Posts from 2011

Music, Mathematica, and the Computational Universe

This week I’m giving a talk at a conference on Mathematics and Computation in Music (MCM 2011)… so I decided to collect some of my thoughts on such topics…


How difficult is it to generate human-like music? To pass the analog of the Turing test for music?

Though music typically has a certain formal structure—as the Pythagoreans noted 2500 years ago—it seems at its core somehow fundamentally human: a reflection of raw creativity that is almost a defining characteristic of human capabilities.

But what is that creativity? Is it something that requires the whole history of our biological and cultural evolution? Or can it exist just as well in systems that have nothing directly to do with humans?

In my work on A New Kind of Science, I studied the computational universe of possible programs—and found that even very simple programs can show amazingly rich and complex behavior, on a par, for example, with what one sees in nature. And through my Principle of Computational Equivalence I came to believe that there can be nothing that fundamentally distinguishes our human capabilities from all sorts of processes that occur in nature—or in very simple programs.

But what about music? Some people used their belief that “no simple program will ever create great music” to argue that there must be something wrong with my Principle of Computational Equivalence.

So I became curious: is there really something special and human about music? Or can it in fact be created perfectly well in an automatic, computational way?

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A Precociousness Record (Almost) Broken

I got started with science quite early in my life… with the result that I got my PhD (at Caltech, in physics) when I was 20 years old. Last weekend a young woman named Catherine Beni (whom I had met quite a few years ago) sent me mail saying she had just received her PhD from Caltech (in applied math)—also at the age of 20.

Needless to say, we were both curious who had the record for youngest Caltech PhD. Catherine said she was 20 years, 2 months and 12 days old when she did her PhD defense. Well, I knew I’d finished my PhD in November 1979—and I was born August 29, 1959. So that would also have made me around 20 years and 2 months old.

I quickly searched the OCR’ed archive that I have of my paper documents, and found this:

Stephen Wolfram PhD

The month was confirmed, but frustratingly, no day was filled in. But then I remembered something about my PhD defense (the little talk that people give to officially get their theses signed off). In the middle of it, I was having a rather spirited discussion (about the second law of thermodynamics) with Richard Feynman, and suddenly the room started shaking—there was a minor earthquake.
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