Subject: The Unberarable Randomness of Mathematics

From: mulix <[email-masked]>
Date: Mon, 19 Mar 2001 15:20:32 +0200 (IST)

an interesting article about the apparent "holes" in the foundation of
mathematics. 

http://www.newscientist.com/features/features.jsp?id=ns22811

from slashdot: "Here's a link to an article in New Scientist about
mathemetician Gregory Chaitin, who seems to have thrown some of the basic
foundations of math into question with his work on the 'omega number.'
Among the more provocative statements in the article: '[Chaitin] has found
that the core of mathematics is riddled with holes. [He] has shown that
there are an infinite number of mathematical facts but, for the most part,
they are unrelated to each other and impossible to tie together with
unifying theorems. If mathematicians find any connections between these
facts, they do so by luck" 

-- 
mulix 
http://www.advogato.com/person/mulix

linux/reboot.h: #define LINUX_REBOOT_MAGIC1 0xfee1dead

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From: Chen Shapira <[email-masked]>
Date: Mon, 19 Mar 2001 17:05:10 +0200

> facts, they do so by luck" 

One thing that caught my eyes was the fact that this was published as a
"popular" book, as opposed to a ground breaking article in a prestigious
mathematics journal.

Popular books don't go through peer review, and what is worse, the deep
ideas are explained in easy language by examples and extremes.

Ofcourse the statement quoted above isn't a mathematical statement, it isn't
even a meta-mathematical statement, its an explanation of an idea in
non-exact terms. Not to mention that there's no proof attached.

This remainded me abit of the book on Chaos I read a while back, it was an
nice book with pretty pictures and exciting descriptions, but there were all
simple applications of simple mathematical concepts. 
They are also similar in discussing mostly what math *can't* do, like
predict weather or connect itself.

I searched the library for some of his articles, and he seemed to be writing
mostly about complexity - the difficulty of solving problems.

And now I'm wondering if there's any one here who is knowledgable enough
about complexity to understand how this person could get from researching
complexity (which isn't too close to the foundation of mathematics - I would
expect him to be doing set theory, logic, model theory, computability and
such) to his ground breaking conclusions?

And I'm also wondering - in what sense is math random? randomness is about
things being unpredictable (at least precisly predictable), did he mean that
you can't predict what can be proved? you can't predict what they will prove
next?

*sigh*

Chen.

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From: Chen Shapira <[email-masked]>
Date: Mon, 19 Mar 2001 18:31:00 +0200

> i'm afraid i don't get you here, chen. what are you trying to say? 
> 
> just a quick note, the /. story also references the transcript of a
> lecture Chaitin gave on this subject, at  
> http://www.cs.umaine.edu/~chaitin/cmu.html
> 
> the lecture is much more interesting than the brief article mentioned
> previously, i just spent an hour reading it instead of listening to my
> 'programming languages' instructor. i should've known 
> bringing the laptop
> to that class was a bad idea, attention wise ;)

This lecture is very very interesting, and nicely sums up my Logic II course
and Computability.

But if I learned most of this in 2nd year course, this isn't ground breaking
math work, and definetly not news.