🚀 go-pugleaf

snodgras@crash.cts.com (John Snodgrass) writes:
|> Ummmmmm. I thought John Von Neumann proved that automata of
|> sufficient complexity can reproduce themselves. What is Rosen
|> saying that Von Neumann did not?
|
|	 Can you even give the broadest outlines of how Von Neumann
|proved this?  I think not. 

Why not?

In article <BILL.92Sep2120437@ca3.nsma.arizona.edu>
bill@nsma.arizona.edu (Bill Skaggs) writes:
|Well, *I* can.  He gave a mathematical proof that a self-duplicating
|structure exists in the Game of Life (which is a finite-state
|automaton).  He proved it by showing how to construct one.  The
|structure he describes is very large.

I think Conway's "Life" post-dated von Neumann. It was other people
who found a way to implement the idea in a "life" cellular automaton.

The basic idea is quite simple. The machine has certain equipment for
producing other machines from a "blueprint". In the case of living
things, this includes the cellular "machinery" for translating DNA
into proteins; in the "life" cellular automata, it involves sequences
of gliders being collided so as to give rise to other automata.

The machine is then instructed to manufacture a machine according to a
blueprint, and then copy the blueprint into a designated "blueprint
slot" in the other machine. The machine is then equipped with a
blueprint of itself (aside from the blueprint). This side-steps the
need for an infinite regression of blueprints.

It is a popular pastime of programmers to write programs which
generate their own source code, by essentially this method.

Keith Ramsay
ramsay@unixg.ubc.ca