There are ways to 'approximate' a uniform distribution by just choosing greater and greater ranges and then normalising the result. One problem with this is th

There are ways to 'approximate' a uniform distribution by just choosing greater and greater ranges and then normalising the result. One problem with this is that there's no one way to do it. You could argue equally well that the result should be a uniformly random point on the S100 sphere. What it definitely cannot be is a random point on the [-1,1]^100 cube because if you divide by the greatest absolute value then one of the coefficients will be -1 or 1