Re:Executing gradient descent on the earth
by Strilanc on Friday April 20, 2018 @05:37AM
(#16883429)
The spheres and the cubes are of the same dimension, so it's not like trying to put flat things inside of a thing with volume. (Technically I should have said million dimensional balls instead of spheres. Sorry if that was confusing.)
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Then isn’t the answer 1? For 2 dimensions, one circle fits in a square, in three dimensions one sphere fits in a cube. Should be the same for any value of n?
Re:Executing gradient descent on the earth
by Strilanc on Friday April 20, 2018 @12:36PM
(#16886257)
Consider that the distance between opposite corners of a square is √2 meters, but for a cube it's √3 meters. In general, for an n-dimensional hypercube of diameter 1m, the exactly-opposite corners are √n meters apart.
Meaning, in a million-dimensional meter-diameter hypercube, exactly-opposite corners will be a kilometer apart. There's a lot more diagonal wiggle room than you think.