CONCEPT
Wild Randomness
Mandelbrot's name for the kind of uncertainty that lives in power-law distributions—where single events can dwarf all others combined, averages are unstable, and the bell curve's promise of negligible extremes is a systematic and dangerous lie.
The distinction Benoit Mandelbrot drew between “mild” and “wild” randomness is the most consequential contribution to the theory of uncertainty since the central limit theorem—and the one the modern world has done the most to ignore. Mild randomness is the world of the
bell curve: human heights, IQ scores, the average of many independent coin flips, where no single observation dominates, the average is stable and informative, and extreme deviations are exponentially rare. Wild randomness is a different regime entirely, governed by
fat-tailed distributions where the largest observation can always exceed the sum of all previous observations, the average may not even be finite, and the rarity of extreme events is measured by a power law that falls off far more slowly than exponential.
Mandelbrot found wild randomness in cotton prices in the 1960s, in flood heights, in the distribution of city sizes and word frequencies and financial returns, and he spent the second half of his career warning