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Benoît Mandelbrot - Pathological shapes (72/144)

400 views · Published 21 August 2017 · 2:00 · Indexed 20 September 2026

Channel: Web of Stories - Life Stories of Remarkable People · 2017 · Science & Technology

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To listen to more of Benoît Mandelbrot’s stories, go to the playlist: https://www.youtube.com/watch?v=0ABtOHVhr6E&list=PLVV0r6CmEsFwl4HlrIKxKmdpBAGYJ9AbR

The late French-American mathematician Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance, and is famous for his work on fractal geometry, the maths of the shapes found in nature. [Listeners: Bernard Sapoval and Daniel Zajdenweber; date recorded: 1998].

TRANSCRIPT: The people who around 1900 introduced the shapes called them mathematical monsters, pathological shapes, because their only intent was to show that certain ideas that had become intuitive were incorrect. Now, intuition was certainly believed at the time to be quite invariant in time, quite inbred in humans, and it didn't occur to them that what they viewed as intuitive had any relation with their time and space. Fifty years later- well for some, seventy-five for others - I thought that these constructions could be models of reality and increasingly proved them to be so, and then built upon an enormous variety of variants which very many people continue to do. Then we went to the next stage which was to construct those random novelties and random shapes obtained by iteration, of which I will speak later - the theory of iteration, the theory of Julia sets and Mandelbrot sets and the like. Those shapes are found by many people to be very attractive visually, in fact artistically. And in due time the readers of my books pointed out to me that the shapes which I was creating around 1900 in the work of like Peano, Sierpinski, like Cantor even; in fact familiar in decoration in many, many cultures. So we find here a circle, a very virtuous circle I must say immediately, which goes from art to mathematics to physics and to art again, with the help of the computer in the passage from the second to third stage.

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