Notes for the Lifebox, the Seashell, and the Soul - Rudy Rucker

Notes for The Lifebox, the Seashell, and the Soul, by Rudy Rucker
working with von Neumann at Los Alamos during those years. Ulam’s suggestion was that
instead of talking about machine parts in a reservoir, von Neumann should think in terms of
an idealized space of cells that could hold finite state-numbers representing different sorts of
parts.
Ulam’s first published reference to this idea reads as follows:
An interesting field of application for models consisting of an
infinite number of interacting elements may exist in the recent theories
of automata. A general model, considered by von Neumann and the
author, would be of the following sort:
Given is an infinite lattice or graph of points, each with a finite
number of connections to certain of its “neighbors.” Each point is
capable of a finite number of “states.” The states of neighbors at time
T n induce, in a specified manner, the state of the point at time T n+1 .
One aim of the theory is to establish the existence of
subsystems which are able to multiply, i.e., create in time other
systems identical (“congruent”) to themselves. 3
By 1952, von Neumann had completed a description of such a self-reproducing
“cellular automaton” which uses 29 states. Von Neumann’s CA work was not published
during his lifetime; it seems that once he saw the solution, he became distracted and moved
on to other things.
Wolfram On Discovering CAs
It really is quite remarkable that, starting from an initial condition of a single marked
cell, something as simple as a “Rule 30” can generate Class 3 randomness and that a “Rule
110” can generate a Class 4 process resembling a complex computation. In his own
somewhat hyperbolic style, Wolfram expresses his excitement as follows.
And what I found — to my great surprise — was that despite
the simplicity of their rules, the behavior of programs was often far
from simple. Indeed, even some of the very simplest programs that I
looked at had behavior that was as complex as anything I’d ever seen
... I have come to view [this result] as one of the more important single
discoveries in the whole history of theoretical science. 4
Mathematicians have never discussed very much the fact that you can get
complicated things from simple causes like CA Rule 30 or CA Rule 110. The one area
where they have talked a bit about complexity emerging from simple rules is in the
distribution of the primes and the irregularity of the digits of pi.
Wolfram expresses surprise over this in these words. “Often it seemed in retrospect
3 From “Random Processes and Transformations,” 1950, reprinted in : Stanislaw Ulam, Sets, Numbers
and Universes, MIT Press, Cambridge 1974, p. 336.
4 Stephen Wolfram, A New Kind of Science, p. 2.
p. 68