Eduardo having preferred (wisely) not to try to edit down both sides of a discussion with a lot of quoting, I will follow his lead and summarize one side of it with context quotes from the other side. Eduardo Dubuc wrote (in part)
I am right about the fact that introducing Einstein and differential geometry into our present discussion on the interaction of string theory and category theory was an infantile attempt to attack Motl's views. Worst than that, it introduces a distraction to Marta's principal issues.
I responded: Sorry, Eduardo. I refuse to write out a hundred times "I will not attempt to attack the views of Lubos Motl". As for introducing distractions, Marta suggested (Mar. 12) that we should as a community not "quietly accept getting discredited by a minority of us presumably applying category theory to string theory", and that we should "react and point out that this is not what (all of) category theory is about" and "give a thought about what we, as a community, can urgently do to repair this damaging impression." On Mar. 14, it was suggested that meeting organizers might want to take this into account while choosing invited speakers. Now, I do accept that there are such things as bad mathematics and bad physics. However, this call for collective action against an entire field of research seems uncomfortably close to an organized boycott, an extreme enough breach of tradition that only an emergency - if that - could justify it. And, in such circumstances, the question of whether the emergency really exists is certainly relevant, and not (_pace_ George W. Bush) a presumptuous distraction. My response (Mar. 14) was twofold. I suggested that the general credibility of category theory does not depend on the credibility of its applications to physics. But I also pointed out, which I think is even more relevant, that physicists are quite used to tentative theories being studied for many years before they are accepted or rejected, and that there is no loss of credibility among physicists for those involved in this process. Neils Bohr is not remembered as "that crackpot who thought the atom was like a solar system". Note that only credibility among physicists is at stake here. Mathematicians are unlikely to base a negative judgement of _any_ branch of mathematics on what physicists may be doing with it, and in particular know perfectly well that this is not "what all of category theory is about". The rest of the world will not have a clue what all of category theory is about, and will never know the debate took place. We expect mathematics to be correct by the time it sees print; internal consistency is a comparatively easy goal. Physics, despite using almost as many equations, has a real and sometimes uncooperative universe to contend with, and cannot afford the luxury of progressing only through unassailable, permanently-established truths. Mathematics was once in a similar position: we recognize the genius of Euclid's axiomatic system even while realizing that (by our standards) it was fatally flawed. (Why do the circles in Euc.I.1 intersect? None of his axioms assert that any pair of circles whatsoever do so.) Ramanujan is perhaps alone among modern mathematicians in having been permitted, by general consent, something like the latitude to err freely that the physics community customarily grants itself - and his was a very special case. Had he lived to see the greater part of his work in print, he too would have proved, retracted, or labelled as conjecture many of the speculative claims that ended up as his legacy. I mentioned Einstein in passing, assuming that readers would have some idea of the initial skepticism with which relativity was viewed, and the length of time it took before that skepticism ceased to be justified. (Actual hostility was a separate, later, phenomenon, more related to antisemitism and Stalinism than to physics.) If I assumed too much, and should have explained more, I apologize. Eduardo then responded (in part)
Einstein using differential geometry to develop general relativity is not at the same level that John Baez using category theory to develop and/or understand string theory. I imagine John himself is probably the first to laugh at such a comparison.
and I responded to that (in part) If category theory happens to be the approach that works, and significant progress is made in fundamental physics as a result, it will be very much on the same level as relativity. If it isn't, it will be, from most physicists' point of view, an honorable attempt on the same level as many other theories such as the steady-state universe, tachyons (Remember tachyons? No? _They_ remember _you_...), magnetic monopoles, or the luminiferous ether, that were seriously considered in the past by respectable physicists. Until the results are in, it is, I think, not unreasonable to make comparisons with Einstein's early work on relativity - at a time when Einstein could not get results consistent with observation and many of his talented contemporaries had serious doubts about whether he was using the right approach. (Not whether he was a fool or a charlatan, just whether he was using the right approach.) Or, equally, with Einstein's later work on quantum mechanics, when history seems to have shown that he backed the wrong horse - but it was not so clear at the time. -Robert Dawson