Proposed Manuscript Chronology

[npcompl33t]

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.

Yes, it greatly depends on the curve's path. 

Think of it like this: if you did PCA on a spring / slinky / spiral, one dimension , looking at it from the top, would show a circle. the 2nd might show a series of descending lines. A spiral does have a single path connecting all the disjoint points across multiple dimensions, but because PCA is squashing them all down into the ones with the highest separation, no pair of PCA dimensions recovers the path. To recover the path, you must trace a higher dimensional curve through multiple dimensions. Examining the order in the first 2 dimensions alone will not produce the correct order, and in fact, points that appear very close to each other may actually be on opposite ends of the path.

Another example is how dinosaur fossils appear squashed completely flat, making it hard to reconstruct their actual skeleton. Just because two bones are next to each other in the fossil, doesn't mean they were next to each other on the 3d dinosaur.

If you look at the Guttman Horseshoe studies i shared in the OP, they are all discussing this exact confound. Points near each other on the PCA curve may actually be misleadingly far apart, but that distance is captured across several of the higher order dimensions. This is why performing the curve correction is necessary to recover the true sequence.

The green curve is essentially tracing that spiral. It appears odd in the plots, because those plots are still only showing the top down and profile dimensions, making some points appear closer than they actually are, and distoriting the overall sequence. In a sense this is showing the 'squashed dinosaur', and the portions of the curve that appear odd are portions that are moving in directions that are perpendicular to the ones being shown on the 2 MDS dimensions. The green curve is connecting them through the unseen dimensions, but it also still appears squashed on the MDS1 and MDS2 for the same reason.

In this case, the things that separate Stars and Bio, are not particularly things that separate the other sections, which is why that differentiation is not as visible.

EDIT: 
This shows what  i'm talking about. I have isolated the dimensions that appear to separate bio and stars. The green line in these dimensions is the same path shown in the OP. It is still possible that a different path could be drawn that connects the points differently through the higher dimensions. An alternate initialization may connect the points better and adjust the final ordering, swapping stars and Bio. This is just the best curve i was able to draw. But looking at a few dimensions in isolation may warp or skew the order.

   


Additional work can help to narrow down the exact sequencing.  If we can identify the exact mechanical changes that are occurring, perhaps we can reconstruct the specific sequence here with more certainty. Using alternative methods and seeing which sequences result in the most cross-method agreement would also help us understand which sequence is best supported.


EDIT 2: 

Here is an alternate initialization that traces a different path through stars and bio changing the ordering. This fit is *slightly* worse, but only by a few percentage points. It captures 0.1% more pooled bifolio variation, and the proposed curve has about 2% lower held out pooled error. The proposed version fits Stars-S better, while this version fits Bio/Stars T better. I think this shows that this particular ordering sequence is very sensitive and we probably need additional work to fully resolve the exact ordering of these 3 sections.

   


The differences between these two curves imply more than just an alternative ordering though. Note under the proposed, the spread of Stars T and Bio along the curve is much tighter, while in the alternative, they are much more dispersed along the line.

This means the different curves would actually have pretty significant impacts on the mechanical interpretation of these sections:

• Proposed: Bio represents a comparatively stable production phase, with its internal differences mostly unrelated to progression.
  
• Alternative: Bio contains a stronger internal progression that the sequence follows.
  

So the alternative attributes more of Bio’s internal variation to the proposed chronological progression, potentially suggesting a more extended or more internally changing production phase, compared to the proposed curve.

More importantly, the alternative curve dramatically changes the initial sequence, swapping the 2 Herbal A sections. This seemed like a less reliable ordering of the Herbal A sections, which is why i ultimately favored the proposed curve.