John von Neumann and the
Evolutionary Growth of Complexity:
Looking Backward,
Looking Forward...

Barry McMullin
Research Institute in Networks and
Communications Engineering (RINCE)

Dublin City University
Barry.McMullin@dcu.edu

ALife VII: August 2000
(FoilTeX Presentation)

Burks' Problem:
Machine Self-Reproduction

Trivial Self Reproduction?

Trivial Self Reproduction?

Trivial Self Reproduction?

Burks' Criterion:

But...
Herman's Counter Example

But...
Herman's Counter Example

But...
Herman's Counter Example

Langton's Critique

Langton's Criterion

But...
Langton's Counter Example!

von Neumann's Criterion?

von Neumann's Criterion?

von Neumann's Problem:

Degeneration of Complexity
(Engineering)

\includegraphics{engineering.eps}

Growth of Complexity
(Biology)

\includegraphics{biology.eps}

von Neumann's Problem:

The General Constructive Automaton

\includegraphics{constructor.eps}


\begin{displaymath}(u_0 \oplus d(m)) \leadsto (m \oplus d(m)) \end{displaymath}

Von Neumann SR: Minimal Case

\includegraphics{vnsr.eps}


\begin{displaymath}(u_0 \oplus d(u_0)) \leadsto (u_0 \oplus d(u_0)) \end{displaymath}

Von Neumann SR: Generic Case

\includegraphics{vnsr-plus.eps}


\begin{displaymath}((u_0 \oplus m) \oplus d(u_0 \oplus m)) \leadsto
((u_0 \oplus m) \oplus d(u_0 \oplus m)) \end{displaymath}

Growth of Complexity
(von Neumann)

\includegraphics{biology.eps}

Looking Backward

Looking Forward

Coda...

Science Foundation Ireland
(the other SFI...)

http://www.sfi.ie/

...multidisciplinary proposals in Biotechnology/ICT will be welcomed.

Bibliography

Burks, A. W. (1970),
Von Neumann's Self-Reproducing Automata, in A. W. Burks, ed., `Essays on Cellular Automata', University of Illinois Press, Urbana, pp. 3-64 (Essay One).

Herman, G. T. (1973),
`On Universal Computer-Constructors', Information Processing Letters 2, 61-64.

Langton, C. G. (1984),
`Self-Reproduction in Cellular Automata', Physica 10D, 135-144.

von Neumann, J. (1949),
Theory and Organization of Complicated Automata, in A. W. Burks, ed., `Theory of Self-Reproducing Automata [by] John von Neumann', University of Illinois Press, Urbana, pp. 29-87 (Part One).
Based on transcripts of lectures delivered at the University of Illinois, in December 1949. Edited for publication by A.W. Burks.

Related Online Resources


Copyright

This work is copyright ©2000 by Barry McMullin.

Permission is hereby granted to private individuals to access, copy and distribute this work, for purposes of private study only, provided that the distribution is complete and unmodified, is accompanied by this copyright notice, and that no charges are levied. The work may not be accessed or copied, in whole or in part, for commercial purposes, except with the prior written permission of the author.

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Copyright © 2000 All Rights Reserved.
Timestamp: 2000-08-16

Barry.McMullin@dcu.ie