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

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 05/12/04 

Date: 12 May 2004 07:28:02 -0700

Hello there,

I have come across this strange review by a certain philosopher, and
mere philosopher I must add, of Chaitin's work:
http://www.ams.org/notices/200109/rev-panu.pdf

I think he makes some rather ignorant statements about Chaitin's
results, but first, I would like to hear the opinion of other
mathematicians and computer scientists. (Preferably I would like to
hear nothing from some philosopher of logicist persuasion! I have
heard enough mumbo-jumbo!)

The most problematic part is:

"But appearances notwithstanding, this is simply wrong. In fact, there
is no direct dependence between the complexity of an axiom system and
its power to prove theorems..."

Wow! I am truly impressed! I didn't read any of Chaitin's more
philosophical books, just the proofs in AIT, so this comes as a shock
to me. I could find no errors in the proofs, and they did show that
there *is* a direct dependence between the complexity of a FAS and its
power to prove theorems (say in determining digits of Omega) as
defined in AIT!!!

Needless to say the reviewer also attacks Chaitin's intuition-building
device of saying "the digits of Omega are true for no reason". Analyze
well, dear mathematician, how this "philosopher" criticizes him:

"...The individual bits of Omega are 0 or 1 depending on whether
certain Turing machines halt or not..."

It seems, nowadays, cow excrete could easily pass off as philosophy!
The reviewer perhaps believes that he understands what "reason" means,
but I think not. The very question is *which* Turing machines halt,
and the answer is that there is no structure, it is truly random.

>From the lack of additional information [H(a|b) ha!] in his statement,
it is evident that he doesn't understand what redundant means either.
In my opinion, he desparately needs a lesson in complexity, though the
chances are that he will never pass that course...

I suspect there are some computers among us, which, when they look at
theorems in AIT, detect only garbage. Check another tick for the
empirical evidence that there is a minimal complexity required to
understand a theory.

Perhaps mathematical truth is even more random to them than to us?

Secondly, and most imporartantly, has Chaitin himself answered these
"criticisms"?

Comments most welcome, 

--
Eray Ozkural