The 'Chinese' Theory: For and Against

[Jorge_Stolfi]

taking recourse to apparent homophony between daiin, dair and laiir should increase, rather than decrease, the entropy, because allowing additional spellings should make the bigrams less, rather than more, predictable, raising the entropy.

Basically I am proposing that there is a non-negligible amount of misspellings in the transcription files, and in the manuscript itself.  Is that hard to believe?

Maybe those changes in the "rooster" are not misspellings, but inflections, tone sandhi, or other normal linguistic phenomenon.  But let's say they are misspellings for this question.

Based on that tiny tiny sample, it would seem that there is 14% probability of initial d being changed to l, and 14% probability that final in changed to r.  How much effect could those "random" changes have on the per-character entropy?  

In my word model, d and l are both members of the "dealers" set D, together with r and s.  So at that initial slot, before the errors, there was already some prob distr between those four characters.  If 14% of the d are mapped to l by scribal or dictation error, that may increase or decrease the entropy depending on whether the distr becomes more uneven or more even.   I am too lazy to get the true numbers now, but suppose that the probs without errors are  d=1/2, l=1/4, r=1/8, s=1/8.  Then that slot would contribute 1/2+2/4+3/8+3/8 = 10/8 = 1.25 bits of entropy to the word entropy.

Noy suppose that the error rate is such that half of the d become l.  Then the probs would become d=1/4, l=1/2, r=1/8,  s=1/8.  Surprise: the entropy of that distribution is still 1.25 bits, so the word entropy would not change.  (But of course now a fraction of that entropy is no longer meaningful information, it has been replaced by noise.)

So you may see that errors may raise or lower the entropy, as computed from the word frequencies.  They will always destroy meaningful information, but need not replace it with noise.

Same for the hypothetical mutation of the ending in to r in daiin ⟶ dair In fact, when I developed my crust-mantle-core word model (which is actually a "seven layer" model), I defined the set N of "coda" elements as being 

    113.500000  0.00091 {n}     868.250000  0.00697 {m} 
   1665.500000  0.01336 {in}     40.000000  0.00032 {im} 
   3779.000000  0.03032 {iin}    15.000000  0.00012 {iim}
    159.000000  0.00128 {iiin}    1.0       0.00001 {iiim}
     
    487.750000  0.00391 {ir}
    130.500000  0.00105 {iir}
      1.0       0.00001 {iiir}

(The two numbers are counts (fractional because of commas) and relative frequencies among all elements.) 

I was unhappy with those codas ending in r, because I already had r as a member of the class D, and I could not let r by itself be a coda, like n or m. 

But that was before I looked at that "rooster" recipe. Now I have the strong suspicion that all the endings ir and iir are quillos ("typos, but with a quill") for iin and iiin, respctively; and that a fraction of the words that end in r should actually end with in...

All the best, --stolfi