Humility in the face of mathematics

Our professor for Fractal Geometry, Michael Frame, a wonderfully sweet and somewhat melancholy man who worked extensively with Benoit B. Mandelbrot, likes to make lectures more interesting by telling us bad jokes, Mandelbrot stories and existential musings on life.

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It’s 11/11 today, which started as an ironic celebration of young-adult singlehood in a culture that has an odd relationship with romantic relationships, namely, that they should be avoided at all costs before college, as long as a partner and multiple babies spontaneously manifest by age 30. Alibaba and other clever merchants have turned it into the Chinese equivalent of Black Friday. Happy 11.11, I guess. I’d like to share something a little less depressing and blatantly consumerist.

Our professor for Fractal Geometry, Michael Frame, a wonderfully sweet and somewhat melancholy man who worked extensively with Benoit B. Mandelbrot, likes to make lectures more interesting by telling us bad jokes, Mandelbrot stories and existential musings on life.

Today’s Mandelbrot story was that back in the 40s or 50s, when Mandelbrot was studying at Princeton under John von Neumann, people were fond of walking around (and driving) lost in theoretical contemplation without paying much attention to their environs. Once Mandelbrot nearly ran over three people who meandered into the path of his vehicle. The three were Albert Einstein, John von Neumann, and J. Robert Oppenheimer, who were a little cross but went on their way.

Most of the class had been about cellular automata: fun little machines, if you can call them that, comprised of very simple rules that are applied iteratively to 1s and 0s. Rules as simple as “a 0 to the right of a 1 changes into a 1 on the next timestep”.  You give it a certain starting configuration, start it, the automaton follows the rules, and things happen. Apparently at least four known cellular automata are Turing-complete. That the automaton is Turing-complete means that it is capable of universal computation – in theory, capable of executing every possible computer program that could ever be created. This is a very powerful claim that looks far less important than it actually is.

Today’s existential thought was hence that every text in the history of Earth – the works of Shakespeare, the speeches of Churchill, the first words you spoke, the last words I will say – every image – every video – every sound – could be created on one of these simple, stupid machines, if you just had the right combination of initial conditions and enough time. It’s quite remarkable, really.
He ended with a sentence that I quite liked, and have added to my to-calligraph list.

“We should have a little humility in the face of mathematics.”

Author: krysjez

I'm a student of computer/cognitive science, artist and geek. Nice to meet you! Follow my adventures at https://inmannheim.wordpress.com

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