Tuesday, April 05, 2011

The Irony Age

One problem that continues to plague discussions over the safety of particle colliders, though the issue is relevant to other areas of cutting-edge science, such as synthetic biology and genetics, is that it is impossible to have what could sensibly be called an informed public debate on the issues. The people who understand the issues best work in the field under debate, so the accusation of vested interests cannot be avoided. Ironically, the most high-profile opponents to a new technology are often so badly informed they are quickly dismissed as crackpots, and rightly so. The result is an illusion of public debate. Ill-informed opponents do a disservice to people with genuine interest and concern by squandering the opportunity for an even-handed discussion of the risks.
That paragraph is from p.193 of Ian Sample’s Massive (Virgin Books, 2011), and it reminded me of the following, from the bottom of p. 640 of R. W. Hamming’s ‘Mathematics on a Distant Planet’, American Mathematical Monthly 105 (1998), 640–650, the gist of which was that we should have based our mathematics on known truths, not—as was increasingly done throughout the twentieth century—on axioms taken to lie beyond truth and falsity.
I need to mention a few things in my life that have shaped my opinions. The first occurred at Los Alamos during WWII when we were designing atomic bombs. Shortly before the first field test (you realise that no small scale experiment can be done—either you have a critical mass or you do not), a man asked me to check some arithmetic he had done, and I agreed, thinking to fob it off on some subordinate. When I asked what it was, he said, “It is the probability that the test bomb will ignite the whole atmosphere.” I decided I would check it myself! The next day when he came for the answers I remarked to him, “The arithmetic was apparently correct but I do not know about the formulas for the capture cross sections for oxygen and nitrogen—after all, there could be no experiments at the needed energy levels.” He replied, like a physicist talking to a mathematician, that he wanted me to check the arithmetic not the physics, and left. I said to myself, “What have you done, Hamming, you are involved in risking all of life that is known in the Universe, and you do not know much of an essential part?” I was pacing up and down the corridor when a friend asked me what was bothering me. I told him. His reply was, “Never mind, Hamming, no one will ever blame you.” Yes, we risked all the life we knew of in the known universe on some mathematics. Mathematics is not merely an idle art form, it is an essential part of our society.
Academics are of course free to pursue whatever interests them; and a hundred years ago, set theory interested many pure mathematicians. But academics will only be successful if their interests are those of their peers (or industry), so there’s some irony there. Any young mathematician bothered by set theory would have been unlikely to have gone into pure mathematics. Perhaps physicists uninterested in string theory are unlikely to choose theoretical physics; but certainly, a slight bias can become the rule, over a century or so. And a rule will tend to exclude other possibilities (even in the absence of corruption), making it impossible to estimate costs and benefits properly. (To be continued.)

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