The 'Chinese' Theory: For and Against

[Jorge_Stolfi]

Given the range of possible variations and the fact that there are still so many words that have no equivalent, I'm wondering if you have a clear rule for determining when one paragraph does NOT fit with the other?

My program has one "must" criteria for an SPS parag to be a candidate for a given recipe: its size must be within a certain range, proportional to the size of the recipe.

For example for the BLAR entry, which is 44 hanzi long, the program considers only parags that have between 180 and 261 EVA letters (not counting punctuation and other fluff).  It found 72 (out of 243) parags in that range.

The parags that pass this criterion are ranked by a "badness score" that takes into account which translations were accepted for the cribs, and the gap size errors -- the differences between the predicted and actual distances between the crib translations found in the parag.  

Among all possible pairings of hanzi cribs in the recipe and their allowed translations in the parag, the program chooses the pairing with minimum badness.  The algorithm is a variant of the "dynamic programming" method used to compare DNA strings, choose the locations of power line towers, and find the best line breaks in TeX documents.  This algorithm will fail if the parag does not have at least one set of substrings that are allowed translations of all the requested cribs, in the proper order.  So that is another "must" criterion, that can be effective when I ask for several cribs with few allowed translations.

The formula of this score is currently rather ad-hoc, and depends on parameters that are still somewhat uncertain, like the expected number of EVA letters per hanzi and the penalties assigned to each accepted translation of each crib.  

Thus there is no specific threshold for the score that decides when a parag is or is not the transcription of a recipe.  I must look at the few top-ranked candidates and decide whether tentatively assign one of them as the transcripton, or just leave the recipe without an assignment -- either because it is not among the 243 usable parags, or because the cribs were lost or were translated into unexpected Voynichese strings.

That said, with the current formula the parags that definitely seem to be true matches end up with badness score less than 1, or just above 1.  So that is one of the things I take into account when inspecting the results.

One of the things that I must do before finishing and publishing the paper is to define 

• a plausible model H0 for "random" SPS paragraph unrelated to the SBJ,   Maybe the list of all 243 parags can be used for this purpose, assuming it is a sample of H0.
  
• a proposed model H1 for the translation process (including a specific distribution for the gap size errors and a confusion matrix for crib variants)
  

and determine (probably experimentally), a la Bayes, what is the probability P that the the parag is indeed the translation of the recipe, rather than a meaningless coincidence, by considering the the probabilities that, under each model, an optimal pairing of the hanzi cribs with substrings of the parag would produce the observed crib variants and gap size errors as small as the observed ones.  

Then the badness score can be -log(P), and one can set the threshold to a specific P, like 95% or 99%.

Eventually.

All the best, --stolfi