Once of the most frustrating conundrums in the Voynich ms. is the ambiguity of the numbers 17 and 18.
The ambiguity seems to be deliberate. We find it on two occasions.
For a start, in the volvelles on f57v there is uncertainty as to how many glyphs are displayed in each of the four quarters of the wheel. There are seventeen glyphs, but one of them is double - two separate glyph-forms joined - and (arguably) occupies two spaces. We can count this as 18 glyphs and 18 spaces, not 17.
It is very tempting to do so because the number 18 is astrologically coherent, whereas the number 17 is not. The number 17 is just confounding.
If it is 18 then we have 4 x 18 = 72 which would make each glyph (or space) 5˚ because 72 x 5 = 360.
This is very familiar astrological arithmetic and also invokes such systems as the 72 Letter Name in Kabbalah. It is thoroughly medieval.
But 17 offers no such neat arithmetic. It is not a number of importance - or usefulness - in any familiar astrological system.
This is an important matter. If it is 18 then a panoply of astrological symbolisms opens up. If it is 17 then we are dealing with a system that is completely unfamiliar and perplexing. If it is 17, then the Voynich astrology is truly eccentric or even bizarre. Not just esoteric, bizarre.
For this reason, it must be 18.
But the ambiguity is also repeated on another page: f67v1. Here we find an 18 armed Sun, but two of the arms blend together leaving 17 words marked as radials in the outer circle.
This is unmistakeable. The inner circle has 18 units, but the outer circle has 17. There is play here between the 17 and the 18.
So the ambiguity on f57v is not accidental or the result of sloppy scribes and we cannot just wish the 17 away. There is indeed an ambiguity and tension between 17 and 18.
* * *
I have puzzled over this ambiguity. It must be important in itself. It is deliberate. But what could it indicate?
Where and why do we find 18 reduced to 17 sometimes? In what astrological system? In what system of any kind?
It is very inconvenient. It would be nice if the Voynich astrology was familiar and straightforward, but it is not.
Worse, I fear it is misleading. Most researchers count 17 glyphs on f57v which leaves them with a system that makes no obvious sense. It is a prime number so it allows no divisions, and we do not find a continuation of any 17 symbolism - systems of 34 etc. - in any other diagrams, search as we may. It is a dead end.
I have devoted many hours to exploring how a system of 17 might work. With no results.
The best I was able to do was to note that the factor 17 is (possibly) an important number in the workings of the Antikythera Mechanism, the ancient Greek calendrical device. It is conceivable that the Voynich manuscript contains similarly complex systems. Possibly 17 represents some offset necessary to calculate irregular or long-term cycles, such as eclipses or transits or such?
If so, I have not been able to detect it. Nor have others. There has been some discussion of this issue over the years. Looking over it, it is more confusing than illuminating.
However, it remains the case that if we take the number of glyphs on f57v as 18 and not 17 then we have some cogent arithmetic to work with. A system of 18 x 4 = 72 x 5 = 360 is astrologically meaningful. Moreover, this arithmetic is continued in other diagrams in the manuscript and f57v is no longer anomolous.
For these reasons - and others - I want to insist that the number is 18, and that the accompanying astrological arithmetic is operative throughout.
For example, it means that one glyph = 5˚ of the ecliptic, a meaningful unit.
Sometimes in Voynich Studies, in order to overcome an impasse, you have to make a call. There are 18 glyphs.
On reflection, this solution is obvious. It is another case where methodological puritanism has impeded progress. Some insist on stark literalism and count 17 glyphs and call the "leap" to 18 "unscientific" and out of order.
I will take Pascal's Wager here. There is everything to be gained from 18, and nothing to be gained from 17.
I am settled in my view that we ought to count 18 glyphs (and spaces) and that the arithmetic 18 x 4 = 72 x 5 = 360 is crucial to the manuscript as a whole, certainly as a working framework.
But this is not to deny the ambiguity. There is no doubt a visual gesture made whereby the 18 is presented as only 17.
In the volvelles of 57v, there might be 18 glyphs, or 18 spaces, but we cannot deny that two of them are joined such that they appear as one. And the two arms of the Sun of 67v1 are distinctly tangled making the 18 into 17.
What the hell?
* * *
I can provide a simple explanation.
In a recent post to these pages I underlined the glaring, but often unnoted, fact that some of the Voynich glyphs are numerals.
Specifically, I posted concerning the glyphs [d] and [y] which appear as the common bigram [dy] together.
The glyph transcribed in EVA as [d] is the numeral 8, and the glyph transcribed as [y] in EVA is the numeral 9.
Moreover, the glyph transcribed as [q] is the numeral 4.
All three of these glyphs appear in the paradigmatic word QOKEEDY.
I have proposed that, in the context, they indicate divisions of the ecliptic and that QOKEEDY is like a formula of the same.
The 4 divides the ecliptic into quarters. The 8 signifies the division of these quarters by two. The 9 signifies the division of these quarters by three.
The glyphs represent factors of division.
This is how the symbolism of the zodiac is generated.
Be that as it may, there is a simplier and more stark observation to make.
Let us take it that these are factors of multiplication. (Division, after all, is a form of multiplication. One becomes two...)
Now we discover this equation:
8 x 9 = 72
Is this what the suffix [-dy] indicates?
It is an extension of what I noted previously, because divisions by two and divisions by three are reconciled in 72.
However: note that if we add 8 and 9 together we get 17. If we multiply them we get 72 which is 18 x 4.
What is the tension between 17 and 18? It is the difference between addition and multiplication.
8 + 9 = 17
8 x 9 = 72
This, I propose, is the direct source of the ambiguity.
It is signalled, and built into, the bigram [dy], that is, the numerals [89].
When to add and when to multiply is another question, but it would seem that both operations are used in the manuscript.
* * *
Let me present this realization as follows:
Are there 17 or 18 glyphs in each four quarters of the volvelle on f57v?
Are there 17 or 18 arms of the Sun on f67v1?
What do 17 and 18 have in common? Can we reconcile their arithmetic?
We can reconcile them in the numbers 8 and 9.
8 plus 9 = 17, but 8 times 9 = 72 which is 18 x 4.
But wait! Aren't the numerals 8 and 9 (and 4) members of the Voynich alphabet?
In fact, they appear together in our text as a bigram [dy] - over 6800 times!
The text is utterly replete with this numerical bigram.
If we want to find a way to reconcile the numbers 17 and 18 - and explain the ambiguity between them - we need only refer to the numerals 8 and 9.
This is true arithmetically - and perhaps we should say 'numerologically' - quite independent of the Voynich manuscript. It is simple arithmetic. Find an arithmetic way to reconcile 17 and 18. The simplest solution involves 8 and 9 and the operations addition and multiplication.
In the context of the Voynich cosmology, this allows us to retain both 17 and 18 and to make sense of both.
The solution is staring us in the face. In the Voynich text the numbers 8 and 9 are altogether conspicuous. The text says over and over again: look at these two numbers!
* * *
Readers can see that over the lifetime of this blog I have abandoned all hope that Voynichese is linguistic.
I am led to the conclusion that it is largely numerical: some manner of (astrological) notation that features a number system.
As an aside here, I note that the entropy of the text, as it is usually calculated - an on-going 'problem' - falls somewhere between what is typical of a linguistic text and a text consisting solely of numbers.
There are many ways this might be calculated, and much depends on the texts involved.
But in number systems there is usually a small set of digits - if there are only ten digits their combinations will be quite predictable.
In linguistic texts, alphabets have more than ten units and so there is more complexity and combinations are less predictable.
Voynichese is too predictable to be typical of a linguistic text. Linguistic solutions typically seek ways to improve the entropy of the text, bringing it nearer to linguistic norms.
The suggestion is that a linguistic text has been compacted or abbreviated, fouling up the entropy.
On the other hand, the possibility the Voynich text is just numbers has been tested too. We can find samples of numerical texts, or construct dummy ones.
The results are that the entropy typical of such texts does not match that of the Voynich text. On that criterion, the Voynich text is not just a collection of numbers.
It is somewhere in between. It is nearer to being linguistic than a text of just numbers, but it is nearer a text of numbers than a fully linguistic text.
Frankly, I think some researchers, dazzled with algorithms, fetishize entropy. Rather, it is a rough guide as to what the text might and might not be.
In this instance it does not tell us much. The text consists of letters and numbers and is likely to be somewhere in between linguistic and numerical in nature, like a system of notation.
R.B.
No comments:
Post a Comment