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The question of whether your observations are consistent with the laws of physics is pretty much a mathematically defined question.

To say that the laws of physics are consistent with your observations means that a certain mathematically defined property of all the observations you have ever made holds. If you can't do the mental math to see that that statement is actually true because it takes so long to compute, how do you know it's actually true?

For example, people say that the brain follows the laws of physics, and that it is consistent with the laws of physics that the sequence of all actions you have ever done were possible according to the laws of physics. If (1) all such proofs that the sequence of everything you observed yourself do was explained by your brain following the laws of physics, and (2) all proofs that the sequence of everything you have done actually was consistent with the laws of physics, are so long that you cannot yet figure out those proofs, then how do you know that the sequence of everything you have done actually is consistent with the laws of physics?

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  • You have the cart before the horse. The observations of reality came first. Then brilliant minds tinkered with the maths until the maths matched the observations. In cases where the maths is simple and cosmically beautiful, the equations get called laws.
    – Richard
    May 3, 2019 at 23:05
  • @Richard I think you're using circular reasoning. You're making the assumption that the universe follows the laws of Physics, and then using that to deduce that the laws of Physics came first and then that's what created brains. How do you know those actually are the laws the universe follows if you can't make the huge number of computations to check that that the laws are consistent with our observations if you include a very complex system of your own brain as part of the universe? People have made mistakes in what laws the universe follows. They used to be sure a noble gas could never form
    – Timothy
    May 3, 2019 at 23:36
  • compounds but they turned out to be wrong. Are you saying we can define ourselves to know that it's true because it seems to be working so well to derive other stuff that a contradiction has not yet been derived in?
    – Timothy
    May 3, 2019 at 23:37
  • Do you mean the laws of physics as God sees them, as in the laws of the universe? If there even are any such things? Or do you mean the humanly contingent laws of physics as developed by physicists and written down in books?
    – user4894
    May 3, 2019 at 23:41
  • @user4894 I don't believe in God myself. However, I asked this probably because I think knowledge maybe can be defined in such a way that we don't know that the laws of Physics are consistent with observations and I think in Philosophy, maybe we can define ourselves to not know anything. I don't need to believe in God to tell whether or not I verified by my own mental calculation a mathematical statement is true no matter what reason I already had to be really sure that mathematical statement was true.
    – Timothy
    May 3, 2019 at 23:47

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The question of whether your observations are consistent with the laws of physics is a mathematically defined question.

This assertion is somewhat confused.

I assume what you are getting at is that modern physical theories are generally given in mathematical form and hence require mathematical aptitude and calculations to work out predictions and consequences. That’s a very different thing. After all, it takes mathematics to work the results of an election, ie votes have to be counted, nevertheless, no-one would call electoral politics a ‘mathematically defined’ question.

Physics is called physics for a reason. It’s not mathematics in the guise of physics. This is much clearer in the early accounts of physical reasoning because they didn’t use mathematics to quantify their reasoning.

It’s also why the early modern physicists like Galileo, Newton, Faraday, Maxwell called themselves natural philosophers.

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  • It has become somewhat widely accepted that none of particle or theoretical physics describes any 'actual' space whatsoever. Everything described in 'all' of physics represents hypothetical spaces and renders analogous observations. So no they do not match our observations. CS
    – user37981
    May 4, 2019 at 23:39
  • @CharlesMSaunders: That's nothing new - it's been known since Platos time. After all he pointed out that the actual forms are merely rough imitations of ideal forms. Nevertheless, to say that the edge of a ruler is straight is something that can be checked by observation; and to say that the space in my kitchen is euclidean is again something that can be checked by observation - not that anybody would bother.
    – Mozibur Ullah
    May 5, 2019 at 9:02

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