Tim May wrote: > One thing that Tegmark got right, I think, is the notion that a lot of > branches of mathematics and a lot of mathematical structures probably go > into making up the nature of reality. > > This is at first glance dramatically apposite the ideas of Fredkin, > Toffoli, Wheeler1970, and Wolfram on the generation of reality from > simple, local rules. Wolfram has made a claim in interviews, and perhaps > somewhere in his new book, that he thinks the Universe may be generated > by a 6-line Mathematica program! I'd like to point out that it was Konrad Zuse himself ("inventor of the computer": http://www.idsia.ch/~juergen/zuse.html ) who was the first to propose that the physical universe is running on a grid of simple computers, each communicating with its neighbors: a cellular automaton. He called this "Rechnender Raum," which means "Computing Space." As always, Zuse was way ahead of his time. Perhaps the best reference is: Zuse, Konrad: Rechnender Raum, Schriften zur Datenverarbeitung, Band 1. Friedrich Vieweg & Sohn, Braunschweig (1969). And here is the simple method for computing all universes, including ours, if it is computable indeed (adapted from page 1 of the 97 paper http://www.idsia.ch/~juergen/everything/html.html ): Order all programs lexicographically. The first is run for one instruction every second step, the next for one instruction every second of the remaining steps, and so on. As a by-product, this program also outputs descriptions of all formally describable mathematical systems, and all proofs of all their theorems. A bit of thought shows that the method even has the optimal order of complexity. For example, it outputs our universe history as quickly as the history's fastest program, save for a (possibly huge) constant that does not depend on output size. Juergen Schmidhuber http://www.idsia.ch/~juergen/

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