TITLE: This and That from Douglas Hofstadter's Visit
AUTHOR: Eugene Wallingford
DATE: March 09, 2012 3:33 PM
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Update: In the original, I conflated two quotes in *

"Food and Hygiene". I have un-conflated them.

In addition to
his lecture on Gödel's incompleteness theorem,
Douglas Hofstadter spent a second day on campus, leading
a seminar and giving another public talk. I'll blog on
those soon. In the meantime, here are a few random
stories I heard and impressions I formed over the two
days.
**The Value of Good Names**. Hofstadter told
a story about his "favorite chapter on Galois theory"
(don't we all have one?), from a classic book that all
the mathematicians in the room recognized. The only
thing Hofstadter didn't like about this chapter was that
it referred to theorems by number, and he could never
remember which theorem was which. That made an otherwise
good text harder to follow than it needed to be.
In contrast, he said, was a book by Galyan that gave each
theorem a name, a short phrase evocative of what the
theorem *meant*. So much better for reader! So he
gave his students one semester an exercise to make his
favorite chapter better: they were to give each of the
numbered theorems in the chapter an evocative name.
This story made me think of my favorite AI textbook,
Patrick Henry Winston's
*Artificial Intelligence*. Winston's book
stands out from the other AI books as quirky. He uses
his own vocabulary and teaches topics very much in the
MIT AI fashion. But he also gives evocative names to
many of the big ideas he wants us to learn, among them
the representation principle, the principle of least
commitment, the diversity principle, and the eponymous
"Winston's principle of parallel evolution". My
favorite of all is the convergent intelligence principle:
*
The world manifests constraints and regularities. If
a computer is to exhibit intelligence, it must exploit
those constraints and regularities, no matter of what
the computer happens to be made.
*

To me, that is AI.
**Food and Hygiene**. The propensity of
mathematicians to make their work harder for other
people to understand, even other mathematicians,
reminded
Doug Shaw
of two passages, from famed mathematicians
Gian-Carlo Rota
and
André Weil.
Rota said that we must *guard ... against confusing
the presentation of mathematics with the content of
mathematics*. More colorfully, Weil cautioned
*[If] logic is the hygiene of the mathematician, it
is not his source of food*. Theorems, proofs, and
Greek symbols are mathematical hygiene. Pictures,
problems, and understanding are food.
**A Good Gig, If You Can Get It**. Hofstadter
holds a university-level appointment at Indiana, and his
research on human thought and the fluidity of concepts
is wide enough to include everything under the sun.
Last semester, he taught a course on *The Catcher in
the Rye*. He and his students read the book aloud
and discussed what makes it great. Very cool.
**If You Need a Research Project**... At
some time in the past, Hofstadter read, in a book or
article about translating natural language into formal
logic, that 'but' is simply a trivial alternative to
'and' and so can be represented as such. "Nonsense",
he said! 'but' embodies all the complexity of human
thought. "If we could write a program that could use
'but' correctly, we would have accomplished something
impressive."
**Dissatisfied**. Hofstadter uses that word
a lot in conversation, or words like it, such as
'unsatisfying'. He does not express the sentiment in
a whiny way. He says it in a curious way. His tone
always indicates a desire to understand something better,
to go deeper to the core of the question. That's a sign
of a good researcher and a deep thinker.
~~~~
Let's just say that this was a great treat. Thanks to
Dr. Hofstadter
for sharing so much time with us here.
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