6 Conclusion: Looking Forwards

John von Neumann and

4 Looking Backwards

The 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 call * Genetic Absolutism*
[13, Section 5.3]. I
should note that, in the latter 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.

But the key point is
that even though this may *suffice* for von Neumann's
immediate purposes, nonetheless his framework is actually capable
of going well beyond this; and I will claim that there may be
advantages in doing so.

As I indicated in the previous section, the alternative to
Genetic Absolutism is *Genetic Relativism*
[13, 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
(in order to establish pathways for evolution of the mapping
itself).

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. At face value, the only benefit in this
approach seems to be the rather weak one 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 behavior 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 behaviors).

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 [6, 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.

A final consideration here is the ``compositionality'' of the
genetic mapping or language. 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 [13, p. 11],
Dawkins [7, 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 from the
rest of the machine--i.e., a
genotype/phenotype division).

6 Conclusion: Looking Forwards

John von Neumann and

4 Looking Backwards

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Timestamp: 2002-11-07