In 1 or 2 dimensions, random walks return to the origin infinitely often. In 3 dimensions, they have but a 34% chance. There are nontrivial qualitative differences between numbers of spatial dimensions that we don’t see when we think “2? 3? 5? 179? It’s just a choice of N!”
In 1 or 2 dimensions, random walks return to the origin infinitely often. In 3 dimensions, they have but a 34% chance. There are nontrivial qualitative differences between numbers of spatial dimensions that we don’t see when we think “2? 3? 5? 179? It’s just a choice of N!”