Genetic Relativism and Evolvability

**Barry McMullin
http://www.eeng.dcu.ie/~mcmullin/**

**©2000
Presented at the **

Research Institute for Networks and Communications Engineering

Artificial Life Laboratory

Technical Report Number:

Within any suitable framework of primitive automaton components
(CA or otherwise) the von Neumann architecture for
self-reproduction can generally give rise to (an infinity of)
infinite sets of self-reproducing automata. The automata
within any single such set are characterised as sharing a
particular ``constructing'' or ``decoding'' subsystem (a
``general constructive automaton''). This means that all the
automata within such a set share the same formal ``genetic
language''; this, in turn, means that they are connected by a
network of potential mutations. The latter was an important
and significant finding by von Neumann, as it established that
some, at least, of the conditions for the evolutionary growth
of automaton complexity can be met in such mechanistic
frameworks, within any single one of these von Neumann sets of
self-reproducers (McMullin, 2000).
This note explores a further elaboration of these results,
based on the possibility of mutational pathways *between*
(as opposed to *within*) von Neumann sets; i.e., pathways
between automata implementing *different* genetic
languages. Von Neumann himself considered this issue briefly,
but apparently discounted it
(von Neumann, 1949, p. 86). By contrast, I
argue that it may be deeply significant for both natural and
artificial evolutionary systems.

In a paper at the main ALife VII conference
(McMullin, 2000) I mention in passing
that von Neummann's architecture for self-reproducing machines
supports the possibility of *genetic relativism* and that it
seems to me that this allows for a more profound form or degree
of evolvability in von Neumann's system compared to, say,
`Tierra` (Ray, 1992). This note elaborates briefly on
this point. It is drawn from comments originally presented in my
PhD thesis (McMullin, 1992*a*, Chapter 4).

I will refer several times below to what I call *von
Neumann's Problem*. By this I will mean the problem of how
machines can manage to construct other machines more ``complex''
that themselves, in a general and open-ended way--i.e., with the
potential for unbounded evolutionary growth of complexity. This
is, of course, essentially a problem of *artificial
evolvability*.

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 . is, in effect,
a programmable constucting machine. In a manner reminiscent of a
turing machine, if a ``tape'', , is attached to then
will interpret this tape as a description of some other
machine, which is intended to construct. We require that
should also *copy* the attached description tape (and
attach this copy in turn to the constructed machine). We assume
that 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
denote a tape describing target machine (relative to
the decoding conventions, or genetic language, realised by
). We then write:

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

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 as a
*subsystem*:

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

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 (
) with arbitrarily complex
elements. Exhibiting the detailed design of a particular 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}

Now this set of von Neumann self-reproducers anchored on a single
have precisely this in common: they process the same formal
``genetic language'' for describing machines. In biological
terms we may say that this set incorporates a fixed, or
*absolute* mapping between genotype (description tape) and
phenotype (self-reproducing automaton).

Thus, in committing ourselves (following von Neumann) to solving
the problem of the evolutionary growth of complexity purely
within the resources of a single such set, we are also committing
ourselves to the equivalent of what I have elsewhere called * Genetic Absolutism*
(McMullin, 1992*b*, Section 5.3), within the
analysis of our formal or artificial system.^{2} I
should note that, in that paper, I argue at length against the
idea of Genetic Absolutism; but not in the sense that it is
``bad'' in itself--it just is not a tenable theory of biological
evolution. Now von Neumann is not yet trying to capture all the
complications of biological evolution: he is merely trying to
establish that some key features, at least, can be recreated in a
formal, or artificial, system. If this can be done within what
is, in effect, a framework of Genetic Absolutism, *and if
there is some advantage to doing this in that particular
way,* then the fact that it is still ``unbiological'' (in
this specific respect) should not be held too severely against
it. (Indeed, there are arguably much more severe discrepancies
than this in any case.)

Now, as it happens, adopting Genetic Absolutism *does*
have a significant advantage for von Neumann. Working within
such a framework it *is* necessary (for the solution of
von Neumann's problem) to exhibit one core general constuctive
automaton, ; and it *is* necessary to establish that
this is sufficiently powerful to satisfy the informal
requirements of the evolutionary growth of complexity; and it
*is* finally necessary to show that, based on the formal
genetic language processed by , there is a reasonable likelihood
that most, if not all, of the corresponding self-reproducers will
be directly or indirectly connected under mutation. But if all
this can be done, then the problem immediately at issue for
von Neumann can, indeed be solved.

In any case, what would be the alternative if Genetic Absolutism were not adopted?

Well, the alternative to Genetic Absolutism is *Genetic
Relativism* (McMullin, 1992*b*, Section 5.4),
which envisages that the mapping between genotype (description
tape) and phenotype (self-reproducing automaton) is *not*
fixed or absolute but may vary from one organism (automaton) to
another.

If we tackle von Neumann's problem in a framework of
Genetic Relativism, we do *not* restrict attention to a
single , giving rise to an ``homogenous'' set of
self-reproducers, all sharing the same genetic language.
Instead we introduce the possibility of having many * different* core automata-- etc. Each of these
will process a more or less *different* genetic
language, and will thus give rise to its own unique set of
related self-reproducers. We must still establish that most if
not all self-reproducers in each such set are connected under
mutation; but, *in addition,* we must try to show that
there are at least some mutational connections between the * different* such sets.

The latter is, of course, a much more difficult task, because the mutations in question are now associated with changes in the very languages used to decode the description tapes. But, if such connections could be established, then, for the purposes of solving von Neumann's problem we are no longer restricted to considering the range of complexities of any single von Neumman set of self-reproducers (i.e., anchored on a single , with a common description language), but can instead consider the union of many--indeed a potential infinity--of such sets.

Now clearly, in terms simply of solving von Neumann's problem,
Genetic Relativism introduces severe complications which are not
necessary, or even strictly useful. For now we have to exhibit
not one, but multiple core general constructive automata,
processing not one, but multiple genetic languages; and we
have to characterise the range of complexity, and mutational
connectivity, of not one but multiple sets of self-reproducers;
and finally, we still have to establish the existence of
mutational links *between* these different sets of
self-reproducers. The only benefit in this approach
seems to be that maybe--just maybe--the distinct general
constructive automata can be, individually, significantly simpler
or less powerful than the single one required under Genetic
Absolutism; but it seems quite unlikely that this could outweigh
the additional complications.

Let me say then that I actually accept all this: that for the
solution of von Neumann's problem, as I have stated it, adopting
the framework of Genetic Absolutism seems to be quite the
simplest and most efficacious approach, and I endorse it as such.
Nonetheless, I think it worthwhile to point out the * possibility* of working in the alternative framework of
Genetic Relativism for a number of distinct reasons.

Firstly, it would be easy, otherwise, to mistake what is merely a
pragmatic preference for using Genetic Absolutism in solving von
Neumann's problem with the minimum of effort, for a claim that
Genetic Absolutism is, in some sense, *necessary* for the
solution of this problem. It is not. More generally, our chosen
problem is *only* concerned with what may be possible, or
sufficient--not what is necessary.

A second closely related point is this: *prima facie,* our
solution based on Genetic Absolutism may seem to imply that a
*general* constructive automaton (i.e., capable of
constructing a very wide range of target machines) is a
pre-requisite to *any* evolutionary growth of complexity.
It is not. Indeed, we may say that, if such an implication
*were* present, we should probably have to regard our
solution as defective, for it would entirely beg the question of
how such a relatively complex entity as (or something
fairly close to it) could arise in the first place. Conversely,
once we recognise the *possibility* of evolution within the
framework of Genetic Relativism, we can at least see how such
prior elaboration of the powers of the constructive automata
could occur ``in principle''; this insight remains valid, at
least as a coherent conjecture, even if we have not demonstrated
it in operation. This has a possible advantage in relation to
the solution of von Neumann's problem in that it may permit us to
work, initially at least, with significantly more primitive
constructive automata as the bases of our self-reproducers.

Thirdly, Genetic Absolutism views all the self-reproducers under
investigation as connected by a *single* ``genetic
network'' of mutational changes. This is sufficient to solve von
Neumann's problem, as stated, which called only for exhibiting
the *possibility* of mutational growth of complexity. In
practice, however, we are interested in this as a basis for a
*Darwinian* growth of complexity. Roughly speaking, this
can only occur, if at all, along paths in the genetic network
which lead ``uphill'' in terms of ``fitness''. If the genetic
network is fixed then this *may* impose severe limits on
the practical paths of Darwinian evolution (and thus on the
practical growth of complexity). Again, once we recognise the
*possibility* of evolution within a framework of Genetic
Relativism--which offers the possibility, in effect, of
changing, or jumping between, *different* genetic
networks--the *practical* possibilities for the
(Darwinian) growth of complexity are evidently greatly increased.

This last point represents a quite different reason for favouring the framework (or perhaps we may now say ``research programme'') of Genetic Relativism, and it is independent of the ``power'' of particular core constructive automata. In particular, even if we can exhibit a single full blown general constructive automaton, which yields a mutationally connected set of self-reproducers spanning (virtually) every possible behaviour supported in the system, there could still be advantages, from the point of view of supporting Darwinian evolution, in identifying alternative constructive automata, defining alternative genetic networks (viewed now as evolutionarily accessible pathways through the space of possible automaton behaviours).

Indeed, this need not be all that difficult to do: it provides a
particular reason to consider combining a basic constructive
automaton with a turing machine (or something of similar
computational powers): the latter is arranged so that it
``pre-processes'' the description tape in some (turing
computable) fashion. The program of the turing machine could
then effectively encode a space of alternative genetic
languages (subject to the primitive constructional abilities of
the original constructive automaton); with moderately careful
design, it should be possible to open up an essentially infinite
set of constructive automata, which are themselves connected
under mutation (of the program for the embedded turing
machine--another tape of some sort), thus permitting a multitude
of *different* genetic networks for potential exploitation
by a Darwinian evolutionary process. This should greatly enhance
the possibilities for Darwinian evolution of *any* sort,
and thus, in turn, for evolution involving the growth of
complexity.

This particular idea seems to have been anticipated by Codd:

A further special case of interest is that in which both a universal computer and a universal constructor [sic] exist and the set of all tapes required by the universal constructor is included in the Turing domain . For in this case it is possible to present in coded form the specifications of configurations to be constructed and have the universal computer decode these specifications ...Then the universal constructor can implement the decoded specifications. Codd (1968, pp. 13-14)

While Codd did not elaborate on *why* such flexibility
in ``coding'' should be of any special interest, it seems
plausible that he had in mind precisely the possibility of
opening up alternative genetic networks.

I close this brief review with two final remarks relating to Genetic Relativism.

Firstly, von Neumann himself seems to have discounted even the
*possibility* of Genetic Relativism being applicable to his
models. In his discussion of different kinds of mutations, he
stated explicitly that mutations affecting that part of a
description tape coding for the core part of the self-reproducer
(i.e. coding for in the terms used above) would result in
the production of ``sterile'' offspring
(von Neumann, 1949, p. 86): the implication is
that this would *always* be the outcome of such mutations.
I suggest that such a claim is too strong, in general. My view is
that, on von Neumann's model, it is probably fair to say that
such mutations would *almost* always yield sterile
offspring--but that, depending on the detailed design of the
constructive automaton, and the nature of the particular
mutation, there *might* be exceptional cases where the
offspring would still be an self-reproducer, but containing an
altered core constructive automaton.

Secondly, when tackling von Neumann's problem within the
framework of Genetic Absolutism, it was *necessary* to
assume a degree of compositionality in the genetic language,
to assure that there would exist a range of mutations *not*
affecting the core constructive automaton in a self-reproducer;
without this assumption it would be difficult, if not impossible,
to argue that the set of self-reproducers anchored on this single
core general constructive automaton would be connected under
mutation. This compositionality assumption is more or less
equivalent to the biological hypothesis of *Genetic Atomism*,
which holds that genomes may be systematically decomposed into
distinct *genes* which, individually, have absolute effects
on phenotypic characteristics (see
McMullin 1992*b*, p. 11;
Dawkins 1989, p. 271). This again represents a
divergence between von Neumann's pragmatically convenient
solution schema for his particular problem, and the realities of
the biological world (where any simple Genetic Atomism is quite
untenable). I conjecture therefore that, should we wish to move
away from a strict Genetic Absolutism in our formal or artificial
systems we might well find it useful, if not essential, to
abandon simple compositionality in our genetic language(s)
(i.e. Genetic Atomism) also. This, in turn, would ultimately
lead away from self-reproducer architectures in which there is
any simple or neat division between the core constructive
automaton and the rest of the automaton (though there might still
be a fairly strict separation of the description tape--i.e. a
genotype/phenotype division).

**Codd, E. F. (1968),**-
*Cellular Automata*, ACM Monograph Series, Academic Press, Inc., New York.

**Dawkins, R. (1989),**-
*The Selfish Gene*, new edn, Oxford University Press, Oxford.

**McMullin, B. (1992***a*),- Artificial
Knowledge: An Evolutionary Approach, PhD thesis, Ollscoil na hÉireann,
The National University of Ireland, University College Dublin, Department of
Computer Science.

http://www.eeng.dcu.ie/~alife/bmcm_phd/

**McMullin, B. (1992***b*),- Essays on
Darwinism. 3: Genic and Organismic Selection, Technical Report
`bmcm9203`, School of Electronic Engineering, Dublin City University, Dublin 9, Ireland.

http://www.eeng.dcu.ie/~alife/bmcm9203/

**McMullin, B. (2000),**- John von Neumann and the
Evolutionary Growth of Complexity: Looking Backwards, Looking Forwards...,
*in*M. A. Bedau, J. S. McCaskill, N. H. Packard & S. Rasmussen, eds, `Artificial Life VII: Proceedings of the Seventh International Conference', MIT Press, pp. 467-476.

http://www.eeng.dcu.ie/~alife/bmcm-2000-01/

**Ray, T. S. (1992),**- An approach to the
synthesis of life,
*in*C. G. Langton, C. Taylor, J. D. Farmer & S. Rasmussen, eds, `Artifical Life II', Vol. X of*Series: Sante Fe Institute Studies in the Sciences of Complexity*, Addison-Wesley Publishing Company, Inc., Redwood City, California, pp. 371-408.

Proceedings of the workshop on Artificial Life held February, 1990, in Sante Fe, New Mexico.

**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.

Acknowledgements

I particularly appreciate the encouragement from Chrystopher Nehaniv to submit this paper, and the very helpful and constructive comments from the workshop reviewer. I am grateful to John McCaskill, Lee Altenberg, Günter Wagner, Roger Burkhart and Tim Taylor for subsequent helpful discussion and critique of the ideas presented here. Financial support for the work has been provided by the Research Institute in Networks and Communications Engineering (RINCE) at Dublin City University.

Revision History

Published in August 2000 as Technical Report No. `bmcm-2000-02` of
the Artificial Life
Laboratory
of Dublin
City University. Based on material
originally contained in
(McMullin, 1992*a*, Chapter 4). First presented
at the *Evolvability Workshop*
at
*Artificial Life VII*
August
1-6, 2000, Portland, Oregon.

Author Contact Information

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Retrieval

The resources comprising this paper are electronically retrievable, in various formats, via the World Wide Web, from:

- Presentation Slides:
- Reviewer Comments on draft manuscript:
- ALife7 Plenary Paper: (McMullin, 2000)
- DCU Alife Laboratory:
- Research Institute for Networks and
Communications Engineering (RINCE):

Copyright

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All other rights reserved.

- ...
complexity.
^{1} - This is, of course, an extremely concise summary; see (McMullin, 2000) for much more detail.
- ... system.
^{2} - Note
carefully that this is strictly a limitation of the way
*we choose to analyse*the automata framework in question; it need not, and generally will not, reflect an inherent limitation of any such framework*in itself.*

Copyright © 2000 All Rights Reserved.

Timestamp: 2000-08-16