FOM: General Intellectual Interest

[Harvey Friedman]

Friedman:

But I am confident that you will join me and many others on the FOM list in
enthusiastically celebrating this recognition of Turing and Godel!!

Hayes:

I dont think it is really a cause for celebration

Friedman:

I am not surprised that you said this in light of your earlier statement
that "Maybe the question to ask is, how many mathematicians work for TIME,
Inc.?"

Hayes:

I fail to follow your point here. You seem to attribute significance to my
having said 'mathematicians' instead of 'logicians'. Whatever the
importance this distinction has for you, it doesnt have much for me (in
this context, anyway.)

Friedman:

Here was my point. You seemed to me to be saying that no mathematicians
work for TIME, and so consequently no mathematicians got mentioned. I was
saying that also no logicians work for TIME, and one or two or three
logicians were mentioned.

The approach to intellectual life represented by mainstream mathematicians
of the century is on the whole quite different than that of foundational
logician(s) such as the one(s) mentioned.

Hayes:

Sorry if I was too elliptical. I meant only to suggest that one shouldnt
take a survey conducted by a magazine such as TIME as being in any way
authoritative in any matter requiring intellectual insight or specialized
technical knowledge of almost any topic, except perhaps Washington
politics. Sorry if this sounds snobbish. My cynicism is however based on my
own experience.

Hayes:

Again, I fail to comprehend what you are insinuating about my state of
mind, or indeed how you manage to apparently know more about it than I do.

Friedman:

What you wrote in the paragraph beginning with "sorry" is something that
probably absolutely everybody, especially TIME magazine, agrees with. But
your other responses about not wanting to celebrate, and about
mathematicians versus logicians in this context, and the pragmatic cynicism
you express (which you have every right to express!), has far from any
consensus. Hence the contrast I drew between what you wrote above with what
you wrote later. I am not criticizing your writing. I'm just trying to draw
out a substantial disagreement that was going to be lost to the world.

Hayes:

because I dont think it
really is recognition in the sense that would be worth celebrating.

Friedman:

It is certainly worth celebrating since it is TIME magazine - which has
such an enormous readership. Your speculations as to how Turing and Godel
got on the list are not only just speculation, but also self defeating. Do
you want your speculations to be true?

Hayes:

Whether or not I want them to be true has no bearing on whether they are in
fact true.

Friedman:

People making cynical speculations often either want them to be true; or,
often having made them, then want them to be true. Perhaps you are
different.

Hayes:

I think it kind of inevitable that the reasons why academicians
become sufficiently widely known in the general culture to appear in TIME
magazine have only a very peripheral connection with their actual
intellectual achievements.

Friedman:

There is a significant positive correlation between having done something
great of great g.i.i. and getting widely known in the general culture. The
imposters will eventually get weeded out. The great will generally remain.
It could be very much otherwise, in which case even Godel would disappear
into anonymity by 2200 or earlier. But occasional appearances in huge
forums makes this much less likely.

Hayes:

Do you think that the West End success of a play
about Alan Turing leads directly from his mathematical work, or requires a
widespread comprehension of it? If so, I think you are living in a
mathematical logician's paradise.

Friedman:

The fact that there is a West End success of a play about Alan Turing at
all is something more to celebrate (I saw the play, and was deeply moved).
I just opened another bottle since you reminded me of this play! I hope you
did too.

By the way, I know I am already living in a mathematical logician's
paradise since I believe we are in the beginnings of the reemergence of
foundational studies as the leading general intellectual force of our time.
This force will revolutionize the way education and research is done
throughout the intellectual landscape.

Hayes:

I think
that Turing is there largely because he is now a national hero in England,

Friedman:

TIME magazine is published by Time/Warner, a large U.S. Corporation.

Hayes:

I know, but old Blightly still has a cultural influence way beyond what it
deserves from its mere size, and Turing has been a household name there for
about a decade, but for exactly the wrong reasons. There has been a
successful play, a best-selling biography and a TV series about him.

Friedman:

But why was there a successful play, a best-selling biography and a TV
series about him? It is certainly probabilistically connected with his
achievments. Isn't it wonderful that this happens to a genuine intellectual
force?

Hayes:

(I'm
not trashing these things, by the way, all of which are excellent of their
kind. But they hardly mention his mathematical work. It's impossible to
explain the notion of a Turing machine to a general TV audience.

Friedman:

Yes you can at some level of detail. And that level of detail - which is
awfully restrained - is precious. It gets filtered down to kids in school
that maybe there is a different kind of role model to at least be conscious
of. I take what I can get - and celebrate it.

Hayes:

My point
is only that Turing's fame doesn't arise simply from his mathematics.

Friedman:

Gee whiz, what a revelation!! But so what?? Take what you can get. Don't
look a gift horse in the mouth. Etc.

Hayes:

>People don't first comprehend his ideas and then put him on a pedestal
>because of them (contrast, say, Newton.)

Friedman:

Newton has been around for so long, and gotten so much filtering down into
the schools, that he is now really somebody. Same will happen to Turing and
Godel in varying degrees, partly because of things like TIME magazine and
plays over a long period of time. E.g., the Turing machine will be
presented in some very watered down form with imaginative exercises for the
pre high schoolers. Just like we have watered down physics going back to
the Greeks.

Hayes:

He is revered as a pioneer of
computers (in England, yet another in the list of names known to every
schoolboy of Great English Pioneers: John Logie Baird, the Scottish
inventor of Television; Frank Whittle, the English inventor of the jet
engine, Roger Bannister, the English first man to run the mile in under 4
minutes, and so on) and as a tortured genius who was persecuted to suicide
because of his homosexuality, and now has become a kind of emblem for a
national feeling of guilt (or maybe relief) about how hidebound and
narrow-minded England used to be (if Turing had lived to a ripe old age, I
bet he wouldnt be in that list) and of course because of the WW2 work, with
its wonderful plot lines of spying and secrecy and of having, apparently,
been a decisive factor in the Allied victory in the last "good war". None
of this is very controversial: Im just parroting much longer and more
detailed analyses of this stuff by others. It is naive to think that Turing
is in the list because of his contributions to mathematics.)

Friedman:

But let me repeat. He's on a probably permanent list, which will make
people take notice when people like you and I write about his foundational
achievments in a gripping way. Much more notice will be taken by what we
write than if he was not on a permanent list.

Friedman:

But so
what? Don't you want to celebrate that someone like Turing is a national
hero in England - who doesn't play sports, act in the movies, or guess
stocks?

Hayes:

largely as a result of the romantic image produced by his secret WW2
codebreaking work and the tragic outcome of his persecution as a
homosexual.

Friedman:

The codebreaking is reasonably thought of as intellectual achievment (which
it certainly partly is), and this is obviously something I would rather see
people celebrate than the usual things people celebrate people for.

Friedman:

There are many many people with analogous nonintellectual achievments
(although the codebreaking work is partly intellectual) who didn't make the
list. Now isn't that interesting and remarkable? Why Turing and not the
others? Join me in celebration.

Hayes:

If you feel like celebrating, go ahead. I dont want to be a party-pooper.
However I have to comment on the following:
>....

Hayes:

Several best-selling recent books put Gödel into center stage in order to
'prove' that AI is impossible, for example.

Friedman:

I celebrate that they are best selling. This increases the exposure to
Godel, and hence one can now write further books disucssing Godel in new
ways - perhaps drawing competing conclusions - and get a bigger audience
than otherwise. Don't you want to celebrate this?

Hayes:

Most emphatically not. Many readers of these books, including most
*educated* readers of them, are so impressed by their veneer of
mathematical sophistication and the undoubted authority of their author
(Sir Roger Penrose, the eminent physicist), and so ill-equipped to
critically analyse the arguments made in them, that they fail to notice the
fact that they misuse and distort Godel's results to draw philosophical
conclusions which are totally unwarranted and often explicitly fallacious.

Friedman:

But this is much better than nothing. Because as I have said in other
postings, a lot more attention will be paid when you and I write great
g.i.i. accounts of what Turing and Godel did, with OUR spin on them. We can
even get more people interested by calling certain people fools with funny
cartoons on the cover!!

Hayes:

And most readers aren't interested in Godel's undecideability theorem, but
in what are widely seen to be its consequences for wholly non-mathematical
topics (such as whether human thinking is computation [no], whether or not
all truth is culturally relative [yes], etc. etc.)

I note, by the way, that the TIME article never mentions Godel's
*completeness* theorem, which seems to me to be at least as important as
the much more famous undecideability theorems.

Friedman:

Ah! Just think of the audience for a book titled: "What TIME magazine
didn't tell you."

Hayes:

I think that 99% of the
educated adult population don't have even a glimmering of comprehension of
what Godel's theorems actually mean, and they probably think that Turing
machines were sold by IBM in 1950.

Friedman:

Not after we get through with them. Now that they have really heard of
Turing and Godel, they will look at what we write.

Friedman:

More people are more likely to understand more about Godel's work because
of this exposure; and also Turing. Don't you want to celebrate this?

Hayes:

If it were true I might celebrate, but regrettably I think it is likely to
be false. More people will think they understand Gödel's work, while in
fact not understanding it.

Friedman:

There will be a spectrum. This spills off into schoolchildren, some
fraction of which will be brilliant and influenced properly.

Hayes:

This combination of shallowness and
self-confidence is alarmingly resistant to rational debate.

Friedman:

But the inevitable march of great ideas overtakes everything. And this
stuff helps.

Hayes:

But like I
said, go ahead and celebrate, if you think that what FOM needs most is a
kind of Hollywood name-recognition of its celebrities.

I never said that, as you know. What f.o.m. need most is the right kind of
advances.

Hayes:

I won't raise the
issue again.

Friedman:

I am sure that no one on the FOM is annoyed. Please continue.