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Joined 3 years ago
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Cake day: June 10th, 2023

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  • It’s been a while so bits of this might be wrong. Manifolds give me PTSD.

    A euclidean space is one where pythagoras’ theorem is true, like on a piece of paper. Even if you roll up the paper, everything still works the same. The angles of a triangle still add to 180 etc

    But the surface of a sphere doesn’t work like that. You can’t fold up the paper into a sphere, it’s fundamentally different. Geometry changes a bit on the surface too, and you have to modify pythagoras theorem for it to describe triangles in one of these spaces. And the internal angles don’t add to 180 anymore.

    These are non-euclidean spaces, aka Riemannian spaces.

    So the meme is saying “ha ha you’re in a non-Euclidean space, it just looks like that because you’re small, dumb dumb! Why don’t you draw a big triangle, measure the angles and then cry yourself to sleep?”


  • The meme is funny, this isn’t criticism of that.

    BUT this general point always rubs me the wrong way. Do people realise how fucking big space is? The observable universe contains so many fucking planets that we don’t even know exist, some of which have their own oceans we know absolutely nothing about. We have literally no idea what like 95% of the stuff out there even is (dark matter, dark energy).

    And that’s just the observable universe. The rest of it likely comprises even more space than the observable universe. And that isn’t “stuff we don’t know yet,” it’s literally “stuff we could probably never know based on the laws of physics.”

    Like we know surprisingly little about the ocean. That is shocking. But there is no need to make such a bizarre claim to get that across.

    OK, rant over.