principles.fyi · the brain · concept

power law

Make something ten times bigger, get a steady, predictable jump in quality.

y = x^p (straight line on log-log axes)

A power law links two things by multiplication, not addition: when you multiply one by ten, the other changes by a fixed factor every time. Drawn normally it's a swooping curve, but if you stretch both axes so equal steps mean "times ten" instead of "plus one," the curve straightens into a line. A model's loss falls along such a line as you grow it, so each tenfold scale-up buys you the same reliable slice of improvement.