Re: an true information theory

From: Daryl McCullough (stevendaryl3016_at_yahoo.com)
Date: 03/04/05 

Date: 4 Mar 2005 06:31:17 -0800

Stephen Harris says...

>I appreciate your comments, but I have to question them.
>
>> From this infinite
>> sequence of algorithms, strike off every algorithm that appears
>> only a finite number of times. If the resulting list has only
>> one algorithm in it, and that algorithm is correct, then P
>> has guessed correctly.

Stephen,

I was trying to sketch a more general notion of "computing an answer",
but now that I think about it, I don't think it's a very interesting
notion, so perhaps I should just drop it.

The basic idea is that if the correct algorithm is A, then eventually
the guessing program will guess A. However, there might be a time when
a *different* algorithm A' appears to be a better choice than A. Then
the guessing program may temporarily switch his answer to A'. But that's
only temporary---eventually he will switch back to A. An incorrect algorithm
can appear to be better than the correct algorithm for a brief amount of
time. That's because the correct algorithm might take longer to compute
some output than the incorrect algorithm. For example, a program that
correctly generates primes will take longer to run than the incorrect
program that uses the algorithm: 2 is prime, and every odd number is
prime, although the incorrect program generates the correct answer
for 2, 3, 5, 7. 

--
Daryl McCullough
Ithaca, NY

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