Science > Physics > Algebraic Geometry and Algebraic Topology in Physics Pro-and-Con Critique 5: The Atiyah-Jaffe Controversy
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Science > Physics |
| User: |
"OsherD" |
| Date: |
08 Feb 2006 08:38:30 PM |
| Object: |
Algebraic Geometry and Algebraic Topology in Physics Pro-and-Con Critique 5: The Atiyah-Jaffe Controversy |
From Osher Doctorow
In 1 Apr 1994 on math.HO/9404229 v1 1 Apr 1994 and the next day in
Bulletin of the American Mathematical Society 30(2), 1994, pp. 178-207,
a paper appeared entitled "Responses to 'theoretical mathematics:
toward a cultural synthesis of mathematics and theoretical physics' by
A. Jaffe and F. Quinn," by Sir Michael Atiyah, Armand Borel., G. J.
Chaitin, Daniel Friedan, James Glimm, Jeremy J. Gray. Morris W.
Hirsch, Saunders MacLane, Benoit B. Mandelbrot, David Ruelle, Albert
Schwarz, Karen Uhlenbeck, Rene Thom, Edward Witten, and Christopher
Zeeman (30 pages). HO in the paper stands for History and Overview.
The paper is very relevant to this thread regarding algebraic topology
and algebraic geometry in physics. Sir Michael Atiyah has been a major
contributor to K-theory and to the above branches, and Edward Witten
has already been mentioned earlier. I'll concentrate here mostly on
Atiyah, Chaitin, MacLane, Mandelbrot, Ruelle, Thom, and Witten for
brevity.
The paper in question by Jaffe (Harvard) and Quinn (Virginia
Polytechnic and State U.) appeared in math.HO/9307227 v1 1 Jul 1993 and
in Bulletin of the American mathematical Society 29(1), July 1993,
pages 1-13.
I'll try to continue this shortly.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Algebraic Geometry and Algebraic Topology in Physics Pro-and-Con Critique 5: The Atiyah-Jaffe Controversy |
08 Feb 2006 08:58:12 PM |
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From Osher Doctorow
Jaffe and Quinn wanted mathematicians to appreciate physicists and even
publish theoretical physics without necessary complete "formal proofs"
that mathematicians usually require. In their paper, they made this
rather clear, but they included some example sections which offended
Mandelbrot for example who claims in slightly different language to
have been picked on. Jaffe and Quinn were a bit too tolerant of
journal editors and peer reviewers and a bit too unclear on them such
as urging them to admit papers on Jaffe and Quinn's standards. They
also confused things somewhat regarding "speculation" which they
strongly condemned, even though the word "speculation" isn't so far
from intuition and has a lot of positives to recommend it in certain
contexts.
The reactions by Sir Michael Atiyah and the others reveal as much about
their own hangups or limitations and advantages as about Jaffe and
Quinn's paper. Roughly speaking, the more negative the reaction to
Jaffe and Quinn's paper (except for Mandelbrot, who may or may not have
been "slighted"), the more the researchers belong to the algebraic
geometry and algebraic topology schools or their mentality at least as
far as they had developed until 1994.
David Ruelle was the least offended and the most noncommital of the
repliers, although Chaitin was the most positive of the repliers -
Chaitin essentially endorsed Jaffe and Quinn's positions. Ruelle is
an exceptionally interesting person, even compared to Mandelbrot whose
work overlaps with his. Ruelle experienced such a level of rejection
of his work in his earlier years (Mandelbrot did too, but he had IBM to
fall back on) that in his little book Chance and Chaos (if I have the
title right) he writes one of the most amusing stories about editors
and peer reviewers that has ever appeared in print to my knowledge.
Chaitin is a Creative Genius whose work is largely concerned with parts
of Knowledge/Semantic Information even though he calls it by other
names such as Algorithmic Complexity.
Several of the authors in Sir Michael Atiyah et al's paper thank
"*****", which isn't identified in the paper as far as I can tell, but
perhaps this stands for Atiyah's middle name (Richard?).
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Algebraic Geometry and Algebraic Topology in Physics Pro-and-Con Critique 5: The Atiyah-Jaffe Controversy |
09 Feb 2006 12:30:06 AM |
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From Osher Doctorow
Jaffe and Quinn basically wanted mathematicians to allow theoretical
papers to be published, where "theoretical" is distinguished by them
from "rigorous" within mathematics in the sense that "intuition and/or
speculation" are distinguished from "formal mathematical proof". They
considered that this would help mathematicians to advance in
mathematical physics (the branch of mathematics that studies physics,
roughly speaking) and would draw mathematicians and physicists closer
together. They qualified this by suggesting that ideas in theoretical
mathematical papers be labelled "conjectures" rather than "theorems".
These ideas met a negative reception by Sir Michael Atiyah, who claimed
to dislike their general tone and too authoritarian attitude. He
claims in slightly different language that Jaffe and Quinn, whom he
hyphenates as Jaffe-Quinn, "target" the whole area between QFT and
geometry and combinatorial and algebraic techniques, and even accuses
them of making disparaging remarks. The only places where Jaffe and
Quinn even remotely attacked specific individuals was a rather obscure
reference to the Dehn lemma in 1910 and 1957 and their claim that the
Italian school of algebraic geometry collapsed for a long time and
Poincare's work was slow to be followed up because both the Italians
and Poincare claimed too much, proved too little, and their essentially
nonstandard methods were too lacking in specificity to be imitated and
so on -except that I should add that Jaffe and Quinn criticized Thom's
later work but not his earlier work quite correctly for the failures of
catastrophe theory.
The reactions of Thom (of France) are quite interesting, and I hope to
discuss them soon.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Algebraic Geometry and Algebraic Topology in Physics Pro-and-Con Critique 5: The Atiyah-Jaffe Controversy |
09 Feb 2006 12:48:21 AM |
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From Osher Doctorow
Before discussing Thom's reaction, my favorite "nemesis", the late
Saunders MacLane of U. Chicago, gave what have to be the wildest
reactions to Jaffe and Quinn that I have seen "outside a zoo". MacLane
disparages "the formal advice of the logicians," (p. 14), apparently
having somewhere heard about mathematical and philosophical logic and
finding that he didn't like them. He disparages "the ghost of
Feynmann" (2 n's for the benefit of crank counters, whom I dislike
anyway) (p. 15) and to give the whole quote: "We need not sell
mathematics short, not even to please the ghost of Feynmann." Unlike
Garrett Birkhoff of Harvard, who for a long time was MacLane's
colleague, MacLane cannot be described as the opposite of Birkhoff's
father, also a professor and a self-admitted Nazi. Birkhoff (the
younger) did recommend Germany to MacLane for his Ph.D., and MacLane
got his Ph.D. there and returned back to the USA just a little while
before WWII.
In MacLane's reply to Jaffe and Quinn, MacLane keeps repeating the
magic word "proof" and manages to attack the same Italians whom Sir
Michael presumably was defending because of the inferiority of
intuition (the Italian specialty) to Zariski and Grothendieck's and
Adams' and Serre's "precision". Although MacLane didn't invent
category theory (Eilenberg did to my recollection), he became its most
prominent defender, and it would be interesting to know what category
he put Feynman and the Italians and the logicians (Godel, Lukaciewicz,
etc.) into. He closed with: "mathematics does not need to copy the
style of experimental physics. Mathematics rests on proof - and proof
is eternal." Well, apparently MacLane is not.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Algebraic Geometry and Algebraic Topology in Physics Pro-and-Con Critique 5: The Atiyah-Jaffe Controversy |
09 Feb 2006 01:09:51 AM |
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From Osher Doctorow
Well, I have to put somebody else before Thom, namely Edward Witten.
Witten notices that Jaffe and Quinn aren't wild about string theory,
and his main argument is a rather well-behaved (in the sense of not
raging, unlike some people whom I won't mention) discussion of some
reasons why string theory has stronger and more focused motivations
than Jaffe and Quinn convey. Unfortunately or fortunately, events were
to prove Witten wrong about "string theory" at least as he understood
it then, though if we replace "string" by "superstring" and then by
"brane", we do get a different set of arguments that Witten could have
later on written about and did in fact (though not to Jaffe and Quinn).
On the other hand, some people might describe this as a different
series of assumptions or fads.
We do get an insight into why Witten keeps plugging away at algebraic
geometry and algebraic topology, namely Witten's claim in the Atiyah et
al paper that "the core geometrical ideas...have not yet been
unearthed," (p. 28). If we change "geometrical" to "topological", we
do get a new fad - oops, perhaps I should say, we get closer to the
present era, though both geometry and topology are still with us.
Well, perhaps we do have to dig up something or someone. On the other
hand, it's interesting that Witten looks for answers in the algebraic
interaction with geometry and topology, presumably on the theory that
the way to look for things is to look for their subsets or supersets or
objects and compositions ad infinitum. Like Atiyah, there's no logic,
no probability-statistics, no combinatorics, little experiment, etc.
Perhaps one should call this view the Witten-Atiyah (WA for short) view
:>) Oops, the Witten-Atiyah-Saunders MacLane (WAS) view?
Osher Doctorow
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