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
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/