The 'Chinese' Theory: For and Against

[Jorge_Stolfi]

I was curious about this, so I looked for an English cookbook, and on my very first (!) try, I found a match with—I think—similar requirements. 3 daiin out of 6 daiin

Oh wow!  So the SPS could be a cookbook? 

Seriously, first I must commend you for choosing the right type of text, rather than a novel or theological treatise.  I wish everybody did the same in their tests.

Indeed the BLAR example by itself (or any other recipe with three or fewer cribs) is not a strong proof of SPS=SBJ.  It is only a modest confirmation of it.  The proof requires more exampleas and/or more cribs.

You are taking an SPS parag and looking for a (cookbok) recipe that matches.  I do the opposite, for various historical and practical reasons.  But I suppose it does not make a difference for the analysis of your example.

But a problem with your example is that your tolerance of ±5 EVA letters is quite a bit more than the errors I consider reasonable.   If you are measuring the positions from the centers of TAKE and DAIIN, you have ~66 positions out of 237 that count as "hits".   

That is, it is like you had 237 closed boxes, 66 containg a colored ball of one of 6 dfferent colors, 11 of each color; and you opened three of the boxes at random. The probability of getting a colored ball in the first try is 66/237.  If that happens, then the probability that the second box has a ball of a different color is 55/236.  For the third box, the probability of getting ball with a color different from the first two is 44/235.  

Thus the probability P of getting three balls of different colors is the product of those three numbers, which is ~0.012 or 1.2%.  If you repeat the exercise 100 times -- that is, if you scan 100 recipes with about that size -- you have 1- (1-P)^100 = ~70% chances of success.  With 200 tries, the probability of a success is more than 90%.  How many recipes are in that cookbook?

In my tests I expect that, in a correct match, most size errors will be less than ±3 EVA letters.  (To reduce the noise I measure N+1 gap sizes instead of N positions, but since the sum of the gap sizes is fixed, effectively I have N independent datums to match).  Then instead of 11 boxes for each color I have only 7.  On the other hand, if I count the main alternatives to daiin like kaiin and daiiin, there are 11 (not 6) sets of 7 colors, which raises P to ~2.5%.  On the third hand I penalize those alternative choices in the badness score, which is somewhat equivalent to reducing the number of boxes for those colors.  So it is not clear that I had as much chance of a meaningless coincidence with BLAR as you had in the reverse search.

Another question is how you picked the word "take" to be the anti-crib of daiin.  In my case, the pairing 主 = ~daiin was determined from the ROOS = f105v.32 matching; and I had no other viable choice there.  I then use that same crib for all other recipes; I don't have the choice of redefining 主 = ~chedy or something else for BLAR.   Can you say the same of your anti-thesis, "SPS=FOC"?

All the best, --stolfi