Obviously, physics never creates any math but discovers it, there are no new things under the sun.
Physics is unreasonably good at creating new math
81–90 of 231 posts
Re: Physics is unreasonably good at creating new math
#82Try to make some innovative software product without talking to any user. You'll see why physics is good at crating new math.
Do you value the quality of a mathematical theory by the number of applications, or the intrinsic beauty of the theory itself?
I judge the beauty of math and code by the how concisely and simply they can model the object in question - if the math exists abstractly and isn't trying to model any actual thing or concept it isn't particularly beautiful to me because it isn't an accomplishment of expressiveness - it's instead just a coincidence that if you put some symbols together you only need those symbols.
There are, of course, times that concise expressions aren't possible and multiple strange and arbitrary values come into play (coefficients of friction or earth's gravity at sea level aren't particular nice numbers or expressions) and that just tends to highlight how beautiful things are when those icky real-world numbers can be canceled out and you're left with a clean expression.
Re: Physics is unreasonably good at creating new math
#83Obviously, physics never creates any math but discovers it, there are no new things under the sun.
Discovered Vs invented
Re: Physics is unreasonably good at creating new math
#84Earlier quoted context omitted.
> Math, of course, is that stuff which can’t be invalidated by observations. This is a misunderstanding of what math is, I think. You can invent a perfectly valid mathematical theory that conflicts with observations. Math is just a sequence of "if this, then this" and if the conclusions follow from the premises, it's math. But if you demonstrate that in the universe we occupy, a premise isn't true , then the mathemat…
I think this is a disagreement about the word invalidate, and maybe it was a bad pick on my part. The observations don’t make the math wrong, maybe less useful. But, I say the math can’t be invalidated by observations; and you describe some cases where the math is valid but might or might not be applicable to certain physical cases. So actually, I’m not clear as to what you are saying I’m misunderstanding.
> I say the math can’t be invalidated by observations
I meant, isn't a counter-example or proof by contradiction an invalidation by a type of observation?
Re: Physics is unreasonably good at creating new math
#85Re: Physics is unreasonably good at creating new math
#86Earlier quoted context omitted.
This is a very late-XIX century development. Geometry used to be an integral part of physics, vide Newton's Principia .
Wondering if Euclid’s parallel postulate was independent goes back millennia though. And that’s like the key ingredient for multiple geometries.
No, it's trying to prove that Euclid's parallel postulate can be derived from other axioms is what goes back millennia. People were certain it's a) true, b) necessary consequence of other axioms. Gauss was probably the first to consider the possibility that it may be false; others at best tried reductio ad absurdum, arrived to some wildly unusual theorems, decided those were absurd enough to demonstrate the truth of the fifth postulate, and went back to trying to derive it.
Re: Physics is unreasonably good at creating new math
#87Try to make some innovative software product without talking to any user. You'll see why physics is good at crating new math.
Do you value the quality of a mathematical theory by the number of applications, or the intrinsic beauty of the theory itself?
This is really interesting to me. It could imply that an ugly theorem is less valuable. What if a theorem is ugly but useful vs a beautiful but esoteric one?
Re: Physics is unreasonably good at creating new math
#88Earlier quoted context omitted.
This was the result of Philosophers ultimately winning, despite the fact that they are so annoyingly pedantic that we pretend not to care about their work, and also, by ignoring them we can invent iPhones which are really neat. You can’t prove anything by observation. You can gather evidence through repeat experiment and become reasonably confident as your theory continues to not be incompatible with the observed uni…
“Prove” could mean many things. For physics, prove what? That a given model is the one and only model that accurately explains the known universe? Then I agree. Observation won’t get you there. Asymptotic at best. But by “prove”, that it accurately or usefully makes predictions with respect to certain constraints (which may not be known)? That’s a more modest use of “prove”, where observation is certainly a key facto…
Interesting linguistic aside: "the exception that proves the rule" makes use of this more old fashioned use of prove, to test. So it's the exceptional case that tests the rule.
With that in mind, "prove" is perfectly fine to use in the context of science.
Re: Physics is unreasonably good at creating new math
#89Earlier quoted context omitted.
I think this is a disagreement about the word invalidate, and maybe it was a bad pick on my part. The observations don’t make the math wrong, maybe less useful. But, I say the math can’t be invalidated by observations; and you describe some cases where the math is valid but might or might not be applicable to certain physical cases. So actually, I’m not clear as to what you are saying I’m misunderstanding.
> I say the math can’t be invalidated by observations I meant, isn't a counter-example or proof by contradiction an invalidation by a type of observation?
No, proof by contradiction is a logical construction, has nothing to do with the real world. Proof by counter-example could or could not be observation, depending on whether your example comes from observation or from pure logic.
Re: Physics is unreasonably good at creating new math
#90Earlier quoted context omitted.
> Math, of course, is that stuff which can’t be invalidated by observations. This is a misunderstanding of what math is, I think. You can invent a perfectly valid mathematical theory that conflicts with observations. Math is just a sequence of "if this, then this" and if the conclusions follow from the premises, it's math. But if you demonstrate that in the universe we occupy, a premise isn't true , then the mathemat…
I think this is a disagreement about the word invalidate, and maybe it was a bad pick on my part. The observations don’t make the math wrong, maybe less useful. But, I say the math can’t be invalidated by observations; and you describe some cases where the math is valid but might or might not be applicable to certain physical cases. So actually, I’m not clear as to what you are saying I’m misunderstanding.
Ok, I see what you mean now.
I took your word "invalidate" to mean "be proven false" whereas I meant "valid" as in "logically coherent, even if not true."