Subject: Re: New Yorker article From: Bill Richter Date: Wed, 30 Aug 2006 12:02:35 -0500 I want to comment on Perelman's discussion of honesty: If everyone is honest, it is natural to share ideas. [...] Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest. It looks like an an unfortunate ugly feud, and it sounds sad Perelman to make a "complete break with his profession". But my belief is that Perelman is only complaining about the lesser of two evils. He seems to only be talking about credit. And credit isn't that important in itself, it's just grease that's needed to make the Math engine run. I largely came to this opinion from Richard Stallman's GNU Manifesto, included in the Emacs documentation, and I'll excerpt: People who have studied the issue of intellectual property rights carefully (such as lawyers) say that there is no intrinsic right to intellectual property. [...] All intellectual property rights are just licenses granted by society because it was thought, rightly or wrongly, that society as a whole would benefit by granting them. Mathematicians need to get enough credit to find jobs, and society needs to award credit to mathematicians in order to induce them to `share their ideas'. It's the ideas which are important, the Science, and not who got credit for what. And it is very difficult, most of the time, to see what the crucial ideas are. The obvious truth is that there are only two ethical "laws" of credit: 1) Don't steal from folks that are powerful enough to defend themselves, 2) Don't kill the golden goose---it's in your self-interest to make sure folks you could steal from get enough credit to survive, if you happen to desire their future output. I thought that I had two theorem-credits "stolen" from me, but there's no point in worrying about it. The problem was there was no golden goose: it wasn't valuable enough property to worry about. I think the greater evil is the rejection of the scientific method, seen across the board in Science/Math. I want to define the scientific method as the vigorous scrutiny of our beliefs by reason & evidence. I contend that the violations of the scientific method are so widespread (outside the narrow obligation to not fake proofs or experiments) that we should conclude that Science/Math has actually rejected the scientific method. In Biology & Cosmology, scientists & science writers make pronouncements with great certainty which would be better stated as wild conjectures. Good refutations can be found in Ian Stewart's book "The Collapse of Chaos", coauthored with a biologist Jack Cohen. Clearly, scientists only feel an ethical obligation to scientific method in the sense that the can't fake experiments. When they speak to the general public, anything goes. Mathematicians similarly feel obligated to not fake proofs, and I've never heard of a mathematician faking a proof. So within a narrow focus, mathematicians & scientists, we see strong adherence to the scientific method. But outside this narrow focus of not faking proofs & experiments, I see widespread violations of the scientific methods. So e.g. there's this widespread belief that we're genetically programmed robots (i.e. a combination of genes + environment), and the evidence for this is very slim. The Human Genome Project was just triumphantly completed, after they found our 25,000 partial protein recipes (our genes (3% of our DNA)), and some rudimentary "genetic programming" is known: turning genes on & off is controlled by very complicated combinations of proteins glommed onto binding sites near the gene, and these glommed-on proteins have themselves partial protein recipes. That's not what I'd call genetic programming. So there's no strong case even for life even having a scientific explanation. Now my belief is that this rejection of the scientific method pervades Topology as well as Biology & Cosmology. The upshot of that is that things that could be mathematical problems become political problems. That doesn't mean these problems can't be solved, but they must be solved politically. That's dicey, because I imagine we're all much better mathematicians than politicians :-D There is an important criticism to make of the scientific method, made by postmodernists, and I finally absorbed this from the books of the MIT biologist Evelyn Fox Keller, e.g. "The Century of the Gene", which discusses the HGP, and I'll quote again: ducks have a gene that the duck uses to makes over 300 different proteins involved in ear-cilia. Keller writes in a heavy PoMo style that I was initially irritated by: why doesn't she just say these scientists are violating the scientific method? But if we're to scrutinize our beliefs with reason and evidence, where we do stop? Much of what Keller writes is how biologists say crazy things because they're influenced by culture. Must we scrutinize our culture then? Sounds a lot harder than Biology or Topology! So there's some actual sense to scientists restricting the scientific method to laboratory experiments. I want to point out a violation of the scientific method in Topology, but first let me mention something I don't like that doesn't sound to me like the scientific method ought to apply. The surgeons have not been at all forthright in explaining that the purpose of their field is to reduce manifold problems to homotopy theory. This caused me a great deal of trouble back in the early 80s, when I solved some knot theory problems via the surgery machine, and folks acted puzzled, "What field do you work in?" But the question of the `real meaning of a field' doesn't sound like a scientific question to me. Of course, a lot of my problems were entirely due to me, I did way too much whining and not enough going off to a cave to see what I had & hadn't actually proved. I'm older & wiser now, but I feel stymied by e.g. this violation of the scientific method: The literature is littered with claims that the admissible monomial basis of the lambda algebra follows easily from the Adem relations, and similarly that the Lambda EHP sequence. I'll make a quick argument about the difficulty of these two combinatorial proofs: My proof of the Lambda basis essentially uses Bousfield's A_* action on Lambda, and the A_* diagonal. That's not a proof that second year grad students would likely stumble upon :) Now the Lambda EHP sequence is considerably easier, and there are proofs buried in the literature, but it's still too hard to leave as an exercise, and one way to say it is that the Curtis excess (explained in Wang's paper) is too hard a formula to concoct. The Lambda EHP sequence would be an easy result if it was true that the Steenrod alg excess could not increase after applying an Adem relation. That's false, but it's true for the complicated Curtis excess. Now I claim that the scientific method obliges mathematicians to respond to bug reports such as this. Back to Perelman: he's only talking about credit, and honesty is a meaningless concept if you remove an obligation to the scientific method. It's easy to get the wrong answers without lying: just don't think about it! I think this is a very serious problem in our society, well described in Orwell's 1984, something like, "There was no word for Science in Newspeak. There were of course folks working on weapons research, but there was no word in the language for the empirical habit of thought that scientists would be expected to have." I think that's what we're seeing, with the rejection of the scientific method except in the narrow band of faking proofs/experiments.