Hi: I will put quotations from different postings or Molt's writing in between two "**" Well, I can see the classical reaction of some groups when one of its members points out that something is really wrong with the group. Marta will suffer all kind of "polite" (nothing of the sort of the Benabou-Taylor confrontation) attacks, but not for this less devious or sanguine. Typically she will be taken out of context, or get answers to questions she never had asked, or be treated ironically or in disbelief (**I can't tell if you're kidding. I'll assume you're not **) There are two principal points here: 1. The real value of some contributions of category theory to physics. 2. The lot of rubbish written using category theory and which is fashionable because it claims to have applications to physics. Marta was forced to explicit some of the questions we can clearly see in between lines in her original posting: ** I was trying to elicit an open response from those who *do* know about the value (or lack of it) of categorical string theory. In particular, I would like to have an answer to this question. Why is it that anything which even remotely claims to have applications to physics (particularly string theory) is given (what I view as) uncritical support in our circles? Best, Marta ** I will like to see a clear answer to this question. Or a clear refutation proving that it is not the case. Notice that the existence of point 2. above is perfectly consistent with the existence of really valuable contributions of category theory to string theory, which is one of the points treated by Motl. ** There's nothing wrong with applying category theory to string theory. The papers by Michael Douglas and Paul Aspinwall cited above by Motl are some nice examples of using derived categories to study D-branes.** This make us think that they may be some valuable contributions, but this possibility is also left open by Motl himself. Quoting myself: ** I will like to see here a debate about Motls's writing quoted above. Just about this writing, NOT ABOUT Motls himself or other things he may have done or represent !! ** No luck, just discredit Motl, not refute his sayings: ** Perhaps more to the point, Lubos Motl is famous for his heated rhetoric. He doesn't like me, or anyone else who criticizes string theory. The articles you mention above are mainly reactions to my This Week's Finds. ** ** My reaction to the blog posts you cite is that this is a sting theorist holding his breath and refusing to learn category theory. My guess is that Motl wouldn't want to learn the heavily categorical formulations of mirror symmetry that Yan Soibelman uses, even though they are motivated by string theory.** The following is better in answering Motl: ** Categorical ideas are absolutely central to several competitors to string theory: the Barrett-Crane model of quantum gravity (and to a lesser extent 'loop quantum gravity' with which the BC model is often conflated) and Connes' recovery of the Standard Model from non-commutative geometry (a part of mathematics which has obliged reluctant mathematicians to think about categorical ideas deeper than they originally were comfortable with). There is nothing cracked or crackpot about either. ** I am unable to judge, but it seems to me this gives category theory strong support But does not go against what Motl says concerning category theory. Neither against Marta's warning that category theory is being discredited by many (she says a minority) category theory people. Motl writes: ** I've asked the same elementary questions to many people who've been trying to explain me derived categories - some of them with some success, most of them with no success whatsoever: Are these notions and statements of category theory something that you can prove - or at least check in many situations - to be valid for string theory as we know it, or is it just an unproven conjecture that derived categories describe D-branes? ** Can somebody give a an answer ? He also writes: ** I always feel very uneasy if the mathematically oriented people present their conjectures about physics, quantum gravity, or string theory as some sort of "obvious facts". ** I would say that any serious scientist or mathematician would feel the same way !!, and also that this seems to be a common practice in many papers that claim applications of category theory to physics. ** I have this image of differential geometers saying to each other, a century ago, "Don't you think somebody ought to tell that Einstein to stop trying to use differential geometry to explain gravity, before our whole field gets a bad name?" ** Well, Einstein was not "trying to", he was using it, and presented this use as an accomplished fact. Also, you forgot to mention that he flunk a high-school exam or something of the sort proving by this very fact that a lot of people were stupid, just as they are those which have doubts about the real value of some applications of category theory to physics ! ** I do not see how anybody can possibly discredit category theory by applying it to string theory, even inappropriately, any more than "The da Vinci Code" discredits classical geometry and number theory. ** ** Since Motl's personality is well known, any damage will be minimal. I think we should relax and take it easy.** Well, rubbish category theory always discredits the whole of category theory, specially given the fact that it is not yet a prestigious and established subject (think in SGA4 and the introduction of SGA41/2) It will be nice to relax and take it easy. Will all of us do so ? I hope we will read in this cat-list some valuable considerations about Motl's questions and doubts, and about Marta's courageous warnings. e.d.