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Dirac and Beauty

Nobel laureate Paul Dirac, one of the fathers of quantum mechanics, has been a hero of mine ever since my teens. He was one of a mere handful of scientists whose grasp of theory was so strong he could predict the existence of something unknown in Nature (anti-matter) that was subsequently found exactly as he'd predicted. Recently Freeman Dyson offered a favourable review of a new Dirac biography by Graham Farmelo, in the latest New York Review of books, which contains some very thought-provoking ideas. Toward the end of this review Dyson claims that Dirac left a three-fold legacy to physics: the astounding discoveries of his fertile period 1920-33; a doctrine of mathematical beauty expounded over the remaining 50 years of his career; and a profound distaste for philosophical interpretations of quantum mechanics (which I vigorously share).

Here is Dyson on the second phase: "
The second legacy is summarized in a statement that Dirac wrote at the end of his life: 'If you are receptive and humble, mathematics will lead you by the hand.'
... The doctrine of mathematical beauty is itself beautiful, and there is no doubt that Dirac believed it to be true. But it does not agree well with the historical facts. During the wonder years when he was making his great discoveries, his thinking was more concerned with practical details and less with abstract beauty. And during the long second half of Dirac's life, when he was preaching the doctrine of mathematical beauty, it did not lead him to important new discoveries."

This touches on an interesting question to which there's no sign of an answer yet, and may never be. Perhaps Dirac's faith in mathematical beauty is actually justified, but science also proceeds in fits and starts as described by Thomas Kuhn in "The Structure of Scientific Revolutions". A simple and beautiful principle is discovered which triggers many more discoveries that complicate and muddy the picture; then a deeper simple, beautiful principle emerges that clears the board once more; and so ad infinitum. Modern complexity theory shows clearly that very complex behaviours can arise from applying very simple rules (a beautiful illustration is the computer simulation Conway's Game of Life). So the really big question is this: is the reverse true, that every complex behaviour arises from the application of simple underlying rules that we haven't yet discovered. This is the modern form of an old dispute between rationalism and pragmatism, and therefore one of those philosophical disputes that Dirac so hated. Dyson is clearly on the pragmatist side, namely that Nature is at root complex and messy. I veer to the other pole.

Whichever is right, it's a far more interesting problem than those fashionable fairy-tales that purport to be interpretations of quantum mechanics, such as the many-worlds hypothesis. Such pretentious cosmological speculations always end up in the same place, namely that there's another
copy of you somewhere else in this universe (perhaps infinitely many). The whiff of incense is overpowering - this is just Heaven by another name, the egoists' inability to face the fact that their personal identity will cease upon death. 

originally posted 11 Feb 2010 12:43 by Dick Pountain   [ updated 11 Feb 2010 13:40 ]


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