It's just rotational dynamics from Physics I. The kinetic energy of something spinning is (1/2)Iw^2. The energy of something spinning is proportional to the squ

It's just rotational dynamics from Physics I. The kinetic energy of something spinning is (1/2)Iw^2. The energy of something spinning is proportional to the square of the speed that it spins, or I guess you could say "O(n^2)". If you double the clock frequency, you quadruple the heat, and at a certain point you can't go any farther because you don't have a way of removing heat fast enough before it melts. They even show it in the article: >­underclocking a single core by 20 percent saves half the power 0.8^2 = 0.64, pretty close.