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Re: terminal von Neumann



Tim, I greatly appreciate your digging into these references, which I
wanted to do but couldn't find the time. I would like to cite something
about the logical paradox. What is the best reference for that, the 1951
paper or 1966?

Also, thinking this weekend and reading more of AS and searching on the
web for articles on Von Neumann, it became clear that VN is associated
with the Church-Turing concepts of computablility and responsible for
essentially inventing modern computing and cellular automata techniques.
Chris Langton of SFI developed agent-based modeling automata in a
sofware package called SWARM. It has been used to model many complex
biotic interactions on a landscape, like species competition and
evolution, predation, etc. I am using such a technique myself to model
shrub encroachment (or at least have proposed to do so).

As I have now reasoned it from this cursory exposure to Von Neumann, via
all the comments here and various articles on the Web, I sense that the
issue of "confounding" simulation and construction is a very simple one
to distinguish. VN proposed the idea of a "universal constructor" as a
logical entity based on self-replicating logical structures, i.e.,
computer programs. I'm guessing that idea of self-replicating structures
is what is meant by cellular automata. However, it is not a case where
the agents write their own software, the software written by a human
programmer allows for certain characters of the agent to be modified in
each iterative step, the steps themselves being under control of the
programmer. I don't know if anyone has succeeded in generalizing this
concept to the point where the agents write their own software in its
entirely - I suspect not because that would run into difficulties with
Goedellian incompleteness. In that case, it only works within a given
context - a context given by the programmer, a biological entity. In
realizing any such self-reproduction in the natural world, one would
also have to realize a context and the semantic relationship with that
context. On logical grounds, RR says that would not be possible,
precisely because the model must remain calculable in VN's approach, and
thus semantically incomplete. To be realized, natural systems must be
semantically complete. This to me seems to explain the comment that VN
confounded simulation with construction - it was not that VN didn't
realize or discuss the same problem, it was that his proposed solution
involved making a direct analogy between what could be done in the
computer via calculations and what is happening in nature, and then
speculating that the one could cause the other, or be realized by it. RR
said that cannot happen unless the "model" is a) itself part of a
natural system, and b) non computable. Self-realization of a program
that could write its own software and construct its own hardware would
satisfy criterion (a), but he argued that on logical grounds it could
not do that and remain computable. That to me seems to be the debate. Is
this at all close according to your sources????

John Kineman

Tim Gwinn wrote:

Howard,

As you say, Rosen's comments on "confounding of simulation (computation)
with construction" occur in Life Itself. My statement that you quote was
from my "Part 2" post and was explicitly in regard to Rosen's remark in Life
Itself, not to the 1959 paper (which I discussed separately in my "Part 1"
post). You make it appear here as if I was talking about the 1959 paper in
your "correction" to my statement. I do not know why you bring up the 1959
paper at all in this regard. The 1959 paper does not discuss construction
vs. simulation at all. It has only to do with the logical paradox.

Since confounding simulation with construction obviously involves some case
of simulation, I take it that Rosen (in Life Itself, to reiterate) refers to
simulations by von Neumann, such as the cellular automata. I did not know
there were five types of models and not only two, but Rosen's remarks would
at least apply to the cellular automata ones.

You say that Rosen, in 1959, ought to have read p. 122-126 of "Theory of
Self-reproducing Automata" to see that von Neumann already discussed the
logical paradox. But as you well know "Theory of  Self-reproducing Automata"
was only published in 1966. That would have been quite a feat for Rosen!!
Rosen's reference for the 1959 paper was a 1951 paper by von Neumann "The
General and Logical Theory of Automata" in "Cellular Mechanisms in
Behavior". Was the text presented in the pages 122-126 in "Theory of
Self-reproducing Automata" available in 1959??

As far as I can see from your remarks: 1) von Neumann was aware of the same
logical paradox as Rosen, and that 2) von Neumann was also aware of the "big
interpretational problems" of computer simulations with regard to
construction.

So, if von Neumann was aware of these problems as being entirely legitimate
ones, then why do you feel that Rosen's legacy is damaged by bringing up
Rosen's account of those same issues??? It seems you read Rosen as
insinuating that he is bringing up issues that von Neumann missed or was
ignorant of. If you read Rosen that way, then I can see your complaint. But
I do not read Rosen that way - to bring up von Neumann's automata as an
example of where simulation can be confounded with construction is to me
hardly damning of the man, particularly when von Neumann would have agreed
there was an issue. It is good, though, to learn that von Neumann had these
same kinds of thoughts and concerns about his own theory.

Regards,
Tim




-----Original Message-----
From: ROSEN Forum [mailto:*** Behalf Of Howard
Pattee
Sent: Friday, April 02, 2004 10:58 AM
To: ***
Subject: Re: terminal von Neumann


Tim, I accept the list’s consensus that the von Neumann discussion should not continue since it is apparently causing so much grief. However, you said you would welcome seeing the von Neumann quotes that I promised, so here they are.

I emphasize that there is one and only one issue these quotes are
chosen to address. It is Bob’s statements (I apologize for using
“ accusation”) that von Neumann did not distinguish computation
from construction. I repeat here only one of Bob’s statements
from LI. (The others were not parenthetic.):

Rosen: “I remark parenthetically that the confounding of
simulation (computation) with construction, which lies at the
heart of, e.g., von Neumann’s well-known discussion of
‘self-reproducing automata,’ arises precisely here and rests
entirely on the equivocal and inconsistent hardware/software
distinctions to which I have just called attention.”

HP: The only issue I have ever meant to raise, is that von
Neumann’s extensive discussions show that this assertion has no
basis in fact, and I am sorry if my careless language implied
otherwise. All your other discussions are interesting, but are
not at issue since none of the other authors assert that the
problem is von Neumann’s “confounding.”

I have never found in Rosen’s papers or anywhere else any
specific evidence, such as direct quotations of von Neumann, or
even a reference to a specific page or section of his voluminous
writings, which suggests such confounding. My teachers and
colleagues in physics, some of whom knew von Neumann well, felt
that Rosen’s claim was unfair and unwarranted, and unfortunately
this has biased them against his important ideas.

There are also a few clarifications needed.

Tim: According to Burk, [Arthur Burks] there were two models of
"self-reproducing automata" proposed by von Neumann: the
kinematic automaton and the cellular automaton. I believe it is
in regard to the latter model, the one which was developed into
more detail (e.g., the 29-state machine) by von Neumann, that
Rosen is addressing his remarks.

HP: No. That is incorrect. Bob’s 1959 paper, written while still
a graduate student, was about the kinematic model (according to
Bob in video interview, 4/23/98, by Peter Cariani). The cellular
automaton model is the one (of actually five models) that von
Neumann wanted to “axiomatize” because he could not define
precisely enough the kinematic model. It is the cellular
automaton that has the big interpretational problems just because
a computer cannot actually construct anything. It can only
simulate construction. This is why von Neumann warned that
axiomatizing, “throws half the problem out the window, and it may
be the more important half.” But von Neumann always stated
clearly the need to distinguish between formal logic
(computation) and construction even in the axiomatized cellular automata.

Von Neumann (Theory of  Self-reproducing Automata, Pt. 2, Chap.
1, General Considerations, p. 91):
“The methods that will be used in this paper contribute, however,
only very partially to the effort that is needed in that
direction [the thermodynamics of construction], and at any rate,
we will limit ourselves at this occasion to the establishing of
certain existences (by suitable as hoc constructions) in the
sense outlined above.”

“1.1.2.1 The main questions: (A) – (E). Within the above
limitations, however, we will deal with problems that are rather
central – at least for the initial phases of the subject. We will
investigate
automata under two important, and connected, aspects: those of
logics and of construction. We can organize our considerations
under the headings of five main questions.

(A) Logical universality. When is a class of automata logically
universal, i.e., able to perform all those logical operations
that are at all performable with finite (but arbitrarily extensive) means?

(B) Constructability. Can an automaton be constructed, i.e.,
assembled and built from appropriately defined “raw materials” by
another automaton?

(C) Construction universality. Making the second question, (B),
more specific, can any one, suitably given, automaton be
construction universal, i.e., be able to construct in the sense
of question (B) (with suitable, but essentially standard
attachments) every other automaton?

HP: Von Neumann’s last two headings are (D) Self-reproduction and
(E) Evolution, which I will skip.  If you read this far and still
claim that "von Neumann confounded computation (simulation) with
construction" then I doubt going further will help. But I will
try, since he only gets more explicit about the differences
between formal logics (computation) and construction.

Von Neumann (ibid. pp. 99-101):
“1.2 The Role of Logics – Question (A)
1.2.1 The logical operations – neurons. In evaluating question
(A), one must obviously consider automata which possess organs
that can express the essential propositions of logics and which
need not possess any other organs. This can be done by using
organs each of which possess two stable states, corresponding to
the basic truth-values of true and false in logics. It is
convenient to use a plausible physiological analogy and to
designate these organs (whatever they are or are thought to be in
reality) as neurons, and the two states as excited and quiescent,
respectively.”

HP: Von Neumann goes on for two pages on logics that are
essentially what is needed for Turing-equivalent computations,
and then he takes up construction that he describes as an
entirely different type of activity:

Von Neumann (ibid. pp. 101-111):
“1.3 The Basic Problems of Construction – Question (B)
1.3.1.1 The immediate treatment, involving geometry, kinematics, etc.
The most immediate approach is this. The constituent organs are
the neurons and lines necessitated by (A), plus such additional
organs (B) will require. These constituent organs are to be
conceived of as physical objects in actual space. Their
acquisition and combination (including the establishment of rigid
connections between them) must accordingly take place in actual space.”

HP: Von Neumann goes on in more detail for about 10 pages that I
will skip (I am not taking anything out of context.) It’s all
about implementing construction as distinguished from logics and
computation. I have used only one von Neumann reference. There
are others; but as I said, if the above quotes are unconvincing,
more quotes won’t help.

I want to reemphasize that whether von Neumann’s automata
actually work or not is not the issue. Also as I said, Rosen’s
formally correct argument is not at issue. As a matter of fact,
von Neumann was well aware of the same basic argument that Rosen
used (a form of antinomy of the Richard type, i.e., the
self-reference paradox of sets that are members of themselves).
He discussed it at length (ibid. pp. 122-126.) and shows how it
might be avoided. I feel sure that if Bob had read it before 1959
he would have agreed and saved everyone a lot of grief.

I also feel it is ironic, and over the many years, contrary to
Bob’s interests, that he never refers to those ideas of von
Neumann’s that were not contrary to his own, specifically (1) the
basic epistemology of Hertz, (2) the inadequacy of physical laws
to explain life, (3) the irreducibility (unentailment) of
measurement (coding), and (4) the difficulties of modeling life
by any formal computation.

Howard



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