Why Mathematics works so well with Physics

[BillTre]

It argues that the "happy coincidence" (a phrase coined by philosopher Mary Leng of The University of York) of math applying to the real world (as a language) is best explained by God orchestrating/designing it that way versus the highly improbably coincidence that it does so on its own.

I don't consider this a coincident at all.
The math we understand resides in our brains.
Physical reality is separate from that.
The brain structure/functioning underlying mathematical understanding must be in some way provide a basis for those ideas to occur.
To me, this is the question here. Why is the brain's math abilities so well adapted to this purpose?

The brain's structure/function is an evolved thing, based on at least millions of cycles (generations) of selection, where brain functioning was tested for its ability to match up with the real world around, which affected its ability to survive and reproduce.
This argument should work for counting, logic, and geometry, all things an organism would need to navigate the complex world in which we find ourselves.
Since brain function analyses (mostly) macro (not micro) scale events and is graded on that by evolution, the brain abilities evolved to deal with those scales most naturally (as opposed to say, quantum mechanics, which seems a less natural (more abstract) fit to many people).

Its a kind of circular argument, but to me it makes sense.
Its does not involve invoking God and is not anthropocentric, but one might says its brain-pocentric.

 

[dkotschessaa]

Well some people may disagree with that. It's a strong hunch that I have, but I'm not sure what the pitfalls of that approach is. That's why I posted the thread.

The difficulty for me is that there are mathematical concepts that are, as far as I can tell, pure abstraction. My favorite example is large cardinals: https://en.wikipedia.org/wiki/Large_cardinal

It's probably one of my favorite areas of mathematics, perhaps because it is so entirely divorced from any sort of reality I know. If someone were to find an application for it I'd probably be disappointed!

-Dave K

 

[HAYAO]

Mathematics is all about axioms and definitions followed by logic, at least in my opinion. Within that axioms, any logical derivation is universally true. So anything that applies mathematics, by adding conditions and restrictions, is also universally true under that axioms as long as it is a logical derivation. And of course, science is essentially about finding something that is universally true. So they work well.

 

[FallenApple]

The difficulty for me is that there are mathematical concepts that are, as far as I can tell, pure abstraction. My favorite example is large cardinals: https://en.wikipedia.org/wiki/Large_cardinal

It's probably one of my favorite areas of mathematics, perhaps because it is so entirely divorced from any sort of reality I know. If someone were to find an application for it I'd probably be disappointed!

-Dave K

But the mathematician thinking about a large cardinal corresponds to specific firing pattern of neurons which takes place in the real physical world. One can even say that a specific large cardinal is isomorphic to a specific neuronal electrical pattern.

 

[Dr. Courtney]

For those wishing to avoid forays into philosophy or religion, I think the best one can conclude is that "it does." My personal view is in agreement with Eugene Wigner, but he was a man of faith and seemed to be appealing to faith in his assessment, "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. "

But for a strict naturalist or instrumentalist, all one has is the empirical fact that so many natural phenomena are accurately modeled with mathematics. This trend gives one hope and expectation that the next phenomenon we stumble upon with also be amenable to being accurately modeled with mathematics, but there is no guarantee until it happens.

But for me, it's never a matter of whether a problem is amenable to mathematics, it's a question of which mathematical tool is best for the job. But I admit that is an article of faith, and I trust problems that are yet unsolved are unsolved because the right mathematical tool is not yet found, not because math is not applicable.