[alicebot-aiethics] book review

Thu, 18 Oct 2001 17:22:31 -0700

MATHEMATICIANS WHO FORGET THE MISTAKES OF HISTORY

&copy; 2001 Dr. Richard S. Wallace
a review of
ENGINES OF LOGIC
by Martin Davis
Norton, 2001 (Paperback, 257 pages)

Martin Davis,
one of the greatest living mathematicians and computer scientists,
and one of the few academics supportive of my disability claim against
NYU,
has written a remarkable book.  Taking a page from Turing's biographer,
Andrew Hodges, another professional mathematician, Davis plunges into
the most nonmathematical of subjects: history.
When I last saw Martin Davis at NYU in 1995,
he told me was working on a book about the history of logic.
Around the same time,
I attended a talk Davis gave at the New York Academy of Sciences.
The subject was "Leibniz' Dream", also the title of this book's first
chapter.
The book ENGINES OF LOGIC, originally
published in hardcover under the title THE UNIVERSAL MACHINE,
is the culmination of those efforts.

Only one degree of separation takes us from Martin Davis to the
generation
of Einstein, Goedel, Turing, Mauchly, Eckert, Atanasoff, von Neumann,
Church,
Post and Ulam, many of whom the author met or knew personally.
Martin Davis is both living history
as well as writing it.  He is the link between that generation and those
of
us working today on logic, artificial intelligence and "thinking
machines."

If you want to know why predicates are called "predicates" in AIML,
and not "properties" or "variables", read this book.
The story begins with Leibniz, who, along with Newton, invented the
calculus.
Gottfried Willhelm Leibniz also had a dream, as Davis puts it,
"He dreamt of an encyclopedic compilation,
of a universal artificial mathematical
language in which each facet of knowledge could be expressed,
of calculational rules which would reveal all the
logical interrelationships among these propositions.
Finally, he dreamed of machines capable of carrying out calculations,
freeing the mind for creative thought".  This was around 1680 in
Germany.

ENGINES OF LOGIC is one of those few books to have affected me
profoundly.
Readers of the AIML mailing lists know that I often rail against
computer scientists reinventing mathematical wheels.
"Object oriented programming (OOP)" provides a good example.
What does an OOP system contain that was not already modeled a
century ago as sets of objects and maps between them?
At some level "OOP" is just marketing hype, window dressing for
concepts well known long before computer programmers appeared on the
scene.
Lisp, on the other hand, or Prolog or SETL, are more grounded
in the mathematical tradition that forms the topic of Davis' book.

Even more significantly,
Davis unveils the personal lives of the great logicians.
This is the kind of book that makes me wish I had read
these stories years ago,
because they would have helped me understand my own life
and emotional problems.
The contrast between the presentation of mathematicians
and their work in mathematics classes,
and the reality of their lives in some cases, is striking.

MEN OF MATHEMATICS

Reading through Davis book, you would almost have the impression that
mental health problems were the rule rather than the exception
among mathematical geniuses.
Of the seven scientists named in chapter titles
[Leibiz, Boole, Frege, Cantor, Hilbert, Goedel, Turing],
only two, Leibniz and Boole,
escape the experience of "madness" in themselves or their immediate
family.
Even in the case of Leibiz we can not be so sure.
Davis says, "we have little idea what he was like as a person."
His misfortune with the Dukes of Hanover and his dispute with Newton
over the
invention of the Calculus, remain part the mythology of Leibniz' life.

Leibniz faced a particular form of torment all to familiar to
frustrated scientists today.
The Duke of Hanover, his employer, felt it would be preferable
for Leibniz to work on the
Duke's family geneology, rather than waste his time on unprofitable
pursuits
such as logic, philosophy and mathematics.  Leibniz must have bristled
knowing
that his rival, Newton, had secured an academic appointment at
Cambridge.

Boole's contribution to computer science is so significant that his name

now usually appears in lower case, as in "a boolean expression".
Davis tells the incredible story of this hardscrabble English
schoolmaster who transformed logic into algebra.
Formal logic began with Aristotle, but little progress was made
until the 19th century.  Boole systematized Artistotelian Logic,
putting it on the same footing as algebra
and calculus by applying mathematical symbols.

I first heard the story of Frege and Bertrand Russell when I was
an undergraduate studying logic in the philosophy department.
Frege's life work was a magnum opus called
"Begriffsschrift", an attempt to reduce mathematics to
precise statements in symbolic logic.  The first volume was published,
and the second was at the printer, when Frege, a German,
received a letter from the English mathematician Bertrand Russell.
In one page, Russell had demolished the entire foundation of Frege's
entire Begriffsschrift.  Although Frege was thoroughly discouraged
by what is known today as "Russell's Paradox",
his work remains significant for the introduction of logic
symbols still in use today.

Frege is not described as clinically depressed, but he did cease
work on logic altogether after Russell's letter, and died a bitter man.
In order to practise his profession as a scientist,
Gottlob Frege accepted a nonpaying appointment as a
lecturer at the University of Jena.
Davis says, "Because his colleagues didn't really value his work,
he was never appointed to a full professorship."

On top of all that, Frege was a notorious anitsemite. Although one
could perhaps dismiss his antisemitism to the general political
atmosphere of the times, such outrageous political views would surely
be seen as a "sickness" today, perhaps especially so if they were
held by a university professor.

Davis' discussion of Cantor's psychological problems brought me
back to my student days,
struggling to learn an advanced mathematical concept known as a "Cantor
Set."
The style of both the instructor and the textbook was a kind of
mental perfection, as if understanding the Cantor Set required
a superhuman cognitive ability, an ultimate state of rationality
that would seem the opposite of irrational, mental illness.
It seems odd now that neither the book nor the instructor
mentioned that Cantor struggled with deep emotional pain
while discovering his Set.

Davis writes, "Cantor suffered the first in a series of nervous
breakdowns in 1884, an intense depression that lasted about two months."

Cantor suffered from manic-depressive illness, about which Davis says,
"it is now generally understood that the disorder's
fundamental cause is rooted in defective brain chemistry."

Hilbert is one of the titans of mathematical history.
Years ago I had a historical book called "Men of Mathematics".
Perhaps it is well that I cannot recall the author's name, because
we can not be sure that today he would choose such a gender specific
title.
Hilbert leapt from history with a sort of mathematical workaholism.
His famous "Ten Unsolved Problems"
became the basis for a century of mathematical research that followed.

Hilbert himself was not afflicted with any mental illness,
but his son certainly was.  Martin Davis writes,
"Franz (Hilbert) was a badly disturbed young man, and it
finally became necessary to institutionalize him.
The father's reaction to this tragedy was that he no longer had a son;
the mother felt otherwise."  Does the image of Hilbert as an abandoning
parent reduce the size of his towering figure in mathematics?

ENGINES OF LOGIC includes a number of black and white photographs,
but the most memorable is one of Kurt Goedel and Albert Einstein.
The two were close friends at Princeton.
This is the Goedel of Hofstadter's Goedel, Escher, Bach
who, as Davis says,
"upset the applecart."
The applecart was one of Hilbert's unsolved problems, which now would
never be solved.
Goedel's Incompleteness Theorem, along with the Church-Turing thesis,
set the limits of what can be accomplished with mathematics and
computers
alone.
There will always be true statements which cannot be proved,
computer programs we can't tell will terminate.

Remarks similar to those about Cantor and his Set, apply to Goedel
and his Theorem as well.
Only the select few students who make it all the way to the
most advanced classes will study.
One pictures something like the Olympics,
in which a series of qualifying rounds
eliminates all but the greatest mental athletes.
Goedel's theorem is taught as another work of cognitive perfection.
His struggle his hidden from view.
Surely no one with a "defective" brain could find his way to the
Advanced Symbolic Logic course!

Goedel spent much time in sanatoria, recovering from depression.
Davis writes, "The boundary between Goedel's unorthodox view and
outright
clinical paranoia was not always clearcut.
Morgenstern records his surprise that Goedel took ghosts quite
seriously.
More important, Goedel was convinced that
the refrigerator and radiators in his various apartments in Princeton,
were giving off noxious gases."  Sadly,
"In a paranoid state over the safety of food available
to him...he literally starved himself to death" in 1978.

During my years as an academic scholar, many hours were spent studying
the
theoretical foundations of computer science using an abstract device
known as a "Turing Machine".  In another class, the "Turing Test" was an

important subject in artificial intelligence.  Not to mention, Turing
was
undeniably the father of modern cryptography and codebreaking.
Only in hushed tones was it whispered that Turing had met a tragic fate
owing to his homosexuality, but this was the 1980's,
and gay was becoming mainstream. Today Turing would not be considered
mentally ill for being gay, but his suicide indicates depression.

The subtext, if any, was that
"this could never happen now.  We are far too enlightened
to permit this kind of discrimination today."
Of Turing's fate, Davis writes
"Sex in England had become dangerous, perhaps too dangerous to
attempt...
After his conviction, he lost his security clearance...
Alan Turing was hounded to death by the governing authorities of
a nation he had---unsung---done much to save."
It is the year 2001.  I am reading these words on a train crossing the
English countryside, to catch the Hydrofoil to Holland,
where my vice, marijuana smoking, is not too dangerous, as it remains
in England.  I am wearing a medal, the Loebner Prize,
that bears the likeness of Alan M. Turing.

Davis also mentions the Dutch mathematician L.E.J. Brouwer, who
propounded
somewhat unorthodox views, largely discredited, on the foundations of
logic.
"Although Brouwer never recanted his views, " Davis writes,
"he felt more and more isolated,
and spent his last years under the spell of totally unfounded financial
worries and a paranoid fear of bankruptcy, persecution, and illness."

CONDEMNED TO REPEAT THEM

Academics who have reviewed my disability case against NYU have said,
even though they used terms like "psycho" and "lunatic" to describe my
condition, "we didn't know you were sick."
Or in another variant, even though they documented much irrational
conduct and poor judgment, they didn't know the "severity" of my
illness.
Apart from the obvious objection that not knowing
the law doesn't let them off the hook for violating the law, Davis'
book makes an even more substantial ethical point:
They should have known better.
Don't these mathematicians know their own history?

This reviewer is not claiming to be a Leibniz, a Cantor, a Goedel,
or even a Martin Davis.
I have certainly never saved the world from the Nazis as Turing did.
But I have experienced discrimination in an academic, scientific
research
setting because of my own mental illness.
Many advanced logic and math classes in my academic training included
deep discussions of Cantor's Set, Goedel's Incompleteness Theorem,
and Turing's Machines.
But seldom, if at all, were their personal lives discussed.
Thanks to Martin Davis' book, the gap between their lives and their work
has
been more completely filled.

Once at NYU I met the incoming director of the Courant Institute
of Mathematical Sciences.
I asked him if he knew that Richard Courant, for whom the Institute is
named,
had fought on the side of the Germans in World War I.
The new director did know, and indeed seemed most surprised.
This apparent historical paradox is easily
explained by the fact that many loyal German Jews,
who had served and even been decorated
in the Kaiser's army, were among those who were driven from or
murdered in Germany during the later Nazi regime.
The point of the story is that it makes you wonder,
how many mathematicians know their own history?
I mean, the guy was heading up the Courant Institute!

One can find few faults in ENGINES OF LOGIC.  When the mathematician
approaches the subject of history, however, the results can be somewhat
curious.  Writing about the origins of the first world war, Davis
begins,
"In the summer of 1914, in response to the assassination of Archduke
Ferdinand. and with German encouragement, the Austrains began World
War I by attacking Serbia.  To stress their determination that Austria
not be permitted to destroy their fellow Slavs, Russia began
mobilization."
And so on.  He states the bare facts of August 1914, but one wonders
about the intended audience.  Surely not historians interested in the
history of mathematics, but if it is mathematicians interested in
history,
one has to question why they would be ignorant of such basic facts.

The cause World War I has often been said to be "miscalculation." It
would be interesting to read a mathematician's interpretation of that
"calculation" which went so terribly wrong.  The few other times Davis
delves into political or world history, the words add little to the
story
and if anything only highlight the ontological gap between mathematical
and historical knowledge.

Besides those digressions into nonmathematical history,
I objected only to two adjectives in Martin Davis' remarkable book.
The first was his use "defective" to describe the
"defective brain chemistry" at the root of manic depression.
The label "defective" is a heavy burden for a mental health patient
to bear.  The simple logic most people follow says
"defective brain = defective mind = defective person."
No amount of drugs or therapy can treat that.
The sentence would have worked just as well without the adjective.

The second offensive adjective was his description of the Courant
Institute
building in New York as "handsome".  That building looks like a Hilton
Hotel
and has about as much charm as a suburban cinderblock high school.
When I worked at the Courant Institute, I always preferred the older
building at 715 Broadway, where
some of the computer science department was housed.  That stone edificed
19th
century monument was vastly more "handsome" than the Courant building.

THE BEST OF ALL POSSIBLE WORLDS

Davis' Epilogue reminds me of the IT worker who said,
"If it weren't for Turing, I'd either be unemployed,
or working for the Nazis."

History has a way of crucifying its most creative children, but at the
same
time history has a way of settling scores.  Those who forget the
mistakes of
history do indeed repeat them.  Yet "mad scientist" is a meme in our
society
for a reason.  Scientists today have no justification for being
surprised
that members of their profession suffer from the same mental health
problems
which afflicted scientists in the past.

Scientific progress does not proceed along the same neat, linear paths
as it is presented in textbooks.  Scientific revolutions are known to
be painful for the revolutionaries.  Mathematics and computer science
texts are written in a style that makes the evolution of knowledge seem
quite orderly, proceeding neatly from proposition, to lemma and theorem.

Martin Davis' reveals a far less tidy picture of the mental life of
mathematical revolutionaries.  More of his colleagues could do worse
than
to study this oral history of their profession, and then to recite it
to the younger generation of students, alongside the axioms and theorems

of mathematics.

Davis writes: "The Dukes of Hanover thought they knew what Leibniz
should be
doing with his time: working on their family history.
Too often today, those who provide scientists with the resources
for their lives and work try to steer them in directions
most likely to provide quick results.
This is not only futile in the short run, bot more importantly,
by discouraging investigations with no obvious immediate payoff,
it shortchanges the future."

They should have known better.