How does mathematics relate to the physical world?

[rangrz]

^

It is both. Mathematics (esp with regards to physical systems) is simply an abstract, formalized model of our understanding of that physical system. If we don't understand the physical system properly, our model of it (the math) can not be perfect, and hence it will not make perfect predictions.

That is tossing aside the issue where our math tells us that we won't be able to make perfect predictions to begin with. (The Fourier limit? Heisenberg uncertainty? n-body problem in classical mechanics? Observer effect in quantum mechanics? Randomness in Q.M.? All of these say right from the get go that is a upper bound to how accurate our predictions can even possibly be)

 

[Sodacrates]

Yes, Physics tells us we can only be certain to a degree. You seem to have an idea that physics and mathematics are the same? I would say that there is definitely overlap between math and physics, but I don't believe they are the same. The degree which you can be certain within any variation of the Uncertainty principle is very accurate translated to any macroscopic effect, but in complex macroscopic systems our best predictions can be off by quite a bit. Even if we understood the system perfectly, there is a chance that the math we are using is not perfectly representative of the system, because the real physical system and our reason's model of it are not exactly the same.

 

[PlurPsyed]

math is logic

 

[rangrz]

Yes, Physics tells us we can only be certain to a degree. You seem to have an idea that physics and mathematics are the same? I would say that there is definitely overlap between math and physics, but I don't believe they are the same. The degree which you can be certain within any variation of the Uncertainty principle is very accurate translated to any macroscopic effect, but in complex macroscopic systems our best predictions can be off by quite a bit. Even if we understood the system perfectly, there is a chance that the math we are using is not perfectly representative of the system, because the real physical system and our reason's model of it are not exactly the same.

Since the thread is "How does does mathematics relate to the physical world" and since I seen mention of the term "physical system" and stuff about the flight path of rockets, I feel it is entirely appropriate to bring physics and it's use of mathematics into this discussion. I am quite familiar with that subject, being a physics grad student and all. It would be irrelevant if this discussion was about pure mathematics or some non physical science (economics, comp sci for e.g) But that is not the case.

The uncertainty re: Heisenberg can come become appreciable on a microscopic scale at high energy scales too. The other ones I mentioned apply independent of scales of magnitude and for e.g. the Fourier limit affects such pedestrian concerns as the fidelity of an audio recording.

 

[Sodacrates]

Yes I know the uncertainty principle has some macroscopic effects. Energy time uncertainty, I could imagine has effects on things like audio recording makes sense. Does it not effect video recording? Do you know why it effects the fidelity of audio recording? I've never heard of this and it sounds quite interesting.

I think you understand what I am saying, but maybe not. Do you think that we could come to a better understanding of a system and correct our predictions? I'm not saying that we don't understand the physics of a system perfectly so we make predictions that are slightly off. We create a model of the world in our minds that follows mathematics perfectly. In our minds, Plato may as well have been right because to make predictions we act as if math is descriptive, and math is descriptive of the world we painted with our own reason. I mean logic it self could be flawed as we use logic to describe the picture of reality in our heads which may not be accurate.

 

[P A]

You seem to have an idea that physics and mathematics are the same? I would say that there is definitely overlap between math and physics, but I don't believe they are the same.

The extent to which one overlaps with the other (to say nothing of their historical relationship) blurs the line for many people. It's exceedingly difficult to divorce any of our rigorous physics from mathematics proper, even though much of mathematics has nothing to do with physics. It is very telling that, almost without exception, the very best physical scientists in human history were also highly accomplished mathematicians and/or philosophers.