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This is a compelling way of looking at things for sure; to me it seems like you're saying math is just a language (like English) that we can use to describe the

This is a compelling way of looking at things for sure; to me it seems like you're saying math is just a language (like English) that we can use to describe the world. English is no more "right" than some other made up language, so same goes for math, and thats certainly seems true in some cases. However there are things that are intrinsic to mathematics that also seem intrinsic to existence, like prime numbers. Many things about prime numbers are 'discovered' as if they were elements of nature that need to be revealed through study. For example, the distribution of primes and the distribution of twin primes are things likely to have been discovered by an alien intelligence, assuming one exists. What would their math look like? Different for sure, but I think it's likely they still studied the primes, hypothetically.

svara 3y ago
I agree with you that what I'm saying is that maths is ultimately a kind of language that we use to describe the world. I wouldn't agree with calling it "just" language or "like English". It's different in that consistency is strictly enforced, such that simple rules can lead to rich emergent structures. That's what I was getting at with the game of life metaphor. So, if you follow my argument, the fact that there are prime numbers is not 'intrinsic to mathematics', it's the other way around -- we use rules that lead to rich structures, because those provide useful, consistent abstractions to talk about things. Prime numbers are among those rich structures. To respond to a sibling comment that seems somewhat related -- The fact that we can calculate some physical constants with high precision is not a counter argument to that. What we are doing is fitting a mathematical abstraction to data; once we have done that, we can find more physical truths by assuming consistency and performing logical inference. The fact that a constant can be calculated then just means that we have a consistent theory for the physical structures from which that constant arises.

svara 3y ago

I agree with you that what I'm saying is that maths is ultimately a kind of language that we use to describe the world. I wouldn't agree with calling it "just" language or "like English". It's different in that consistency is strictly enforced, such that simple rules can lead to rich emergent structures. That's what I was getting at with the game of life metaphor. So, if you follow my argument, the fact that there are prime numbers is not 'intrinsic to mathematics', it's the other way around -- we use rules that lead to rich structures, because those provide useful, consistent abstractions to talk about things. Prime numbers are among those rich structures. To respond to a sibling comment that seems somewhat related -- The fact that we can calculate some physical constants with high precision is not a counter argument to that. What we are doing is fitting a mathematical abstraction to data; once we have done that, we can find more physical truths by assuming consistency and performing logical inference. The fact that a constant can be calculated then just means that we have a consistent theory for the physical structures from which that constant arises.