Re: terminal von Neumann

[Howard Pattee <***>]

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