-----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