Yeah, I mean, when you study closely the history of scientific discoveries based on unexpected mathematics, you often find that say, Einstein knew he had made a discovery that had a systematic relationship he didn't understand. So he talked to all of the mathematicians he knew and eventually somebody pointed him to a paper Poincare had written thirty years earlier- but that was only after he'd looked at and rejected hundreds of other mathematical frameworks. That's where selection bias comes in. It wasn't like Poincare's theorems had an inherent and immediately obvious rightness over other theorems that don't have any physical value.
We simply designed (or borrowed from existing work) mathematics that worked. I mean, it's interesting that a sort of convergence happened, where over the course of human history neither the physics or the math existed, and then within a thirty year period you had both, but you could equally hypothesize that had Poincare not written the paper, Einstein would have had to find a mathematician and force him to develop it. Or else maybe Einstein's great discovery would have gone nowhere. Who knows what physical discoveries we can't act on now because we haven't yet come up with mathematics to explain them?
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timeasmymeasure
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Date: 2013-01-13 03:57 pm (UTC)We simply designed (or borrowed from existing work) mathematics that worked. I mean, it's interesting that a sort of convergence happened, where over the course of human history neither the physics or the math existed, and then within a thirty year period you had both, but you could equally hypothesize that had Poincare not written the paper, Einstein would have had to find a mathematician and force him to develop it. Or else maybe Einstein's great discovery would have gone nowhere. Who knows what physical discoveries we can't act on now because we haven't yet come up with mathematics to explain them?