Executing gradient descent on the earth

Re:Executing gradient descent on the earth by sudhirj on Friday April 20, 2018 @09:20AM (#16884491)

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?

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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.

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Re:Executing gradient descent on the earth by therein on Friday April 20, 2018 @03:07PM (#16887640)

That blew my mind but it still sounds like it would generalize, wouldn't it?

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