Re: Raatikainen's critique of Chaitin

From: Tim Ball (tb_at_timball.net)
Date: 09/03/04 

Date: Fri, 03 Sep 2004 16:55:37 -0400

Craig Feinstein wrote:

>Timothy Murphy <tim@birdsnest.maths.tcd.ie> wrote in message news:<jw%Zc.26478$Z14.8531@news.indigo.ie>...
>
>>Craig Feinstein wrote:
>>
>>>I'll ask a question to the people who criticize Chaitin's work. What
>>>in general about Chaitin's work, which I happen to think is some of
>>>the best mathematics of the past century, bothers you so much?
>>>
>>(1) I think it's an absurd exaggeration to say Chaitin's work contains
>>"some of the best mathematics of the past century".
>>There are some moderately difficult bits of mathematics in his theory -
>>I mean the sort of thing that might lead a good graduate student
>>to think for an hour or two -
>>but it would be absurd to put it beside the classification
>>of the finite simple groups, for example.
>>
>I am more impressed with his results than classification of finite
>simple groups. Classification of finite simple groups is nice to have,
>but it doesn't shake up the foundations of mathematics like his result
>does. In my opinion, mathematics in the last 100 years is relatively
>boring compared to other centuries. His result and other results like
>his (for instance, Godel's Theorem) at least made things interesting.
>
>[ snip ]
>
Now of course what is _best_ mathematics is a matter of opinion, and you
are entitled to your own. If the classification of finite simple groups is
not deep enough for you, then there is little anyone can say to convince
you otherwise.

But you asked what bothers people about Chaitin's work. I think many
mathematicians are bothered exactly by these exaggerated claims more than
by anything in Chaitin's mathematics itself. You may not agree with that,
but you asked what other people think and this is your answer.

As for being boring, the mathematics of the last 100 years has certainly
been less _ambiguous_ than prior to that. Not-quite-precise concepts
have been
formalized to the extent that there is now very little argument about
admissible
operations with them (e.g. probability and computability in the 20th
century,
continuity toward the end of 19th century).

As a result of that, mainstream mathematics has seen less controversy about
what is a legitimate proof, and more deep results. Sophisticated tools
have been developed, long-standing open problems have been solved, new
concepts have been defined and successfully applied to areas outside of
pure
mathematics, such that physics, statistics and informatics.

In other words, we have stopped arguing about the rules, and now we
concentrate
on getting better at playing the game.

So if you are looking for ambiguity and controversy then yes, modern
mathematics
must seem boring. But if you appreciate the insights required to solve
difficult
problems, the elegance of tools and concepts that have been refined through
many iterations, and the unexpected connections between seemingly unrelated
disciplines, then the 20th century mathematics has been very exciting.

TB

 

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