Why 4xBB?

[manpower]

We all know that the standard opening pf raise in NL is 3-5xBB. I've wondered ever since I've started poker why this is the magic figure but have never really felt much of a need to voice the question.

Of course, I know that 2xbb is too small in that it offers too good implied odds. And that 10xbb is too much in that you wager too much to win too little. But I've never seen any sort of mathematical explanation as to why this is.

So that's it, has anyone seen any mathematical, logical, or otherwise non-laymans arguments for pre flop betting amounts?