Eh, I see it as a means to describe some ideas about something that you can reason about. Like programming languages, the description can be a leaky abstraction. Math used to be much more cowboy before some folks started trying to proof it from axioms, for rigorousness sake.
The thing I think that's really neat is that you can come up with new ideas and create your own symbols and language to describe it if you wanted.
There was some paper I looked at forget ago that gave me the impression that it was bespoke maths. I'm sure, though, that it could still be built with assumptions about some axioms.
But that argument is backwards, as integrals and complex numbers appeared beforehand (derivatives where directly inspired though) their use in physics. Just as vector fields and matrix operators. It’s mighty suspicious that you can go from like parallel lines not real into metrics and general relativity in very little logical steps.
Complex numbers have applications all over the place though it seems like it's enough just to solve the 'but what about sqrt(-1)' problem. Doesn't sqrt come from geometry?
Integrals... yeah, not sure where those ideas for inspiration from. If you have some line, why would you care about the area underneath? Then again, maths types always be curious about every little thing.
Well, yeah. But sqrt of -1 makes zero sense geometry wise. It’s just very useful for shorthanding a lot of waves into cute exponents. But nature don’t give a shit about complex part itself :thonk-cri:
Hah, yeah. I guess the applications of complex numbers is usually using the real and complex as a sort of x and y, literally for rotations in multiple dimensions, or just as amplitude and phase (for electronic signals).
So there's no sweet discoveries in quantum stuff or whatnot that can use complex numbers outside of waves? Surely there's something else.
Sorta? I’m not super experienced there, so cannot say. I think, in the end they come down it’s much easier to work with complex numbers, last step is usually either get abs/re part or im part, cause it’s a phase typically.
That’s a fair argument, but suspicious effectiveness of math (or however this thing is called) is mainly in continuous thingies
Eh, I see it as a means to describe some ideas about something that you can reason about. Like programming languages, the description can be a leaky abstraction. Math used to be much more cowboy before some folks started trying to proof it from axioms, for rigorousness sake.
The thing I think that's really neat is that you can come up with new ideas and create your own symbols and language to describe it if you wanted.
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There was some paper I looked at forget ago that gave me the impression that it was bespoke maths. I'm sure, though, that it could still be built with assumptions about some axioms.
But that argument is backwards, as integrals and complex numbers appeared beforehand (derivatives where directly inspired though) their use in physics. Just as vector fields and matrix operators. It’s mighty suspicious that you can go from like parallel lines not real into metrics and general relativity in very little logical steps.
Complex numbers have applications all over the place though it seems like it's enough just to solve the 'but what about sqrt(-1)' problem. Doesn't sqrt come from geometry?
Integrals... yeah, not sure where those ideas for inspiration from. If you have some line, why would you care about the area underneath? Then again, maths types always be curious about every little thing.
Well, yeah. But sqrt of -1 makes zero sense geometry wise. It’s just very useful for shorthanding a lot of waves into cute exponents. But nature don’t give a shit about complex part itself :thonk-cri:
Hah, yeah. I guess the applications of complex numbers is usually using the real and complex as a sort of x and y, literally for rotations in multiple dimensions, or just as amplitude and phase (for electronic signals).
So there's no sweet discoveries in quantum stuff or whatnot that can use complex numbers outside of waves? Surely there's something else.
Sorta? I’m not super experienced there, so cannot say. I think, in the end they come down it’s much easier to work with complex numbers, last step is usually either get abs/re part or im part, cause it’s a phase typically.
why are you so :thonk-cri:
Hmm, dunno, I think it symbolizes frustrated thoughts and funny