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for one reason, if you're just thinking about it as fancy 2d, you will miss a lot of phenomena that occur in higher dimensional spaces. for example, almost all
by adgjlsfhk1 2y ago
for one reason, if you're just thinking about it as fancy 2d, you will miss a lot of phenomena that occur in higher dimensional spaces. for example, almost all vectors are almost completely orthogonal which isn't true at all in low dimensional spaces
- kaffekaka 2y agoPhrased like that it sounds like a qualitative difference between "low" and "high" dimensional spaces. But isn't it simply a consequence of the fact that the more dimensions you have, the less likely that randomly distributed, sparse non-zeros will end up in the same positions? I.e. simply a quantitive difference.
- klodolph 2y agoAny extreme quantitative difference is going to be a qualitative difference.