Sunday, June 16, 2013

What I Gave Stephen Wolfram On His 50th Birthday

To celebrate the 25th anniversary of Mathematica's release, I will post some Mathematicana. I'll explain this chart more fully later but here is a prĂ©cis. Stephen developed Mathematica in part so that he'd have a powerful tool with which to explore the targets of his curiosity. (And we benefit by having a powerful tool with which to explore the targets of our curiosity!) The principal result of his explorations is A New Kind of Science (NKS for short), during the writing of which,  thanks to Mathematica, he made "more discoveries than I ever thought possible" (NKS p 22).

Until recently the history of science and separately, mathematics, displayed the great theme of logical reductionism, by which I mean our success at reducing disparate phenomena to a relatively few postulates or axioms. Viz, physics, or mathematics. While Wolfram's key discovery was that a short sequence can generate unlimited complexity (NKS Ch 2) and while "short sequence" does imply reductionism, the unlimited complexity is anti-reductionistic. To expose the phenomena described by some short sequences we must compute them interminably. This chart, an attempt to place NKS in history, is what I gave Stephen on his birthday several years ago (click to enlarge).

Thales, Pythagoras, Eudoxus, Aristotle, Euclid, Riemann, Bolyai, Schweikart, Gauss, Lobachevsky, Hilbert, Godel, Turing, Chaitin, Wolfram

The "flowstream" term is from the lectures of Andrew J. Galambos, a great, but largely unsung, philosopher. When I mentioned the concept of an intellectual flowstream to my friend Dave Waltz, he pointed me to the fascinating work of Eugene Garfield, notably the Web of Science.

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