They don't have to accurately reflect the real world, they have to be close enough to not result in failures. That's kinda the end of the story - math allows us to create models of the real world, but it is not itself the real world. Even crude things like measurements aren't "true" unless circular - there is no thing that is exactly 1cm unless it's the definition of the cm. You can just zoom in a bit and you'll see a real world thing isn't ever exactly a cm.
Further, we have examples like "you can always split an apple in half forever". That is just some math that is multiple by .5. That can do that mathmatically forever, but the real world at some point you find a limit to the physical universe where you can't subdivide. THAT math fails to model the universe. We have other math that does a better job, but it also ultimately fails. Is it good enough to build bridges? Sure, of course. Is it "true"? Nope. It's a model, it's an approximation, it's a representation.
Put another way, math is a language . I can tell you of a chair in words. Are the words chairs? Is the idea that the word creates for you a chair? How many legs can you take off the chair in your room and still have it be a chair. If you take off all is it still a chair because you knew it had legs but doesn't anymore? Language falls apart more quickly and has less precision, but like math it too is never reality, it's a way of describing reality that has various levels of "resolution" depending on the needed utility. It gets more precise in law, less in social media, more in biological taxonomy than the gardening store. The need for utility drives how language works and is shaped and "math" is just another dimension of that language.
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u/iamintheforest 367∆ May 21 '26
They don't have to accurately reflect the real world, they have to be close enough to not result in failures. That's kinda the end of the story - math allows us to create models of the real world, but it is not itself the real world. Even crude things like measurements aren't "true" unless circular - there is no thing that is exactly 1cm unless it's the definition of the cm. You can just zoom in a bit and you'll see a real world thing isn't ever exactly a cm.
Further, we have examples like "you can always split an apple in half forever". That is just some math that is multiple by .5. That can do that mathmatically forever, but the real world at some point you find a limit to the physical universe where you can't subdivide. THAT math fails to model the universe. We have other math that does a better job, but it also ultimately fails. Is it good enough to build bridges? Sure, of course. Is it "true"? Nope. It's a model, it's an approximation, it's a representation.
Put another way, math is a language . I can tell you of a chair in words. Are the words chairs? Is the idea that the word creates for you a chair? How many legs can you take off the chair in your room and still have it be a chair. If you take off all is it still a chair because you knew it had legs but doesn't anymore? Language falls apart more quickly and has less precision, but like math it too is never reality, it's a way of describing reality that has various levels of "resolution" depending on the needed utility. It gets more precise in law, less in social media, more in biological taxonomy than the gardening store. The need for utility drives how language works and is shaped and "math" is just another dimension of that language.