🚀 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. 

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.

   > Moreover, whatever the type of logic he utilizied, the only real
   > proof would be to build one. 

No, Life is a mathematical structure, so the existence can be shown by
a mathematical proof.

But this is mostly a historical curiosity nowadays.  The workings of
DNA are now understood sufficiently to make it clear how
self-replication can arise.  For a nice brief explanation, look at the
chapter about DNA in Douglas Hofstadter's "Metamagical Themas".  (I
don't remember the chapter title offhand, and the book is at home.)

	-- Bill