Tomorrow Elephant

It’s rare that I’m actually able to use computers in my PhD work: the state of the art in mathematical physics, for the most part, is still scribbling symbols on paper, and that’s pretty much as high-tech as it gets. However, recently I had reason to familiarise myself with Stephen Wolfram’s Mathematica, and I was positively surprised. Mathematica is symbolic computation environment (and a programming language) that allows one to automate some of the algebraic drudgery associated with all forms of mathematics. It’s not applicable to everything, of course, but it works very well where it does, in particular linear algebra. I also like the somewhat LISP-like way it represents its expressions internally: this allows for some nifty programming shortcuts.

Stephen Wolfram, the creator of Mathematica, is a story by himself. A certified genius (the recipient of a MacArthur grant at the age of 21), people were expecting Wolfram to make great strides in physics and cosmology. Instead, he became convinced that cellular automata were the underlying machinery of the universe, developed Mathematica as a handy calculational tool and later (after becoming a software millionaire) self-published a vast tome called A New Kind of Science, in which he lays out his personal vision of the future of physics. Freeman Dyson dismissed it with one word – “worthless”. I’m not enough of an expert on CAs to really comment on CA-based models of physics, but one trap one can fall into here seems to be that CAs are Turing-complete – that is, you can construct a CA that does what any Turing machine can do, which presumably could include the kinds of physics simulations that Wolfram and others (notably Ed Fredkin, uncredited in Wolfram’s rather egocentric book) have come up with.

Still, CAs are kind of pretty, and there are many uglier things that could live beneath the floor of the Universe…