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