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Pentashagon comments on Math is Subjunctively Objective - Less Wrong
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Actually, the pythagorean theorem and pi still apply regardless of what dimension of geometry the world obeys (3-dimensional newtonian physics, 4-dimensional relativistic spacetime, 11-dimensional string theory, etc).
I don't know what you mean by that.
The Pythagorean theorem doesn't apply to curved space, only to flat space (regardless of number of dimension). And pi is the number 3.14159..., which can be defined in ways that have nothing to do with geometry, so I'd put it as "in convex (concave) space, the ratio of a circumference to its diameter is less (greater) than pi", not as "in convex (concave) space, pi is less (greater) than 3.14159...)".