Notes from a Medium-Sized Island

Hmm. First I thought my math was all wrong. Then I thought it was wrong just when δ(1-σ) ≥ 1/8. Then I thought about a way of doing something entirely different for that case, and turned the crank for a while and got exactly the same answer as for δ(1-σ) ≤ 1/8. This is either incorrect or spookily correct. In fact, if it's correct, it's sort of very correct, since it shows that, quantitatively, things oughtn't be nonsmooth across that boundary, even if conceptually they are.

Man, I totally never understood Gödel's Theorem until now.

Math status: tentative confidence that the math is right, but the implementation is wrong, since the latter says that the giant component forms more easily for greater σ, and we pretty much know that to be false. The thing is that I took a shortcut in approximating a certain function is linear, and some subsequent experiments proved that approximation is probably not at all safe.

( Collapse )