Turbulent Waters

In this video clip, Benoit Mandelbrot explains how Kolmogorov inspired his works on fluid turbulence, published in the years immediately before he coined the term “fractal”.

I had the pleasure of seeing Mandelbrot in person when he visited Microsoft, and he described his lifelong fascination with things chaotic. One of the great accomplishments of complexity theory is that it proscribes some mathematical limits on how deep or how far we can understand certain otherwise deterministic phenomena. Robert Frost wrote, in his poem “Neither Out Far Nor In Deep”:

The people along the sand
All turn and look one way.
They turn their back on the land.
They look at the sea all day.

As long as it takes to pass
A ship keeps raising its hull;
The wetter ground like glass
Reflects a standing gull

The land may vary more;
But wherever the truth may be–
The water comes ashore,
And the people look at the sea.

They cannot look out far.
They cannot look in deep.
But when was that ever a bar
To any watch they keep?

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