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I would disagree with the idea that maths is man-made. It is discovered. If it were man made, then we should have power to change it as we wish. But you could

I would disagree with the idea that maths is man-made. It is discovered. If it were man made, then we should have power to change it as we wish. But you could still say: A mathematical structure is analysing mathematics.

thoraway66 5y ago
You mean physical structures. Math is just glyphs we use to cart around awareness of the motions of this reality. I know it’s romantic to escape into the neverending-ness of reality, but we exist in a pretty well established perimeter of physical constraints, and we have yet to find even a theory that would let us break them. A few academic tricks here and there is hardly concrete proof we can. I think we’re looking the wrong way. What if we’re each a metaverse forced to live literally? Give me designer drugs that bootstrap such a detailed hallucination, I think it happened. Way less wasteful than these toys like VR we just throwaway. Don’t make the math literal, make the cognitive simulation so detailed it feels like it’s literal. Maybe aliens didn’t die off. They just took resource consumption seriously.
shrimpx 5y ago
One way I’ve seen it put, that resonates with me, is that axioms are invented but theorems are discovered. That is nicely self-evident. The idea that axioms are also discovered is … iffy, but it happens in some cases. E.g., discovering that your theory is unsound and the only way to fix it is by adding the obvious axiom.
cgriswald 5y ago
I would disagree there are quick and easy answers to the question of whether math is man-made or discovered. What is the qualitative difference between discovery and invention? Consider the product of no factors being equal to the multiplicative identity. Is that a discovery or a choice made because it is more useful? Is it a discovery because we 'discovered' it was more useful?

thoraway66 5y ago

You mean physical structures. Math is just glyphs we use to cart around awareness of the motions of this reality. I know it’s romantic to escape into the neverending-ness of reality, but we exist in a pretty well established perimeter of physical constraints, and we have yet to find even a theory that would let us break them. A few academic tricks here and there is hardly concrete proof we can. I think we’re looking the wrong way. What if we’re each a metaverse forced to live literally? Give me designer drugs that bootstrap such a detailed hallucination, I think it happened. Way less wasteful than these toys like VR we just throwaway. Don’t make the math literal, make the cognitive simulation so detailed it feels like it’s literal. Maybe aliens didn’t die off. They just took resource consumption seriously.

shrimpx 5y ago

One way I’ve seen it put, that resonates with me, is that axioms are invented but theorems are discovered. That is nicely self-evident. The idea that axioms are also discovered is … iffy, but it happens in some cases. E.g., discovering that your theory is unsound and the only way to fix it is by adding the obvious axiom.

cgriswald 5y ago

I would disagree there are quick and easy answers to the question of whether math is man-made or discovered. What is the qualitative difference between discovery and invention? Consider the product of no factors being equal to the multiplicative identity. Is that a discovery or a choice made because it is more useful? Is it a discovery because we 'discovered' it was more useful?