“Guest Column”: Randall’s Thoughts

Starting the New Year by receiving new comments on your blog is always a wonderful thing. In 2021 it is Randall Galera, who stumbled upon my recent post about Cistercian Numbers and used the opportunity to throw in a few ideas of his own. Rather than discussing this in private, i suggested “coming out in the open” and present Randall’s thoughts for discussion in a larger forum. (Getting only answers from a single bloke like me probably wouldn’t do him justice.)

So, with Randall’s permission, here goes:

Origins.
Facts: The book was found on this planet. Its pages have been dated and are consistent. (Someone grabbed a stack off the printer and set to work). The ink and paper coincide with materials available during the time period. So physically we can say the book is real and is aged correctly.

One must then make a couple of assumptions. It was written by a human or it was not.
On one hand, the precision and consistency are impressive for a mortal scribe. Since to this day, we can not attribute the letter-word-cypher model, we are either dealing with an extremely complex code that today’s quantum computers might have a crack at, divine inspiration, demonic whisperings, multidimensional influence, or extraterrestrial copy. The mortal writer/artist either contained this knowledge first hand, learned it, copied it, or it was dictated.

That being the case, let us look at the artwork.
For my taste, it is too close to what we call familiar while simultaneously being unnervingly alien. First what appears to be women are depicted throughout the manuscript. ONLY women. They appear to have hairstyles, fair features, breasts, and pubic hair. Some are naked and others clothed, one has a crossbow. Most, if not all, have enlarged abdomens. (customary for ‘plump’ women in middle age art.) Feet are rarely depicted. They all appear to have a natural feminine appearance (https://brbl-zoom.library.yale.edu/viewer/1006205) There appears to be a queen depicted at the top. Nothing described as ‘man’ could be found. If we are to ascribe to the “alien” theory, we are looking at a society that 1)Is devoid of the male sex. 2) depicts humans comprised of both sexes in one or one in which there need be only one sex for reproduction 3)that has males but views them insignificant or irrelevant to included in the manuscript. (girl scouts handbook)

In all cases, I asked but why the medieval dresses? It’s too similar, yet distinctly strange. I’m leaning towards a ‘multiverse/dimensional/back to the future’ theory.

Plants.
Obviously, the example of flora are detailed and we assume descriptions are included. We see a similarity that is either the fault of the artist or of design. The root systems follow rules similar to that of the text itself. Some are snake-like, some bulbous, others square, most short, and almost all unlike anything we have growing out of the ground. If there is a soil system (barring hydroponics or another undiscovered agricultural system), it is not earth.

This means to me, the source material of the VM has not been discovered on this planet in current or fossilized form. It either originates from someone’s very vivid and detailed imagination, or from one of the aforementioned external influences.

Numbers:
As stated in your earlier entry, there are no recognizable numbers in the manuscript. If there are astrological charts, it defies our reality to assume one could chart stars, dates, and time without numerical reference. So if numbers are in the manuscript we have not identified them. Please correct me if I am wrong, but what if the entire manuscript ARE numbers? Is the number 12 always written in its long-form, twelve? Are there letters that are numbers, or words, or both?

It is said math is the universal language. We’ve sent out probes with equations written on them in hopes of contact with an alien race. Now, we can’t assume everyone in the universe understands roman numerals, but the core concept of math should be universal.

The issue of language is that it is fluid and ever-changing. Words die out, change meaning, and shift over time. But a language based on math would make sense in an alternate/advanced civilization. If the text in the manuscript depicts equations instead of words, perhaps that could answer many of the anomalies we encounter when trying to decipher the VM, and still adhere to a strict grammatical construct. It would eliminate dialects, and different languages altogether. No more French vs English vs Russian.

If 1+1=2, and two equals love, we run into other issues with the definition of love but as a written text, we can modify 1-1=0. (Death) Now of course this is an oversimplified view on the concept, but my point is has anyone looked at the universal language of math? I haven’t found any examples. What if the language is an actual mathematical equation that then translates into something we understand as language.

I’m just throwing out wild ideas here, and if you have already explored these concepts I’m quite happy to read about them.

To sum up: I think the VM although found on this planet, depicts things we understand in a way we haven’t seen. Raising several existential questions. Little green men from mars? Intelligent design? Simulation code? The magical world of fairies and elves? Thanks for taking the time, let me know your thoughts.

So far Randall’s ideas. A few comments of mine:

  1. Of course the suggestion of an extraterrestrial source for the VM material is a bit outlandish, raising many more questions than it answers. I’ll simply ignore this idea for the minute
  2. Overall, with the C14 dating of the vellum, the handwriting and the illustrations all pointing to a 15th century origin, I think the most workable idea is one or more scribes in Renaissance Italy with a few unconventional ideas about enciphering and scientific ideas.
  3. It has been suggested by a number of people (last but not least by myself: see The “Face Value”-Fallacy) that, rather than being “words” in the conventional sense, the ciphertext character “groups” in the VM might be “codes” of some kind. Ideas suggested have included, but are not limited to —
    • an upgraded system of Roman numerals
    • something akin to the Dewey Decimal system (where the plaintext “value” of the VM word might be the word of the title of a book found in a universal library)
    • coordinates pointing… somewhere?
    • a constructed a priori language, where words aren’t derived from an existing language, but the vocabulary is synthetically constructed, with eg a particular prefix for all things living and a different prefix for all things dead, a second syllable denoting the size etc., so that hopefully in the end the string of attributes will allow one to identify the object in question.

The last item is something which probably comes closest to Randall’s ideas of a “mathematical” language, though I might add a few observations of my own: First, while I think such an enciphering system is conceivable, I’d hardly rate it probable. Secondly, “a priori languages” are virtually unknown before the 18th century, so one would have to admit the dating of the VM is substantially flawed, or our authors were far ahead of their time. (To be fair, whatever their actual enciphering method was, it is still unknown today, so they were in any case ahead of their time.) Thirdly, and that’s more of a personal opinion, the whole concept of the VM with it’s wildly imaginative illuminations to me seems to point more to a “stream-of-consciousness” approach to it, than to a strictly scientific/logical concept. (In this context I still think that Churchill and Kennedy’s glossolalia hypothesis is worth a thought.)

But, dear readership, don’t let this discourage you: Fire away!

*) Last but not least by myself:

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Cistercian Numbers

Probably this isn’t particularly relevant for the VM as such, but I found it interesting nonetheless when Wikipedia today pointed my attention to Cistercian numerals.

Cistercian_numbers_in_Turin_mss

From what I gather from the article, these numbers or numerals were in limited use through the latter part of the European middle ages, and are particularly interesting since they for the first time (in Europe), and independently of arab-hindu numerals developed a “digit” system where the numeric value of a character would be indicated by its position within a number. (In other words, as opposed to roman numerals, where “M” would always indicate “1000”, in the arab-hindu system the character “2” will represent a different value depening on whether it’s been inserted at the end of a number (where its value is always “two”) or anywhere else (in the last-but-one position, the value will be “twenty”, etc)

The Cistercian system takes a little to wrap one’s head around it, but once you get the idea, it’s not that difficult: There is a basic “stave”, vertical or horizontal, plus nine different shapes, representing digits “1” through “9”. The digit shapes are attached to the four “corners” of the stave, with each position representing the ones, tens, hundreds and thousands, resp. (Top left could be the tens, top right the hundreds, etc — details vary according to the particular use) This means that one character consisting of a stave and four digit symbols attached to the corners was enough to represent any integer between “1” and “9999”, so it was fairly powerful, compared eg to roman numerals.

You will notice that there is no need for a zero in this sytem, and probably this was also the reason why it never saw widespread application: If zero was lacking, the artithmetic power of the system was limited (doing divisions would still have been a nightmare, for example), and the Cistercian numerals stayed limited to page foliation and simple numbering tasks, as opposed to calculations. So near, and yet so far to have invented a real rival to arab-hindu numerals…

So, what impact does this have on the VM? Little in particular, since none of the VM characters much resembles the Cistercian numerals, and it also doesn’t look like the characters or words of the VM were composed in a directly comparable manner. Yet, the Cistercian numerals show a surprisingly sophisticated encoding system for numbers, and so it’s not implausible that the VM author employed a similarily complex system for enciperhing his text.

The general view is that in the times of creation of the VM (15th century, as the mainstream opinion is) (quiet, Rich!), not much more than simple monoalphabetic substitution ciphers were in use, hence the VM must be considerably younger, or contain nonsense.

Cistercian_numeral_concordance

On the other hand, the above picture shows a concordance from a 13th century (sic) MS, twohundred years before the creation of the VM. The Cistercian numbers in the center column refer to occurences of the word “aqua” in the corresponding manuscript, giving the page or columns numbers where the word occured. Now it would only be a small leap for any would-be encipherer to create his ciphertext by replacing his plaintext words with the numbers corresponding to this word from his concordance — in this example, he would have plenty of Cistercian numbers to chose from to represent the word “aqua”. Provided the recipient of this message has the same MS available, they are able to reconstruct the plaintext by simply looking up the numbers written in the ciphertext.*) This system**) would have two advantages:

  • The message is safe as long as anyone trying to intercept it doesn’t know which MS was used for reference.
  • It’s a poly-subtitution cipher, meaning one and the same plaintext word can be enciphered in different ways, making any codebreaking attempt so much more difficult.

And, as the Cistercian numerals show, such a system would have been within the intellectual grasp of any educated person in central Europe during the second half of the middle ages. So maybe it really is time to scour the VM for clues to some more complex enciphering systems beyond simple subsitution.


*) Of course this isn’t practical in this example, because on one page of the reference MS there would be many words found. But rather than refering to the page numbers of the word’s occurences, one could use the position of the word in the stream of the text (numbering all the words in the MS as they occured).

**) I know it has a name, but I’ve forgotten what it’s called.

(Images taken from Wikipedia.)

Theory of the Month: Rainer Hannig

Who is the candidate for the “Voynich Theory of the Month” in June 2020?

It is Prof. Dr. Rainer Hannig, who has even managed to briefly be featured in the VM’s Wikipedia entry before being excised again. Hannig has followed the usual spiel of VTotM to the letter:

  1. He is an “outsider”, namely an Egyptologist with no direct links to cryptography, or medieval manuscripts, or…
  2. His solution doesn’t build on previous work, but is the result of a maverick approach.
  3. He assumes an initially simple substitution cipher where one letter represents one sound, and one ciphertext word is equivalent to one plaintext word. He is original inasfar as he assumes the underlying plaintext language to be Hebrew, which would be exotic enough not to have been considered by other researches, and at the same time not completely implausible.*)
  4. After having some initial success in manufacturing Hebrew words out of this, the enciphering rules become increasingly complex the longer he progresses. Things turn into a labyrinthine set of rules with multi-value letters, the ommission and reintroduction of vowels, etc.
  5. At the same time, little thought is given to problems of the transcription, which may well hold surprises for the would-be decipherer — have we correctly identified different and identical characters? Is <ch> really <cc> or a different character? Is <r> the same as <s>?
  6. The multi-faceted structure of VM words, the complex rules governing their composition, is ignored. Which is odd considering such a large number of alternative ways the author had in enciphering his text — if he had so many different options to compose his ciphertext, why do all the words so strictly adhere to only a narrow selection of rules?
  7. While it is possible to create a string of words in this way, the creation of meaningful sentences remains elusive, even when one discards most of Hebrew grammar from the game (as Hannig apparently does.) A coherent narrative spanning paragraphs is nowhere in sight. And this is where I consider the case closed and loose interest.

As an example, let me give you Hannig’s translation from f17r:

I am a bull ready which facilitates and renews house and ruins.
You are a piece of lamb which opens the mouth and is discouraged
when eye-in-eye.

Or f2v, the nymphaea page:**)

Surely, Nymphaea is the twin. Enough juice in the tip.
Drink carefully, this is like something which provides spirit.
Will come juice with repetition. Juice facilitates prophecies...
like rebellion in presence of philosophers.
All which is in Greek about is silence without talking. [sic]
When not speaking about juice, spoke: Do dig... spoken in Arabic.

We’ve had a number of those theories, and I do not only present this piece of scientifically and methodologically somewhat unsound work out of malice (though I wonder about the quailty of Hannig’s other work, if his VM paper is representative for it) or to ridicule it. But it is exemplary for a mistake made so often in VM approaches that it cannot be pointed out often enough.

No, really.


*) Interestingly enough it seems that Hannig never bothered with the question whether the text is supposed to be read left-to-right as in Western languages, or right-to-left as in Hebrew, but opted for left-to-right from the start. Which is strange, considering his background in hieroglyphics.

**) Notice the highly repetitive text with a very limited vocabulary.

 

How Bad is Bad Enough?

Recently, I made my first tests to revive the Strokes theory of how the VM was enciphered and arrived at a quota of around 80% of the VM text (by volume, Currier A) which could be composed of Robert Firth’s 24 building blocks (or “syllables”). Now, is that a good or a bad result?

  • It can be considered bad inasfar as it’s “only” 80%. There are a number of degrees of freedom involved in the experiment, namely as regards transcription and block composition. Assuming that the VM text wasn’t written as a completely random string of symbols but governed by some kind of “grammar” which dictates possible word compositions, it’s not surprising that it’s possible to reconstruct a good chunk of this tome from some set of building blocks, especially if this building blocks are freely chosen. (And some of them consist only of a single letter, hey!) So one could argue that, if Firth’s blocks are any good, they should be able to cover more than 80% of the ciphertext.
  • On the other hand, one can consider the 80% surprisingly good. For example, the current set of 44 blocks allows for the representation of just two sets of characters forming the latin alphabet, one of uppercase and one of lowercase letters.*) This means that any special characters — arab digits, greek letters — aren’t covered from in this repertoire and drop through. Likewise Firths blocks didn’t include some gallows letters from the start, and thus are unable to compose words containing them.
    Let us add to this the high probabilities that

    • Firth’s block set isn’t completely correct, and
    • There are errors in the transcription system. With this I don’t mean a mistake in the transcription process, but an error in the transcription system, ie two different ciphertext letters are consistently considered the same (or vice versa), or two seperate letters are transcribed as one letter (or the other way around.) The ciphertext character set being unknown has notoriously been one of the obstacles of tackling the VM.**)

Any of these mistakes would naturally result in lower composition rates, and in the light of this, one could consider the 80% surprisingly good.

How to proceed from here?

As opposed to everyone else who seems bored under the Corona lockdown, I myself am actually quite busy. Nevertheless, there are two avenues of attack I’d like to write little pieces of software for:

  • One would be an interactive “Fiddler”. Basically, a piece of interactive software which lets you reassign plaintext letters to blocks and to change the blocks on the fly to see what effect this would have on a “decipherment.” With a little luck, and patient fiddling, one or the other readable word might come out of this, hinting at the “true” composition and assignment of the block…
  • Of course, there’s also the opportunity for a brute force attack. Empty diskspace is unused assets. The idea is to introduce random variations to the block set and see how these variations influence both the “composition rate” (ie the volume of text that can be synthesized with the blocks) and the number of blocks required for the composition.***) Letting the software run for a few hours and leaving the “better” results to survive (and discarding those which make the result “worse” might start an evolution towards a better optimized set of blocks.

Now all I need to do is find the time to hack the code.


*) Depending on whether some of the fancier renaissance additions like “j” and “w” or seperate letters for “u” and “v” should be considered.

**) The other being the underlying unknown plaintext language.

***) This might require a bit of explanation. I tried similar “evolition runs” in the past, but one problem was that they tend to “erode” the blocks used further and further until you’re left with a set of single-letter blocks. And this is only logical, because if you have a transcription which uses, say 44 different transcription letters, it will be possible to cover 100% of the transcription with 44 single-letter blocks, if each “block” contains exactly one letter of the set of transcription symbols. Thus there have to be two criteria whether one set of blocks is “better” or worse than the other in explaining the ciphertext:

  • The “better” set must cover more volume of the ciphertext, and
  • The “better” set must not use more blocks than the previous set. (Or, in other terms, the blocks used must be larger or of equal length.)

“C’est ne pas un mot”

Edit: I’ve just added a whole page dedicated to the “Face Value-Fallacy“, because I feel it’s important more people are aware of it.

One of the pitfalls of VM research is the presumption to take its text at face value — these letters that make up the text look so very much like latin letters (except… not quite ;-)), that it’s tempting to presume that each ciphertext letter indeed does represent one plaintext letter. And from that starting point the next logical step is to presume that each chipertext word corresponds to one plaintext word.

But upon closer inspection, this presumption is not borne out by observation, except by the fact that the letters are grouped into small sequences, seperated by visual spaces. A lot of features speak against this assumption or “words”,*) namely —

  • The words of the VM show a high internal structure: Many letters appear only word-initial, some only word-terminal, and many show a high dependency on their neighborhood. While these features are not unheard of in natural languages — compare “q”, which is always followed by “u” in most western languages, or the German “ß”-s which has a strong tendency to appear word-terminal — no language exhibits so many of these features and such a strongly regulated word-internal grammar.
  • The letters aren’t evenly distributed on the page. It’s common knowledge that the gallows characters are concentrated on the page tops and paragraph starts. While this could be explained by them being ornamental versions of regular characters, Julian Bunn’s analysis from 2016 shows a bunch of certain characters “crowd” in line-initial or line-terminal positions, which is a pretty odd feature, if one character really represents one plaintext letter.
  • Unless we are very wrong about the character set used for the VM, one VM word simply doesn’t have enough information content to encipher a plaintext word.**)
  • “Sentences” often differ by only slight changes from word to word or show word repetitions or show word repetitions, so that it almost looks like words are not independent but “morphing” one into the other, and the true information content doesn’t lie in the words themselves, but in the changes introduced between them.***) This is also difficult to reconcile with the idea that each VM word corresponds to a plaintext word.

No. There is much too much going on in the encipherment of the VM. A ciphertext word is not a plaintext word, and a ciphertext letter does not correspond to a plaintext letter, I’m willing to bet on both.

It’s still my convinction that the fiendishness of the VM encipherment doesn’t lie in it’s complexity, but in it’s seeming simplicity: Taken at face value, it looks like something dead simple to solve, and so even a moderately complicated scheme escapes the eye of the beholder. We’re missing the forest for the trees which look like shrubbery.


*) Subsequently I’ll use the term “word” for “a short sequence of glyphs in the VM, seperated from the rest by visual breaks.

**) It could be that the VM character set is much more complicated than presumed and contains many more fine details which discriminate between different character, but I doubt this for reasons of practicability: The VM characters are already quite small, and it would have been impossible for the author to write down his letters so exactly on rough vellum that small nuances would have been legible for a reader. (Not to make too fine a point on this.)

***) Wouldn’t it be fascinating if the word sequence “walter winter” would be used in such a manner to encipher the word “in”?

Fresh attempt at the strokes (1): Robert’s observation

When all you’ve got is a hammer, then everything looks like a nail. For the VM, the same holds true for number crunching, which seems to be about the only tool we have to get any information out of the VM — no matter how misleading it may be.

Now I’ve decided to go back to my notorious “Strokes” theory, which, as I found out to my shock, dates back to early 2005 (without having made much progress, I have to admit.) Read all about it!

Continue reading “Fresh attempt at the strokes (1): Robert’s observation”

Breathing space

Many Voynicheros assume that the enciphering system of the VM treats the space between words as a particular character, like any other of the alphabet.

This is an attitude we have grown accustomed to, since we’ve grown up with computers, where the space has an ASCII code like the rest of “A” to “Z”, and before that the typewriter, where the space bar was a key similar to the others.

But it’s a fairly modern attitude. Until fairly recently, a space was just that — an empty gap between words, but not a character or symbol in its own right. (Even the venerable Engima cipher machine of WWII fame didn’t feature that character in its symbol set.) Rather, it was considered a part of visual design, like a line break (for with the Engima didn’t have a symbol either). Word breaks were useful to discriminate between word boundaries, but they contained no information in themselves. Throughout much of the middle ages, textswerewrittenassimplyalongsequenceofletters, and it was up to the reader to find the word breaks. (Compare this to modern typography, where it’s for the better part up to the reader to learn about stressed syllables etc.)

Even though this practice had pretty much ended by the presumed genesis of the VM (early 15th century), and word breaks were regularly used to increase readbility, I don’t think that any encipherer would already have thought of treating the spaces thus generated as particular characters which would be enciphered like regular letters. Hence, I also think it’s futile to search for such enciphering characteristics in the VM.

Starstruck?

The one thing constant when examining the VM is the fact that nothing is as it looks at first glance. Whether this is Voynich’s personally devised conundrum, designed to enhance the appeal of the book, or simply the result of an otherwise innocent enciphering scheme developed by a 15th century scholar, Voynicheros learn quickly not to trust superficial appearances.

This thought struck me while perusing Julian Bunn‘s new book about the Puzzles of the VM, and coming across his description of f68r2, which is generally assumed to depict the Moon, the open star cluster of the Pleiades, and maybe Aldebaran, the singularly brightest star in the Pleiades vicinity.

not_the_pleiades.jpg
Click this link for a high-res scan of f68r2 courtesy Jason Davies

As usual, attempts to use the names “Pleiades” and “Aldebaran” as cribs to break the VM cipher led to nothing, and also the mysterious wavy line connecting the stars and the Moon has only been met with tortuous, hardly convincing explanations. But what if these are not the Pleiades?

In terms of astronomy, the Pleiades are an open cluster of around 500 stars in relative proximity to Earth. Depending on visibility conditions, usually either six or eight, but rarely seven of these stars can be discerned with the naked eye, since numbers 7 and 8 have almost the same apparent brightness. In many cultures, the Pleiades are nevertheless associated with the number “7” (probably due to the “magic” qualities of this number). The Pleiades supposedly are depicted in the shape of seven dots on the early bronze age Nebra sky disk and are also known in German as the “Siebengestirn”, the “seven stars.” OTOH, in japanese astronomy six of its stars form the constellation of “Mutsuraboshi” (conveniently meaning “six stars”), and the paintings in the caves of Lascaux apparently feature a suspicious cluster of six, not seven stars.

So, under the impression that interpreting the f68r2 constellation as the Pleiades is leading us nowhere, what else could it depict?

I was reminded of the fact that classical astrology always spoke of seven “planets” — not planets in the modern astronomical sense, but objects changing their position relative to the fixed stars. Namely, these were the Sun and the Moon, plus those bodies visible to the naked eye we consider planets today: Mercury, Venus, Mars, Jupiter, and Saturn. What if the f68r2 objects really depicted the seven planets — Where would that lead us?

Being a reader of comic books, the wavy line between Moon and “Pleiades” reminded me of “speed lines”, used to indicate motion in comics. By analogy, let’s take a wide leap and say, the “Pleiades” are moving away from the Moon in this picture — after the Moon has been hit by “Aldebaran”, maybe? Using this as a starting point, as usual there is no difficulty in coming up with wild speculations: Is this maybe a picture explaining an early astronomical theory about the creation of the solar system — A massive star struck the Sun, and the collision broke seven pieces of rock free which went on to become the planets, Moon and Earth?

Of course, that would be an unusually advanced theory for a manuscript presumably written in the 15th century — It would predate Copernicus‘ ideas of a heliocentric universe by at least half a century.*) Also, it requires one to assume that the VM author got a little confused by his own genius when he drew the Moon in the centre of the picture rather than the Sun. (And it pretty clearly is the Moon.**) On the other hand, it has been assumed that the VM is a collection of advanced scientific theories, and if the balneological section is interpreted as a treatise about anatomy, similar advanced views on astronomy could not be ruled out either.

It is certainly tempting to fantasize that the author had developed a theory for the creation of the planets which could still have held up its head in the 19th century. But, the longer I sort my thoughts about it, the less I believe in it. While I’m also unconvinced that the f68r2 object are the Pleiades, the “heliocentric hypothesis” simply requires too many stretches of the imagination.

So, once more, not only the first appearance, but also the second one of a feature in the VM seems to be misleading.


*) While the idea of a heliocentric universe had been known since antiquity, it had never found much acceptance before the middle of the 16th century.

**) A “weaker” version of the heliocentric hypothesis would be the assumption that the body in the centre of f68r2 is not the Moon, but the Earth. In that case, one could assume a geocentric universe being depicted, with the planets being the result of the collision of the Earth with a massive object which later vanished into deep space again. This being a very early depiction of Earth in a modern astronomical context, it’s unclear how the VM author would have drawn it.