Re: Life without evolution/evolution without life

[Tim Gwinn <***>]

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Howard
> Pattee
> Sent: Saturday, March 20, 2004 11:02 PM
> To: ***
> Subject: Re: Life without evolution/evolution without life
>
---snip---
> [Howard] Many people now agree. Von Neumann showed that the essential
> embodiment that allows endless emergent properties is the non-dynamic
> symbolic description of the cell we call the genome. This recognition of
> symbols as distinct from dynamics has given rise to both the new field of
> biosemiotics  http://www.gypsymoth.ento.vt.edu/sharov/biosem/geninfo.html
> as well as many artificial life studies.
>
> I think it was unfortunate that Bob began early in his career to
> claim that
> von Neumann?s argument was faulty. Bob?s logic was correct. He found what
> would have been a formal paradox. But von Neumann was not talking formal
> logic. He was making an informal analogy. In any case, Burton Guttman
> (Bull. Math. Biophysics, 28, 191-193, 1966) showed that Bob?s paradox
> disappears if replication has errors, and if evolution is to occur it must
> have errors (mutations).
>
> Unfortunately, Bob never engaged his critics, and so even though he
> discussed the requirement of error for life, he continued to miss von
> Neumann?s fundamental argument why the evolution of complexity requires
> symbolic (non-dynamic) memory as distinct from state-determined dynamics.

> Bob even came close to von Neumann?s point. In Anticipatory Systems  Bob
> recognized that genes require two distinct processes: ?(a) a replicative
> process whereby genetic information is transmitted to descendants, and (b)
> a decoding process comprising a transcription step and a translations step
> [protein synthesis]? (AS, p. 315). But the following discussion shows he
> did not see von Neumann?s essential argument.


First paragraph of Guttman:
"J. von Neumann (1951) proved a general existence theorem for a
self-reproducing automaton that is of considerable interest for a general
theory of biotic systems. However, the validity of this theorem has been
challenged by Rosen (1959). He argues that an automaton can be represented
as a mapping f:A -> B. A self-reproducing automaton is therefore mapping f
which is itself a part of B. But f cannot be specified unless both A and B
are given, and f is a member of B; hence, no such automaton can be made
unless it already exists, thus leading to an infinite regress and to the
conclusion that a self-reproducing automaton of this type is impossible."

It is unclear to me whether von Neumann was making an informal analogy.
Guttman refers to it as a proved theorem; in the part of "General and
Logical Theory of Automata" that I have (which is incomplete), von Neumann
labels the section as "Outline of the Derivation of the Theorem Regarding
Self-Reproduction", and seems more like a discussion of a theorem than an
analogy.

Guttman's article does not seem to me to be relevant to Rosen's particular
paradox. Guttman remarks: "It is true that we have changed the definition of
self-reproduction a little by explicitly allowing errors, and it may be
argued that this is not "true" self-reproduction." And he notes: "In
commenting on this model, Rosen (personal communication) has re-emphasized
that his argument was never intended to rule out all possible cases of
self-reproduction, but only the specific model discussed by von Neumann."

Conversely, by those comments, Rosen's paradox does not seem to be intended
to be relevant to the general notion of self-reproduction, but it seems that
it is often portrayed this way (not implying that you are doing so), such
that Guttman's article therefore appears somehow more devastating than it
actually is - as if Rosen's paradox was a broader claim that Guttman's
article torpedoed.

In any case, it is unclear to me how von Neumann's automata are perforce
relevant to organisms, or what is the "essential argument" that von Neumann
elaborated and which Rosen missed. Can you elaborate on this?

Regards,
Tim