Howard,
I consider your charge that Rosen "falsely accused von Neumann" and
insinuating that he was acting unethically a grotesque and absurd
personal attack. You say that "the science of the matter is not the
issue", but for an accusation to be false it must be that it indeed
claims something that is not the case. You cannot divorce the
scientific truth or falsity of his ideas from the ethics charge.
There are several specific and distinct topics that I am aware of
where Rosen makes claims about concepts that were related to ideas
generated by von Neumann. However, these topics do not affect only
ideas emanating from von Neumann, as though he we were a singular
target. You seem to be conflating these topics such that it appears
that Rosen made a "repetition of essentially the same charge for over
40 years."
1) The 1959 BMB paper "On a Logical Paradox Implicit in the Notion of
a Self-Reproducing Automaton". Rosen begins the paper:
"The purpose of this note is to point out a paradox which arises
when one attempts to provide a precise formulation of the notion
of self-reproducing automaton, as originally introduced by J. von
Neumann (1951) and discussed subsequently by a number of different
authors. If this paradox cannot be resolved, then the conclusion
to which we are forced is that the existence of a self-reproducing
automaton is a logical impossibility. We shall investigate the
implications of this result for biological problems, and we shall
also discuss in the light of this result several of the models for
replicating structures which have been proposed."
Rosen then states the argument asserting the paradox, which you
yourself agree in your post of 3/22/04 is "formally correct".
Essentially, it consists of the following: if an arbitrary automaton f
can be represented by a set-mapping f:A->B, where A is the input and B
the output, then self-reproduction consists of f being able to
generate a copy of itself as part of the output, B. But, f cannot be
defined until its range, B, is defined and yet B cannot be defined
until f (which is a member of B) is defined. Thus the paradox. Note
that at this point, the argument is about any arbitrary automaton
which can be mapped as f:A->B.
Later in the paper he notes: "It may be instructive at this point to
review von Neumann's construction of a self-reproducing automaton and
to observe the manifestation of the above paradox in his model." He
then spends three paragraphs applying the paradox to an set-mapping
model of such an automaton and concluding, "Hence it appears that the
notion of universal automaton involves the same type of difficulty as
does the notion of self-reproduction."
He then discusses the paradox relative to the self-replicating
structures of Penrose (1958) and Jacobson (1958). Since they are not
truly self-reproducing the paradox does not arise in them. However,
Rosen's own models do not emerge uncriticized. At the conclusion of
the paper, Rosen discusses the issue of the paradox relative to his
own (M,R)-system:
"Finally, it may be useful to examine the relation of the
results enunciated above to the notion of the (M,R)-system, as
introduced by us (Rosen, 1958a, 1958b, 1959). The (M,R)-system was
primarily constructed to provide a model for metabolic activities
of a single cell, but as we have remarked, it is necessary for
such a theory to deal with the replication problem if it is to
have any claim to completeness. In one of these works (1959) we
proposed a model of the duplication of the components R-sub-f
which correspond to the genetic material of the cell, based on the
notion of induced mappings which exist formally in the abstract
representation of the (M,R)-system. It will be noticed that these
induced mappings play a role very similar to the auxilary automata
which appear to be required in order to fabricate structures which
can be duplicated. It will further be seen that since the domains
and ranges of all the induced mappings are perfectly well-defined
sets, there is no question of encountering the paradox we have
described above. Since these induced mappings will correspond to
environmental objects (at least in the form in which they were
enunciated in Rosen 1959), there is no need to consider mechanisms
for their replication, so that we avoid thereby an infinite
regress which would destroy the usefulness of the model.
Nevertheless, it appears that the replicative mappings induced
in abstract (M,R)-systems in the manner described (Rosen 1959) may
not correspond to the actual coarse structure of biological
systems. In order to conform to the discussion set forth above, it
seems that the mappings which are of importance for replicative
procedures should be chosen so as to be of the form of the
auxiliary automata occurring in the models of Penrose and
Jacobson. This modification does not appear to be too difficult,
and appropriate investigations are currently in progress."
I do not find this paper to be particularly structured as an assault
on von Neumann or on his ideas. Certainly, as Rosen states up front,
the question of a paradox germinates from the very idea of a
self-reproducing automaton, which in turn was originated by von Neumann.
I think you may have previously argued that Rosen was too narrow in
his interpretation of "self-reproducing automata" as conceived by von
Neumann, thereby causing this paper to be some kind of straw-man
argument by Rosen. But Rosen's characterization seems quite valid.
Burk, in the Introduction of Essays on Cellular Automata remarks:
"In the first essay I also describe von Neumann's kinematic model
of self-reproduction and compare it with his cellular model. This
comparison is of interest because of the vague nature of the
general problem of self-reproduction which von Neumann posed. Once
a particular cellular space (e.g., von Neumann's 29-state system)
and a "universal" class of automata (e.g., initially quiescent
automata) are defined, the question of the existence of a
universal constructor is a precisely logical one. But von Neumann
was interested in this question because it is a special case of a
more general question: What kind of logical organization is
sufficient for an automaton to reproduce itself? This question is
not precise and admits to trivial versions as well as interesting
ones. Von Neumann had the familiar natural phenomenon of
self-reproduction in mind when he posed it, but he was not trying
to simulate the self-reproduction of a natural system at the level
of genetics and biochemistry. He wished to abstract from the
natural self-reproduction problem its logical form." [p. xv]
So, Burk asserts that the logical form of self-reproduction, divorced
from concerns of chemistry and genetics, was the focus of von Neumann,
which is precisely what Rosen engaged.
Further, the cellular automata, as well as the more complicated
kinematic automata (controlled by a Turing machine), are clearly not
beyond the scope of Turing-computability. Is Burk then
mischaracterizing von Neumann or improperly focusing on these
Turing-computable models?
To my knowledge, there are only two rebuttals to this paper. One is
Guttman (1966) and the other is Moore, which I find in Burk's Essays
on Cellular Automata (1970). In neither case do the authors question
Rosen's characterization of von Neumann's automaton as too narrow or
otherwise misrepresenting von Neumann's automata.
As I mentioned in a previous post (3/21/04), Guttman does not
refute Rosen's paradox, but instead provides an alternative mechanism
by which to circumvent the paradox. In doing so, he utilizes the same
set-mapping characterization of automaton as did Rosen. Nor did Rosen
fail to "engage his critics", since Guttman notes that Rosen
acknowledged to him that Rosen's argument was restricted to a specific
form of self-reproduction, and did not include all possible forms of
self-reproduction (such as Guttman's mutation approach).
Edward Moore begins his essay "Machine Models of Self-Reproduction" as
follows:
"The ability of living organisms to reproduce themselves has long
been considered to be one of their most characteristic features.
Von Neumann was the first to treat in any detail the problem of
how to make machines reproduce themselves in a purely mechanistic
fashion as a way of throwing light on some fundamental problems of
biology and as a problem (of intrinsic interest aside from
biology) concerning the capabilities and limitations of machines."
[p. 187]
Here again, Moore asserts that von Neumann approached
self-reproduction from a "purely mechanistic fashion". Moore's
complaint [p. 191] about Rosen's paper is that he feels that Rosen has
confused the distinction between the tesselation space (which stands
in for the "universe" in the tesselation model) with the configuration
of cells, and that no paradox exists. However, this to me seems
confused since Moore acknowledges [p. 188] that the state transition
rules are part of the underlying tesselation structure, and not part
of the configuration. Therefore, any changes in the configuration of
the cells - including any replication of a configuration - relies on
the computations induced by those rules external to the configuration.
Replication of a configuration is therefore not self-reproduction,
since the tesselation structure which drives the process is not also
reproduced. As Rosen notes at the end of chapter 15 "Morphogenesis in
Networks" in Essays on Life Itself:
"Von Neumann's original problem was the following. Suppose that we
define an initial configuration of the tesselation, in which a
finite number of the constituent automata are in active states,
and all the other automata are "off". Can we define state
transition rules such that at the end of some definite time, the
configuration of the tesselation will consist of two copies of the
original active configuration, with everything else "off"? This
question has been answered in the affirmative by a number of
authors, and a large literature with strongly morphogenetic
overtones has been elaborated within this framework. However,
these problems are entirely network problems, interpretable as
differential birth-and-death by allowing birth to mean the forcing
of a neighboring inactive cell into an active state, and death to
mean the opposite." [p. 245]
This post has become longer than I originally intended. For time and
size considerations, I will break it up into at least two posts.
I also note here in passing that Kampis, in his book Self-Modifying
Systems in Biology and Cognitive Science, spends many, many pages
(primarily in chapter 7 "Self-Reproduction and Computation") on von
Neumann's self-reproducing automata, and comes to many (and perhaps
more) of the same kinds of critical conclusions about von Neumann
self-reproducing automata as Rosen. Was Kampis therefore also "falsely
accusing" von Neumann?
Tim
> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Howard
> Pattee
> Sent: Tuesday, March 30, 2004 9:34 PM
> To: ***
> Subject: Re: Howard's challenge #1
>
>
> Judith,
>
> I apologize for calling Bob's friends (is that OK) by other
> names. I'm generally in agreement with most of your long
> responses, but I think you have lost the issue that I first raised.
>
> Judith: The biggest problem my father had with von Neumann's
> theory was not the secondary stuff, which as you mentioned, seems
> to agree quite a bit with
> "Rosennean" findings-- it's the primary concern that made my father
reject
> the whole shebang. Von Neumann's basic premise was what he disagreed
with
> entirely and wanted to distance himself from.
>
> HP: I understand all that, but it is not the issue I raised. All
> I suggested is that it would be best for Bob's reputation if his
> friends, colleagues, relatives, (what should I call them?), would
> not continue to defend Bob's specific no-longer defensible
> argument with von Neumann over self-replication. This has nothing
> to do with whether von Neumann's had a good philosophy or even a
> good model of replication. It has nothing to do with the
> technical meanings of "equivocation" or "confounding" or
> "invalidation" or any other words that Bob has used to discredit
> von Neumann's model.
>
> The issue, to put it bluntly, is whether Bob falsely accused von
> Neumann. In other words, the science of the matter is not the
> issue. It is the ethics of Bob's refusal to engage his critics on
> the issue and his unresponsive, uncritical repetition of
> essentially the same charge for over 40 years.
>
> If this is the case, then I think you would understand why it is
> not good for Bob's reputation to continue to justify it by a
> diversion, explaining that the biggest problem Bob had was that
> he just disagreed entirely with von Neumann's basic premise
> (whatever that is?) and that led him to reject the whole shebang.
> That is not considered a good scientific or philosophical
> argument, although it may be a good psychological explanation.
>
> I have given brief quotations from von Neumann showing that Bob's
> assumptions (in his paper, Bull. Math. Biophysics, 1959) were
> mistaken. There are a lot more. I can also find Bob's
> restatements of this misinterpretation in many papers. I think it
> had become a habit. In Life Itself, p. 234, he says it
> "parenthetically," and with no references, as if it were an
> established fact that von Neumann confounded simulation with
construction.
>
> I would like go on to discuss why I think some of von Neumann's
> ideas were consistent with Bob's, specifically his Theory of
> Games. I think that iterative game theory might fall in the
> category of Bob's impredicative models.
>
> Howard