Subject: Re: two postings From: Bill Richter Date: Tue, 5 Jul 2005 20:33:23 -0500 Andrew, I like that, the Deconstructionist Institute for Surreal Topology, which, I assume, you are not a member. I've been thinking a lot about Topology and postmodernism (related to your word deconstructionism). If we defined postmodernism roughly as the rejection of the scientific method, and a preference for subjective rather objective, then Topology (and Science in general, I think) has thoroughly embraced postmodernism. Let's call the Naive Scientific Method the "habit of thought" (as in Orwell's 1984: in Newspeak there was no word for the habit of thought that scientists used) of vigorously scrutinizing our scientific claims with the 2 tools of reason and evidence. I say Naive because only a naive person would think that scientists actually feel compelled by such an obligation to scrutinize their claims. To put it another way, an obligation to debug our proofs, and to respond to bug reports. Since you posted a fine joke, I won't bore you on how the meaning of surgery theory is solving manifold problems via the unstable homotopy of Poincare complexes. That's not really a scientific claim anyway. But for the last 4+ years, I've been trying to write up clean versions of Mahowald's unstable work, mostly his 1967 AMS Memoir. I think I can do it, because I'm a 60s guy, meaning mostly surgery and Toda's book. But I've been stymied by the refusal of a large number of people to respond to my bug reports. Just to take a simple example, the literature is full of claims that the Lambda admissible monomial basis follows easily from the Adem relations. I concocted such a proof (10 page version on my web site), but it not trivial, and I think I have the first combinatorial proof ever. The result was known to be true by geometric arguments of the 6 authors and Priddy.