After spending two hours in the middle of the day hearing about unexpected uses of twistors to study particle scattering amplitudes, yesterday I went down to Manhattan’s relatively new Museum of Mathematics, which had scheduled a “Family Friday” event, featuring Edward Frenkel and Jim Holt. The event began with Frenkel giving a presentation about math, kind of an introduction to his wonderful new book Love and Math. Everyone in the audience hoped that the kids in attendance didn’t catch his comment about a typo in reference to the LHC (given Frenkel’s film experience, some had suggested that a joint event with the neighboring Museum of Sex would have been a good idea).
Things really got exciting though when Jim Holt joined him on the stage, for a no-holds-barred discussion of Platonism and mathematics in front of a standing-room-only crowd. Holt ripped into Frenkel as engaging in “mysticism” by claiming that mathematical objects are “real” and “exist”. He quoted from Bertrand Russell, who early in life took Platonist positions, but in his old age renounced them. Frenkel countered, dismissing Russell’s later quotes as those of someone who had gone soft in the head. He went on to quote arch-Platonist Kurt Gödel, with the response from Holt a low blow: he told the story of how Gödel had died a paranoid, starving himself to death. Holt continued the attack in the same vein, telling about Georg Cantor, and his end in the loony-bin. The implication was that Platonists are not just mystics but nuts.
Frenkel then decided to try taking the high road, invoking W.V.O. Quine and Hilary Putnam (distinguished non-nuts Harvard professors I took courses from) and their Indispensability Argument. The basic idea there is that the best choice of what “exists” is those entities that are an indispensable part of our best theory of the material world. Not sure yet whether twistors count, but if they become part of the new unified theory of gravity and the Standard Model, then they surely exist as much as anything does. Holt parried with Hartry Field’s Science Without Numbers: A Defence of Nominalism which supposedly shows you can do Newtonian physics without math. Frenkel (together with much of the rest of the audience) scoffed at this, making the obvious riposte: what about GR?
This was finally brought to an end with a few questions from the audience, a sizable contingent of which was underage. They seemed to be having a great time, far more entertained by this sort of thing than by the usual flashy trinkets people use to try and get them interested in math (but which seem to work better on the pre-verbal baby crowd). All in all, a highly edifying experience, I hope the Frenkel/Holt show gets taken on the road.
For a picture of the action, see here.