Since posting about Voynichese’s strange single leg gallows behaviours a few days ago, I have continued to think about this topic. On the one hand, it’s clear to me how little of any genuine substance we actually know about how they work; and on the other, I’ve been wondering how I can start some broadening conversations about them (by which I mean ones that ask more questions than they answer).
As today’s experimental contribution, I’m going to write a post listing a load of the questions I have in my head to do with single leg gallows but without really trying to answer any of them. I can’t tell how this will work, but here goes regardless. 🙂
Incidentally, for anyone who wants to run their own statistical experiments on single leg gallows, I would strongly recommend using Herbal-B + Q13 + Q20 as their basic test corpus, because I’m acutely distrustful of any Voynich stats that combine Currier A and Currier B. Even though I’m basically doing the latter here. 😉
Questions: final flourish
Rather than finishing with a second vertical leg on the right hand side, single leg gallows instead cross over the left hand leg and finish with a slight flourish to the left. This final flourish can be (1) short, (2) long and straight, or (3) long and curved (i.e. finishing with something like an EVA c-shape).
- Have the variations in the finishing flourish of single leg gallows been catalogued and/or transcribed?
- Are these variations found uniformly throughout the manuscript, or are they strongly correlated with the various scribal hands (as recently proposed by Lisa Fagin Davis)?
- If they have been transcribed, is each flourish type statistically associated with any neighbouring textual behaviours (e.g. contact tables, etc)?
Questions: followed by EVA e?
One huge difference between single leg gallows and double leg gallows is that non-struckthrough single leg gallows are very rarely followed by EVA e. If you count strikethrough gallows separately from normal gallows, the statistics are quite, umm, striking:
- k:ke = 9758:3809 = 39.03%
- t:te = 5802:1748 = 30.13%
- p:pe = 1383:5 = 0.36%
- f:fe = 416:3 = 0.72%
- ckh:ckhe = 876:242 = 27.63%
- cth:cthe = 905:190 = 20.99%
- cph:cphe = 212:64 = 30.19%
- cfh:cfhe = 73:14 = 19.18%
Moreover, looking at the eight instances in Takahashi’s transcription where EVA p and EVA f are followed by EVA e, I suspect that many of these may well be transcription errors (i.e. where Takahashi should have instead written EVA pch / fch).
Hence it seems to me that Voynichese has a secret internal rule that almost completely forbids following EVA p and EVA with EVA e. This is a massively different usage scenario from EVA t / EVA k (which are followed by EVA e 39.03% and 30.13% of the time respectively).
OK, I know I said I was only going to ask questions in this post, but looking at these numbers afresh, I can’t help but speculate: might it be that EVA p/f are nothing more complex than a way of writing EVA te/ke?
- Has anyone looked closely at the eight places where pe/fe occur?
- Why is there such a huge difference between pe/fe and the other six gallows?
- Might this be because EVA p and EVA f are optional ways of writing EVA te and EVA ke?
- Has anyone considered this specific possibility before?
- How similar are the contact tables for EVA te/ke and EVA p/f?
Questions: Followed by EVA ch?
Similarly, comparing the stats for instances where gallows are followed by the (almost identical looking) EVA ch glyph reveals more differences:
- k:kch = 9758:1074 = 11.01%
- t:tch = 5802:975 = 16.80%
- p:pch = 1383:733 = 53.00%
- f:fch = 416:190 = 45.67%
- ckh:ckhch = 876:5 = 0.57%
- cth:cthch = 905:3 = 0.33%
- cph:cphch = 212:1 = 0.47%
- cfh:cfhch = 73:0 = 0.00%
Here, we can see that both p and f are followed by ch about half the time (53% and 45.67% respectively), which is significantly more than for k and t (11.01% and 16.80% respectively).
At the same time, the dwindlingly tiny number of places where strikethrough gallows are followed by ch (only nine in the whole manuscript) again raises the question of whether these too are either scribal error or a transcription error.
As an aside, I previously floated the idea here that c + gallows + h may have simply been a compact (and possibly even playful) way of writing gallows + ch, which would be broadly consistent with these stats.
- Is there anything obviously different about Voynichese words containing EVA kch / tch and Voynichese words containing EVA pch / fch?
- Has anyone looked in detail at the eight instances where strikethrough gallows are immediately followed by EVA ch?
- If you remove paragraph-initial p- words from these stats, do the ratios for p:pch and f:fch settle down closer to the ratios for k:kch and t:tch?
- How similar are the contact tables for EVA tch/kch and EVA cth/ckh?
- How similar are the contact tables for EVA tech/kech and EVA pch/fch?
Questions: Double Leg Parallels?
Some researchers (perhaps most notably John Tiltman, if I remember correctly) have wondered whether EVA p / f might simply be scribal variations of (the much more common) EVA t / f.
- Beyond mere visual similarity, is there any actual evidence that supports this view?
- I would have thought that the pe/fe stats described above would have meant this was extremely unlikely, but am I missing something obvious here?
Questions: Paragraph-Initial?
Yes, single-leg gallows (mainly EVA p) are very often found as the first letter of the first word of paragraphs. But…
- How often do single leg gallows (and/or strike-through single leg gallows) appear in the first word of a paragraph but not as the very first letter of the word?
- Do these these paragraph-initial -p-/-f words show any pattern?
- Are there structural similarities between paragraph-initial p-/f- words and other paragraph-initial?
- Might there be some kind of numbering system embedded in paragraph-initial p- words (particularly in Q20)?
Questions: vs Double Gallows?
Yes, single-leg gallows are to be found mainly in the top line of paragraphs, but that’s imprecise and unscientific.
- Are the number of gallows characters (whether single or double) per line roughly constant for both the first lines of paragraphs and for the other lines of paragraphs?
- Do these statistics change between sections?
And Finally…
Please feel free to leave comments asking any other single leg gallows questions, I’m sure there are plenty more that could sensibly be added to this page. 🙂
All answers happily received too. 😉
Hi, Nick:
Partial answer to Flourish (Q1): Yes, Glen Claston’s Voynich 101 (v101) differentiates between two of the three flourishes you describe. In v101, EVA f is divided into f (curved flourish) and u (straight flourish). EVA p is divided into g (curved flourish) and j (straight flourish).
Partial answer to Flourish (Q3): Yes, at http://inamidst.com/voynich/stacks
Shawn B. Parker notes that (using v101 annotation) f and g (curved flourishes) are found “fairly evenly” as either the first or second “character” in a “word,” while u and j (straight flourishes) are “much more inclined” to come “only second.”
In theory, any analysis that uses v101 has the possibility of finding differences between the two flourish forms, as Parker’s work did.
Michelle Lewis: thanks very much for that, I’d completely forgotten that Glen Claston’s transcription differentiated between the two forms.
Also: I was unaware of that page by Sean B. Palmer, very interesting indeed, so thanks for that as well! 🙂
Yes, Palmer – sorry about that! You’ve given me a lot to think about since l’ve jumped down the Voynich rabbit hole – happy to contribute where l can. If l see any other answers out there l’ll be back.
=rule that almost completely forbids=
Whatever is the nature of the language of the VMS it’s naive to assume that it contains every word of that language. So there are “existing” words that didn’t get into the manuscript, and producing rules without knowing them – is a big mistake. Do we need “almost completely working”-rules is the matter of taste.
As an example take sufficiently long “Tale of Tsar Saltan” by Pushkin (might be his most popular work for children). It’s known fact that Pushkin “didn’t like” letter ф(f). In this verse this letter occurs with frequency 0.016% with theoretical frequency 0.26% according to Wiki*. Actually it occurs 3 times as 1 word type – флот (fleet). What a beautiful set of rules one can derive reading this work…
=rule that almost completely forbids following EVA p and EVA with EVA e=
It might be that some of rarest combinations are rendered as ligatures. EVA-sh if perfect candidate there.
=single-leg gallows (mainly EVA p) are very often found as the first letter of the first word of paragraphs=
There is a good old theory that words which with first gallow letter start sentence (or at least some block). It’s weird when the choice of word depends on the position in text, but it is as weird as VMS itself. And synthetic language imho makes that choice almost always possible.
=At the same time, the dwindlingly tiny number of places where strikethrough gallows are followed by ch (only nine in the whole manuscript) again raises the question of whether these too are either scribal error or a transcription error.=
If word can be discarded because of low frequency or potential scribal error I’m afraid we will soon be left with daiin and chedy only. I suppose that “quality of occurence” is more important than frequency. For example the word poldaky (occurring only once) is written so clearly that it cannot be so simply written off. On the other hand word doin according to voynichese.com occurs 5 times but neither of them is clearly readable.
*For the sake of completeness here is some extra data:
“The Tale of Tsar Saltan” file size is 40K (approx. 30000 letters)
ф frequency in “Eugene Onegin” by Pushkin is 0.084% (file size 360K)
ф frequency in “Dead Souls” by Gogol (friend of Pushkin) is 0.119% (file size 1300K)
ф frequency in “War and Peace” vol 1 by Tolstoy (1860s) is 0.223% (file size 1500K)
Nick Pelling: “Have the variations in the finishing flourish of single leg gallows been catalogued and/or transcribed?”
Yes, my transcription includes flags to distinguish these differences specifically because I thought it might matter.
I may also have posted a chart on the voynich.ninja forum that separates them based on the shape of the cross-stem.
An interesting observation: p/f rarely followed by e.
It reminds me of languages where one would write “ps” or “ks”, but where “c” is pronounced “ts”, so there is no need to write “cs”. Or languages that use “ps and “ts”, but use “x” for “ks”, so no need for “xs” as first letters.
Or the other way around.
Consider a Dutch book explaining Latin quotes. The quote would be the first line in the paragraph which then explains its meaning. Dutch almost has no letter “Q” in its regular text but Latin has. So this curious phenomenon will surface of the letter “Q” mostly appearing in the first lines and often as first letter of the first word in the paragraph. And strangely in the top lines “u” is often preceeded by “Q” whereas that almost never happens in the remaining lines.
So Dutch must be a mysterious language unlike any other language and it surely is 🙂
Well-spotted about the pe. I checked those five occurrences, and three of them – 103r and 114v (twice) are undisputed transcription errors. The one in 89r1 might have been cph with the faded crossbar, but ceteris paribus it’s epe. And 50r is clear pe.
So with three transcription errors it drops to 2/1620 = 0.12%. (counts on voynichese.com differ from yours).
As for fe, 26r is transcription error, and, I think, 46r is as well, 48v is not clear, the parchment is somewhat greasy here, and, furthermore, there might be a word break between the f and the e, and 66v is just somehow poorly preserved, so it’s difficult to say, but the two latter cases look more fe than fch, so that would be 2/499 = 0.4%
About the backtails. I’ve been wandering whether they matter, but unfortunately in many cases the curvature is only half-manifested, so it’s difficult to judge whether it’s curved or not. The first thing which I would have done is to explore this for paragraph-initial gallows, because here we can exclude the consideration that the shape of the backtail has any relation to the preceding characters (for there are none). I would expect either only one variant (e.g. curved) or a roughly even distribution between curved and straight – both options would mean that the backtail just has no significance at paragraph start.
Next one can proceed to vord-initial non-paragraph-start cases, where there are no preceding characters in the same vord as well. In particular, it’s interesting whether the backtail of such gallow can cover the last character(s) of the preceding vord.
The most complicated case is non-vord-initial occurrences where both curvature and length might matter. Sometimes the tail covers only one preceding char, sometimes two chars, and it can be either straight or curved. I wonder whether the curvature is just an emphasis for the coverage.
In short, I suspect that the backtail is the tool of backward coverage.
One thing omitted in your post, and strangely ignored by all quantitative Voynich research initiatives, is the gallows coverage, or, to distinguish from backward coverage just discussed, – the forward coverage, that is, the loop hanging over subsequent chars. I can think of it either as some operation over the subsequent chars or as the means to convey a digit. Say, if the loop covers three subsequent chars, you have number 3. It this light, it’s interesting to look at those loops which have dots inside, and check whether they cover as many chars as there are dots. I once posted some examples at VN, and I vaguely remember that there was some correspondence.
I think the very reason that gallows are the only glyphs raising above the baseline is that that allows to employ coverage over adjacent characters.
Anton Alipov: coincidentally, I read Claire Bowern’s latest preprint this morning, and that too mentioned the pe/fe gap, so it’s obviously something that’s “in the air” right now. 🙂
Thanks for checking the pe/fe instances, I had checked them briefly in voynichese.com but thought it best to look directly at the high resolution scans to be absolutely sure. 🙂
As for backward coverage, this would need a far more detailed analysis than a mere blog post can sensibly marshall. Though WordPress can now show tables, which is quite helpful. 🙂
Forward coverage is another topic altogether! I’d still be writing that post this time next week.;-)
I want to emphasize that the goal (my goal) is to get this text figured out.
But I do think it is worthwhile to note that Stolfi pointed out the pe/fe statistics in his grammar in 2000 but did not present any suggested reasons for this.
https://www.ic.unicamp.br/~stolfi/voynich/00-06-07-word-grammar/
In the core layer section:
“Note the almost absolute lack of e after p and f. The anomaly of these counts can be approciated (sic) by comparing the ratios pe/te with p/t, cph/cth, and cpe/cte.”
As a final aside (I promise), I do think he meant cphe/cthe for that last ratio, given the data immediately above the statement.
Anton, thanks for looking at the pe/fe examples more carefully. Just out of curiosity, what alternative transcription/transliteration do you have, for example, for f103r (peshol)? Do you propose breaking the sh into e and S and then ligating the ee into ch? So it would now be pchSol? I am not challenging your finding, just trying to expand my ability to read the text and work effectively with EVA.
Michelle Lewis: I didn’t claim that I had discovered the pe/Fe behaviour, what was (possibly) new here was the suggestion that p/f might be proxies for te/ke. But thanks for raising Stolfi’s discussion, I’ll be updating the page in a few days with useful information like this. 🙂
Hi Michelle,
You’re welcome.
103r line2 is a clear pchsol (or, if we use capitalized EVA, it’s pchSol rather). Not sure what you mean by breaking, I’m just reading it sequentially glyph by glyph. What follows p is the typical Voynichese ch sequence (compare with the preceding opchedy and with the following chep); the horizontal portion of it is a bit faded, but is clearly distinguishable on the Beinecke scan.
Hi everyone,
From the conversation here, it strikes me that one thing Voynich Manuscript researchers are missing is a proper set of annotated contact tables, along with other really basic analyses.
As here, I usually include relevant highlights in my posts, but for anyone trying to make sense of Voynichese from scratch, plenty of things (such as the way EVA handles ch/sh/c+gallows+h, common pairs such as or/ar/ol/al/ain/aiin/am/ee/eee, Currier A/B, labelese, etc) add noise, getting in the way.
But even though contact tables are one of the cryptanalytical basics, the practical problem is that you have to have quite a sophisticated conception of how to parse Voynichese (what makes up a single character?) before you can even populate the two axes of a contact table, let alone decide whether you would need to use a specific subset of the data (e.g. Currier A, Q20, labelese).
So I think my next step will be to go back to real basics, because I have a horrible feeling that a lot of researchers are fast-forwarding past a load of really fundamental properties of Voynichese without even realizing they’re doing it. That is, I suspect a lot of people are simply assuming that Voynichese is flat, when it is not.
Cheers, Nick
Nick – Noble project. My hope is that it may lift the fog in one small corner of this groundhog-day bedevilled field. Not least because you accurately cite the priors and precedents as you find them.
More strength to your arm.
PS – to Anton. I read all your papers on Voynichese; only wish I had the know-how to do more than just read linguistic analyses.
It was Currier who stated the following in the 1976 Seminar reported by D’Imperio:
“These two, , are never, ever, anywhere in the manuscript, followed by .
(I replaced the symbols by Eva).
Now it is not true that this never happens, but it is certainly extremely rare, and some cases can be confused due to similarity with (Eva) ch.
While this statistic is clearly significant, I am of the opinion that this does not justify the conclusion that (p,f) are different from (k,t). Symbols in ME handwritten documents can take a different form depending on the following character. This could be an example.
Rene: all these scenarios overlap and interfere with each other, leaving everyone’s theories somewhat high and dry.
“” These two, f p , are never, ever, anywhere in the manuscript, followed by e. “”
(I now really replaced the symbols by Eva).
Nick, I just wanted to point out that Currier’s conclusion does not follow from the evidence present, i.e. it is faulty logic. I did not express my opinion about it.
However, I can do that too.
I do not think that f and p are just variants of k and t.
The reason is that with this replacement one does not end up with ‘good’ Voynich words.
However, nothing is ever perfect because I have no answer for cFh and cPh.
Rene: indeed, that’s why I commented that these behaviours “[leave] everyone’s theories somewhat high and dry”, including Currier’s. 😐
Similarly, why should it be the case that ch/sh are found before e/ee so much more than after them? Anyone looking for asymmetrical behaviour in Voynichese doesn’t really have very far to look (note that e/ee here are the parsed counts, i.e. counting e and ee separately):
eech:chee = 32:742 = 4.3%
eesh:shee = 16:493 = 3.2%
ech:che = 92:4132 = 2.2%
esh:she = 18:2042 = 0.9%
Reading “Voynich statistics, and why Voynichese is not flat…”
http://ciphermysteries.com/2016/01/21/voynich-statistics-and-why-voynichese-is-not-flat I can not help but getting the impression of false comparisons being made to ensure Voynychian to be the only language in the world that is not “flat”.
One can not say Voynichian is not flat, simply because we have only one book, only one example of Voynichian, and we have no clue as to what it says. But the text at hand is not “flat”.
Also one can not say other languages ONLY produce books, only written in flat text. I am not repeating my examples here, but I think to have shown that in numerous languages numerous books exist that show non-flat behavior as much as the VM does or even more so.
The false suggestion being made that Voynichian is “unique” in this respect comes from comparing what (for all we know) might be a non-flat example(!) of Voynichian text with flat examples(!) from other languages.
One can only claim that Voynichian as a language is non-flat if one already knows what is written in the VM and knows all other books in Voynichian (the first one still has yet to come up) to be non-flat too. And, to drive things further, that the Voynichians would speak(!) in paragraphs starting their sentences differently from the remaining text…
When one refuses to include even the possibility that the VM contains strange words and/or letters foreign to the Voynichian language, and written in, what looks like Voynichian characters, and in specific places, one does not show an open mind and narrows the possibilities of finding a solution.
It is of course tempting to compare p and f to the other gallows and thinking that their visual resemblance means they should be compared to k and t, while ignoring any of the other letters. Although coming in between c and h gives some reason, others suspected big differences. Like here where p/f are even thought to be soft and not hard like k/t in a note where words are split into pre-, mid- and postfixes:
“Note that the 24 root occurrences that begin with p are listed here only because I assumed that that p was always a “hard” letter. But we have conjectured before that p is sort of a “joker”—probably an “ornate capital”
So the ps above may well be soft letters, perhaps ds or qs. that can be used for several distinct letters, much as the “gallows” in Cappelli’s illustration.”
https://www.ic.unicamp.br/~stolfi/voynich/97-11-12-pms/
Ornate capitals would typically figure in first words and first lines and would not be part of the language as such.
Ger Hungerink: the trump card reasoning so often played by Voynich linguist theorists is that ‘Voynichese’s behaviour X is similar to Language Y’s behaviour Z’, and therefore Voynichese can reasonably be dealt with as the sum total of all those linguistic parallels.
It’s a hopeful dream: but what quickly happens is that each parallel brings along its own linguistic baggage, and so can’t be dealt with in isolation without wrecking loads of the other parallels the theorist would like to draw.
For example, it’s easy enough to propose blithely that EVA p/f are simply top-line ornaments for paragraphs, self-indulgent follies to amuse the (plainly bored stiff) scribes. And it’s easy enough to explain away the lack of instances of EVA pe/fe by proposing that certain letters in certain languages take different shapes before certain letters. But… that’s only two linguistic behaviours explained away, and they already don’t fit together.
As a general point, I’d add that the final paragraph of your comment is dangerously close to outright trolling. If you can resist that particular temptation, I’ll resist the urge to delete your comments without even reading them. Thanks!
Nick wrote:
“But… that’s only two linguistic behaviours explained away, and they already don’t fit together.”
Again, I am giving examples(!) not explanations, not explaining them away – they are possibilities. only to show “Voynichian” is not unique in that respect. Because there are several possibilities, often for the same phenomenon, they are of course not all true at the same time. If at all – they are only examples.
If Voynichian is unique because it has a unique combination of these peculiarities then every language is unique. Then even the “languages” in different English reference books are unique. A book on Latin quotes and a book on Greek quotes might have similar top line behavior but different frequency counts for letters and letter combinations.
Still it remains valid to reckon with all examples and not throw them away, some might actually appear to be true, others might be a dead end.
Ger Hungerink: examples are useful, if only for demonstrating how little of Voynichese’s overall mystery each one resolves – as well as the amount of secondary assumptions those examples require to be true about the data for them to match what we see.
The key issue with the idea of using linguistics as a primary toolkit for trying to understand Voynichese is that even though Voynichese presents a high degree of regularity / predictability at the character level, it’s still missing so many of the things that linguistics takes for granted – morphology, syntax, grammar, etc. Even finding any trace of semantics or meaning is a real stretch (results here are thin and contested).
The key analogy here is with statistics: so many things in the statistical toolbox rely on there being something approximating (however roughly) a normal distribution, that without that you have to question whether you are using the right toolkit at all.
Hi, Nick,
I hadn’t seen this blogpost until today, and I’m glad I didn’t see it before because I have independently developed a similar notion about p, f, te, and ke, along these lines (but not exactly): “Might this be because EVA p and EVA f are optional ways of writing EVA te and EVA ke?” A work in progress which I will likely include as part of my lecture at the fall conference, looking at one-legged gallows from a paleographical rather than linguistic perspective.
And I have indeed looked closely at the places in the transcription where [pe] and [fe] are said to occur. With only two [pe] exceptions they are all errors on the part of the EVA transcription. They’re all [pc] or [fc] rather than [pe] or [fe]. I suspect that there are lots of similar transcription errors (mixing up [ee] and [ch], which can look quite similar), probably due to the transcription having been based on lower-resolution images. I plan to review the whole thing sometime in the future and see what corrections are necessary. And I’ll be spending a day with the manuscript in the next few weeks to take a closer in-person look at some ambiguous readings. Happy to take requests…
Hi, Lisa.
Lisa. You certainly haven’t seen that colleague much more. That the characters P and F. are the same. So I wrote about it 12 years ago. Jewish substitution cipher. Number 8 = F, P. And so when you massage yourself at that autumn conference. So you can also tell everyone there. Do you know, dear colleague, what is the Jewish substitution cipher? As it looks, I guess not. I’ll write you what it means. Read so well. Each letter has its own numeric value. You can also announce this to everyone at the conference. Then it will be good. There are many dates in the manuscript. And dates. So how do you find them? You can find out by converting letters to numbers. At the same time, you will know and find out who was ever born or died. If you also add the names that are in the manuscript, you will also find out the author. And you will also find out what is written in the text.
It’s complicated ? Understand. I don’t think so.
Just don’t examine the parchment. Learn substitution.