Re: [lojban] Re: Are Natlang the best case for entropy in communication ?

[Escape Landsome <escaaape@gmail.com>]

> EVIDENCE is date gathered from experiments designed to support or refute a
> hypothesis.

* In hard science like Mathematics or Physics, yes, but those do not
have the monopoly of scientificity, and Linguistics being a much more
"human social science", accepts scientific argument in a more laxist
way.

In social sciences, probability is accepted under the subjective form
it has, concurrently to objective measurement it has too (if you go
read the articles on Probability theory in Wikipedia or Britannica,
you'll see the foundations of probability theory accepts both
interpretation of probability, and it is still discussed which one is
the true one)

* So, first, in the case of Example 2, since the utterance says how
many people there are, and it is impossible to tell outside of the
utterance, there is equiprobability, and this is proved.  Thus
S(Example 2) = -5*(0.2)*log_2(0.2) = 2.32 is *PROVED*

If you are not convinced, or if you look for a qualitative reasoning
that confirms it, think that there are thus 5 equiprobable
possibilities, so you need to code {a,e,i,o,u} in binary digits, and
you need a little more than 2 bits for that, 2.32 is then the good
result.

* For the Example 1, "bouche" is highly probable, and the 6 others
highly strange.   Let P be the probability of the "probable event",
that is "X = b in bouche".

Then S(Example 1) is -P.log_2(P) + other terms

where other terms is between P.log_2(1-P) and (P/6).log_2((1-P)/6) [as
can be proved mathematically]

The value of P should be computed from a corpus, but without that we
can bound it by minoration and it is certainly > 0.8, so, do the
calculations, and you'll see this holds.

* Anyway, you want something else, that nobody can give you at the
present, that is (unnecessary) precise studies, and even then, I bet
you won't be convinced.   What would convince a believer ?

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