This is not true even in an extremely idealized model. For example, if you pick two random points in a unit cube, they are much more likely to be a moderate dis

This is not true even in an extremely idealized model. For example, if you pick two random points in a unit cube, they are much more likely to be a moderate distance apart (on average, about 0.66 units) than they are to be very close together. https://people.kth.se/~johanph/habc.pdf https://people.kth.se/~johanph/habc.pdf