Mandelbrot v. Cohen, Fractals v. Forcing, Morris v. Steve and Eric, ‘Errol Morris Dancing’

 

“Errol Morris Dancing” >> play both of these short films simultaneously, and vary the effect by muting one or the other for sound

self-reference to Errol Morris Dancing, at 4:06 in each film

self-reference to Errol Morris Dancing, at 4:06 in each film

 

Cohen is noted for developing a mathematical technique called forcing, which he used to prove that neither the continuum hypothesis (CH), nor the axiom of choice, can be proved from the standard Zermelo–Fraenkel axioms (ZF) of set theory. In conjunction with the earlier work of Gödel, this showed that both of these statements are logically independent of the ZF axioms: these statements can be neither proved nor disproved from these axioms. In this sense, the continuum hypothesis is undecidable, and it is probably the most widely-known example of a natural statement that is independent from the standard ZF axioms of set theory.>>

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.
  —Mandelbrot, in his introduction to The Fractal Geometry of Nature

edit to add: Sean Li, a mathematician and fellow WordPress blogger, better contextualizes the work of Mandelbrot and Cohen.

About markweiss86

Mark Weiss, founder of Plastic Alto blog, is a concert promoter and artist manager in Palo Alto, as Earthwise Productions, with background as journalist, advertising copywriter, book store returns desk, college radio producer, city council and commissions candidate, high school basketball player; he also sang in local choir, and fronts an Allen Ginsberg tribute Beat Hotel Rm 32
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