famous measurement of the electron
charge with the oil drop experiment.
Richard Feynman, who received the No-
bel Prize in 1965, was one of the most
popular of the teachers and scientists;
physics graduate students just adored
him. Sometime during my stay there,
James Watson of DNA fame showed up.
There was such intense research activ-
ity that you almost felt “I haven’t done
anything today. I should. Everybody
else is producing great results.”
I enjoyed my stay at CalTech very
much. California was a great place,
and life in Pasadena was exciting.
There was Hollywood, the beaches, the
mountains, the Rose Parade—life was
just beautiful. I enjoyed it even more
when I met Elly Rehwald, who is now
my wife; just recently we celebrated our
50th wedding anniversary.
Collaborating with Robert Dilworth
I do not recall exactly how I selected
or was selected to work with Professor Robert Dilworth, an algebraist who
worked in lattice theory. After I passed
my qualifying exams Dilworth suggested I work on the partition lattice embedding problem: showing that partition lattices contain any other lattice as
Well, I worked on it. It was interesting, but it was hard. I realize now that
the partition lattice embedding theorem was a first-class problem that after
decades had not been solved.
I struggled with it, and finally said,
“Let’s think around it. Let’s look at the
terrain around the problem.” I invented
generalized partitions, and realized they
behaved like lines in geometry. There is
at least some intuition about lines and
subspaces. I started developing techniques to solve the embedding problem
for generalized partition lattices.
I did not keep a log, so I do not know
exactly when I started working in this
problem and when I solved it. My recollection is that it was a very intensive
period of research. I gained real insights about the lattice of geometries
and solved the embedding problem. I
gave a seminar on my results that was
very well received. Dilworth urged me
to write up my results, and I was told
that I had my thesis.
This research experience taught
me a tremendous amount. First,
how to do research; that thinking
about the whole intellectual terrain
around problems is important. It is
like climbing mountains: there may
be different ways to the top than the
I also discovered, during my education and early research experience, that
you do not have to know that much to
do research. With a good background
education, one can very quickly absorb
the necessary specialized knowledge
for a specific research area. I think
what Caltech really taught me was to
be independent, and to try to go to the
essence of a problem.
Moving East, to Cornell
During my last year at Cal Tech, professor Bob Walker from Cornell visited.
After discussions with Dilworth and on
his recommendation, my friend Johnny Johnson and I were, on the spot,
given verbal offers to come to Cornell
as instructors of mathematics. In those
days, you did not start as an assistant
professor; you started as an instructor.
Without having seen Cornell, both of
us accepted the offers.
The Cornell campus is charming. We were immensely taken by the
beauty of the surrounding area and
the campus itself. In the math department we were very junior members
and started by teaching calculus. It
was a very friendly environment. We
easily made friends and really felt like
Next: General Electric
Dick Shuey, the General Electric Research Lab manager in nearby Schenectady, was a very far-sighted person who had convinced GE that they
should become a great computer company, and that a science base is needed for that. He traveled around finding
people to do research in “
information,” which we quickly translated as
me not really
knowing what I
wanted to do.”
computer science. He was immensely
impressed by Shannon’s work, and so
was I. Shuey visited me in the math department and convinced me to take a
The research traditions there are
old, and the laboratory has a string of
successes. The information section
was still quite small, and so any newcomer was very welcome. By the end
of the summer I published a paper on
linear coding networks in the IRE (later
IEEE) Transactions on Circuits. The experience was very encouraging—that
in such a short time I managed to produce a refereed paper that was accepted—and it opened up some new areas
for me to think about.
That period was almost ideal. The
computer science research people
were quite free; I never had any explicit
orders to work on particular problems.
Under Shuey’s guidance, one of the
very early papers I studied was Shannon and Weaver’s book on information theory, Mathematical Theory of
Communication. It impressed me immensely that from what seemed to me
vague concepts such as channel capacity and coding for error-correcting
codes, one could make a mathematical theory that guides you in how to
communicate and gives you quantitative measures of what is the best you
can do with a certain channel and with
a certain information source. Unfortunately, in my attempts to apply it
to computing there was no success. I
played with information theoretic concepts, and I wrote a paper about entropy, but that was exploratory work that
did not lead to very much.
Doing Corporate Research
Our job was just research, full-time,
with no teaching obligations. We read
whatever we could lay our hands on
that said something about computing.
At Caltech I had not been exposed
to concepts of computability, undecid-abilty, or Turing machines. At the lab
we read all those classic papers, and I
realized how absolutely beautiful those
ideas are. I had large photographs of
Shannon, Turing, and von Neumann
in my office; those were the people I admired and thought to be the pioneers
in computer science.
Dick Stearns and I started working
together during the summer and hit