Chronological Path Stability/Uncertainty Analysis

[npcompl33t]

The existence of multiple families of fitted curves, that yield different t orders for the pages and sections, is an argument against your thesis -- that the chronological order of writing (COW) can be deduced from the oredering of the points in R^256 space.  Right?  

Not at all, as i have explained with the multiple examples of paths between cities.  I will use some maps below to illustrate.

   

In the above example, lets say we are taking a road trip, with a general NE direction, and can only measure the distance we travel and the distance between each point. We can be relatively sure that:

• Austin and Houston are both at the beginning of the trip, but Austin->Houston->Dallas is roughly identical to Houston->Austin->Dallas. We can't say for sure which the path stars in, but its clear it must start in one of these and the other must be 2nd.
  
• Dallas and Oklahoma City are adjacent points on the path, occupying positions 2 and 3
  
• Kansas City and Springfield are slightly ambiguous, going from OKC -> Springfield -> Kansas City is roughly the same distance as OKC->Kansas City -> Springfield. Its clear they both occupy the same 2 slots, but the relative ordering is uncertain
  
• We can be certain that St Luis is the final point, the most NE.
  

We can be relatively certain as to the structure of the path while still being uncertain about relative order of certain pieces. Rather than present a single path and claim it is the only option, this analysis gives us a way to understand where those ambiguities fall. It is fully in agreement with my overall theory, and I am being extremely transparent about which specific components my methodology cannot resolve the ordering of. 

Let v be the dominating direction of the current fitted curves.   In those plots, the projection of v run mostly left to right.  What would happento the fitted curves if you stretched the data along a direction u in R^256 that is perpendicular to v?  Wouldn't the new fitted curves run mostly in the direction u? Wouldn't that completely scramble the t order of the sections?

The projections run mostly left to right because I have the same dimension on the X axis in each plot, MDS1. MDS1 captures the most obvious temporal gradient, so viewing it this way makes it easy to consistently follow the paths. Basically, this is because of the way that I've plotted them, it is not an artefact of the method. The line does indeed move in different directions perpendicular to this in certain regions, which is why i included the MDS5 and MDS6 charts. None of this 'scrambles' the order. The only uncertainty is injected when relative distances between certain points in certain regions create equally viable paths, as in my city example. 

 Do you mean that, for a single curve, the projections of the H-1a pages span a range of ~0.10 in t values? Not ~0.02, as I had assumed above?

yes, this is correct.  

In You are not allowed to view links. Register or Login to view. there are some white vertical streaks across all color swabs.  I had assumed that they were due to the use of a small number of curves.  That assumption influenced my misunderstanding that the t projections of the H-1a pages, for each single curve, spanned only ±0.01.  But you say you had thousands of curves, and now I see that those white bands are equally spaced in t.  So now I guess that they are plotting artifacts, perhaps due to something as banal as writing the data out to some intermediate file with too few decimal digits.  Is that so?

A vertical white streak cannot exist across all color swabs, and they are not plotting artefacts. This chart is similar in theory to a bifurcation diagram. A vertical white streak means that whatever page does occupy that, is preferred across all of the curve variants. For whatever reason, the paths all exhibit some sort of stability or attractor in that area. Thus these are the most confidently assigned positions. In my map /city example, Dallas -> OKC conceptually could resemble the 1.5a and 2a sections. Regardless of the different Austin/Houston and later Kansas City orders, all paths converge and agree on a particular stretch. So the vertical white bands mean that there is mostly agreement across all generated curves that whatever color is present is in the correct

All other color swabs in that plot are roughly rectangular.  With the new information, I interpret this fact a meaning that the t-ordering of the pages of those sections is drastically different for different curves, even within the same family.   Which would mean that the order of the projections of those pages along a direction u in R^256 space changes drastically even with small changes in u.  Which seems to imply that the pages of each section are not mostly aligned along some direction v, but are scattered randomly in a roundish cloud.  No?

No, this again can be seen in my city example. Consider Houston and Austin 1a and 1b. Regardless of which comes first, they both occupy the exact same region of t on the curve. Neither can appear after Dallas. So their possible positions on t are identical, and their distribution appears rectangular.

But H-15a seems to be different: its swab is a parallelogram instead of a rectangle.  So I suppose that not only its pages project in the same order along any curve, but in fact that order is highly correlated with the order of those pages in your data file.  Which order is this?

This is similar to the stretch between dallas and OKC. If you consider each page to be a small city in between dallas and OKC, virtually every possible path has to pass through these point in the same order. So they end up appearing staggered along the T axis. Does that make sense?

But if the anomalies of You are not allowed to view links. Register or Login to view. are so scattered, then I retract my idea of an "aardword" effect and the proposal to move it to Bio.  Instead, I propose that You are not allowed to view links. Register or Login to view. is not really part of Bio, although it may be related to it (like an epilogue about the history of the section). It is a section by itself, another "unknown" section, like the next page f85r1.  The illustrations logically belonged to the previous page, but did not fit there so the Scribe spilled them over to the unrelated page You are not allowed to view links. Register or Login to view. (something that happens all the time on books and papers even today).

It may also be that only the lower half of You are not allowed to view links. Register or Login to view. is anomalous and is not part of Bio proper (like the lower half of You are not allowed to view links. Register or Login to view. does not seem to be part of the Starred Parags section proper).  That half seems to be a single long parag, twice as long as the average parags of other Bio pages

I tested both the lower portion and the lower circular together. Including the circular does reduce how much of an outlier this is, but not by enough to resolve it's anomalous status. Many of the astro/cosmo sections exhibit word construction that seems somewhere in between pharma and Herbal B. It's clear that something transformative is happening to the language during this time, I'm not claiming to have a full understanding of what is going on here, your explanation could be correct. As i mentioned, the missing bifolia from Quire 8/H would likely greatly have aided in understanding more about this transition if we had them. 

If you listed the pages in order of mean t-value along some curve, and you fitted that curve to a bunch of statistics, and those statistics happen to be correlated with the frequency of chol, then the frequency of chol will tend to vary gradually along that ordering.  

It is again like sorting books by height, and observing that the number of words per page (along with many other book properties) varies gradually along the resulting ordering.

If this were just chol, I would agree with you, but it is not. It is ALL vocabulary. When arranged in the way my chronology , the total vocabulary retained from the start falls gradually each step, such that by the end (bio) almost nothing remains. 

The book size example completely falls apart here, and the gradient separates known topical sections. Why do some Herbal A pages vastly prefer forms with eo in them? Why does chol drop by over 50% within the same topic? This should be the same topic, same language?