Turing's Analysis of Computation
Last Update: Wednesday, 3 July 2024 |
Note 1: Many of these items are online; links are given where they are known. Other items may also be online; an internet search should help you find them.
Note 2: In general, works are listed in chronological order. (This makes it easier to follow the historical development of ideas.)
§8.1: Introduction:
§8.7.2: "Writing Symbols on Paper":
§8.8.1: "Man" and "Machine":
§8.13: "The Universal Computing Machine":
the author writes:
'Aware', of course, is an anthropomorphic term (though one that might be
used with Large Language Models such as ChatGPT). But even if we use it in
a more neutral sense, we might say that a Turing Machine is not "aware" of
its own program, but a Universal Turing Machine
— although not "aware" of its own fetch-execute
program
—
is "aware" of the program that it is fetching and executing.
§8.14: Further Information on Turing:
See also:
is a fascinating version of Turing 1936 aimed at a(n intelligent) general
audience. In this article, he shows that many, if not most, puzzles can
be put into a "kind of 'normal form' or 'standard form'" (p. 587)
called a "substitution type of puzzle" (p. 588),
which turns out to be essentially the notion of a formal system or a
Turing Machine. He states a kind of "Turing's Thesis" for such puzzles, noting
that such a …
In this article, he also proves a version of the Halting Problem, in the
sense that he proves "that there cannot be any systematic procedure
for determining whether a puzzle be solvable or not" (p. 590).
Several websites offer background and critiques of the film:
There are several
Turing Machine simulators and implementations, some quite curious:
For more information on the business-card Turing Machines, see:
"A 1923 play called The Adding Machine lampooned the monotony of
assembly-line office work and prefigured fears about machine automation.
Its main character, 'Mr. Zero,' writes down numbers all day long, 'upon
a square sheet of ruled paper.'"
(Lepore, J. (2018). These Truths: A History of the United States. W.W.
Norton, New York, p. 404.)
"… it is surely obvious that every theory is only a scaffolding or
schema of concepts together with their necessary relations to one another,
and that the basic elements can be thought of in any way one likes. If in
speaking of my points, I think of some system of things, e.g., the system:
love, law, chimney-sweep … and then assume all my axioms as
relations between these things, then my propositions, e.g., Pythagoras'
theorem, are also valid for these things … [A]ny theory can always
be applied to infinitely many systems of basic elements."
Hill, I.D. (1972),
"Wouldn't It Be Nice If We Could Write Computer
Programs in Ordinary English
—
Or Would it?", The Computer Bulletin (London: British Computer
Society), 16(6) (June): 306–312
At least when a computer follows a ludicrous program, it is not itelf (so
far as we know) aware of what it is doing. (p. 310, col. 1)
"… statement is moreover one which one does not attempt to
prove. Propaganda is more appropriate to it than proof, for its status is
something
between a theorem and a definition. In so far as we know a priori what is a
puzzle and what is not, the statement is a theorem. In so far as we do not
know what puzzles are, the statement is a definition which tells us something
about what they are." (p. 588).
Stern, H. and Daston, L. (1984). Turing & the system. New
York Review of Books, pages 52–53, with a reply by Toulmin.
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William J. Rapaport
(rapaport@buffalo.edu)
http://www.cse.buffalo.edu/~rapaport/OR/A0fr08.html-20240703