Introducing the U-function.
XI. PR, HHR, and U-functions of Voynich paragraph text-lines in succession.
XII. The SQS Computer Program
XIII. Comments

Calculations were at least triple-checked, but I would appreciate it if you point out to me any errors you find, so that the tables can be corrected if necessary. In the following experiments two ratios are used repeatedly: the PR and HRR, which are explained. The vocabulary and notation are still in development and subject to improvement. Suggestions on that are also welcome.


If we have a series of sequence spectra, say these 8 groups:

{I -1} 123_12345_123_1232_123456_1231_123_12345634

then for the series there exists a distribution of the counts of its sequence spectra, here totaling eight:

{I -2} Spectrum of sequence-spectra for {I -1}

(01) 123 : 3
(02) 1231 : 1
(03) 1232 : 1
(04) 12345 : 1
(05) 123456 : 1
(06) 12345634 : 1

Such a distribution can itself be regarded as a kind of spectrum analysis for series of sequences, and we might refer to such as {I -2} as a super-spectrum. Now, we saw in J.VS communication #191 that every sequence and its sequence spectrum belongs to its own family of hh-spectra [1]. Therefore a similar distribution exists for the hh-spectra. Lets expand {I -2} to include the hh-family affiliations:

{I -3} Super-spectrum for {I -1} with hh-family affiliations

(01) 123 : 3 : 123
(02) 1231 : 1 : 1233
(03) 1232 : 1 : 1233
(04) 12345 : 1 : 12345
(05) 123456 : 1 : 123456
(06) 12345634 : 1 : 12345666

and now show just the distribution of hh-spectrum counts for {I -1} :

{I -4} Super-spectrum of hh-spectra for the series {I -1}

(01) 123: 3
(02) 1233: 2
(03) 12345: 1
(04) 123456: 1
(05) 12345666 : 1

Therefore in {I -1} three members of the series belong to the 123 hh-spectrum family, two members belong to the 1233 family, and so on. With {I -4} we are of course focusing on less information available in {I -1} than compared with the {I -2} analysis. However, in our search for invariances associated with sequence spectra, it seems reasonable that we have a better chance of discovering some of them sooner when we look first at the behaviour of the counts of hh-functions, that is the behaviour of spectral families as a whole, rather than all their family members individually. At this point, of the many ways to branch out further, this next question defines attractive paths to explore:

How do various transformations of a groups-series affect its hh super-spectrum?

Answering the question is some considerable theoretical mathematics work, unless we can find it somewhere already done in a notation suitable for our requirements. We've asked a good question; given our overall priorities it may take us quite a while to gather satisfactory answers, but with each little experimental step along the way we become more familiar with sequences, and might suddenly get a new angle on the VMS text. [2]

One factor is immediately apparent: if any same hh-spectra are to be present before and after transformations, then the before and after series must both have at least some groups of equal spans / widths. If the before and after series have no common spectral spans, then they cannot have common hh-spectra either.

One simple obvious answer is that hh super-spectra are invariant under transformations that merely shuffle, or transpose the groups in a series. Of course that's true first for the groups' sequence super-spectra as individuals - as they might appear in {I -2}. But suppose instead of just shuffling groups, shuffling of both the groups, as well as the elements within the groups, is done. We will see that in some situations, although individual spectrum counts may change, the hh-counts do remain invariant.

For our work we will find it useful to define the hh ratio for groups-sets, the sets typically being series in our work. The hh ratio is a gauge of the hh-spectral bandwidth, per the system used in {I -4}.

{I -5} The hh-spectrum ratio:

HHR = (no. of hh-spectrum components in a set of groups) / (no. of groups in the set)

For the 8-groups series {I -1}, consulting {I -4} we obtain: HHR = 5/8 = 0.6250

For natural language series, or in general series made up of groups that are limited as to their construction, we would expect the HHR to drop off as the series get longer. Thus it may be of interest to investigate the drop-off curve via an HHR-function of the number of groups in a series, and series type / language.


To begin exploring hh-family super-spectra versus transformations, lets borrow from the table {5-7} in J.VS communication #191. There in {#191: 5-7} the sequence neighboring order was defined according to Arabic numbers hierarchy. And in that system, the family of sequences belonging to the hh-function sequence 1222 consists of 4 members, ordered like this:

{II -1} 1211; 1212; 1221; 1222

Now lets consider a groups-series consisting solely of seven 1222 family members:

{II -2} hihi_gaga_gooo_euee_ikki_mooo_afaa

{II -3} 1212_1212_1222_1211_1221_1222_1211

Perhaps, like the VMS text sometimes is, {II -2} is reminiscent of baby talk. Transposing its groups in any way will leave its detailed counts invariant:

{II -4} Super-spectrum of {II -2} with 1222-hh family affiliation:

(01) 1211: 2 : 1222
(02) 1212: 2 : 1222
(03) 1221: 1 : 1222
(04) 1222: 2 : 1222

If we diagrammed just the hh super-spectrum here, it would consist of only one spectral component, 1222, with an amplitude of 7, and the HHR = (1/7) = 0.1429. Low hh ratios are an indication of narrow-band hh family dominance in a series.

Now lets try a transfomation on {II -2} which is merely a reverse-direction sequencing of the series [3], as might arise from boustrophedon:

{II -5} aafa_ooom_ikki_eeue_ooog_agag_ihih

{II -6} 1121_1112_1221_1121_1112_1212_1212

{II -7} Super-spectrum of {II -5} with hh-family affiliations:

(01) 1112 : 2 : 1112
(02) 1121 : 2 : 1122
(03) 1212 : 2 : 1222
(04) 1221 : 1 : 1222

We see that a drastic change has occurred from the transformation, and at the expense of the 1222 hh-family. Two new hh-families, 1112 and 1122, have arisen as a result of the transformation. But, if as in {I -4} we look at just the hh-families super-spectrum:

{II -8} Super-spectrum of hh-spectra for the reverse {II -5}:

(01) 1112 : 2
(02) 1122 : 2
(03) 1222 : 3

we see that 1222 is still the strongest family-component. Metaphorically, we might say that 1222 fought fiercely to keep its family intact against the assault of the reverse-direction transformation, and although it could not keep invariance, and now shares the ground with two new families, it still remains the dominant family. Furthermore, since the direction-reversal was a reversible transformation, a metaphorical reversal of fortunes would bring the situation back to {II -4}. Therefore, considering together the forward and reverse versions of the groups-series, the 1222 hh-family is its dominant one.

The {II -7} and {II -8} super-spectra suggest a pair of more comprehensive super-spectra that include all the hh components:

{II -9} hh super-spectrum for the forward {II -2}:

(01) 1112 : 0
(02) 1122 : 0
(03) 1222 : 7

{II -10} hh super-spectrum for the reverse {II -5}:

(01) 1112 : 2
(02) 1122 : 2
(03) 1222 : 3

With these two super-spectra we can now subtract one from the other, component from component, and form the differential super-spectrum:

{II -11} Differential hh super-spectrum for {II -2} under reverse-direction transformation, {II -10} - {II -9} :

(01) 1112 : +2
(02) 1122 : +2
(03) 1222 : -4

As expected, the sum of the positive and negative changes balances to zero. A little thought on this gives us another invariance condition: if the mirror version of a series is joined / concatenated to the series to form a new twice-as-long series, with or without a group-separator signal between the two concatenated sub-series, then the differential hh super-spectrum of the new series has all zeroes. That is, the differential hh super-spectrum, of a series plus its mirror, is invariant under direction-reversal transformation. Therefore, if with a cryptic series we find its differential hh super-spectrum invariant under direction-reversal, it is worthwhile investigating if the cryptic series is really an inflation constructed by joining a series with its mirror.

The source series, the line {II -2}, had spectra all belonging to the 1222 hh-family. In surveys of series of sequences, the series units, say lines or paragraphs etc., would of course show considerable variety in represented hh-families. Using hh super-spectra we could classify kinds of texts according to hh-family survivals, under specific transformations, with results ranging from invariance to the irreversible vanishing of pre-transformation hh-families.

The {II -11} differential super-spectrum, which shows the original series going from a "monochromatic" spectrum of amplitude 7 to a broader tri-chromatic spectrum, is by analogy reminiscent of an effect between a curve and the curve of its Fourier transform: if one is a broad bell-curve, the other is sharply peaked.


Lets have a look at the simplest invariance of hh-families under transformation. First we state a near-trivial (on account of it being pretty much obvious) theorem:

{III -1} The sequence spectrum of a group of all the same, or all different elements, is invariant under all transpositions of the elements. This follows from the definitions of extremes of wall {1-1} and ramp {1-3} in J.VS comm. #191. This invariance obviously also leaves the hh-spectrum family membership unaffected.

We illustrate this with an example ramp sequence and its sequence spectrum, and a direction reversal transpose:

{III -2} polarity : 1,2,3,4,5,6,7,8,
{III -3} ytiralop : 1,2,3,4,5,6,7,8,

Alternate text lines in a boustrophedon format would effectively transform {III -2} into {III -3}. Let us look at more possibilities flowing from {III -1}. Consider the groups-series {III -4}, and some simple transformations of it:

{III -4} the vms bug hit him

{III -5} The series reversed, perhaps as a result of boustrophedon: mih tih gub smv eht

{III -6} The series with random within-group anagramming: the mvs bug hit mih

{III -7} The groups of the series shuffled, randomly or by some system: him hit the vms bug

More transformations of {III -4} could be had with combinations of those listed, and even others like alternating groups subjected to their elements anagrammed / transpositioned. But their group-framed sequence-spectrum series remains invariant under all the transformations - a series consisting of identical spectral ramps:

{III -8} 123_123_123_123_123


Now lets consider a slightly more complicated 18-ramps series:

{IV -1} the vms draws to it many mixed views and reactions to shed light about its place in history

{IV -2}


Again some invariances pertain here for the entire series, and as an aside it motivates the question:

How do different kinds of groups-series, say VMS and Greek texts, measure up with respect to density of ramps?

We see that {IV -2} contains two appearances of the ramps cluster 12_1234_12345_12345_123 separated by the 123456789 spectrum. Let us see what happens when {IV -1} is taken per boustrophedon direction-reversal:

{IV -3} yrotsih ni ecalp sti tuoba thgil dehs ot snoitcaer dna sweiv dexim ynam ti ot sward smv eht

{IV -4}


As expected, the aforementioned clusters appear as reversed versions about the spectrum 123456789. Both {IV -2} and {IV -4} have the following (selected) ramps clusters:

{IV -5} cluster: count in {IV -2}, count in {IV -4} :

(01) 123_123 : 1, 1
(02) 123_12345 : 2, 2
(03) 12345_123 : 2, 2
(04) 12345_12345 : 2, 2
(05) 12345_123_12345 : 1, 1

However, of course these clusters don't always correspond with the same groups in the two original series, instead arising sometimes from the particular adjacencies in the series. This is the case with the cluster 123_12345 . The counts are 2 and 2, of which one, for both {IV -2} and {IV -4} arises from symmetry as overlap sub-clusters from 12345_123_12345 . But the other appearance is asymmetric: in going from {IV -2} to {IV -4} an isolated 123_12345 vanishes, and an isolated 12345_123 reverses to appear as 123_12345 .

At first this may seem trivial, except perhaps for the curiosity that here the counts remain equal. But, on further thought an interesting analytic question is stimulated:

How do cluster counts, whether arising symmetrically or asymmetrically, vary across different samples, VMS and other, with respect to sequence direction reversal? This question on spectral clusters is clearly related to our beginning question.

Another perspective on this is: how difficult or easy is it to construct a long text, meaningful or "gibberish", whose cluster counts remain more or less invariant with respect to simple direction-reversal transformations?


Lets now look at series of groups that are not all ramps. First we look more closely at the fact that certain constructions of groups, like those of ramps and walls, leave the group's sequence spectrum invariant under direction-reversal transformations, transformations that in symbolism-based analysis could wipe out some n-gram / n-graph relationships, for example:

{V -1} pillow : 123345
{V -2} wollip : 123345

We'll refer to these kinds of groups as "pillows" [4]. Consider this series of 9 groups:

{V -3} how does the pillow density vary across various series

{V -4} 123_1234_123_123345_1234567_1234_123455_1234567_123421

The only group here that is not a pillow is "across", as we can see from:

{V -5} across : 123455
{V -6} ssorca : 112345

Let us define PR, the pillow ratio for a set (typically a series) of n groups, of which p are pillows:

{V -7} PR = p/n

We see that the range for the possible PR is 0-1. For the above series {V -3} we have PR = 8/9 = 0.8889

Earlier in section IV. we implied the ramps ratio, RR. Our current explorations favor working with the more general PR. The PR (and likewise the RR) may be generalized to a PR-function that can be handy for detecting changes in PR as we move through a long series. [5]

Now then, here is a 13-groups series having 9 pillows, 8 of them ramps, borrowed from the Latin Vulgate Genesis chapter:

{V -8} in principio creavit deus caelum et terram terra autem erat inanis et vacua

{V -9} 12_123453136_1234567_1234_123456_12_123345_12334_12345_1234_123214_12_12342

For {V -8} we calculate PR = 9/13 = 0.6923 which will of course be the same for the reversed series:

{V -10} aucav te sinani tare metua arret marret te muleac sued tivaerc oipicnirp ni

{V -11} 12314_12_123432_1234_12345_12234_123345_12_123456_1234_1234567_123245263_12

We know that the spectra of the 9 pillows are invariant under the reverse-direction transformation, so lets discard them and look just at the so-abbreviated super-spectra:

{V -12} Partial super-spectrum (no pillows) for {V -9}, with hh-family affiliations:

(01) 12234 : 0 : 12234
(02) 12314 : 0 : 12334
(03) 12334 : 1 : 12334
(04) 12342 : 1 : 12344
(05) 123214 : 1 : 123334
(06) 123432 : 0 : 123444
(07) 123245263 : 0 : 123345566
(08) 123453136 : 1 : 123455556

{V -13} Partial super-spectrum (no pillows) for {V -11}, with hh-family affiliations:

(01) 12234 : 1 : 12234
(02) 12314 : 1 : 12334
(03) 12334 : 0 : 12334
(04) 12342 : 0 : 12344
(05) 123214 : 0 : 123334
(06) 123432 : 1 : 123444
(07) 123245263 : 1 : 123345566
(08) 123453136 : 0 : 123455556

We see that the 12334 hh-spectrum is an invariant feature of the original Latin source series under the transformation. The significance of this, to this point, is that this invariance occurred among the few non-pillows of the series. The complete differential picture for the transformation is:

{V -14} Differential hh super-spectrum for {V -8} under direction-reversal, (reversed super - forward super) :

(01) 12 : 0
(02) 1234 : 0
(03) 12234 : +1
(04) 12334 : 0
(05) 12344 : -1
(06) 12345 : 0
(07) 123334 : -1
(08) 123345 : 0
(09) 123444 : +1
(10) 123456 : 0
(11) 1234567 : 0
(12) 123345566 : +1
(13) 123455556 : -1


Lets now try a line of Voynich text for a source series. We'll go with the first line of the f68v3 "spiral galaxy" panel. Its illustration even looks like it could plausibly be commentary on creation like the beginning of Genesis. GC's voyn_101.txt transcription [6] has the 68v3.1 line as:

{VI -1} k1c89.1cj19.8aI89.2oe.h1coe9.1okcoe.2oe,s.1c9.2o8am.1ck2c89.ok2o.4ooko,sd9-

After carefully examining the Beinecke provided hi-res SID image of f68v3 we will fairly closely accept GC's transcription of 14 groups, thereby ignoring the possibility of an incognito symbol in the second-last group (the apparent GC-k). We will, using his alphabet, make some changes:

a.) expand I to ii
b.) expand 8am to 8aiiN
c.) expand d to ccc

For our present analytics we also take the logical step of equalizing the inter-group spaces. And, instead of using GC's periods and commas for inter-group spaces, we will use "_" as usual. And so we have:

{VI -2} k1c89_1cj19_8aii89_2oe_h1coe9_1okcoe_2oe_s_1c9_2o8aiiN_1ck2c89_ok2o_4ooko_sccc9

{VI -3} 12345_12314_123314_123_123456_123425_123_1_123_1234556_1234256_1231_12232_12223

The pillow ratio is: PR = 9/14 = 0.6429 which is fairly close to the Latin Genesis in the previous section. We note that the non-pillows of the f68v3.1 series are distributed in the beginning and ending portions of the series, away from the middle portion. This reminds us of Currier's observation on VMS lines based on his symbols-frequencies counts versus line-portion. Interestingly, the Latin series {V -9} is approximately similar in this regard, but presently this cannot be taken as much more than a coincidence. The plotted curve of a simple well-designed PR-function as per [4] would plainly show this as peaks at the beginning and end surrounding a valley. As an experimental side-track we might try matching this spectral series to a sentence in another language. [7]

The reverse-direction series are:

{VI -4} 9cccs_okoo4_o2ko_98c2kc1_Niia8o2_9c1_s_eo2_eocko1_9eoc1h_eo2_98iia8_91jc1_98c1k

{VI -5} 12223_12113_1231_1234536_1223456_123_1_123_123425_123456_123_123342_12342_12345

We already know that the hh-spectra of the pillows remain invariant. To sift out the more subtle results of the reverse-direction transform, lets start over and discard the 9 pillows in {VI -1}:

{VI -6} 1cj19_8aii89_2o8aiiN_1ck2c89_4ooko

{VI -7} 12314_123314_1234556_1234256_12232

Almost two-thirds of the series has been thrown out! Not to worry, this will not affect what we are investigating at the moment. Lets continue: now the direction-reversal of {VI -6}:

{VI -8} okoo4_98c2kc1_Niia8o2_98iia8_91jc1

{VI -9} 12113_1234536_1223456_123342_12342

Now lets compare the groups, their spectra, and hh-family affiliations:

{VI -10} group, spectrum, hh-family for the forward {VI -6}:

(01) 4ooko : 12232 : 12233
(02) 1cj19 : 12314 : 12334
(03) 8aii89 : 123314 : 123334
(04) 1ck2c89 : 1234256 : 1234456
(05) 2o8aiiN : 1234556 : 1234556

{VI -11} group, spectrum, hh-family for the reverse {VI -8}:

(01) okoo4 : 12113 : 12223
(02) 91jc1: 12342 : 12344
(03) 98iia8 : 123342 : 123344
(04) Niia8o2 : 1223456 : 1223456
(05) 98c2kc1 : 1234536 : 1234556

We can now see what we were after detecting. The transformation from forward to reverse has erased the representation of four hh-families and replaced them with different ones. But, the hh-family 1234556 has survived the transformation intact, more so interesting because its group in the forward series and its group in the reverse series are entirely different groups. In the forward series the group 2o8aiiN was the sole appearing member of the hh-family 1234556. In the reverse series the group 98c2kc1 is the sole appearing member of the 1234556 hh-family.

We discarded the pillows from the original series because we already knew their hh-family affiliations would remain invariant under the transformation. Here we see a more general case of hh-family representation intactness, and even invariance in its count: the groups 2o8aiiN and 98c2kc1, and their reversed versions, are not pillows. Yet their roles under the transformation are such so as to preserve the 1234556 hh-family. We saw a similar thing happen in the previous section with the Latin.

Altogether then, with the pillows figured in, the VMS f68v3.1 series is highly resistant to a change in its hh-spectra under reverse-direction transformation - not quite complete invariance, but a significant degree of survival. It is this that reinforces the analytic usefulness of hh-spectra in investigating series of sequences - the changes that do occur under various transformations are likely to be well characteristic of the series. To see the reasoning here, lets show the complete before and after-transformation super-spectrums of the hh-spectra (complete insofar as hh-spectra appear in either):

{VI -12} Super-spectrum of hh-families for the forward VMS f68v3.1 series {VI -2} with HHR = 12/14 = 0.8571 :

(01) 1 : 1
(02) 123 : 3
(03) 1233 : 1
(04) 12223 : 1
(05) 12233 : 1
(06) 12334 : 1
(07) 12344 : 0
(08) 12345 : 1
(09) 123334 : 1
(10) 123344 : 0
(11) 123445 : 1
(12) 123456 : 1
(13) 1223456 : 0
(14) 1234456 : 1
(15) 1234556 : 1

{VI -13} Super-spectrum of hh-families for the reversed VMS f68v3.1 series {VI -4} with HHR = 11/14 = 0.7857 :

(01) 1 : 1
(02) 123 : 3
(03) 1233 : 1
(04) 12223 : 2
(05) 12233 : 0
(06) 12334 : 0
(07) 12344 : 1
(08) 12345 : 1
(09) 123334 : 0
(10) 123344 : 1
(11) 123445 : 1
(12) 123456 : 1
(13) 1223456 : 1
(14) 1234456 : 0
(15) 1234556 : 1

We note the differences in HHR between the forward and reversed series.

{VI -14} Differential hh super-spectrum for VMS f68v3.1 : {VI -13}-{VI -12}

(01) 1 : 0
(02) 123 : 0
(03) 1233 : 0
(04) 12223 : 1
(05) 12233 : -1
(06) 12334 : -1
(07) 12344 : 1
(08) 12345 : 0
(09) 123334 : -1
(10) 123344 : 1
(11) 123445 : 0
(12) 123456 : 0
(13) 1223456 : 1
(14) 1234456 : -1
(15) 1234556 : 0

The super-spectra can of course be taken as points-curves and subjected to curve analysis, including transformations between them.


The common "4o" in Voynich text has long been taken as a pair of distinct glyphs, a digraph of "4" and "o". A "4" without an "o" immediately to its right is quite rare in the VMS text. However, when we look closely at the "4o" examples in the VMS, we see them scripted almost always with the 4 and the o connected, as if the whole thing was a single text element. This motivates investigating the VMS text transcribed so that "4o" is a single character. The observations should be useful also in considerations of spellings - archaic versus modern.

Unfortunately the common Voynich transcription alphabets do not make it easy to transcribe "4o" as a single character - it is my opinion that this is a deficiency that needs correcting. Of course with signal transcription like we are using for sequences, a direct-from-VMS-textpage transcription would have no problem taking the "4o" as a single sequence-thing or sequence signal unit.

To have a look at the effect on the previous f68v3.1 analysis when the "4o" in that line is taken as a single character, we will have to improvise upon the GC-based transcription a little.

In f68v3.1 per {VI -2} and {VI -4} the groups of concern appear as:

{VII -1} 4ooko : 12232 : 12233
{VII -2} okoo4 : 12113 : 12223

So they are non-pillows, and also belong to different hh-families. Let us improvise transcription and make the "4o" portion a single character by just replacing it with "4":

{VII -3} 4oko : 1232 : 1233
{VII -4} oko4 : 1213 : 1223

Again, the group and its reverse are non-pillows and their hh-family affiliations are different. Therefore the PR in the previous section VI. is unaffected but the hh spectra are of course affected by there taking "4o" as a single character instead of a digraph.

A quite common VMS word is GC-4ohoe . It is a pillow. Lets examine it as per just now with 4ooko.

{VII -5} 4ohoe : 12324 : 12334
{VII -6} eoho4 : 12324 : 12334

{VII -7} 4hoe : 1234 : 1234
{VII -8} eoh4 : 1234 : 1234

We see that treating the "4o" as a single glyph changes it from a complicated pillow to a simple ramp pillow.

Lets try another common VMS "4o" word: GC-4ohco89 :

{VII -9 } 4ohco89 : 1234256 : 1234456
{VII -10} 98ocho4 : 1234536 : 1234556

{VII -11} 4hco89 : 123456 : 123456
{VII -12} 98och4 : 123456 : 123456

This is the most radical change yet: it goes from a non-pillow, to a simple ramp pillow.

Overall, we might consider that when having some almost-but-not-quite-working-problem in symbols-based deciphering attacks on VMS text series containing 4o groups, that if the spectral changes resulting from changing the 4o-digraph to the 4-unigraph was a spectrally mild change, as for example with GC-4ohoe, then it might be worth a try to see if the deciphering attack improves.


Lets devise a way to compare the VMS f68v3.1 series with a series of "random" numbers in some fair way. The VMS series {VI -2} is characterized by:

{VIII -1}

number of groups in the series = 14
range of group lengths: 1 - 7
average group-length (agl) = 66/14 = 4.71
maximum number of different alphabet letters in any group = 6

We need a test series of numbers, apparently random, that fits the above characteristics. We'll here skip discussion of the problems that arise in obtaining a "random" series of numbers. Lets proceed and create a suitable random test series with an easily generalized scheme, as follows:

{VIII -2} Obtain a random series of 14 integers from the integer set 1 - 7, such that the average length is as close to 4.7 as practical. These integers will fix the lengths in the test series.
{VIII -3} Obtain a second random series, of somewhat more than 14 integers, from the set 1 - 9999999. These are the raw test series members, to be length-formatted.
{VIII -4} Impose the lengths series onto the raw members series in some way, say picking off from the left of the raw numbers. Discard excess length from a raw member if it has it. If a raw member is too short, then join it to the next raw number. Before imposing length upon raw, if the result will have more than 6 different numerals, then throw the raw out. For example, don't use 1234567 as a raw.
{VIII -5} In the result series regard the Arabic numerals as if they were alphabet letters, and form the corresponding series of sequence-spectra.

We will consider the result to be "a random series of random sequences". For a random integer generator I used the one provided online by RANDOM.ORG [8]. After several trials I obtained for a lengths series:

{VIII -6} 7, 4, 6, 1, 5, 7, 4, 7, 3, 4, 4, 4, 5, 5

Its average length = 66/14 = 4.71

For the raw series I obtained:

{VIII -7} 365977, 1585456, 6363868, 9808814, 5815034, 7634155, 5885606, 4546736, 5447807, 2234775, 2149439, 1505886, 531478, 4449835, 4622978, 5449017, 8112705, 9598571, 4520162, 813542

{VIII -8} The constructed random numbers test series:


{VIII -9} for which the random sequence-spectrum series is:


We observe that the non-pillows are distributed somewhat more randomly across this random series, this contrasting with what we saw with the VMS f68v3.1 series.

{VIII -10} The reverse random sequence-spectrum series:


There are 6 pillows: 1212, 1, 12345, 1234, 1234, 12345

Therefore, for the random numbers test series, or its reverse, PR = 6/14 = 0.4286

I repeated the above with another set of numbers generated with the RANDOM.ORG generator where the average length turned out to be an un-usable too-low 3.786. But, its PR was 7/14 = 0.500 and this got me to thinking about the possibility of DEFINING a "random series of sequences" to possess certain characteristics that include a PR of, or approximately 0.5. Then, comparitive classifications of sequences series by their PR's would have equal ranges above and below 0.5 to fall into, perhaps leading to easy recognition of certain types of series. Coincidentally, as we will see, here the random series, and its reversed direction series, have the same HHR. This is fortuitous, and suggests that the definition of random series include invariant HRR under direction reversal, by analogy with the bandwidth of white noise remaining the same in a given physical system, when in its analysis the time variable t is replaced with -t, that is the noise sampling is run backwards in time.

Continuing, lets have a look at the super-spectra:

{VIII -11} Super-spectrum, and corresponding hh-spectra for the forward random series {VIII -9}:

(01) 1 : 1 : 1
(02) 112: 1 : 112
(03) 1212 : 1 : 1222
(04) 1213 : 1 : 1223
(05) 1232 : 1 : 1233
(06) 1234 : 2 : 1234
(07) 11123 : 1 : 11123
(08) 12345 : 2 : 12345
(09) 123224 : 1 : 123334
(10) 1221343 : 1 : 1222344
(11) 1223453 : 1 : 1223455
(12) 1234556 : 1 : 1234556

{VIII -12} Super-spectrum, and corresponding hh-spectra for the reverse random series {VIII -10}:

(01) 1 : 1 : 1
(02) 122 : 1 : 122
(03) 1212 : 1 : 1222
(04) 1213 : 1 : 1223
(05) 1232 : 1 : 1233
(06) 1234 : 2 : 1234
(07) 12333 : 1 : 12333
(08) 12345 : 2 : 12345
(09) 122324 : 1 : 122334
(10) 1213443 : 1 : 1223444
(11) 1223456 : 1 : 1223456
(12) 1231445 : 1 : 1233445

{VIII -13} Super-spectrum of hh-families for the forward random series {VIII -9} with HHR = 12/14 = 0.8571 :

(01) 1 : 1
(02) 112 : 1
(03) 122 : 0
(04) 1222 : 1
(05) 1223 : 1
(06) 1233 : 1
(07) 1234 : 2
(08) 11123 : 1
(09) 12333 : 0
(10) 12345 : 2
(11) 122334 : 0
(12) 123334 : 1
(13) 1222344 : 1
(14) 1223444 : 0
(15) 1223455 : 1
(16) 1223456 : 0
(17) 1233445 : 0
(18) 1234556 : 1

{VIII -14} Super-spectrum of hh-families for the reverse random series {VIII -10} with HHR = 12/14 = 0.8571 :

(01) 1 : 1
(02) 112 : 0
(03) 122 : 1
(04) 1222 : 1
(05) 1223 : 1
(06) 1233 : 1
(07) 1234 : 2
(08) 11123 : 0
(09) 12333 : 1
(10) 12345 : 2
(11) 122334 : 1
(12) 123334 : 0
(13) 1222344 : 0
(14) 1223444 : 1
(15) 1223455 : 0
(16) 1223456 : 1
(17) 1233445 : 1
(18) 1234556 : 0

{VIII -15} Differential hh super-spectrum for random series: {VIII -14}-{VIII -13}

(01) 1 : 0
(02) 112 : -1
(03) 122 : +1
(04) 1222 : 0
(05) 1223 : 0
(06) 1233 : 0
(07) 1234 : 0
(08) 11123 : -1
(09) 12333 : +1
(10) 12345 : 0
(11) 122334 : +1
(12) 123334 : -1
(13) 1222344 : -1
(14) 1223444 : +1
(15) 1223455 : -1
(16) 1223456 : +1
(17) 1233445 : +1
(18) 1234556 : -1

We see with the random series, with its PR = 0.4286, that 12 of 18 hh spectral components, or 67%, change during the reverse-direction transformation. In contrast, with the VMS f68v3.1 series, PR = 0.6429, we see from {VI -14} that 8 of 15 components, or 53% of the total relevant hh super-spectrum changes. The Latin series of section V. with its PR = 0.8889 had a 47% change. And, the section IV. English sentence of 18 ramps, would have a PR = 1.0 and 0% change.

This is all consistent: the sequence spectra of pillows remain invariant under reversing transformations, and therefore also their hh-spectra remain invariant, and so therefore we expect the hh super-spectra of series with higher PR's to change less under such transformations, and vice versa. This is a tendency, but not the only determining factor - we saw an example earlier with the hh-1222 baby-talk series of {II -2}, which when undergoing transformation had its hh- super-spectra {II -9} and {II -10} show 100% of the components changing; the PR for the {II -2} series is a relatively modestly-low 3/7 = 0.429 and the full 100% change comes more from the series being entirely hh-1222 family members. In contrast, we have also earlier seen a couple of times, that non-pillows in series can support hh-invariance under reverse-direction transformation.

Presently it appears that within the scope of these few experiments, the behavior of the Voynich f68v3.1 text is something like a cross between the Latin text, and the random numbers series.


To have them handy all together, we list here the PR's along with other data of the example series we worked with above, plus data for a few more series. As before, the percent change refers to percent of components affected among the total of components in the hh super-spectrum, under the direction-reversal transformation. The amounts by which individual components change is not figured in. The HHR is for the un-transformed series.

{IX -1} Comparisons of various series under reverse-direction transformation:

* Mixed ramps long English sentence {IV -1}
PR = 18/18 = 1.0000; RPR = 18/18 = 1.0000; HHR = 6/18 = 0.3333; xfrm change = 0/18 = 0%

* Start of Greek N.T. Gospel of John [9]
PR = 17/17 = 1.0000; RPR = 14/17 = 0.8235; HHR = 5/17 = 0.2941; xfrm change = 0/5 = 0%

* Equal ramps English vms bug sentence {III -4}
PR = 5/5 = 1.0000; RPR = 5/5 = 1.0000; HHR = 1/5 = 0.2000; xfrm change = 0/5 = 0%

* All-ramps-but-one English sentence {V -3}
PR = 8/9 = 0.8889; RPR = 6/8 = 0.7500; HHR = 6/9 = 0.6667; xfrm change = 2/7 = 28.6%

* Rhyming German Proverb [10]
PR = 7/9 = 0.7778; RPR = 6/7 = 0.8571; HHR = 6/9 = 0.6667; xfrm change = 3/8 = 37.5%

* Reverend Drury's stammering [14]
PR = 122/158 = 0.7722; RPR = 112/122 = 0.9180; HHR = 25/158 = 0.1582; xfrm change = 29/37 = 78.4%

* De-coded radiotelegraph series [11]
PR = 10/13 = 0.7692; RPR = 9/10 = 0.9000; HHR = 8/13 = 0.6154; xfrm change = 6/11 = 54.5%

* Mixed series {I -1}
PR = 6/8 = 0.7500; RPR = 5/6 = 0.8333; HHR = 5/8 = 0.6250; xfrm change = 4/7 = 57.1%

* Beginning of Latin Genesis {V -8}
PR = 9/13 = 0.6923; RPR = 8/9 = 0.8889; HHR = 10/13 = 0.7692; xfrm change = 6/13 = 46.2%

* Friedman's 1959 VMS Anagram [13]
PR = 13/19 = 0.6842; RPR = 12/13 = 0.9231; HHR = 13/19 = 0.6842; xfrm change = 12/19 = 63.2%

* Voynich f68v3.1 text-line {VI -2}
PR = 9/14 = 0.6429; RPR = 6/9 = 0.6667; HHR = 12/14 = 0.8571; xfrm change = 8/15 = 53.3%

* Binary bytes series [15]
PR = 7/13 = 0.5384616; RPR = 0/7 = 0.0000; HHR = 6/13 = 0.4615; xfrm change = 5/7 = 71.4%

* Random numbers series fair reference for VMS f68v3.1 with agl=4.71 {VIII -8}
PR = 6/14 = 0.4286; RPR = 5/6 = 0.8333; HHR = 12/14 = 0.8571; xfrm change = 12/18 = 66.7%

* All hh-1222 "baby-talk" series {II -2}
PR = 3/7 = 0.4286; RPR = 0/3 = 0.0000; HHR = 1/7 = 0.1429; xfrm change = 3/3 = 100%

* All non-pillows English sentence [12]
PR = 0/13 = 0.0000; RPR = 0/0 ; HHR = 12/13 = 0.9231; xfrm change = 25/25 = 100%

We note the table shows that English sentences can range from PR=1 to PR=0, and 0% to 100% change in the differential hh super-spectrum for reverse-direction transformation. This is likely true for many languages. But it would also seem likely that different languages prefer their own ranges of PR for most of their sentences.

The table shows a general pattern: when a series contains pillows, the majority of them are ramps. If most of the groups in a series are short, then this would not be surprising. Either way, this alone makes ramps attractive as good potential spectrum cluster markers. But the baby-talk series is a counter-example.

It is noteworthy that Friedman's constructed anagrammatic English sentence stands out with its PR, HHR, and transform change ratios nearly all the same. The mixed series of {I -1} and the decoded radiotelegraph series seem to be next closest to this behaviour, and all their RPR's are not far apart either.

The Drury stutter series is much longer than the others, and as anticipated, its HHR seems to have leveled off low. Lets have a rough look at its HHR drop-off curve: we'll abruptly shorten the series at about halfway through. The thus shortened series has HHR = 19/75 = 0.2533. Shortening again to about the first quarter of the original series we get HHR = 13/43 = 0.3023. Shortening one more time again by about half to get into the range of the longest of the other series above, we get HHR = 10/25 = 0.4000, which is among the lower HHR's in the table - Drury's speech seems to stammer across ramps. The progression of HHR's of the stutters series, approximately doubling in length with each step, is then: 0.4000, 0.3023, 0.2533, 0.1582.

For detailed assessment of the HHR curve , an HHR-function of the progressively expanding series, by groups added one per analytic step, starting with the first group, is necessary. Lets obtain some reference data in this vein. We define the function:

{IX -2} HHR{Gj} for a sequence-groups series where:

Gi = ith group of the series, with G1 = 1st group, and Gn = last group in the series, and {Gj} denotes the set of groups i=1 to i=j. Therefore for example, HHR{G4} is the HHR calculated for the first four groups of a series (here n => 4) and the set is comprised of groups G1, G2, G3, and G4. And so on.

{IX -3} j: HHR{Gj} for Latin {V -8} : random nos. {VIII -8} : VMS f68v3.1{VI -2} : radiotelegraph [11] : bytes [15]

01: 1.0000 : 1.0000 : 1.0000 : 1.0000 : 1.0000
02: 1.0000 : 1.0000 : 1.0000 : 1.0000 : 1.0000
03: 1.0000 : 1.0000 : 1.0000 : 1.0000 : 0.6667
04: 1.0000 : 1.0000 : 1.0000 : 1.0000 : 0.7500
05: 1.0000 : 1.0000 : 1.0000 : 0.8000 : 0.6000
06: 0.8333 : 1.0000 : 1.0000 : 0.6667 : 0.5000
07: 0.8571 : 1.0000 : 0.8571 : 0.7143 : 0.5714
08: 0.8750 : 1.0000 : 0.8750 : 0.6250 : 0.6250
09: 0.8889 : 1.0000 : 0.7778 : 0.6667 : 0.6667
10: 0.8000 : 1.0000 : 0.8000 : 0.6000 : 0.6000
11: 0.8182 : 1.0000 : 0.8182 : 0.6364 : 0.5455
12: 0.7500 : 0.9167 : 0.8333 : 0.5833 : 0.5000
13: 0.7692 : 0.8462 : 0.8462 : 0.6154 : 0.4615
14: x.xxxx : 0.8571 : 0.8571 : x.xxxx : x.xxxx

As expected, the random numbers series maintains wideband behavior most tenaciously. Interestingly, except for the random bytes, the radiotelegraph curve is the earliest to drop off into more or less narrower bandwidth stability, it by nature able to communicate the most with the least, another pleasing little analogy with communications physics in these analytics. The bytes series, with all its groups fixed to the same length and consisting of only 1 or 2 unique signals, is thus highly restricted as to the structure of its groups, and therefore we expect its hh spectrography to be very narrow. For example, all bytes of the form 01XXXXXX and 10XXXXXX are members of the 12222222 hh-spectrum family. Lets have a quick look at the groups in the bytes series to fully appreciate how its narrow-band hh-spectral behavior comes about:

{IX -4} For the [15] binary bytes series. Group : sequence-spectrum : hh-spectrum, in spectral-neighbor order:

01 P: 00000000 : 11111111 : 11111111
02 P: 11111111 : 11111111 : 11111111
03 : 00000001 : 11111112 : 11111112
04 : 11111101 : 11111121 : 11111122
05 : 00001000 : 11112111 : 11112222
06 P: 11110000 : 11112222 : 11112222
07 : 00110111 : 11221222 : 11222222
08 P: 11000011 : 11222211 : 11222222
09 P: 01010101 : 12121212 : 12222222
10 P: 10101010 : 12121212 : 12222222
11 P: 01100110 : 12211221 : 12222222
12 : 10010010 : 12212212 : 12222222
13 : 10000011 : 12222211 : 12222222

As for the Voynich curve, its behaviour seems to oscillate between the behaviors of the random numbers and the biblical Latin. From section VIII. we already had indications suggesting that the VMS f68v3.1 series acts like a random numbers and Latin hybrid.

Granted, the five series tabulated in {IX -3} are short ones, but two represent complete messages, we have Currier's word that the VMS series, being a VMS text-line, ought to be considered a functional entity, the random numbers and random bytes series behave as expected even though they are short, and above all, we expect most of the dramatic action of HHR{Gj} to be in the early part of series of any length when the groups of the series are restricted by some rules, say grammar, as to their construction. In any case, we have only begun to investigate these things and always look forward to new surprises further along. Needless to say, we could define various dHHR{Gj} and plot difference functions too.


Let us now choose some series that are connected in some way by a common thread, in other words a non-arbitrary super-series of series, and see how the PR and HHR vary from series to series. It will be convenient to define dPR and dHHR according to:

{X -1} dPRij = PRj - PRi where j = i + 1

In the following the ith PR and ith HHR will be the PR and HHR of the ith text-line. When there is no confusion, the i and j subscripts can be dropped.

For analysis let us take some successive lines from the 8 JAN 1639 Latin letter of Fr. Moretus to Fr. Kircher. We'll use the unpolished available transcription given in file MtoK8JAN1639.txt, as it is in the J.VS Library [16]. Here from it are the nine lines 3 to 11:

{X -2} Taken from MtoK8JAN1639.txt

03: Quatord ecim dies sunt, quando R.V. scribebim, rogabamyz
04: Veram mensurum palmi et pedis Veteris Romani. iam autem
05: ab octiduo M. Etliny C cum quo mi tui de eo meo desiderio ali=
06: quindo fermo inciderat J mi tui exhibuit Vtramque manu
07: R.V. positer meam fsem et exspectationem citius descrip-
08: tam. Palmi^ achitecturici mensura a R.V. annotata omnino ea en
09: quam antea accepionm. Sed pedis Romani mensura cum nulla
10: meanim conue nit, Vide magit maneo perplexus; si tamen R.V.
11: eam accepit au fide digno monumento, Vtar ea Quamguam Veriore.

03: PR = 6/8 = 0.7500 :: HHR = 7/8 = 0.8750
04: PR = 7/9 = 0.7778 : dPR = +0.0278 :: HHR = 6/9 = 0.6667 : dHHR = -0.2083
05: PR = 13/14 = 0.9286 : dPR = +0.1508 :: HHR = 7/14 = 0.5000 : dHHR = -0.1667
06: PR = 7/9 = 0.7778 : dPR = -0.1508 :: HHR = 9/9 = 1.0000 : dHHR = +0.5000
07: PR = 5/8 = 0.6250 : dPR = -0.1528 :: HHR = 7/8 = 0.8750 : dHHR = -0.1250
08: PR = 6/10 = 0.6000 : dPR = -0.0250 :: HHR = 9/10 = 0.9000 : dHHR = +0.0250
09: PR = 7/9 = 0.7778 : dPR = +0.1778 :: HHR = 8/9 = 0.8889 : dHHR = -0.0111
10: PR = 8/10 = 0.8000 : dPR = +0.0222 :: HHR = 6/10 = 0.6000 : dHHR = -0.2889
11: PR = 7/10 = 0.7000 : dPR = -0.1000 :: HHR = 8/10 = 0.8000 : dHHR = +0.2000

agl = 433/85 = 5.0941
Average PR = 66/87 = 0.7586
PR max/min: (0.9286 / 0.6000) = 1.5477
Average HHR = 66/87 = 0.7701
HHR max/min: (1.0000 / 0.5000) = 2.0000

We note that the HHR doubles going from line 5 to line 6, and the average PR and HHR are very nearly the same.

We just now analyzed an early raw transcription of the signals on the paper of Moretus's letter with the unification of the nine series being that they are successive physical lines-units on the document. We took the punctuation marks as legitimate signal units, and in most cases it made no difference affecting the pillow or non-pillow status of the words they were attached to.

Now lets do it again differently. We will recast the successive series according to sentences. We will then throw out the commas and sentence periods and such, and for convenience use all lower-case letters. We get the following super-series of four lines with an overall average group-length of agl = 433/85 = 5.094.

{X -3} The Moretus text from {X -2} recast according to sentences:


iam_autem_ab_octiduo_m._etliny_c_cum_quo_mi_tui_de_eo_meo_desiderio_aliquindo_fermo_inciderat_j_mi_tui_ exhibuit_vtramque_manu_r.v._positer_meam_fsem_et_exspectationem_citius_descriptam

03: palmi^_achitecturici_mensura_a_r.v._annotata_omnino_ea_en_quam_antea_accepionm

sed_pedis_romani_mensura_cum_nulla_meanim_conue_nit_vide_magit_maneo_perplexus_si_tamen_r.v._ eam_accepit_au_fide_digno_monumento_vtar_ea_quamguam_veriore

01: PR = 11/15 = 0.7333 :: HHR = 10/15 = 0.6667
02: PR = 25/32 = 0.7813 : dPR = +0.0479 :: HHR = 17/32 = 0.5313 : dHHR = -0.1354
03: PR = 7/12 = 0.5833 : dPR = -0.1979 :: HHR = 11/12 = 0.9167 : dHHR = +0.3854
04: PR = 19/26 = 0.7308 : dPR = +0.1474 :: HHR = 14/26 = 0.5385 : dHHR = -0.3782

agl = 433/85 = 5.0941
Average PR = 62/85 = 0.7294
PR max/min: (0.7813 / 0.5833) = 1.3395
Average HHR = 52/85 = 0.6118
HHR max/min: (0.9167 / 0.5313) = 1.7255

The PR data can be plotted as PR-functions and dPR-functions versus series / line, yielding points-curves, in the last case very short curves. Likewise with the HHR data. In effect variable-window PR-functions have been run [5]. Even though the last run was only four points worth, nevertheless it is interesting that the variations in the PR-function and HHR-function between {X -2} and {X -3} are very noticable. This leads to the question:

Could consistently large variations in the PR-function and HHR-function of successive lines series, be an indication that logical units akin to sentences have been disrupted?

If for Moretus's Latin here we take the average of averages:

{X -4} Average of the averages of {X -2} and {X -3}: PR = 128/172 = 0.7442

then it is not far different from the PR = 0.6923 for the beginning series of the Latin Genesis from {V -8}, as we can see from the ratio: (0.7442 / 0.6923) = 1.075. We could substitute the Genesis in place of one of the Moretus lines and not see much difference in the average PR of the super-series. Of course mathematically the average PR must equal the PR calculated on the set of all groups in the super-series.

And so we have a first primitive idea of the variation of the pillow and hh ratios with a super-series of natural language: Latin.

So then now let us try a super-series of English. I adapted the following from Robert Hooke's 1665 Micrographia [17]. The average group length turned out to be agl = 416/104 = 4.000. In order to get four series reasonably close in dimensions to the four Moretus series of {X -3} I had to break up Hooke's long sentences into logical self-standing sub-sentences:

{X -5} Adapted from Hooke's Micrographia: Observ. II. Of the Edge of a Razor.



a_razor_doth_appear_to_be_a_body_of_a_very_neat_and_curious_aspect_till_more_closely_viewed_by_the_ microscope_and_there_we_may_observe_its_very_edge_to_be_of_all_kind_of_shapes_except_what_it_should_be


01: PR = 19/24 = 0.7917 :: HHR = 10/24 = 0.4167
02: PR = 8/14 = 0.5714 : dPR = -0.2202 :: HHR = 9/14 = 0.6429 : dHHR = +0.2262
03: PR = 34/42 = 0.8095 : dPR = +0.2381 :: HHR = 15/42 = 0.3571 : dHHR = -0.2857
04: PR = 22/24 = 0.9167 : dPR = +0.1071 :: HHR = 8/24 = 0.3333 : dHHR = -0.02381

agl = 4.0000
Average PR = 83/104 = 0.7981
PR max/min: (0.9167 / 0.5714) = 1.6043
Average HHR = 42/104 = 0.4038
HHR max/min: (0.6429 / 0.3333) = 1.9286

Lets try it again, this time splitting the 3rd long sentence into two self-standing sentences, and re-indexing:

{X -6} Splitting line 3 into two self-standing halves:



01: PR = 19/24 = 0.7917 :: HHR = 10/24 = 0.4167
02: PR = 8/14 = 0.5714 : dPR = -0.2202 :: HHR = 9/14 = 0.6429 : dHHR = +0.2262
03: PR = 18/22 = 0.8182 : dPR = +0.2468 :: HHR = 11/22 = 0.5000 : dHHR = -0.1429
04: PR = 16/20 = 0.8000 : dPR = -0.0182 :: HHR = 10/20 = 0.5000 : dHHR = 0.0000
05: PR = 22/24 = 0.9167 : dPR = +0.1167 :: HHR = 8/24 = 0.3333 : dHHR = -0.1667

agl = 4.0000
Average PR = 83/104 = 0.7981
PR max/min: (0.9167 / 0.5714) = 1.6043
Average HHR = 48/104 = 0.4615
HHR max/min: (0.6429 / 0.3333) = 1.9286

We note how the average HHR has changed as a result of splitting line 3. The overall macroscopic PR situation has of course not changed from the splitting, but following its changes from line to line we see that the greatest dPR in the 5-lines version is greater than the greatest dPR in the 4-lines version: 0.2468 versus 0.2381.

{X -7} Summary for the 17th century Moretus and Hooke super-series:

Moretus Latin unpolished 87 groups in 9 series with series = document lines, from {X -2} :

agl = 443/87 = 5.0920
Average PR = 66/87 = 0.7586
PR max/min: (0.9286 / 0.6000) = 1.5477
Average HHR = 67/87 = 0.7701
HHR max/min: (1.0000 / 0.5000) = 2.0000

Moretus Latin unpolished 85 groups in 4 series with series = sentences, from {X -3} :

agl = 433/85 = 5.0941
Average PR = 62/85 = 0.7294
PR max/min: (0.7813 / 0.5833) = 1.3395
Average HHR = 52/85 = 0.6118
HHR max/min: (0.9167 / 0.5313) = 1.7255

Hooke English 104 groups in 4 series with series = sub-sentences, from {X -5} :

agl = 416/104 = 4.0000
Average PR = 83/104 = 0.7981
PR max/min: (0.9167 / 0.5714) = 1.6043
Average HHR = 42/104 = 0.4038
HHR max/min: (0.6429 / 0.3333) = 1.9286

Hooke English 104 groups (same) in 5 series with series = sub-sentences, from {X -6} :

agl = 416/104 = 4.0000
Average PR = 83/104 = 0.7981
PR max/min: (0.9167 / 0.5714) = 1.6043
Average HHR = 48/104 = 0.4615
HHR max/min: (0.6429 / 0.3333) = 1.9286

Lets try something and define a U{Sj} function analogous to the manner of {IX -2}:

{X -8} U{Sj} = (agl)(Super-series PR)(max PR)(no. of series of max PR) / (min PR)(no. of series of min PR)

Si = ith series of the super-series, with S1 = 1st series, and Sn = last series, and {Sj} denotes the set of series i=1 to i=j. Therefore for example, U{S4} is the U calculated for the first four series (here n => 4) and the set is comprised of series S1, S2, S3, and S4. And so on. It is clear that U{S1} = (S1 agl)(S1 PR) .

For Moretus Latin : U{S4} = 4.9764; U{S9} = 5.9782
For Hooke English: U{S4} = 5.1210; U{S5} = 5.1210

Interesting. It may be worthwhile to keep an eye on U when the super-series have many sub-series, and the sub-series are known to be in logical units that do not arbitrarily distort sub-series PR's. If the U develops into a useful number, then it can be rewritten in terms of its elementary variables, and then the functional form of the U can be studied. The U of a cryptic or uncertain super-series, calculated for sets of different trial sub-series, may possibly prove useful in detecting the logical sub-series units, perhaps by finding a reasonable minimum U for the super-series, as suggested above with the Moretus numbers. In this vein, a sub-series need not be a single sentence, but could be two or more short ones. This procedure may be prove useful in non-cryptographic work too, for example attempts to refine transcriptions from damaged documents.

The U has a peculiarity: in some cases this number can be determined by just two series of the super-series set, no matter the size of the set. To dramatize this, consider a set of one thousand series, say one thousand successive text-lines. Suppose it happens that there are exactly one line with the maximum PR, and one line with the minimum PR. Further, suppose that the agl in these two lines is exactly equal to the agl of the entire set of lines. Then these two lines alone determine the value of U. If they happen to be lines 1 and 2, then lines 3 - 1000 do not change the calculation of U. This may make U appear useless, until seen from a different perspective: lines 1 and 2 can be thought of as bounds, and then lines can be added in any number, after or even between lines 1 and 2, but so as not to affect the U calculated when the set consisted of only the first two lines. Thus the adhering to the bounds determined by the original 2-lines U value, generates families of sets of arbitrary size, all with the same U. The definition of U is thus seen as an attempt to identify yet another invariance of super-series, hopefully one that proves worthwhile.


The foregoing gave us a minimal preparation for a first reference-based look at Voynich text-lines that on the page come one after the other. Regardless of Captain Currier's observation that the VMS line is a functional entity, we can choose series for sequence spectroscopy analysis in whatever length-chunks we please, and collected in whatever order we please, but given our present experience with series of a dozen or two groups, plus that VMS text-lines fit into that range, our curiosity practically demands we next tackle some successive VMS lines to see if there are hints of any common mathematical patterns unifying the lines in succession, that is: are successive VMS lines members of a logical super-series? Just knowing the progression of PR with lines should be interesting. Naturally, no matter what we find with successive Voynich lines, it must eventually be gauged against successive lines from many other texts to obtain a comprehensive assessment. As we proceed, it will become yet further indicated just how rich are the possibilities for analytic techniques when signal transcription is combined with sequence spectroscopy.

Let us use the Voynich Currier language A and Currier language B text blocks from the VMS music transcription work [18]. For our experiments here we will modify those transcriptions only in equalizing the spaces that define the groups.

{XI -1} Voynich f20r 1st paragraph (Currier language A):

f20rL1: F8S089_S0B9_SCC9_40PS0E_40P0CC9_8S0R_SAIID
f20rL1: 123425_1234_1223_123425_1232445_1234_12334

f20rL2: S08_C9_QC9_S0P0E_08AIIR_40PS9_Q089_S08S9
f20rL2: 123_12_123_12324_123445_12345_1234_12314

f20rL3: 40PCC9_S0_S08AIID_Z0_40S9_SC9_PSC08AE_8ARAE
f20rL3: 123445_12_1234556_12_1234_123_1234567_12324

f20rL4: 0_S0E_0E_PCC9_0PAESC9
f20rL4: 1_123_12_1223_1234567

f20rL1: PR = 5/7 = 0.7143 : HHR = 5/7 = 0.7143 : U{S1} = 3.6735
f20rL2: PR = 6/8 = 0.7500 : HHR = 6/8 = 0.7500 : U{S2} = 3.5420
f20rL3: PR = 6/8 = 0.7500 : HHR = 7/8 = 0.8750 : U{S3} = 7.0860
f20rL4: PR = 5/5 = 1.0000 : HHR = 5/5 = 1.0000 : U{S4} = 4.7929

agl = 122/28 = 4.3571
Average PR = 22/28 = 0.7857
PR max/min: (1.0000 / 0.7143) = 1.4000
Average HHR = 23/28 = 0.8214
HHR max/min: (1.0000/0.7143) = 1.4000

From what we know of this kind of analysis to this point, admittedly elementary, a first glance at these numbers does give the impression that the VMS f20r1 first paragraph was algorithmically created, and is neither something completely random nor straightforward natural language in disguise. From the 3 out of 4 times HHR=PR it seems as if some kind of formula was used to generate sequences in line-series units: entirely in tune with Currier's observation.

Both PR and HHR rise as the paragraph progresses. We see successive lines 2 and 3 with identical PR, and also unlike any of the lines in Moretus and Hooke that we worked with, line 4 is all pillows. All the "40" digraphs can be changed to "4" unigraphs and their groups' pillow / non-pillow status will not change. The flexibilities of sequence analysis might have us say that the first paragraph of f20r itself shows a 1223 pillow sequence spectrum:

{XI -2} (5/7)(6/8)(6/8)(5/5) : 1223

Doing likewise with the HHR numbers would give us a 1234 ramp pillow.

Lets have a look at the detailed sequence spectrographics of this paragraph.

{XI -3} Super-spectra, and corresponding hh-spectra for the first paragraph of VMS f20r:

1223 : 1 : 1223
1234 : 2 : 1234
12334 : 1 : 12334
123425 : 2 : 123445
1232445 : 1 : 1233445

12 : 1 : 12
123 : 2 : 123
1234 : 1 : 1234
12314 : 1 : 12334
12324 : 1 : 12334
12345 : 1 : 12345
123445 : 1 : 123445

12 : 2 : 12
123 : 1 : 123
1234 : 1 : 1234
12324 : 1 : 12334
123445 : 1 : 123445
1234556 : 1 : 1234556
1234567 : 1 : 1234567

1 : 1 : 1
12 : 1 : 12
123 : 1 : 123
1223 : 1 : 1223
1234567 : 1 : 1234567

Let us now combine the above four into a progressive super-spectrograph:

{XI -4} Progressive hh super-spectra for VMS f20r 1st paragraph, text-lines 1,2,3,4 :: amplitudes total

(01) 1 _______: 0 : 0 : 0 : 1 :: 1
(02) 12 ______: 0 : 1 : 2 : 1 :: 4
(03) 123 _____: 0 : 2 : 1 : 1 :: 4
(04) 1223 ____: 1 : 0 : 0 : 1 :: 2
(05) 1234 ____: 2 : 1 : 1 : 0 :: 4
(06) 12334 ___: 1 : 2 : 1 : 0 :: 4
(07) 12345 ___: 0 : 1 : 0 : 0 :: 1
(08) 123445 __: 2 : 1 : 1 : 0 :: 4
(09) 1233445 _: 1 : 0 : 0 : 0 :: 1
(10) 1234556 _: 0 : 0 : 1 : 0 :: 1
(11) 1234567 _: 0 : 0 : 1 : 1 :: 2

The first thing here that stands out boldly is how narrow the overall spectrum is: just eleven components for the 28 groups across the progression of four lines. The numerical patterns, both vertical and horizontal, are fairly simple - it probably would not be difficult to come up with a simple system to generate the numbers in the {XI -4} array. Of course they are all hh-spectra, and have their own hh family members. If in some system the hh spectra were the critical codes, able to be represented by any same family member arbitrarily, then various daughter arrays of {XI -4}, being in general progressive spectrographs with mixed hh and sequence spectra, would all reduce to {XI -4} via contraction to hh only. That is to say, the {XI -4} matrix is an invariant of all its daughter matrices, which are not necessarily of the same size.

Lets now look at the Currier language B block from the music work:

{XI -5} Voynich f95r2 1st paragraph (Currier language B):

f95r2L1: FZC89_0R_S89_8AEVS9_40_8AIID_SX9VS9_8ARAIID_8AE_AE
f95r2L1: 12345_12_123_123456_12_12334_123413_1232445_123_12

f95r2L2: 8AIID_Z089_SFAID_S0E_SX9_0PAID_0P9_0PCC89_FAR_0FAJ
f95r2L2: 12334_1234_12345_123_123_12345_123_123345_123_1234

f95r2L3: 1234556_123_1234_12324_1234_12_123445_1234_12345_12_12

f95r2L4: 8AIID_Z089_P0R_0R_0FAID_SXC9
f95r2L4: 12334_1234_123_12_12345_1234

f95r2L1: PR = 7/10 = 0.7000 : HHR = 7/10 = 0.7000 : U{S1} = 2.8700
f95r2L2: PR = 9/10 = 0.9000 : HHR = 5/10 = 0.5000 : U{S2} = 4.2171
f95r2L3: PR = 9/11 = 0.8182 : HHR = 7/11 = 0.6364 : U{S3} = 4.2144
f95r2L4: PR = 5/6 = 0.8333 : HHR = 5/6 = 0.8333 : U{S4} = 4.1981

agl = 149/37 = 4.0270
Average PR = 30/37 = 0.8108
PR max/min: (0.9000 / 0.7000) = 1.2857
Average HHR = 24/37 = 0.6486
HHR max/min: (0.8333 / 0.5000) = 1.6667

{XI -6} Progressive hh super-spectra for VMS f95r2 1st paragraph, text-lines 1,2,3,4 :: amplitudes total

01: 12 ______: 3 : 0 : 3 : 1 :: 7
02: 123 _____: 2 : 4 : 1 : 1 :: 8
03: 1234 ____: 0 : 2 : 3 : 2 :: 7
04: 12334 ___: 1 : 1 : 1 : 1 :: 4
05: 12345 ___: 1 : 2 : 1 : 1 :: 5
06: 123345 __: 0 : 1 : 0 : 0 :: 1
07: 123444 __: 1 : 0 : 0 : 0 :: 1
08: 123445 __: 0 : 0 : 1 : 0 :: 1
09: 123456 __: 1 : 0 : 0 : 0 :: 1
10: 1233445 _: 1 : 0 : 0 : 0 :: 1
11: 1234556 _: 0 : 0 : 1 : 0 :: 1

Finally let us combine {XI -4} and {XI -6}, using [] to separate the f20r and f95r2 data columns:

{XI -7} Progressive hh super-spectra for VMS f20r and f95r2 1st paragraphs, text-lines 1,2,3,4 :: amplitudes total

01: 1 _______: 0 : 0 : 0 : 1 :: 1 [] 0 : 0 : 0 : 0 :: 0
02: 12 ______: 0 : 1 : 2 : 1 :: 4 [] 3 : 0 : 3 : 1 :: 7
03: 123 _____: 0 : 2 : 1 : 1 :: 4 [] 2 : 4 : 1 : 1 :: 8
04: 1223 ____: 1 : 0 : 0 : 1 :: 2 [] 0 : 0 : 0 : 0 :: 0
05: 1234 ____: 2 : 1 : 1 : 0 :: 4 [] 0 : 2 : 3 : 2 :: 7
06: 12334 ___: 1 : 2 : 1 : 0 :: 4 [] 1 : 1 : 1 : 1 :: 4
07: 12345 ___: 0 : 1 : 0 : 0 :: 1 [] 1 : 2 : 1 : 1 :: 5
08: 123345 __: 0 : 0 : 0 : 0 :: 0 [] 0 : 1 : 0 : 0 :: 1
09: 123444 __: 0 : 0 : 0 : 0 :: 0 [] 1 : 0 : 0 : 0 :: 1
10: 123445 __: 2 : 1 : 1 : 0 :: 4 [] 0 : 0 : 1 : 0 :: 1
11: 123456 __: 0 : 0 : 0 : 0 :: 0 [] 1 : 0 : 0 : 0 :: 1
12: 1233445 _: 1 : 0 : 0 : 0 :: 1 [] 1 : 0 : 0 : 0 :: 1
13: 1234556 _: 0 : 0 : 1 : 0 :: 1 [] 0 : 0 : 1 : 0 :: 1
14: 1234567 _: 0 : 0 : 1 : 1 :: 2 [] 0 : 0 : 0 : 0 :: 0

We see that there is a representation difference of just three hh-spectral components between them. If we imagine a piano with 14 keys, then the Currier-A and Currier B paragraphs can be likened to scores being played, each avoiding three particular keys, that the other score uses. Currier used the analogy of A and B languages; perhaps it is more telling to say A and B systems of group structures.

Very noticable is that the Currier-A f20r distributes its spectral activity in its paragraph far more evenly across the entire spectral band than does the Currier-B f95r2, the latter concentrating more in a lower part of the band, or hh-piano keyboard if you will. Perhaps this relates to the subjective observation that the f20r music sounds more pleasing than the f95r2 music, and that the f20r music becomes more dissonant when played in boustrophedon than does the f95r2.


Nearly all the preceeding results were calculated by hand, scattered across experimental sessions. Eventually I found it desirable to write some computer routines for handling some of the more tedious steps, as well as check the hand calculations. The routines naturally grew in number, and then condensed under something of a user interface into a fairly practical Version 1.0 program suitable for this kind of analysis, that I named: SQS. The program runs under DOS or an equivalent operating system. It calculates the basics, but not everything shown above is fully automated in Version 1, as it remains to be seen which analytic formats are the most useful and worth the progamming effort to automate them. I am sending SQS to our Librarian Greg Stachowski and requesting that he deposit it in the J.VS Library [19] from where it may be downloaded. Once downloaded, it is only necessary to rename SQS to SQS.EXE and it is ready to run. Comments on SQS, including bug reports and suggestions for upgraded versions will be appreciated.

SQS initializes with an example series that is designed to familiarize the new user with the program's essentials in under one minute: start SQS, and the Main Menu screen appears; press "S" to show the analysis screen, and you will get the picture quickly. Then the various analytic options available will be easily understood. Also, a separate text screen is devoted to general help information. SQS has an option, "Z", for displaying the reversed sequence spectra of the groups underneath the groups forward sequence spectra - this display is slightly different from the direction-reversal diagrams we've used above, and is for convenience. Actual direction-reversal display is of course available, and direction-reversal transformation calculations are computed as per above.

SQS can analyze series containing groups that have as many as 36 different unique signals. Sequence-spectrum neighboring in SQS is calculated as an extension of the numerical hierarchy system employed in J.VS comm. #191. The following 36-signals ramp-sequence group illustrates the sequence-spectrum analytic format of SQS:


Any of the above 36 alphanumerics can of course also appear in the original source series to be analyzed.


Within the scope of the preceeding limited data, it seems to me that there are indications that the analyzed Voynich text is definitely not totally random, but is at least partly mathematically generated. With the Eulerian text-circuits analysis (J.VS comms. #176, 177, 178) as limited as it too was, there were indications of numerical influences across the bulk of the VMS text, so there is at the least no conflict in results between the two entirely different analytic approaches. And anyway, it is not a new idea in Voynich literature that the VMS text, or at least some of it, was generated with the help of mathematical formulas cranking out certain numbers, while avoiding others.

There also seems to be in some of the VMS text analyzed, an indication of the influence of Latin, but it may not at all be from Latin plain-text being enciphered: rather, it seems possible that purely mathematical characteristics of Latin writing, or grammar if you like, enter the VMS text generator as contributing group-structure determinators.

Whereas the above material is quite massive, it really just scratches the surface of the analysis of series of signal sequences. Much more source material of diverse natures must be characterized. I think Voynich text work ought to broaden its reference base and include more radiotelegraph copy, baby-talk, stammering, and other non-traditional source material for comparison with the VMS text. Admittedly, it can be difficult obtaining good transcripts - I was rather surprised how little there is online in the way of transcripts of stammering speech.

We saw again and again how numerous are the analytic branches one can take. What are the best analytic functions to define? I think the above material shows that analytics proceeding from the high-history functions are productive. The pillow ratio (PR), easily calculated, also seems a very useful single number that tells us a lot about a given series of sequences. By extension to super-series, the U-number may turn out to be a useful single number, even though like all the others it lends itself naturally to functional duty.

For further sequence-spectrum analysis of the Voynich manuscript it would be very handy to have some specifically tailored resources available. For example, Glen Claston (GC) constructed and made available his excellent voygroup.txt Concordance of Separate Voynich Groups [6]. Granted, the VMS vocabulary that GC presents is transcribed according to his interpretations of VMS words using Latin abbreviations, and such interpretations greatly affect the sequence spectra of words so interpreted - we saw in section VII. how just the "4o" versus "4" interpretation of a glyph can affect the spectra of their words. However, GC's transcription alphabet usually permits reinterpreting a particular transcribed word from abbreviated to unabbreviated: his bias on the VMS vocabulary may have him frown on such, but with his transcription alphabet he does provide the mechanics for disagreeing with his interpretations. In any case, producing a version of voygroup.txt with the sequence spectra of the words added, would be very handy, and not especially difficult computer work given available the dedicated time for it. Here for example are a few lines from voygroup.txt, with sequence spectra, and their hh-spectra added:

{XIII -1} Adapted selection from GC's voygroup.txt, with sequence and hh-spectra added:


where P: means pillow sequence, and X: means non-pillow sequence. A refinement would distinguish ramp and wall pillows from more complex pillows. The next step further from this would be to produce a list of VMS words classified by their sequence spectra, and a separate list of them classified by their hh-spectra - this would amount to a sorting operation on the above list. Such lists could then be used to more easily investigate a variety of VMS text questions - for example, do VMS labels significantly exhibit certain spectral tendencies?

There are indeed spectral peculiarities found among some Voynich labels. For example, the center of the f68v3 "Spiral Nebula" illustration is a double-perimeter circle sectioned with a perpendicular, all containing text. A circle sectioned with a perpendicular sends, via its geometry, several messages to the mathematical observer, for example: 1+2+3=1x2x3=6.

As we know, the perpendicularly sectioned circle was also used as a diagram platform for socalled ancient T/O maps, variously filled in with geographic details, sometimes only geographic names. The distribution of the spectra and spectral clusters in the double-perimeter sectioned circle of f68v3 hint at what I briefly mentioned in a conversation with Marke Fincher in a recent vms-list post [20] as: "write in mathematics language" as in "abc cba" = "symmetry". The immediately easiest to see mathematics-language expression of the possible statement "symmetry versus asymmetry" in the sectioned f68v3 circle, is the spectral series of the first two lines under the perpendicular's horizontal:

{XIII -2} spectral series / clusters of the first two lines under the VMS f68v3 circle's sectioning-horizontal:


From the mindset of "mathematics language", we could replace these two lines in f68v3 with:

And there was symmetry
And with it its inseparable twin anti-symmetry

Interestingly also, for the first line the PR=1.0 while for the second line PR=0.5, holding true also when the lines are each split into two separate halves, thereby further signalling, to the mathematically sensitive mind, existence's most unique and important number, the one and only even prime number: 2, the twin number. Given the VMS author's sophistication, it is not inconceivable that he / she would try communications in this manner: using a language of mathematics, readable and understandable only by the mathematically sensitive, to say something fundamental about the cosmology depicted in f68v3. And optionally for him / her, the symbols-dressing of the sequences might be just necessary noise, or further literal communication riding atop the mathematics communication. A handy Voynich spectral vocabulary list would make it much easier for all interested researchers to investigate VMS text along these lines - someone might notice a spectral pattern that proves significant and leads to further clues, for example crypto Fibonacci series expressed with sequence spectra.

I remarked in endnote [5] of communication #191 that it will eventually be necessary to make a precise distinction between "series of sequence spectra", and "sequence of sequence spectra". Presently we are still proceeding without difficulties because we have confined ourselves to unambiguous series, the members of which are groups taken as sequence spectra each framed to their individual group. The concept of a "sequence of sequence spectra" is more complicated, it requires extensive considerations before a spectrography for it can be developed, and in the future I would like to devote a separate communication to my perspective on it, as time permits.

Berj / KI3U

[1] J.VS communication #191 (Vol. II):
J.VS: Possible versus Impossible Sequence Spectra, and Associated Relations

[2] Additional background material is found in recent vms-list discussions in these list threads:
VMs: The phenomenon: VMS can be read in language X, 05-08-2008 12:04:12 AM, thread launched by Berj / KI3U.
VMs: Re: The phenomenon: ... (Att. Berj), 05-13-2008 5:55:19 PM, thread launched by Knox Mix.
VMs: Possible versus Impossible Sequences, 05-22-2008 2:12:09 AM, launched by Berj / KI3U.

[3] In this communication there will be no ambiguity about what we mean by the reverse-direction transformation of a series because the idea is straightforward and we illustrate it over and over. However, let us briefly lay down a precise defining notation for it that may be needed sometime further along, and in any case is useful during development of computer programs for the analytics discussed in this communication. Parts of the SQS computer program are based on the following.

Direction-reversal transformation for a series of signal units:

The letters i,j,k,q,r,t,z, are taken as subscripts. Let Si denote the ith signal series under consideration. If only one series is to be analyzed, then i can be omitted. The signal-elements of the series Si are signal units at the maximum resolution being considered. That is, a signal-element is a final resolution unit, and it either exists whole or it doesn't exist. Therfore we write Si in expanded form:

[3a] Si{uj} = Si{u1, u2,....., un}

The index j specifying the order of the signal units in the series ranges 1 to n, that is there are n signal units in the Si series. The reversible direction-reversal transformation DR is then:

[3b] S'i{u'k} = DR[ Si{uj} ]

where k = n+1-j . Therefore for example: k = n+1-(n-1) = 2 , and u'sub2 = usubn-1. And so on. So in a sense the direction-reversal is an ordinary linear transformation.

Following is a specific example; we keep open the possibility that the transcription of this example series assigned say "n" to stand for the signal unit: blank space.

[3c] DR[ S3{k,a,n,U,c,n,u,*,h,*} ] = S'3{*,h,*,u,n,c,U,n,a,k}

[3d] or abbreviated: DR[ S3 ] = S'3

The above is all there is to the transformation. However, often prior to transformation, and also after, we recognize groups within the series, say those defined by blank spaces, and perform group-framed sequence spectrum analysis upon the before and after series. In order to connect those acts notationally with the Si definitions, we now distinguish signal-elements in the series from groups of signal-elements in the series. To do that we introduce the signal group-function G:

[3e] Giqr(g1,...,gz) specifies a sub-series where:

i identifies G specific to Si. Again, if there is no confusion, it may be omitted.
q identifies a particular grouping sheme; if only one scheme is ever used, then q may be omitted.
r identifies the rth group and ranges 1 to m, where m is the total number of groups generated by the q scheme.
gz (read g sub z) identifies one or more signal elements g known to be in Si. If only one g is in play, the index z can be omitted.

An example: In the S3 series of [3c] select g such that g = "n", the element "n" known to be in S3. Only this single g will be involved. We now have G3qr(n) with q and r to be clarified. Let q=1 identify a parsing sheme on S3 such that proceeding from the start of S3 everything between successive g's is a subseries / group, and also everything between the start of S3 and the first g is a group, and also everything between the last g and the end of the series is a group. The r index then identifies the groups in their order from the start of S3. Lets show this for S3:

[3f] The G31r(n) :

G311(n) = {k,a}
G312(n) = {U,c}
G313(n) = {u,*,h,*}

We see that here m=3. Using our customary "_" notation we would write the G31r(n) series of groups:

[3g] ka_Uc_u*h*

[3h] Showing with another example, that G31r(k) has only one group:

G311(k) = {a,n,U,c,n,u,*,h,*}

[3i] Showing with another example, that G31r(*) has two groups:

G311(*) = {k,a,n,U,c,n,u}
G312(*) = {h}

Similarly to [3c] we can now write:

[3j] DR[ Giqr(g) ] = G'iqt(g)

where t = m+1-r

To see if the notation works, lets use [3j] to get G'31t(n) from [3f], where m=3 :


G'311(n) = {*,h,*,u}
G'312(n) = {c,U}
G'313(n) = {a,k}

[3l] Writing these in "_" notation we get: *h*u_cU_ak

which is the reverse-direction groups-series of [3g]. So the notation seems to work ok.

Here there is the appearance that we took "n" to mean a logical space separating groups, that may be identical with physical interword spaces on the page. In the Voynich text we really do not know if the blank spaces between the "words" are really separating logical words, or if they are really crypto-symbols while some other symbols play the role of group separating spaces. In one of the discussions referenced in [2] in the thread launched by Knox Mix, we looked at a quick example of the problem of logical spaces in the VMS text and showed the implications for symbols-based n-gram / n-graph analysis.

As we can see from the examples [3h] and [3i] the signal group-function Giqr(gz) can easily handle analytical variations for logical group separators. More complicated parsing shemes can be specified via the q and z indexes.

[4] Ramps and walls are of course pillows, and also the sole members of their hh-families. Experiments to gain familiarity with pillows and non-pillows are simple enough: write some groups and their reversals. For example: the reverse of WITHIN is NIHTIW and for both the sequence sprectrum is 123425, and so they are pillows. But, the spectrum of GAZOO is 12344, and the spectrum of its reverse, OOZAG, is 11234, and they are clearly not pillows. From inspection of the structure of WITHIN versus GAZOO, it is apparent that a general mathematical analysis of pillows versus non-pillows entails symmetry versus asymmetry with respect to the midpoints of groups. The midpoint of a group with an odd number of elements is an element, while a group with an even number of elements has its midpoint as an imaginary axis between a pair of elements. Pillows can be of either an even or odd number of elements. Simple pillow generators computer programs would not be difficult to write. Interestingly, MIRROR and its mirror RORRIM, with 123343 versus 121134, are not pillows. Neither are SYMMETRY and ASYMMETRY and their reverse versions. The Greek LOGOS and its reverse SOGOL have an odd number of elements, and they are pillows, with the same sequence spectrum: 12324.

Even at this early stage it is apparent that for comparison of some general types of series, typically sentences in different natural languages, the distribution of pillows within the series / sentences, AND the various pillow structures so distributed, are of study interest. It would first be necessary to develop some classifications and notation for different pillow structures beyond just wall, ramp, even and odd-number-of-elements pillows.

[5] The ratio of the number of ramps to pillows in a series of groups is of interest in this work:

[5a] RPR = r/p

Of course all ramps are pillows, but not vice versa, and so when any pillows are present, the RPR ranges from 0 to 1. If no pillows are present we will simply define the RPR as the indeterminate "0/0" and leave it at that. From [5a] and {V -7} we have a simple relationship between the ramps ratio RR and PR and RPR:

[5b] RR = r/n = (PR)(RPR)

Although the PR as a single number is a handy rough gauge for comparing series, a well-defined PR-function can provide far more resolution of the differences. Perhaps the simplest PR-function is like a fixed-width interval-window on the series, moving through it in fixed steps, and the PR of the window is taken at each step. Thus a PR-function points-curve is generated. Of course there is an asymmetry from the window's far end reaching the end of the series, and groups within that last window not getting a chance to step out of the left window edge. This can be delt with by running a companion PR-function in reverse starting from the end of the series. Or let the series be a ring, and keep going around until all groups have had equal or fair window participation.

Another interesting type is the PR defined as a balloon function on the series taken as a ring: the window, initially at its minimum needed width, is centered somewhere in the ring, and then it balloons in size, symmetrically or asymmetrically, the expansion steps maybe even governed via some other function, say the exponential function, until opposite edges of the window meet. Advanced balloons can even be made to float in the "atmosphere" of the groups, changing inflation and drift with "altitude" and "wind", the bag profile and the meteorological analogs of temperature and pressure differentials and so forth coming from the bag's contact with certain sequence spectra - quite suitable for 2D paragraph and page analysis, and even a fully 3D sequences- or "text-atmosphere" in stacked blocks or folios of text. Flying the balloons through various text-atmospheres can answer questions concerning their detailed profile and flight path versus the text-group the balloon was launched from. These powerfully illuminating balloon functions in their elementary forms can be cast really pretty simple, and working with them is like playing with great toys.

[6] The voyn_101.txt transcription and other GC resources are now available online here:

[7] The following sentence, which arguably makes sense in the context of a manufacturing plant, has the same spectral series {VI -3}, and therefore also the same PR, as the Voynich f68v3.1 line in {VI -2}:

[7a] alvin_ester_croocy_and_joseph_kalman_and_i_had_moretti_viewing_pulp_added_toooz

Admittedly, the last word, with its difficult inner-triplet 12223 structure, is a bit of a stretch and relies on the ambiguity of the lack of any discernable punctuation in the VMS, and where also we invoke some local dialect to express: "to'ooz" meaning "to the ooze".

A language-rare spectrum like 12223 seems easiest to handle with acronyms or made-up names. Perhaps nouns and pronouns in western languages prefer certain sequence spectra for their constructions. Following is a try at the {VI -4} reversed version of f68v3.1. Imagine an interview being conducted at a custom motorcycle shop named "zooot sissy" that specializes in tuning engines and exhausts to achieve distinctive sounds:

[7b] zooot_sissy_says_retorts_cooling_gas_a_bit_slowly_brings_out_reggae_samba_sound

In a reply to Voynich researcher Knox Mix in one of the discussions in [2] I stated that sequence spectrum analysis can split the VMS text problem (i.e. the text is presumed to be meaningful) into two problems: the spectral sequences as the more fundamental, and once they are well understood, the problem of how they are dressed with Voynich alphabet letters, spaces, line units, etc.

Now, assuming Captain Currier's assertion that he derived from symbols frequencies versus line-portions, that the VMS text-line is a functional entity, then whether or not the VMS text is an anthology of one-liners in some language, experimental work in this vein includes investigating systems of reversible transformations between the likes of [7a] and {VI -2}. In that case, it is clear from inspection of [7a] and {VI -2} that alphabet mapping is changing from group (word) to group. It seems a possibility that alphabet mapping could be based on word order, plus the word's hh-family membership.

If the objective behind the VMS text is not a practical cipher, but instead a kind of polymathic literary challenge to be unraveled at one's own pace and pleasure, a kind of literary genre in its own right, then it is conceivable that the tract of the book could have been written as a synthesis of existing text-series from other published or available books, typically in lines units, and the lines of the tract written in different languages, Greek, Latin, German and so on, and the lines then shuffled like cards in a deck, before being scripted onto the VMS folios. I doubt this is actually the case with the VMS, but it seems that such an effort could end up resembling the VMS text.

In addition to the random integer generator, there is available also a "random sequence generator", but there the definition of "sequence" is quite different from what it is here. Nevertheless that generator can also be used: to generate a random series of integers without repeats, and that series, treating it like a series of strings, can be used as a test source series for sequence analysis per our understanding.

[9] Using Latin letters to transcribe Greek from the opening of the New Testament Gospel of John:



[10] This rhyming German proverb, here written using "u" for u-umlaut, has 6 components in its hh-spectrum:



[11] Typical de-coded amateur radiotelegraph transmission series, showing abbreviations and special groups. Its hh-spectrum has 8 components with HRR = 8/13 = 0.6154. The reverse-direction series HRR is the same.



[12] This English sentence series has no pillow sequences. Its HRR = 12/13 = 0.9231, and for its reverse-direction series the HRR = 13/13 = 1.0000. In our current analytic view it is, fitting its message, a highly broad-band series:



Its differential hh super-spectrum under direction-reversal transformation, ( reverse - forward ) is:

(01) 112 : +1
(02) 122 : -1
(03) 1123 : +1
(04) 1233 : -1
(05) 12234 : +1
(06) 12344 : -1
(07) 112345 : +1
(08) 123334 : -1
(09) 123344 : +1
(10) 123455 : -1
(11) 1223456 : -2
(12) 1233455 : +1
(13) 1234455 : -1
(14) 1234556 : +1
(15) 1234566 : +1
(16) 12334567 : -1
(17) 12344456 : -1
(18) 12345566 : +1
(19) 12345567 : +1
(20) 1233455666 : -1
(21) 1234445567 : -1
(22) 1234455566 : +1
(23) 1234456667 : +1
(24) 1234555566 : +1
(25) 1234556666 : -1

[13] Friedman's 1959 anagrammatic anagram statement about the Voynich manuscript:


Adapted from pg. 42: The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7.

Its differential hh super-spectrum under direction-reversal transformation, ( reverse - forward ) is:

01: 1 : 0
02: 12 : 0
03: 123 : 0
04: 1234 : 0
05: 12344 : 0
06: 12345 : 0
07: 123334 : -1
08: 123344 : +1
09: 12234556 : +1
10: 12345666 : -1
11: 12345667 : +1
12: 12345677 : -1
13: 12345678 : 0
14: 1234456778 : +1
15: 1234566678 : -1
16: 122344555678 : -1
17: 123455567788 : +1
18: 1234456667778900 : +1
19: 1234556788999900 : -1

delta = 12/19 = 0.6316

[14] The Billy Graham Center has a transcript of a 1997 interview by Robert Shuster of the Rev. William A. Drury that was prepared with great care and records Drury's stammering / stuttering: Billy Graham Center, Archives, Collection 492 - Rev. William A. Drury. T3 Transcript. Online (6 MAY 2008) here:

For analysis purposes here, the following was adapted from the Drury interview:


This series has 796 signals of which 639 make up the groups, and the other 796-639=157 are the inter-group separators. There are 158 groups, with agl= 4.0443 and mgl= 13. There are 23 unique signals counting the separator signal, and 22 appear across the groups.

[15] Series of some random bits in 13 bytes groups:

[16] J.VS Library deposit # 0-5-2007-12-18

The Project Gutenberg eBook, Micrographia, by Robert Hooke. March 29, 2005 [eBook #15491].

[18] See J.VS Volume-II communications #170, #168, #165, #166, #167, #169, and #172:

[19] J.VS Library deposit # 19-1-2008-06-29

[20] vms-list post: VMs: Voynich words and grammar and meaningfulness, Sent Date 04-12-2008 7:47:34 PM, by Berj.

From Berj Ensanian
Sent Date 07-02-2008 2:57:49 PM

Subject J.VS: Distribution of pillows and non-pillows in comm. #203 series examples; NvP Topography

Dear Colleagues

Here follow some supplementary data for J.VS communication #203 [1]. We look at the distribution of pillow versus non-pillow sequences in the examples considered in #203.

1 = pillow sequence in the series
0 = non-pillow sequence

{#203: IV -1} Mixed ramps long English sentence PR = 18/18 = 1.0000


{#203: [9]} Start of Greek N.T. Gospel of John PR = 17/17 = 1.0000


{#203: III -4} Equal ramps English vms bug sentence PR = 5/5 = 1.0000


{#203: V -3} All-ramps-but-one English sentence PR = 8/9 = 0.8889


{#203: [10]} Rhyming German Proverb PR = 7/9 = 0.7778


{#203: [14]} Reverend Drury's stammering PR = 122/158 = 0.7722


{#203: [11]} De-coded radiotelegraph series PR = 10/13 = 0.7692


{#203: I -1} Mixed series PR = 6/8 = 0.7500


{#203: v -8} Beginning of Latin Genesis PR = 9/13 = 0.6923


{#203: [13]} Friedman's 1959 VMS Anagram PR = 13/19 = 0.6842


{#203: VI -2} Voynich f68v3.1 text-line PR = 9/14 = 0.6429


{#203: [15]} Binary bytes series PR = 7/13 = 0.5385


{#203: VIII -8} Random numbers series fair reference for VMS f68v3.1 PR = 6/14 = 0.4286


{#203: II -2} All hh-1222 "baby-talk" series PR = 3/7 = 0.4286


{#203: [12]} All non-pillows English sentence PR = 0/13 = 0.0000


{#203: X -2} Moretus Latin taken from MtoK8JAN1639.txt, document-lines series:

03: 1_1_1_1_1_0_0_1 ______________ PR = 6/8 = 0.7500
04: 1_0_1_1_1_0_1_1_1 ____________ PR = 7/9 = 0.7778
05: 1_1_1_1_1_1_1_1_1_1_1_1_0_1 __ PR = 13/14 = 0.9286
06: 1_1_0_1_1_1_0_1_1 ____________ PR = 7/9 = 0.7778
07: 0_1_1_1_1_0_0_1 ______________ PR = 5/8 = 0.6250
08: 1_1_0_1_1_0_0_0_1_1 __________ PR = 6/10 = 0.6000
09: 1_1_0_1_1_1_1_1_0 ____________ PR = 7/9 = 0.7778
10: 1_1_1_1_1_1_0_1_1_0 __________ PR = 8/10 = 0.8000
11: 1_0_1_1_1_0_1_1_0_1 __________ PR = 7/10 = 0.7000

{#203: X -3} Moretus Latin taken from MtoK8JAN1639.txt, logical sentences series:

01: 1_1_1_1_1_0_0_1_1_0_1_1_1_0_1 ____________________________________ PR = 11/15 = 0.7333
02: 1_1_1_1_1_1_1_1_1_1_1_1_1_1_0_0_1_0_1_1_1_0_1_1_0_1_1_1_1_0_0_1 __ PR = 25/32 = 0.7813
03: 1_0_1_1_0_0_0_1_1_1_1_0 __________________________________________ PR = 7/12 = 0.5833
04: 1_1_1_1_1_0_1_1_1_1_1_1_0_1_1_0_1_0_1_1_1_0_1_1_0_0 ______________ PR = 19/26 = 0.7308

{#203: x -5} Hooke English from Micrographia in 4 logical units series:

01: 1_0_1_1_1_1_1_1_0_1_1_0_1_1_0_1_1_1_1_1_1_1_1_0 __ PR = 19/24 = 0.7917
02: 1_0_1_0_0_1_1_1_0_1_0_1_1_0 ______________________ PR = 8/14 = 0.5714286
03: 1_1_1_0_1_1_1_1_1_1_1_1_1_1_1_0_1_1_0_1_1_0_1_0_1_1_0_1_1_1_1_1_1_0_1_1_1_0_1_1_1_1 PR = 34/42 = 0.8095
04: 1_0_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_0_1_1 __ PR = 22/24 = 0.9166667

{#203: x -6} Hooke English from Micrographia in 5 logical units series:

01: 1_0_1_1_1_1_1_1_0_1_1_0_1_1_0_1_1_1_1_1_1_1_1_0 __ PR = 19/24 = 0.7917
02: 1_0_1_0_0_1_1_1_0_1_0_1_1_0 ______________________ PR = 8/14 = 0.5714
03: 1_1_1_0_1_1_1_1_1_1_1_1_1_1_1_0_1_1_0_1_1_0 ______ PR = 18/22 = 0.8182
04: 1_0_1_1_0_1_1_1_1_1_1_0_1_1_1_0_1_1_1_1 __________ PR = 16/20 = 0.8000
05: 1_0_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_0_1_1 __ PR = 22/24 = 0.9167

{#203: XI -1} Voynich f20r 1st paragraph (Currier language A):

L1: 1_1_1_1_0_1_0 __________ PR = 5/7 = 0.7143
L2: 1_1_1_1_0_1_1_0 ________ PR = 6/8 = 0.7500
L3: 0_1_0_1_1_1_1_1 ________ PR = 6/8 = 0.7500
L4: 1_1_1_1_1 ______________ PR = 5/5 = 1.0000

{#203: XI -5} Voynich f95r2 1st paragraph (Currier language B):

L1: 1_1_1_1_1_0_0_0_1_1 ____ PR = 7/10 = 0.7000
L2: 0_1_1_1_1_1_1_1_1_1 ____ PR = 9/10 = 0.9000
L3: 0_1_1_1_1_1_0_1_1_1_1 __ PR = 9/11 = 0.8182
L4: 0_1_1_1_1_1 ____________ PR = 5/6 = 0.8333

{#203: XIII -2} spectral series / clusters of the first two lines under the VMS f68v3 circle's sectioning-horizontal:

01: 1_1_1_1 PR = 4/4 = 1.0000
02: 0_1_0_1 PR = 2/4 = 0.5000

Let us construct a non-pillows vs pillows topograph from the {#203: XI -1} f20rp1 data. To do it we must first scale the L1 to L4 rows to equal length, and that requires a length number which has 7, 8, and 5 as common factors: 7x8x5 = 280. Now, that is way too many columns to work here with this plaintext format, it requires graphics format. Nevertheless we are lucky - the L4 row is all 1's, and since the topograph maps to area, we can get away with a slightly non-linear scaling for the L4 because it will map uniformly anyway. So we need: 7x8 = 56 columns, which we can do. [2]

So, we multiply the L1 horizontal scaling by 8, the L2 and L3 by 7, and for L4 we fill in all the same plateau topography. To make sure no breakdown or confusion of analytic formalism enters, we will use "+" to map the 0's of the non-pillows, and "-" to map the 1's of the pillows. Furthermore, to make it easier to see the topography, we will also stretch the column scaling by a factor of 8. Lets see what the non-pillows floating in a sea of pillows are doing.

{1} NvP Topograph of {#203: XI -1} Voynich f20r 1st paragraph (Currier language A):

groups progression: from left to right
series progression: downward
"+" = non-pillow group sequence
"-" = pillow group sequence

L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L1: --------------------------------++++++++--------++++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L2: ----------------------------+++++++--------------+++++++
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L3: +++++++-------+++++++-----------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------
L4: --------------------------------------------------------

The technique of 2D and 3D topographic plots is ideal for quickly seeing patterns and comparing them among super-series. If we had an NvP topo of the f95r2p1 paragraph to compare with {1} we would see at a glance:


In the Voynich f20r 1st paragraph (Currier language A) the non-pillows essentially drift across the series while maintaining roughly approximate separation within series, as the paragraph progresses, and by the end of the paragraph they have drifted out.

In the Voynich f95r2 1st paragraph (Currier language B) the non-pillows oscillate within series and across series, as the paragraph progresses.

Great amounts of data can be quickly surveyed with topographic frames, which can be blinked. A step up from blinking, when the amount of data and its complexity is quite great, then topographic frames can be run like a movie. In that manner I have successfully surveyed some functions of the entire VMS text - in any other way it would have taken a very long time to get an idea of the functional behaviour of relatively small blocks of text across the entire VMS text corpus.

Berj / KI3U

[1] J.VS comm. #203 (Vol. II): J.VS: Reference Data for Analysis of Signal Sequence Series

[2] If {1} does not display rectangular, then adjust viewer.

From Berj Ensanian
Sent Date 07-14-2008 7:41:53 PM

Subject J.VS: Series of Sequences vs Sequences of Sequences: Super-sequence Deviation Reference Data

Dear Colleagues

In sequence spectrographic work there arises the need to distinguish precisely between "series of sequence spectra" and "sequence of sequence spectra", that is super-sequences. I mentioned this in J.VS communication #191, in its endnote 5, and most recently in the concluding comments of communication #203. [1]

Voynich text sequence spectrography is greatly and interestingly expanded with the introduction of the concept of super-sequence. Here I would like to address this issue from my perspective on it, with these sections:



Up to this point we have done various analyses of series of sequence spectra. The series is a more general concept than its special case of sequence: a series can have its sub-series, that are sequences groups, appear serially in any order. But if a series of sequences is also to be recognized as a sequence of sequences, if it is to be regarded as a super-sequence, then we must remain consistent with our sequence analytics. Let us look at the situation diagramatically - consider the series of n sequences S{si} :

{I -1} s1_s2_s3_......._sn

Typically we might have for n = 6 :


{I -3} 12343_123_123456_123_12_123421

As long as we consider {I -2} a "series" of groups, and {I -3} the "series" of its sequence spectra, then we are consistent with all work so far along these lines. To introduce the concept of sequence of sequences, super-sequence, we choose a definition and classify {I -3} either as a super-sequence, or not. Logically, the key point is that the definition of super-sequence must have at its core the concept of spectrum neighboring: there must be some rule for serial ordering observed between any si and s(i+1) throughout the series s1_..........._sn

And with that we have reached the point of ambiguity, regarding the neighboring order of sequences, that was discussed in comm. #191:

" With sequences of sequence spectra there are ambiguities as regards their serial order, and therefore any metric between sequence spectra must be settled in the context of a particular system of analysis. ....... In this system we could define the spectra in table {5-7} to be each other's nearest neighbors by their numerical hiearchy order, despite sometimes belonging to different hh-families. By extension, the nearest next higher neighbor of 1234 would be 11111. And so on. "

Thus back there we chose numerical hierarchy to determine spectrum neighboring in the analytic proceedings: this is the system used to this point to constuct super-spectrum diagrams like {#203: I -2}, and we understand that it is not the only possible system. For {I -3} above, its contracted sequence super-spectrum is:

{I -4} spectrum component order : spectrum component : component amplitude

01: 12 : 1
02: 123 : 2
03: 12343 : 1
04: 123421 : 1
05: 123456 : 1

Clearly, the serial order of the spectra in {I -3} is different from the ordering observed in its super-spectrum {I -4} where numerical hierarchy ordering is observed. In comm. #203 the numerical hierarchy system's notation was extended well beyond the convenient notation of it with only the Arabic digits 1 - 9.

Let us then choose numerical hierarchy to determine the serial spectrum neighboring in a super-sequence:

{I -5} Definition of a sequence of sequences (super-sequence), in the analytic system which determines spectrum neighboring according to numerical hierarchy:

{I -5-1} The series S{si} of i=1 to n sequences: s1_s2_s3_......._sn

is considered a sequence of sequences, a super-sequence, when the corresponding individual sequence spectra are in numerical hierarchy spectrum-neighbor order according to:

{I -5-2} s1 <= s2 <= s3 <= ....... <= sn

It is not necessary that si and s(i+1) be immediate spectral neighbors, but only that their order conforms to numerical hierarchy in general. Also, a series of identical spectra may be considered a degenerate super-sequence.

Let us see a clarifying example:

{I -6} Conforming to definition {I -5}, an example true super-sequence [2]:



By analogy with sequence rule {3-c} in comm. #191, it is clear that the ith group in a super-sequence cannot be shorter than any earlier group. We can already tell that as ordinary natural language series become longer with more groups, it will be more rare that they be super-sequences. Poetry and songs do remain a possibility for logically constructed super-super-sequences of natural language: line after line of super-sequences.

The SQS analysis computer program (ref.. comm. #203) in its show-analysis screen provides the (O) and (N) display options where option (O) shows the source series' sequence and hh spectra in series order, and option (N) shows the sequence and hh-spectra in spectrum neighbor order. If the sequence super-spectrum in (O) is identical to the sequence super-spectrum shown in (N), then the source series is also a super-sequence per our convention {I -5} above.

The {I -5} definition of super-sequence could be generalized to any order of nested super-sequences, even serving a potentially "infinite sequence space", although presently that degree of analytic generality seems inapplicable to Voynich text work. But lets for a moment consider a second order super-sequence to the first order one of {I -6}: suppose that one or more of the groups are resolved further, say that one or more of the H, A, V, and E, in "HAVE" are also resolvable into sequences, perhaps because the letters had originated as telemetry code groups. If the resolution preserves the condition of {I -5-2} so that spectrum-hierarchically H <= A <= V <= E then we could say we have altogether a 2nd order super-sequence. If any of the other groups / words are also resolved one depth lower, then they too must conform to {I -5-2} for the 2nd order super-sequence characterization to remain valid. We will be concerned mainly with 1st order super-sequences, but I thought it worth mentioning nested super-sequences in case with them an idea comes up for dealing with that thorny VMS text problem: the intruding gallows symbols.

We now introduce an operator on series, one that acts upon the group indexes, an operator that we will use later, the linear M operator:

{I -7} Definition of the M operator for series of sequences:

M{S{si}} = M{mi} such that: mi = sj

where j = n + 1 - i


m1 = sn
m2 = s(n - 1)
mn = s(n + 1 - n) = s1

So we see that M{mi} is essentially a reflection-shuffled version of S{si}, but without otherwise disturbing the sequences / groups; this is a bit different from the direction-reversal transformation we have worked with [1]. Lets show the M operation for the n=6 spectral series of {I -3} :

{I -8}

S{si} : 12343_123_123456_123_12_123421

M{mi} : 123421_12_123_123456_123_12343

If it happens that S{si} consists of all pillow sequences, that is its PR = 1, then the M operation and the direction-reversal transformation yield identical results. That is not quite the case in {I -8} because there is one non-pillow group in S{si}.


The {I -5} definition of super-sequence immediately suggests acknowledging the hh super-sequence: identical hh super-spectra resulting in the series order and spectral-neighbor order analyses. Observing the definitions and rules for sequences in comm. #191 it can be shown that with numerical hierarchy spectrum-neighbor ordering, every super-sequence maps to an hh super-sequence. The new point here is that it is quite possible that a source series itself may not be a super-sequence, but its series of hh sequences is. Here is an example:

{II -1} An example source series itself not a super-sequence, but mapping to an hh super-sequence [3]:


{II -2} Its sequence-spectrum series, not a super-sequence, is:


{II -3} Its hh-spectrum series is the hh super-sequence:



Now, as already noted, in general as the usual series become longer we expect super-sequencing to become rarer. Naturally we are interested in knowing the functional behaviour of this effect versus series length n, for different kinds of series, notably Voynich text-lines. Let us then develop an analytic notation for it. We will build up from an example series: the random numbers series fair reference for VMS f68v3.1 that we worked with in comm. #203:

{#203: VIII -8}


{#203: VIII -9} for which the random sequence_spectrum series is:


Now, {#203: VIII -8} is obviously not a super-sequence. But, if we take its groups and re-arrange them in spectrum neighbor order, we can create a super-sequence. Here it is shown in {III -1}, and underneath we show again for comparison the original random spectrum series {#203: VIII -9} in {III -2} :

{III -1} 1_112_1212_1213_1232_1234_1234_11123_12345_12345_123224_1221343_1223453_1234556

{III -2} 1234556_1212_123224_1_12345_1221343_1213_1223453_112_1234_1232_1234_12345_11123

From inspection alone it is clear that according to {I -5} the series {III -1} is indeed a super-sequence. In general, for a series of sequences S{si} we will call the re-arrangement of its groups into a super-sequence its reference super-sequence, and denote it R(ri}. Thus above, {III -1} is the R{ri} of the S{si} shown in {III -2}. Of course, if an S{si} is already a super-sequence, then it is also its own R{ri}.

Let us tabulate both these series with respect to group order.

{III -3} group order i : group si from source-series {III -2} : group ri from its corresponding reference super-sequence {III -1}

01: 1234556 : 1
02: 1212 : 112
03: 123224 : 1212
04: 1 : 1213
05: 12345 : 1232
06: 1221343 : 1234
07: 1213 : 1234
08: 1223453 : 11123
09: 112 : 12345
10: 1234 : 12345
11: 1232 : 123224
12: 1234 : 1221343
13: 12345 : 1223453
14: 11123 : 1234556

From table {III -3} we can see that in S{si} the sequence 1234556, namely s1, is the maximum out of order with respect to the corresponding super-sequence, by amount: n - 1 = 13 positions too soon, where n is the total number of groups / series positions, here = 14. The sequence 1213 in {III -2} is 3 positions later than where it should be for a super-sequence. And so on.

The definition of the groups-series-relative super-sequence deviation points-curve now suggests itself straightforwardly. We say groups-series-relative so as to leave open the future possibility of an absolute deviation.

{III -4} Definition of the groups-series-relative super-sequence deviation number-function curve V(i) :

V(i) = j[ rj ] - i[ si ]


i[ si ] is the group-order index i of si, and
j[ rj ] is the group-order index j of rj, such that rj = si, and
identical groups (like 1234 in our current random series example) are taken in order: the second in the source is compared with the second in the reference, and so on. Both i and j run 1 to n of course.

So for example, using table {III -3}, here is the calculation of curve-point V(3) in the defined notation:

{III -5} V(3) = j[ rj ] - i[ si ] = j[ rj ] - 3[ 123224 ] = 11[ 123224 ] - 3[ 123224 ] = 11 - 3 = +8

Doing this for all the si of {III -2}, using table {III -3}, we obtain {III -2}'s super-sequence deviation curve as the following set of n=14 plot-able points:

{III -6} For series {III -2} the set {V(i)} : +13, +1, +8, -3, +4, +6, -3, +5, -7, -4, -6, -5, -3, -6

It is hardly surprising that for this random numbers series the deviation curve would enclose so much area. The sum of the absolute values of these numbers is: 74. Of course the plot of the deviation curve of a super-sequence itself would be as V(i) = 0. Oppositely, maximum deviations depend directly on n, and studying them leads naturally to the super-sequence deviation factor, VF, via an interesting function I(n) which allows us to fairly compare deviations for series of different n.


For quick rough comparisons of series it would be nice to have a single integration number reflecting the entire V(i) deviation, however roughly so. To define such a super-sequence deviation factor so that its range of values is universally referenced, we already have the lower bound V(i) = 0 for no deviation, but we need an upper bound for maximum deviation, one that will take into account different values of n and allow fair comparisons between different sized series. To get one, we consider a special case R{ri} and a mirroring of the groups order of it that we obtain with the M operator.

{IV -1} Definition of a pure reference super-sequence. Let:

R'{r'i} be such that: r'1 < r'2 < r'3 < ....... < r'n

So, here R'{r'i} is a super-sequence with no two successive groups equal. Let us call such an R'{r'i} a "pure" super-sequence. In contrast, since {III -1} has a pair of 1234 and a pair of 12345 sequences, it is therefore an impure super-sequence. Lets show an example pure R'(r'i} for n = 5 along with the result of the M operation:

{IV -2}

R'{r'i} : 112_1233_1234_123334_123455

M{mi} : 123455_123334_1234_1233_112

Now, if we write the abstractions of {IV -2} :

{IV -3}

R'{r'i} : r'1_r'2_r'3_r'4_r'5

M{mi} : r'5_r'4_r'3_r'2_r'1

then it is seen that for all particular possibilities of pure super-sequences of n=5, there is in {IV -3} an invariance: V(i) always calculates to the same linear points-curve:

{IV -4} V(i) for {IV -3} : +4, +2, 0, -2, -4,

If we had chosen n=6, where n is an even number, the result would be V(i) : +5, +3, +1, -1, -3, -5,

In both cases the sum of the deviations is zero. Shortly we will sum their absolute values instead. The results in {IV -4} will be similarly reflected for all pure super-sequences of length n groups, according to whether n is even, or odd. And of course for n=1 the V(1) = 0.

The deviation curve calculated, as above, from a pure R'{r'i} of n groups and its derivative M{mi}, represents what we will take as the maximum possible deviation that any series S{si} of n groups could attain against a super-sequence constructed of the identical groups. Thus it is the mechanism for obtaining an upper reference bound for super-sequence deviation. Let us sum the absolute values of such a V(i) and denote this sum I(n) :

{IV -5} Integer Progression Deviation Function I(n), the sum of the absolute values of the V(i) between a pure super-sequence R'{r'i} and its M{mi} :

I(n) = (i: 1 to n)SUM | V(i) | = (i: 1 to n)SUM | j[ rj ] - i[ mi ] | = (i: 1 to n)SUM | (n + 1 - i) - i |

= (i: 1 to n)SUM | n + 1 - 2i |

This sum evaluates to:

{IV -6}

I(n) = [ ( n^2) - c ] / 2

where c = [ 1 + (-1)^(n+1) ] / 2

Although we conceptualized toward I(n) with specific series of sequences, it is seen that the I(n) function is independent of the structures of the groups and its value depends only on n. Therefore I(n) can be regarded as a function first and foremost connected to the progression of the integers, aside all considerations of the sequences we have been studying: I(n) gives the progression-order-deviation between the progression of integers and their reflected progression. And so we will call it the Integer Progression Deviation Function. And we will shortly press it into service with our sequence analysis. The behaviour of I(n) is strongly governed by the number 2, its values rise quadratically with n, with an oscillation component arising from the alternating even and odd integers, and showing interesting plateaus in the rate of rise:

{IV -7} I(n = 1,2,3,....) : 0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, .......

As it turns out, I(n) seems to produce the identical values of another well-known function [4]: Floor( (n^2)/2 )

The conception of Floor(n^2/2) does not help us understand the analytics we are doing here, so we will retain the descriptive name Integer Progression Deviation function and stick with its I(n) specification per {IV -5} and {IV -6}, which is a pure generating formula not involving number comparisons like Floor. The relationship between the two conceptions is of course of mathematical interest.

Before continuing with the work at hand we observe from {IV -6} that I(-n) = I(n) and I(0) = 0. Now in our present work we always have n=>1 of course, but in case it comes in handy sometime we note that different conventions as regards what are taken as positive and negative integers, whole numbers, and natural numbers, allow us to define a variation of I(n):

{IV -8} The Natural Deviation Function nu(n) :

nu(n) = I(n) for n not equal to zero

nu(0) = sqr(-1)

Perhaps one way to use nu(n) is in attacks on the intruding gallows problem: define a complex series, and then also a complex super-sequence, such that when no intruding gallows are present in the series, the imaginary components of the complex series are zero and it becomes an ordinary real series as heretofore. And so on. We'd have to think about this a while, and if it begins to appear attractive for development, then our Greek friend nu(n) is ready if needed.


We can now proceed and define a good deviation factor with its values ranging from 0 for no deviation, to 1 for maximum deviation, for series of any length n > 1.

{V -1} The super-sequence deviation factor VF is defined for n => 2 :

VF = { (i: 1 to n)SUM | V(i) | } / I(n)

In other words, the sum of the absolute values of V(i) calculated for S{si} versus its R{ri}, divided by the summed maximum possible deviation for the n involved. For a pure super-sequence like the R'{r'i} of {IV -2} all the V(i) = 0 and therefore its VF = 0. Oppositely, a series of length n that happens to be a reflection of a pure super-sequence, and is the very opposite of a pure super-sequence, causes the numerator in {V -1} to sum identical to I(n), and its VF = 1. Thus low values (min of 0) of VF indicate that the series is close to being a true super-sequence, while higher values (max of 1) indictate that the series deviates greatly from being a super-sequence.

For the random numbers series {#203: VIII -8} we obtain: VF = 74/98 = 0.7551. If, per previous analytic proceedings we investigate a series of sequences not just as given, that is its forward, but also under reverse-direction tansformation, that is its reverse, then we can regard this VF as the forward fVF. The VF for the reverse-direction transformed {#203: VIII -8} series calculates to: rVF = 58/98 = 0.5918. Therefore the reverse-direction transformation of the random numbers series results in a series that is nearer to being a super-sequence. Finally, we can define the difference:

{V -2} drfVF = rVF - fVF

The drfVF can range over +/- 1.

For the {#203: VIII -8} random numbers series: drfVF = (58 - 74)/98 = -0.1633

When VF is written alone without an "f" and there is no confusion, we take it to mean fVF.

Here is an n=5 example series for which drfVF = 0.5 - 0.5 = 0

{V -3} 1_11_12_11_1

That is, for this series there is no change in deviation from super-sequence proximity between its forward and reverse versions: they are equally deviant from a true super-sequence. And this yet again shows just how complex is the problem of the definition of a "random" series, as was touched upon to some extent in comm. #203. We saw a moment ago that the change in the random series' drfVF is not much, -0.1633, and indeed we might expect little change with a random series forward versus reverse. But a zero change, like with {V -3}, wouldn't do: the {V -3} series does not look at all "random" on account of the high degree of symmetry it bears.


If in the {V -3} series we chop off the last group, the resulting n=4 series is much nearer to being a super-sequence. And chopping off from it, its last group, indeed results in an n=3 super-sequence. This suggests another measure of the proximity of a series to super-sequence:

{VI -1} Definition of the super-sequence ratio SSR

Let S{si} be a series of sequences with i=1 to i=n

SSRjk( S{si} ) = (k - j + 1) / n

where j and k are indexes such that sj_......._sk is a sub-series that when taken by itself is a super-sequence.

If j=1 and there is no confusion, then we simply write: SSR = k/n

Furthermore, as with VF, when there is no confusion we can take SSR as fSSR, and also look at the reverse-direction rSSR, and their difference and / or ratio. For {V -3} we obtain: fSSR = rSSR = 3/5 = 0.6000, showing a symmetry of the series.

With the full SSRjk definition the j and k indexes allow handling embedded super-sequences, which may come in handy with analysis of sequence clusters. Clearly there is a fairly complicated relation between SSRjk and VF for which the equations, if needed, may be calculated with some work. Needless to say, SSR ranges from 1/n for an essentially non-super-sequence, to n/n = 1 for a super-sequence.


Following are the deviation curves, factors, and ratios, supplementing the reference data of comms. #203 and #204.

* {#203: IV -1} Mixed ramps long English sentence. PR = 18/18 = 1.0000
fVF = 78 / 162 = 0.4815 : rVF = 112 / 162 = 0.6914
fSSR = 3 / 18 = 0.1667 : rSSR = 1 / 18 = 0.0556
f V(i): 4, 4, 8, -3, -3, 3, 5, 5, -2, 8, -8, -2, 1, 1, -7, 0, -13, -1,
r V(i): 16, -1, 8, 1, 7, 7, 2, -6, 9, -4, 3, 3, -3, -11, -11, 0, -10, -10,

* {#203: [9]} Start of Greek N.T. Gospel of John. PR = 17/17 = 1.0000
fVF = 74 / 144 = 0.5139 : rVF = 96 / 144 = 0.6667
fSSR = 2 / 17 = 0.1176 : rSSR = 1 / 17 = 0.0588
f V(i): 3, 9, 2, -3, 10, 2, -5, 8, -3, 2, -2, 1, -3, 0, -8, -13, 0,
r V(i): 14, -1, 1, 7, 3, 6, 2, 5, -4, 6, -9, -2, 4, -11, -9, -2, -10,

* {#203: III -4} Equal ramps English vms bug sentence. PR = 5/5 = 1.0000
fVF = 0 / 12 = 0.0000 : rVF = 0 / 12 = 0.0000
fSSR = 5 / 5 = 1.0000 : rSSR = 5 / 5 = 1.0000
f V(i): 0, 0, 0, 0, 0,
r V(i): 0, 0, 0, 0, 0,

* {#203: V -3} All-ramps-but-one English sentence. PR = 8/9 = 0.8889
fVF = 12 / 40 = 0.3000 : rVF = 36 / 40 = 0.9000
fSSR = 2 / 9 = 0.2222 : rSSR = 2 / 9 = 0.2222
f V(i): 0, 1, -1, 1, 3, -2, 0, 1, -3,
r V(i): 6, 6, 2, -1, 4, 0, -6, -4, -7,

* {#203: [10]} Rhyming German Proverb. PR = 7/9 = 0.7778
fVF = 24 / 40 = 0.6000 : rVF = 26 / 40 = 0.6500
fSSR = 1 / 9 = 0.1111 : rSSR = 2 / 9 = 0.2222
f V(i): 5, 1, 5, 0, -3, -5, 0, 1, -4,
r V(i): 2, 7, 4, -3, -3, -2, -1, -3, -1,

* {#203: [14]} Reverend Drury's stammering. PR = 122/158 = 0.7722
fVF = 8108 / 12482 = 0.6496 : rVF = 7628 / 12482 = 0.6111
fSSR = 1 / 158 = 0.0063 : rSSR = 1 / 158 = 0.0063
f V(i): 68, -1, 75, 12, 74, 64, 73, 9, -7, 116, 70, 24, -10, 68, 22, 108, 59, 20, 64, 122, 18, 62, 54, 121, 115, 101, 116, -10, 42, 106, 90, 8, 78, 51, -31, 92, 49, 3, 107, 32, 1, 87, 44, -1, -40, 104, -28, 40, 92, -6, 96, -7, -33, 35, 75, 100, 100, 100, 92, -14, -40, -40, 89, -17, 60, 24, -19, -19, 68, 83, 84, 19, -67, 18, -25, 17, -70, 16, -28, -28, 67, -9, -75, 11, -32, -63, 44, -79, 7, -36, 47, 47, -38, -84, 2, -40, -73, 24, -42, -42, -42, -42, -78, 28, -7, -80, -46, -34, -47, 25, -84, -13, -85, 9, -52, -105, -53, -89, -54, -20, -91, -91, -9, -92, -10, -25, -15, -26, -96, -55, 2, -16, -30, -17, -17, -32, -18, -103, -127, -27, -36, -129, -37, -37, -111, -2, -39, -134, 0, 4, -85, -43, -86, -20, -45, -141, -89, -38,
r V(i): 112, 68, -2, 74, 121, 30, 72, 29, 144, 138, -9, 68, 129, 2, 66, 66, -14, 65, 104, -16, 14, 92, 61, 91, 91, 59, 90, 99, 42, -13, 55, 92, 54, 84, -17, 83, -18, -18, 49, -2, -20, -3, -38, -4, 75, -24, 42, -25, 87, -9, 21, -10, -29, 36, 73, -31, -14, -14, -14, -14, 60, -36, -16, 27, -59, -18, 71, 71, -20, 22, -64, 57, -46, -24, 18, -68, -4, 72, -28, -28, 13, -73, 12, -31, 11, -76, 10, 67, 62, 50, -37, -37, 5, 17, -39, 56, -69, -69, -42, 54, 55, 55, 55, 26, -6, -76, -49, 39, -50, 25, -11, -81, 36, -103, -55, -15, 14, -57, -45, 25, -59, -20, 9, -112, -22, -1, -64, -6, 12, -55, -99, 11, 0, 3, 11, -68, -33, -74, 5, -35, -76, -73, -31, -78, -39, -133, -80, -41, -15, -136, -118, -44, -77, -45, -121, -46, -142, -81,

* {#203: [11]} De-coded radiotelegraph series. PR = 10/13 = 0.7692
fVF = 40 / 84 = 0.4762 : rVF = 54 / 84 = 0.6429
fSSR = 4 / 13 = 0.3077 : rSSR = 1 / 13 = 0.0769
f V(i): 0, 1, 3, 6, 2, -2, 6, 0, 2, -1, -9, -7, -1,
r V(i): 12, 1, -1, 2, 6, 1, 5, -4, -1, 0, -2, -7, -12,

* {#203: I -1} Mixed series. PR = 6/8 = 0.7500
fVF = 14 / 32 = 0.4375 : rVF = 24 / 32 = 0.7500
fSSR = 2 / 8 = 0.2500 : rSSR = 1 / 8 = 0.1250
f V(i): 0, 4, -1, 1, 2, -2, -4, 0,
r V(i): 7, -1, 2, 3, -1, -4, -1, -5,

* {#203: V -8} Beginning of Latin Genesis. PR = 9/13 = 0.6923
fVF = 58 / 84 = 0.6905 : rVF = 44 / 84 = 0.5238
fSSR = 2 / 13 = 0.1538 : rSSR = 1 / 13 = 0.0769
f V(i): 0, 11, 9, 0, 6, -4, 3, -2, -1, -5, -2, -9, -6,
r V(i): 6, -1, 7, 0, 3, 0, 2, -6, 2, -5, 1, 1, -10,

* {#203: [13]} Friedman's 1959 VMS Anagram. PR = 13/19 = 0.6842
fVF = 78 / 180 = 0.4333 : rVF = 142 / 180 = 0.7889
fSSR = 2 / 19 = 0.1053 : rSSR = 1 / 19 = 0.0526
f V(i): 0, 3, -1, 7, -2, 12, 8, 8, -3, -1, -4, -8, 0, -4, -1, 1, -9, -6, 0,
r V(i): 18, 10, 2, 13, 9, 3, 6, -6, -3, 0, -4, 4, 2, 4, -12, -5, -13, -10, -18,

* {#203: VI -2} Voynich f68v3.1 text-line. PR = 9/14 = 0.6429
fVF = 78 / 98 = 0.7960 : rVF = 68 / 98 = 0.6939
fSSR = 1 / 14 = 0.0714 : rSSR = 1 / 14 = 0.0714
f V(i): 8, 6, 7, -2, 7, 5, -4, -7, -5, 4, 2, -7, -6, -8,
r V(i): 6, 4, 2, 10, 8, -4, -6, -5, 2, 2, -7, -2, -5, -5,

* {#205: I -6} Super-sequence series. PR = 5/8 = 0.6250
fVF = 0 / 32 = 0.0000 : rVF = 30 / 32 = 0.9375
fSSR = 8 / 8 = 1.0000 : rSSR = SSR = 1 / 8 = 0.1250
f V(i): 0, 0, 0, 0, 0, 0, 0, 0,
r V(i): 7, 4, 4, 0, 0, -3, -5, -7,

* {#205: II -1} Non-super-sequence series with an hh super-sequence. PR = 5/8 = 0.6250
fVF = 2 / 32 = 0.0625 : rVF = 30 / 32 = 0.9375
fSSR = 6 / 8 = 0.7500 : rSSR = 1 / 8 = 0.1250
f V(i): 0, 0, 0, 0, 0, 1, -1, 0,
r V(i): 7, 5, 3, 0, 0, -3, -5, -7,

* {#203: [15]} Binary bytes series. PR = 7/13 = 0.5385
fVF = 66 / 84 = 0.7857 : rVF = 66 / 84 = 0.7857
fSSR = 6 / 13 = 0.4615 : rSSR = 3 / 13 = 0.2308
f V(i): 6, 11, 8, 1, 1, 6, -6, -5, -5, -8, -2, -2, -5,
r V(i): 5, 8, 8, -3, 3, 7, -5, 1, -6, -6, 1, -5, -8,

* {#203: VIII -8} Random numbers series fair reference for VMS f68v3.1. PR = 6/14 = 0.4286
fVF = 74 / 98 = 0.7551 : rVF = 58 / 98 = 0.5918
fSSR = 1 / 14 = 0.0714 : rSSR = 2 / 14 = 0.1429
f V(i): 13, 1, 8, -3, 4, 6, -3, 5, -7, -4, -6, -5, -3, -6,
r V(i): 7, 7, 3, 0, 2, -4, 7, -3, 3, 0, -10, -1, -10, -1,

* {#203: II -2} All hh-1222 "baby-talk" series. PR = 3/7 = 0.4286
fVF = 16 / 24 = 0.6667 : rVF = 12 / 24 = 0.5000
fSSR = 3 / 7 = 0.4286 : rSSR = 3 / 7 = 0.4286
f V(i): 2, 2, 3, -3, 0, 1, -5,
r V(i): 2, -1, 4, 0, -3, -1, -1,

* {#203: [12]} All non-pillows English sentence. PR = 0/13 = 0.0000
fVF = 58 / 84 = 0.6905 : rVF = 54 / 84 = 0.6429
fSSR = 1 / 13 = 0.0769 : rSSR = 1 / 13 = 0.0769
f V(i): 12, 6, -2, 3, 4, -1, 4, -5, -5, -4, -9, -2, -1,
r V(i): 11, 7, -1, 4, 0, -3, 4, -4, 1, -3, -10, -6, 0,

* {#203: X -2} Moretus Latin taken from MtoK8JAN1639.txt, document-lines series:

03: PR = 6/8 = 0.7500
fVF = 12 / 32 = 0.3750 : rVF = 26 / 32 = 0.8125
fSSR = 1 / 8 = 0.1250 : rSSR = 2 / 8 = 0.2500
f V(i): 5, 0, 0, 0, 0, -5, 1, -1,
r V(i): 6, 6, -2, 1, -1, -4, -4, -2,

04: PR = 7/9 = 0.7778
fVF = 24 / 40 = 0.6000 : rVF = 22 / 40 = 0.5500
fSSR = 2 / 9 = 0.2222 : rSSR = 1 / 9 = 0.1111
f V(i): 2, 7, 1, -3, 0, 1, 1, -6, -3,
r V(i): 2, 0, 5, 3, -1, -5, -2, 1, -3,

05: PR = 13/14 = 0.9286
fVF = 46 / 98 = 0.4694 : rVF = 62 / 98 = 0.6327
fSSR = 2 / 14 = 0.1429 : rSSR = 2 / 14 = 0.1429
f V(i): 1, 11, 0, 8, -4, 1, 1, -4, 0, -5, -5, -2, 1, -3,
r V(i): 10, 12, 4, -2, -2, 2, -3, 1, 1, -9, 1, -7, 0, -8,

06: PR = 7/9 = 0.7778
fVF = 28 / 40 = 0.7000 : rVF = 30 / 40 = 0.7500
fSSR = 1 / 9 = 0.1111 : rSSR = 2 / 9 = 0.2222
f V(i): 5, 3, 6, -3, -3, -3, 0, 0, -5,
r V(i): 3, 6, 4, -1, -3, -5, 2, -3, -3,

07: PR = 5/8 = 0.6250
fVF = 16 / 32 = 0.5000 : rVF = 28 / 32 = 0.8750
fSSR = 2 / 8 = 0.2500 : rSSR = 1 / 8 = 0.1250
f V(i): 2, 4, -1, 0, -4, 2, -2, -1,
r V(i): 6, 3, 5, -3, -1, -3, -1, -6,

08: PR = 6/10 = 0.6000
fVF = 44 / 50 = 0.8800 : rVF = 26 / 50 = 0.5200
fSSR = 3 / 10 = 0.3333 : rSSR = 4 / 10 = 0.4000
f V(i) = 4, 5, 7, 4, -4, -2, 2, -2, -7, -7,
r V(i) = 1, 1, 3, 5, -1, -5, 1, 2, -2, -5,

09: PR = 7/9 = 0.7778
fVF = 28 / 40 = 0.7000 : rVF = 28 / 40 = 0.7000
fSSR = 3 / 9 = 0.3333 : rSSR = 1 / 9 = 0.1111
f V(i): 2, 3, 6, -3, 1, 1, 1, -6, -5,
r V(i): 3, -1, 5, 3, 1, -4, 2, -3, -6,

10: PR = 8/10 = 0.8000
fVF = 32 / 50 = 0.6400 : rVF = 24 / 50 = 0.4800
fSSR = 1 / 10 = 0.1000 : rSSR = 2 / 10 = 0.2000
f V(i): 8, 3, 0, 0, 1, 1, 3, -7, -1, -8,
r V(i): 1, 3, -2, 6, 1, 1, -4, -4, -1, -1,

11: PR = 7/10 = 0.7000
fVF = 24 / 50 = 0.4800 : rVF = 38 / 50 = 0.7600
fSSR = 2 / 10 = 0.2000 : rSSR = 2 / 10 = 0.2000
f V(i): 2, 5, -2, 0, 1, 4, -2, -6, -1, -1,
r V(i): 8, 6, -2, 0, 5, 0, -2, -6, -2, -7,

* {#203: X -3} Moretus Latin taken from MtoK8JAN1639.txt, logical sentences series:

01: PR = 11/15 = 0.7333
fVF = 70 / 112 = 0.6250 : rVF = 84 / 112 = 0.7500
fSSR = 1 / 15 = 0.0667 : rSSR = 2 / 15 = 0.1333
f V(i): 11, 1, 1, 1, 4, -4, 8, 6, -3, 3, -4, -11, -5, -3, -5,
r V(i): 8, 9, 3, -3, 2, 7, 1, 7, 5, -8, -1, -9, -9, -9, -3,

02: PR = 25/32 = 0.7813
fVF = 248 / 512 = 0.4844 : rVF = 424 / 512 = 0.8281
fSSR = 2 / 32 = 0.0625 : rSSR = 1 / 32 = 0.0313
f V(i): 9, 18, 0, 20, -1, 17, -6, 3, 3, -5, 2, -6, -6, 0, 14, 14, 4, 10, -17, -12, -6, 4, 4, -6, -8, -1, -11, -9, -20, 2, -9, -1,
r V(i): 30, 20, 29, -1, 13, 11, 18, 8, 10, 17, 15, -2, -9, -13, 15, 4, 12, 10, -8, -15, -15, -10, -16, -11, -11, -24, -4, -20, -5, -21, -10, -17,

03: PR = 7/12 = 0.5833
fVF = 54 / 72 = 0.7500 : rVF = 42 / 72 = 0.5833
fSSR = 2 / 12 = 0.1667 : rSSR = 1 / 12 = 0.0833
f V(i): 7, 10, 6, -3, -1, 4, 0, -6, -6, -5, -5, -1,
r V(i): 10, 4, 2, -2, -2, 1, 3, -4, -8, -1, 1, -4,

04: PR = 19/26 = 0.7308
fVF = 206 / 338 = 0.6095 : rVF = 208 / 338 = 0.6154
fSSR = 4 / 26 = 0.1538 : rSSR = 2 / 26 = 0.0769
f V(i): 3, 11, 17, 19, 0, 6, 12, 6, -3, -1, 4, 4, 12, -13, 2, -8, -10, 3, -17, -10, -3, 4, -12, -21, -1, -4,
r V(i): 20, 22, -2, 5, 20, 7, 3, -6, 13, -6, -3, 2, -10, 12, 0, 0, -6, -13, -2, -1, -9, -16, 0, -4, -7, -19,

* {#203: X -5} Hooke English from Micrographia in 4 logical units series:

01: PR = 19/24 = 0.7917
fVF = 204 / 288 = 0.7083 : rVF = 168 / 288 = 0.5833
fSSR = 2 / 24 = 0.0833 : rSSR = 1 / 24 = 0.0417
f V(i): 8, 19, 9, 9, 5, 9, 9, -5, 11, -6, 0, 10, 5, -9, 8, -10, -16, -1, -5, -13, -19, -3, -15, 0,
r V(i): 23, 1, 15, -3, -1, 6, 8, -6, -4, 10, -5, 7, 9, -5, -8, 5, -9, -2, -2, -10, -8, -8, 0, -13,

02: PR = 8/14 = 0.5714
fVF = 64 / 98 = 0.6531 : rVF = 52 / 98 = 0.5306
fSSR = 2 / 14 = 0.1429 : rSSR = 1 / 14 = 0.0714
f V(i): 2, 11, 1, 5, 9, 1, -2, 0, 3, -9, 0, -10, -7, -4,
r V(i): 8, 1, -2, 7, -3, 6, 0, -4, -1, 4, -1, -7, 0, -8,

03: PR = 34/42 = 0.8095
fVF = 536 / 882 = 0.6077 : rVF = 528 / 882 = 0.5986
fSSR = 2 / 42 = 0.0476 : rSSR = 2 / 42 = 0.0476
f V(i): 0, 29, 20, 29, -1, -1, -5, 16, -3, -7, 14, 14, 3, 25, 22, 6, 10, 22, 16, -13, -4, 20, -5, 8, -17, -7, 14, -8, -1, -9, -22, -22, -22, -19, -6, -24, -1, -4, -9, -27, -3, -28,
r V(i): 3, 35, 2, 19, 31, 29, -1, 16, 6, -3, -3, -3, 9, 11, 1, 23, 0, -8, 12, -2, 21, -3, -12, 9, 15, 0, -6, 10, 12, -10, -4, -4, -32, -22, -6, -34, -24, -24, -5, -10, -9, -39,

04: PR = 22/24 = 0.9167
fVF = 190 / 288 = 0.6597 : rVF = 144 / 288 = 0.5000
fSSR = 2 / 24 = 0.0833 : rSSR = 3 / 24 = 0.1250
f V(i): 8, 21, 12, -1, -4, 11, 13, 2, -7, 11, 0, 6, 3, -2, 4, -12, -12, -5, -5, 2, -15, 2, -16, -16,
r V(i): 2, 2, 20, 1, 15, 3, 3, -2, -2, 7, 0, 3, 5, -2, 6, -15, -4, 4, 0, -18, -13, -6, 1, -10,

* {#203: X -6} Hooke English from Micrographia in 5 logical units series:

01: PR = 19/24 = 0.7917
fVF = 204 / 288 = 0.7083 : rVF = 168 / 288 = 0.5833
fSSR = 2 / 24 = 0.0833 : rSSR = 1 / 24 = 0.0417
f V(i): 8, 19, 9, 9, 5, 9, 9, -5, 11, -6, 0, 10, 5, -9, 8, -10, -16, -1, -5, -13, -19, -3, -15, 0,
r V(i): 23, 1, 15, -3, -1, 6, 8, -6, -4, 10, -5, 7, 9, -5, -8, 5, -9, -2, -2, -10, -8, -8, 0, -13,

02: PR = 8/14 = 0.5714
fVF = 64 / 98 = 0.6531 : rVF = 52 / 98 = 0.5306
fSSR = 2 / 14 = 0.1429 : rSSR = 1 / 14 = 0.0714
f V(i): 2, 11, 1, 5, 9, 1, -2, 0, 3, -9, 0, -10, -7, -4,
r V(i): 8, 1, -2, 7, -3, 6, 0, -4, -1, 4, -1, -7, 0, -8,

03: PR = 18/22 = 0.8182
fVF = 112 / 242 = 0.4628 : rVF = 178 / 242 = 0.7355
fSSR = 2 / 22 = 0.0909 : rSSR = 1 / 22 = 0.0455
f V(i): 0, 14, 8, 13, -1, -1, -5, 4, -3, -7, 2, 2, -5, 6, 4, -6, -2, 3, -1, -13, -12, 0,
r V(i): 21, 6, 1, 13, 15, 5, 3, 11, 12, -1, 1, 1, -12, -9, -1, -14, -11, -11, -1, -5, -5, -19,

04: PR = 16/20 = 0.8000
fVF = 126 / 200 = 0.6300 : rVF = 122 / 200 = 0.6100
fSSR = 2 / 20 = 0.1000 : rSSR = 2 / 20 = 0.1000
f V(i): 8, 14, -2, 6, 15, 5, 6, 4, -7, -7, -7, -4, 1, -9, 3, 1, -2, -12, 0, -13,
r V(i): 0, 17, -1, 9, 13, 11, -4, 6, -1, -6, -6, -6, -1, 1, -6, 4, -7, -11, -3, -9,

05: PR = 22/24 = 0.9167
fVF = 190 / 288 = 0.6597 : rVF = 144 / 288 = 0.5000
fSSR = 2 / 24 = 0.0833 : rSSR = 3 / 24 = 0.1250
f V(i): 8, 21, 12, -1, -4, 11, 13, 2, -7, 11, 0, 6, 3, -2, 4, -12, -12, -5, -5, 2, -15, 2, -16, -16,
r V(i): 2, 2, 20, 1, 15, 3, 3, -2, -2, 7, 0, 3, 5, -2, 6, -15, -4, 4, 0, -18, -13, -6, 1, -10,

* {#203: XI -1} Voynich f20r 1st paragraph (Currier language A):

L1: PR = 5/7 = 0.7143
fVF = 16 / 24 = 0.6667 : rVF = 16 / 24 = 0.6667
fSSR = 1 / 7 = 0.1429 : rSSR = 1 / 7 = 0.1429
f V(i): 4, 0, -2, 2, 2, -3, -3,
r V(i): 3, 0, 4, 1, -4, -3, -1,

L2: PR = 6/8 = 0.7500
fVF = 14 / 32 = 0.4375 : rVF = 30 / 32 = 0.9375
fSSR = 1 / 8 = 0.1250 : rSSR = 1 / 8 = 0.1250
f V(i): 1, -1, 0, 2, 3, 1, -3, -3,
r V(i): 5, 2, 4, 4, 0, -4, -6, -5,

L3: PR = 6/8 = 0.7500
fVF = 20 / 32 = 0.6250 : rVF = 22 / 32 = 0.6875
fSSR = 1 / 8 = 0.1250 : rSSR = 2 / 8 = 0.2500
f V(i): 5, -1, 4, -2, -1, -3, 1, -3,
r V(i): 4, 6, 0, 0, -4, 1, -5, -2,

L4: PR = 5/5 = 1.0000
fVF = 2 / 12 = 0.1667 : rVF = 12 / 12 = 1.0000
fSSR = 2 / 5 = 0.4000 : rSSR = 1 / 5 = 0.2000
f V(i): 0, 1, -1, 0, 0,
r V(i): 4, 2, -1, -1, -4,

* {#203: XI -5} Voynich f95r2 1st paragraph (Currier language B):

L1: PR = 7/10 = 0.7000
fVF = 30 / 50 = 0.6000 : rVF = 32 / 50 = 0.6400
fSSR = 1 / 10 = 0.1000 : rSSR = 3 / 10 = 0.3000
f V(i): 6, -1, 1, 5, -3, 0, 1, 2, -4, -7,
r V(i): 0, 2, 7, 4, 1, -4, 2, -3, -6, -3,

L2: PR = 9/10 = 0.9000
fVF = 38 / 50 = 0.7600 : rVF = 30 / 50 = 0.6000
fSSR = 1 / 10 = 0.1000 : rSSR = 1 / 10 = 0.1000
f V(i): 6, 3, 5, -3, -3, 3, -4, 2, -5, -4,
r V(i): 4, -1, 7, -2, 3, -3, -3, 1, -3, -3,

L3: PR = 9/11 = 0.8182
fVF = 44 / 60 = 0.7333 : rVF = 24 / 60 = 0.4000
fSSR = 1 / 11 = 0.0909 : rSSR = 3 / 11 = 0.2727
f V(i): 10, 2, 2, 4, 1, -5, 3, -1, 0, -8, -8,
r V(i): 0, 0, 6, 1, 5, -3, -1, 0, -2, -6, 0,

L4: PR = 5/6 = 0.8333
fVF = 12 / 18 = 0.6667 : rVF = 12 / 18 = 0.6667
fSSR = 1 / 6 = 0.1667 : rSSR = 2 / 6 = 0.3333
f V(i): 4, 1, -1, -3, 1, -2,
r V(i): 2, 4, -2, -2, -1, -1,

* {#203: XIII -2} spectral series / clusters of the first two lines under the VMS f68v3 circle's sectioning-horizontal:

01: PR = 4/4 = 1.0000
fVF = 4 / 8 = 0.5000 : rVF = 4 / 8 = 0.5000
fSSR = 3 / 4 = 0.7500 : rSSR = 3 / 4 = 0.7500
f V(i): 0, 1, 1, -2,
r V(i): 0, 1, 1, -2,

02: PR = 2/4 = 0.5000
fVF = 6 / 8 = 0.7500 : rVF = 2 / 8 = 0.2500
fSSR = 1 / 4 = 0.2500 : rSSR = 2 / 4 = 0.5000
f V(i): 2, -1, 1, -2,
r V(i): 0, 1, -1, 0,


The above numbers were produced with SQS, which was updated for the purpose as version V1.2. I have sent SQS V1.2 to the J.VS Librarian Greg Stachowski and he has installed it in the SQS Library deposit # 19-1-2008-06-29 [5]. Again, please let me know of errors if you find them, and suggestions - thanks.

We now have a total of 49 series, 11 of them Voynich, available for reference in signals sequence analysis, investigated with various analytic functions in J.VS communications #203, #204, and here. Quite a bit of study is necessary to evaluate the results altogether, while acknowledging that many more series of different kinds and lengths must be analyzed for a proper perspective of practical use. The new data here immediately presents these obvious features:

{VIII -1} Number of series (of the 49 reference series) with fSSR = rSSR : 14
Percent of the 14 that are Voynich series: 35.7%

{VIII -2} Number of series (of the 49 reference series) with fVF = rVF : 5
Percent of the 5 that are Voynich series: 40%

{VIII -3} Number of series (of the 49 reference series) with fVF=rVF and also fSSR=rSSR : 3
Percent of the 3 that are Voynich series: 67%

These results are to some extent indicative of emphasized symmetries in the Voynich series. In the {VIII -3} category two of the three series achieve their status with pillow ratios PR = 1, and in fact one of those is just a degenerate super-sequence. The more unique or "difficult" achievement with a PR = 5/7 = 0.7143 is by the first line of the first paragraph of Currier-language-A Voynich text-line f20rp1 - {#203: XI -1} above. From the perspective of the particular analytics developed here in this communication, gauging the super-sequence characteristics of series of sequences, this Voynich series stands apart by itself from all the other 48 series.

Once again, under the caution that far more data must be analyzed in order to approach reliable general conclusions, and that we are investigating the signal-sequence properties of series stripped of their particular symbols dressing, nevertheless the super-sequence results here are at least consistent with the earlier indications discussed in comm. #203: hints of algorithmic generation of the Voynich text, plausibly a hybrid of random numbers, and some mathematical properties of Latin writing, contributing to generating VMS vocabulary, and their concatenation into line-unit series, and the Latin, if indeed entering the generating process, doing so as a mathematics contributor, rather than a plaintext-to-be-enciphered contributor.

Perhaps after all the VMS labels are generated similarly to the text-lines, and reflect the text mechanism in its simplest form. All this is no more than an interesting possibility at this stage, but we might well entertain it - it does not rule out the additional possibility that the algorithmic process is also functional as an enciphering mechanism parametrically. We had some discussions along these lines last year. [6]

If there is no plaintext enciphering at all, then the suggestion is that the VMS text is a kind of mathematical artform: a mathematically generated stream of groups of glyphs that convincingly simulates sensible writing, at least visually. We might understand this by analogy: suppose an artist specializes in painting landscapes, and she has much experience out in the field copying the real scenery onto canvas. She then gets an idea: differentiate general characteristics of various landscapes into generative components. Once she has those components well understood, she can create realistic-appearing scenes of landscapes back in her studio without ever even looking out the window. I think many artists use such a process naturally. Similarly, a study of the visual appearance of writing, especially a mathematical study, could result in mathematical differentiations yielding components, that when concatenated with the proper algorithm, yield realistic looking writing. And then dressed in a mysterious alphabet the so-generated series of groups of glyphs evades immediate demonstration that it is simulated writing rather than the real thing. Like the landscape painted entirely in the studio, it has become a convincing work of art.

Berj / KI3U

[1] J.VS communications #191, #203, and #204 are in the J.VS archive Vol. II, online here:

[2] Additional data for the super-sequence series {I -6} :
PR = 5/8 = 0.6250; RPR = 5/5 = 1.0000; HHR = 7/8 = 0.8750; xfrm change = 6/10 = 60%
Distribution of pillows vs non-pillows (1 = pillow sequence) :

[3] Additional data for the non-super-sequence series {II -1} which maps to an hh super-sequence:
PR = 5/8 = 0.6250; RPR = 5/5 = 1.0000; HHR = 6/8 = 0.7500; xfrm change = 5/9 = 55.6%
Distribution of pillows vs non-pillows (1 = pillow sequence) :

[4] Floor(n^2/2) and related are described in id:A007590 in The On-Line Encyclopedia of Integer Sequences:

[5] The SQS computer program is available online from the J.VS Library deposit # 19-1-2008-06-29 :

[6] J.VS: Philosophical math-text versus practical cipher-text; see comms. #62, #63, and #64 in J.VS archives Vol. I:

From Berj Ensanian
Sent Date 07-21-2008 1:55:38 PM

Subject J.VS: The signals series in evolution: VF(j) Reference Data

Dear Colleagues

The super-sequence deviation factor VF for signals sequence analysis work, is calculated on the whole length of a source series (measured by the number of sequences / groups in the series), according to the definition of VF in J.VS communication #205. The VF is a single number that can be calculated for any series of sequences, and gives a rough indication of the deviation of the series from, or alternatively its proximity to, its own reference super-sequence. For the 49 reference series accumulated in this line of work there was provided in comm. #205 reference data for both the forward VF, that is the fVF, and also the rVF for each of the series after undergoing direction-reversal transformation. [1]

Here I would like to experimentally extend the concept of VF to the super-sequence deviation factor function, VF(j). The essential idea is to use VF to track the proximity to, or deviation from super-sequence, or if you like the "super-sequence-ness", of a series as it evolves - as its groups are added one at a time.



Consider the series of n=13 sequences familiar to us as the Beginning of the Latin Vulgate Genesis that we have studied among the set of 49 reference series:

{I -1} in principio creavit deus caelum et terram terra autem erat inanis et vacua

For it we calculated fVF = 58/84 = 0.6905, and rVF = 44/84 = 0.5238, indicating that under direction reversal the series is closer to being a super-sequence than it is in its normal form. The calculation of both fVF and rVF is of course for the whole series of n=13 groups. From the definition of VF in {#205: V -1} we recall that VF is defined for n => 2.

Now, if we view a series of n groups as developing in steps of one group at a time, from j=2 to j=n, then we can ask: how does VF versus j progress within the series? We already know that with the usual series, as they become longer, we expect them to tend to recede from proximity to super-sequence status, that is, their VF will tend to rise toward the maximum 1. With VF(j) we get a look at the bumps and dips along the journey, and perhaps the peculiar bumps and dips can tell us something about the particular series we are analyzing, say if there is some rhythm of the bumps and dips. Hence the motivation for defining VF(j) :

{I -2} The values of the super-sequence deviation factor function VF(j) for the series of sequences S{sj} where j=1 to j=n are calculated on the sub-series of S such that 1 < j <= n. A complete set of calculations over j then gives us a set of (n-1) numbers that can be plotted as a points-curve and otherwise analyzed.

{I -3} Detailed VF(j) for {I -1}

index j of the last group in the sub-series : sub-series : VF(j)

02 : in principio : VF(2) = 0/2 = 0.0000
03 : in principio creavit : VF(3) = 2/4 = 0.5000
04 : in principio creavit deus : VF(4) = 4/8 = 0.5000
05 : in principio creavit deus caelum : VF(5) = 8/12 = 0.6667
06 : in principio creavit deus caelum et : VF(6) = 12/18 = 0.6667
07 : in principio creavit deus caelum et terram : VF(7) = 16/24 = 0.6667
08 : in principio creavit deus caelum et terram terra : VF(8) = 22/32 = 0.6875
09 : in principio creavit deus caelum et terram terra autem : VF(9) = 28/40 = 0.7000
10 : in principio creavit deus caelum et terram terra autem erat : VF(10) = 34/50 = 0.6800
11 : in principio creavit deus caelum et terram terra autem erat inanis : VF(11) = 42/60 = 0.7000
12 : in principio creavit deus caelum et terram terra autem erat inanis et : VF(12) = 50/72 = 0.6944
13 : in principio creavit deus caelum et terram terra autem erat inanis et vacua : VF(13) = 58/84 = 0.6905

0.0000, 0.5000, 0.5000, 0.6667, 0.6667, 0.6667, 0.6875, 0.7000, 0.6800, 0.7000, 0.6944, 0.6905,

If we take the preceeding as fVF(j), then for the reverse-direction transformed {I -1} the rVF(j) are:

{I -4} rVF(j) for {I -1}:

1.0000, 0.5000, 0.7500, 0.6667, 0.6667, 0.5833, 0.6250, 0.5000, 0.6000, 0.5000, 0.4167, 0.5238,

Obviously there is a lot of difference between the forward and reverse curves. The reverse series, ultimately at full length n=13 being closer to a super-sequence than the forward series is, progresses with somewhat less stability along the way.


The following fVF(j) and rVF(j) data for the 49 reference series supplements the other data on them in J.VS communications #203, #204, and #205. [1]

P-P means the (Hi - Lo) peak-to-peak difference.
dP-P = (forward P-P) - (reverse P-P)
dAv = (forward average) - (reverse average)

* {#203: IV -1} Mixed ramps long English sentence. PR = 18/18 = 1.0000
fVF(i): 0.0000, 0.0000, 0.7500, 1.0000, 0.7778, 0.5833, 0.4375, 0.5000, 0.4000, 0.5667, 0.5833, 0.5238, 0.4694, 0.5000, 0.4531, 0.5278, 0.4815,
rVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.5556, 0.5833, 0.6875, 0.5500, 0.6400, 0.6000, 0.5556, 0.5952, 0.6122, 0.6786, 0.6250, 0.6667, 0.6914,
f P-P = 1.0000; r P-P = 0.4500; dP-P = 0.5500
Averages: f = 0.5032; r = 0.6740; dAv = -0.1708

* {#203: [9]} Start of Greek N.T. Gospel of John. PR = 17/17 = 1.0000
fVF(i): 0.0000, 0.5000, 0.7500, 0.5000, 0.5556, 0.7500, 0.5625, 0.6000, 0.5600, 0.5667, 0.5278, 0.5238, 0.4898, 0.5179, 0.5781, 0.5139,
rVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.5556, 0.5833, 0.5000, 0.5500, 0.4400, 0.5333, 0.5833, 0.5000, 0.5918, 0.6607, 0.6250, 0.6667,
f P-P = 0.7500; r P-P = 0.5600; dP-P = 0.1900
Averages: f = 0.5310; r = 0.6379; dAv = -0.1069

* {#203: III -4} Equal ramps English vms bug sentence. PR = 5/5 = 1.0000
fVF(i): 0.0000, 0.0000, 0.0000, 0.0000,
rVF(i): 0.0000, 0.0000, 0.0000, 0.0000,
f P-P = 0.0000; r P-P = 0.0000; dP-P = 0.0000
Averages: f = 0.0000; r = 0.0000; dAv = 0.0000

* {#203: V -3} All-ramps-but-one English sentence. PR = 8/9 = 0.8889
fVF(i): 0.0000, 0.5000, 0.2500, 0.1667, 0.3333, 0.3333, 0.2500, 0.3000,
rVF(i): 0.0000, 1.0000, 1.0000, 0.6667, 0.7778, 0.8333, 0.8750, 0.9000,
f P-P = 0.5000; r P-P = 1.0000; dP-P = -0.5000
Averages: f = 0.2667; r = 0.7566; dAv = -0.4899

* {#203: [10]} Rhyming German Proverb. PR = 7/9 = 0.7778
fVF(i): 1.0000, 0.5000, 0.7500, 0.8333, 0.8889, 0.7500, 0.5625, 0.6000,
rVF(i): 0.0000, 0.5000, 0.7500, 1.0000, 0.8889, 0.8333, 0.7500, 0.6500,
f P-P = 0.5000; r P-P = 1.0000; dP-P = -0.5000
Averages: f = 0.7356; r = 0.6715; dAv = 0.0641

* {#203: [14]} Reverend Drury's stammering. PR = 122/158 = 0.7722
fVF(i): 1.0000, 0.5000, 0.7500, 0.5000, 0.5556, 0.4167, 0.5625, 0.6500, 0.5200, 0.4667, 0.5556, 0.6429, 0.5714, 0.6250, 0.5625, 0.5833, 0.6296, 0.5889, 0.5300, 0.5727, 0.5455, 0.5606, 0.5139, 0.4872, 0.4615, 0.4341, 0.4643, 0.4905, 0.4756, 0.4708, 0.5039, 0.5000, 0.4948, 0.5261, 0.5123, 0.5088, 0.5291, 0.5026, 0.5200, 0.5405, 0.5283, 0.5260, 0.5455, 0.5652, 0.5406, 0.5598, 0.5590, 0.5450, 0.5616, 0.5415, 0.5577, 0.5741, 0.5734, 0.5635, 0.5434, 0.5246, 0.5065, 0.4931, 0.5111, 0.5280, 0.5453, 0.5313, 0.5469, 0.5464, 0.5482, 0.5624, 0.5753, 0.5697, 0.5559, 0.5429, 0.5440, 0.5578, 0.5588, 0.5718, 0.5734, 0.5877, 0.5884, 0.5987, 0.6081, 0.5982, 0.6056, 0.6167, 0.6156, 0.6235, 0.6328, 0.6274, 0.6369, 0.6354, 0.6430, 0.6367, 0.6304, 0.6378, 0.6474, 0.6458, 0.6519, 0.6594, 0.6564, 0.6616, 0.6664, 0.6710, 0.6751, 0.6806, 0.6742, 0.6713, 0.6760, 0.6796, 0.6814, 0.6855, 0.6797, 0.6847, 0.6821, 0.6867, 0.6833, 0.6866, 0.6917, 0.6952, 0.6998, 0.7031, 0.6997, 0.7038, 0.7076, 0.7039, 0.7076, 0.7038, 0.7004, 0.6969, 0.6936, 0.6974, 0.6989, 0.6932, 0.6901, 0.6872, 0.6841, 0.6811, 0.6782, 0.6752, 0.6784, 0.6820, 0.6788, 0.6759, 0.6792, 0.6763, 0.6732, 0.6762, 0.6692, 0.6664, 0.6696, 0.6622, 0.6540, 0.6558, 0.6530, 0.6546, 0.6497, 0.6472, 0.6504, 0.6522, 0.6496,
rVF(i): 1.0000, 1.0000, 0.7500, 0.5000, 0.6667, 0.6667, 0.7500, 0.6000, 0.5200, 0.6000, 0.6111, 0.5714, 0.6327, 0.6250, 0.6250, 0.6667, 0.6543, 0.6333, 0.6500, 0.6727, 0.6446, 0.6288, 0.6111, 0.5962, 0.5858, 0.5714, 0.5459, 0.5524, 0.5689, 0.5583, 0.5430, 0.5404, 0.5294, 0.5588, 0.5463, 0.5760, 0.6039, 0.6053, 0.6225, 0.6429, 0.6576, 0.6775, 0.6942, 0.6779, 0.6956, 0.6920, 0.7066, 0.6833, 0.6928, 0.7015, 0.7115, 0.7251, 0.7202, 0.6997, 0.7117, 0.7204, 0.7277, 0.7356, 0.7433, 0.7290, 0.7388, 0.7460, 0.7393, 0.7472, 0.7521, 0.7326, 0.7137, 0.7185, 0.7118, 0.7183, 0.7029, 0.7102, 0.7159, 0.7112, 0.7175, 0.7206, 0.7028, 0.7071, 0.7125, 0.7085, 0.7151, 0.7108, 0.7149, 0.7104, 0.7155, 0.7109, 0.6947, 0.6803, 0.6677, 0.6715, 0.6753, 0.6721, 0.6686, 0.6720, 0.6589, 0.6633, 0.6676, 0.6714, 0.6584, 0.6455, 0.6328, 0.6207, 0.6139, 0.6132, 0.6191, 0.6240, 0.6159, 0.6205, 0.6142, 0.6130, 0.6180, 0.6100, 0.6150, 0.6189, 0.6171, 0.6110, 0.6145, 0.6169, 0.6097, 0.6134, 0.6117, 0.6063, 0.6106, 0.6091, 0.6049, 0.6084, 0.6047, 0.5986, 0.6012, 0.6051, 0.5987, 0.5941, 0.5890, 0.5830, 0.5863, 0.5853, 0.5885, 0.5828, 0.5818, 0.5853, 0.5888, 0.5874, 0.5909, 0.5898, 0.5935, 0.5968, 0.5961, 0.5921, 0.5963, 0.6004, 0.5995, 0.6024, 0.6016, 0.6054, 0.6047, 0.6086, 0.6111,
f P-P = 0.5833; r P-P = 0.5000; dP-P = 0.0833
Averages: f = 0.6087; r = 0.6474; dAv = -0.0387

* {#203: [11]} De-coded radiotelegraph series. PR = 10/13 = 0.7692
fVF(i): 0.0000, 0.0000, 0.0000, 0.1667, 0.3333, 0.2500, 0.3125, 0.3000, 0.3200, 0.4667, 0.5278, 0.4762,
rVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.5556, 0.5000, 0.5000, 0.5500, 0.5600, 0.5667, 0.5833, 0.6429,
f P-P = 0.5278; r P-P = 0.5000; dP-P = 0.0278
Averages: f = 0.2628; r = 0.6563; dAv = -0.3935

* {#203: I -1} Mixed series. PR = 6/8 = 0.7500
fVF(i): 0.0000, 0.5000, 0.5000, 0.3333, 0.4444, 0.5833, 0.4375,
rVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.7778, 0.7500, 0.7500,
f P-P = 0.5833; r P-P = 0.3333; dP-P = 0.2500
Averages: f = 0.3998; r = 0.8135; dAv = -0.4137

* {#203: V -8} Beginning of Latin Genesis. PR = 9/13 = 0.6923
fVF(i): 0.0000, 0.5000, 0.5000, 0.6667, 0.6667, 0.6667, 0.6875, 0.7000, 0.6800, 0.7000, 0.6944, 0.6905,
rVF(i): 1.0000, 0.5000, 0.7500, 0.6667, 0.6667, 0.5833, 0.6250, 0.5000, 0.6000, 0.5000, 0.4167, 0.5238,
f P-P = 0.7000; r P-P = 0.5833; dP-P = 0.1167
Averages: f = 0.5960; r = 0.6110; dAv = -0.0150

* {#203: [13]} Friedman's 1959 VMS Anagram. PR = 13/19 = 0.6842
fVF(i): 0.0000, 0.5000, 0.2500, 0.5000, 0.3333, 0.3333, 0.3125, 0.3500, 0.4400, 0.5000, 0.5556, 0.5476, 0.5510, 0.5357, 0.4844, 0.4861, 0.4815, 0.4333,
rVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.7778, 0.7500, 0.8125, 0.8500, 0.8400, 0.8667, 0.7778, 0.7143, 0.6327, 0.6429, 0.6719, 0.7222, 0.7531, 0.7889,
f P-P = 0.5556; r P-P = 0.3673; dP-P = 0.1882
Averages: f = 0.4219; r = 0.7787; dAv = -0.3568

* {#203: VI -2} Voynich f68v3.1 text-line. PR = 9/14 = 0.6429
fVF(i): 1.0000, 0.5000, 0.7500, 0.5000, 0.4444, 0.6667, 0.8125, 0.9000, 0.7200, 0.6333, 0.6944, 0.7619, 0.7959,
rVF(i): 1.0000, 1.0000, 0.5000, 0.5000, 0.6667, 0.8333, 0.9375, 0.8500, 0.7600, 0.8000, 0.7222, 0.7143, 0.6939,
f P-P = 0.5556; r P-P = 0.5000; dP-P = 0.0556
Averages: f = 0.7061; r = 0.7675; dAv = -0.0614

* {#205: I -6} Super-sequence series. PR = 5/8 = 0.6250
fVF(i): 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
rVF(i): 1.0000, 1.0000, 0.7500, 1.0000, 1.0000, 1.0000, 0.9375,
f P-P = 0.0000; r P-P = 0.2500; dP-P = -0.2500
Averages: f = 0.0000; r = 0.9554; dAv = -0.9554

* {#205: II -1} Non-super-sequence series with an hh super-sequence. PR = 5/8 = 0.6250
fVF(i): 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0833, 0.0625,
rVF(i): 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 1.0000, 0.9375,
f P-P = 0.0833; r P-P = 0.0625; dP-P = 0.0208
Averages: f = 0.0208; r = 0.9911; dAv = -0.9702

* {#203: [15]} Binary bytes series. PR = 7/13 = 0.5385
fVF(i): 0.0000, 0.5000, 0.7500, 1.0000, 0.7778, 0.8333, 0.8750, 0.9000, 0.9600, 0.9000, 0.8333, 0.7857,
rVF(i): 0.0000, 0.0000, 0.7500, 0.8333, 0.5556, 0.7500, 0.7500, 0.8000, 0.8400, 0.7333, 0.7222, 0.7857,
f P-P = 1.0000; r P-P = 0.8400; dP-P = 0.1600
Averages: f = 0.7596; r = 0.6267; dAv = 0.1329

* {#203: VIII -8} Random numbers series fair reference for VMS f68v3.1. PR = 6/14 = 0.4286
fVF(i): 1.0000, 1.0000, 0.7500, 0.8333, 0.6667, 0.6667, 0.5625, 0.6500, 0.7200, 0.7667, 0.7778, 0.7619, 0.7551,
rVF(i): 0.0000, 1.0000, 1.0000, 1.0000, 0.8889, 0.6667, 0.7500, 0.6500, 0.5600, 0.6667, 0.6111, 0.6667, 0.5918,
f P-P = 0.4375; r P-P = 1.0000; dP-P = -0.5625
Averages: f = 0.7624; r = 0.6963; dAv = 0.0661

* {#203: II -2} All hh-1222 "baby-talk" series. PR = 3/7 = 0.4286
fVF(i): 0.0000, 0.0000, 0.7500, 0.6667, 0.4444, 0.6667,
rVF(i): 1.0000, 0.5000, 0.5000, 0.6667, 0.5556, 0.5000,
f P-P = 0.7500; r P-P = 0.5000; dP-P = 0.2500
Averages: f = 0.4213; r = 0.6204; dAv = -0.1991

* {#203: [12]} All non-pillows English sentence. PR = 0/13 = 0.0000
fVF(i): 1.0000, 1.0000, 1.0000, 0.8333, 0.7778, 0.6667, 0.6875, 0.8000, 0.8400, 0.8667, 0.7778, 0.6905,
rVF(i): 1.0000, 1.0000, 1.0000, 1.0000, 0.8889, 0.7500, 0.7500, 0.7000, 0.7200, 0.7333, 0.7500, 0.6429,
f P-P = 0.3333; r P-P = 0.3571; dP-P = -0.0238
Averages: f = 0.8283; r = 0.8279; dAv = 0.0004

* {#203: X -2} Moretus Latin taken from MtoK8JAN1639.txt, document-lines series:

03: PR = 6/8 = 0.7500
fVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.5556, 0.4167, 0.3750,
rVF(i): 0.0000, 1.0000, 1.0000, 1.0000, 0.8889, 0.9167, 0.8125,
f P-P = 0.6250; r P-P = 1.0000; dP-P = -0.3750
Averages: f = 0.6806; r = 0.8026; dAv = -0.1220

04: PR = 7/9 = 0.7778
fVF(i): 0.0000, 0.5000, 0.7500, 0.6667, 0.5556, 0.5000, 0.5625, 0.6000,
rVF(i): 1.0000, 0.5000, 0.5000, 0.5000, 0.6667, 0.6667, 0.5000, 0.5500,
f P-P = 0.7500; r P-P = 0.5000; dP-P = 0.2500
Averages: f = 0.5168; r = 0.6104; dAv = -0.0936

05: PR = 13/14 = 0.9286
fVF(i): 0.0000, 0.5000, 0.5000, 0.6667, 0.6667, 0.6667, 0.6250, 0.6000, 0.5600, 0.6000, 0.5556, 0.4762, 0.4694,
rVF(i): 0.0000, 1.0000, 1.0000, 1.0000, 0.8889, 0.9167, 0.8125, 0.7500, 0.7200, 0.6333, 0.6389, 0.5714, 0.6327,
f P-P = 0.6667; r P-P = 1.0000; dP-P = -0.3333
Averages: f = 0.5297; r = 0.7357; dAv = -0.2060

06: PR = 7/9 = 0.7778
fVF(i): 1.0000, 0.5000, 0.7500, 1.0000, 1.0000, 0.8333, 0.6875, 0.7000,
rVF(i): 0.0000, 0.5000, 0.7500, 1.0000, 1.0000, 0.7500, 0.7500, 0.7500,
f P-P = 0.5000; r P-P = 1.0000; dP-P = -0.5000
Averages: f = 0.8089; r = 0.6875; dAv = 0.1214

07: PR = 5/8 = 0.6250
fVF(i): 0.0000, 1.0000, 0.7500, 0.8333, 0.5556, 0.5833, 0.5000,
rVF(i): 1.0000, 0.5000, 0.7500, 1.0000, 1.0000, 0.9167, 0.8750,
f P-P = 1.0000; r P-P = 0.5000; dP-P = 0.5000
Averages: f = 0.6032; r = 0.8631; dAv = -0.2599

08: PR = 6/10 = 0.6000
fVF(i): 0.0000, 0.0000, 0.2500, 0.6667, 0.8889, 0.7500, 0.7500, 0.8500, 0.8800,
rVF(i): 0.0000, 0.0000, 0.0000, 0.3333, 0.6667, 0.5833, 0.4375, 0.4500, 0.5200,
f P-P = 0.8889; r P-P = 0.6667; dP-P = 0.2222
Averages: f = 0.5595; r = 0.3323; dAv = 0.2272

09: PR = 7/9 = 0.7778
fVF(i): 0.0000, 0.0000, 0.7500, 0.6667, 0.5556, 0.5000, 0.5625, 0.7000,
rVF(i): 1.0000, 0.5000, 0.5000, 0.5000, 0.6667, 0.5000, 0.5625, 0.7000,
f P-P = 0.7500; r P-P = 0.5000; dP-P = 0.2500
Averages: f = 0.4668; r = 0.6161; dAv = -0.1493

10: PR = 8/10 = 0.8000
fVF(i): 1.0000, 1.0000, 1.0000, 0.8333, 0.6667, 0.5000, 0.5625, 0.5500, 0.6400,
rVF(i): 0.0000, 1.0000, 0.5000, 0.5000, 0.4444, 0.5000, 0.6250, 0.5500, 0.4800,
f P-P = 0.5000; r P-P = 1.0000; dP-P = -0.5000
Averages: f = 0.7503; r = 0.5110; dAv = 0.2392

11: PR = 7/10 = 0.7000
fVF(i): 0.0000, 1.0000, 0.7500, 0.6667, 0.4444, 0.5000, 0.6250, 0.5500, 0.4800,
rVF(i): 1.0000, 1.0000, 1.0000, 0.6667, 0.7778, 0.8333, 0.8125, 0.8000, 0.7600,
f P-P = 1.0000; r P-P = 0.3333; dP-P = 0.6667
Averages: f = 0.5573; r = 0.8500; dAv = -0.2927

* {#203: X -3} Moretus Latin taken from MtoK8JAN1639.txt, logical sentences series:

01: PR = 11/15 = 0.7333
fVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.5556, 0.4167, 0.3750, 0.4500, 0.4400, 0.5000, 0.6111, 0.6429, 0.6327, 0.6250,
rVF(i): 0.0000, 1.0000, 1.0000, 1.0000, 0.6667, 0.7500, 0.5625, 0.5000, 0.5600, 0.6000, 0.6667, 0.7381, 0.7959, 0.7500,
f P-P = 0.6250; r P-P = 1.0000; dP-P = -0.3750
Averages: f = 0.6190; r = 0.6850; dAv = -0.0660

02: PR = 25/32 = 0.7813
fVF(i): 0.0000, 1.0000, 0.5000, 0.8333, 0.6667, 0.7500, 0.7500, 0.7500, 0.7600, 0.7333, 0.7222, 0.7143, 0.6735, 0.5893, 0.5156, 0.5139, 0.4815, 0.5222, 0.5600, 0.5636, 0.5372, 0.5152, 0.5139, 0.5192, 0.4970, 0.5111, 0.5204, 0.5476, 0.5111, 0.5125, 0.4844,
rVF(i): 1.0000, 0.5000, 0.7500, 1.0000, 1.0000, 0.9167, 0.8750, 0.8500, 0.7600, 0.7000, 0.6944, 0.7381, 0.7551, 0.6964, 0.7031, 0.6528, 0.6173, 0.6556, 0.6900, 0.7273, 0.7603, 0.7955, 0.8194, 0.8397, 0.8580, 0.8407, 0.8520, 0.8333, 0.8400, 0.8250, 0.8281,
f P-P = 1.0000; r P-P = 0.5000; dP-P = 0.5000
Averages: f = 0.5893; r = 0.7863; dAv = -0.1970

03: PR = 7/12 = 0.5833
fVF(i): 0.0000, 0.5000, 0.7500, 1.0000, 0.7778, 0.8333, 0.8750, 0.9000, 0.8800, 0.8667, 0.7500,
rVF(i): 1.0000, 1.0000, 1.0000, 1.0000, 0.7778, 0.6667, 0.6875, 0.8000, 0.7200, 0.6000, 0.5833,
f P-P = 1.0000; r P-P = 0.4167; dP-P = 0.5833
Averages: f = 0.7393; r = 0.8032; dAv = -0.0639

04: PR = 19/26 = 0.7308
fVF(i): 0.0000, 0.0000, 0.0000, 0.5000, 0.6667, 0.6667, 0.6250, 0.6500, 0.6800, 0.6667, 0.6389, 0.5476, 0.5918, 0.5893, 0.6250, 0.6528, 0.6049, 0.6556, 0.6800, 0.6636, 0.6033, 0.6439, 0.6806, 0.6410, 0.6095,
rVF(i): 0.0000, 1.0000, 1.0000, 0.6667, 0.7778, 0.8333, 0.8125, 0.7500, 0.7200, 0.7667, 0.7500, 0.7857, 0.6735, 0.6786, 0.6719, 0.6806, 0.7037, 0.6889, 0.6700, 0.6636, 0.6777, 0.6439, 0.6250, 0.6090, 0.6154,
f P-P = 0.6806; r P-P = 1.0000; dP-P = -0.3194
Averages: f = 0.5553; r = 0.6986; dAv = -0.1433

* {#203: X -5} Hooke English from Micrographia in 4 logical units series:

01: PR = 19/24 = 0.7917
fVF(i): 0.0000, 0.5000, 0.5000, 0.5000, 0.4444, 0.4167, 0.5625, 0.5000, 0.6400, 0.7333, 0.6111, 0.5952, 0.6735, 0.5893, 0.6719, 0.7361, 0.7160, 0.7222, 0.7600, 0.7909, 0.7521, 0.7727, 0.7083,
rVF(i): 1.0000, 1.0000, 0.7500, 0.8333, 0.7778, 0.7500, 0.7500, 0.7000, 0.6000, 0.6333, 0.5833, 0.5238, 0.5510, 0.5893, 0.5469, 0.5833, 0.5802, 0.5889, 0.6100, 0.6182, 0.6198, 0.5758, 0.5833,
f P-P = 0.7909; r P-P = 0.4762; dP-P = 0.3147
Averages: f = 0.6042; r = 0.6673; dAv = -0.0631

02: PR = 8/14 = 0.5714
fVF(i): 0.0000, 0.5000, 0.5000, 0.3333, 0.4444, 0.5833, 0.6250, 0.6000, 0.6400, 0.6000, 0.6667, 0.6905, 0.6531,
rVF(i): 1.0000, 1.0000, 0.5000, 0.8333, 0.5556, 0.6667, 0.6875, 0.7000, 0.5600, 0.5667, 0.5833, 0.5238, 0.5306,
f P-P = 0.6905; r P-P = 0.5000; dP-P = 0.1905
Averages: f = 0.5259; r = 0.6698; dAv = -0.1439

03: PR = 34/42 = 0.8095
fVF(i): 0.0000, 0.5000, 0.2500, 0.5000, 0.6667, 0.7500, 0.6875, 0.7000, 0.6800, 0.6333, 0.5833, 0.5952, 0.5102, 0.4643, 0.4844, 0.4861, 0.4321, 0.4222, 0.4700, 0.5091, 0.4628, 0.5000, 0.5000, 0.5321, 0.5621, 0.5275, 0.5510, 0.5524, 0.5733, 0.5917, 0.6133, 0.6324, 0.6471, 0.6405, 0.6543, 0.6345, 0.6177, 0.6105, 0.6200, 0.6000, 0.6077,
rVF(i): 0.0000, 0.5000, 0.5000, 0.5000, 0.4444, 0.5000, 0.5000, 0.6000, 0.6400, 0.6667, 0.6944, 0.7143, 0.6735, 0.6786, 0.5938, 0.6111, 0.6173, 0.6000, 0.6100, 0.5545, 0.5702, 0.5909, 0.5764, 0.5385, 0.5266, 0.5495, 0.5255, 0.4952, 0.5111, 0.5125, 0.5117, 0.5404, 0.5606, 0.5621, 0.5833, 0.5965, 0.6066, 0.5974, 0.5925, 0.5857, 0.5986,
f P-P = 0.7500; r P-P = 0.7143; dP-P = 0.0357
Averages: f = 0.5501; r = 0.5593; dAv = -0.0092

04: PR = 22/24 = 0.9167
fVF(i): 0.0000, 0.5000, 0.7500, 1.0000, 0.7778, 0.6667, 0.6250, 0.7500, 0.6400, 0.6667, 0.6389, 0.6429, 0.6531, 0.6250, 0.6406, 0.6667, 0.6667, 0.6778, 0.6200, 0.6455, 0.5868, 0.6288, 0.6597,
rVF(i): 0.0000, 0.0000, 0.2500, 0.3333, 0.3333, 0.4167, 0.4375, 0.4500, 0.4400, 0.4333, 0.4167, 0.4048, 0.4082, 0.3750, 0.4375, 0.4583, 0.4198, 0.4111, 0.4900, 0.5273, 0.5289, 0.4848, 0.5000,
f P-P = 1.0000; r P-P = 0.5289; dP-P = 0.4711
Averages: f = 0.6404; r = 0.3894; dAv = 0.2510

* {#203: X -6} Hooke English from Micrographia in 5 logical units series:

01: PR = 19/24 = 0.7917
fVF(i): 0.0000, 0.5000, 0.5000, 0.5000, 0.4444, 0.4167, 0.5625, 0.5000, 0.6400, 0.7333, 0.6111, 0.5952, 0.6735, 0.5893, 0.6719, 0.7361, 0.7161, 0.7222, 0.7600, 0.7909, 0.7521, 0.7727, 0.7083,
rVF(i): 1.0000, 1.0000, 0.7500, 0.8333, 0.7778, 0.7500, 0.7500, 0.7000, 0.6000, 0.6333, 0.5833, 0.5238, 0.5510, 0.5893, 0.5469, 0.5833, 0.5802, 0.5889, 0.6100, 0.6182, 0.6198, 0.5758, 0.5833,
f P-P = 0.7909; r P-P = 0.4762; dP-P = 0.3147
Averages: f = 0.6042; r = 0.6673; dAv = -0.0631

02: PR = 8/14 = 0.5714
fVF(i): 0.0000, 0.5000, 0.5000, 0.3333, 0.4444, 0.5833, 0.6250, 0.6000, 0.6400, 0.6000, 0.6667, 0.6905, 0.6531,
rVF(i): 1.0000, 1.0000, 0.5000, 0.8333, 0.5556, 0.6667, 0.6875, 0.7000, 0.5600, 0.5667, 0.5833, 0.5238, 0.5306,
f P-P = 0.6905; r P-P = 0.5000; dP-P = 0.1905
Averages: f = 0.5259; r = 0.6698; dAv = -0.1439

03: PR = 18/22 = 0.8182
fVF(i): 0.0000, 0.5000, 0.2500, 0.5000, 0.6667, 0.7500, 0.6875, 0.7000, 0.6800, 0.6333, 0.5833, 0.5952, 0.5102, 0.4643, 0.4844, 0.4861, 0.4321, 0.4222, 0.4700, 0.5091, 0.4628,
rVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.5556, 0.6667, 0.6250, 0.5500, 0.5600, 0.6000, 0.6389, 0.6905, 0.7347, 0.7321, 0.7500, 0.7778, 0.7901, 0.7556, 0.7300, 0.7091, 0.7355,
f P-P = 0.7500; r P-P = 0.4500; dP-P = 0.3000
Averages: f = 0.5137; r = 0.7152; dAv = -0.2015

04: PR = 16/20 = 0.8000
fVF(i): 0.0000, 1.0000, 0.7500, 0.5000, 0.5556, 0.5833, 0.5625, 0.6000, 0.6800, 0.7667, 0.8333, 0.7619, 0.7959, 0.7143, 0.6406, 0.6111, 0.6420, 0.5889, 0.6300,
rVF(i): 0.0000, 0.5000, 0.5000, 0.5000, 0.4444, 0.5000, 0.5000, 0.6000, 0.6400, 0.6667, 0.6944, 0.7143, 0.6735, 0.6786, 0.5938, 0.6111, 0.6173, 0.6000, 0.6100,
f P-P = 1.0000; r P-P = 0.7143; dP-P = 0.2857
Averages: f = 0.6430; r = 0.5602; dAv = 0.0827

05: PR = 22/24 = 0.9167
fVF(i): 0.0000, 0.5000, 0.7500, 1.0000, 0.7778, 0.6667, 0.6250, 0.7500, 0.6400, 0.6667, 0.6389, 0.6429, 0.6531, 0.6250, 0.6406, 0.6667, 0.6667, 0.6778, 0.6200, 0.6455, 0.5868, 0.6288, 0.6597,
rVF(i): 0.0000, 0.0000, 0.2500, 0.3333, 0.3333, 0.4167, 0.4375, 0.4500, 0.4400, 0.4333, 0.4167, 0.4048, 0.4082, 0.3750, 0.4375, 0.4583, 0.4198, 0.4111, 0.4900, 0.5273, 0.5289, 0.4848, 0.5000,
f P-P = 1.0000; r P-P = 0.5289; dP-P = 0.4711
Averages: f = 0.6404; r = 0.3894; dAv = 0.2510

* {#203: XI -1} Voynich f20r 1st paragraph (Currier language A):

f20rL1: PR = 5/7 = 0.7143
fVF(i): 1.0000, 1.0000, 0.5000, 0.3333, 0.5556, 0.6667,
rVF(i): 1.0000, 0.5000, 0.5000, 0.6667, 0.7778, 0.6667,
f P-P = 0.6667; r P-P = 0.5000; dP-P = 0.1666
Averages: f = 0.6759; r = 0.6852; dAv = -0.0093

f20rL2: PR = 6/8 = 0.7500
fVF(i): 1.0000, 0.5000, 0.2500, 0.1667, 0.2222, 0.3333, 0.4375,
rVF(i): 1.0000, 0.5000, 0.2500, 0.6667, 0.7778, 0.9167, 0.9375,
f P-P = 0.8333; r P-P = 0.7500; dP-P = 0.0833
Averages: f = 0.4157; r = 0.7212; dAv = -0.3056

f20rL3: PR = 6/8 = 0.7500
fVF(i): 1.0000, 0.5000, 0.7500, 0.8333, 0.7778, 0.5833, 0.6250,
rVF(i): 0.0000, 1.0000, 1.0000, 1.0000, 0.7778, 0.7500, 0.6875,
f P-P = 0.5000; r P-P = 1.0000; dP-P = -0.5000
Averages: f = 0.7242; r = 0.7450; dAv = -0.0208

f20rL4: PR = 5/5 = 1.0000
fVF(i): 0.0000, 0.5000, 0.2500, 0.1667,
rVF(i): 1.0000, 1.0000, 1.0000, 1.0000,
f P-P = 0.5000; r P-P = 0.0000; dP-P = 0.5000
Averages: f = 0.2292; r = 1.0000; dAv = -0.7708

* {#203: XI -5} Voynich f95r2 1st paragraph (Currier language B):

f95r2L1: PR = 7/10 = 0.7000
fVF(i): 1.0000, 1.0000, 0.5000, 0.6667, 0.6667, 0.5833, 0.4375, 0.5000, 0.6000,
rVF(i): 0.0000, 0.0000, 0.2500, 0.3333, 0.5556, 0.5000, 0.5000, 0.6500, 0.6400,
f P-P = 0.5625; r P-P = 0.6500; dP-P = -0.0875
Averages: f = 0.6616; r = 0.3810; dAv = 0.2806

f95r2L2: PR = 9/10 = 0.9000
fVF(i): 1.0000, 0.5000, 0.7500, 1.0000, 0.6667, 0.8333, 0.6250, 0.7500, 0.7600,
rVF(i): 1.0000, 0.5000, 0.7500, 0.6667, 0.6667, 0.7500, 0.6250, 0.6000, 0.6000,
f P-P = 0.5000; r P-P = 0.5000; dP-P = 0.0000
Averages: f = 0.7650; r = 0.6843; dAv = 0.0807

f95r2L3: PR = 9/11 = 0.8182
fVF(i): 1.0000, 1.0000, 0.7500, 0.6667, 0.6667, 0.5833, 0.5625, 0.5500, 0.6400, 0.7333,
rVF(i): 0.0000, 0.0000, 0.2500, 0.1667, 0.3333, 0.4167, 0.4375, 0.4500, 0.4800, 0.4000,
f P-P = 0.4500; r P-P = 0.4800; dP-P = -0.0300
Averages: f = 0.7153; r = 0.2934; dAv = 0.4219

f95r2L4: PR = 5/6 = 0.8333
fVF(i): 1.0000, 1.0000, 1.0000, 0.6667, 0.6667,
rVF(i): 0.0000, 1.0000, 1.0000, 0.8333, 0.6667,
f P-P = 0.3333; r P-P = 1.0000; dP-P = -0.6667
Averages: f = 0.8667; r = 0.7000; dAv = 0.1667

* {#203: XIII -2} spectral series / clusters of the first two lines / labels under the VMS f68v3 circle's sectioning-horizontal:

upper, symmetric label, PR = 4/4 = 1.0000
fVF(i): 0.0000, 0.0000, 0.5000,
rVF(i): 0.0000, 0.0000, 0.5000,
f P-P = 0.5000; r P-P = 0.5000; dP-P = 0.0000
Averages: f = 0.1667; r = 0.1667; dAv = 0.0000

lower, anti-symmetric label, PR = 2/4 = 0.5000
fVF(i): 1.0000, 0.5000, 0.7500,
rVF(i): 0.0000, 0.5000, 0.2500,
f P-P = 0.5000; r P-P = 0.5000; dP-P = 0.0000
Averages: f = 0.7500; r = 0.2500; dAv = 0.5000


The paired labels from the Voynich f68v3 Spiral Galaxy folio, {#203: XIII -2}, show interesting VF(j) numbers. These two labels, with their strong respective spectral symmetry and anti-symmetry, were discussed in some detail in the COMMENTS section of communication #203. From their VF(j) data above, we note:

{III -1} VMS f68v3.1 upper, symmetric galaxy circle label: fVF(j) - rVF(j) = constant = 0

{III -2} VMS f68v3.1 lower, anti-symmetric galaxy circle label: fVF(j) + rVF(j) = constant = 1

I noticed that the {#203: VI -2} Voynich f68v3.1 text-line series' dP-P and dAv were closest to those of the Rev. Drury stutter series {#203: [14]}. The Voynich VF(j) curve is just 13 points, while the Drury VF(j) curve is 157. Nevertheless I plotted both curves on the same graph. I found it remarkable that there is great similarity between the first 13 points of the Drury curve and the VMS f68v3.1 curve - this is even more easily seen when the difference curves of the curves are plotted and compared. The 14-groups source series of the transcribed VMS f68v3.1, and the first 14 groups of the Drury source series are:

{III -3} k1c89_1cj19_8aii89_2oe_h1coe9_1okcoe_2oe_s_1c9_2o8aiiN_1ck2c89_ok2o_4ooko_sccc9


So then, as far as it goes in this experimentation, the super-sequence proximities, or deviations, of these two series, evolve quite similarly. An intriguing psycho-mathematics question is suggested: suppose for a moment the mathematical artform model of creating simulated writing, that was speculated at the end of comm. #205. Is it plausible that a mathematical artist, who happens to be a stammerer, while creating the simulated-writing algorithm, structures the algorithm, consciously or unconsciously, to reflect stammering speech?

One more pattern is quickly noticed in all the data above: when the series of series, that is the paragraphs of Moretus, Hooke, and the two Voynich paragraphs are compared, the Voynich text-lines are seen to tend to lower forward dP-P numbers:

{III -5} Nine document-lines of Moretus Latin {#203: X -2}, average forward dP-P = 0.7423

{III -6} Four sentences-lines of Moretus Latin {#203: X -3}, average forward dP-P = 0.8264

{III -7} Four logical-lines of Hooke English {#203: X -5}, average forward dP-P = 0.8079

{III -8} Five logical-lines of Hooke English {#203: X -6}, average forward dP-P = 0.8463

{III -9} Four lines Currier language-A {#203: XI -1} Voynich f20r, average forward dP-P = 0.6250

{III -10} Four lines Currier language-B {#203: XI -5} Voynich f95r2, average forward dP-P = 0.4615

So, as far as it goes, there is less fluctuation in super-sequence proximity / deviation with the Voynich lines as they evolve and form a collection (paragraph), than there is with both Moretus and Hooke. If this holds up across a much broader database, then it would seem that if a very-restricted "language" is unlikely, it is yet another indication suggesting that the Voynich text is at least partly the product of a generating algorithm. As we've considered a number of times, that algorithm may be using random numbers in some way, but that does not mean that the algorithm is itself some random process.

Among the 49 reference series the Drury stammer series at n=158 groups / sequences gives the first indications as to how the VF(j) curve proceeds over the long run in general. I took the VF(j) curve of an even longer series, n=358 groups of plaintext English with punctuation marks and all, with these characteristics: 2356 series-signals, 1999 groups-signals, 358 groups, agl= 5.584, mgl= 18, PR = 255/358 = 0.7123, RPR = 231/255 = 0.9059, HHR = 88/358 = 0.2458, SSR = 2 / 358 = 0.0056, VF = 40310 / 64082 = 0.6290. At 0.7123 its PR is comparable to the 0.7722 of the Drury series. The VF(j) curves for this series and that of the Drury series show general similarities.

From the point of view of j=t = time, with each successive group a tick on the time axis, the curves resemble a type of shockwave, with further similarity to a frequency-modulation downward sweep. An initial pulse is dominated by high-frequency components. The ratio of amplitudes of the high to low frequency components drops quickly and by about j=20 both curves transition to being dominated by longwave components, and oscillate along an amplitude offset-band that includes the eventual settling final VF(n) amplitude, this band much wider with the considerably shorter Drury curve. I have not had time to study the wave envelopes, but from the appearances of the graphs they are only roughly negative exponential in shape, with suggestions that strong non-linearities are affecting the envelopes in the region around j=20 where the higher frequencies give way to the lower ones.

The above VF(j) super-sequence deviation factor function data was generated with the SQS computer program, updated for the purpose to version V1.3. The round-offs were done by hand. The numbers can be generated manually with SQS V1.2 using repeatedly its remove-last-group option, but V1.3 takes care of everything automatically. I have sent SQS V1.3 to our J.VS Librarian Greg Stachowski and requested that he place it in the J.VS Library. [2]

Berj / KI3U

[1] Journal of Voynich Studies communication #205 (Vol. II): J.VS: Series of Sequences vs Sequences of Sequences: Super-sequence Deviation Reference Data. Comm. #205 and #204 and #203 are archived online here:

[2] SQS is available for download from J.VS Library deposit # 19-1-2008-06-29 :

From Berj Ensanian
To Journal of Voynich Studies
Sent Date 07-24-2008 10:51:56 PM

Subject: J.VS: NvP Sequence Spectra Topographic comparisons: Voynich folio f111r text vs Askham's Menta Rubea

Dear Colleagues

Lets have a quick topo-spectrographic look at an essentially all-text Voynich page, all of its text as a block of text-lines, and then compare it to the topo-spectrograph of a comparable sized ordinary text. For the following experimentation I chose Voynich page f111r pretty much at random. It is among the star-pages [1] of the VMS, and has some 17 tailed stars of differing designs running down its left margin, and these are the only illustration elements on the page. It has 54 lines of text, and depending on your judgment, these group into five paragraphs. Similar to the procedures of J.VS communication #204 let us try on it some NvP topography, with a resolution of two elevation levels - pillow sequences versus non-pillows. [2]

Let us use GC's voyn_101.txt transcription [3] as the source data to reflect the VMS f111r text. The transcription caution here is that GC's transcription, per his perspective on the VMS text, transcribes using Latin abbreviations, so that some of the VMS text-groups wind up transcribed as shorter and spectrally modified groups. Also, like about everyone else, GC transcribes the "4o" as two signals. We've considered these and other transcription issues in some detail in previous sequence analysis work. But here we will not change anything in GC's transcript for this experiment; we will take it as is except to convert the few short "soft" inter-group spaces into regular "hard" spaces. So then, we are below experimenting with GC's transcript of VMS f111r.

Using SQS [4] we obtain the following distributions:

{1} VMS f111r, from voyn_101.txt with soft spaces replaced with hard spaces:

0 = non-pillow sequence
1 = pillow sequence
_ = group separator

line number: number of groups: pillows vs non-pillows distribution

01:11: 0_1_1_0_1_1_1_1_1_1_1
02:13: 1_1_1_1_1_1_1_1_1_1_1_1_1
03:12: 0_1_1_1_1_1_1_1_1_0_1_1
04:14: 1_1_1_1_1_1_1_1_1_1_0_1_1_1
05:08: 1_0_1_1_1_0_1_1
06:14: 1_1_1_1_1_1_1_1_1_1_1_1_1_1
07:13: 1_0_1_1_1_1_1_0_1_1_1_1_1
08:12: 1_1_1_1_1_1_1_1_1_1_1_1
09:13: 0_0_1_1_1_1_1_1_1_1_1_1_1
10:15: 1_1_1_1_1_1_1_0_1_1_1_1_1_1_1
11:13: 1_1_1_0_0_0_1_1_1_1_1_1_1
12:12: 1_1_0_1_1_1_1_1_1_1_1_1
13:17: 0_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1
14:12: 1_0_1_1_1_1_1_1_1_0_1_1
15:13: 0_1_1_1_1_1_1_1_1_0_1_1_1
16:13: 1_1_1_1_1_1_1_1_1_0_1_1_1
17:13: 1_1_1_0_0_1_1_1_0_1_0_0_1
18:13: 1_1_0_1_1_1_1_1_0_0_1_1_1
19:12: 1_1_0_1_0_0_1_0_1_1_1_1
20:14: 1_0_1_1_1_1_1_1_1_1_1_1_1_1
21:22: 1_1_1_1_1_1_1_1_1_1_1_1_0_1_1_1_1_1_1_1_1_1
22:16: 1_1_1_1_1_1_1_1_1_1_1_1_1_1_1_1
23:10: 1_1_0_1_1_1_1_1_1_0
24:15: 1_1_1_1_0_0_1_1_1_1_1_1_1_1_1
25:14: 1_1_1_1_1_0_1_1_1_1_1_1_1_1
26:14: 1_1_1_0_1_1_1_1_1_1_1_1_1_1
27:16: 1_1_1_0_1_1_1_1_1_1_1_1_1_1_1_1
28:13: 1_1_1_0_0_1_0_1_1_1_1_1_1
29:14: 1_1_1_1_1_1_1_1_1_1_0_1_1_1
30:12: 1_1_1_1_1_0_1_1_1_0_1_1
31:10: 0_1_1_1_0_1_1_0_1_1
32:10: 0_0_1_1_1_1_1_1_0_1
33:13: 0_1_1_1_0_1_1_1_1_1_0_0_1
34:13: 1_1_1_1_1_1_0_1_1_0_0_1_1
35:05: 1_1_1_1_1
36:10: 0_1_1_1_1_0_1_1_1_1
37:15: 1_1_1_1_1_1_1_1_1_0_1_1_1_1_1
38:13: 1_1_1_1_0_1_1_1_1_1_1_1_1
39:10: 1_1_1_1_1_1_1_1_1_0
40:15: 1_1_1_1_1_1_1_1_0_0_1_0_1_1_1
41:11: 1_1_1_1_1_1_1_1_1_1_1
42:13: 0_1_0_1_1_1_1_1_1_0_1_1_1
43:05: 1_1_1_1_1
44:11: 1_0_0_1_1_0_1_1_1_1_1
45:14: 1_1_1_1_1_1_1_1_1_1_0_1_1_1
46:13: 1_1_1_0_1_1_1_1_1_0_1_1_1
47:09: 1_1_1_0_1_1_1_0_1
48:10: 0_1_1_1_1_1_1_1_0_1
49:12: 1_1_1_1_0_1_1_0_1_1_1_1
50:11: 1_1_1_0_0_1_1_1_1_1_1
51:13: 0_1_1_1_1_1_1_1_1_1_1_1_1
52:14: 1_1_1_1_1_1_1_1_1_1_1_1_1_1
53:14: 1_1_1_1_0_1_1_1_1_1_1_1_1_1
54:06: 1_1_1_1_1_1

From {1} it would appear that the non-pillows mostly tend to be posititioned away from the middles of the lines. Lets have a better look by constructing a kind of topograph with the lines centered in a raster frame, using our space symbol "_" as fills, and also injecting a couple of extra "_" in the middles of the lines that have an even number of groups. We'll also change the symbols denoting the pillows and non-pillows so as to obtain a better visualized graphic, emphasizing the more complex and rarer non-pillows. Hopefully the below diagram will come out nice and rectangular on your screen - if it does not, then just copy it into MS Notepad, wherein it was prepared, and it should look as intended:

{2} VMS f111r, from voyn_101.txt with soft spaces replaced with hard spaces:

# = non-pillow sequence
~ = pillow sequence
_ = group separator

line number: number of groups: pillows vs non-pillows distribution

01:11: ____________#_~_~_#_~_~_~_~_~_~_~____________
02:13: __________~_~_~_~_~_~_~_~_~_~_~_~_~__________
03:12: __________#_~_~_~_~_~___~_~_~_#_~_~__________
04:14: ________~_~_~_~_~_~_~___~_~_~_#_~_~_~________
05:08: ______________~_#_~_~___~_#_~_~______________
06:14: ________~_~_~_~_~_~_~___~_~_~_~_~_~_~________
07:13: __________~_#_~_~_~_~_~_#_~_~_~_~_~__________
08:12: __________~_~_~_~_~_~___~_~_~_~_~_~__________
09:13: __________#_#_~_~_~_~_~_~_~_~_~_~_~__________
10:15: ________~_~_~_~_~_~_~_#_~_~_~_~_~_~_~________
11:13: __________~_~_~_#_#_#_~_~_~_~_~_~_~__________
12:12: __________~_~_#_~_~_~___~_~_~_~_~_~__________
13:17: ______#_~_~_~_~_~_~_~_~_~_~_~_~_~_~_~_~______
14:12: __________~_#_~_~_~_~___~_~_~_#_~_~__________
15:13: __________#_~_~_~_~_~_~_~_~_#_~_~_~__________
16:13: __________~_~_~_~_~_~_~_~_~_#_~_~_~__________
17:13: __________~_~_~_#_#_~_~_~_#_~_#_#_~__________
18:13: __________~_~_#_~_~_~_~_~_#_#_~_~_~__________
19:12: __________~_~_#_~_#_#___~_#_~_~_~_~__________
20:14: ________~_#_~_~_~_~_~___~_~_~_~_~_~_~________
21:22: ~_~_~_~_~_~_~_~_~_~_~___~_#_~_~_~_~_~_~_~_~_~
22:16: ______~_~_~_~_~_~_~_~___~_~_~_~_~_~_~_~______
23:10: ____________~_~_#_~_~___~_~_~_~_#____________
24:15: ________~_~_~_~_#_#_~_~_~_~_~_~_~_~_~________
25:14: ________~_~_~_~_~_#_~___~_~_~_~_~_~_~________
26:14: ________~_~_~_#_~_~_~___~_~_~_~_~_~_~________
27:16: ______~_~_~_#_~_~_~_~___~_~_~_~_~_~_~_~______
28:13: __________~_~_~_#_#_~_#_~_~_~_~_~_~__________
29:14: ________~_~_~_~_~_~_~___~_~_~_#_~_~_~________
30:12: __________~_~_~_~_~_#___~_~_~_#_~_~__________
31:10: ____________#_~_~_~_#___~_~_#_~_~____________
32:10: ____________#_#_~_~_~___~_~_~_#_~____________
33:13: __________#_~_~_~_#_~_~_~_~_~_#_#_~__________
34:13: __________~_~_~_~_~_~_#_~_~_#_#_~_~__________
35:05: __________________~_~_~_~_~__________________
36:10: ____________#_~_~_~_~___#_~_~_~_~____________
37:15: ________~_~_~_~_~_~_~_~_~_#_~_~_~_~_~________
38:13: __________~_~_~_~_#_~_~_~_~_~_~_~_~__________
39:10: ____________~_~_~_~_~___~_~_~_~_#____________
40:15: ________~_~_~_~_~_~_~_~_#_#_~_#_~_~_~________
41:11: ____________~_~_~_~_~_~_~_~_~_~_~____________
42:13: __________#_~_#_~_~_~_~_~_~_#_~_~_~__________
43:05: __________________~_~_~_~_~__________________
44:11: ____________~_#_#_~_~_#_~_~_~_~_~____________
45:14: ________~_~_~_~_~_~_~___~_~_~_#_~_~_~________
46:13: __________~_~_~_#_~_~_~_~_~_#_~_~_~__________
47:09: ______________~_~_~_#_~_~_~_#_~______________
48:10: ____________#_~_~_~_~___~_~_~_#_~____________
49:12: __________~_~_~_~_#_~___~_#_~_~_~_~__________
50:11: ____________~_~_~_#_#_~_~_~_~_~_~____________
51:13: __________#_~_~_~_~_~_~_~_~_~_~_~_~__________
52:14: ________~_~_~_~_~_~_~___~_~_~_~_~_~_~________
53:14: ________~_~_~_~_#_~_~___~_~_~_~_~_~_~________
54:06: ________________~_~_~___~_~_~________________

There does indeed seem to be a tendency of the non-pillows to stay away from the centers of the lines. Among lines with an odd number of groups, only lines 10, 28, 34, and 44 have a non-pillow exactly in the center of the line. Among lines with an even number of groups, only lines 19, 30, 31, and 36 have a non-pillow at line-center. And, although line 19 almost achieves it, there is not a single line among the 54 having a cluster of non-pillows bridging the center of the line. In contrast, 12 lines start with a non-pillow, but only two end with a non-pillow.

Is all that unusual? To find out we must of course do many comparisons, both with other Voynich text blocks, and non-Voynich texts. Lets get started with another transcription by GC, a non-Voynich one. GC makes available online some transcriptions of the 16th c. works of Anthony Askham. Said Askham of course we know as being the fellow that Dr. Strong in the 1940's had advanced as the author of the VMS. I chose Askham's "A litle Herball", and from it the text entry for "Menta rubea". [5]

I prepared the Menta rubea text by removing all its punctuations, and then dividing it into lines so as to have group counts per line be equal to those of the VMS f111r lines. The so-worked source results in 47 usable lines, a bit shy of 54, but close enough for now:

{3} Menta rubea text from [5] stripped of punctuation and divided into lines as per {1} :

line number: number of groups: source text

01:11: This is named the red Minte it is hote and dry
02:13: in the seconde degre and there be two other mintes but I meane
03:12: house Myntes the whiche properlye is saide garden Mintes for that most
04:14: comonly is in medecines both grene and drye for greate holsomnes it shulde be
05:08: dried in a shadowe place and so it
06:14: wyl be kepte a yere in great vertue to dissolue or louse to consume
07:13: of his proper qualite and to comfort of his swete sauoure for the
08:12: stinking of the mouth and filth in the gummes and of the
09:13: teth washe thy mouth and gummes with vineger that Mintes be soden in
10:15: and after rub them with the powder of Mintes or with dry Mintes to prouoke
11:13: the appetide whan an impediment of the stomake that commethe of cold humours
12:12: being in the mouth of the stomake make a salue of Mintes
13:17: and vineger with a lytell Sinamon and Peper and vse it well against vomites that cometh of
14:12: feblenesse of the stomake or of colde causes Seeth Myntes in Sauge
15:13: water and vyneger and lay it on the mouth of the stamake with
16:13: the Myntes that be sodden therein Also giue to the pacient to eate
17:13: of the same Mintes for the sycopyn and febleness in feuers and without
18:13: feuers or of medecine or of what cause it be stampe Mintes with
19:12: vineger and a lytel wine if the pacient be without feuer and
20:14: yf he be with feuer stampe Mintes with vineger alone than make a tost
21:22: of sower breade and tost it wel tyl it be almost brent than put it in that licoure and let it lai
22:16: therin tyl it be wel soked than put it into his nose and rubbe his lyppes
23:10: gums teeth and temples therewith and bynde it to the
24:15: pulse vaine of his armes and let the pacient eate the moystnes that is left
25:14: and swalowe it in For to clense the mother take the tender croppes of
26:14: Mintes and seeth them in water or wyne and playster it to the share
27:16: and to the raynes against the congeling in a womannes breast take the small stalkes of
28:13: Mintes and seeth them in wine and oyle and playster it about the
29:14: tetes Also be it knowen that whan any medecine shulde be giuen against venim
30:12: it shulde be giuen with the ioyce of Mintes for Myntes haue
31:10: a maner of strength of drawynge oute of venym for
32:10: els it shuld be with wine that Mintes hath be
33:13: sodden in for stopping of the splenne and the lyuer and of the
34:13: waies of the vryn of a colde humour and of a hote without
35:05: feuer Take the ioyce of
36:10: Mintes alone or Mintes soden in wine or the ioyce
37:15: of Mintes medled with hony and giue it to the patient To flee wormes in
38:13: the bellye take the ioyce of Myntes and drynke it and thou shalte
39:10: be hoole Also the ioyce of Mintes fleth wormes in
40:15: thy cares For a tetter take the ioyce of Mintes and put thereto brymstone and
41:11: vineger and medle them wel togither and annoynt the Tetter therwith
42:13: and thou shalte be hole For a wounde in the head stampe Mintes
43:05: and lay them on the
44:11: wounde &c. For paine in the side take Mintes and seeth
45:14: them in olde wine or ale and with it stampe xviii graynes of peper
46:13: and drinke it in the night there is but lytel difference betwene this
47:09: Mynte and the Romayne Minte this is the garden
48:01: Minte

And with help from SQS we transform {3} to obtain:

{4} Askham Little Herbal, Mentua Rubea section minus punctuations

# = non-pillow sequence
~ = pillow sequence
_ = group separator

line number: number of groups: pillows vs non-pillows distribution

01:11: ____________~_~_~_~_~_~_~_~_~_~_~____________
02:13: __________~_~_#_#_~_#_~_~_~_~_~_~_#__________
03:12: __________~_~_~_~_#_~___~_~_~_~_~_~__________
04:14: ________#_~_~_#_~_#_~___~_~_#_#_~_~_~________
05:08: ______________~_~_~_~___~_~_~_~______________
06:14: ________~_~_#_~_#_~_~___#_~_#_~_~_~_~________
07:13: __________~_~_#_~_~_~_#_~_~_#_~_~_~__________
08:12: __________#_~_~_~_~_~___~_~_~_~_~_~__________
09:13: __________#_~_~_~_~_~_~_#_~_~_~_~_~__________
10:15: ________~_~_~_~_~_~_~_~_~_~_~_~_~_~_~________
11:13: __________~_#_~_~_#_~_~_~_~_#_~_~_#__________
12:12: __________~_~_~_~_~_~___~_~_~_~_~_~__________
13:17: ______~_#_~_~_#_#_~_~_~_~_~_#_#_~_~_~_~______
14:12: __________#_~_~_~_~_~___~_#_#_~_~_~__________
15:13: __________~_~_#_~_~_~_~_~_~_~_~_~_~__________
16:13: __________~_~_~_~_~_~_~_~_~_~_~_~_~__________
17:13: __________~_~_~_~_~_~_~_~_#_~_#_~_#__________
18:13: __________#_~_~_#_~_~_~_~_~_~_~_~_~__________
19:12: __________#_~_~_~_~_~___~_~_~_#_~_~__________
20:14: ________~_~_~_~_~_~_~___~_#_~_~_~_~_~________
21:22: ~_~_#_~_~_~_~_~_~_~_~___~_~_~_~_~_~_~_~_~_~_~
22:16: ______~_~_~_~_~_~_~_~___~_~_~_~_~_#_~_~______
23:10: ____________~_#_~_~_#___~_~_~_~_~____________
24:15: ________~_~_~_~_~_~_~_~_~_~_~_#_~_~_~________
25:14: ________~_~_~_~_~_~_#___~_~_~_~_~_#_~________
26:14: ________~_~_#_~_~_~_~___~_~_~_~_~_~_~________
27:16: ______~_~_~_~_#_~_#_~___~_#_~_~_~_#_~_~______
28:13: __________~_~_#_~_~_~_~_~_~_~_~_~_~__________
29:14: ________#_~_~_~_#_~_~___~_#_~_~_~_#_~________
30:12: __________~_~_~_~_~_~___~_~_~_~_~_~__________
31:10: ____________~_~_~_~_~___~_~_~_~_~____________
32:10: ____________~_~_~_~_~___~_~_~_~_~____________
33:13: __________~_~_~_~_~_~_#_~_~_~_~_~_~__________
34:13: __________~_~_~_~_~_~_~_~_~_~_~_~_#__________
35:05: __________________~_~_~_~_~__________________
36:10: ____________~_~_~_~_~___~_~_~_~_~____________
37:15: ________~_~_#_~_~_~_~_~_~_~_#_~_#_~_~________
38:13: __________~_#_~_~_~_~_~_~_~_~_~_~_~__________
39:10: ____________~_#_~_~_~___~_~_~_~_~____________
40:15: ________~_~_~_~_#_~_~_~_~_~_~_~_#_~_~________
41:11: ____________#_~_#_~_~_#_~_#_~_~_~____________
42:13: __________~_~_~_~_~_~_~_~_~_~_~_~_~__________
43:05: __________________~_~_~_~_~__________________
44:11: ____________~_~_~_~_~_~_~_~_~_~_#____________
45:14: ________~_~_~_~_~_~_~___~_~_~_#_~_~_#________
46:13: __________~_~_~_~_~_~_#_~_~_~_#_#_~__________
47:09: ______________~_~_~_~_~_~_~_~_~______________

Here too with Askham's text we don't see clusters of non-pillows bridging the exact centers of lines, so at this stage that does not appear to be particularly unusual, and indeed the lines could be re-divided to force bridging.

However, there are striking differences between {2} Voynich f111r and {4} Askham Menta rubea. It is convenient to print out hard copies of {2} and {4} for comparison. We quickly observe:

1.) Askham has many more PR=1 all-pillows lines, almost twice as many if we compare just 47 lines. Moreover, the all-pillows lines in f111r are scattered, whereas in Askham we find groups of successive such lines, of two and three.

2.) In Askham in lines 15 - 45, being a major bulk of the entire text-block, the pattern #_# is completely absent. In contrast, the occurrences of #_# in the VMS f111r text are more or less evenly scattered throughout.

3.) f111r has far fewer #_~_# patterns than Askham. Also, in f111r they first appear late - with line 17. Further, the f111r occurrences are more often part of more complex patterns, notably #_#_~_# and #_~_#_#.

4.) Askham has no #_#_# pattern. But f111r has one on line 11.

5.) The greatest non-pillows density is 5 per line: Askham has two such lines, but f111r has only one.

6.) Within any line, in both texts, the greatest separation between any two #'s is 8 intervening pillows. Askham has one such line, but f111r has two of them.

These then are just some quick observations, and with them we have some initial data for full page comparisons. If someone can suggest an interesing enciphering method for the Askham text we can then have a look at how its NvP topo-spectrograph changes as a result. Note that we focused on non-specific NvP clusters. For example:

{5} #_#_~_# NvP clusters in VMS f111r
{5-1} line 28: 1234225_123435_12345_123445
{5-2} line 40: 1234456_12331_1234_12331

{6} #_#_~_# NvP cluster in Askham's Mentua Rubea
{6-1} line 2: 1234562_12342_123_12343

The specific spectral clusters are all different, but all three are of the general NNPN pattern.

I also took the VF(j) curves [6] for the entire f111r, and the entire Askham texts, after first connecting their respective lines with group separator spaces. The minimum summary data is:

{7} VMS f111r text series:
2683 groups-signals, 53 unique signals across all groups, 673 groups, agl= 3.99, mgl= 10, PR = 584/673 = 0.8678, RPR = 540/584 = 0.9247, HHR = 35/673 = 0.0520, hh differential super-spectrum transform change under direction-reversal = 75.6%, SSR = 1 / 673 = 0.0015, VF = 142568 / 226464 = 0.6295.

{8} Askham litle Herball, Mentua Rubea:
2398 groups-signals, 34 unique signals across all groups, 593 groups, agl= 4.04, mgl= 10, PR = 516/593 = 0.8702, RPR = 475/516 = 0.9205, HHR = 50/593 = 0.0843, hh differential super-spectrum transform change under direction-reversal = 68.7%, SSR = 1 / 593 = 0.0017, VF = 107546 / 175824 = 0.6117.

Both VF(j) plots show the expected shockwaves, and again in the region about j=20 transition to longwaves dominance. But the Askham curve settles into the longwaves much more rapidly, whereas the Voynich f111r curve still exhibits noticable disturbances over fully half of its duration. Perhaps with some work VF(j) shockwave parameters can be generally related to observations like points 1.) - 6.) above.

Berj / KI3U

[1] Note: some writers refer to the group of VMS pages to which f111r belongs, as "recipes", as in herbal recipes.

[2] Journal of Voynich Studies communication #204 (Vol. II): J.VS: Distribution of pillows and non-pillows in comm. #203 series examples; NvP Topography.

[3] The voyn_101.txt transcription and other GC resources are available online here:

[4] The SQS computer program for signals sequence spectrum analysis is available for download from the J.VS Library here:

[5] "A litle Herball of the properties of Herbes, ..... ", by Anthony Askham, transcribed by Glen Claston from both the 1550 and 1553 editions.

[6] Journal of Voynich Studies communication #206 (Vol. II): J.VS: The signals series in evolution: VF(j) Reference Data.

From: Greg Stachowski
Date: Sat 07/26/2008 03:52 AM

Subject: J.VS: Re: NvP Sequence Spectra Topographic comparisons: Voynich folio f111r text vs Askham's Menta Rubea


Excellent work! I had been just about to ask you to write something on how this methodology could be applied to draw conclusions. More of this, please!

Anyway, you asked about encryption suggestions for the Askham text. I'd start with the classics: monoalphabetic, simple polyalphabetics like Vigenere ... so that we can get a feel for how your method represents known ciphers before we go deeper.


From Berj Ensanian
To Journal of Voynich Studies
Sent Date 07-26-2008 11:55:14 AM

Subject: J.VS: Re: NvP Sequence Spectra Topographic comparisons: Voynich folio f111r text vs Askham's Menta Rubea

Greg Stachowski wrote 7/26/2008 in comm. #208: " More of this, please! "

Greg, indeed I am currently working on maximum resolution spectrographs of the VMS f111r and Askham Mentua Rubea text-blocks. The comm. #207 topo-spectrographs of course resolve only at two levels. I will communicate my results as soon as I have them completed. I may be submitting graphics pictures to you for the J.VS Library with that, as it will probably be impossible to diagram the results effectively in this ordinary plain-text medium.

" ... I'd start with the classics: monoalphabetic, simple polyalphabetics like Vigenere ... "

Right. Now, a simple one-to-one monoalphabetic substitution operating on the source plain-text of course leaves the spectrograph invariant. We also have to remember that in the case of the Voynich page there already are not-one-to-one substitutions in play via the transcription method - notably GC's Latin abbreviations and their effects, as already mentioned.


From Berj Ensanian
Sent Date 08-22-2008 8:22:37 PM

Subject J.VS: Wave propagation along the center-longitudinal in the sequence-spectrum space of the Voynich f111r text

Dear Colleagues

There are indications from some experimental results that the text of Voynich star-page f111r has waves propagating through the text's sequence spectrum space, waves that may have been built-in by design, and referenced to a longitudinal axis that runs down the centers of text-lines. Said in another way, the text may have been generated via wave propagations of simultaneous and different waves. If these waves are analyzed as fully dimensioned, then they can be thought of as intertwined different helixes, their respective arcs being portions ranging from less than one-quarter cycle to a complete cycle, and perhaps longer, moving downward through the sequence-spectrum space corresponding to the f111r text-page, referenced to a longitudinal axis defined by the centers of the text-lines. I have obtained some analytic graphs of this effect, as well as comparison plots of the Menta Rubea text from Askham's Little Herbal. The waves are also used to probe some old controversial VMS text problems. This communication is devoted to the details of the experiments, preceeded by the necessary theoretical preparations.

In J.VS communications #204 and #207 we developed topographic analyses of super-series of sequences [1]. It is already clear that these have many exploitable analytic possibilities for Voynich text research - one of their greatest advantages is an efficient assessment of global characteristics in a large set of data. The work in comms. #204 and #207 using Voynich and Askham source text-blocks, focused on non-specific NvP spectral distributions, at a topo-level resolution of two elevations. In a sense they were "low-resolution" spectrographs, but from the perspective of filtering so as to investigate certain general characteristics of super-series, the resolution there was the proper one. And much more awaits being done along those lines, as for example was briefly discussed in the exchange between Greg Stachowski and me in comms. #208 and #209: cryptographic transformation effects on the spectrographs.

But first here I would like to develop an expansion of the analytic scope to higher resolution spectrographs of super-series. The main task is the obtaining of an information-rich Z(x,y) from a super-series under investigation - once it is obtained, the appropriate mathematics in comparing and transforming between different Z(x,y) can proceed, and graphical analytics can topographically map Z(x,y) in 2D and / or 3D for their advantages. The SQS sequence-spectrum analysis computer program for this work has been upgraded to version V1.4, which includes all necessary routines for preparing the Z(x,y) of interest for 2D and 3D graphing with a suitable graphing program. A new SQS utilities section has some dozens of operations available, and all the below-described data-handling used some of these utilities. Again, your comments and bug reports are welcome. [2]



Converting a series of sequences into a graphable points-curve Z(x) is not at all difficult. As we have seen there is any number of ways to do it, depending on what aspect of the series is to be investigated. Indeed, way back in comm. #189 [1] we converted the transcribed Voynich f77r Currier-B text-line 11 in a very simple way:

{I-1} {#189: 2} 4ohcc89_e1c9_e2cc9_4ohcc89_4ohcc89_4ohay_4ohcc9_eaiiN_1c9

into a series so formed as to show the distribution of equal and unequal groups:

{I-2} {#189: 3-2} 1_2_3_1_1_4_5_6_7

and it is a simple step to take {I-2} as the nine points of a graphable curve:

{I-3} {Z(x)} of {I-2} where x = serial integer order of the group for which Z(x) is its elementary sequence identity:

1, 2, 3, 1, 1, 4, 5, 6, 7,

And so this curve has a plateau near its middle of the same height as its start, and a glance at its graph would tell us it represents a series with three identical groups so distributed, and so on.

Moving on to including more information from a source series into its Z(x), again there are many ways to do it, and we have to have some idea of what we are interested in investigating so as to define Z(x) effectively. Currently we are interested in the spectra of the sequences of the series, and comparing them with other series. For {I-1} using SQS we obtain:

{I-4} 1234456_1234_12334_1234456_1234456_12345_123445_12334_123

which has a rather low PR = 3/9 = 0.3333. We could take Z(x) = V(i), x=i, the nine values of the super-sequence deviation function:

{I-5} 6, 0, 0, 4, 4, -1, -1, -4, -8,

Another possibility is of course to take its shockwave function, Z(x) = VF(j), x=j, where x starts with x=2 :

{I-6} 1.0000, 1.0000, 0.5000, 0.3333, 0.5556, 0.6667, 0.6875, 0.7000,

and perhaps if convenient, force the definition Z(1) = 0 to get nine points altogether.

But let us zero in on the sequence spectra themselves, and with {I-4} as the source S{si} suppose we define:

{I-7} Z(x) = si where x=i and the si sequence spectrum is taken as an ordinary number:

1234456, 1234, 12334, 1234456, 1234456, 12345, 123445, 12334, 123,

It works, we can certainly plot these points on a graph, but the range makes it a bit awkward and we would likely be plotting their logarithms, or plotting their square-roots or something along those lines. A more serious problem for this scheme of straightforwardly taking the spectra as if they were ordinary numbers ready for curve-plots is when the spectra exceed nine signal-elements in length. For example, lets inject into {I-4} one more sequence spectrum in our usual notation:

{I-8} 1234456_1234_12334_1234456_1234456_12345_123445_1234567890A765B_12334_123

We have been quite successfully using numerical hierarchy with Arabic numerals 1-9 notation, and its extension with 0 and A-Z, as our defined system for spectrum neighboring. SQS handles it nicely, and here there is no problem determining, precisely, that per the rules of the numerical hierarchy system, the injected spectrum is obviously the "highest" spectrum in the series. But until now the numerical hierarchy system has had required of it only precision in neighboring-order, and has not been called upon to deal with spectrum-numbers in ratios, which is of course implicit in mapping directly the sequence spectra of a series as a curve. If we want {I-7} to apply to {I-8}, then we must have a precise answer for the meaning of ratios like this one:

{I-9} 1234567890A765B / 1234456

True enough, if as in {I-8} there is only one of these monsters, then we could go ahead and graph anyway, getting away with the handwaving arguement:

{I-10} [ 1234567890A765B / 1234456 ] is much greater than 1

However, the problem of {I-9} has to be delt with precisely sooner or later. One fairly simple (relatively speaking) way to do it seems to be to throw the sequences-series into a vector space, where the sequences become vectors, and if they happen to be long ones, like 1234567890A765B, then it just means that they have more non-zero components than the "little" vectors. And the solution to {I-9} would then come via a metric tailored for a specially defined vector magnitude, involving weighting, that makes sure no vector "shorter" than a given vector can exceed it in magnitude. I haven't thought about this much more, but it seems do-able alright, and perhaps will become worth developing down the road. Presently we have a much simpler, and I think very satisfactory solution to the {I-9} problem in the obtaining of a useful Z(x). Lets develop it with an example series of 11 sequences:

{I-11} the_cartoon_characters_said_they_wanted_megazilyobunch_junkfood_megazilyotimes_every_day

{I-12} The sequence-spectrum series for {I-11} is:


The PR = 6/11 = 0.5455. Lets have a look at the sequence super-spectrum for this series, ignoring the component amplitudes, and focusing just on the spectral components that make up its sequence spectrum-band:

{I-13} Sequence super-spectrum band for {I-11} and {I-12} :

Spectrum component index i : spectrum component

01: 123
02: 1234
03: 12134
04: 123456
05: 1234556
06: 12345667
07: 1234315647
08: 1234567890612A
09: 1234567890ABCD

The simple solution to obtaining Z(x) for the S{si} of {I-11} is now obvious:

{I-14} In the numerical-hierarchy system of sequence-spectrum neighboring, let a high-resolution spectrum-series to spectrum-series-curve mapping of S{si} be relative to its super-spectrum according to:

Z(x) = i[si] where i[si] is the spectrum component index i of the ith sequence si.

And so we convert the {I-12} example series of 11 sequences into the curve of 11 points:

{I-15} 1, 5, 7, 2, 2, 4, 9, 6, 8, 3, 1,

Provided we keep in mind that {I-13} is the spectrum-band within which the action is taking place, the progression of the curve {I-15} tells the sequence story of {I-12}. Clearly {I-14} can handle any sized sequences / groups, and the problem of {I-9} has been disposed of in a very simple manner.

The generalization of {I-14} is now also immediately obvious: we can expand the spectrum in any manner desirable, linearly or non-linearly. For example, for one reason or another we might like to include a couple more spectrum components, even though they do not arise in {I-12}:


Spectrum component index i : spectrum component

01: 112
02: 123
03: 1234
04: 12134
05: 123456
06: 1234556
07: 12345555
08: 12345667
09: 1234315647
10: 1234567890612A
11: 1234567890ABCD

This spectrum-band for the mapping is now 11 components wide, and so therefore relative to it the new Z(x) curve for {I-12}, again 11 points, becomes:

{I-17} 2, 6, 9, 3, 3, 5, 11, 8, 10, 4, 2,

Of course in expanding the spectrum band from {I-13} to {I-16}, ratios like [ 1234567890612A / 123 ] have changed in value, in this case from 8.0 in {I-13} to 5.0 in {I-16}. Nevertheless, they have remained precise, and operations involving the ratios within their reference spectrum-band are also precise. We haven't compromised anything, since sequence-spectrum neighboring we know is an ambigous concept that is necessarily resolved within a particular system. If the system expands in scope, as it does here, then it may be necessary to further define spectrum neighboring particulars, as we have just done.

The choice of the spectrum band is what provides the analytic flexibility for Z(x), especially in comparing different series - the spectrum band is chosen to cover all their spectra. Lets state the general definition:

{I-18} HIGH-RESOLUTION SEQUENCE-SPECTRUM MAPPING: In the numerical-hierarchy system of sequence-spectrum neighboring, let a high-resolution spectrum-series to Z(x) spectrum-series-curve mapping, of the series of sequences S{si}, be relative to a super-spectrum band B{bj} which includes all the spectrum components in S{si}, the mapping being according to:

Z(x) = j[bj]


j[bj] is the spectrum index j of spectrum component bj, and
x = i, and
si = bj

The formal definition may read a bit dry, but from the above examples we've seen that the mapping system is quite simple and logical. In metaphorical plain street language, we choose a reference B{bj} flower-garden that is divided into j lots. We then compare other flower-gardens S{si} to it, and when we identify lot si = bj, we assign Z(i) = j.

The updated SQS version V1.4 calculates Z(x) for the source S{si} referenced to its own sequence super-spectrum. That is, B{bi} = S{si}. The Z(x) values are provided in the analysis screen under the (S) command for displaying the sequence super-spectrum. It is easy to expand to any B{bj} needed: temporarily just add the required spectra to the source series. For example to reference {I-11} to {I-16}, make a temporary source series:


and calculate its Z(x). Finally, discard the last two Z(x) values to obtain {I-17}.


The collecting of series into a super-series, in the case of text a paragraph or more, adds a y-dimension to the analytics under consideration. Thus whereas with one series we map it to a curve Z(x), a set of series maps to a surface Z(x,y). The surface is in the sense of a surface as defined by the points of the nails of a bed of nails of differing heights, or the intersections of the perpendicularly running ropes of a fishnet. The Z(x) is after all a number function mappable as a points curve, it is not a continuous curve, and likewise the Z(x,y) is a number function mappable as a points surface. When appropriate, interpolation techniques in the graphing process can produce the appearance of a more substantial surface than just that suggested by points.

In general, if the series are of unequal lengths, then the surface is ragged - compared to a bounding rectangular frame there are some undefined Z(x,y) values. This is easily rectified with fill values.

The Z(x,y) are calculated in the manner of {I-19}:

{II -1} Using same group-separators, join all the separate series of the super-series set into one grand series. [3a]
{II -2} Calculate the Z(x) for the grand series.
{II -3} Partition the Z(x) according to the lengths of the member series. Then Z(x,1) refers to the first series in the set (in our case here the first text-line); saved as its own diskfile, it is the Z(x) curve of the first series calculated upon the entire set's spectrum-band. Z(x,2) refers to the second series, and so on.

With a ragged surface it remains to rectify it with a carefully chosen fill value for every Z(x,y) requiring one. First the surface frame dimensions must be decided - commonly we can make its width equal to the width of the longest series in the set, its maximum x-value. The length is logically the maximum y-value. For ultimate graphing we may expand the frame somewhat both in length and width with fill values - if the graphing will be done with interpolations in those areas of the frame that do not receive source Z(x,y) values, then the interpolated edges of the surface may be smoothed with a fill border. Also, if two separate surfaces are to be plotted and viewed in the same graph for comparison, they can be separated by a fill band, either with y-fill lines (rows), or x-fill points (columns), depending on the format desired. Thus they become sub-surfaces of a larger surface that has fill areas separating the sub-surfaces so as to make identifying them easy.

The NvP topographs in comm. #209 were placed onto their graphing frame so as to have each y-line centered on the longitudinal mid-axis x-value of the defined frame. The procedure involved various fills. The same can be done with the present Z(x,y), effectively creating a Z'(x,y). In the present work a fill value of zero will work well, because under normal circumstances Z(x,y) is equal to, or greater than 1, always.


III-A. PREPARATION of the Voynich f111r and Askham Menta Rubea texts for side-by-side topo-graphing, with their respective sequence-spectra Z(x,y) calculated from their COMMON SUPER-SPECTRUM. In the following, the filenames are a matter of choice, and can be whatever is convenient.

{III -1} Collect the total VMS f111r text by joining all text-lines with a group-separator signal into one file: rF111R.txt. This file then holds all 673 groups of the f111r text transcription from voyn_101.txt.

{III -2} Likewise collect the total MR text: file rMR.txt holds 593 groups.

{III -3} In the rF111R.txt file change all group separators from period (ASCII 46) to space (ASCII (32) and save as file sF111R.txt. The Menta Rubea file already uses space for the group separator.

{III -4} Using one group separator (space), combine sF111R.txt and rMR.txt into one seamless text-block in its own file: VMAM.TXT : 673+593 = 1266 groups. 6346 series-signals. 5081 groups-signals. VMAM.TXT can now serve as the source for calculating Z(x) spectrum values on a common sequence super-spectrum of VMS f111r and Askham's Menta Rubea. [3b]

{III -5} Calculate Z(x) per {I-18} for VMAM.TXT. The Z(x) data is saved in file ZXVMAM.TXT. In this data-set the Z(x) values range from 1 to 98, and therefore 98 different sequence spectra constitute the common sequence-super-spectrum for f111r and MR. The value 98 occurs only once: Z(538) = 98, so it is among the 673 f111r spectrum values, and in the super-spectrum therefore it is f111r that contributes the topmost spectrum.

{III -6} Partition ZXVMAM.TXT into two files: Z111R.TXT (the first 673 groups), and ZMR.TXT (the 2nd 593 groups).

{III -7} Using Notepad create the partition file P111R.TXT :

11, 13, 12, 14, 8, 14, 13, 12, 13, 15, 13, 12, 17, 12, 13, 13, 13, 13, 12, 14, 22, 16, 10, 15, 14, 14, 16, 13, 14, 12, 10, 10, 13, 13, 5, 10, 15, 13, 10, 15, 11, 13, 5, 11, 14, 13, 9, 10, 12, 11, 13, 14, 14, 6,

These 54 numbers are the lengths (number of groups) of the series (text-lines) 1-54 of the VMS f111r text transcription, as in comm. #207, {#207: 1}. The sum of these 54 numbers is of course = 673.

{III -8} Create the partition file PMR.TXT :

11, 13, 12, 14, 8, 14, 13, 12, 13, 15, 13, 12, 17, 12, 13, 13, 13, 13, 12, 14, 22, 16, 10, 15, 14, 14, 16, 13, 14, 12, 10, 10, 13, 13, 5, 10, 15, 13, 10, 15, 11, 13, 5, 11, 14, 13, 9,

These are the first 47 numbers from P111R.TXT, and they sum to 593. Thus they are the lengths of the series (text-lines) 1-47 of the Askham Menta Rubea text, as in comm. #207, {#207: 3}.

{III -9} Partition Z111R.TXT with P111R.TXT and name the created 54 files: 1V.TXT - 54V.TXT

{III -10} Partition ZMR.TXT with PMR.TXT, and name the created 47 files: 1M.TXT - 47M.TXT

{III -11} Create, with Notepad, the 7 textfiles 48M.TXT - 54M.TXT containing the data:

48M.TXT: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
49M.TXT: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
50M.TXT: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
51M.TXT: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
52M.TXT: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
53M.TXT: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
54M.TXT: 0, 0, 0, 0, 0, 0,

These are filler series files, of corresponding lengths, so that now both the VMS f111r and the Askham Menta Rubea series sets have the same number, 54 total, of series files, and so they may be horizontally joined: corresponding series per text-line, placed side-by-side on the same x-axis, and then finally graphed together.


At this point a decision must be made on how to rectify: a.) keeping the relative positions of the groups in their series the same between series, or b.) centering the series with respect to a lines-center longitudinal, regardless of their lengths. Both approaches have their analytic uses: the former is best for seeing if columns going down through the text, columns as defined by the groups in their appearance order, show any patterns with respect to the starts of text-lines. The centered rectification is best for seeing if during the generating of the text an imaginary longitudinal center-axis was used as a reference. I created graphs of both rectifications.


{III -12} Using the fill-value = 0, rectify the set 1V.TXT - 54V.TXT to a width (i.e. lengths of all series in the set) of 24, with one fill at the starts of each series, and the necessary other fills for each line appended to their ends. The results files are named: 1VR.TXT - 54VR.TXT. The longest series, line 21 with 22 source-groups, will therefore show in its file 21VR.TXT the rectification like this:

0, its 22 Z(x,21) numbers, 0,

{III -13} Do the same for 1M.TXT - 54M.TXT, resulting in: 1MR.TXT - 54MR.TXT.


{III -14} Horizontally join the nVR.TXT and nMR.TXT files to become the nVMR.TXT files. Therefore:

1VR.TXT joined with 1MR.TXT and the result is file: 1VMR.TXT
2VR.TXT joined with 2MR.TXT and the result is file: 2VMR.TXT
53VR.TXT joinded with 53MR.TXT and the result is file: 53VMR.TXT
54VR.TXT joinded with 54MR.TXT and the result is file: 54VMR.TXT

These nVMR.TXT files, where n=1 to n=54, each contain 24+24=48 data points. Each is a Z(x,y=const.) curve data-set, where the y=constant is the text-line number from among 1 to 54. These files are ready for topo graphing directly, in a left-handed reference frame, or they may be further operated on with mathematics chosen to transform the Z(x,y) surface in some desired manner into a Z'(x,y) surface. (Note: unless stated otherwise, all diagrams in this communication were prepared for right-handed plotting frames. More about that further on.)

Taking the raw nVMR.TXT set I plotted the surface both in 2D and 3D and had my first look at a high-resolution sequence-spectrum comparison, upon a common super-spectrum, of VMS f111r and Askham's Menta Rubea. The graphs of course suggest a terrain. There were major differences immediately noticable.

WHAT SHOULD BE LOOKED FOR? Well, many things, like symmetries and dis-symmetries, which are routine analytic points for those who are experienced with data topo-graphing. As we said above at the beginning, the advantage of 2D and 3D graphs is the ability to efficiently survey for patterns a large amount of data in one graph, data that at its source may have nothing whatsoever to do with geo-physical topography. It is important to understand that patterns arise in many ways, including as artifacts of analysis, and the problem of determining the origin of any pattern comes after first spotting it. So then, most important in our present experimental investigation is to see if in the Z(x,y) data terrain there is EVIDENCE OF ORGANIZED TERRAIN, rather than just apparently randomly scattered valleys, hills, and mountains.

Viewing the 2D and 3D Z(x,y) graphs of the nVMR.TXT and nMR.TXT data-sets, both spectrographs show some hints of longitudinal waviness arising from the varying line widths - analytic artifacts. Otherwise, it appears that the spectral complexity of the Askham text decreases as we move down the text from the top of the page. Its terrain complexity is greatest in the first third of the text: there is much jumping around across the entire super-spectrum, whereas further down in the text the spectrum jumping is dampened. With f111r the spectrum complexity is about the same throughout.

But the most dramatic difference between the two topo-spectrographs is that: whereas Askham shows little obvious organization of its terrain features from top to bottom, the f111r suggests a definite organized terrain feature moving down the page, from the very top to the very bottom. I first noticed it in the 3D graph, appearing suggestive of a curving, actually wavy mountain range, when "flying" my perspective from above, and approaching the rectangular framed data terrain from the bottom end. From the poor definition of this possible feature provided by the raw nVMR data, I guessed, that if it truly were an organized feature across the f111r text from top to bottom, it would become clearer if the rectification of the surface data were centered. Also, if the perceived feature were merely an artifact of the changing line widths, then it should begin to appear in the center-rectified Menta Rubea spectrograph also. Accordingly, I started over.


{III -15} Using the fill-value = 0, center-rectify the set 1V.TXT - 54V.TXT to a width of 25. The result filenames are: 1VCR.TXT - 54VCR.TXT. The longest series, line 21 with an even 22 groups, file 21VCR.TXT, will therefore receive just three fills, and show the center-rectified format:

0, its first 11 Z(x,21) numbers, 0, its second 11 Z(x,21) numbers, 0,

{III -16} Do the same for 1M.TXT - 54M.TXT, resulting in 1MCR.TXT - 54MCR.TXT.

{III -17} Horizontally join the nVCR.TXT and nMCR.TXT files to become the nVMCR.TXT files.

The 54 nVMCR.TXT files thus each contain 50 data points, and are ready for direct topo-graphing in a left-handed reference frame.

Viewing the results graphed, the impression is reinforced that the f111r spectrograph, in contrast to the MR, does have distinct and organized terrain features runnning down the page. Indeed, the center-rectification seems to resolve and suggest a further complexity: two exactly out-of-phase waves run down the page and alternately determine the sequence spectra / groups on opposite sides of the center-longitudinal. The appearance suggests something like a 2D shadow of two flattened braided double-helixes a la DNA running down the f111r page. Or alternatively, weaving chains of islands in an ocean.

Even though the Askham text has been forced into the f111r line lengths (by groups), it is far more difficult to see a convincing organized waves pattern in it. The Askham spectrograph is more suggestive of randomness, even though forcing it into the lines-lengths variations of f111r has introduced the artifacts of line-lengths waves, clearly visible, and again overall it does seem to have decreasing spectrum terrain complexity as the lines proceed, and this might be taken as a possible organized-across-all-its-data characteristic, although considering the source of the MR data there is no compelling reason I can think of at the moment to do so.

I found that the f111r features were best seen with thermographic 2D plotting, and full interpolation so as to substantialize the surface. After several graphing experiments in left-handed and right-handed frames, I settled on making two copies of an image of the spectrograph, 1VMCR.JPG, and 2VMCR.JPG. On 2VMCR.JPG I drew by hand two wavy arrow-lines to indicate the perceived tentative features. I have sent these pictures, along with others discussed here later on, to our J.VS Librarian Greg Stachowski for deposit. [4]

These results suggested re-calculating the f111r and Menta Rubea spectrographs, each upon its own super-spectrum only. First here, some explanations about 2D and 3D data graphs.


As already mentioned, a rectified set of Z(x,y) data numbers plots in 3D like the tips of the nails of a bed of nails of differing heights. Such points plots can be difficult to visualize properly, so the next step up is to connect the points with lines, most basically along either the x-axis, the y-axis, or both. The connecting lines can simply be straight ones, between each pair of adjacent points, or curve-fitting calculation can introduce smoothing. The individual points have expanded into curves. If only the x-axis is so treated, then the graph shows parallel curves, parallel to each other, and to the x-axis. Similarly for the y-axis. If both axes are so treated, then the result is a so-called 3D fishnet graph, where the original data-points are the intersections of the Y-parallel and X-parallel curves.

Interpolations can be calculated and plotted so that new curves appear between the original curves, and the surface thus becomes denser, more substantial. Socalled "hidden line removal" prevents a confusing display: from the perspective of the observer, if a curve runs behind another curve, then it is blanked out for that portion of it. That is, you can see a bump in the fishnet, but not see anything through the bump. The name is rather a poor one, since the better 3D graphing programs do not "remove" portions of lines, but rather calculate and render their on-screen visibility according to the chosen perspective.

Next, thermographic techniques can be introduced to make the data visualization even better. This amounts to changing the color of the fishnet locally, according to its height there with respect to the reference X-Y plane. Customarily, low elevations are given cooler colors (down to blue), and higher elevations are given warmer colors (up to white). The number of thermographic colors, and the elevation ranges they are assigned to, is flexible and is adjusted with particular investigations. A big data bump or mountain on the fishnet is thus rainbow colored, the colors changing along its height. So with one glance across the data-surface we can tell similar data-elevations by color.

To obtain from such a 3D thermograph a 2D thermograph, we flatten it: we scale, proportionally, all the Z(x,y) elevations way down, until, practically, the graph looks like a flat board. But, the thermo-colors are unaffected by this procedure, and they form flat patches of color, flat islands and so forth, showing the corresponding elevations with colors only. Here it is often best to interpolate fully and make the surface smoothly complete, leaving no holes in it. The effect is similar to what you see routinely in television weather reports, say storms and precipitation thermographically depicted upon the local, or regional map.

So then, what we are looking at in the 1VMCR.JPG and 2VMCR.JPG pictures are the 2D thermographically plotted distributions, of sequence spectra of their common super-spectrum, of the Voynich f111r and Askham Menta Rubea texts. And for each text-block, Voynich on the left and Askham at its right, the distributions are positionally referenced by their textlines arranged horizontally so as to have a common longitudinal / vertical center-line - just like we did with their NvP topographs in comm. #207. The thermo-topographs are fully interpolated, giving the illusion of a continuous surface, but we understand the mechanics and know we are viewing a limited data-set of Z(x,y), not a continuous, infinite one.

The hotter colors show those locations on the center-rectified-reference text pages where the sequence spectra are higher in the reference super-spectrum. Conversely, the cooler colors show how the lower spectra are distributed. The elevations run from 0, the fill value, to 98. Six thermographic colors, from blue to white, cover equal elevation ranges on 0 - 98. A big thermographic island indicates that the sequence spectra in that part of the text are close neighbors in the super-spectrum.

In the 2VMCR.JPG, where I've drawn in the tentative wave arrows on the f111r part, we see that they cross the longitudinal center-axis at lines 7 and 41, thus indicating an oscillation period of 2 x ( 41 - 7) = 68 text-lines. Of course the entire f111r text is just 54 lines, we do not get full cycles of these waves, and also they are (7/68)(2 pi) = 0.647 radians phase shifted when the text starts at the top with the first line. Another viewpoint is to see there a standing wave, with successive nodes at lines 7 and 41. The caution here is that these wave indications are based on only 6 thermo-levels covering 54 spectral-component elevations, and many details are washed out. But they are enough to show some wave tendencies in f111r that are absent in Askham, and to motivate further, more detailed analysis - we need more evidence for the existence of these waves in the distribution of the sequence spectra. Even if the waves are there, they may run differently from the way my drawn-in arrows try to depict them. The drawn arrows may well be just indicative of envelopes averaging several different waves.


If the spectrum waves are a true pattern peculiar to f111r, then they ought to show up even better when f111r is calculated on its own super-spectrum only, with the "noise" of the Askham spectral influences absent. Similarly, anything by way of patterns in Askham should be easier to see on its own also. When we plotted them together on their common super-spectrum, we were interested in answering the question: are there any striking differences? It looks like the answer is yes, and so now it makes sense to analyze them, each isolated from the other.

{III -18} Calculate Z(x) on the file rF111R.TXT from {III -1}, which is the grand series of all the f111r text only. Name the results file ZX111R.TXT. This file holds the 673 sequence-spectrum data points for f111r. The super-spectrum evidently has 53 components, as the Z(x) values range 1 to 53. Whether or not it is meaningful that f111r's number of distinct spectral components, 53, is almost equal to the number of text-lines, 54, or is just a coincidence, is not clear at this stage.

{III -19} Partition ZX111R.TXT with P111R.TXT to obtain the 54 series / files named 1ZV.TXT - 54ZV.TXT. These files hold the raw Z(x,y) data for f111r, with x proceeding from left to right corresponding to groups on text-lines from left to right, and y proceeding from top to bottom, corresponding to text-lines following one another from top to bottom. Here is the collected data-set, followed by a basic summary of it:

III-G-1: Un-rectified raw sequence-spectrum Z(x,y) data-set of the voyn_101.txt transcript of Voynich f111r text:

For (x,y,z) graphing in left-handed ref. frame: x-axis to the right; y-axis downward

subset #: subset size: subset

01: 11: 49, 5, 5, 33, 45, 7, 10, 5, 4, 2, 5,
02: 13: 5, 10, 10, 10, 2, 2, 10, 10, 10, 10, 5, 18, 21,
03: 12: 13, 26, 5, 21, 21, 31, 5, 2, 10, 39, 5, 21,
04: 14: 5, 21, 21, 5, 31, 10, 31, 1, 10, 5, 17, 5, 2, 2,
05: 08: 5, 22, 1, 1, 10, 24, 10, 10,
06: 14: 5, 10, 10, 10, 5, 5, 31, 31, 10, 5, 10, 5, 10, 10,
07: 13: 21, 30, 15, 21, 21, 5, 10, 39, 5, 21, 10, 2, 2,
08: 12: 5, 1, 21, 5, 10, 21, 31, 5, 31, 18, 10, 31,
09: 13: 46, 16, 2, 10, 21, 21, 21, 10, 10, 10, 5, 5, 5,
10: 15: 31, 5, 2, 10, 31, 10, 10, 30, 2, 2, 10, 31, 2, 2, 5,
11: 13: 10, 26, 21, 12, 36, 12, 2, 5, 10, 5, 5, 5, 2,
12: 12: 10, 31, 43, 10, 26, 10, 31, 8, 5, 2, 21, 10,
13: 17: 19, 10, 21, 31, 1, 1, 2, 1, 1, 2, 5, 5, 2, 2, 5, 5, 31,
14: 12: 31, 17, 10, 21, 2, 10, 21, 21, 10, 28, 10, 21,
15: 13: 32, 2, 7, 5, 8, 2, 26, 5, 5, 13, 31, 5, 21,
16: 13: 8, 5, 31, 8, 5, 5, 31, 21, 5, 17, 10, 10, 10,
17: 13: 10, 10, 21, 42, 37, 21, 5, 5, 14, 2, 17, 12, 10,
18: 13: 5, 15, 24, 2, 5, 21, 5, 5, 42, 42, 10, 31, 10,
19: 12: 5, 26, 42, 10, 50, 3, 10, 49, 21, 21, 1, 10,
20: 14: 21, 30, 21, 10, 15, 10, 10, 21, 31, 10, 2, 2, 1, 5,
21: 22: 5, 1, 5, 2, 7, 10, 2, 1, 1, 5, 5, 2, 12, 5, 5, 5, 2, 2, 1, 5, 2, 2,
22: 16: 10, 1, 10, 5, 10, 15, 10, 2, 2, 2, 10, 31, 10, 5, 10, 21,
23: 10: 10, 10, 43, 31, 21, 31, 10, 21, 40, 52,
24: 15: 5, 10, 10, 8, 28, 17, 40, 8, 1, 2, 5, 5, 5, 2, 2,
25: 14: 2, 10, 21, 10, 21, 19, 1, 21, 6, 5, 10, 2, 10, 10,
26: 14: 2, 2, 10, 34, 10, 31, 2, 8, 21, 1, 10, 31, 21, 2,
27: 16: 5, 10, 21, 19, 2, 10, 21, 2, 10, 5, 21, 5, 1, 21, 2, 5,
28: 13: 27, 10, 27, 38, 28, 21, 30, 2, 5, 10, 21, 2, 2,
29: 14: 45, 26, 5, 1, 2, 5, 8, 2, 2, 2, 42, 31, 31, 5,
30: 12: 31, 31, 31, 10, 2, 17, 10, 2, 10, 30, 5, 2,
31: 10: 51, 5, 2, 10, 30, 31, 21, 42, 10, 10,
32: 10: 46, 29, 1, 5, 10, 21, 21, 45, 25, 31,
33: 13: 9, 1, 2, 2, 30, 10, 10, 10, 31, 2, 11, 42, 2,
34: 13: 5, 18, 2, 10, 10, 2, 13, 21, 2, 41, 47, 10, 1,
35: 05: 21, 2, 2, 5, 5,
36: 10: 20, 21, 21, 45, 31, 12, 31, 45, 21, 10,
37: 15: 5, 5, 1, 7, 1, 10, 21, 21, 1, 12, 21, 21, 5, 5, 21,
38: 13: 8, 5, 2, 10, 25, 21, 21, 10, 1, 31, 5, 1, 10,
39: 10: 5, 21, 10, 21, 5, 45, 40, 10, 21, 28,
40: 15: 5, 2, 7, 31, 21, 5, 2, 10, 42, 16, 10, 16, 1, 5, 2,
41: 11: 8, 5, 21, 31, 21, 21, 21, 31, 5, 10, 2,
42: 13: 19, 1, 30, 27, 2, 21, 1, 10, 10, 53, 10, 10, 2,
43: 05: 21, 21, 31, 21, 10,
44: 11: 31, 13, 36, 21, 5, 49, 5, 5, 18, 10, 5,
45: 14: 1, 2, 2, 5, 5, 15, 2, 10, 10, 8, 17, 10, 21, 10,
46: 13: 1, 5, 10, 17, 26, 31, 5, 10, 2, 19, 2, 2, 10,
47: 09: 10, 21, 7, 42, 10, 2, 10, 17, 10,
48: 10: 35, 26, 21, 10, 31, 5, 10, 10, 24, 5,
49: 12: 10, 5, 2, 5, 30, 21, 10, 17, 26, 10, 21, 2,
50: 11: 10, 1, 10, 23, 48, 5, 10, 5, 21, 10, 8,
51: 13: 44, 5, 31, 2, 5, 1, 5, 5, 5, 2, 21, 21, 10,
52: 14: 1, 2, 2, 21, 21, 10, 31, 5, 5, 5, 5, 2, 2, 2,
53: 14: 1, 2, 2, 21, 17, 5, 1, 2, 2, 2, 5, 21, 5, 5,
54: 06: 5, 10, 5, 21, 10, 10,

n = 673 data points; Hi = 53; Lo = 1; P-P = Hi - Lo = 52; ( P-P / n ) = 0.0773
SUM = 9049; Average = 13.4458
Absolute SUM = 9049; Absolute Avg. = 13.4458
Root-mean-square R.M.S. = 464.4836

If the sequence-spectrum waves exist as an organized feature of the entire f111r text, then they must be evident in these above numbers. Analytic care must be taken so as to keep separate from any sequence-spectrum waves, the waves that are unquestionably present due to variation of line lengths. Advanced mathematical techniques can easily remove the effects of line-length variations, but we will avoid those for now and use the simplest analytic procedures we can make do with.

If the data are to be plotted in a right-handed reference frame, then they must first be reflected in the x-direction. That is, file 1ZV.TXT above would need to be converted so as to hold: 5, 2, 4, 5, 10, 7, 45, 33, 5, 5, 49,

And so on, for all 54 files.

{III -20} Using the fill-value = 0, center-rectify the set nZV.TXT to a width (lengths of all series in the set) of 25. Rename the results filenames to 1VCR.TXT - 54VCR.TXT. The files are ready for direct topo-graphing. The Z values range 0-53.

{III -21} Repeat the equivalent of steps {III -18} to {III -20} above for the Menta Rubea text, starting with file rMR.txt from {III -2}. The Menta Rubea data-set is of course just 47 lines, not 54, but if graphed separately from f111r this is no problem. The final MR files ready for topo-graphing are: 1MCR.TXT - 47MCR.TXT. The Z values range 0-69.

The thermo-topographs of the nVCR and nMCR data-sets reinforce the original impression: aside from the artifact waves introduced by line-lengths variations, some sort of organized waving is spanning the Voynich f111r text from top to bottom, and an analog to that is missing in the Askham Menta Rubea text. This is further reinforced when the data surfaces are clipped at 50% elevation, so that only the upper half, or lower half, of Z(x,y) data elevations are plotted. For nVCR this means for the upper half case plotting only spectral components 26-54, having set all others to zero first. For nMR the upper 50% is components 34-69. In the Library deposit [4] is the picture UHVMR.jpg showing the upper 50% clips of f111r and MR. Experimenting with clipping bands, I found that the wave effect in f111r seemed most easily seen in the 65% - 95% elevations band. Since the nVCR data elevations run 1-53, this corresponds to plotting only the f111r spectral components 34-50, having set all others equal to the ground level, zero. That is, if a Z(x,y) falls outside the range of values 34-50, set it = 0 before plotting. (Note: SQS provides both absolute and relative clipping, with explanations; the two must not be confused. Here absolute clipping is referred to.)

Another very important and useful result emerges with the self-based spectrographs of nVR versus nMR: these self-based spectrographs, each calculated on its own super-spectrum band, and available for side-by-side comparison, now make it much easier to recognize the line-lengths artifacts-waves common to both: this is excellent, because now the Menta Rubea data can serve as a check on resolving / creating artifact waves in the f111r data, when they might not really be there in any meaningful manner. Further, it must be remembered that with sufficiently powerful techniques we can decompose any data-set into waves. We want to see if the data has waves that were built-in, and not de-compose data into universal waves, say Fourier waves, just because we can. We can always get waves, but the question is: were some of them built-in by some process?

As a first check of the artifact-waves influence, we can point-by-point subtract the Menta Rubea data-surface from the f111r data-surface, and plot the resulting difference surface - common artifacts will be diminished or gone. However, for this to work, the two data-sets must have, in addition to identical rectification, identical elevation ranges, low to high Z(x,y). Since in this case they do not, they must first be identically normalized, via a projection transform, before a fair difference surface can be calculated. This all done, I found that the difference surface retains the wave-feature of interest, and if anything, reinforces the indication of it running from the top of the f111r text to the bottom.

The range of analytic possibilities for Z(x,y) data topography is enormous. Even just the basic and elementary operations, like taking difference surfaces, are very numerous, and combinations of the elementaries on up from there. Data array and file handling can become a chore: even a basic set of 54 data files can result in thousands of data files to be created and named, experimented with, and deleted or saved, in a single experimental sesssion, by the experienced data topographer. The practical minimum mathematical power should be used for analytic transformations, because the more powerful the math, so also it tends to become more of a chore to identify inadvertently created artifacts, much much more so with this Z(x,y) surface data than when dealing with just single Z(x) curves. I have made the data files that SQS works with and saves, ordinary plain vanilla text-files, so that they can be adapted to all requirements, from writing up communications like this one, to being usable by advanced math programs and 2D and 3D graphics programs.


The analysis up to this point suggested the best next step to be narrowing the focus upon a specific spectral component, and trying to fit all its appearances in the f111r text into a wave or waves. The analysis also indicated that the particular spectrum component should be chosen from the upper half of the full f111r spectrum band of 53 components. The component amplitudes (counts of occurrences) in the band ranges from just 1 for many of the components, to the 140 for component 10, which corresponds to the ramp-pillow sequence-spectrum 1234 :

{IV-1} Sequence-spectrum band of Voynich f111r text (GC voyn_101.txt transcription), file rF111R.TXT

Spectrum component : component amplitude

01 P: 1 : 38
02 P: 12 : 98
03 : 112 : 1
04 P: 121 : 1
05 P: 123 : 125
06 P: 1212 : 1
07 P: 1223 : 6
08 P: 1231 : 12
09 : 1232 : 1
10 P: 1234 : 140
11 : 11234 : 1
12 : 12234 : 6
13 : 12314 : 4
14 : 12322 : 1
15 P: 12324 : 5
16 : 12331 : 3
17 : 12334 : 11
18 P: 12341 : 4
19 : 12342 : 5
20 : 12343 : 1
21 P: 12345 : 87
22 : 122314 : 1
23 : 122345 : 1
24 : 123145 : 3
25 : 123245 : 2
26 P: 123345 : 9
27 P: 123425 : 3
28 : 123435 : 4
29 : 123442 : 1
30 : 123445 : 9
31 P: 123456 : 46
32 : 1223456 : 1
33 : 1231245 : 1
34 : 1231456 : 1
35 : 1232456 : 1
36 : 1233456 : 2
37 : 1234156 : 1
38 : 1234225 : 1
39 : 1234256 : 2
40 P: 1234356 : 3
41 : 1234425 : 1
42 : 1234456 : 9
43 : 1234546 : 2
44 : 1234552 : 1
45 P: 1234567 : 6
46 : 12334567 : 2
47 : 12341235 : 1
48 : 12342356 : 1
49 : 12342567 : 3
50 : 12343567 : 1
51 : 12345267 : 1
52 : 12345467 : 1
53 : 1234526789 : 1

Some further thought suggested choosing a component with an amplitude approximately equal to the number of text-lines, 54. That way there is a chance of less confusion that might result from too few covering too great a span (54), or too many making it difficult to identify which belong to which proposed wave traces. From {IV-1} we see there is only one component that fits the requirements, component 31, with 46 occurrences in the f111r text. It corresponds to the ramp-pillow sequence 123456, which, fortuitously, as we've seen from earlier sequence-spectrum work, is a common sequence spectrum, regardless of source material. From III-G-1 above, we see that the first instance of component-31 is on the third text-line.

I center-rectified the III-G-1 data, and proceeded to fit curves connecting the occurrences of component-31, trying to keep the curve arcs as much as possible similar to sinewave arcs. Of course any built-in waves need not have been sinewaves, they could for example be sawtooth waves, or a variety. But, on the assumption that the text was generated with mechanical help, and that the simplest such arrangement would be a set of rotatable disks, then within a rectified analytic space there is consequently likely to be sinewave evidence.

There is of course also transcription uncertainty and transcription distortion (say from abbreviations) to consider, factors we have gone over in detail a number of times in sequence spectrum work. Suffice it to say that the curve fitting can tolerate the arcs deviating a bit from perfect sinewave arcs, and still remain within arguable bounds for the basic hypothetical premise of the investigation: that at least some of the text-groups of f111r were positioned on the page, via their sequence spectra tracing out waves.

The results are shown in the picture diagram SspctrmC31vmsf111r.jpg [4]. As you can see, I was able to fit all 46 occurrences of component-31 onto a total of 10 arcs, colored two red, two orange, two green, two black, and two blue curves, and all of them fairly good sinewave arcs. It is seen that many occurrences of component-31 are intersections for arcs, as many as 4 arcs crossing one of the points.

One of the red curves is a complete full-cycle, and excellently shaped sinewave propagating through 6 occurrences of component-31, spanning text-lines 4 to 52. It alone makes the case that investigating sequence-spectrum waves in Voynich text blocks is worthwhile.

It is entirely possible that other, better curve-fits could be found, for at least some of the points of component-31. But to proceed with the analysis let us identify the 10 waves in diagram SspctrmC31vmsf111r.jpg :

{IV-2} Identification, using Wi-j with i=31, of the ten component-31 wave-arcs in SspctrmC31vmsf111r.jpg :

wave ID : color in diagram; its total (x,y) points; (x,y) points referenced to the center-longitudinal (0,y), and +x to the right and +y downward per text-lines, and y=0 taken as "unscripted"; comment

W31-1 : red; 6; (1,4), (6,14), (2,26), (-1,31), (-2,33), (1,52); complete excellent sinewave cycle.
W31-2 : red; 9; (3,10), (-4,22), (-5,26), (-5,29), (-5,32), (-3,38), (-2,41), (1,48), (4,51)
W31-3 : orange; 5/6; (-8,13), (-4,15), (2,23), (4,30), (2,41), (0,43); 6th point if slight distortion is taken.
W31-4 : orange; 5; (5,13), (-1,23), (-1,31), (1,36), (4,40)
W31-5 : green; 9; (3,4), (1,6), (-1,8), (-4,15), (-5,18), (-5,29), (-2,36), (2,41), (5,44)
W31-6 : green; 5; (7,10), (4,16), (2,23), (4,40), (5,44)
W31-7 : black; 6; (-1,6), (-3,8), (-4,10), (-4,15), (-2,20), (2,23)
W31-8 : black; 6; (5,12), (0,16), (-4,22), (-6,29), (-2,41), (0,43); the only W31 wave covering both (0,16) & (0,43)
W31-9 : blue; 6; (1,3), (3,10), (4,16), (5,30), (4,40), (1,52)
W31-10 : blue; 6; (-6,8), (-4,10), (-1,12), 6,30), (4,40), (1,46)

Assuming that these waves are there by design, that is, they are traces of a VMS-text generator, it is nevertheless still uncertain if the modulation components controlling the waves are capricious, are encoding functions, or are also just being generated methodically. For example, consider the W31-10 blue wave: aside from its absolute amplitude, phase, and offset, a modulation action of some kind, say a switching function, switches in W31-10 's presence at its 6 points, and switches it out everwhere else. Is that action capricious in the sense of mechanical text generator disks being turned one or more clicks at whim?

A more complicated view is that this blue wave is not being switched in and out, but is being switched from component-31 to another component or components. Inspection of SspctrmC31vmsf111r.jpg or III-G-1 above shows that component-31 is often associated, within text-line, that is for the same y-coordinate, with components 5, 10, and 21. Sequence-spectrum cluster-modulation may be involved. In any case, a study of the modulation components for the above waves, simultaneous with analysis of the waves themselves, is of serious interest.

For a first foray into that area we could use either modulus arithmetic, or adapted continuous functions - trigonometric waves. My guess is that in these early stages of analysis there is more potential for insight into the entire f111r waves picture with trig waves, allowing estimates of transcription deviations for example, and that as the picture becomes clearer, then going over to modulus arithmetic as perhaps a closer analog to hypothetical mechanical disk text generators, is the way to proceed.

So lets have a look. We'll start by describing the W31-1 wave. First we need its curve equation:

{IV-3} x = f(y) = Int{ B + Asin[ (y + C)(2pi/ P) ] }

where: Int{ real number} = integer nearest to the real number, with sign preserved

The offset from the center-longitudinal, x=0, is easily seen from SspctrmC31vmsf111r.jpg to be: B = +1
The amplitude A = 6 - 1 = 5
The period P = 52 - 4 = 48 lines or units on the y-axis
The phase C = -4 upon the arbitrarily chosen point (1,0), lying on the "unscripted" line-zero, as the reference for calculating the curve - we really do not know its absolute calculations reference: it could be anywhere on the x=B=1 line, and could be calculated from an interior point outward, both upward and downward on the y-axis. Perhaps even the f111r text is a continuation of text elsewhere in the manuscript, and the W31-1 starts there, whereever that is.

Therefore: f(y) = Int{ 1 + 5sin[ (y - 4)(pi/24) ] }

Lets check it against the {IV-2} data for W31-1 :

{IV-4} y : f(y) from {IV-3} : F(y) from {IV-2}

y=4 : f(4) = 1 : F(4) = 1
y=14 : f(14) = Int{5.8296} = 6 : F(14) = 6
y=26 : f(26) = Int{2.2941} = 2 : F(26) = 2
y=31 : f(31) = Int{-0.9134} = -1 : F(31) = -1
y=33 : f(33) = Int{-2.0438} = -2 : F(33) = -2
y=52 : f(52) = 1 : F(52) = 1

So, the curve-fit is perfect. Let us show it here with a plain-text diagram that is a simplification of the one in the SspctrmC31vmsf111r.jpg picture.

{IV-5} Showing the W31-1 wave in the sequence-spectrum space of Voynich text-page f111r, being a simplified version of the diagram from SspctrmC31vmsf111r.jpg . If your screen does not display a perfect rectangle and sinewave, then copy the diagram into Notepad.

~~ = group or rectification fill
[] = indicator of the +1 offset data-column to the right of the longitudinal text-line cL
&& = W31-1 group of sequence-spectrum component-31 (123456)
## = W31-1 wave trace indicator

01: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
02: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
03: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
04: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ && ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
05: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ## ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
06: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
07: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
08: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
09: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~ ~~
10: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
11: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
12: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~
13: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
14: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ && ~~ ~~ ~~ ~~ ~~ ~~
15: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
16: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~
17: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
18: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
19: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
20: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~ ~~
21: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
22: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
23: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
24: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ## ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
25: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
26: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] && ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
27: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
28: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
29: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
30: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
31: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ && ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
32: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
33: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ && ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
34: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
35: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
36: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
37: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
38: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
39: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
40: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
41: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
42: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
43: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
44: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
45: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
46: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
47: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
48: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
49: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
50: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
51: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ## [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
52: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ && ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
53: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~
54: ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ [] ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~ ~~

From the offset B = 1 some interesting peculiarities of W31-1 are observed. Of the curve's 6 points, the two end-points lie on the x = B = 1 intrinsic zero-amplitude line, and the peculiarity is that all the other points are a prime number distant from that zero line, measured on the x-axis. For example, the point (6,14) is 6 - B = 5 distant on the x-axis from the x = B line. Astoundingly, the placement of the points with respect to the y-axis has the same peculiarity! It is only necessary to recognize y = 33 of the point (-2,33) as the reference, and then count from it the number of lines to the other five points:

{IV-6} W31-1 point : y-axis distance from point (-2,33)

(1,4) : -29
(6,14) : -19
(2,26) : -7
(-1,31) : -2
(-2,33) : 0
(1,52) : +19

One further pattern is quickly found in this particular arrangement of primes: moving the 0 reference upward, while contracting the span with the removal of the two remaining endpoints, the prime distances peculiarity remains intact:


-19 : -17
-7 : -5 : 0
-2 : 0 : 2
0 : 2

Now, we have often noted the emphasis on prime numbers in various places in the Voynich manuscript [5]. Here prime numbers may be serving in the role of modulation / switching function parameters for the basic waves.


Lets have a look at the set of actual scripted Voynich groups / words in f111r that correspond to the sequence spectrum component-31, that is the sequence spectrum 123456 :

{V-7} GC voyn_101.txt transcription groups in f111r with the sequence spectrum 123456

585: 4ohcay
586: ohc7ae
587: 4ohc89
588: oe1c89
589: 4ohC79
590: 4ohc79
591: ok2c89
592: 4ok189
593: 9hC8am
594: 4ohcay
595: ehCo8(
596: 4ohC89
597: 4ohC89
598: oehd79
599: 1co8am
600: 81c7ay
601: okc7ay
602: 4ohC89
603: 2cokaQ
604: eohC79
605: 4ohC89
606: 4ohcAy
607: hC2o89
608: 4ohc79
609: okc7ay
610: 4ohC89
611: 4ohc79
612: 4okC79
613: 4oHc79
614: 4ohC19
615: 4ok1c9
616: 2kco79
617: 4ohc19
618: hCo8ae
619: g9hcAy
620: 4og1c9
621: 4ohC69
622: okc8an
623: 4ohc19
624: 4ohCae
625: ehc6ay
626: g1c7ay
627: ohC5c9
628: 4ohC79
629: 1cohCm
630: 4ohcan

There are 630 - 585 + 1 = 46 different groups, so therefore the 123456 spectrum is completely diversified in its letters-dressed guises among the 673 groups of f111r. Such a complete absence of guise-duplicates for a common spectrum like 123456 in a text-mass the size of f111r, itself casts some doubt on f111r being the script of a discourse in some natural language. For example, in just the opening three paragraphs of this communication, taken exactly as is punctuation and all, with their 385 groups, there are 12 occurrences of the 123456 spectrum, and a third of these, 4 of them, come in the same guise as the group: " Z(x,y) ".

We see that there are many of the "4o" digraphs in the component-31 guises set. It is always a good question whether or not the 4o should be transcribed as a unigraph, rather than the traditional digraph [6]. What effect would such a change have on the component-31 waves?

If the GC-4o is replaced with a single symbol, one that does not appear elsewhere within the 46 groups, then 25 of the 46 groups change spectra from 123456 to 12345. Therefore the waves analysis for component-31 as depicted in SspctrmC31vmsf111r.jpg would have to change radically. To probe this further, let us focus on just the W31-1 wave, and identify the script-guises of its points:

{V-8} Voynich script-guises of the 6 points of f111r wave W31-1

Coordinates of W31-1 point in center-rectified right-handed frame : corresponding script-guise group per GC voyn_101.txt

(1,4) : 4ohc89
(6,14) : 81c7ay
(2,26) : okc7ay
(-1,31) : 2kco79
(-2,33) : hCo8ae
(1,52) : 4ohcan

It is immediately clear that if we replace the 4o with a single symbol, one that does not appear elsewhere within the two affected groups, that we lose the two end-points of W31-1, and it is no longer the compelling full-cycle sinewave. Assuming that W31-1 is valid, then this might be taken as evidence in favor of the hypothesis that transcribing "4o" traditionally as a digraph, is correct, at least with f111r. Unfortunately there are no GC-m (EVA-iin) glyphs in the 6 groups, so we cannot use this line of thinking to probe Glen Claston's transcription theory / policy with respect to that famous VMS text problem.

However, we have something almost as good: the GC-n (EVA-in) in the GC-4ohcan group. If it were transcribed without Claston's abbreviations theory, then it would be written GC-4ohcaiN and become a 1234567 sequence, and thus be lost from W31-1. And there is one more: the GC-C in GC-hCo8ae. Transcribed unabbreviated it would become GC-hcco8ae with the spectrum 1223456 and also be lost from W31-1.

Therefore, if we assume that the W31-1 wave is valid as found, then it waves in favor of GC's transcription rules regarding Voynich glyphs GC-n and GC-C, at least for portions of page f111r.


This particular series of experiments flowed from the original objective of developing high-resolution sequence-spectrographs. The techniqes so developed are seen to be capable of efficiently detecting patterns in large blocks of data. As noted, the SQS computer program has been greatly expanded with version V1.4 to help apply these techniques. [2]

Specific to the above experiments, we found that the Voynich f111r text from top to bottom shows indications of some sort of complex organization of its sequence spectra, much more so than does the comparison Askham Menta Rubea text. Four data analysis images, discussed above, from among the many generated during the course of these experiments, have been sent to the J.VS Library. [4]

Pursuing a study of the nature of this f111r text organization, especially as to whether or not it was built-in by design, we identified ten arcs of ten waves in the f111r sequence-spectrum space. Most important among these arcs is the so-denoted W31-1 wave, which is a perfect full-cycle sinewave, that is also saturated with prime numbers relationships. We used the assumption of this wave having been built by design into the f111r text, to determine plausible evidence for or against some old Voynich text problem assumptions. And the results were, that if the W31-1 wave is valid as found, then it waves in favor of GC-4o being transcribed as a digraph, as has been traditional, and also in favor of some of Glen Claston's controversial Voynich manuscript transcription rules.

Currier's assertion that the Voynich text-line is a functional entity, continues to be among the most valuable ideas in VMS text analysis. Additionally, the sequence-spectrum results in the present experiments point to the existence of an invisible longitudinal center-line in blocks of VMS text, this line being the locus of points connecting the centers of text-lines as measured by their groups, and serving as the reference axis for the placement of groups, to the left and right of the longitudinal, on the intersecting text-lines. I suppose there could be a symbolic side to this also: the VMS text during its generation, and precipitation upon the page, being referenced to a cross. The cross symbol does after all crop up elsewhere in the VMS, most noticably on f79v, where in the upper-left illustration a VMS lady is blessing the f79v text with a cross held in her hand.

Berj / KI3U

[1] See J. Voynich Studies, Volume II:

[2] The SQS computer program for signals sequence spectrum analysis, version V1.4, is available for download from the J.VS Library here:

[3a] If when using SQS for the Z(x) calculations with massive sources, the program's capacity is exceeded, then accomplish the calculations with a simple trick as suggested in {I-19}. Suppose A and B stand for the two massive series, and SQS can handle either one alone, but not both together. Separately calculate the super-spectra of source A, and of source B. Append the super-spectrum of B to source A, and recalculate A, and then discard from the results the excess due to B. Do likewise with B. Both A and B will then have been calculated upon the A+B super-spectrum.

[3b] The source capacity of SQS is stated conservatively at about 3800 signals. It cannot be given precisely because it depends on the host operating system's current memory management: SQS uses a lot of dynamic arrays. I routinely use SQS to process source files of much greater size than 3800, as for example the 6346 above. Once in a while, as with other programs, the SQS program bombs, indicating that the host operating system has failed to manage the memory, or something. The cure is to shut down some concurrent demands on the OS, and start SQS over.

[4] Library of the Journal of Voynich Studies deposit # 20-1-2008-08-22, available online at:

[5] Search "prime number" in the several files in J.VS Library deposit # 1-1-2007-05-05 :

[6] See for example section VII. in J.VS communication #203 (Vol. II).

From Berj Ensanian
Sent Date 08-23-2008 11:06:39 AM

Subject J.VS: Re: Wave propagation along the center-longitudinal in the sequence-spectrum space of the Voynich f111r text

Dear Colleagues

I have spotted an error in comm. #210. Commenting on Table {V-7} I wrote:

" ..... so therefore the 123456 spectrum is completely diversified in its letters-dressed guises among the 673 groups of f111r. Such a complete absence of guise-duplicates for a common spectrum like 123456 in a text-mass the size of f111r, itself casts some doubt on f111r being the script of a discourse in some natural language. "

There are actually several cases of guise-duplicates in {V-7} :

585: 4ohcay
594: 4ohcay

589: 4ohC79
628: 4ohC79

590: 4ohc79
611: 4ohc79
608: 4ohc79

596: 4ohC89
597: 4ohC89
605: 4ohC89
602: 4ohC89
610: 4ohC89

601: okc7ay
609: okc7ay

617: 4ohc19
623: 4ohc19

I also wrote a little further on, just before dealing with GC-n :

" Unfortunately there are no GC-m (EVA-iin) glyphs in the 6 groups ..... "

But the table does have two examples:

599: 1co8am
629: 1cohCm

These errors are so blatant, that as best as I can tell I must have been looking at the wrong list when I drafted the above erroneous statements, while later placing the correct table in the final draft of communication #210. My apologies. As mentioned, thousands of operations and files, and filenames, are involved in experiments like these, and it is quite a chore to keep everything straight.

Fortunately, only the above comment about natural language needs to be thrown out. All else seems to be ok, and the GC-m examples can be taken to either help the GC-n and GC-C observations, or not affect them.


From: Dennis M. Fedak
To: Journal of Voynich Studies
Sent Date: 08-22-2008 11:05:21 PM

Subject: J.VS: Byzantine Musical Notation

I've never seen this before!

Dennis / N3ZCK

From Berj Ensanian
Sent Date 09-02-2008 12:26:14 AM

Subject J.VS: Are Gold and other metal particles embedded in the Voynich manuscript parchments?

Dear Colleagues

If you recall, in the spring of 2006 well-known Voynich researcher David Suter reported in detail to vms-list his observations upon examining the actual Voynich manuscript, shortly after he had inspected it at the Yale Beinecke Library. [1]

David concluded his very interesting and well-written report thus:

" Turning some page, the number of which I did not have time to note, my eye was caught by a single "gallows"- like marking in the middle of some text; I believe it was formed of gold leaf. "

The word "gold" has occurred often in VMS discussions, as for example: gold ducats, golden ratio, alchemical gold, and gold paint, where in the latter example is actually meant the light yellow paint or ink that is quite common on the VMS pages. But here David was bringing up the possibility of actual gold metal in the VMS.

The possibility that pieces of true gold metal were embedded in the VMS was immediate intriguing news to me, I had never read of it before, and I had a few brief exchanges about this with David on vms-list after he posted his report. Most recently this last April, two years past his Beinecke visit, I told David that with respect to possible gold metal in the manuscript I had a couple of items (in my very extensive, and unfortunately not adequately well-organized collection of VMS SID image detail-crops, gathered from my steganographic survey of the VMS) that needed rechecking [2] :

" Drawing on my mineralogy hobby experiences, including finding gold, a speck of gold will sparkle gold from all angles. Not so with, say, a little speck of mica, that from some angles will sparkle indistinguishable from gold, only to vanish when the perspective is shifted. One major problem with the Beinecke SID images is that there is no color reference provided. I don't know how visually dramatic a little speck of gold should appear in a SID image. Presently I don't know of a likely candidate, although I have a couple of items that need rechecking. If I remember right, you examined the VMS well after the SID images were taken. "

I have now had a chance to go over my collection of well over a thousand SID-images detail-crops, at least a cursory going-over, and indeed I found some very interesting possibilities that metal particles might be embedded in some places in the parchment of some of the Voynich folios: these are tiny specks, the color of which is strikingly different from the normal coloring in the SID images - they suggest metallic luster. These lustrous specks I find are of these basic kinds: gold, copper, copper-gold, and yellow to white suggesting perhaps various alloys, perhaps silver and gold electrum. Pure silver we would expect to be tarnished, unless it had been coated in some kind of clear lacquer. Depending on its impurities and particular oxidation and environment, some in the range of the colors of copper can stabilize somewhat to retain a metallic appearance for long periods. I have also begun to wonder if some of the red colors we see in the VMS are from mercury (II) oxide, and from some of the metallic specks one can fathom copper amalgams. Naturally, real metal particles in the Voynich offer interesting laboratory tests possibilities, and perhaps the chemistry of the Voynich inks and paints is far more complex than heretofore suspected.

I have prepared a composite of SID / tif image crops of some of these unusual specks. The pictures are intended to serve as location guides for those who next have the opportunity to examine the Beinecke MS 408 manuscript, and hopefully report back some more detailed observations on this Voynich precious metals and metallurgy question. While of course it is possible that the metals, if indeed the real thing, came into the book by some means other than the doing of its author, it is surely intriguing to ponder that the alchemical trio of copper, silver, and gold, perhaps even accompanied by mercury oxide, were purposefully put into the VMS by its author - if so, then one might speculate that the book, whatever else its purpose, served the author as an instrument of alchemy magic during esoteric rituals.

As just mentioned, my findings are from a cursory look, and there may well be more lustrous candidate specks of potential interest. Also, we've remarked in the past, that as good as they are, the best currently available SID images of the VMS, even when their tif's are reconstructed, are still of inadequate resolution for settling many questions with high confidence, about what is actually there on the parchment. That must apply here too with the hypothesis of metallic lustre. That said, the best concentration of these specks that I found occur on folio f46v: this is the botanical / herbal illustration folio with the "Eagle" as the plant's root. The annotated composite image of the f46v examples I created is:


This picture [3] shows ten crops from f46v, so numbered, showing tiny specks, with specks 1-6 located with colored lines to a large crop of the upper-right approximate quadrant of f46v. As you can see, some of the specks occur in the text, and others near the plant, and also at the trough running down the gutter between f46v and f47r.

Speck #5 appears to be partly obscuring an intruding GC-K gallows in the text, as if pressed onto it. This one, and its similars, might be pieces of very thin gold leaf, as suggested by David.

Speck, or particle #2, located close to the trough at upper-right, is the most substantial of the possibly-gold examples I have so far found. Its shape is of a thick stem, from which protudes on its right side a right-angled hook, turned downward. The substantiality of this piece suggests to me it is a particle, and that it was not flattened thin like nearly translucent gold leaf. Its color and texture are reminiscent of highly pure "sponge gold". This one is a perfect example of the problem of just-not-enough resolution available from the MS 408 SID images to be reasonably confident of an assessment as to what that object really is, other than that it is highly unusual in the VMS, perhaps even unique.

Specks / particles 7-9 are also near the trough - they can be quickly found and zoomed into on the high-resolution SID of f46r. #10 is one of a group located off one of the tips of the plants's green right upper leaf.

I have not had time to assemble more images, but altogether possible metallic specks can be looked for on these folios:

f7v, f9v, f42v, f43r, f46v, f47r, f47v, f48r, f49v, f50v, f51r, f55r, f56v, f96v, and f111v.

They seem to be concentrated in the neighborhood of f46v. As there was enough space left in 1VMSgoldF46v.tif, I inserted a crop from folio f49v, and one more from f56v.

Berj / KI3U

[1] vms-list post: Re: VMs: Beinecke visitor tips...? : A Recent Visit; Fri, 21 Apr 2006 10:32:02 EDT; posted by David Suter (MONET273).

[2] vms-list post: RE: VMs: Steganographics and the Voynich MS Binding; 04-16-2008 4:25:54 PM; posted by Berj / KI3U

[3] The 1VMSgoldF46v.tif picture will be sent to the J.VS Library for deposit # 21-1-2008-08-31. Unfortunately we are currently experiencing technical difficulties in uploading new material to the Library, and in particular the Library items pertaining to J.VS communication #210 are not yet available for download. I've decided to temporarily make 1VMSgoldF46v.tif available for download as a bmp from here:

From: Berj Ensanian
Date: Sun, 14 Sep 2008 10:32:23 -0400 (EDT)

Subject: J.VS: 14th c. Canterbury brass astrolabe, and the 13th c. Dering Roll ms

Dear Colleagues

Here are a couple of 2008 BBC online articles on two unique antiquities of some interest:

The 14th c. Canterbury Astrolabe Quadrant (includes a picture of the brass instrument):

The 13th c. Dering Roll of English Coats of Arms (includes picture):

Berj / KI3U
From: Dennis Fedak
Date: Sun, 14 Sep 2008 19:59:24 -0500

Subject: J.VS: Re: 14th c. Canterbury brass astrolabe, and the 13th c. Dering Roll ms

Between the questionable accuracy of the charts, and their timepieces, I wonder what accuracy the astrolabe of the 1300's could produce.

( Although, with fair winds ( 10knots ) one can traverse 1 minute of arc in 6 hours, so 60nm accuracy would be more than sufficient! ).

I sent off the link to a ex-Navy navigator who had to shoot sun several times/day and compare their readings to our electronic ones ( 90-tube Loran-A, SRN-9 SatNav, and the InertialPlatform ). ( pre GPS days ).

Dennis / N3ZCK
From: Berj Ensanian
To: Journal of Voynich Studies
Date: Tue, 16 Sep 2008 13:03:46 -0400 (EDT)

Subject: J.VS: Re: 14th c. Canterbury brass astrolabe, and the 13th c. Dering Roll ms

Our colleague Dennis sent me an interesting online reference: "Longitude at Sea", by The Galileo Project:

Thanks Dennis! Several familiar Voynich NOI names are in this piece, including Thomas Harriot (1560-1621), Claude Fabri de Peiresc (1580-1637), Gian Domenico Cassini (1625-1712), and John Harrison (1693-1776). There is a lot more of interest at the Galileo Project.

Coinicidentally I had just been revisiting Fabri de Peiresc - the mentor of Athanasius Kircher. Peiresc possessed, among other amazing artifacts such as the Barberini Ivory [1], the now-lost Carolingian copy of the Chronography of 354, the Codex Luxemburgensis, wherein the celebration of Christmas is first known.

Now, Peiresc was one of the earliest astronomers to explore the idea of using telescopic measurements of the eclipses of Jupiter's moons [2], as a universal clock for accurate determinations of longitude. Here and there in the Voynich manuscript, including even from some of the botanical illustrations, one can get the impression that clockwork and time may have been a theme in the mind of the VMS author. Brumbaugh, we recall, christened the circular device at the lower-left of the nine rosettes: the clock. It does resemble a clock [3], and as we have long noted from a careful inspection of the high-resolution SID image, its two "hands" can well suggest they are depicting a key or keys.

Therefore, it does not seem far-fetched to include among the considerations of plausible symbolic messages projected by the VMS nine-rosettes foldout: the key to an accurate navigation of the wonderful universe, is the mastery of time via clocks / chronometers.


[1] From time to time the clothing (not to mention hairstyles) of the human figures in the VMS is analyzed for possible period clues. How reliable is that idea? One item in the Byzantine Barberini diptych (6th c. ?) that is often noted is that one of the figures is wearing trousers / pants. There are, as I recall, in Achaemenid Persepolis (ruined per revenge by Alexander the Great) relief sculptures of Armenian, and possibly other, tribute bearers dressed in rather modern-appearing suits-of-cloth, including trousers.

[2] Galileo discovered the first four moons of Jupiter, realizing they were Jovian satellites, in 1610, and that year published his observations and ideas on them in his book: Sidereus Nuncius. That work had a major impact on the Copernican controversy, and of course Galileo personally. Incidentally, if we have a clear night-sky view of Jupiter, we can easily see the Galilean moons with a good binoculars.

[3] Two-handed dial-face clocks are usually thought to come along in the 15th century, but every-time we think we've got some developmental time-line pinned down, we ought to pause and revisit the ancient, unique and incomparable, Greek Antikythera mechanism, with its roots pondered all the way back to Archimedes of Syracuse.

From: Berj Ensanian
Date: Thu, 18 Sep 2008 15:21:30 -0400 (EDT)

Subject: J.VS: The latest Mozart discovery, and the adventures of worthy documents

Dear Colleagues:

A new handwritten musical document of Mozart's has been re-discovered:;_ylt=As6RQmTHZDQqjufbwDAJkBpbbBAF

Here are some excerpts from this picture-accompanied, dateline-today article by AP writer John Leicester, titled " New Mozart piece of music found in French library " :

" PARIS - A French museum has found a previously unknown piece of music handwritten by Mozart, a researcher said Thursday. The 18th century melody sketch is missing the harmony and instrumentation but was described as important find. "

" Ulrich Leisinger, head of research at the International Mozarteum Foundation in Salzburg, Austria, said there is no doubt that the single sheet was written by the composer. "

" The work, described as the preliminary draft of a musical composition, was found by a library in Nantes in western France as staff were going through its archives. Leisinger says the library contacted his foundation for help authenticating the work. "

" The sheet was bequeathed to the library by an autograph collector in the 19th century and was catalogued back then as part of the library's collection, he said. "

" The sheet appears also to have been examined in the 19th Century by Aloys Fuchs, a well-respected autograph hunter who collected works from more than 1,500 different musicians. Fuchs wrote "authenticity of this present handwriting of W.A. Mozart is confirmed," in an annotation dated Aug. 18, 1839, in Vienna. "

So, a piece of Mozart cataloged, and even expertly commented upon back in 1839 in Vienna no less, and it is forgotten for 169 years! I should think that this example of the adventures of worthy documents, from a field far, far greater in size and manpower and resources than Voynich manuscript studies, ought give us hope that there is out there after all on some forgotten dusty shelf a cataloged piece of Voynich text, perhaps even referred to by an Aloys Fuchs type person.

Berj / KI3U

From Berj Ensanian
To Journal of Voynich Studies
Sent Date 09-20-2008 9:40:48 PM

Subject J.VS: Baresch's Alembic / Retort, and Voynich f88r

Dear Colleagues

The alchemists could indicate an alembic or retort, or the use of same, with a curled-teardrop symbol. [1]

The alchemist M. Georgius Baresch's 1639 letter to Athanasius Kircher, S.J., the very letter that is so central to the Voynich manuscript's reconstructed, and still unfortunately not water-tight standard history, may have the alembic symbol intentionally, though perhaps slightly subtly, incorporated in it. Lets have a look at this. [2]

The images of the letter show Baresch using the letter "p" several times, lower and upper-case, on both sides. But one of the occurrences of Baresch's lower-case "p" is unusual from all other occurrences of p, and all the other letters - the loop of its descender-stem is distinctly enlarged, and most noticably it is solid, filled in, as if intentionally so rendered.

This particular p-letter occurs as the 1st letter on the 6th line of the communication's verso side. It is part of the word "post", followed by "salutem". Now, judging from the interesting and quite tiny diacritic marks in the text - if that is what they are - the resolution of the online image of 353v is just good enough to allow an estimate on the question of this p's genesis: accidental overflow of ink, or intentionally so formed?

Two lines above it, the initial word "diversarum" has a fairly heavy ascender-stem for comparison. The other stroke-components in both this d, and the p in question, show no evidence of any problem with inkflow, and neither do the letters immediately preceeding and immediately following them. If we tried to take the view that Baresch was characteristically re-inking his quill before starting every line, we could not make that view hold up, after examining all the lines in the letter.

The bulbuous portion of the filled-in lower loop is not perfectly sharp, but it is certainly sharp enough to make us wonder if it was intentional, and especially when we consider that there has been over three hundred fifty years of humidity and what-not to cause diffusion or transfer of the ink's constituents outward on the paper from its original deposit, not to mention physical distortion of the paper. It is noticable that Baresch scripted this particular p in two distinct parts - the bulbous portion we are considering, and the little remainder at top right which is necessary to unambiguously result in a "p".

If we take the view that it is conceivable that the rendering was intentional, then the next question is: could an alchemist, or someone familiar with alchemy, take this p as a semi-subtle signal for "retort", or the action of distilling? Well, it's basic shape is of a tear-drop with a hooked tapered end: it possesses the minimum unambiguous geometry, and really no other contrary geometry, to suggest: distillation.

Lets have a look at the translated sentence within which this word's ("post") occurs:

" From the pictures of herbs, of which the number in the Codex is enormous, of various images, of stars and of other things which appear like chemical secrets, I conjecture that it is all of medical nature; a science to which none other, except that of the health of the mind, is more healthy for the human species. " [3]

This happens to be the critical key sentence in Baresch's entire letter upon which the essence of the currently reconstructed standard history of the Voynich manuscript rests. Take this sentence out of Baresch's letter, and the impressions the letter conveys shift away from a connection to the Voynich manuscript (i.e. Beinecke MS 408), and arguably toward something along the lines of an Egyptian herbal written in Coptic letters, consistent with the type of material Kircher was becoming world-famous for, and soliciting.

If Baresch intentionally signalled "alembic" or "distillation" to Kircher, was it part of a further, second hidden alchemical message embedded in his letter? For example, could the entire word that starts with this p be part of a message, and mean: "... distill next ..., or "... following the distillation ....." ?

Such would of course entail many new questions about Baresch's communication to Kircher.

Even with the less-than-desirable resolution of the available APUG image, there is much more analysis that can be done with Baresch's letter - bracketing of some of the text, and the curious "diacritic" marks in particular. Directly from these diacritics, and some forms in the main script, if only ligatures, we can see suggested in Baresch's letter at least the following Voynich alphabet glyphs:


GC-1 / EVA-ch
GC-a / EVA-a
AGC-207 / EVA-b
GC-e / EVA-l
GC-o / EVA-o
GC-s / EVA-s
GC-4 / EVA-q
GC-8 / EVA-d

Actually, a time or two in his letter, the ductus of Baresch's lower-case "p" suggests he would be comfortable writing a GC-g (EVA-p) gallows letter. And of course there awaits the answer to the testable question from J.VS comm. #130, concerning Baresch's manu propria at the end of his letter: is the GC-k / EVA-t gallows that is embedded in the manu propria, intentional?

If Baresch really possessed and worked on MS 408 for many years, then it would be reasonable to expect his hand in it here and there. Conversely, if Baresch saw a retort in the VMS, we might entertain that he modeled his "p" on it. It turns out that on the Voynich pharmaceutical-section folio f88r there is indeed a little thing that could suggest an alembic or retort. The SID image of f88r is required to see its details, although it is big and bright enough in its natural state to catch the unaided eye.

At the top of f88r there are from left to right 6 major objects: a big pharma-section-characteristic cylindrical object, and five herbs / plants attended by 6 labels. The 6th, or right-most herb, has 6 tentacles for its root-structure. The left-most tentacle extends leftward the most, and very near its tip, at the right of it, is the little object in question. We don't have dimensional information for the "p" in Baresch's letter, but the little f88r object is perhaps half its size. Zooming in on it we see that it too has the minimum necessary geometry to suggest a retort, and no contrary geometry. It appears quite a lot like Baresch's "p" : a tear-drop bulb terminating in a left-pointing narrow hooked neck.

What is it, and how did it get there? Was it intentional? On f88r it is not totally unique: it seems to have a similar in the first character of the four-characters group that forms the label for the second herb in the second row of herbs: that glyph, which is not a cataloged glyph in the common VMS transcription alphabets, appears horizontally flipped with respect to our former left-pointing alembics, and it is rendered in ordinary dark-brown ink, darker than its following GC-ay9 glyphs. It is different also in one other detail: the mouth of this "retort" flares open, terminating with a suggestion of a little face, like we so often see in many of the Voynich glyphs, when they are magnified.

If Rich SantaColoma's suggestion, that some of the VMS pharma-section cylindrical objects are to be taken as depicting early microscopes, is correct, then do we have here in f88r a suggestion that alchemy is to be advanced with the microscope - that perhaps alchemical processes in action can be observed / partaken-of under optical magnification? Thus: the alchemical microscope.

Although yellowish in color, the little object at the top in f88r is not really convincingly lustrous as per the considerations of J.VS comm. #213, and it would have to be just a little of a stretch to argue that alchemical gold is part of its symbolism. The SID resolution is however enough to give the impression that this object was pressed into the f88r parchment - that it was put there intentionally. If we look close we see what appears to be a press-line along its bottom portion that exits it, and just continues on the parchment. This press-line may not have been involved with affixing the object, but it must have come after the object was already solidly in place.

There is also a slight difference in the whitish color of the parchment at the borders of the object - a brighter white, suggesting further that some action was involved when the object came onto the parchment, action beyond that of a random flake merely falling on, and adhering to the parchment.

I have no idea if these f88r objects are in any way connected with Baresch's hypothetical p-alembic, but all are data good to know about in case of new developments down the road. And, in light of the tenuousness, and criticality to the VMS standard history, of Baresch's letter to Kircher, we are I think justified in pushing the limits of what we can get out of the available materials: the more data the better; interpretations and theories can always be adjusted as necessary.

Berj / KI3U

[1] Online Encyclopedia of Western Signs and Ideograms, Symbol 32:8 :

[2] Baresch's 27 April 1639 letter to Kircher, handwritten on both sides of one sheet, is APUG 557, 353r and 353v, online here:

[3] Taken from the Baresch-letter materials produced by Rene Zandbergen:

From Berj Ensanian
To Journal of Voynich Studies
Sent Date 09-26-2008 6:49:39 PM

Subject J.VS: Some non-English language Voynich websites

Gathered from off-J discussions in the last few days, here is brief list of Voynich websites conducted in languages other than English:

In the Czech language ( CESKY ):

In the French language ( FRANCAIS ):

In the German language ( DEUTSCH ):

From: Berj N. Ensanian
To: Journal of Voynich Studies
Date: Thursday, 9 OCT 2008, 2011 GMT

Subject: J.VS: CM: The Journal's new mailing address

Dear Colleagues

Theoretically, a J.VS communication can reach the J.VS publishing desk (normally manned by me) by any suitable means, even I suppose carrier pidgeon :-). However, normally we employ electronic mail. As you know from recent off-J discussions, circumstances now require a change of address. After doing some testing, I decided that the simplest thing at this time is that effective tomorrow morning, the new J.VS electronic address is ki3u followed by the at-symbol followed by lycos followed by dot followed by com.

I hope the change will occur smoothly.

Berj / KI3U
From: Berj N. Ensanian
To: Journal of Voynich Studies
Date: Mon 10/13/08 6:52 PM

Subject: J.VS: Image artifacts, or obliterated Voynich-similar script?

Dear Colleagues

Many online images of old parchment and paper documents, including the papers of Athanasius Kircher, give me indications that in places on a document there has been deliberate obliteration of original markings. A closer look at such obliterated areas frequently suggests that alphabet symbols and script have been obscured, and sometimes these even seem to me to resemble the more characteristic Voynich glyphs. The effect is so ubiquitous across the online APUG images of the Kircher papers, that I find it truly puzzling and requiring serious investigation in order to understand it: are these indications just artifacts, optical illusions, and random albeit psychologically suggestive marks, or is there something more significant related to Voynich script going on?

To make some progress, I undertook to assemble some data that you may view and judge for yourself. Naturally, some documents are of greater interest to us, for example the letters of Marci to Kircher, and these are more numerously represented in the following data.

It turns out to be a rather tedious challenge to obtain likely meaningful data, but the following is a first best effort. Early on in the investigation and data gathering I found it necessary to have some hypotheses in place in order to measure the plausibilities of the perceived markings. These hypothetical ideas, and other background information, are here given first.

The following presentation of new data is divided into these sections:

V. BARESCH'S 1639 LETTER TO KIRCHER: Does it show traces of obliterated Voynich script?
VI. SELECTED MORETUS LETTERS TO KIRCHER: Do we have complete Voynich words?


Let us return once more to a major problem, among the many, in the standard reconstructed Voynich manuscript history: the near total absence of evidence of characteristic Voynich manuscript particulars, especially the VMS script, among the papers of Kircher, Baresch, Marci, Moretus, and others who, according to the standard history, should have known of the Beinecke MS 408. [1]

Toward a solution of this problem, all we have at best to date in Kircher's papers is the few snippets of Voynich script in Kircher's 1664 letter (a draft, or archival copy?) to fellow Jesuit, and astronomer, Adamus Schall [2]. Those examples, although quite clearly visible, are complicated by being bleedthroughs or transfers from the verso, or another letter or document, and so far their source has not been found.

One obvious thought for explaining the absence of VMS script in the Kircher papers, an explanation that is especially reinforced by the Schall examples, is that Kircher did have VMS particulars including script, but for one reason or another he was meticulously suppressing them, and the Schall examples somehow got by his suppression protocols.

Upon that hypothesis it is natural to wonder if traces of other pieces of Voynich script can be discovered in the Kircher papers. It would really be welcome if we could find some VMS script in the letters of Marci, and in the one available letter of Baresch. In the context of plausible hints of hidden signals transmitted by the overt ink, we just recently looked at the Baresch letter in J.VS communication #218.

We've looked at the Marci letters, beginning in comm. #4, with a survey of the signatures, noting their differences, for example with or without sine (manu propria). There our focus was of course on the overt writing in the letters. When we step back a bit and view the Marci letters as whole objects, we notice that many of them are stained. There are of course other documents among the Carteggio Kircheriana collection of Kircher's papers in the APUG archive that are variously stained. But what is notable with the Marci letters is the relatively high percentage of them that are very heavily stained. A further look at this, and it is not difficult to wonder if the stains were deliberately done with chemical treatment, rather than resulting from accidents and the ravages of the passing centuries.

It is also notable that the staining in the Marci letters often shows portions with a purple hue, and although we do not have color references for the APUG Marci letters and the Yale Beinecke VMS images, there are suggestions of this purple hue in some VMS folios where it appears that obliteration has been done, for example the large stain at the top-right of f13r. Purple is otherwise generally absent among the VMS colors. This stained area of VMS f13r is an excellent check for the following investigation of the Kircher documents - more on this shortly in section II.

Regarding stains in the VMS we should also note that some of them give indications they were not totally pure accidents (see regarding the f93r Sunflower folio stain, J.VS comm. #173 in Vol. II). For example, the large stain at the top of VMS f32r seems to have been partly involved with a cover sheet at some point, perhaps even during its creation, affecting also the folio number to its right. This is amplified by the corresponding stained area on the other side of the parchment, f32v, where within the stain at the top edge of the paper is some obliterated Voynich-similar text. On another folio, the stain at upper-left on f39v, partly into the second word of line 1, indicates it got there after the text had been scripted. It too seems to be obliterating VMS-similar markings within it, very effectively.

Altogether then, the question becomes: are some of the stains in the Marci letters indications that Kircher treated them chemically so as to obliterate writing by Marci, sensitive writing in addition to Marci's overt writing? There follows that if Kircher felt it necessary to obliterate communications from Marci, communications carried in apparently ordinary letters the texts of which do not overtly point to obliterated material in the same letter, then it is quite conceivable that Marci wrote the sensitive communications with invisible ink, so that in case a letter became compromised before reaching Kircher, its secret contents would remain somewhat secure. Communicating with invisible ink writing would not necessarily need to be secure in the pure steganographic sense, in a context where "everyone is doing it".

Checking into the art of invisible writing back in that time, we find that it was already highly advanced. Giambattista della Porta (~1536-1615), long familiar to us in Voynich studies as for example from D'Imperio, had already published in 1558 the first four books of his "Magia Naturalis", Natural Magick. The work would eventually encompass twenty books, produced in one volume in 1584, and be translated into other languages from its original Latin:

" It is in fact a work on popular science, cosmology, geology, optics, plant products, medicines, poisons, cooking etc. Included are books on transmutation of the metals, not however confining transmutation to the alchemistical signification, but including chemical changes generally; distillation, artificial gems, the magnet and its properties; known remedies for a host of ailments; cosmetics used by women, fires, gunpowders, Greek fires including preparations of Marcus Gracchus; on invisible and clandestine writing. " [3]

It is the sixteenth book of Magia Naturalis wherein Porta presents techniques of invisible writing. It makes evident that the art of invisible writing was quite advanced at his time, and involved all sorts of chemical processes of varying sophistications. We are I think justified in assuming that by the time Marci and Kircher began their correspondence, the Jesuits of the time, their society already over a hundred years in existence, would have familiarized themselves well with Porta's popular work, and in any case with the art of invisible writing:

" The Jesuits had devised a cunning method of using invisible ink made of common orange juice. " [4]

Athanasius Kircher, S.J., and Joannes Marcus Marci first met in 1638 in Rome, and struck up a lifelong friendship. We now ponder the possibility that, if indeed Marci's alchemist friend M. Georgius Baresch had already in 1637, with a still-not-found letter to Kircher delivered by Theodorus Moretus, S.J., opened the subject of the mysterious script in Baresch's possession, then perhaps some of the stains in the Marci-to-Kircher letters are traces of an invisible-ink writing system hiding that assumed-Voynich-script.

With this hypothesis attached to the puzzle of apparently obliterated VMS-like markings in so many of the APUG documents images, I undertook another survey of the Marci and other APUG letters. Of course a major problem is that the images of the letters, as made available online as jpeg's, provide a resolution that is rather limited, well less than for example the Beinecke SID images of the VMS. Therefore this investigation cannot hope to reach a conclusive stage with the presently available sources.

Moreover, to make matters worse, it appears to me that some of the Kircher APUG images, including the Marci letters, were subjected to some measure of image processing before being placed online, almost certainly to improve legibility of the overt writing. We must consider that improving the legibility of the overt writing would not necessarily help image analysis seeking to answer the question of invisible-ink writing, and could even hinder it, for example with more false artifacts.

With that caution in mind I proceeded to examine the letters. Soon it became necessary to have a rather detailed hypothesis for an invisible ink writing system, taking into account also various kinds of obliterations. I finally settled on the outline given next, seeming to me to best fit the indications from both, obliteration areas in the VMS, and the Kircher correspondence letters, on the assumption that the perceived traces in the letters are indeed from invisible ink writing. The following is subject to modification of course, as more and better data becomes available.



a.) The system involves three processes:
Process-P : Preparation of the secret-communications letter or document, by the sender.
Process-D : Developing (making visible) of the secret writing / graphics by the receiver.
Process-O : Obliteration of the secret writing / graphics by the receiver.

b.) Three different ink formulations are used:
N-ink : the noise ink - it is used to create background-noise patterns upon which the secret-writing is done. N-ink is invisible when dry, is developed visible along with S-ink, but is more resistant to fading than S-ink from the obliteration process.
S-ink : the invisible-when-dry-and-undeveloped ink used to write the secret message. It may have alternate formulations that, under the development process, are better visible through optical color filters.
V-ink : the ordinary ink used to write the plainly visible and non-secure portion of the communication. It is mostly unaffected by processes D and O.

c.) The system in use: Preparation-P by the sender
1.) When possible use standard paper or parchment sheet specific to the system.
2.) If the document will be folded, pre-fold the blank sheet, then unfold and flatten.
3.) Lay out the overt and covert areas of the document - they may overlap.
4.) Create noise patterns in the blank document with water marks.
5.) Using N-ink, paint into the covert areas, and optionally into the overt areas, random monster faces, animals, geometric patterns, etc. so as to create a noise background for the S-ink material.
6.) Write the overt communication using V-ink.
7.) Write and / or sketch the covert communication using S-ink, employing techniques:
7a.) Use the edges and other standard locations on the (rectangular) document for special system marker signals.
7b.) When desirable, write in very tiny script (perhaps requiring a magnifying lens) along the document's fold-creases.
7c.) If desirable, add more noise with N-ink.
7d.) If desired, use parts of overtly-written glyphs, for example their loops, to make up parts of the covert glyphs.
7e.) When advantageous, use the natural indents and rilles in the sheet.
7f.) When desired, write the secret script in different orientations, for example upside down, and mirrored.
7g.) Change the size of the secret script frequently.
7h.) If a known-to-the-receiver-only glyph or graphic is so unique that it is unmistakable even when rendered only partly or distorted, optionally render it so.
7i.) If desirable, and sufficiently thin suitable paper is available plus the time and skill to do it, break the secret glyphs in half, write one half of a glyph on the recto side, and write its other half, carefully aligned and in mirror orientation, on the verso side.
8.) Fold, seal, and submit for transport to the receiver. All physical aspects of the document, including dogears and the seal and its placement, may be used as special system signals, for example specifying a color filter for viewing.

d.) The system in use: Recovery Process-D, and Obliteration Process-O by the receiver
1.) Develop the secret / covert areas with exposure to vapors or liquids of one or more chemicals-D. If necessary, view the covert material through appropriate optical filters. An additional fixing chemical may be involved if the covert material is to be preserved.
2.) Obliteration:
2a.) Overwrite the secret covert (developed) script with noise markings and scratches, or innocent text using S-ink or N-ink.
2b.) Erase the covert areas with exposure to vapors or liquids of chemicals-O. If the overt and covert areas are distinctly separated by fold-lines, optionally fold the document so that the overt areas receive less exposure to chemicals-O. Optionally apply chemicals-O in such a way so as to introduce more noise patterns with the resulting stains.
2c.) If chemical obliteration is insufficient, and the document must otherwise by saved, reinforce the obliteration as necessary with scraping, burning, overwriting or staining, and tearing off for destruction part(s) of the document.


At some point into a long investigation like this one it is apparently a natural result that one goes from merely seeing if there are curiously puzzling marks jumping out at you from an image, to actively and habitually scanning for subtle oddities. And that is a two-edged sword: on the one hand the ability to spot potential markings of interest is improved and habituated, but on the other hand the danger of self-induced optical illusions increases.

Many of the puzzlings marks, regardless of whether they are or are not potential secret writing examples, are exceedingly faint and will require real effort to see them. When trying to resolve new potential marks, it is important to frequently change the effective size of the area being investigated, and also rotate the image to different orientations: the traces of possible significant patterns could be any size, in any orientation, and the eye-brain combination requires help with size and orientation information to detect promising integratable patterns. Blinking processed images against their aligned and very slightly mis-aligned originals or negatives is very helpful in resolving and evaluating potential obliterated material.

CAUTION: the nature of this work is such that if continuous sessions are carried on for long periods, eye-strain may occur.

The Voynich manuscript itself is constantly used as a check on potential traces of patterns in the other documents. And, insofar as the question of Voynich script in non-VMS-documents is concerned, it is not enough to find plausible indications of Voynich symbols like GC-a, GC-c, GC-e, GC-i, GC-o, GC-N, GC-1, GC-4, GC-8, and GC-9: those forms we know occur often enough in old European documents totally unrelated to the VMS. It is necessary that we find plausible examples of the unique Voynich glyphs, in particular the tall-stemmed looped symbols, a.k.a. gallows letters, and ideally intruding gallows forms. We would of course expect that in a Table II-1 type secret communications system employing gallows and intruding gallows, the post-received obliteration of those gallows would be especially emphasized.

DIFFERENTIAL OPTICAL INSTRUMENT (DOIT): Especially when resolving tiny traces, and working in unavoidably bright daylight, and in particular for checks on optical illusions, a simple optical aid is very helpful: a stiff opaque cardboard tube about 4 cm in diameter and about 30 cm long. The tube is held fixed against one eye shutting out all light except from the front opening of the tube, and both eyes focus on the same object and its surrounding area to be investigated, while moving toward and away from the object beginning at a distance of about one tube-length between the object and the front of the tube. The eyes may be alternately blinked. Viewing so also the fainter portions of the overt writing is a check on optical illusions: in the present images context, any pair of faint, comparably sized, co-diametric arcs, arising from scratches, dents or whatever non-script, could give rise to an optical illusion of Voynich glyphs.

Periodically alternating the DOIT between eyes reduces eye-fatigue, and gives more comprehensive differential observations. This optical maneuver works by creating differential optical sensitivities for the pair of eyes. A variation is a double-DOIT, a pair of tubes of different lengths, used together, one for each eye. Telescoping tubes providing for adjustable tube-lengths and glued to goggles are a further advancement, but for our purposes the simple uni-DOIT works fine, and only once in the below work did I resort to a double-DOIT for an extra check: UDOIT to get a better and more rational perspective on the objects under investigation. [5]

Up-front in this work are required: a thorough familiarity with the variations of the Voynich glyphs as they appear in the manuscript, AND how, in detail, the individual Voynich glyphs were rendered, that is how they were stroked - this I must emphasize.

We must be familiar not just with the extreme variations, like the 4th glyph of the first word in VMS f36r, and the first glyph of f47r (it has a cousin on the first line of f24v) which might be better described as a compound form.

See for example the GC-g variation on the first line (under the label) of VMS f41v, specifically the first glyph of the first word. Note how in this GC-g the tail loops back to the bottom of the stem. If this glyph were partly obliterated and in addition very faint and even in some abnormal orientation, then only a thorough familiarity with VMS glyphs variations would stand a chance of correctly recognizing it for what it is. This example illustrates an important concept: the geometries of the Voynich alphabet glyphs are peculiarly well suited for invisible-ink writing per the procedures of Table II-1.

The investigated objects, and therefore the images of their documents, must be viewed in several orientations, including upside down, and horizontally flipped (mirrored). For example, lets take a look at the nominal GC-K (AGC-75) intruding gallows glyph that occurs at the beginning of line 9 on VMS f108r. It presents a rather pronounced distinct visual impact compared with the usual idea we have of the GC-K, and if it were partly or mostly obliterated, it could easily cause false impressions: say its right half, just before the right loop, was obliterated; one could then believe that we have there a GC-k (AGC-107) non-intruding gallows that is both rotated ~90 degrees counter-clockwise, and horizontally flipped.

For this investigation of apparently obliterated markings of potential VMS glyphs affinities, the first glyph on Voynich folio f87v is an important reference to remember: a GC-g intruding on, or perhaps better said, sharing a common stem structure with, another GC-g. It is a VMS rarity. While on that same folio, lets go down to line 7, and look at the GC-j variation of GC-g in the long first word - note its box-shaped torso. This variation is not super-rare in the VMS, but it is not common either. Patterns like these are perceivable in the documents we are investigating here. Just because a variational form or transcription-cataloged glyph is rare in the VMS, that does not mean it would be equally rare or absent in the documents under investigation. And if indeed Kircher et al were working with the VMS script, they might even have been focusing on the more rare variations. [6]

Also lets have a look at the start of the last text paragraph of VMS f8r: a complication where a GC-k is bridging / intruding the first two groups, GC-1o and GC-1c9. As we know, even more complex examples of this kind are found in the VMS text, further along in its pages. We note that if this compound structure were embedded with carefully sketched simple noise consisting of a few straight lines, loops or circles, and ligatures and rectangles, it could overall give the impression not of script, but of some sort of diagram or schematic, perhaps a crude architectural detail. Something suggesting just exactly this strategy is seen at the top-right of the VMS f68v3 "Spiral Nebula / Galaxy" folio, above the line-1 last group, GC-sccc9 (GC-sd9), and to the top edge of the parchment. This mostly obliterated rectangular device has embedded within it several Voynich-glyphs forms, variously difficult to identify as GC-4o, GC-k, GC-g, etc.

Another odd variation example is the GC-f that starts the text of VMS f20v. Then lets go to f106r, line 18, and note the variation of GC-g in the 7th word - its stroking is markedly different from that of the usual GC-g.

Other kinds of intrusions than the transcription-cataloged ones must be kept in mind, those not found in the commonly used Voynich transcription alphabets. For example, in VMS f82v, at the start of lines 6 and 7, is a GC-4o strongly intruding on a GC-g below. GC-4o's that contact a GC-o underneath are seen here and there in the VMS, for example lets take a close look at the beginnings of the last two lines of VMS f53r, involving the GC-4o and underneath it the GC-ok. Suggestions of similar patterns are not uncommon in the documents studied below.

CHECKS ON OPTICAL ILLUSIONS: Let us take a fresh blank sheet of ordinary white paper, write a test line of text on it in our smallest and hurried hand, and then digitally photograph it, a couple of times from slightly different angles. Then subject the images to various image processings - the test text lets us know when the image processing is reaching the point where fine details are becoming distorted. If we have not done this before, we might be surprised how easy it is for our eyes to "find" somewhere on an image of the sheet, and not necessarily associated with the marks of our written test line, an apparent marking that is a dead-ringer for a Voynich glyph, like a classic GC-g gallows.

I have a favorite example of this kind where the phantom GC-g remains a GC-g at practically all zooms. Having once found it in the processed image, I can even see it on the unprocessed image. I know from the conditions that went into the experiment that it is a phantom - arising from the combinations of un-smooth paper surface, the lighting under which the photograph was made, and the image processing.

But if I did not know those conditions, how could I determine that it is a phantom, and not the real thing? Given the constraints under which this work must be done, examining online provided digital images, with unspecified lighting conditions, and often already image processed to some unspecified degree, the question is of critical importance to the entire objective of the investigations: are there traces of obliterated writing in the documents, and are the obliterated marks the remains of Voynich-script-related glyphs, yes or no or possibly?

Studying the just-mentioned phantom GC-g with the DOIT, while blinking back and forth between the processed and unprocessed images, I saw that the phantom, as appealing a GC-g as it pretended to be, could not be a true GC-g: its "strokes" were wrong. No true GC-g in the VMS is stroked like that, including even the GC-g on line-18 of f106r we looked at a moment ago. The phantom was arising from artifact arcs that just happened to group together such that their visual integration, driven by a Voynich mindset, gave the illusion of a VMS GC-g. I was surprised by the subtlety of the effect! But familiarity with how Voynich glyphs are stroked, coupled with the DOIT attack, decisively revealed the difference between truth and phantom.

A target indicator to search for when first attacking a new document is "4" forms immediately adjacent to the left of looped stems forms, suggesting GC-k and GC-g gallows Voynich glyphs. But we must be very cautious with all indicated 4's because a short diagonal scratch or irrelevant mark, together with rilles in the document paper, can bring about the illusion of a "4". Also, the obliterator may have, during the obliteration process, written in the 4's as noise.

I should point out that by familiarity with how Voynich glyphs are scripted, I mean not just studying their strokes in the high-resolution images, but also practicing a lot of Voynich script handwriting, until the VMS script flows more or less naturally from our hand, while conforming to its ductus as it appears in the VMS. Yes of course there is the controversy about different hands in the VMS, and left-hander versus right-hander, but there are plenty of sizable VMS text-blocks suitable for simulation by our own personal hands, for the purpose of gaining familiarity with how the scripting was done.

Unfortunately the possibilities presented by the secret system of Table II-1 would make our investigations very difficult, even if we had the actual physical documents to examine. Nevertheless, here then are some factors that help evaluate from the images the plausible genuineness of apparent markings on the documents of interest to us:

TABLE III-1 : considerations for evaluating potential obliterated markings

1.) Does the document, or at least do documents in its family of documents, show clearly obvious indications of obliterated marks, like rubout scraping, or chemical attack?
2.) Alternative to obliteration, might the marking be never-developed invisible ink that has undergone a chemical change over a long time, thereby becoming partly visible?
3.) If an image of document-A shows plausible obliterated secret markings of interest, are there similar images of similar documents, same image source, same paper, similar photography etc., that are relatively free of plausible markings of interest, so as to reinforce the conclusion that document-A has a genuine peculiarity?
4.) Are there patterns of a system suggested by similar markings on different, but related documents? For example, is an indicated obliterated GC-g often found in a certain relative location within the documents?
5.) Is the construction of the suggested glyph consistent with VMS script strokes and ductus?
6.) Are the trace-thicknesses within practical bounds for the physical conditions?
7.) Is the image processing within bounds where overt material is still recognizable for what it is?
8.) Does the candidate marking retain its essential features under a wide variety of image processings, and DOIT viewing?
9.) If the candidate marking is suggesting a VMS glyph, is the overall context logically consistent with that, or at least not totally out of the question?
10.) Does the candidate marking retain its perceived characteristics across different investigation sessions, when general experimental conditions including psychological and fatigue-versus-rest, are different?
11.) Does someone else see the same thing?

Fortunately a few of the obliteration candidates below are strong enough to be fairly obvious marks of some kind suggesting alphabetics, even Voynich alphabetics, and thus motivate further investigations.

I used Irfanview Version 3.99 for image processing and viewing. I'm sure more effort could produce better processed images. The processing specifications given below are, unless otherwise noted, for a computing environment moderately illuminated by overhead incandescent lighting (and of course my own optical sensitivities). The processing steps are all done by clicking the IrfanView "Image" menu, and then clicking either "Rotate", "Negative", or "Enhance colors....". The latter provides settings which below are notated as follows:

TABLE III-2 : notation for IrfanView Enhance Colors settings

Brg = Brightness (default = 0)
C = Contrast (default = 0)
GA = Gamma correction (default = 1.00)
S = Saturation (default = 0)
R = R (Color balance for red, default = 0)
G = G (Color balance for green, default = 0)
B = B (Color balance for blue, default = 0)

I began above by noting that to my eyes many old documents show puzzling obliterated forms, some of which suggest VMS glyph similarity. Let me now show a first example puzzle. Lets have a look at folio f. 81 of the familiar 15th century illuminated parchment Higden Polychronicon manuscript, Huntington Library HM 28561:

The resolution of the image is fairly good. Lets set the image processing per Table III-2 as follows: C=22, GA=0.13, S=-93, R=-37, G=-5, B=-255, and blink the processed image against the unprocessed image. The DOIT will also be helpful.

From the online images of the Higden it is apparent that obliterations or gesso-ing typically were done between text columns, and on the margins, and so it appears with f81. The traces of the obliterated marks suggest to me that possibly the marks were originally some kind of preparatory notation for the scribes, and had to be removed or covered after the scripting of the page was completed. Lets look at one of the fainter traces, so faint that it is not certain if it is in fact a scribal notation, an artifact, a random accidental result over the course of time, some writing from a previous use of the parchment that was scraped clean or covered with some gesso, or what.

The object is in the right margin, at the level of the gap between text-lines 19 and 20 of the right column, and a little to the right of the text-column. On inital glance it does resemble the upper half of a Voynich GC-g. Its similars are not uncommon in the images of old documents, and it has such similars nearby on the same folio - it is not a rare form. But, assuming it was actually scripted and is not an artifact, the flow of its strokes is not correct for a VMS GC-g.

Nevertheless, it can easily be contemplated that it may have been a pre-cursor symbol to the GC-g. We see that it appears to be connected to something similar to a GC-k directly underneath it. And there may be more connections, to other marks in the neighborhood, giving an impression like a schematic diagram. To my eyes, these "schematics", sometimes resembling scaffolds with VMS-like forms integrated in them, are not uncommon in the online images of the old documents. As we will see in the data to come below, sometimes marks like these are remarkably similar to the familiar VMS gallows glyphs. We note that this Higden f. 81 object can actually be seen fairly well in the unprocessed image, once it has been noticed.

Before proceeding to the below data, it is really essential to review familiarity with apparent obliterations in the Voynich manuscript itself - many of its folios indicate obliterated material, as is now and then discussed in VMS circles, obliterated material aside the manuscript's steganographically hidden material, including Voynich glyphs and glyphs as parts of patterns (we just a moment ago considered a pattern in the Spiral Galaxy folio).

Across the top area of VMS f11r runs a stain of varying size. Within it are many faint markings suggesting obliterated alphabet elements, especially many apparent Voynich glyphs. It is quite a challenge resolving the patterns: only one GC-k, in normal orientation, is relatively easy to be reasonably confident of. One can certainly get the impression of an experimental modified Voynich script being tried. It is even possible with some processings to perceive "ROAK" or "RIAX", in something of a crossword-layout of apparent Latin letters groups, but with different processings to more or less dismiss it because the right half of the "R" suddenly appears to be a GC-y. This underscores that this is not an easy investigation!

Given we are forced to work, not with the primary physical documents, but with their available online images, and given the less than ideal resolution and spectral samples of these images, we must constantly expect ambiguities and watch out for false indications - we have no choice but to proceed anyway if we want to understand the puzzle, but only with very great rational caution grounded in thorough familiarity with all relevant Voynich materials, and knowledge of the known tricks that our eyes and psychological priorities can play on us, armed with UDOIT. This f11r stained area is thus excellent as a comparison reference for the following work. Here are some initial processing settings to try on its Beinecke images:

C=46, GA=0.23, R=-2, G=37, B=28

Now lets have a look at the letters Kircher received. I surveyed them first as is, noting puzzling marks, and then did some image processing, confining the processing, as much as practical, to a level where the overt script remained clear and legible.

IV. SELECTED LETTERS OF MARCI TO KIRCHER FOR STUDY OF POSSIBLE INVISIBLE INK WRITING (in date order, not necessarily the order of best invisible ink examples)

IV-1.) 3 August 1640, APUG 557 124r : J Marcus Marci + sine
Processing: C=25, GA=0.45, R=-41. Blink against the Negative of this.
Indications to look for:
A GC-e similar in the upper-left fold-quadrant, near top-edge of paper, about 2/3 into the quadrant from left, apparently part of something more complex. To this GC-e's immediate right is a suggestion of a GC-k gallows reaching the top paper edge - its upper-right loop is clearly visible.

IV-2.) 15 March 1642, APUG 557 71r : J Marcus Marci + sine
Processing: C=-38, GA=0.23, R=31, G=50
Alternate processing for moderate daylight-illumination viewing: C=48, GA=0.14, G=41, S=100
Indications to look for:
GC-g in top-left fold-quadrant, about 1/3 in, at top edge just under the horizontally running black linear stain. This GC-g may be long-stemmed, and intruding a tiny GC-1. In the same fold-quadrant, some GC-4's, perhaps the left-portions of GC-k's.

IV-3.) 19 September 1643, APUG 557 107r : J Marcus Marci + sine
Processing: C=11, GA=0.45, R=-15, G=8, B=-47
Indications to look for:
Above the 2nd word of the first line, a GC-g. If the Table II-1 system was at work, then here we see a suggestion that the chemicals reacted much more strongly with the S-ink than the paper.
At upper-right, to the right and below the "107", close to the paper-edge, a fairly big GC-k, with sharply formed "4", quite faint.
GC-W about halfway down between the date-line and the lowest horizontal fold-line, right on the leftmost vertical foldline. It is easy to see, but either it is just part of some sketched pattern, or it is well integrated into the surrounding N-ink noise pattern.
GC-f beneath lowest horizontal fold-line, and right-side adjacent to the leftmost vertical fold-line - to see it better, blink the processed image against a negative of itself.

IV-4.) 29 October 1644, APUG 557 115r : J. Marcus Marci + sine
Processing: C=67, GA=0.81, R=-70
Indications to look for:
To the left of "Rnde" in the first line, the upper-half remains of a GC-g.
GC-f or GC-g or GC-k at top-left corner of letter.
At the top, to the immediate right of the "BEATUS" bleedthrough from the verso side, several indications, notably GC-4's and / or GC-k.
GC-g halfway between the end of the dateline and the right margin, straddling the next-down foldline. It looks like it has been noised over, but a DOIT study indicates all its stroking is correct. This GC-g's stem is pointing down to a GC-4, or into a GC-k. Other looped indications in the vicinity, including GC-9, and perhaps a GC-h.
A complete word, possibly Voynich beginning with GC-j or GC-k, and ending with GC-e, just above "Add..." in the Servus line above the signature.

IV-5.) 25 February 1645, APUG 557 111r : J. Marcus Marci + sine

Processing for lower part of the letter: C=14, GA=0.59, R=-70, G=-28, B=47
Indications to look for:
Above the signature, to the left of "Servus", and per the crossing fold-lines there, in the lower left quadrant they make, and against the origin they make, sits a fairly strong GC-k gallows glyph.
There are many indications of Voynich glyphs, of different sizes, including intruding gallows, in this general part of the letter within the large multi-colored stain.
Big GC-k to left of the signature, butting up against, from underneath, the horizontal-foldline.

Processing for the left margin area of letter: C=35, GA=0.32, S=-122, R=2, G=-5, B=31
Indications to look for:
The left margin part of the image is poorly focused, making determinations much more difficult. But it neverthless suggests that there was much writing there before obliteration. Fairly easy to see is a column of glyphs, not necessarily all Voynich, running down right on the first vertical fold-line, very close to overt left text-margin. GC-e at left margin, to the left of line 17, in a vertical column of letters.

IV-6.) 7 January 1646, APUG 557 424r : no identifying signature
This letter was identified by well-known Voynich researcher Philip Neal [7]. The letter is heavily stained, and its online APUG image shows that its lower portion was removed prior to being affixed into the Kircher Carteggio. That would account for the missing Marci signature because it is common in Kircheriana correspondence for there to be large blank gaps between the date-line and the writer's signature near the bottom of the letter. Perhaps the removed part of the letter held secret material.

Processing: GA=0.28, R=47, G=44. Rotate the image right (clockwise 90 degrees). Blink against its negative.
Indications to look for:
Obliterated words with Voynich glyphs in the area-band from the bottom edge (being in normal orientation the right edge of the paper) to up well into the overt writing. There is a suggestion of a possible GC-am (GC-aiiN) - to find it, start at the lower left edge where the suggestive GC-k is and move right until between the 4th and 5th traversed overt-text lines: the plausible GC-am is there at just about the same elevation as the upper half of the aforemention GC-k.

Alternate processing for moderate daylight-illumination viewing: GA=0.3, R=-60, G=24, letter in normal orientation.
Indications to look for:
Long-stemmed GC-g with extended torso, the torso intruding from immediate left into the "R" of the first word, "Rnde", in line 1. Note similar case in IV-8.). The shape of this extended-torso GC-g is rather good by VMS standards, but this example either uses the rilles in the paper, or it is an artifact. But, the IV-8.) similarity suggests it is the real thing. Also, contrary to Preparation-P item 6.) above, here the V-ink overt writing may have been done after the S-ink work, since the "R" appears to be doing the intruding rather than the torso of the GC-g.

IV-7.) 19 March 1649, APUG 557 118r : JM. Marci + sine
This is the letter that has in it a series of several listed names, where on line 17 is "Barsch : Petit" - Barsch or Baresch, the Younger ?
Processing: C=38, GA=0.3, S=-148, R=-18, G=11, B=-54
Indications to look for:
GC-g and intruding gallows GC-K in the stain area, and also in the poorly focused left margin area. Underneath the tj_16 portion of the date-line is a suggestion of a variation of a fairly large GC-g with belly-down torso, having a sharply defined "4", its size being on the order of Marcy's sine following his signature.

IV-8.) 9 July 1655?, APUG 557 97r : JM Marci
Processing: C=28, GA=0.59, S=-21, R=-34, G=18, B=24
Indications to look for:
A possibility: this letter actually may have more covert Voynich script than the overt script, and Marci basically used the entire sheet, writing between the covert script-lines freely.
A good GC-4o near the top-left corner, it is slightly rotated counter-clockwise. Another GC-40 at the top of the paper, its horizontal position is the left margin of the overt writing.
A bold GC-g to the left of, and against the first letter ("R") of the first word (abbreviated Reverende) on line 1. Note similar case in IV-6.)
Above it, possibly an AGC-92 (GC-\) right-walking "picnic table", or else it is part of another construction.
To the left of overt text-lines 8-10, suggestions of GC-g and / or GC-k.

IV-9.) October 1655, APUG 557 95r : J Marcus Marci
Processing: C=19, GA=0.45, R=-54, B=-47, Rotate left once (90 degrees c.c.w.)
Alternate processing for moderate daylight-illumination viewing: C=49, GA=0.23, G=15, Rotate left once (90 deg. c.c.w.)
Indications to look for:
The letter may contain obliterated material everywhere on it, but the easiest first areas for discovery of potentials seem to be at the upper part of the letter above the second overt script-line, and the left margin between the overt script and the paper's left edge. In the rotated view, run an imaginary vertical reference line down from the first word, "Spes". On that line, just a little below "Spes", is a GC-k, or GC-h. That GC-k appears to touch beneath it a GC-4h, with the GC-4 sharply delineated, and considerably un-obliterated. The GC-4h in turn touches underneath it a GC-4o.
At the height where the GC-k or GC-h meets the GC-4h, move left about three widths of the "4". There sits an indication of a short-stemmed GC-g or GC-j with a tight upper-right loop. There are short-stemmed GC-g's and GC-j's here and there in the VMS, and this possible example somewhat resembles the short-stemmed GC-j that occurs as the second glyph in the second word of line 22 in f105r.

IV-10.) 19 August 1658?, APUG 557 99r : Jo Marcus Marci
Processing: C=59, GA=0.37, S=-70, R=21, G=8, B=-5
Indications to look for:
It's pretty obvious that a lot of material in the left margin area has been obliterated, and it may be both Voynich script and normal Latin? script - perhaps attempts to match the VMS script to Latin. But the obliteration is effective, and it is difficult being sure of the presence of VMS script.
At the level of line 5, which begins with "et Bohemie", there is a suggestion of two Voynich words, and underneath them a somewhat different script that includes an "8". The first word starts with a GC-k and seems to end with a GC-9. The second word appears to start with GC-4o. There seem to be several 9's in this area, and at the level of the next lower line there are indications of a GC-89 or GC-*9.
At the level of line 27 (the second-last line before the date-line), to the left of the first word, "ipsi", by about 2.5 word-widths, appears a suggestion of the stemless upper half of a GC-g or GC-j. Possibly broken traces of its stem are underneath. To its left, about halfway to the edge of the paper, is a suggestion of a GC-k.
At the level of lines 22 and 23, especially close to the paper's left edge, seems an area worth more image processing effort.

IV-11.) 10 SEPT 1665, APUG 562 114r : Joannes Marcus Marci a Cronland
Processing: C=28, GA=0.85, R=-44, G=21, B=-5, rotate to upside down, blink against the unprocessed image
Indications to look for:
This letter may have obliterated script all over it, and written between the overt script lines upside down from normal orientation, or perhaps alternating rightside up and upside down. There are many indications of Voynich forms. One can get the impression that Marci was writing with Voynich script as if it were the script for a natural language. But the secret writing has been heavily obliterated, and resolving more than bits and pieces is very difficult.
Line 12 ends with "majoris momenti". To the right of momenti halfway to the right margin is an indication of a GC-k: it is upside down, faint, but correctly stroked. In the upside down orientation it is seen that this GC-k is ligatured to some other loops, as if a cursive version of Voynich script is there - reminiscent of ligatura steganographia. The right loop of the GC-k contacts what appears somewhat like a GC-f with a small loop.

IV-12.) Beinecke 408A includes the last known letter of Marci to Kircher of 19 August 1666?, on which hinges the standard VMS history. Like the letter above in IV-11.) which is a natural comparison for it, this letter has "a Cronland" as part of the signature. An online image of this letter, originating with Wilfrid Voynich and being Plate I from Newbold's book edited by Kent, is provided by Rene Zandbergen's Voynich website:

Another online image of this Plate I is provided by Pastor Ross Bender's website:

And google books also has an image of it online, and of course there is the reproduction of the letter in D'Imperio's book.

Some other images of the letter, processed, including its back-side, are provided online by our colleague Dana Scott:'s%20Letter.htm

Dana's pictures are perhaps the best for examining the dateline specifically; in the Newbold Plate I pictures the left side of the letter, where the dateline is, is somewhat out of focus.

We would like better natural colors resolution than any of these images provide, so instead of detailing an image processing analysis, I'll just make some observations from the images as they are, and some rather speculative comments.

Under the "R" of the "Reverende" it is possible to bring into perception something resembling a GC-k.

We all know about the problematically scripted date on this letter: 1665 or 1666? Was the date tampered with? In the APUG Marci letters, across their hands, the year of the date is written so that the initial "1" resembles a dot-less "j". This letter shows a glaring exception - a short straight stroke.

In a recent vms-list post [8] I commented about the "600" of the "600 ducatos" in this letter's text. The "6" of the 600 is markedly different from the other two or three 6's in the date. Furthermore, this "6" is also very different from the 6's in the APUG letter of IV-11.). It seems possible to me from its appearance that the "600" represents not a number, but a symbol: "alchemical". And then the much-analyzed sentence it is part of, could be indicating that some alchemical gold changed hands:

" ..... and he presented the bearer who brought him the book alchemical ducats. "

In other words:

" ..... and he presented the bearer who brought him the book alchemical gold. "

Also, I recall that somewhere in Capelli are a couple of Latin abbreviations with component superscripts that are quite similar to the "600".

But lets take the alchemy a little further. From Dana's pictures, it is possible to perceive that in the year of the date the first "6" is scripted the same as the "6" of the 600 ducatos, and arches over the next 6, plus also the problematic last numeral. In other words, whereas the last two numerals of the year are quite different from the "6" in the ducatos 600, the first 6 may well be scripted similarly, and is covering its next two numerals, just like the ducatos 6 is covering its next two numerals.

Now lets look closely at the problematic last numeral of the year. If we take it as a "6", then its shape is definitely different from all the other 6's. Its ascender has a distinct hook added to it at the top, aimed to the right. Turning now to the recent consideration of a hypothetical "Baresch's Alembic" [9], we take it as a possibility that this last numeral reinforces the symbolism of alchemical alembic, and therefore in the letter both the "600" from the ducatos, and the year "1666", are together suggesting that the intended reader of the letter is to take, aside from any other messages in the letter, the message that the book being talked about in the letter has alchemical connections.

V. BARESCH'S 1639 LETTER TO KIRCHER: Does it show traces of obliterated Voynich script?

27 April 1639, APUG 557 353r and 353v

Processing for recto side: C=83, GA=0.42, S=-119, R=-50 to -70, G=5 to 15
Indications to look for:
There are some faint indications of possibly partial Voynich script forms along the top of the recto side, some 4's and perhaps GC-k, GC-f, GC-g, or GC-j.
Down the very left edge of the paper, which is unfortunately mostly covered by the wrinkled glue-strip of the Carteggio Volume binding, it seems possible that Baresch wrote a column of individual symbols, including Voynich. The "4" is seen a few times. There is even the suggestion that Kircher covered the recto side of the letter with a sheet reaching almost to the left edge, and then applied the obliteration Process-O to the uncovered edge. A further difficulty in addition to the glue-strip is that the column glyphs are tiny. But we mention the wrinkled glue-strip possibility just exactly because it first suggests the generation of artifacts and would thus be prone to immediate dismissal; but not so fast - let it too be investigated.

There are I count 32 overt script-lines on the recto. At the level of line 13, which starts with the word "personaliter" there appears in the possible column at the left edge of the paper an indication of a small GC-4h, or GC-k (EVA-t) with a sharply defined "4" component. It may be short-stemmed in the normal VMS fashion, or it is intruding a GC-1 (EVA-ch). Another possible interpretation I think is that it is a short-stemmed GC-k / EVA-t gallows, and directly underneath it has been written the small similar Latin abbreviation "quis", as if a comparison was being made. In any case, as poor as this indication is, it is one of the relatively stronger ones in Baresch's letter. [10]
At the level between lines 16 and 17 the edge column indicates a GC-j or GC-f (EVA-f) or GC-h (EVA-k) gallows, but it might be arising as an artifact from the glue-strip.
At the level between lines 27 and 28 (which starts with "sit Librum") the column indicates a GC-s / EVA-s. Directly underneath is a possible GC-e / EVA-l, and underneath that a more strongly plausible GC-e / EVA-l.

Processing for verso side: C=51, GA=0.45, S=41, R=-63, G=34
Indications to look for:
The most promising area in the entire letter is I think the bottom of the verso side, to the left of Baresch's signature, a blank area that is free of bleedthroughs from the recto side, and which shows signs of scraping obliteration. With considerable study and effort it may be possible to resolve in this area at least one large correctly stroked GC-g, and perhaps a GC-4o. Otherwise, overall the indications in Baresch's letter are relatively slim compared with the other documents.

VI. SELECTED MORETUS LETTERS TO KIRCHER: Do we have complete Voynich words?

We have much studied the letters of Moretus beginning with J.VS comm. #121 (Vol. I).

VI-1.) 25 DEC 1638, APUG 567 7r
Processing: C=30, GA=0.37, S=15, R=-34, G=31, B = -37, rotate 90 deg. c.c.w.
Indications to look for:
There are indications of various alphabet symbols, including Voynich, all over this letter, at different orientations, and of greatly varying plausibilities, each requiring individual image processing for best determination. The letter has in addition to normal layout of its text, another block written along the left margin that requires rotating the letter 90 deg. c.c.w. in order to read. In that block, in the area between "Veneti" and "R.V.", just to the right of Veneti and slightly above it, is a good candidate for a GC-J or GC-G / EVA-cph intruding gallows glyph that may be the initial symbol of a complete word using mixed alphabets. A little to its left at its top part level, is an "8".

VI-2.) 22 FEB 1642, APUG 567 55r
Processing: C=44, GA=0.5, S=-50, R=-24, G=31, B=34
Indications to look for:
All areas of the letter have indications. At the level of line 4, to the left of "Accepi" and closer to the left margin, suggestions of at least one, fairly large, GC-k. Underneath line 14, under "Mathematicis" several indications of complete Voynich words with gallows, intruding gallows, GC-9 and GC-4o.

VI-3.) 10 or 16 MAY 1642 (this letter is 4 pages long)
APUG 567 126v
Processing: C=28, GA=0.72, S=-76, R=-44, G=28
Indications to look for:
To the left of the first word "Quod" on line 2, a GC-k, or upper-half of a GC-j or GC-g.
To the left of the first word on line 3, the upper half of a GC-f or GC-g.

VI-4.) 30 JUL 1642, APUG 567 80r
Processing: C=51, GA=0.28, S=-54, G=60, B=18
Indications to look for:
At top right, between the stamped "80" and the top edge of the paper, a fine, carefully scripted GC-g, with its tail coming back to meet the stem, as we see for example with the VMS GC-g in f41v noted earlier in section II. Or else, the appearance is of the upper half of a GC-g intruding directly upon a soft "4", with a slightly sharper-angled 4 to its right.
The letter has many indications of 4's to the immediate left of stemmed loops, in various sizes. A large example is to the left of the "80", about four of its widths to its left.

VI-5.) 9 OCT 1642, APUG 567 56r
Processing: R=-50
Indications to look for:
This image was obviously heavily processed before being placed online, hence we confine further initial processing of it to just reducing its red color component.
At top left and continuing across the top there are VMS-reminiscent looped forms integrated with lines and rectangles. On, and above the "R de." at the start of line 2 appear GC-kg sharing a common stem.


Jacobi Dobrzensky de Nigro Ponte was a student of Athanasius Kircher. We will look at one of his letters. Godefridi Kinner wrote many letters to Kircher. We will look at the particular Kinner letter: " A letter written by G.A. Kinner to Kircher in January 1667 refers to a question by the ailing Marci about the Voynich MS. " [11]

VII-1.) 22 APR 1658, APUG 562 132r&v : Dobrzensky writing from Parma to Kircher

Processing for the recto side: C=46, GA=0.28, S=-15, R=2, G=24, B=11
Indications to look for:
In the upper part of the 38-text-lines recto, especially at left by the edge of the paper, GC-g and GC-k, unfortunately some under the glue-strip. At the line-1 level ("Admodum") at left under the obscuring band, a fairly large GC-g that looks like it has been slightly noise over-written.
A GC-g immediately left of "Quod" at the start of line-30. Continuing below on the margin, indications of complete Voynich groups, written smaller size, some with tall but narrow GC-k's and GC-h's.
The bottom blank area also shows many indications: at the bottom right corner highly suggestive indications of intruding gallows, at least GC-K.

Processing for the verso side: GA=0.23, S=-67, G=31, B=-11, blinked against C=19, GA=0.23, R=-57, B=8.
Indications to look for:
Obliterated marks suggesting large Voynich forms are all over this side. Perhaps the easiest one to see mostly intact is a finely scripted GC-j or GC-f gallows, slanted slightly rightward, located on the right margin. It is immediately to the right of the last overt word, "Stylio" ?, of line-16 (5th line of the 2nd paragraph). The tail of this GC-g contacts the last letter of the overt word.

This letter of Nigro Ponte is scripted in a fine clear hand and should be relatively easy to transcribe for translation. From first glance it seems to concern all sorts of subjects: books, philosophy, mathematics, Egyptian alchemy, astronomy, metals transmutations and amalgams, herbs and botany. His scripting displays those familiar ligature-formed GC-k's.

VII-2.) 5 JAN 1667, APUG 562 151r&v : Kinner writing from Prague to Kircher

Processing for recto side: GA=0.23, S=80, R=-21, G=15, B=-21
Indications to look for:
Many obliterated marks suggesting various written-large alphabet forms, including Voynich, but I have not yet found a good example for further investigation.

Processing for verso side: GA=0.23, S=-34, R=-21, G=11, B=-18
Indications to look for:
Again quite a few indications of obliterated forms, possibly intruding gallows, most being difficult to resolve into a good example. Across the top of the page, and also in the area of the right margin above "Tuus quem nosti" are the better possibilities. The best indication is in the latter area, a large GC-j slanted slightly left-leaning, horizontally centered on the position of "quem", and the bottom end of its stem is at the level of the date-line, which is also a fold-line.


As we know, APUG has put online thousands of images of Kircher's papers. There are online some Kircher papers also from non-APUG sources. Naturally we must look at some of these, including those papers which, as far as we know, are unrelated to Kircher's assumed involvement with the VMS. We have to get a better idea of Kircher's document obliterations, and certainly also obtain checks regarding image artifacts that may be leading to false indications.

We will find that many Kircher papers show indications of obliterated markings, often all over the paper, including markings suggesting Voynich script-forms. Following are some selections of promising examples.

VIII-1.) 15 DEC 1608, APUG 567 60-61 r&v, a letter to someone at the Collegio Romano from Hippolito Gianotti, among Kircher's papers. It shows suggestions of obliterations. We take a look at the 3rd page:
Processing: C=23, GA=0.32, R=-21, G=5
Indications to look for:
Above line 1, just above and slightly left of the "6" a GC-k, with a fairly sharp "4" loop, and a slight variation of its right loop. To its right, above the overt "4", a GC-g that appears to have its stroking quite similar to the VMS GC-g.

VIII-2.) 31 JUL 1632, APUG 561 16r, letter to A.K. from Mutius Vitillejius, apparently a Jesuit.
Processing: GA=0.33, R=-24, G=8, B=-15
Alternate processing for daylight viewing: C=27, GA=0.45, S=-102, R=-44, G=21, B=-47
Indications to look for:
The many apparently obliterated marks resemble scaffoldings / schematics modified with curves, loops, circles and triangles, some resembling Voynich glyphs. At bottom right, just under the "Roma" in the last full-length text-line, a GC-1, and at least one very VMS-like intruding gallows GC-K that is possibly overlapped with another.

VIII-3.) 1633 letter or affidavit by ? in Italian ? to A.K., APUG 566 50 r&v, not sealed as its own envelope.
Processing: C=-6, GA=0.28, S=-76, R=-21, G=9, B=-75
Indications to look for:
Scaffolded forms including Voynich-script similars with many 4's.
Small-sized writing on the lowest horizontal fold-line, including a GC-1. A GC-g variation with a large and sharp 4-component overlaps the foldline with its upper portion, at just to the left of the right-most major vertical rille, i.e. a horizontal position a little past the ending "e" in the signature.
At the bottom of the paper take a quadrant defined by the lowest horizontal fold-line and two major vertical-running rilles: within this quadrant is the last word, "Roma". In the upper quarter of this quadrant, upward from Roma, a rather good GC-g indication, being larger than the "R" in Roma.

VIII-4.) 27 APR 1634 letter from Liantandus?, APUG 567 150r
Processing: C=11, GA=0.28, R=-15, G=2, B=-50
Indications to look for:
When working with this letter it is especially important to first adjust its screen-size for the sharpest overt text. Between the last body-text-line and the date-line is an obviously obliterated line of text. Under the "qui" the descender of its initial "q" just touches the right loop of a fairly well-defined GC-k, faint but distinct, that may even be an intruding GC-K. Possibly also it has been noised with surrounding 4's per Process-O 2a.).

VIII-5.) 7 FEB 1635 letter to A.K. from Ferrand, apparently a Jesuit, APUG 567 30r
Processing: C=48, GA=0.19, S=-73, R=28, G=57, B=-83, blink against unprocessed image
Indications to look for:
Large GC-g left-adjacent to Reverende at top. Its upper right loop is large, touches the top edge of the paper, and is directly over the "R". Its stem is curved and slanting rightward. A noise cross-bar may have been added to make it appear like a script capital "F".

VIII-6.) 14 OCT 1636 "Rota Geographica" work by Athanasius Kircher, S.J., it is a compass rose diagram with geographical information, plus commentary and A.K.'s signature, APUG 561 84r&v

Processing #1: C=11, GA=0.59, S=24, R=-8, G=15, B=-47, rotate 90 degrees counter-clockwise, blink against unprocessed image.
Indications to look for:
This document is an excellent reference for stylus characteristics: note how sharp the very thin radials are in the compass rose, drawn on the type of paper that is common in APUG documents. (This paper is often water-marked, apparently by the maker, and one of the watermarks seen is a circle that has an anchor in it, with a left-facing crescent moon-face underneath the circle, and the shaft of the anchor extending up out of the circle and being crossed by a pair of bars. Perhaps similar watermarks on documents may prove useful in some sorts of correlations.)
In the compass rose are indications of glyphs between and on the radials, from the center on outward, reminiscent of some VMS circular diagrams. Between the 60 and 75 degrees radials, at the same near-outer concentric on which the numbers 60 and 75 are, a GC-g with a round left loop that is larger than its right loop. Its long stem, in a paper rille, is mostly obliterated.

Processing #2: C=54, GA=0.23, R=5, G=5, B=86, blink against unprocessed image.
Indications to look for:
At the top, above the word "observatione" suggestions of GC-g, GC-k or GC-K.
At bottom right, the "J" of "S.J." following the signature, is intruded upon from its immediate right by a GC-g or GC-j. Its body is relatively narrow. Its "4" component, with a trace-thickness about the same as that of the overtly written "S", sits atop the "J" and almost reaches the "S". It is difficult to be sure if its upper-right loop is a very small one that crosses the right-most vertical rille in the paper, or a much larger loop adjacent to the right side of the rille. For either possibility the stroking is correct for a Voynich GC-j or GC-g. Quite faint, and very difficult to be convinced of, but as this is Kircher's signature in 1636, the year before first Baresch contact, it is well worth further investigation. Stronger Voynich-like forms are to its right running up the edge of the paper.

VIII-7.) 26 FEB 1637 letter fm Hermannus Georgius, Elector?, APUG 556 201r
Processing: C=64, GA=0.37, R=-42, G=37, B=-57, rotate c.w. 15.8 degrees
Indications to look for:
To the left of line 13 ("batia"), about 40% of the way toward the left edge, a suggestion of a well-formed long-stemmed GC-g, slanted leftward / c.c.w. 15.8 degrees, its main body about twice the lines-gap dimension, slightly noised, but on account of its faintness and essentially Voynich-perfect form, it is difficult to decide if it is the real thing, or just an amazing artifact.

VIII-8.) 30 JUL? 1637 letter to A.K. from Mutius Vitillejius, APUG 561 19r
Processing: C=44, GA=0.37, R=-18, G=11, B=-31
Indications to look for:
On the date-line, but in left margin, the upper half of a tail-less and stemless GC-g, or alternatively a short-stemmed GC-k with the feet of its stems bridged, easy to see, even without processing. Many other forms in the overt-unwritten areas of the letter.

VIII-9.) Undated letter to A.K. from Queen Christina of Sweden, APUG 556 174r&v
Processing: C=11, GA=0.4, S=-109, R=-44, G=11, B=-83
Alternate processing: GA=0.45, G=-8, B=-76
Indications to look for:
The blank area in the upper-left quadrant shows obvious obliterations. Running down the left margin are suggestions of VMS-similar forms, but just different enough to be either a distinct related script, or a distinct style. The easiest to resolve obliteration is a stylistically modified GC-g in the bottom left quadrant, almost up against the glue-strip, and at a level that is the same as a tangent against the bottom of the rightmost flourish loop that ends Christina's signature. The stylistic variation in this GC-g is seen in its tail - she has made it into a braid. Once seen in the processed image, it can just be perceived in the unprocessed image also. Too bad we don't know the date: if she wrote this to Kircher well before she began being converted by the Jesuits, and abdicating in 1654. If she did, then the Voynich script or its similar was evidently in use also outside Catholic / Jesuit circles. The verso of this letter has two words only, apparently translating to "Queen of Sweden". Perhaps they can provide more data.

There is online an image, of not-adequate resolution and color, of A.K.'s 28 FEB 1650 letter to Prince Carl Gustav, Christina's cousin and successor:

At the beginning, underneath and touching the large "S" of the "clementiSs.^me" on line 2, we can discern a faint pattern quite readily suggesting a GC-g. Other suggestions of obliterated writing, even with GC-k forms, can be well pondered: as for example between lines 4 and 5, but the image data is just too limited to make much of it.

VIII-10.) The website of Sammlungen der Herzog August Bibliothek Wolfenbüttel has online images (as well as transcriptions and translations of the Latin into German) of a number of Kircher's letters to Duke August the Younger, written 1650-1666:

Kircher and August discussed a wide variety of subjects in their correspondence, including steganography. In the APUG, the preserved correspondence between August and Kircher indicate many obliterated Voynich-similar forms, and are worth investigating especially because they tend to be written large.

Unfortunately, the resolution of the online images of the Bibliothek Wolfenbüttel collection is not good. But we will try a processsing experiment and see what happens. One of the letters, catalog BA-II-5-358, dated 20 JUN 1663, shows heavy staining with indications of obliterated writing (presumably obliterated by August):

This letter accompanies a gift copy of Kircher's book "Polygraphia", which Kircher describes as the invention of a universal language. Kircher thanks August for his support and encouragement of the Polygraphia work.

Processing #1: C=41, GA=0.37, S=120, R=-50, G=37, B=73
Processing #2: C=41, GA=0.37, S=120, R=-37, G=34, B=57
Indications to look for:
In the stained area, to the left of lines 14 and 15, is what appears as a distinct Latin letters group: "god", or "goo", or "go9". Beneath it are some forms of interest.
Rotate the #1 and #2 processed images clockwise 195 degrees. As well rotate a copy of the unprocessed image 195 degrees. These three images will be blinked against each other.
Indications to look for:
In the normal orientation line 10 begins at left with the word "personam". In the rotated orientation draw an imaginary horizontal at the level of the gap between lines 9 and 10. About halfway to the right from the overt writing to the edge of the paper (the left edge in the normal orientation) is a suggestion of a large long-stemmed GC-g variation, its torso stretched rightward, and having a small right loop that suggests a lone "S". This GC-g appears to have both a normal "4" left loop and a curved loop directly underneath the 4. This GC-g also gives the appearance of being partly superimposed upon another, slightly higher GC-g. If it is the real thing, then perhaps it has been noised.

VIII-11.) 16 MAY 1670 letter to A.K. from Leibniz, APUG 559 166r&v
Indications to look for:
On the recto, at the top between and above the first and second words, a GC-f. Its top is up against the upper edge of the paper. Otherwise both recto and verso show few indications that I can see in this densely writing-covered letter.

VIII-12.) OCT 1670 letter from Christophoru de Mendoza, S.J., APUG 559 206r&v
Processing: GA=0.45, R=41, G=37
Indications to look for:
A plainly visible large GC-g variation at upper left near edge of paper, at the level of the "Qui ... " line bleeding through from the verso side. Perhaps it was penciled in by a later hand?

VIII-13.) It is actually not all that easy to find among the APUG images some examples that are relatively free of these curious, apparently obliterated VMS-similar markings. That is a major part of the puzzle - they seem almost to be all over everywhere. But, in tune with the idea of item 3.) of Table III-1 above, we require some relatively clean references. I have a changing set of references. The below is currently the best of the set:

1674 letter to A.K., APUG 566 60r


We've examined images of documents as far back as the 15th century, and concentrated our attention on 17th century documents. Altogether the documents exhibit numerous apparent indications of markings ranging from very insubstantial and possibly purely subjective, to obviously obliterated markings of likely original writing. The puzzle remains: why are these markings so numerous across so many documents, and why do so many of them suggest forms so similar to Voynich script glyphs, in particular the Voynich characteristic gallows glyphs?

I believe there is enough data above to motivate further investigation into this puzzle, and that one working hypothesis for such that makes sense is: that Voynich-script, or at least a proto-Voynich-script, was in use, at least covertly by Jesuits, and / or professional scribes, long before 1637 when Baresch is assumed to have first written Kircher. Indeed, we have indications that Kircher was familiar with the script years before he had ever heard of Baresch and Marci.

True, it is technically conceivable that Kircher first learned of Voynich-script from Baresch, and then started annotating all his papers with it, including papers he possessed as an adult, but papers dating back to 1608 when he was a little child, and then also later he or his followers obliterated all these annotations again. Technically possible, but how likely is that? It's much easier to see Kircher well familiar with Voynich-script as a result of training in it by his Jesuit teachers, and annotating, even with invisible ink, long before Baresch came into the picture.

The Voynich-script as we know it may be an evolutionary derivative, or even a subset of a more complex scripting system, in use by Jesuits and / or Holy Roman Empire officials, or even all the intellectual elites of the times seeking vehicles for philosophical communication transcending political constraints.

This communications system, which I'll temporarily call "Jesuit Secret Script", JSS, may have died out as a result of the suppressions of the Jesuit order. There are indications of these JSS forms even in the images of the APUG catalog pages, which were not written by Kircher.

If JSS is real, then it appears that the GC-g / EVA-p symbol is special in it, and when it is placed in certain relative locations such as at the start of addresses, like "Reverende", it means that a signal of special significance is being sent [12]. This indication is seen in quite a few other APUG letters not detailed above.

Can we find some strongly suggestive institutional evidence, as opposed to personal/ private evidence, for this JSS, in the APUG? Yes I think so, and in multi-colors:

APUG 560 107r

1664? Dialectica Spina rosetum expositio, Cabala, A.K. and Joanne Walt, illustrated title page featuring a wreath of 16 roses, 8 red, and 8 blue, alphabet and numerals correspondences tables; the image shows markings that can be resolved as per the procedures above.

For the hypothetical JSS as an institutional activity, note the integrated GC-k, GC-h, GC-f, and GC-g in the Jesuit IHS trigram. It may even be possible to resolve a line or two of Voynich text with several VMS glyphs including GC-1: just above "P.ATHANSIO Kircher".

Baresch's 1639 letter seems notably weak for indications of the kind we have been considering, although there is still the possibility of the scraped area to the left of his signature yielding a breakthrough. If the mysterious script Baresch was talking about is indeed Voynich-script, then perhaps he stumbled upon JSS accidentally, not realizing it was an established communications system. But I am equally inclined to believe that Baresch was wise enough not to be so mystified by JSS, as he seems to be about the script in his letter to Kircher, and I give equal probablility to his mysterious script being something else, or at least a variation he was baffled by. It seems not impossible that Baresch too was actually schooled in JSS, and using it in writing to Kircher, while the mysterious script in his puzzling manuscript, with its enormous number of herbal illustrations, was something entirely different.

It is very desirable of course to have as a comparison check, letters from the 17th century that are positively known to have invisible-ink writing. But, my minimum impression so far, is that many of the obliterated forms in the letters to Kircher are not idle doodles, and that they are strikingly similar to the obliterated forms in the actual Voynich manuscript: standard Voynich glyphs forms, modified and distorted "noisy" forms, or experimental forms. And quite plausibly that a secret writing system along the lines of Table II-1, written in JSS, was in use by Kircher and his trusted circle.

If JSS did not exist, or was not a fully developed system by the time of Kircher and Marci, then from the indications in the letters, I think it is worthwhile to consider the alternative possibility that Marci and Kircher et al may have been comparing Voynich manuscript alphabet glyphs with glyphs from other alphabets, and experimenting with variational forms of the Voynich script, much as if they were in the process of inventing the Voynich script, experimenting with forms not freqently found in the VMS, like gallows intruding on gallows, notably GC-g intruding upon GC-k.

Other experimentations forms might include horizontal flips (mirrored versions of the glyphs), and mixing of Latin and other alphabet letters, Armenian, Greek, Hebrew etc., with pure Voynich alphabet glyphs in the composition of groups / words, or mixing of Voynich and non-Voynich groups in series of groups. We do see quite clearly some suggestions of such mixing on the last page of the Voynich manuscript, folio f116v. Another impression one can get is that Marci and Kircher et al were considering the gallows and their various intruding forms as constituting a minimal alphabet on their own. Overall from the indications in the Marci letters, one can get a sense of general experimentation with the art of secret writing.

Some other pertinent questions to consider:

Why are the Voynich indications in the above studied documents primarily of Voynich-like script, and devoid of other specific-to-the-Voynich-manuscript particulars, like diagrams or sketches indicating the nine rosettes etc. ?

Although it is not unusual to have archive catalog entries out of sync with dates, nevertheless is the archival catalog order of the Marci letters in the Carteggio Kircheriana, being different from serial date order, in any way possibly significant to all this? [13]

Are the well-noted gaps in the Marci-Kircher correspondence suggestive of letters that were totally suppressed by Kircher, or suppressed by others, say his follower-students?

If JSS is real, was it society-wide, including also trusted Holy Roman Empire officials, or was it practiced only by a sub-society with the Societas Iesu? Now, if the VMS script was indeed originally derived as a block-print version of a JSS that itself originated as a ligatura steganographia, and also a secret writing system along the lines of Table II-1 were being practiced, with the VMS script, then sooner or later it would occur to practitioners that the VMS glyphs when forming words might once again be reconnected with "diagram noise". Such a technique might manage to turn the starting text groups of VMS f10r into a suggestion of a mechanical diagram involving a lever. [14]

Some of the overt "diacritic" marks like GC-e in Baresch's letter are patently common Voynich alphabet glyphs. If the hypothetical column of obliterated Voynich glyphs in the Baresch letter is indeed that, then are the obliterated glyphs in the column somehow horizontally correlated with the overt diacritics in the normal text? [15]

How well could a thorough chemical etc. analysis of the original documents reconstruct the specifics of the secret invisible-ink writing system, after all the intervening time? Is anyone today still using a similar system?

What can be done to gain better access to the original documents for any level of physical examinations? Marci's last letter at the Beinecke is apparently still to be examined by appointment, perhaps now with mouthmask and plastic gloves. But one would love to get a chance at the APUG documents, if only for half an hour, with some magnifying lenses, a flashlight and camera, a color reference card, and some optical filters, say a green-transmitting filter for the flashlight, and a red-blocking filter for viewing and photographing.

A couple of weeks ago off-J, we had discussions on the ultra-violet plates of VMS f1r that are kept at the Beinecke. And from Dana, who had personally inspected them, we learned a bit more about these UV plates, but unfortunately Dana could not confirm that they showed any hypothetical details, like "Tepenec", any more plausibly than do the online SID images. However, a study of the chemistry of the invisible ink procedures of the 17th century may make a case for some of the chemicals involved being metallic salts that do glow under ultra-violet. Then, if one did get a chance at the APUG documents, the take-with-you kit should include a little battery-operated mineralogy UV-lamp, or two, one for short and the other longwave UV. I have one that fits in the palm of my hand.

Much of modern Voynich research relies on examining images of documents that have been placed online. The obliterated marks, some of them very much suggesting Voynich glyphs similarity, are there in the images of documents both within, and outside the standard VMS history scope.

What is their significance?

Berj / KI3U

[1] TABLE I : Persons theoretically cognizant of the Prague ms ...; J.VS communication #13 (Vol. I):

[2] J.VS: Pictures: possible Voynich-alphabet word in Kircher's letter to Schall; J.VS comm. #83 (Vol. I):

[3] Extensive materials on della Porta are available online here:


[5] While investigating with the DOIT the VMS nine-rosettes foldout one cannot help wonder about all those different-lengths tubes in the illustration: could they be representing DOIT's if not telescopes? But how the animals, dogs or sheep or cows?, that appear in the mouths of some of the lower tubes of the central rosette in panel VMS f86r3 would fit such an optical instrument symbology requires further explanation: are they suggesting improved resolution via DOIT, until a dog is clearly recognized?

[6] Incidentally, the Voynich f87v folio actually has a number of unusual offerings. For example, in the top-right area of the folio is a fair-sized spot that gives just a tiny bit of a suggestion of metallic luster in the vein of J.VS communication #213 [6a]. Examined at best available resolution in the SID image, and rotated 90 deg. c.c.w., it appears that the head of an animal has been rendered, fairly realistically, within the material that makes up that spot: it looks like a sheep. To its right there seems to be another animal - it appears to me closest to a camel. So perhaps an Agnus Dei symbolism is intended with that spot.

[6a] J.VS: Are Gold and other metal particles embedded in the Voynich manuscript parchments?; J.VS comm. #213 (Vol. II):


[8] vms-list post: RE: VMs: RE: Ducats, Sent Date 10-10-2008 5:25:48 PM, by Berj.

[9] J.VS: Baresch's Alembic / Retort, and Voynich f88r; J.VS comm. #218 (Vol. II):

[10] See the sub-table from the Capelli-work Latin abbreviation given as Fig. 17, pg. 95, in D'Imperio's Elegant Enigma. The entire Capelli book is also online:

[11] Rene Zandbergen, Voynich MS - Biographies:

[12] see Christianity symbolism in J.VS comm. #48 (Vol. I):
J.VS: Images: PM-curve; gallows-letters Christianity symbolism

[13] see:

[14] See the discussion of "Ligatura Steganographia" in the vms-list post: Re: VMs: Possible Voynich text in a Kircherr letter; Monday, February 19, 2007 5:51 PM. This post is preserved in the J.VS Library, deposit # 1-1-2007-05-05, file: 4vmsKI3Ulab.htm

[15] For more on these "diacritics" see J.VS comm. #218 (Vol. II):
J.VS: Baresch's Alembic / Retort, and Voynich f88r

From: Berj N. Ensanian
To: Journal of Voynich Studies
Date: Sun 10/19/08 2:30 PM

Subject: J.VS: Variations on the name: Baresch / Barschius

Dear Colleages

From at least 29 JUL 2005 well-known Voynich researcher Jeff Haley has from time to time on vms-list been advancing the idea that certain historical variations of the name "Baresch" ought to be investigated for possible breakthroughs concerning all matters "M. Georgius Baresch". Jeff has produced data around period names including:

Jan Baresch, Bares, Michael Bartsch, Jan Brozek, Brocius, Jacob Bartsch, and Bartschius.

And in December 2007 on vms-list I briefly discussed with Jeff the variation: "Bartz".

Jeff has commented on a number of mysteries surrounding the available data on Baresch and its fit, or mis-fit, into the standard Voynich manuscript history. For example, in a 17 APR 2008 vms-list post, Jeff wrote this interesting comment:

" If Baresch was really not Baresch at all but someone well known it would make more sense. I have long suspected that 'Baresch' was assuming the identity of a dead man. This is why the records in Prague do not record him as a resident. "

The problem of Baresch's identity even had myself recently suggest, via a question in a 12 SEP 2008 vms-list post, pondering if the 27 APR 1639 letter from Baresch to Kircher might have been back-dated by the writer.

In any case, the search for period, or approximate period names that may be variations of "Baresch", is I think a very good idea. As you recall from off-J this last September, I did some searching and found some names that may or not tie in with our Baresch, but which nevertheless expand the list of variations. I'd like to list them here, so that together with those above produced by Jeff we have them all in one handy place:

1.) Gyorgy Barsony, S.J., 1626-1678. I found his name in the index directly under "George Barschius" in Evans' 1979 book (The Making of the Habsburg Monarchy):

Evans says he was an ultramontane. Evans gives for Baresch the usual Marci reference (Philosophia Vetus Restituta). I found another website mentioning Barsony, in a language that our colleague Jan Hurych identified as Hungarian:

Barsony would have been just 11 years old in 1637 when Baresch first wrote to Kircher, but it did occur to me that perhaps he was a son of our Baresch: Baresch the Younger. It would surely be interesting to find Barsony's written hand and compare it with Baresch's hand in the 1639 letter.

2.) Benedictus Barsch, 1535-1560. Appears in a list of people who have acted as official executioners (Berlin):
Perhaps he was an ancestral relative of our Baresch.

3.) In a list of foreigners imported in the ship Brittania of London, Michael Franklin, Master, from Rotterdam. Qualified Sept. 21, 1731:
BARSCH, Hisbertus
BARSCH, Johannes

Perhaps they are descendants of our Baresch.

4.) In J.VS comm. #221 I mentioned, just in passing, the "Barsch : Petit" among a list of names on line 17 of Marci's 19 MAR 1649 letter to Kircher, APUG 557 118r. The transcription / spelling needs a correction:

Barsh : Petit

which I speculated might mean: Barsh the Younger. We note that the above Jesuit Gyorgy Barsony would have been 23 years old when Marci wrote this letter.

Philip Neal has transcribed differently [1], like this: Barth: Petit

To me the hand-script in the APUG image indicates equal probability of "s" and "t", that is equal probability of "Barsh" and "Barth". Of course whichever it is, we would expect it be contextually consistent with the other names among which it appears, a determination of which awaits a translation of the letter. Among the names in the list are:

A.) Miguel Florencio : ?
B.) Puteani : presumably Erycius Puteanus, 1574-1646, author of the 1627 " Cryptographia Tassiana, sive, Clandestina scriptio "
C.) Wendelini : perhaps searchable with the terms: Kirchneri, Typis Wendelini Moewaldi, 1678.
D.) della Faille : presumably Jean-Charles de la Faille or Jan-Karel della Faille, S.J., Antwerp, March 1, 1597 - Barcelona, November 4, 1652, a formidable Belgian Jesuit mathematician who had his portrait painted by Anthony van Dyck.
E.) Juan de Bagnee (per Philip Neal), or Fran de Bignec ??? Perhaps some connection to: Bucholoudis de Bignec.

One more thing concerning getting a better handle on Baresch - in the analysis of Baresch's manu propria in J.VS comm. #130 (Vol. I) I remarked that Baresch's sine seems to end with a word whose last character is "8". If it is a word, it would of course be good to know what it was. Since it does seem that there is a consensus that the "M." in "M. Georgius Baresch" stands for "Magister", then perhaps that group at the end of Baresch's sine can be transcribed:


refined to: MagS. or Magd.

and if MagdS., then taken as an abbreviation meaning: Magister.

Unfortunately, even if correct, that does not tell us anything we don't know from the few other records on Baresch. But at least it is something Baresch that "fits".

Berj / KI3U


From: Berj N. Ensanian
Sent: Mon 10/20/08 1:23 PM
To: Journal of Voynich Studies

Subject: J.VS: Re: Variations on the name: Baresch / Barschius?

Dear Colleagues

Concerning "Wendelini" of item C.) in J.VS communication #222, the APUG Kircher papers TOMUM IX. catalogs a 22 SEP 1660 letter from "Godefridi Wendelini" in Gandani:

The images of this letter's recto and verso are online here:

The letter is signed both "Gottifridum Wendolmum" and "Vendelin9" or "Vendelinus".

Wendelini's hand and inking are not easy to deal with. He intersperses Greek with the Latin at will. He mentions Riccioli, and seems to be concerned with scientific measurements, possibly astronomical-event correlations with magnetic phenomena, and gives a table of measurements - I'm not sure from cursory glance just what it is all about. The dates 1643 and 30 OCT 1659 appear in his text.

Berj / KI3U
From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent: Mon 10/20/08 10:44 PM

Subject: J.VS: Mnissowsky's Jesuit coals

Dear Colleagues

The google books service has available for download in pdf format the Vol. II of:

The Reformation And Anti-Reformation in Bohemia, by Christian Adolph Pescheck, from the German, In Two Volumes, London, Houlston and Stoneman, Paternoster Row, 1845.

You can get to it by googling: "The_Reformation_and_Anti_Reformation_in_.pdf"

Our Santinus is mentioned on page 109, so listed in the book's index. Raphael Mnissowsky appears on page 108, but is not in the index that I can see. The brief anecdotes on these two seem tangential to our Voynich concerns, but you never know, as every tiny piece of information may lead to something. There is a lot of material on the Jesuits during the times, including their destroying Protestant books. The pdf download works well, and is 12.6 MB in size.

Another brief Santinus mention, in footnote 79, is available here:

Chapter 6: Reform, Mission, and Propaganda (1580-1630)

I am not sure what the parent document of this one is.

Berj / KI3U

From: Berj N. Ensanian
Sent: Wed 10/22/08 11:05 AM
To: Journal of Voynich Studies

Subject: J.VS: Re: Mnissowsky's Jesuit coals

Reference J.VS comm. #224, our colleague Jan Hurych has found that Vol. I of:

The Reformation And Anti-Reformation in Bohemia, by Christian Adolph Pescheck

is also available for download, 12.2 MB, from google books: eformation&ei=sv_-SJP5JYuYMpnV7KQL

I just downloaded it - I had to add a "1" to the front of the .pdf name so as to distinguish it from Vol. II, but otherwise it worked well, and immediately provided interesting new information. Thanks Jan!

This Pescheck book is a welcome little goldmine of information for us. It appears to me that Pescheck's ancestor, perhaps his nth-great grandfather, was one of the persecuted Bohemian Protestants. Pescheck is not entirely negative toward the Catholics, and writes also about those he respects, for example Pessina, Balbin, and Pelzel.

One would like to know more about those "coals" that Mnissowsky was getting from the Jesuit "colliers".

Jan is researching Pescheck, as well as variations on Czech names that this book may help with. He apparently is a Bohemian by blood, transplanted to Germany.

Speaking of variations of names, and which may be complicated by transcription problems, ref. comms. #222 and #223, I am wondering if the Wendelini variation in his letter should be "Vendelinij" or "Vendeliny" or "Vendeliniz" rather than "Vendelinus" - really hard to tell from his letter in APUG, and would take comparing all his characters versions in the letter. He does clearly spell out "Ricciolus" rather than write "Ricciol9". He writes an interesting long word, something like: Anagrammatismorui9.

Also, regarding item E.) in comm. #222, I now wonder if it might be transcribed "Jean de Bignec" rather than "Fran de Bignec".


From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent: Tue 10/28/08 2:29 PM

Subject: J.VS: Asterisms in Voynich illustration f85r2

Dear Colleagues

As you recall from off-J discussions early this last September, I was struck by a peculiarity in the Voynich f85r2 cosmological illustration, namely: that the man at the top of the ring surrounding the sun is with his hand and its finger pointing directly at a group of dots which is located inside the upper-right fanning sprout of water (or whatever that is) which originates from the central ring. That group of dots, examined at best available resolution, appears to me to be intentional and organized.

The f85r2 panel is part of a 12-panel foldout. The f85r2 illustration is referred to by some as "The four ages of Man", a designation dating to well before the availability of the high-resolution SID images, and subsequently no longer convincing in my view.

The basics of the illustration are an inner circular structure residing within an outer circular text-bearing band. The inner circle contains a depiction of the sun, one with a face and the thick wavy rays, residing on a blue field. Four somewhat unevenly spaced-apart jets of water ? sprout radially from the central structure, and penetrate the peripheral circular band, and then bend back toward it and re-enter. The jets create four wedges in the overall circular diagram. In these wedges, on the inner circle surrounding the sun, are four male figures of different presentations. Blocks of Voynich text fill the wedges, and bands of text run around both the inner and outer circles. At about 9:30 o'clock on the outer band a rectangular device penetrates it, thus separating the ring of text there. Similarly a pair of parallel lines separates the inner-circle ring of text.

The four men around the central sun are variously easy or difficult to interpret. Altogether they do seem to convey a statement only about men, aside from women and children.

The man at 9 o'clock seems to have six fingers on his right hand, with which he holds out what I take to be a representation of a little "herb man", and so I see the 3 o'clock man as a cultivator of herbs, or a farmer. The man at 6 o'clock appears like a craftsman, artisan, or laborer. If this panel were known to be about maple sugaring, he would be the fellow operating the sugar shack. The man at 3 o'clock I take to represent a merchant or pharmacist holding a finished item of value in a bottle. The man at the top, presumably thereby symbolically the superior, by virtue of his pointing upward toward the sky with his hand signals himself as a provider of superior knowledge and guidance - thus he is a healer / doctor / philosopher attuned to the celestial, and its gifts of well-being and wholeness.

So it seems that an alternative (to four ages of man) simple integrated interpretation for these four men is that they represent specializations in the process of astronomy-related herbal healing: cultivator, preparer, pharmacist, and doctor: The four men of the art of herbo-astrological healing.

In the high-resolution SID image we see that there is a suggestion of the philosopher-doctor man wearing a finger-ring on an adjacent finger to the one he is pointing with. In the most minimal way this finger-ring arises from a rectangle with a single dot in its center. This finger-ring dot reinforces the suggestion that the dots in the fan-plume being pointed to are significant. We note that not uncommonly in the VMS, the drawings of hands seem to require reflections or mirroring, or even more, to make sense with the rest of the body presentation - that may be the case here too.

It appears to me that the two jets which frame the philosopher both contain within their outer fan-plumes groups of variously colored dots that together suggest patterns. The lower two jet plumes lack dots like these. The dots in the upper-right fan-plume are easier to become aware of as possibly significant, than those of the upper-left plume.

Let us consider the dots in the upper-right fan-plume. Now, if one is unfamiliar with the many subtleties in the VMS illustrations, then this group of dots might well go un-noticed, or even if noticed, be dismissed as having arrived upon the parchment unintentionally, and not be connected to the pointing philosopher, especially since in the illustration the pointing hand and the dots are quite far apart and also on opposite sides of the outer peripheral diagram band. There is a big scaffold-like stain to the left of the plume that may have been put there intentionally by the artist specifically to misdirect the thinking of the observer and increase the subtlety of the group of dots.

As you recall, I wondered if this group of dots in the plume, being directly pointed to by the philosopher, might be an intentionally rendered asterism, or some code signal. Indeed, if the f85r2 image is negatived, the area under consideration more takes on the appearance of a starry night-sky scene. Some of the group's "stars" are golden, some are plainer paint / ink, and especially in the negatived image this reinforces an impression of different brightness magnitudes. The color of some of the dots almost give an impression of metallic lustre in the sense of J.VS comm. #213. The largest dot appears to have structure: a thick perimeter surrounding either a hollow center, or a brighter center.

Assuming that the dots were intentional, then it is quite evident that they mean to convey either a pattern, or some numbers relationships - they are clearly not random in their relative positions. Suppose they are indeed stars in the sky - which ones? Which asterism or constellation? Our colleague Robert Teague expressed an initial cautious comment that the group of dots might suggest the constellation Perseus, though upside down.

Allowing for variability in the magnitudes of stars as observed by someone at an uncertain time in the past, centuries in the past, unknown as to with or without telescopic aid, plus allowing for how the artist managed to convey the relative magnitudes with those dots, further allowing for wear and tear of the dots over time, and perhaps even allowing for an apparently mirrored hand of the pointing man in f85r2 suggesting an abnormal orientation to be corrected for, I can indeed see how Robert can arrive with a first guess at Perseus.

My own best guess so far is that the group of dots indicate the Big Dipper portion of Ursa Major, plus underneath Leo Minor, as seen from mid-northern latitudes, late in the evening around the middle of November.

Although its stars were noted much earlier by the ancient Greeks as being in the part of the northern sky they called "amorphotoi" (unformed / unshaped), Leo Minor was named only about 1687, by the famous astronomer Johannes Hevelius (a correspondent of Kircher, and whose family traced to Bohemia). [1]

Leo Minor seems to hold surprises: the enigmatic and ghostly astronomical object "Hanny's Voorwerp", an irregular glowing green blob with a big internal hollow, was discovered there in 2007 by Netherlands high school physics teacher Hanny van Arkel. [2]

So then, if the dots are asterisms being pointed to by the f85r2 astronomer-philosopher-doctor, then presumably a further message is being conveyed in this panel. It has plenty of VMS text, which appears rather clean and normal by VMS text standards, and is easily transcribed. But since the VMS "text" is still an unresolved mystery, in the meantime other indications in the panel need investigation for further clues, including the aforementioned scaffold-like stain.

Logically, the next thing to do is to see if the group of dots in the upper-left fan-plume can be fitted to constellations or asterisms. I have been trying to this, but so far do not have anything I can suggest with confidence.

Berj / KI3U

[1] National Audubon Society Field Guide to the Night Sky, Mark R. Chartrand, astronomical charts by Wil Tirion, 1991/1995, Chanticleer Press, ISBN 0-679-40852-5

[2] What is Hanny's Voorwerp?, NASA Astronomy Picture of the Day, 2008 June 25, with photograph and description and more links:

From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent: Thu 10/30/08 6:52 PM

Subject: J.VS: Estimating the Geo-latitude of the Voynich f85r2 philosopher

Dear Colleagues

In J.VS communication #226 began an analysis upon the hypothesis that the Voynich f85r2 illustration showed one of its human figures, the one I named the "philosopher" or "doctor", pointing directly at a group of dots which were asterisms. My best guess was that the asterisms depicted the Big Dipper portion of Ursa Major, plus underneath Leo Minor, as seen from mid-northern latitudes, late in the evening around the middle of November. [1]

Exploiting this hypothesis further, can we obtain from f85r2 further information, specifically can we estimate the philosopher's geo-latitude?

We can easily come up with half a dozen reasons why, even given the hypothesis as being plausible, a latitude estimate will be quite imprecise. But let us proceed with the experiment anyway. Here is a strategy:

1.) Assume that the philosopher is pointing to the Big Dipper and Leo Minor as per stated above.
2.) Estimate in the f85r2 illustration the relative location of the north celestial pole.
3.) Determine for the philosopher a ground-plane in the illustration, that he is standing on.
4.) Measure the elevation angle of the north celestial pole with respect to the philosopher's ground-plane contact-point.
5.) Use the elementary astronomical geometry theory, that yields as practically equivalent the elevation angle of the north celestial pole with the northern latitude of its measurement.

Proceeding, I estimate that the north celestial pole would be above the Big Dipper, in the direction of the arrow formed by its two rightmost stars, by approximately the same distance that separates the Big Dipper from Leo Minor on the parchment. We see that as far as a practical estimate goes, the upper-right jet, specifically its inner blue line, can be used as the elevation radial for the elevation angle.

As before, we note that in the f85r2 illustration the wedges formed by the jets are unequal. That is, the angle that this jet has been drawn at, may have been drawn by considerations of fitting the illustration into the rectangular format of the folio's parchment, and not any astronomical considerations. But, mitigating for a possibly astronomical angle, is seen in how all four jets come into the inner circle: it is quite evident that the illustrator did, within limits of course, what he/she wanted to do with the angles of the jets at the inner circle.

The groundplane for the philosopher must be estimated from his body depiction. My best estimate then for the elevation angle of the north celestial pole implied under the hypothesis is 50 degrees.

Therefore, hypothetically the f85r2 philosopher is indicating his northern geo-latitude as 50 degrees.

The major European cities of likely Voynich manuscript interest that lie closest to a latitude of 50 degrees north are Frankfurt (the Frankfurt Fair), Krakow, and:


Berj / KI3U

[1] Journal of Voynich Studies communication #226 (28 OCT 2008, Vol. I):
J.VS: Asterisms in Voynich illustration f85r2

From Berj N. Ensanian
To Journal of Voynich Studies
Sent Date 11-02-2008 1:09:16 PM

Subject: J.VS: The Chateau de Lusignan castle of the Duc du Berry

Dear Colleagues

In the search for images of castles, both fictional, as well as real, so as to have comparisons for the castles depicted in the Voynich nine-rosettes foldout, we have a rich source in the illuminated manuscript:


This exceptionally beautiful 15th century work, begun about 1410 by the Limbourg brothers, is a classic example of the medieval book of hours for the wealthy. It was made expressly for the very wealthy art-loving Duc du Berry, a contemporary and patron of Christine de Pizan. Among the numerous period details to be seen in its illustrations are many of the Duke's castles.

There are some good quality reproductions of the manuscript's illustrations for the twelve months of the year available both in books (for example the medieval history books by Gies & Gies) as well as conveniently online:

" The extremely fine detail which was the characteristic feature of the Limbourgs needed extremely fine brushes and, almost certainly, lenses. " [1,2]

Details in these pictures, including subtly psychological, abound, showing us a tremendous range of medieval items from clothing through astrological themes, the styles of numerals in those times, and of course architecture. For example, we can study those "antennas" on castle towers, items that have received some discussion in connection with Voynich castles, here and on vms-list.

The December panel is interesting in that it seems to convey the impression that medieval people were conscious of a medieval artificial skyline. Our colleague Dana Scott just posted to vms-list under the subject "Medieval Skyscrapers", a notice of pictures of the towers-studded San Gimignano, stimulating comparison with the former Twin Towers of New York City.

But for comaprison with the Voynich castles, and keeping in mind that medieval castles often underwent changes, even major changes and expansions, the highly detailed picture of the now-no-longer-standing Chateau de Lusignan castle, seen in the month of March panel, is of particular interest to us I think: it is like conglomeration of smaller castles, and the smaller castle at the left is quite VMS reminiscent. The entire conglomeration must have been quite a sight during its glory years.

Berj / KI3U

[1] see: " How did they paint the Très Riches Heures? " :

[2] online images of the months illustrations of Tres Riches Heures are also here:

From Berj N. Ensanian
To Journal of Voynich Studies
Sent Date 11-02-2008 10:36:23 PM

Subject: J.VS: The Voynich f67-68 parchment: Heliocentrism versus Geocentrism

Dear Colleagues

The Quires 9 - 11 of the Voynich manuscript contain the book's astronomical, astrological, and cosmological pages. At the beginning of this astro-cosmological section Quire 9 is a single piece of multiply-folded parchment holding altogether ten illustrated text-bearing panels on its two sides:

67v2, 67v1, gutter, 68r1, 68r2, 68r3
67r2, 67r1, gutter, 68v1, 68v2, 68v3

and as we can painstakingly verify from examination of the parchment cuts etc. in the Beinecke SID images, Rene Zandbergen has provided a very clear diagram of the physical details of this piece of parchment, so that for example as per above, the f68v1 and f68r1 panels are directly-to-each-other on opposite sides of the parchment. [1]

Now let us consider:

Suppose that the total Voynich manuscript consisted ONLY of the f67-68 parchment - what would our impressions be of what it was all about?

In this Gedanken experiment we would have none of the strange botanicals, and the even stranger balneological folios, in our minds - they wouldn't exist. Neither would the strange "zodiac", code and star pages, and the nine-rosettes foldout and its castles and its other side, alchemical suggestions, and so on and so forth. This Gedanken experiment postulates viewing the VMS as just a single-parchment ten-page manuscript: the f67-68 pages.

Now, our colleague Robert Teague has for years advanced his belief that the portraits of Copernicus and Tycho are represented on the f68 panels. On 12 JUL 2004 Jeff Haley on vms-list strongly challenged list members to look at panels f67r1 and f67r2 as Copernican. And my own f68r3 PM-curve work pointed not only to Copernican knowledge in that particular panel, but actually at least Keplerian.

In our cosmology discussions recorded in J.VS communication #179 (Vol. II) our astronomer colleague Greg Stachowski stated:

" Copernicus lived across the turn of the 15th and 16th centuries, which is compatible with some assessments of the VMS dating, and his ideas published in 1543 were not universally accepted for another two hundred or so years, covering the 'late' range of datings. So a document with a geocentric cosmology could have been written a hundred years 'post-Copernicus'. "

Exactly. BUT, a ten-page, patently helio-centric book we would, conventionally, assign a genesis NO EARLIER than 1543.

What are our impressions of what this ten-page Gedanken book is all about? We see it has a strange and beautiful mysterious script. But the illustrations do not seem all that strange: it is rather easy to get the impression that the author is discussing, in his own way, and in varying degrees of complexity and precision across the ten pages, the theme of:

the heliocentric versus the geocentric traditions / views of the world.

Now, if this is accepted, then it makes not the slightest difference what the rest of the actual Voynich ms projects for its genesis period, Roger Bacon's time or even earlier; the book, Beinecke MS 408, was completed no earlier than Copernicus's revolution. And therefore a 15th century origin for the Voynich manuscript, a long popular notion, is ruled out, unless we wish to invoke a pre-Copernican, and obscure, heliocentrist as the VMS author.

With its mysterious script suggesting a need for great discreetness, we might ponder that this ten-page book was written during a time when it was still dangerous in parts of Europe to be openly discussing heliocentrism, say Galileo's time, in Catholic ruled areas.

My impressions are that the ten-page f67-68 VMS Gedanken book covers the heliocentric vs geocentric views rather comprehensively, from Graeco-Roman mythology as suggested in f68v1 [2], to hard advanced 17th c. level mathematical astronomy encoded in the f68r3 PM-curve, that is, scientific Copernicanism to at least Kepler. That is what the subject of the f67-68 mini-book is, it appears to me.

Other Voynich panels besides f67-68 also suggest, in my opinion, helio-centrism: we just worked in comms. #226 and #227 with an illustration, f85r2, that makes it quite difficult to analyze it even cursorily, without thinking that its author had thoughts of heliocentrism. But no matter, we can condense the entire Gedanken experiment to this simplification:

Any hypothesis claiming for the complete Voynich manuscript an origin earlier than the 16th century, must flatly deny that the f67-68 author, whoever he / she was, had heliocentric and / or Copernican thoughts.

Berj / KI3U

[1] R. Zandbergen, Voynich MS - Quire 9:

[2] The f68v1 illustration is quite beautiful in overall effect. Like elsewhere in the f67-68 parchment it has some spots on it that are lustrous in the sense of J.VS comm. #213. For example, in the 7:30 o'clock wedge, the central female face's wavy lock of hair ends at some stains, and there one of the stars gives some slight indications of a coppery luster. Copper is associated with the mythical goddess Aphrodite, the Roman Venus. Coincidentally, if we carefully measure the angle at which the lady is gazing upwards, using a line through the centers of her eyes, referenced against the horizontal of the Beinecke image frame, we get 47.5 degrees - this is just about exactly the elongation angle of the planet Venus.

From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent Date: 11-05-2008 11:10:44 PM

Subject: J.VS: Voynich Manuscript folios for heliocentric content evaluation

Dear Colleagues

To help investigations of the theme of J.VS communication #229 [1] I thought it would be useful to make a list of all the Voynich folios that seem to me to warrant consideration in discussions of the question:

Does the Voynich Manuscript author project thoughts of heliocentric astronomy?

The question as phrased is broad enough to encompass an author who may be pro, con, or neutral on heliocentrism, while nevertheless having it in mind. Conceivable also is a pre-Copernican author having heliocentric thoughts.

Before proceeding with the listing, it is I think good to remind ourselves, that the possibility of heliocentrism representations in the VMS, and those together with other VMS particulars making for a consequent implication of dating the VMS as a post-Copernican revolution (1543) document, is technically not really a recent idea.

For example, D'Imperio has plenty of information regarding John Dee (1527-1609) in the familiar hypothetical vein that he at some point handled the VMS [2]. But most importantly, D'Imperio presents the thoughts of Dr. Charles Singer in his 1957 communications with John Tiltman and G.M.J. Flemming, and it is clear that Singer considered the possibility of Dee not only having handled the VMS, but also being its originator. Now, unless one wants to assert that the Cambridge-trained mathematician John Dee, who began making his own astronomical observations in 1546, was oblivious to the Copernican revolution, the implication of Singer is that a possible author of the VMS (Dee) was familiar with Copernicus and heliocentrism.

So, by implication or direct suggestion, the possibilities of heliocentrism-familiarity on the part of the VMS author, and even explicit suggestions that Copernican heliocentrism is projected in some of the VMS folios, have now and then come up in Voynich manuscript proceedings, both within and without the VMS mainstream (in particular vms-list). And this has been against the background atmosphere of the traditional view that the manuscript dates no later than around 1550 at the latest. When the Copernican idea has come up on vms-list, it has not taken hold, and the vms-list archives show that the idea can be quickly squashed before it receives a reasonably fair exploration. [3]

TABLE 1 : Voynich folios for heliocentric content evaluation

1-1.) f57v : the code-wheel diagram, famous for its four repeated runs of 17 Voynich symbols. It has at its very center the archaic universal symbol of the sun: a little circle with a dot at the center. The diagram includes 4 persons around and oriented toward the sun symbol, and four concentric bands of Voynich text. At the bottom right of this folio, well below the circular diagram, is inked a large symbol that somewhat resembles a numeral "5". This symbol is rather close in appearance to one of the symbols for Jupiter given by the mysterious alchemist Basilius Valentinus (Basil Valentine) [4].

If it is assumed that this f57v symbol was from the hand of the f57v illustrator (and there seems to be no reason to think otherwise), and that it was intended to symbolize Jupiter, and that it is connected with the circular diagram, then one interpretation of f57v is immediately suggested: it concerns the four Galilean moons (symbolized by the diagram's four persons) orbiting Jupiter, discovered and announced by Galileo in 1610, and dealing a strong blow against Aristotle's conception of the world. If the VMS astro section does indeed discuss Copernican heliocentrism, and post-1610 at that, then the f57v panel is fittingly bound within the manuscript as an introduction to the subject. As for the 17, curiously, that number comes up a lot in Galileo's life, and in matters Jupiter to this day.

1-2.) f67-68 : see J.VS comm. #229 [1]. This group of ten panels includes the f68r3 panel with its PM-curve, which in my view projects at least Keplerian astronomical knowledge. [5]

1-3.) f69v_f70r1_f70r2 : these three panels may go together, depicting from left to right the creation of our star, the sun. Indeed, if one removes the mysterious Voynich text and goes by the illustrations alone, these three panels seem to depict a progression of a kind of mythological and organic Big Bang cosmology culminating in the emergence of the sun-god at the center of the universe.

1-4.) f85r2: Here we have an unambiguous depiction of the sun at the center of the illustration, surrounded by four divisions each containing an earthman, and, as noted by D'Imperio, perhaps the four seasons are being implied. And it is quite plausible that what the man at the top is pointing to, is star constellations at the upper right - see J.VS comms. #226 and #227 [6,7].

I ended the Gedanken experiment in comm. #229 with the suggestion:

" Any hypothesis claiming for the complete Voynich manuscript an origin earlier than the 16th century, must flatly deny that the f67-68 author, whoever he / she was, had heliocentric and / or Copernican thoughts. "

It is I think possible, in all seriousness, to conjecture a prediction: that those who steadfastly claim a VMS genesis prior to Copernicus, or in any case a VMS genesis completely unconnected with heliocentric thought, must either produce sound arguements against the above Table 1 folios, or risk eventually being relegated to the status of Voynich cranks.

Berj / KI3U

[1] J.VS comm. #229 (2 NOV 2008, Vol. II):
J.VS: The Voynich f67-68 parchment: Heliocentrism versus Geocentrism

[2] The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7.

[3] See for example the vms-list archive for what happened when our colleague Dana Scott in February, 2001, suggested, with details, that the VMS may be including depictions of a heliocentric universe.

[4] see entries for Jupiter in "A Table of Chymicall and Philosophicall Charecters" from Basil Valentine's "The Last Will And Testament" :

[5] See J.VS comm. #138 (8 JAN 2008, Vol. II):
J.VS: Comments on the Voynich f68r3 PM-curve question

[6] J.VS comm. #226 (28 OCT 2008, Vol. II):
J.VS: Asterisms in Voynich illustration f85r2

[7] J.VS comm. #227 (30 OCT 2008, Vol. II):
J.VS: Estimating the Geo-latitude of the Voynich f85r2 philosopher

From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent: Sat 11/15/08 1:47 PM

Subject: J.VS: Some proposed corrections to the voyn_101.txt transcription of the VMS

Dear Colleagues

As noted in the past, I maintain a corrections file (unofficial) for Glen Claston's voyn_101.txt transcription of the Voynich manuscript. The process of recording corrections has been random - arising when I come across something in voyn_101.txt that I think could be improved. Glen's tremendously valuable work still awaits an independent systematic check from beginning to end, an effort that would require time and dedication nearly comparable to his original.

The filename I use for the so-corrected voyn_101.txt is: voynC101.txt. I can send it to you per your request. Here below are listed the 26 corrections in the current voynC101.txt.

Table 1 : Proposed corrections to GC's voyn_101.txt transcription [1] of the VMS, per voynC101.txt, to 4 OCT 2008

GC( ){... = the original transcript as it appears in voyn_101.txt
?!(n){... = proposed correction

n = number of proposed (and done below) corrections in the transcript-line

Date of proposed correction / proposer: correction-identification number(s)

9 OCT 2006 / KI3U: 1-2

GC( ){65r.1}okaip.8ap.aeap=

GC( ){87r.1}foae2sae.2oGoy.9j1oGcosam.okco8ae.sam-

20 OCT 2006 / KI3U: 3-13

GC( ){86v5.4}9j1S9.oh9.2d9.4ok9.4okam.s,aie.1cj9.ekc79.8ay.oehay.ap-

GC( ){86v5.16}

GC( ){86v5.19}91C9k9kam.9hCo.1c9.2H9.2oh9.ok9.ok9.okan.oehC8-

GC( ){86v5.21}

GC( ){86v5.23}

GC( ){86v5.25}saz.han.ay.aeo3cc9.4oC9.ehcs9=

GC( ){86v5.28}Î.9kayay-

GC( ){86v5.35}

GC( ){86v5.37}81oe.1c69.4okan.okam.oe.1co.79.oe.hcco89.oyd*-

GC( ){86v5.38}s.oe.o8am.9hcc29.9k1c9.e1o89.9hay.2c9.9kam-

GC( ){86v5.39}9kco89.1c89.4okC9.oK9.79=

29 JUL 2007 / KI3U: 14-17

GC( ){104v.6}soe18.2oe.2coe.4oh19.1oho.e.1c89.3c89.4oWan.1C89.Gco.og1c79.4oka89-

GC( ){106v.28}g2co,89.oehC79.4oho,y.2cos.1ok9.4okam.okco89.okam.4ohay.ok9,89-

GC( ){107r.35}8am.%e.ehCoe.e,1c79.4oho,

GC( ){8r.4}4oko,y.1oy.1o,y.2cc9.81oe.2csc8.1ou.19.8ap-

30 JUL 2007 / KI3U: 18-19

GC( ){49r.1}gA2oe.89.2oy.2oe.2k19.2oyg1oy.og1oy.!oy,h19-

GC( ){49r.2}4okoy.2o.1ok,19.1o#9.4oj1ay.º.8oy.8am-

1 AUG 2007 / KI3U: 20-22

GC( ){103r.52}g1c7ae.okC9.4oe,hcc89.4ohcc9.4ok9.1cj19.4oj1c9.eham.okaes9-

GC( ){103r.53}s2c9.4ohc79.4oham.289.4ohcc9.1c89.4ohcc9.4ohC9.e1c79.eok9-

GC( ){103r.54}85C9.4okd9.7ay,1c89.4ohc9.4ok9=

10 AUG 2007 / KI3U: 23-25

GC( ){85r1.31}go8am.28ay.9j18ay.8ay.9j179.4ojoe.8ay.hc2Ay.818ae.1oe,az,9-

GC( ){85r1.32}9ko,

GC( ){85r1.34}92C7(.h2cc9.4ohoy.oy.1o8.eh1c89.4oko89.4ohay.2k9.okayay-

4 OCT 2008 / KI3U : 26

GC( ){36r.1}j1af8aN.4oyan.1Fae.som.Goy.#am.K9.8az-

Berj / KI3U

[1] The voyn_101.txt transcription of the entire VMS, and associated tools, are available online from Glen Claston here:

From: Berj N. Ensanian
Sent: Mon 11/17/08 10:40 PM
To: Journal of Voynich Studies

Subject: J.VS: The Voynich Manuscript: A Teacher's resource for the education of school children

Dear Colleagues

In Voynich work I have long been in the habit of employing a certain Gedanken device to help me generate and evaluate Voynich scenarios and ideas: creating Voynich fiction, often science-fiction, and runnning with the fantasy plots to see what they suggest for interesting new angles, and possibilities for connecting previously unconnected VMS research nodes. I was looking over one of these Voynich science fiction plots of mine that I was about to set aside in favor of starting a new one, when I thought that it might first be worthwhile to extract from it a piece and present it here. The fiction story from which the extraction comes is rather off the wall as far as realistic Voynich scenarios go, but that is not material, since the purpose of these fantasy devices is to stimulate the power of the subconscious mind into un-restricted thinking in the search for new ideas.

Briefly, the background story revolves around a science professor in a small college for teachers, Prof. Nom de Plume. Although de Plume teaches serious science, he has for quite a few years been something of a closet paranormal investigator, and through an encounter with a poltergeist he was first introduced to the Voynich manuscript, which soon became a favorite avocation. He is astonished when it transpires that every time that he makes what he considers to be a personal breakthrough in understanding the VMS mystery, the breakthrough is surrounded by a re-appearance of the poltergeist, which is apparently nudging de Plume toward a climactic event.

That climactic event is de Plume being confronted by advanced space aliens from a crop-circle UFO. The aliens, who refer to themselves as "The Society" tell him that they are the ones who long ago created and planted the Voynich manuscript, specifically as an experiment in selective breeding: those Earthlings who solve, or at least make significant progress toward solving the several mysteries presented by the manuscript, will be taken with the aliens as worthy specimens to live in the advanced world of The Society (who outwardly appear like ordinary healthy humans, dressed in the garb of monks). All other Earthlings will be de-existed as useless rejects, so that a new experiment can begin on Earth afresh, after a necessary clean-up and re-balancing of the environment of course. De Plume is told that it has been decided that the present experiment appears to be a near total failure, but that he alone has been chosen as the one Earthling to be saved. And in that he has no choice, like it or not, he will be taken to the new world to become a member of the Society, and there his new name shall be Noah.

De Plume is horrified that his "good fortune" may tear him away from those he loves, while also meaning the extinction of all other Earthlings. He weighs suicide as an escape from it all, but the Society who can read his thoughts and emotions at will, make clear they will not allow him, the one success of their experiment, to die, or lead his new life unhappy. They further assure him through demonstration that they are masters of space-time-memory, and thus the reject Earthlings will never know that anything extra-peculiar happened to them as they are faded out of existence.

De Plume then pleads with the Society to give him approximately one percent additional of the already completed duration of the experiment, so for him to try to produce more Earthlings worthy of being saved. He argues that since he is deemed a worthy, then his opinion on extending the experiment slightly should be taken as a reasonable win-win proposition: the continuation may yield more worthies and thus make for an improvement in the Society's current experiment, while de Plume gains some Earthling companions in his new, and inevitable life in the new world.

The Society agree to this, but on the condition that de Plume must operate completely consistently within his present situation: a science professor in a small obscure teacher's college, and of course that he not discuss with anyone, especially those he is motivating, about his encounter with the Society and its VMS connection, unless they figure it out on their own. The Society decline to tell de Plume when the continuation of the experiment will abruptly terminate, but de Plume figures he has about four to five years to create a condition that results in some Voynich-awakened minds who are producing breakthroughs in the mystery.

Well of course after more hair-raising adventures de Plume eventually succeeds to some extent and also gets the girl in the end (one of the teachers in his science class) and all that, but the important part is his strategy for trying to ignite a symbiotic mental revolution chain reaction among teachers and their students, one focused on the Voynich Manuscript mystery. De Plume knows that on completing his general science course, all his teacher-students graduate and are slated for positions to teach children from grades five through nine in schools all around the country. De Plume comes up with the idea of introducing, right at the beginning of his general science course, the Voynich manuscript problem as an ideal philosophical reference for all the general science, and mathematics, that is to come in his course.

And so de Plume prepares the opening lecture of his course for his class of teachers, and so as to be sure that they all have a standard set of good notes, he distributes a hand-out before beginning his lecture.

Below is Prof. de Plume's hand-out to his class, in the above Voynich science-fiction fantasy.

Berj / KI3U

+ + + + + + + + + + + + +

The Voynich Manuscript: A Teacher's resource for the education of school children

by Nom de Plume, a fairly longtime student of the Voynich Manuscript

Dear Thinkers, a subject long of special interest to us is the process of stimulating bright young minds to expand their spectrum of conceptions, that is to say expand their mental horizons. Insofar as it is useful to have a philosophical reference, one sufficiently broad and deep in scope so as to remain useful for nearly all matters of learning that may come up, I suggest consideration of the serious study of the socalled Voynich Manuscript, the VMS, Beinecke MS 408. Here then follow my purely personal opinions on the possibility of connecting the process of the expansion of bright young minds with the study of the VMS.

On account of its polymathic multi-disciplinary challenges, the Voynich manuscript mystery makes for an excellent study project for students, even pre-university students. Actually, if the popular television program "Are you smarter than a 5th grader?" is any indication, bright school children even of that early grade could be productively introduced to at least redacted portions of this remarkable mystery: its depth is second to no fantasy-mystery, while yet being thoroughly grounded in highly serious scientific and scholarly realities.

The Voynich field is so rich, so intrinsically and thoroughly a polymathic cornucopia, that it provides something of great interest for everyone who likes to learn, from the highly mathematically inclined to the artistically inclined. And every sub-field of Voynich study continually demands background historical research: Voynich work continually forces the serious student to evaluate realistic boundaries of space and time, far and wide, past, present and future, within which the Voynich drama takes place. And continually the student is confronted with the sobering reality check that so many brave and bright dedicated Voynich researchers since the beginning of its modern study just before World War I, have failed to make breakthroughs, despite their best, and sometimes lifelong efforts.

If the Voynich mystery, as a learning opportunity, is not utilized by teachers at grade-school level on up, then it is a shame: the field is bursting with ever-exciting opportunities for stimulating the development of young minds.

Now, above the Voynich-tourist level the field can rapidly become exceedingly complicated, and teachers, previously unfamiliar with Voynich studies in detail, could use some guidelines for productively challenging those of their students who are interested in giving the field a try. For example, some good questions that a teacher could pose are:

What happened in the year 2004 that suddenly and seriously challenged the validity of many previously held Voynich notions? Were there psychological consequences of this among longtime Voynich researchers and students, and do the consequences continue to linger in the present day, and if so, to what extent? Is there such a thing as a kind of mass Voynichosis among certain factions of mutually validating Voynich workers, and does its primordial inertia work to retard serious progress toward resolving the mystery, yes or no?

A teacher getting into this field seriously must become aware that in Voynich studies it is the easiest thing of all for a newcomer to be bamboozled by Voynich smoke where there is no Voynich fire, puffed out by a broad spectrum of sources, from outright Voynich cranks taking advantage of the mushrooming exposure of all things Voynich due to the web-internet, through fame-and-fortune seekers of varying grades of Voynich expertise angling for a Hollywood deal, to truly serious workers who deep down have realized that they published mistakes but haven't corrected them.

The newcomer must realize that just under the surface, the Voynich field is often driven by intense emotions - the subject is after all "the world's most mysterious manuscript", an artifact exceedingly rich in details, yet nevertheless to date almost supernaturally resistant to being definitively anchored to one or another historical tradition: it often generates frustrations in those who primarily seek the mystery's resolution. The quest itself though provides phenomenally rich rewards in both knowledge, and opportunities to test oneself in many different ways. But the quest to definitively solve the mystery, and thereby claim a unique prize of sorts, even has political angles to it: tribal competitions we might say, for example cryptographers versus linguists, or thislanders versus thatlanders.

And so, besides attracting formidable thinkers, the manuscript naturally baits the egos of various unconsciously self-styled dragon slayers. The newcomer must, in order to avail themself of accurate and precision facts, learn to judge the relative worth of various sources of Voynich information, must learn to recognize the plagiarists from the real creative sources, must learn to recognize even complicated cases where a source possessing a rather obviously good mind and having promise to contribute substantially toward illumination of the mystery, is nevertheless fatally prevented from doing so by their own characteristic and unshakable arrogance and need to come off as sober, erudite, and distinguished, in the eyes of established conventional circles.

This is one of the characteristics of the Voynich field that is so valuable in schooling: its unique deep mystery is especially good for young students learning the skill of sifting and distinguishing among Voynich talkers, those of merely propagandized expertise, from those of genuine analytic intellectual power and imagination and command of the details of the subject. The serious student has the opportunity to observe and study fine thinkers struggling through mistakes that are far more interesting than the best correct efforts of ordinaries, and observe and study the phony pseudo-intellectuals in action and learn their tell-tale signs, for example an over-reliance on Popperism arguements. The serious student is reminded, for example, that physics reached the quantum physics stage before Popper was even born, and didn't need to be told about "falsifiability" and so forth: a genuine intelligent data-producing researcher in every field routinely has such principles in mind, whether or not with fancy and fashionable labels attached to them. Would Plato and Euclid be in need of being educated about "falsifiability"?

There is no "Voynich expert" in my view. There hasn't been a single one since the field was born with Wilfrid Voynich's announcement of his unique manuscript early in the 20th century. For, a Voynich expert would be one who could immediately, unambiguously, and indisputably, demonstrate WHO created Beinecke MS 408, and WHY he or she created it. At the present time every Voynich "expert" pretender can be instantly brought to their knees with: INDISPUTABLY WHO? and WHY?

But, there have been, and are today around the world, some advanced students of the Voynich manuscript. And some of them are immensely good thinkers. Their number is not great, and they are surrounded by a greater number of advanced-student poseurs. We also distinguish among the advanced students those who are active and superb researchers, devoting countless unpaid hours to develop new data toward the illumination of the mystery. They not only study the problem in depth, but also go and produce data and generate new experimental ideas for other advanced students to evaluate and utilize. As this present essay is all of opinions, I, de Plume, write my opinion that you dear thinker, the teacher preparing to evaluate the relative worth of Voynich workers as sources, might consider:

Does this person project, insofar as goes their Voynich authority, as their absolutely highest motivation the drive for truth, and the excitement of its discovery, un-corrupted by baser motives like applause, or even dispenser-of-applause? That is to say, if this person were trans-imagined as a hermit who came upon the solution of the Voynich mystery, came to discover the definitive answers to the WHO? and WHY?, could they then be fulfilled and require nothing more for their fulfillment?

This thought does not at all invalidate the natural procedure of advanced Voynich workers interacting publicly and satisfying the natural inclination for community involvement. Rather, it is an analytic mechanism for evaluating a Voynich-world personality: deep, deep down, what do they really want out of their involvement with the Voynich mystery? Do they seem like they could be well satisfied being involved with the mystery, without also being visibly involved with the public Voynich world, or even privately as a guru to some little cultic band? Is the Voynich mystery equally if not merely a vehicle for them to satisfy a primary drive for self-serving attention? What is the "smell" of this source - what's this guy really after? Are they producing genuinely valuable VMS and VMS-relevant data, or producing mainly slick public relations for themselves?

What sort of work does it take to become an advanced Voynich student? Suppose an intelligent and learning-loving young newcomer, already well educated generally, and without excessive fear of asking "dumb" questions, learns of the Voynich manuscript mystery today, becomes hooked on it, and with all dedication embarks upon serious Voynich study - when will they arrive at the advanced student level? In my opinion it will take at least five years of dedicated study to reach the level of advanced Voynich student. At least.

It will take that long to read the past and current Voynich literature, print and electronic, and grasp it well enough to follow and gauge the commentary and work of the already advanced students. It will take that long to become sufficiently familiar with all the polymathic foundations of the field. It will take that long to become good at recognizing who is a serious and advanced student worth reading, and who is just a polished phony. It will take that long to recognize advanced students who, although perhaps likely to be wrong with their long-running hypotheses, nevertheless are consistent fountains of fresh and good inspiring ideas; since failure is routine in Voynich work, the consistent production of good new ideas for the next attacks on the problem is essential. Endless fuzzy rehash commentaries and debunkings and dismissals are cheap, but real good fresh and new ideas are not, even when initially sketched and adumbrated in far from perfect form.

It will definitely take that long to become sufficiently familiar with the details of the central focus of the mystery: the Voynich manuscript folios. The alert student will observe that an astounding fraction of those who out there manage to portray themselves as Voynich authorities, are in reality woefully clueless about what is, and is not, actually on the Voynich folio parchments.

It will take that long to understand, that although the hypothesis of the VMS being a variation of hoax presently still retains a non-zero possibility, there have been and still are out there Voynich cowards in prestigous positions, people who fear the manuscript's power to unmask their weak comprehensional capacities and threaten their social and professional status, and who shield themselves from this threat by arrogantly dismissing and even hindering when they can the serious study of the manuscript and its students, by implying that it is a mere hoax unworthy of serious effort. The newcomer must learn to distinguish these types, however rare might be an encounter with them, from those who pursue the hoax hypothesis quite seriously and with dedication.

It will take that long to grasp, and grasp via often painful self-surrender of hard, hard, but ultimately wrong work, why this manuscript justly deserves its label "world's most mysterious manuscript". That a dedicated study of the VMS, regardless of what it is, is a truly rewarding intellectual challenge. It will take five dedicated years of work to reach the point where not just luck, but accumulated knowledge and skills are responsible for producing one's contributions to progress. At least five years it will take.

Lest that seem exaggeration, the teacher may consider just how little solid progress has been made in a hundred years of serious Voynich study. Really not much that is both indisputable, and potentially of major value. Captain Prescott Currier's principle of the Voynich "text" line being a functional entity, announced by him in the 1970's, comes to mind as appearing to be one of the few really major breakthroughs of the last hundred years. There aren't many, and as far as the Voynich manuscript's true history goes, as opposed to its endlessly and widely parroted standard theoretical history, we still don't even know for certain where Wilfrid really got his manuscript - from an Austrian castle, or from the Italian Villa Mondragone, or somewhere else, say from the Library Ambrosiana via his friend Achille Ratti (later Pope Pius XI). And it is an unpleasant fact that we still do not have a single indisputable historical reference to the Beinecke MS 408 Voynich manuscript. In tune with Socrates I know that I do not know much at all for sure about the true history of the Voynich Manuscript.

To make the field of Voynich studies a learning laboratory naturally involves building a tremendous collection of polymathic resources. But the newcomer student's first requirement is a minimal road map for sources specific to the VMS:

1.) Begin orientation with a timeline. The Library of the Journal of Voynich Studies has available online an extensive interactive graphic timeline. Primarily the work of Greg Stachowski, and a work in progress as time permits, it is the best VMS-specific timeline available. [1]

2.) Kennedy and Churchill's popular Voynich book is an easy-reading introduction to this complex field, but be aware that hard-print Voynich material can go out-of-date quickly. My view also is that at the end of their book the conclusions of the authors about the VMS are far less impressive than their presentation of the subject, although with the VMS that is hardly unusual. [2]

3.) Make a decision: to be or not to be on the track of advanced Voynich student. If the decision is to seriously progress on a track toward advanced student, then immediately obtain a copy of D'Imperio's book, read every spot of ink in it, and keep it handy and re-read it for as long as you are involved with Voynich work - it still remains the one and only indispensible reference text in serious Voynich studies, and the use of this book is the sharp dividing line between perpetual Voynich tourists and serious students. With D'Imperio the student will learn, in addition to everything else, what other names to research and what other literature to track down and read. D'Imperio's book, inspired by and built upon the notes of Tiltman, is a masterpiece of 20th century serious literature: the condensing into a comprehensive reference text a broad-scope survey of a unique and extremely complex enigma. [3]

4.) The images of the Voynich manuscript, at all available resolutions, that are provided online by the book's custodian, the Yale Beinecke Library, must be studied over and over. It is advisable to build one's own inventory of image crops showing folio details of interest. It is to be noted that as regards commentary on the VMS, the Beinecke is no more immune than anyone else, to errors, and to inclinations to propagate as fact unproven hypotheses:

" The codex belonged to Emperor Rudolph II of Germany (Holy Roman Emperor, 1576-1612), who purchased it for 600 gold ducats and believed that it was the work of Roger Bacon; .... " [4]

Actually, among advanced Voynich students, especially in private conversations, the attitudes toward the Beinecke as the VMS custodian, are mixed.

5.) Rene Zandbergen's Voynich website, updated to October 2004 and now preserved as a classic by Dana Scott, remains the best online resource for a vast range of Voynichiana. Advanced Voynich students periodically return there for details. For the newcomer to this site it is well to take the homepage hint and start with examining the site's road map. As regards some details in the standard theoretical history of the VMS, I regard Zandbergen's view as "optimistic". [5]

6.) The online vms-list Voynich Mailing list, dating from around 1991, and now owned and administered by Dana Scott, is where the full spectrum of Voynich talkers meet. Or collide, and snarl at each other. Or make a point of flattering or ignoring each other. Or bore each other. The proceedings of the list itself are an interesting study, psychological and sociological, and sometimes comical, and sometimes naive, and sometimes remarkably inspiring and insightful. Now and then the proceedings seem weird, as if press agents are seconding for ego-challenged ghost members of the list. It is a major effort reading the vast archive of the list from its beginning, the portions of it that are available online, but for an advanced VMS student the thorough familiarity with this polymathic treasure trove is necessary. [6]

7.) Extensive Voynich websites in languages other than English are still few, but this could change. The pioneer in this is Jan Hurych (Czech language), and presently Elias Schwerdtfeger (German language) having branched out from an online forum founded by Jonathan Dilas, is also rapidly building an excellent body of work. [7]

The unique nature of the Voynich manuscript mystery is such that it produces non-negligible effects in the personalities of its pursuers. It affects emotions, self-esteem, and perceptions and judgment-abilities, and in some it affects even their dreams. Going into the field at the beginning, the motives for going in can be expected to have a major influence on how the personality will be affected over the long-run. If the motives have significant components of egotistical dragon-slayer, or rank opportunist syndrome, the possibility is real that the personality will eventually suffer, and become less admired by others in general. But if the motive is to take advantage of the unique polymathic reference that the VMS provides, for the pure sake of learning, for the pure sake of the discovery of truths, then like a wonderful poem in progress the personality may gain radiant joys.

Prof. Nom de Plume

[1] J.VS Interactive Voynich Studies Timeline:

[2] The Voynich Manuscript, The Mysterious Code that has defied Interpretation for Centuries; by Gerry Kennedy and Rob Churchill, 2006, Inner Traditions, Rochester Vermont.

[3] The Voynich Manuscript - An Elegant Enigma, by M.E. D'Imperio, Aegean Park Press, c. 1976-80, ISBN 0-89412-038-7




[7] Journal of Voynich Studies, communication #219 (26 SEP 2008, Vol. II):
J.VS: Some non-English language Voynich websites

From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent Date: Mon 11/24/08 10:53 PM

Subject: J.VS: T-glyph Codes

Dear Colleagues

Here and there throughout the Voynich folios there are devices which motivate speculation that they may be cipher elements, or codes, or in any case variously steganographic information carriers. If we allow the notion that indeed the VMS may exhibit a broad spectrum of secret communications mechanisms, then the variety and number of these speculative devices is considerable.

For example, lets have a quick look at the roots of the plant in the Voynich botanical illustration f96r. Going down the stem, the root bifurcates, with the left main branch becoming six appendages, and the right main branch, five. The spaced apparent dots coming down the stem turn into strokes in the root parts. A close look at the strokes shows they have considerable variety, from straight, to forms resembling "c" and "L", to suggestive of "o". One wonders if there is some sort of code here. If so, possibly it is tri-graph based, where a basic unit is three consecutive strokes, with the individual strokes taking on one of the variational forms, and the simplest code is: straight straight straight.

Turning to another possibility, in J.VS communication #49 we looked at what I termed "T-glyphs" in f67r2 [1]. These T-glyphs are also seen on one of the "jars" in the pharma section folio f89v1. Lets have a look: the jar is the green one at the upper left of the folio [2]. It's a bit difficult to tell where its lid meets the jar's body, but nevertheless it is easy to see that moving up from where the green coloring ends, soon there comes a band with some double-T glyphs: pairs of T's, rotated so that their tops face each other.

A close look at these T-glyphs in the high-resolution SID image of f89v1 shows something quite interesting: we can get the impression that they were inked twice, perhaps requiring a magnifying lens, with the second inking reinforcing only portions of the T's. Across the band, the double T-glyphs seem to exhibit, via the second inking, four basic glyph sub-elements for each half, that is each T, of the double-T: long or short straight stroke, angle-bracket, and full T. Only a really close look would notice this. Thus, whether or not the artist who drew this jar intended it, we are seeing a perfectly plausible steganographic communications mechanism. Curiously, we know many Voynich text letters also give the indication of partial, and plausibly system-determined re-inking.

What is remarkable is that as simple as this selectively re-inked double T-glyph stego mechanism is, even in a straightforward scheme each double-T can project one of at least 36 different codes. Therefore each double T-glyph could easily encode any of the letters of the Latin alphabet, and even allow for two or three different codes assigned to some of the letters, say the most frequent ones, like e and s.

If both no re-inking, and total re-inking are also viable, then we get 38 possible codes. On the f89v1 jar, the outermost glyphs show possibly further expansion: the leftmost double glyph appears to have both T's in the same orientation, and the rightmost double "glyph" appears as just an ordinary pair of ornamental parallel strokes. Yet another codes expansion possibility is the order of the T-glyphs, as they are read proceeding from some reference position: each successive T-glyph pair, second, third, fourth and so on, might be assigned to its own different coding table. And yet another possibility is that certain T-glyph codes signal that a nomenclator table, rather than an alphabet table, is to be used. Needless to say a T-glyph pair could simultaneously encode both a table of alphabet letters, plus a table of numerals, Hindu-Arabic or Roman.

In any case, the band of T-glyphs on this VMS upper-left f89v1 jar can easily encode a word of five to seven letters size.

Now of course this type of steganographic device is limited as to the range of its uses. It would seem to work well as a decorative design in illustration elements, especially in densely and variously populated, and apparently quickly and / or crudely drawn illustration frames, like the VMS f89v1 folio. Or as a border decoration, where perhaps only part of the decoration carries payload and the rest is filler.

In the VMS we might conjecture that the T-glyph system is being used as just another member of a suite of secret communications techniques that is being explored, or being demonstrated. But it is possible to imagine a scenario where these T-glyph codes could be employed as the main carrier of routine clandestine communications. We get the basic idea for the scenario from the story of World War II spy Velvalee Dickinson. [3]

Mrs. Dickinson, a doll shop owner normally in routine communications with suppliers and customers far and wide, used steganographic so-called "doll code" to communicate her espionage findings. Her doll code is quite different from the present T-glyphs scheme, but that's not the part of Velvalee's story we can borrow and adapt. Rather we can imagine, while also borrowing from VMS f89v1, a scenario where a T-glyph communicator, by profession a designer of fancy jars, or for that matter a designer of decoration-rich anything, say fabric, is routinely exchanging variously rough or finished drawings within a network of suppliers, manufacturers, and customers, and within that network are fellow T-glyph communicators.

If the T-glyphs in the VMS folios are indeed bearing secret messages, we need more clues, perhaps from nearby text labels, to figure out what the code tables being used are.

Berj / KI3U

[1] Journal of Voynich Studies, communication #49 (23 JUN 2007, Vol. I):
J.VS: The f67r2 circle-perimeter patterns: are they simple codes?; by Berj / KI3U.

[2] Although some of the VMS pharma section cylidrical objects are rather controversial as to what they depict, say incense burner, microscope, mist dispenser, or decorated alchemical distillation column, this particular one of f89v1 really does seem to be depicting a straightforward albarelli apothecary jar with the abarello shape, atop a conical / horn base. Its one detail giving concern is its solid cover-lid, which speaks for later historical dating than is the usual in Voynich manuscript genesis considerations.

[3] The Case of the Treasonous Dolls, THE FBI: A Centennial History, 1908-2008, FEDERAL BUREAU OF INVESTIGATION - FBI History - Famous Cases.

From: Berj N. Ensanian
To: Journal of Voynich Studies
Sent: Tue 12/09/08 11:47 PM

Subject: J.VS: The steganographic Angulis Crucis cipher-codes of Bernardus de Martinitz in Kircher's papers

Dear Colleagues

The steganographic T-glyph codes discussed in J.VS communication #233 [1] motivated me to look for more about them in sources of general interest to us. So far, my searches being by no means exhaustive, I have not found any discussion of them, much less one with a decoding table. However, among Athanasius Kircher's papers there is a crypto system with notable similarities that was used in correspondence between Kircher and one Bernardus de Martinitz, and luckily we have Kircher's decoding notations, and they are sufficient to reconstruct at least one fairly complete table of correspondences with the Latin letters alphabet. Tentatively, it appears to me that the name of this system seems to be "Angulis Crucis", possibly being a creation of Bernardus. It is well worth some attention, if for no other reason than a reference system, so let us get its basics in hand.

The name "Martinitz" or "Martinicz" has come up in Voynich work, for example:

" Marci seems to have been torn four ways in his professional career between the Protestant German princes to the north, the Jesuits, the Bohemian Holy Roman Emperor, and the Pope to the south. Count George (Jaroslav) Adam de Martinitz was certainly one of Marci's more colorful acquaintances. ..... " [2]

There seem to be several individuals, some clearly related, with variations of this basic name, plus associated names, for example "Smeczansky", that come up in general Voynich research of the 17th century. Jaroslav Martinitz, died 1649, famously was one of the Prague Defenestration victims of the Bohemian Protestants in 1618 [3]. As we know, he survived the devastating Thirty Years War fairly successfully.

Then there was an ambassador to Rome, Count George Adam de Martinitz, active in the 1690's [4]. He might be a grandson of the Defenestration Martinitz, and named after him.

In this Martinic spectrum, which may well be mostly one same family, there is one Bernardus Martinitz, a correspondent of Athanasius Kircher, at least in the 1640's and 50's, who used a novel crypto scheme, resembling the T-glyphs, which Kircher decoded right on the original letters of Bernardus.

Before we look at these letters, just who is this particular 17th century Bernardus de Martinitz, who corresponded with Kircher? There can be some difficulty in sorting him out amid terms like "S.R.I." and later 18th century "Rosicrucian Martinists".

An Italian document on the familiar Juan Caramuel Lobkowicz (1606-1682) and the "recapture of Bohemian conscience", mentions, even in connection with steganography, the "Sig. Bernardo di Martinitz Conte del S.R.I.". Apparently this Bernardus was a fellow of some importance in Bohemian circles of the time, a Burgravio / Burgravius. As you know my Italian is not to be relied upon, but this document may be indicating that Bernardus lived 1603-1685, and was the second son of the famous window-navigating Count Jaroslav, and that he also comes under the names Bernhard Ignaz Martinitz and Bernhard von Martinitz. Kircher, and especially Marci appear in this document also (and Arriaga, and a "S. Santita"), and there seems to be considerable discussion of Jesuits in 17th c. Bohemian politics, possibly carried on back then under aliases or nom de plumes. I wish I could read this document fluently - it seems to tell a very interesting story. [5]

It appears that Bernardus had some role with Kircher on a work on Cabala, possibly as part of Kircher's network of patrons. [6]

Now to the letters. The Kircher APUG 555 and 556 have a fair number of Marti*** letters, but we must be careful to distinguish Bernardus Martinitz from Maximiliani Martinez, not so much due to the similarity of the names, but because of the revised-over-the-centuries Kircher documents catalog identifications. I was able to find in APUG some of the letters of Bernardus de Martinitz, and it appears to me that in addition to Latin, he also wrote to Kircher in Italian.

Bernardus's letters in APUG 556 exhibit indications of obliterated writing of the type explored in J.VS communication #221 [7], and also some paper cuts that have removed portions of the writing. But here we will look at some encryptions he wrote inline with his Latin, in two of his letters to Kircher. The letters appear to discuss Trithemian themes. One of them, APUG 556 308-309rv, has "per Doctorem Marcum" in a sentence with the cipher. This might well be our Joannes Marcus Marci. Here are the two letters, written in Latin:

APUG 556

314-315rv = 17 MAR 1640 Prague letter to AK from Martinez in Prague; the heading of the letter specifies "Angulis Crucis", apparently about steganography and/or spiritual symbolism in the exhibited angle-brackets cipher; with AK's decoding; has "herbarum" on 314v; possibly s=z in code on 315v; a crossed circle on 315v likely related to the angular codes; signed in cipher: Bernardus Martinics.

308-309rv = 22 SEP 1640 Prague letter from Bernardy a Martinitz with angular-glyphs cipher; with AK's decoding; mentions Ignatus & Trithemy; exhibits ligature-form GC-k; 309r has "per Doctorem Marcum".

As you can see in these letters, Bernardus's crypto system is based on four simple corner symbols. A pair of them are used as digraphs to represent a single Latin alphabet letter. Thus a total of 16 different digraphs are possible. In Bernardus's letters the codes are written as a linear digraphic script, but their steganographic potential, similar to the T-glyphs, is immediately obvious - they might be used as a border decoration for example.

We see that Kircher has notated his decodings above the angle codes, sometimes too hastily. With a suitable transcription system we can conveniently obtain a table of correspondences of the angle code digraphs and Latin alphabet letters.

Let us define a simple TRANSCRIPTION SYSTEM as follows: Draw a square. Each of its four corners, with full arm lengths, give the four basic angle symbols used in Bernardus's system. Inside the square, write at the lower-left corner an "L", an obvious choice of transcription symbol for that corner. Write an "R" into the upper-left corner. Write a "T" into the upper-right corner. And finally write a "J" into the lower-right corner. We now have all we need for transcription. Let us call it: the LRTJ transcription system.

Following Kircher's decodings, here in LRTJ notation are the values of Bernardus's cipher codes, as I can determine them:

Correspondence Table, Bernardus's Angulis Crucis cipher-codes and Latin alphabet as determined from Kircher's notations in Bernardus Martinitz's letters of 17 MAR, and 22 SEP 1640. (Note: dots, in some way, may be part of the cipher system.)

LRTJ transcription digraph = Latin alphabet letter(s)

JJ = a
LJ = b, p
TL = c
TJ = d, t
JL = e
LL = f
RL = g, j
RJ = h
JR = i, y
LR = l
RR = m
TR = n
JT = o
LT = r
RT = s
TT = u, v

Values for the five letters k, q, w, x, z, are not available from Kircher's decodings in the two Martinitz letters examined, although from Bernardus's coded signature in his 17 MAR 1640 letter it is possible to conjecture the tetragraph assignment: TLRT = cs = z.

It is also seen from the above that Bernardus expects the decoder to employ some mild context clues, for example to figure out which value, b or p, is correct [8]. Thus it is possible that if German were to be written, using the letter "w", that the coding for it would be the tetragraph: TTTT = uu or vv = w. Another possibility is that the system uses a combination of unigraph and digraph, where the digraphs are as in Table I, and an additional 4 unigraph codes are available, covering k, q, x, and z. [9]

Perhaps if some other Martinitz letters in APUG can be found we will obtain values for the uncertain letters. I am assuming that Bernardus's system assigned the angle codes to alphabet letters as graphic glyphs, making it flexible as to how they would be used as regards Latin versus vernacular languages, and pronounciations. In other words it seems quite reasonable to me that Bernardus's system would support all familiar 26 alphabet letters, and not just say 23 for Latin language communications. Quite possibly we can learn more about the system by translating and reading Bernardus's letters, especially the 17 MAR 1640 one. It would be a lot of work, but should not be too difficult to transcribe, as the handwriting is fairly clear.

Lets try Table I. with the opening of Genesis in the Vulgate Bible, per {V -8} in J.VS comm. #203 [10]:

1.} in principio creavit deus caelum et terram terra autem erat inanis et vacua

We have all we need in Table I. to code this in Bernardus's system:


Some apparent same-glyph digraphs and trigraphs have been created. [11]

Lets have a look at the symbols frequencies:

Table II.
Symbols : frequencies for 2.}

J : 45/126 = 0.3571
T : 38/126 = 0.3016
L : 23/126 = 0.1825
R : 20/126 = 0.1587

Very roughly, the table shows half of the symbols, J and T, together carrying about twice the load as the other two symbols carry together. Thus if each Bernardus symbol had an equal probability of appearing in any position in the symbols series, we would get bunching, or high density of the same symbol in some areas of the series. We can see this happening in 2.}, contributing to the creation of apparent same-glyph n-graphs.

On the second-last page of his 17 MAR 1640 letter Bernardus hints at concatenation of the groups:


Expressed in their anglular glyphs this series now readily suggests the steganographic possibilities, for example running the series as a border decoration in an illustration, and if need be adding filler glyphs at the ends to complete a border circuit.

We see that the concatenation in 3.} has created more apparent same-glyph n-graphs, including a JJJJ tetragraph.

In a 1 DEC 1650 letter of Martinitz, APUG 556 279-280rv, wherein Trithemius is again mentioned, he exhibits some interesting devices around Roman numerals that may be of interest:

Berj / KI3U

[1] Journal of Voynich Studies, communication #233 (24 NOV 2008, Vol. II): J.VS: T-glyph Codes; by Berj / KI3U.

[2] vms-list post: VMs: Jaroslav Borzita Graf von Martinitz; Tue, 16 Nov 2004 00:32:52 -0700, by Dana Scott.

[3] The Reformation And Anti-Reformation in Bohemia, by Christian Adolph Pescheck, 1845, Vol. I. See J.VS comms. #224 & #225 (J.VS Vol. II) for how to download this book.
An engraved portrait, which I believe is the Defenestration's Martinitz, is online here:

[4] Biography - Pope Innocent XII, 1691-1700, The Papal Library:

[5] Juan Caramuel Lobkowicz (1606-1682) e la Riconquista delle Coscienze in Boemia, by Alessandro Catalano:

[6] Cabala Hebraeorum, Kircher, Bernardo S.R.I. Comiti De Martinitz, 1652:

[7] Journal of Voynich Studies communication #221 (13 OCT 2008, Vol. II): Image artifacts, or obliterated Voynich-similar script?; by Berj / KI3U.

[8] There are some similarities between Bernardus's values table and the experimental minimal alphabet considered in J.VS communications #66 and #117 (Vol. I):

[9] Regarding decoding ambiguity with mixed unigraphs and digraphs, it seems to me that it could diminish to negligibility between two well acquainted longterm practitioners, just as with two radio-telegraphers who for long have carried on conversations, produce a stream of signals that is totally precise to them, but the transcription of which is incomprehensible to others unfamiliar with telegraph codes and abbreviations styles.

[10] Journal of Voynich Studies comm. #203 (30 JUN 2008, Vol. II):
J.VS: Reference Data for Analysis of Signal Sequence Series; by Berj / KI3U.

[11] Lets have a quick comparative look at the sequence-spectrum properties of the Latin Genesis series 1.}, versus its digraphically encoded angle-cipher version, series 2.} :

For 1.} the basic numbers taken from Table {IX -1} in [10] are:
PR = 9/13 = 0.6923; RPR = 8/9 = 0.8889; HHR = 10/13 = 0.7692; xfrm change = 6/13 = 46.2%

For 2.} the basic numbers, similarly calculated, are:
PR = 2/13 = 0.1538; RPR = 0/2 = 0; HHR = 11/13 = 0.8462; Xfrm change = 22/22 = 100%

We are of course not surprised to see some major changes in the numbers. Again from [10], here are the numbers for the Voynich f68v3.1 text-line:
PR = 9/14 = 0.6429; RPR = 6/9 = 0.6667; HHR = 12/14 = 0.8571; xfrm change = 8/15 = 53.3%

Comparing all three sets of numbers, we could loosely say that Bernardus's cipher coding made the opening Vulgate Genesis series more Voynich-like, however, given how things usually go in VMS text analysis, it is way too soon to make anything much of that.

From: Berj N. Ensanian KI3U
To: Journal of Voynich Studies
Sent: Sat 12/20/08 5:10:04 PM

Subject: J.VS: A new Leonardo discovery

Dear Colleagues

Reminiscent of the recent Mozart discovery [1], there is now a new Leonardo discovery:

" Previously unknown sketches have been discovered on the back of a Leonardo da Vinci painting in Paris that experts think may have been drawn by him. The sketches, which were discovered by accident, feature a horse head, part of a skull and baby Jesus with a lamb. The Louvre Museum discovered them on the back of The Virgin and Child with Saint Anne, which was painted on wood. ..... The museum said some staff members were at first unable to believe the marks were drawings, and thought they must be stains. " [2]

The part about the Louvre staff at first thinking the sketches are stains is VMS-interesting. [3]

Berj / KI3U

[1] J.VS communication #217 (18 SEP 2008, Vol. II):
J.VS: The latest Mozart discovery, and the adventures of worthy documents; by Berj / KI3U.


[3] J.VS comm. #173 (5 MAR 2008, Vol. II):
J.VS: Some hypothetical steganographic faces in the Voynich f93r Sunflower folio spill-stain; by Berj / KI3U.

From: Greg Stachowski
Date: Sun, Dec 21, 2008 at 7:07 PM
To: J.VS

Subject: J.VS: A thought on the 'wave' structures described in J.VS comm. #210

In J.VS communication #210,"Wave propagation along the center-longitudinal in the sequence-spectrum space of the Voynich f111r text", Berj Ensanian described patterns resembling vertical waves which emerged through his analysis of f111r, and which did not appear in a similar analysis of Askham's Menta Rubea.

Here I present a possible reason for such a pattern, as the result of some cyclic feature of the (hypothesised) encryption system of the VMS with a periodicity of order a few words.

Consider the following trivial example. Encrypt


cycling between Caesar ciphers of shift 3, 5 and 7 at each word. The appropriate alphabets are:


and the result is:


where 'FOX' has been encrypted with the same shift-3 alphabet as 'THE'.

Now, represent the different encryption alphabets as different colours. The image "lorem1.jpg", to be found in J.VS library deposit # 2-2-2008-12-21,

shows a block of Lorem Ipsum dummy text coloured in this way (the text itself is not encrypted in this example).

The periodicity introduced by cycling the encryption tables horizontally will also appear as a periodicity vertically as the lines wrap around, due to the combination of the number of words on a line being approximately constant, together with that number not being (in general) an integer multiple of the horizontal period. This is more obvious in the second image, "lorem2.jpg", where I have picked out just two vertical 'waves' in each of red and blue, and coloured the rest white.

Thus, if the subtle changes in letter statistics between consecutive words introduced by such horizontal cycling are detectable by some mathematical analysis, such as the one described by Berj in comm. #210, one might also expect a derivative vertical periodicity to appear in the results.

As noted by Berj in off-J discussion,

" it explains why you can't make progress on the text when you assume the VMS words follow one another serially "

this effect could perhaps, if the differences in letter statistics between consecutive words were large enough, confuse the statistical analysis of the text. It may be worth trying the usual Zipf's law and other statistical analyses for sections of the text where every other, every third, every fourth etc word is taken.



J.VS Archive continued in Vol. III, 2009