the short program

From: Juergen Schmidhuber <>
Date: Wed, 10 Jul 2002 10:16:32 +0200

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": ) 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 ):
  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
Received on Wed Jul 10 2002 - 01:17:28 PDT

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