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C00002 00002	For review of Heims's book
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For review of Heims's book

William Aspray, interested in von N and Wiener or was it von N and Turing
math dept williams

build one like ours

against big memories

no interest in Newell, Simon, Shaw

	Heims has no patience with the reasons people give for
their actions.  For example, as someone who would have finished
basic training at the time scheduled for the invasion of Japan,
I can imagine that President Truman had reasons apart from
rivalry with the Russians for approving use of atomic bombs.
Perhaps he thought that relatives of soldiers who died

More questions for Armer:

When was von Neumann letter against purchase of large memory?

plane geometry was a lovely subject, and the new math people were
wrong to kill it.

	In an undoubtedly apocryphal story, von Neumann is told
that two trains start 100 miles apart moving towards one another
at 40 and 60 miles per hour respectively.  A bee flying 80 miles
an hour starts at the same time from one end, flies till it meets
a train reverses its course, meets the other train, reverses again,
etc. until it is crushed in the collision of the trains.  How far
did the bee fly?  After 30 seconds, von Neumann gives the
correct answer - 80 miles.  On being told that some physicist
also took 30 seconds, he indignantly
replies, "Don't be silly.  No physicist can sum a series that fast."

	Heims's discussion of Wiener's and von Neumann's postwar
work on in the relation of computers and brains misses the fact
that subsequent developments followed a different path than either
envisaged.  Wiener emphasized feedback and non-linear but continuous
phenomena, and von Neumann emphasized the architecture of large
reliable systems and the problem of self-reproduction.  The direction
that has led to fruitful results in artificial intelligence and
cognitive science was pointed out in 1950 by the British logician
Alan Turing.  It is the programming of digital computers to carry
out intellectual processes on the psychological level.  Like almost
everyone interested in artificial intelligence until the middle
fifties, von Neumann thought in terms of new kinds of machines
rather than programming digital computers.  Had it been otherwise,
his enormous ability and familiarity with mathematical logic might
have enabled him to solve easily problems that are still giving
trouble twenty five years later.

	After World War II, Wiener and von Neumann put much
study into the relation between computing and the brain.  Wiener
emphasized the non-linear servo-mechanism theory to which he
had already made mathematical contributions, and von Neumann
wanted to develop a general logical theory of automata.  Unfortunately,
only fragments of the theory of the theory were developed and
these concerned peripheral issues.  While von Neumann was instrumental
in promoting and designing the first American stored program
digital computers, he seemed to think of them primarily for numerical
computations in physics and business.  His approach to the brain,
like that of almost all scientists interested in the brain was
through machines acting like nerve nets.  He showed how reliable
computation could be carried out by machines made of very unreliable
parts, and showed that there were no difficulties in principal to
making machines that could reproduce themselves.  Unfortunately,
both of these questions have so far been of peripheral importance.

	Among scientists active before the middle fifies, only Alan Turing,
the British logician and computer scientist responsible for
the mathematical concept of computability in the 1930s and
wartime machines for breaking German ciphers took the view
that has dominated artificial intelligence research since the
middle 1950s.  In 1950 Turing proposed that the problem wasn't
to build special machines but to program digital computers to
carry out intellectual functions.

	Von Neumann also missed the applicability of his other
specialty of mathematical logic to representing facts about the
world within a machine.

	Heims's portrait of Wiener and von Neumann as people is
unfortunately marred by political bias.  Wiener is accepted as
a good guy because he announced his refusal to work on military
problems after World War II, and von Neumann taken as a bad guy
because he worked on nuclear weapons.  A mixture of psychology
and Marxoid 
Kline

summary
	Each of these books tells some history of mathematics and
mathematicians to support a general thesis.  The history is interesting
mostly accurate, but I don't believe the theses.

	Professor Kline's history of mathematics centers around
the thesis that mathematics has suffered repeated disasters, shocks
and xxx and lacks the certainty that it was once reputed to have.

	When one begins the study of mathematics, one is interested
in learning from others how to solve problems.  Some people, after getting good
at this, then develop an interest in rigorous reasoning.  They want to
develop methods of solving harder problems, and they want to be able to prove
that their new methods are correct.  Eventually they become aware that
what their understanding
of what they took for granted about the elementary parts of mathematics
does not have the rigor that they later learned to appreciate.  Some of
them even become interested in the "foundations of mathematics".
Forgetting their own attitude as beginners, they often become pedantic
pests and suppose that beginners want to have everything proved from
whatever the new rigorist has come to believe are first principles.

	As it was with the individual, so it was with the development of
mathematics itself.  The Babylonians and Egyptians were only interested
in methods of solving problems, and it was left to the Greeks to develop
the rigorous methods of Euclidean plane geometry.  While the higher level
parts of Greek geometry became rigorous, at the bottom vagueness remained.
A point was "defined" as that which has no parts, and the need for having
postulates about when one point on a line is between two others was not
noticed until the late nineteenth century.
Minsky:

1. von N. told Tucker that Minsky's thesis topic would eventually
lead to good mathematics.

2. generally encouraging but not interested in neural nets

3. Wiener was so insecure as to be hard to talk to.

Hurd:

1. look at computers and the brain

2. von N. did not express himself about memory size, was for symbolic
assembly programs, consulted on combining symbolic and numerical
computation.


Simon:

1. contact on economics

2. self-generating complexity, hixon

3. warning against brain analogy

4. computers weren't brains

5. chess playing computers, negative to Shannon idea
Simon motivated by counter-reaction

6. started work in 36

7. mcculloch pitts, grey walter, ashy, rashevsky,

8. selfridge and dineen

Samuel:

1. no opinion of checker efforts

2. mainly numerical computation

3. 1024 words was enough

4. Wiener liked to lecture on Samuel's program, wrong and exalted ideas

5. McCulloch did write some programs but too early to run them