Proposed Manuscript Chronology

[Jorge_Stolfi]

I think far to much effort has been spent arguing over whether the gradient exists rather than trying to understand what could actually explain such a gradient.  ... I strongly believe that VMS research as a whole would benefit from shifting the debate away from 'is there a gradient' to 'what mechanisms could cause this gradient and how can we distinguish between them'.

And I strongly believe exactly the opposite: far too much effort has been wasted trying extract a gradual change (between sections, bifolios, of pages) from page statistics, when the data itself says that there is no such gradual change.

What your plots show is that the pages of each section form a compact cloud that could be fairly well modeled by a single n-dimensional Gaussian distribution.  Apart from sampling noise, the point density has a single maximum, and drops off smoothly from that point in any direction.  

That cloud may be somewhat stretched along some direction, either in space on on a 2D projection.  The points can be ordered by their position along that direction of maximum extent (or any other direction selected by some "sacred" data analysis method).  But that ordering is not significant, because the direction of maximum extent of the cloud (and therefore that ordering) can be changed to any other arbitrary direction, by changing the projection and/or by applying a linear transformation of the data space that squeezes or stretches the cloud appropriately.  That is possible because there is no "natural" distance metric for that data space.

Therefore, from the per-page statistics data we cannot deduce any intrinsic order, temporal or otherwise, for the pages of each section.  

That said, if we now look at the clouds of any two distinct sections X,Y (perhaps with a few exceptions), it can be seen from the plots that the clouds are well separated: each cloud has a distinct point of maximum density,and there is a region of significantly lower density between them.   

The separation is almost certainly more evident in the data space, and could be made more evident with a proper projection (see the last image in my previous plot). 

Those two sets of page data vectors cannot be properly modeled as samples from a single Gaussian distribution, nor as two slices of a single elongated "smoke trail".  

The only minimally acceptable model is the sum of two Gaussian distributions, such that the separation between the means is large enough to create a low "saddle" between them. 

Therefore, what we can say so far is that all the pages of a section X are statistically similar to each other, modulo random variations, with no obvious ordering or evolution; and they are noticeably different from those of most any other section Y.  

A priori, it seems likely (but by no means certain) that there is a temporal order between sections.  That is, the Author probably composed and clean-copied the whole draft of a section X, which he gave to the Scribe, before starting to do the same for another section Y.   

Can we assume that the statistical differences between X and Y are due to the mere passage of time, that somehow caused the Author to change his spelling rules and/or word usage frequencies?  

Well, no.  Most pairs of sections X,Y have very different text structures (paragraphs vs. text rings vs recipes vs. continuous text etc.) and almost certainly very different topics.  These differences, by themselves, are more than enough to explain the statistical differences.  Recall, again, that the frequencies of characters and digraphs in a txt are determined by their presence or absence in the most common words in that text.  Any changes that are the result of mere passage of time (like the Author becoming gradually more fond of daiin and less inclined to use -edy words) would be easily swamped by changes due to those other factors.

It is even possible (not likely, but definitely possible) that the Author created two sections X,Y in parallell - writing some pages of X, then some pages of Y, then back to some pages of X, etc.  But, as he switched back and forth, so would his word usage frequencies, because they would be determined by the topics; and so would the per-page statistics.

But if the clouds of sections X, Y, and Z lie more or less in a straight line, in that order, can't we infer that Y was probably created between X and Z?  Or lies somehow between the two in some variable other than time (like the use of astrology in the discussion, or the education level expected from the intended readers)?

We may tentatively make that hypothesis if the three clouds are mostly aligned in the data space R^n.  In that case, they would be aligned in any projection.  But if they are not aligned in R^n, then, by choosing different projections, we can make them look aligned on the plot, and in any of the 3! = 6 possible orders -- with any of them apparently between the other two.  

And I bet that, in fact, You are not allowed to view links. Register or Login to view..

[A compilation of multiple ur-books] is exactly the thing that would cause a gradient to appear.

As explained above, that is in fact a thing that would cause the clouds to lie in random, non-aligned position in data space -- and mask the effects of mere passage of time.

All the best, --stolfi