hot boys undergo like a 7x hotness multiplier if they are also better than me at math
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like if ur even medium attractive but can successfully explain to me like......manifolds or something i’d probably suck ur dick no questions asked
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Replying to @isosteph
Not super interested in the reward but if you actually want to know about manifolds I'd love to help teach that! It's easy to work in an x-y plane and it's harder to work in spherical polar coordinates (on a sphere) and even worse to work on, like, a hyperboloid and stuff.
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Replying to @physicsandnath @isosteph
But those two still have nice properties: if you zoom in really close, they behave locally just like the x-y plane, so all the things you can do in the latter apply (locally) to the former. (This is why the Earth looks flat until you're flying high enough above its surface.)
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Replying to @physicsandnath @isosteph
This is a local, not global, property: you can treat tiny pieces of a sphere as an x-y plane, but you can't flatten out an entire sphere onto an x-y plane no matter how much you warp or smush it.
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Replying to @physicsandnath @isosteph
For example, visualize the regular mercator projection map of Earth: where's the precise point that is the north pole? It's either the entire northern edge of the map or it's missing entirely.
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Replying to @physicsandnath @isosteph
Things that aren't manifolds: anything with a spike. (The spike's point doesn't look like a plane up close.) Anything with an intersection point, like in a figure 8 (but collisions, like in a Klein bottle, are okay).
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Replying to @physicsandnath @isosteph
This is because the intersection doesn't look like an x-axis (one-dimensional x-y plane) up close, but a collision like in a Klein bottle can be removed by putting it in a higher-dimensional space, and the entire surface will then locally look like a euclidian plane.
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lmao this is lit actually congrats and thx for explaining in a normal and clear way!!
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