Document: Von Neumann, Genetic Relativism and Evolvability
On Genetic Absolutism
The Von Neumann Self-reproducing
Introduction

The von Neumann Architecture for Self-reproduction

The von Neumann architecture for self-reproduction is based on the idea of a `general constructive automaton''. I will denote (an example of) such an automaton by $u_0$. $u_0$ is, in effect, a programmable constucting machine. In a manner reminiscent of a turing machine, if a ``tape'', $d$, is attached to $u_0$ then $u_0$ will interpret this tape as a description of some other machine, which $u_0$ is intended to construct. We require that $u_0$ should also copy the attached description tape (and attach this copy in turn to the constructed machine). We assume that $u_0$ is capable of successfully constructing a wide range of such target machines (this is why it is termed a general or programmable constuctive automaton). Let $d(m)$ denote a tape describing target machine $m$ (relative to the decoding conventions, or genetic language, realised by $u_0$). We then write:

$$(u_0 \oplus d(m)) \leadsto (m \oplus d(m))$$

Assuming that the set $M$ of machines that $u_0$ can construct includes $u_0$ itself, it follows that:

$$(u_0 \oplus d(u_0)) \leadsto (u_0 \oplus d(u_0))$$

This is the essential structure for a single self-reproducing automaton which has been commonly identified as von Neumann's ``result''. But such an interpretation seriously understates the true depth of von Neumann's work. It completely misses the single most significant aspect of this particular architecture, namely that this core design in turn implies the existence of a whole infinite set of general constructive automata which incorporate $u_0$ as a subsystem:

$$u_i = u_0 \oplus i$$

With some limited assumptions about the interactions of $u_0$ and the ``ancillary'' machinery $i$, it follows that there is an infinite set of self-reproducing automata of the form:

$$(u_i \oplus d(u_i))$$

It turns out that the elements of this set are connected by a network of potential mutations (interpreted simply as spontaneous perturbations of the description tape). Which means that there are evolutionary pathways linking the simplest element of this set ( $u_0 \oplus d(u_0)$) with arbitrarily complex elements. Exhibiting the detailed design of a particular $u_0$ in a particular framework (which is what von Neumann actually did) thus leads directly to an effective solution to von Neumann's problem of the evolutionary growth of machine complexity.¹

On Genetic Absolutism
The Von Neumann Self-reproducing
Introduction
Document: Von Neumann, Genetic Relativism and Evolvability

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Timestamp: 2000-08-16