FOM: general intellectual interest/pragmatics
Harvey Friedman
friedman at math.ohio-state.edu
Sat Dec 20 22:58:47 EST 1997
Michael Detlefsen's posting of 12:29PM 12/20/97 part III concerning the
controversy about general intellectual interest was of general intellectual
interest. He touches on one of the main points behind the *pragmatic*
importance of general intellectual interest (general intellectual interest
has other kinds of vital importance not discussed here). Namely, it is
apparent that people have a very wide range of special talents. E.g.,
people are drawn into (pure) mathematics partly because they have some
natural instincts about what constitutes a complete proof (in involved
contexts), and the vast majority of even highly intelligent people do not
have workable natural instincts in this direction. Similarly, there is a
rare kind of "physical intuition" that comes naturually to physicists.
There is a rare kind of musical intuition, rhythmic and expressive in
nature, that professional performing musicians have. I can go on this way
through many many disciplines, including philosophy, statistics,
probability, literary criticism, evolutionary biology, law, finance,
business, politics, chess, public speaking, computer programming,
architecture, acting, etcetera. The vast majority of highly successful
people in such disciplines have relatively ordinary natural instincts in
directions other than their main direction. Even when they do have extra
ordinary natural instincts in multiple directions, these are rarely strong
enough or developed enough to be very useful in understanding the essence
of these multiple directions.
So e.g., for the budding professional mathematician, there is absolutely no
need for any disucssion of the nature of complete proof - and the great FOM
work regarding this. He likely views this as an unnecessary detour - he
just gives complete proofs without comment. However, for the physicist,
"complete proof" is very often an intriguing mystery, and they often are
fascinated by what this means - and as a consequence are extremely open to
FOM, far more than to, say, FLT, which assumes a Mt. Everest, gee whiz,
human interest aspect. The physicist has no idea why mathematicians are so
interested in FLT, but know immediately why FOM people are interested in
predicate logic and the completeness theorem. (I am not denying that some
theoretical physicists are even more interested in some core mathematics
that is directly relevant to the kind of mathematical physics they are
doing). The same is true of people throughout all of these subjects. The
idea of "complete proof" and the idea of its complete analysis, is of
compelling interest to just about every highly intelligent person I know
outside professional mathematics. And part of the reason is that they just
don't have any special rare talent to simply make complete proofs up at
will - like many of us do. Very very very small doses of core mathematics -
if any - have this character. The idea of complete proof and the idea of
its complete analysis is delicious food for thought for every intelligent
person - except the professional mathematician. And the best of FOM is
riddled with such priceless gems.
One can, to some extent, take other fields and identify things that are for
everybody except the professionals in that field. Take music performance. I
have never met any professional music performer who has expressed any
serious interest in an analysis of, say, "musical rhythm" - with its subtle
timing patterns so evident and necessary in retardando and accelerando - as
opposed to "rigid rhythm." They just want to "feel it" and get very upset
at the suggestion that there is much to understand at a cognitive level.
Yet many highly intelligent people outside music are fascinated by such
things. "How are these beautiful renditions constructed?" However there is
a difference: this kind of foundational study has not been done yet at a
high enough level. There is some published work in this area, but the
proper combination of gifted musician and gifted intellectual has
apparently not materialized.
We now come to the special role of FOM in this regard. It is by far the
most highly developed, earthshaking, spectacularly successful foundational
study of all time. There can be no doubt that it has a spectacular future -
we are in a golden age of FOM right now that we haven't seen since the
30's. But, more importantly, it serves as a working model of what we have
in mind - to make the essence of all subjects totally accessible to every
highly intelligent person through foundational studies. No longer will
people need rare special instincts in order to fully grasp the essence of
all disciplines. One expects to be able to reexposit the essence of all
disciplines in a single uniform way, revealing all manner of connections
and interactions between all fields. This *project* will put an end to this
suffocating, stifling, ludicrous, and backward age of intellectual
hyperspecialization which is such a gross debilitating waste of human
resources. However, one cannot even start to contemplate the beginning of
this impending renaissance without coming to grips with "general
intellectual interest."
Indeed, maybe paradoxically, this project can only be carried out by those
of us who have natural instincts regarding "general intellectual
interest"!! But this is OK. After this project is sufficiently completed,
everyone can experience the results. Lou and company can then understand
the essence of, e.g., physics, music, and law. So perhaps the essence of my
argument with Lou and company is that their approach to intellectual life
is incompatible with their significant participation in the completion of
this project. This is of course the most ambitious, important, and far
reaching intellectual project of all time. It's too bad that they may lack
the natural instincts to be of much help!
More information about the FOM
mailing list