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shminux comments on The Dilemma: Science or Bayes? - Less Wrong
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If I could show you an example of mathematicians running ongoing computer simulations in order to test theories (well. Test conjectures for progressively higher values), would that demonstrate otherwise to you?
And it's not as if proofs and logic are not employed in other fields when the option is available. Isn't the link between physics and mathematics a long-standing one, and many of the predictions of quantum theory produced on paper before they were tested?
Here is the difference: the superstring theory is a reasonably good mathematical model which predicts a spacetime with 10 or 11-dimensions on purely mathematical grounds. It also predicts that particles should come in pairs (quarks+squarks). Despite its internal self-consistency, it's not a good model of the world we live in. Whether mathematicians use the scientific method depends on your definition of the scientific method (a highly contested issue on the relevant wikipedia page). Feel free to give your definition and we can go from there.
I feel this reply I made captures the link between proof, evidence, and elegance, in both scientific and mathematical fields.
That is to say, where proof is equivalent for two mutually exclusive theories (because sometimes things are proven logically outside mathematics, and not everything in mathematics are proven), evidence is used as a tiebreaker.
And where evidence is equivalent for two mutually exclusive theories (requiring of course that proof also be equivalent), elegance is used as a tiebreaker.
Not quite. More like abstractly physical gorunds...combining various symmetry principles from preceding theories.
Not quite. it doesn't predict a single world that is different. It predicts a landscape in which our world may be located with difficulty.