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Harry:

	I had "Inversion of functions defined by Turing machines" typed
into the computer.  As you will recall, I intend to provide each of
the papers with a commentary giving my present point of view on its
subject matter.  Here is a draft of the commentary for Inversion.
Have you, as editor, comments on the commentary?

				John

turing.com[f82,jmc]	Commentary on "The inversion ..."

1982 Commentary:

	This paper was written in the summer of 1952 and elaborated
somewhat before it was published in 1956.  It was written to clarify
the meaning of "problem" and to discuss problem solving methods that
work directly from the definition of problem.  A problem was
was called well-defined if a procedure was given for testing a
proposed solution, and the problem solving methods worked backwards
from this test.
Thus no auxiliary facts of general common sense knowledge or of
the specific domain are used.

	Even at the time the idea didn't seem promising.  I cannot
reconstruct my state of mind at the time, but I spent most of my
time thinking about methods that involved knowledge of facts, and
the ideas that were first published with my 1958 paper "Programs
with Common Sense".  However, I was unable to make these ideas sufficiently
definite in the summer of 1952, so I decided to explore this more
limited domain.

	There is nothing about computers
in the "Inversion ... " paper.  This is because I, in common at least
with Minsky and Shannon with whom I discussed the ideas,, thought about
artificial intelligence in terms of machines, not programmable computers,
about which we knew little.  Even von Neumann, who did know about
programmable computers, seemed to think about thinking machines
exclusively as objects analogous to the human brain.  To my knowledge,
only Turing then considered programming computers as the technique
for realizing artificial intelligence.  Newell and Simon were next
in 1954, and I switched my attention to computers in 1955, during a
summer spent working for IBM in Poughkeepsie, New York.

	Perhaps some part of the idea could be rehabilitated, but
it would seem appropriate to use Lisp functions or logic programs
as the way to represent the function to be inverted.  The paper
does not discuss different representations of the same function
nor does it discuss the natural restriction (as long as one hand
is to be tied behind the back) of using the function to be inverted
only extensionally, i.e. by computing values, although some of the
methods observe this restriction.