Fractals, the Hidden Order Beneath Chaos, and the Story of the Refugee Who Revolutionized the Mathematics of Reality – Brain Pickings

by Jeremy

I have learned that the lines we draw to contain the infinite end up excluding more than they enfold. I have learned that most things in life are better and more beautiful, not linear but fractal. Love especially. In a testament to Aldous Huxley’s astute insight that “all great truths are obvious truths, but not all obvious truths are great truths,” the polymathic mathematician Benoit Mandelbrot (November 20, 1924–October 14, 2010) observed in his most famous and most quietly radical sentence that “clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

The Pattern Inside the Pattern: Fractals, the Hidden Order Beneath Chaos, and the Story of the Refugee Who Revolutionized the Mathematics of Reality

A blatant truth a child could tell you.

A great truth that would throw millennia of science into a fitful frenzy sprung from a mind that dismantled the mansion of mathematics with an outsider’s tools.

mandelbrotset
The Mandelbrot set. (Illustration by Wolfgang Beyer.)

A self-described “nomad-by-choice” and “pioneer-by-necessity,” Mandelbrot believed that “the rare scholars who are nomads-by–choice are essential to the intellectual welfare of the settled disciplines.” He lived the proof with his discovery of a patterned order underlying a great many apparent irregularities in nature — a sweeping symmetry of nested self-similarities repeated recursively in what may at first read as chaos.

The revolutionary insight he arrived at while studying cotton prices in 1962 became the unremitting vector of revelation a lifetime long and aimed at infinity, beamed with equal power of illumination at everything from the geometry of broccoli florets and tree branches to the behavior of earthquakes and economic markets.

FractalFlight by MariaPopova1
Fractal Flight by Maria Popova. Available as a print.

Mandelbrot needed a word for his discovery — for this staggering new geometry with its dazzling shapes and its dazzling perturbations of the basic intuitions of the human mind, this elegy for order composed in the new mathematical language of chaos. One winter afternoon in his early fifties, leafing through his son’s Latin dictionary, he paused at fractus — the adjective from the verb frangere, “to break.” Having survived his early life as a Jewish refugee in Europe by metabolizing languages — his native Lithuanian, then French when his family fled to France, English as he began his life in science — he recognized the word’s echoes immediately in the English fracture and fraction. These concepts resonated with the nature of his jagged self-replicating geometries. Out of the dead language of classical science, he sculpted the vocabulary of a new sensemaking model for the living world. The word fractal was born — binominal and bilingual, adjective and noun, the same in English and French — and all the universe were new.

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