I wondered whether physical experiments can find the outcome of otherwise intractable mathematical problems.

For example, solitons or other non-perturbative effects in QFT cannot be seen at any order in perturbation theory, and are difficult to calculate, but could in principle be measured. Is nature doing the whole path integral/the whole perturbative expansion at once? Does that mean a computer could, in principle do it, in a finite time? or can nature solve math problems that are otherwise impossible?

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    $\begingroup$ In my opinion, this contains the philosophical question, whether reality as we perceive it is really a simulation. $\endgroup$ – M.Herzkamp Jul 21 '14 at 14:49
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    $\begingroup$ Nature solves problems simply by having all the variables and letting the system evolve as it should. We try to predict the solution without actually having it happen at the same time and we don't include all the variables $\endgroup$ – Jim Jul 21 '14 at 14:49
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    $\begingroup$ This question appears to be off-topic because it is about philosophy of science (or complexity theory, depending on how you look at it). The question whether nature "carries out" the mathematical calculations we use to describe it or if our descriptions are laughable inept attempts to make nature comprehensible is not, in any way, physically answerable. $\endgroup$ – ACuriousMind Jul 21 '14 at 14:53
  • $\begingroup$ @ACuriousMind don't be so prescriptive! $\endgroup$ – innisfree Jul 21 '14 at 15:02
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    $\begingroup$ While I am not possessing any proof of it, I'm pretty sure that nature is not actually calculating anything, it's just doing it. Much in the same way you don't need to calculate how to throw a baseball, you just do it. $\endgroup$ – Kyle Kanos Jul 21 '14 at 15:11