- Options
- Login
- Desktop Style
Options
Proposed Manuscript Chronology
- Proposed Manuscript Chronology
-
Proposed Manuscript Chronology
npcompl33t > Today, 02:53 AM
I just shared an updated version of some page classifications I have been working on. You can read You are not allowed to view links. Register or Login to view. or view You are not allowed to view links. Register or Login to view. for more information on how these are generated. You can explore the data for this sequence specifcally on You are not allowed to view links. Register or Login to view.
Briefly:- I create a glyph level transition matrix for each page, both for individual words, and the entire line (removing spaces). I then combine these together.
- I then calculate the pairwise Jensen-Shannon Divergence between each page.
- This matrix is viewable on the web app, as a cluster-map.
For this theory, the actual clusters themselves are irrelevant. Instead, we just look at the MDS ( MDS is essentially PCA over this pairwise distance matrix). The graph of the 2 most significant dimensions produces a similar shape to the PCA bigram charts that have been shared on this forum before.
The Guttman Effect
Note, the distinct 'horseshoe' shape. In the above chart
This is what is known as a Guttman horseshoe. It is a You are not allowed to view links. Register or Login to view. You are not allowed to view links. Register or Login to view.that can happen with both PCA and MDS. This occurs in very specific conditions, when a sequential trend moves across some type of environmental gradient. An example is like this: if you walk two blocks north, then turn and walk 2 blocks east, you have walked 4 blocks. Yet the actual distance will be 2.83. PCA cannot recover the full distance because it attempts to fit a straight line, and one straight line cannot capture the full 4 block distance.
The most common way to check is to look at the 3rd dimension compared to the first. This 3rd dimension will normally have an S shape, but it can manifest more complex shapes depending on the dimensionality of the underlying curve. Notably, it can have a 4 factor polynomial curve, which resembles a W or M.
Lets look at this for our data:
The Bifolio Agreement
So how does this relate to manuscript chronology? Well, once you have identified a guttman horeshoe, you can correct it by applying a polynomial curve to reproduce the full nonlinear gradient. This is what that looks like:
Its immediately apparent this achieves very strong split by sections across the manuscript. The curve also splits currier A and B cleanly.
However, where this gets really interesting is when we compare the average variation of pages in the same bifolio along this curve. The 1st MDS dimension already almost perfectly orders pages by bifolio. Pages on the same bifolio's average variation on the first MDS dimension is just 2.5%, and this drops to an even lower 1.5% when applying the curve. Compare that to an average of 15-50% difference across the other MDS dimensions.
How does this connect to chronology?
Think for a second about what this is saying.
- The fact that pages within a bifolio have < 2% divergence across this entire sequence, shows this is measuring some production level feature
- It also forms a smooth continuous gradient across all bifolio in the manuscript.
- It is not correlated to LFD hand.
- What feature could possibly be represented by a smooth continuous gradient between production units?
The most obvious answer is time, and in fact, time is one of the classic known drivers of a Guttman Horseshoe. For example, Flinders Petrie ordered Egyptian graves in time by their pottery styles around 1900, and in the 1970s David Kendall showed that MDS on such data produces a horseshoe whose order along the curve is the chronological order.
Therefore this pattern is not only consistent with chronology, chronology is one of the known major drivers. This, combined with the fact that the sequence has < 2% divergence along known production units, strongly suggests this is the actual chronology of the manuscript.
What is the chronology?
Note the ordering of some points can be sensitive to the exact curve being drawn. The relative ordering in between sequences is fairly reliable, but groups should be interpreted as production batches, not as an exact ordering sequence.
- D25-32 is a strong candidate for the first created bifolio. It is the first in both the word level and word+line level reconstruction, and it appears 1st in 49 attempted leave-one-pool out refits.
- 2 distinct but separate production batches then produced 2 sections of early Herbal A. The exact ordering depends on the polynomial degree used, as either work, but 1a is a slightly better fit.
- A transition Herbal A section bridges the 2nd Herbal A batch with Pharma
- Several Cosmo, along with f58 came next
- Herbal B came after this, followed immediately by half of stars
- Bio follows The first stars half. The final page varies in different curves.
- T08-111 is a strong candidate for the final page of the MS. Layfield and Davis order this 2nd to last. It appears last in 46/50 leave one pool out refits.
This shows that Herbal B was likely created after both pharma and cosmo, yet was re-ordered and interspersed within Herbal A sometime before quire numbers were added. It also implies that Stars was created in two distinct productions, before and after bio.
What else can be derived from this?
It strongly suggests that several features known to be associated with Currier A vs B splits are actually shifts in the way voynich was written, and that the entire sequence contains several such significant shifts. It is exactly this type of stepwise process that would result in a Guttman horseshoe. The next step would be to incorporate these known statistical properties alongside this chronology, to show how the voynich language appeared over time.
Links:
- I create a glyph level transition matrix for each page, both for individual words, and the entire line (removing spaces). I then combine these together.
-
RE: Proposed Manuscript Chronology
magnesium > Today, 03:30 AM
Thanks for this! It's fascinating work. I'll have more to say on this later this year, in a forthcoming paper. It should be noted that at the section level, this broadly recapitulates René Zandbergen's work on extending the Currier languages:
You are not allowed to view links. Register or Login to view.
And Timm and Schinner's (2020) proposed rearrangement of sections based on certain vords' frequencies:
You are not allowed to view links. Register or Login to view. -
RE: Proposed Manuscript Chronology
magnesium > Today, 04:06 AM
It would be interesting to test how both known, meaningful texts and samples of iteratively generated gibberish, à la Timm and Schinner (2020), behave when run through this pipeline. Do all the texts exhibit "Guttman horseshoes" that correlate to the reading order? Or does it appear in one form of text more often than another? Among the meaningful texts, which texts are most Voynich-like? -
RE: Proposed Manuscript Chronology
Amphigorist > Today, 04:22 AM
The math is all far beyond me, so forgive me if this is a silly question, but does this change over time suggest the text is encrypted or generated, rather than a natural language? -
RE: Proposed Manuscript Chronology
npcompl33t > Today, 04:38 AM
(Today, 03:30 AM)magnesium Wrote: You are not allowed to view links. Register or Login to view.Thanks for this! It's fascinating work. I'll have more to say on this later this year, in a forthcoming paper. It should be noted that at the section level, this broadly recapitulates René Zandbergen's work on extending the Currier languages:
Looking forward to that.
You are not allowed to view links. Register or Login to view.
And Timm and Schinner's (2020) proposed rearrangement of sections based on certain vords' frequencies:
You are not allowed to view links. Register or Login to view.
In the You are not allowed to view links. Register or Login to view. i link to in my post, I actually go through the differences and similarities between RZ's currier extension scheme and the clusters i generated. In both the OP, and You are not allowed to view links. Register or Login to view. on the finer splits between Stars and Herbal A. -
RE: Proposed Manuscript Chronology
npcompl33t > Today, 04:50 AM
(Today, 04:06 AM)magnesium Wrote: You are not allowed to view links. Register or Login to view.It would be interesting to test how both known, meaningful texts and samples of iteratively generated gibberish, à la Timm and Schinner (2020), behave when run through this pipeline. Do all the texts exhibit "Guttman horseshoes" that correlate to the reading order? Or does it appear in one form of text more often than another? Among the meaningful texts, which texts are most Voynich-like?
If their hypothesis could be executed over time in the stages I mentioned above, with gradual changes accumulating, it would produce this same shape. Basically this means the text was likely not created all at the same time.
There were different spans, that must have had gradual shifts that collectively evolved over time. In the Flinders Petrie example, Flinders categorized pottery into 9 classes containing several hundred types. If you think about how one style, like midcentury modern, turns into the next style, at any given point in time style is generally consistent. All the mid-century modern pots follow the same style, but gradually they shift, until eventually they are an entirely different style. They don't wake up one day and say: lets all just start this new midcentury modern style -- it gradually and continuously shifts to that. If you think of these charts as showing differences in Egyptian pot styles, it originally showed A Guttman horseshoe, and by applying MDS, it was possible to recover the exact path that traced gradual evolving pot style over time, through Flinders measurements. This is the kind of thing that causes a Guttman Horeshoe.
This doesn't specify an intended reading order. If certain midcentury modern pieces are meant to all be displayed in a certain sequence, you would only be able to recover it if each piece was created sufficiently far enough apart in time that the style has changed between when they are made, and they were created in the same order as the intended sequence.
So this means it is probably not a cypher of any kind. It is something that must have gradually morphed and accumulated changes. It doesn't really say anything about the content, as long as structurally the mechanism has the ability to accumulate changes continuously.
That seems like it could be consistent with self-citation, if each bifolio gradually changes, and they keep copying from the most recent few. I think looking at the portions where multiple scribes appear to have been working at the same time, as well as the gaps between sections, and trying to understand the exact nature of the changes that occur to either prove or disprove that. That is a good follow-up to this.
It seems like the Herbal A section shows gradual change over a much larger span, suggesting it took much longer to create. Bio on the other hand, appears to have been created in a much shorter time span.
My read is LFD hand 1 spends quite a while writing Herbal, then suddenly inlists a few others and they crank out the last few sections in a smaller amount of time than to create all of herbal A. The cosmo section, particularly the You are not allowed to view links. Register or Login to view. wheel, appears before the other people start working . This is more of just an offhand theory, but maybe this means it was some type of mechanism LFD hand 1 used to help teach the other scribes? -
RE: Proposed Manuscript Chronology
magnesium > Today, 06:15 AM
I completely agree that borrowing the concept of seriation from archaeology—as your artifact examples show—and applying it to the VMS is a worthwhile approach. -
RE: Proposed Manuscript Chronology
npcompl33t > Today, 07:06 AM
I'm running some tests on historical reference material. I may have to take back the claim about this NOT specifying reading order. I was able to nearly perfectly recover reading order from Merswin 1352-70 using this technique on a number of different measurements. It doesn't show the same level of horseshoe as voynich, but it does show one. I'll report back after i test a few more.
-
RE: Proposed Manuscript Chronology
npcompl33t > Today, 07:33 AM
Just to show the time scale can be uncertain, here are 8 manuscripts over 300 years, their publishing sequence is recoverable but they don't have an obvious horseshoe. So this can detect reading order, but could also be picking up some other time variable.
-
RE: Proposed Manuscript Chronology
MarcoP > Today, 08:36 AM
Thank you very much for this thread! As far as I know, Guttman and Kendall were never mentioned in the context of Voynich studies. It’s great to know that Rene’s findings fit into a pattern that also shows up in the archeological data of Flinders Petrie.
I have always been puzzled by that V-shape of PCA1 vs PCA2, but I think I can now partially understand why this happens.
A detail I am not sure about is that the first plot in post #1 shows Biological as the extreme B-side subset, while the last post shows part of Stars as the extreme. I guess this depends on the shape of the green line in the second plot (MDS1, MDS2): that green curve seems to me to be a little weird at both extremes, so I am not fully convinced of the stars-bio-stars chronology.