The Voynich Ninja

Spent some hours today in calculations and I believe I nailed upon some idea of these notorious charts. It's a pity that it seems to disprove most of the ideas that I developed in the last couple of weeks.  Will post tomorrow.

It might become a nice example of hypothesis testing

(09-10-2022, 07:25 PM)Anton Wrote: You are not allowed to view links. Register or Login to view....one curious historic calendar - the calendar of Dionysios...

Anton, your idea interests me a lot. 
A few years ago I saw in the single word EVA You are not allowed to view links. Register or Login to view. the name Διενυσος=Διονυσος – Dionysus. 
I look forward to your conclusions so that I can, if necessary, adjust my reading.

Regarding the calendar of Dionysios: the article which I referred to above hints that it had eleven months of 30 days, and the last month contained surplus days to bring the total to 365. However, later yesterday I found one Russian article that debates that assumption. The source of hesitation here is that this calendar, allegedly used by ancient Greek astronomers, did not survive in its completeness in any source, and is known to us only through Ptolemy's Almagest where (if i'm correct) he refers to certain events and names their dates according to different calendars, including that of Dionysios. Based on that, attempts were made by researchers of later times, to reconstruct the calendar of Dionysios. It appears though that they cannot agree on their reconstructions.

On to my idea. In that very unfortunate circumstance that there are no calendars with regular succession of 30-day months (bar the doubtful Dionysios), I decided to explore Rene's suggestion above that the number 30 relates to Zodiacal degrees rather than days. I further supposed that the whole stuff might be not a pure Zodiac, nor a pure calendar, but rather some mix of the two. I dropped the idea that the series starts with March 1st and adopted the more popular idea that it starts with the vernal equinox, as the European tropical Zodiac would.

Now, I decided to translate the succession of Zodiacal degrees into units of time, mapping those to calendar dates, in order, so to say, to reveal the calendar within. At first I adopted the most simple, albeit somewhat anti-astronomical approach. Since the whole Zodiac is 360 degrees, and the year is 365 days (to be precise, it would be 365,25 for the Julian year adopted back then, but this gives only 1 per mille error, so we can neglect that), then one degree stands for 365/360 days. Next, we have to determine the starting point as the point in time. Since the cycle is ever repeating, actually, one can take any year (avoiding leap years for convenience), just correcting the dates for the Julian-to-Gregorian difference. I took the year 1421 (simply the median of the widely cited VMS dating range), in which year the vernal equinox occured on March 12th, 02:12 GMT (this is the Julian date then effective). Then I translated the number of nymphs (Zodiacal degrees) into minutes of time and began to add them, in succession, to the said reference timestamp. What I noticed is that the boundaries of the charts produce dates that are roughly the dates of the Zodiac sign changes. This is of course a bit trivial with roughly 30-day cycles. What was more interesting is that the boundaries between the outer and inner rings of the charts produce dates which are roughly the month boundaries.

Here I must describe the notion of the "outer" and "inner" rings as I use it. This was the result of some reflection of how to fit what we observe into the proposed schema.

For the charts with only two rings (such as Pisces/Mars) it is all self-evident. For Aries and Taurus, both of which are doubled, I combine twe two half-charts. For instance, there are two Arieses each of which has 10 nymphs in its outer ring and 5 nymphs in its inner ring. I treat those as one combined Aries with two imagined rings, of which the outer one would have 20 nymphs, and the inner one would have 10 nymphs. (Why they are split in two, - which is still one of the main questions about the Voynich Zodiac, - I still have no idea).

Next, there is the Cancer chart which is outstanding in that, in contrast to any other, it has three full-featured rings. By "full-featured" I mean that they all have their delineated band filled with the VMS text. So I treat these as three distinct rings - the "outer", the "middle", and the "inner". We'll see below that this deserves further attention.

Finally, there are some charts with "pseudo-rings". For example, Gemini. In my posts above in this thread I treated them as having three rings as well (outer, middle and inner). I then reconsidered this approach, because the outermost "ring" is actually not a ring in the sense of the Zodiac charts. There is no band and no dedicated Voynichese text. These are just a set of nymphs placed on top of the actual outer ring. I had an idea that these might be nymphs "running out" of the previous chart to designate some kind of mathematical correction, but this assumption does not find good substantiation for now, so in the meanwhile I assume that they are used to introduce additional boundary and thus to highlight some important date beside the Zodiac or month boundaries - although what might those dates be I could not grasp. Anyway, I count these nymphs separately as "extra-rings" but I consider/expect the month boundary to be between the "full-featured" outer ring and the inner ring.

Next I should elaborate on the Zodiac boundaries. At first I just took the modern understanding, just correcting it back to the Julian calendar of the year 1421 (9 days difference). This table is shown in Fig. 1 below.

[attachment=6873]

With this in view, I plotted the translated "calendar" and calculated errors encountered on supposed Zodiacal and month boundaries. See the table in Fig 2

[attachment=6874]

In here, the month boundaries are respected subject to error of up to 3 days and Zodiac boundaries - of up to 4 days - the values not as large as to discourage further inquiry. I then supposed that maybe back in 15th century they adopted slightly different Zodiac boundaries, so I consulted the very first 15th century manuscript shown to me by e-codices search in response for criteria such as "15th century" and "computistica". Whenever you meet with "computistica" as the MS description, you hopefully see those tables featuring calendar dates mapped to Zodiac degrees/minutes, along with some other stuff which I fail to understand. I used You are not allowed to view links. Register or Login to view.. Judging by the stuff in f1r, the contents of interest is somewhat pre-1431 (one would hardly be interested in computing stuff for years already past), so it fits our purpose well. The month tables are from You are not allowed to view links. Register or Login to view. onwards. What seems relevant to the purpose is found in the first set of colums to the right named "signa", "gradus" and "minuta". This corresponds to the mapping of Zodiac signs to calendar dates. There are other columns with the same names farther to the right, I don't understand what they designate. E.g. for March (f3r) sign 11 (Pisces) changes to sign 0 (Aries) and that takes place on March 12 (the date of equinox). March 12 is sign 0 (Aries), 0 degrees 54 minutes. Further columns to the right suggest that this date is also somehow asociated with sign 7 (Scorpio), but, as I said, this is something irrelevant to the purpose, so the focus will be on the highlighted columns. Unfortunately there are mistakes there, e.g. two different days may be shown as associated with the same angular position, or the "sign" column contradicts the "degree" column, or (the epic fail!) they show May's table for July and, instead of correcting it, just note that "this is the table for May" (this way July is effectively missed). I wonder whether there was some universally acknowledged table, or each author had his own variant. Anyway, I reconstructed the adopted Zodiacal cycle as shown in Fig 3 (Aquarius is omitted since we don't find it in the VMS)

[attachment=6875]

This is slightly different from what we use today. Re-assessing the calculation against these boundaries only made things slighly worse (increased errors). Hence I don't upload the respective result.

Next I considered that probably the guy did not use the uniform averaged degree-to-day ratio. Instead, if you have a look at tables in MS L 309, the intervals are not averaged even within a given sign: the difference between day N and day N+1 may be 32 angular minutes, while the difference between day N+1 and day N+2 is 84 angular minutes, while the value averaged over the whole sign is, say, 59 angular minutes per day. I guess there is some Ptolemaic set of rules for obtaining those angular values, but for rapidity I adopted the simplified approach, averaging angular intervals within Zodiacal signs. E.g. Aries takes 30 days, so it would be 1440 minutes of time per Zodiacal degree (since the number of days is equal to the number of Zodiacal degrees); but Cancer is 32 days, so it would be 32*1440/30 = 1536 minutes of time per degree. The number of days for each sign is simply derived from MS L 309 (as shown in Fig 3 above). With this approach we neatly fill Zodiac signs along their calendar boundaries just by virtue of the method, and we are left to observe how and whether the month boundaries are respected. The result is shown in Fig 4

[attachment=6876]

This, so to say, "Zodiac-aligned" table uses the same MS L 309 Zodiac boundaries as the previous Zodiac-unaligned calculation (that which is not uploaded) and is not much better in terms of month boundary errors. On the contrary, the sign of Cancer increases July boundary error up to 6 days. This huge discrepancy returns us to the discussion of the outstanding Cancer chart with its three rings. In short, I suspect that the three perceived rings are to be somehow contracted to two rings only, with part of the middle ring being the "end" of the outer ring, and part being the "beginning" of the inner ring. The reason why I think so is that the middle ring features two things not observable in any other non-tub diagram: there is a nymph walking in the opposite direction and there is an ornate "lock" in its band. Either or both of these vaguely hint at some operation of directiing or partitioning. Of course, contracting three rings to just two with a proper proportion of degrees would allow us to correct the boundary of July.

Now, with one or another consideration of these charts as Zodiacal, the old question reappears of why the Zodiac begins with Pisces. In the design under consideration, the answer is that the Zodiac begins with Aries, since it begins with the vernal equinox. But then the question is why the sign of Aries is marked with the picture of Pisces (the sign of Taurus - with the picture of Aries, and so forth). The only answer I can imagine is that the artist depicts the sign that is exiting with the advent of the respective 30-degree cycle, not the sign of the cycle itself. This explanation is counter-intuitive and hardly satisfactory.

Therefore, I decided to apply the similar calculation to the variant where the vernal equinox would be start of the Aries diagram, not the Pisces diagram. This approach is quite intuitive - each diagram depicts the sign which is explored therein. In this, I again use the MS L 309 Zodiac boundaries and average the degree-per-day ratio within each sign. Interestingly, although errors slightly rise, the whole plot still holds. The result is shown in Fig 5.

[attachment=6877]

With this allocation, however, the old questions again remind of themselves: why Pisces hold only 29 nymphs and why the Zodiac starts with Pisces. To the second question one may say that that is because the 1st of March falls in there, and the year begins in March, but MS L 309 shows that such tables begin with January, not with March. Are there examples of "computistica" beginning with March? I do not know.

(In short, all notorious questions about the VMS Zodiac still remain there with no answers that can be considered as deeply satisfactory).

As shown above, it appears that shifting Zodiacal boundaries influences the month boundary errors. Also, I have no doubt that changing the rule of mapping Zodiacal degrees to time units would influence those as well. I am unaware of the exact rules used in those "computisticas", so could not test that, with averaging within each sign being the best effort that I undertook. I believe combining these two considerations may allow one to improve month boundary errors. Also, it's pretty probable that the VMS author was no different to his contemporaries and also made errors in his own charts.

I believe that the above demonstrates that the idea of ring boundaries being month boundaries with chart boundaries being the Zodiac sign boundaries is worth further consideration.

Regarding the reference issue briefly touched above. Some Zodiac charts have explicit reference point, some don't. Some have nymphs facing the way opposite to others ("opposition nymphs" for brevity). Here's the complete picture:




Since there are charts with neither explicit references nor opposition nymphs, this means that opposition nymphs are not meant as reference points. Notably, all opposition nymphs are in the first half of the year. Interestingly, the creators began with opposite directions for outer and inner rings but then abandoned the idea.

While reasons may be speculative, results are more apparent. Having Pisces first and splitting Aries and Taurus in two creates a situation where the occupants of the first five houses of the VMs version of a Zodiac sequence all exist in pairs. Gemini, like Pisces, is a 'natural' pair, while Aries and Taurus are totally 'artificial'. And VMs Cancer is a pair of crayfish, chosen instead of the more typical, singular crab.

The VMs Zodiac thus arranged creates a series of five pairs. Furthermore, there are pairs among the pairs: two pairs of aquatic animals, two pairs of land animals. And there is the marriage in VMs Gemini. Not the pairing of twins, Castor and Pollux, but a pairing of male and female, as a sort of pairing of complementary opposites.

Trying to see things from the VMs artist's medieval perspective, pairing, as a concept and useful pattern, has the advantages that it is simple and clear, and also that it was promoted in the religious laws of Deuteronomy. And further, that a number of other subtle indicators of religious "awareness" exist in the VMs to support this interpretation.

Pairing also exists in the tub patterns at the top of VMs Pisces and this is where armorial heraldry begins. Not to mention the pair of Stolfi's markers on VMs White Aries.

Yes, that pairing paradigm of yours came to my mind more than once whilst calculating all that stuff.

A pair of Pisces, a pair of Aries (can be male and female), a pair of Taurus (can be male and female), a pair of Gemini (male + female), and Libra are also a pair in itself. But they do not pair Lions or Scorpios (though they could). - Why? I doubt that pairing has some computational meaning here, although at times I wondered whether one should not count e.g. the two Gemini as two additional nymphs.

With this Zodiac, as opposed to other VMS charts which are even more enigmatic, we are perhaps most close to mapping it to the outside-world concepts. That's why I focus on the computational side which has good chances to be borrowed from elsewhere, although perhaps with some changes or novelties.

I didn't recall any interpretations of gender for the VMs animals - but VMs Dark Taurus is clear enough. "Armed, langed and pizzled" like the heraldic blazon says.

The thing about VMs Gemini is the choice that was made by the VMs artist to use the *marriage* version of pairing, rather than the *twins* version of pairing - particularly in light that both antiquity and the classical renaissance favored the 'twins' version. It shows that pairing also occurs between things that are "opposite".

Also consider the VMs does not follow the standard, concentric, planetary representation of the cosmos. It appears to have used a very peculiar structure - as related to the cosmic comparisons of E. Velinska. It seems to be a more 'primitive' image of the cosmic sphere than what was 'scientific' standard at the time the C-14 dates. In combination with other VMs illustrations having potential religious interpretations, it may turn out that the written text is more concerned with religion rather than science.

If the medallion(s) of each house of the VMs Zodiac contained a pairing, it would be obvious <that the artist was cross-eyed>. The pairing would be obvious. The VMs is more subtle. As it is, enough ambiguity has been introduced so that something plain and simple has been overlooked. The problem with Pisces is its position. The problem with Aries and Taurus is that they are bisected. They are each split in two to become two pair and fill in the sequence of five pairs.

Why five pairs in sequence? Five is an interesting number, as they say. The fifth glyph [EVA: v] in the VMs 4 x 17 symbol sequence has three (Greek, Roman, & medieval) numerical interpretations each supported by structural (shape & positional) factors in the sequence. But who can determine artistic intent from coincidence?

If the Gemini couple are nymphs, why not Virgo and Sagittarius as well? I see medallions as separate.

It just occured to me that the same model as I described above would apply if we swap inner and outer rings (meaning the inner ring goes first). In that case month boundaries would (ideally) map onto chart boundaries, while Zodiac boundaries would map onto ring boundaries. Thus charts would stand for months, not for Zodiac signs. The Zodiac symbols would designate the sign which enters the respective chart.

This is favourable to the "Pisces problem", since the first chart would then represent the month of March, and March begins in Pisces.