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Take the natural numbers. They were invented for counting things, right? One sheep, two sheep, three sheep, simple as. Yet there’s an immense complexity and st
by aaaaaaaaaaab 4y ago
Take the natural numbers. They were invented for counting things, right? One sheep, two sheep, three sheep, simple as.
Yet there’s an immense complexity and structure in natural numbers, starting with primes, and ending in algebraic- or analytic number theory!
Why is it that this thing we use for counting objects has such rich structure? Where does it come from? Why does it have to be this way?
It certainly feels something divine to me. It certainly feels as something that humans didn’t invent, rather was always “out there” to be discovered. Physical laws (which are mostly just OK approximations) feel much more arbitrary and down-to-Earth compared to mathematics.
- Koshkin 4y ago> invented The words for numbers were indeed “invented,” but the numbers themselves, like much of math, was discovered.
- ivanbakel 4y agoThat's a philosophical view, and I don't think there's any basis for stating it as fact. One of the great debates of mathematical ontology is whether mathematical concepts are discovered or invented.
- Kinrany 4y agoLike most great philosophical debates, it probably comes from humans being bad at understanding their own language.
- Koshkin 4y agoIndeed, the word ‘invented’ is often abused by being used in place of ‘discovered’ or ‘created.’ (No, Faraday did not “invent” the laws of electromagnetism; nor did Linus Torvalds “invent” Linux.)