Re: Panu Raatikainen's review of two of Chaitin's books.

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 05/27/04 

Date: 26 May 2004 15:31:00 -0700

jesse@phiwumbda.org (Jesse F. Hughes) wrote in message news:<87wu2zmbzi.fsf@phiwumbda.org>...
> erayo@bilkent.edu.tr (Eray Ozkural exa) writes:
>
> When Chaitin gives a technical definition of random, proves that
> long initial segments of Omega are random[1]

He proves that it is in fact a random real, so not only "long initial
segments". :)

> and then concludes
> triumphantly that some mathematical facts are true "for no reason,"
> then he is confusing his technical fact with an intuitive idea that
> random things occur without cause. This is the confusion of which I
> spoke.

Umm. Not that simple. You really have to take a look at "The Limits of
Mathematics", which is a shorter version of AIT, or the AIT monograph
itself. (If I'm not mistaken with the former title)

In particular, he shows that Omega is the answer to a legitimate
number theoretic problem, much like "what is 2+2?" And the solution to
these problems are usually considered mathematical fact, and I'll
maintain that it is no confusion to think such. Of course, the
diophantine equation he constructs is rather large, but to a math nerd
it shouldn't matter how large an equation is (if that was your
concern, maybe you found it artificial philosophically?)

> I don't know what the heck you were on about, but it wasn't relevant
> to my comments. On the other hand, the fact that the output of these
> programs are complex in our everyday use of the term complex indicates
> that one must be careful to avoid confusing the technical term and the
> everyday term --- and that perhaps the technical term is badly chosen.

I was referring to Luis's examples, not your post.

However, I kind of think that intuition of complexity is more likely
to be wrong than deep mathematical theorems of complexity. That is my
idea, you may trust your intuition, but don't blame me if it fails you
in the long run. You've been warned :->

Regards, 

--
Eray Ozkural

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