FOM: Re: Re: General intellectual interest/challenges

[Michael Thayer]

Harvey responds in part:


>Reply to Torkel Franzen 5:41PM 12/17/97.
>

>Brilliant expositions of P=NP and surrounding material have surely been
>done and succeeded about 500 times in the last decade in this country
>alone, and without any help from me. In comparison, how many times do you
>think the same has been done for zeta functions? And in comparison, what
>kind of audiences would it draw? It's you that living in a fool's paradise
>- as you like to say - or the wrong part of the world.
>
>>  The technicalities beloved by experts are usually boring to outsiders.
>
>Exactly. There are no technicalities involved in an understanding of what's
>at stake with P=NP.
>

Harvey is clearly right here: an approach to P=NP via computers should be of
interest to many people with no interest in mathematics,  I often talk about
it under the title "What you can never do with a computer", and point out
why the P/NP break is so interesting and many people who are afraid of
computers still get it.  I work with Zeta functions, and it would never
occur to me to discuss it with this same group of people.


Earlier Harvey had said:
> P=NP is something that I would not quite regard as mainstream FOM,
although
>it is clearly close in spirit, or at least far closer in spirit and actual
>connection to FOM than any part of mathematics.

I agree, it is a nice example of F. O. C. S., not FOM.

>It is definitely something
>that emerges very very quickly in foundational studies. This is extremely
>rare for a yes/no mathematical problem. I will save the big guns from
>mainstream FOM in reserve for later.

I would like to see these big guns, since little of what Harvey has posted
in fom on FOM is of such general interest as P=NP.  the one exception might
be his paper `Transfer Principles in Set Theory' which is available on his
web site.

Harvey also made another comment with which I wish to agree:
>What is unclear is to what extent mathematicians are driven by any wider
>intellectual purposes, other than this special kind of process. To real
>outsiders - and I am not really quite an outsider - it has all the
>appearance of an intricate yet aimless art, which is admittedly very
>"precious."  Yet horrifically imbred, and very very snooty. To real
>outsiders, it is supremely impenetrable. And when it is made to look
>penetrable - on the surface - it merely looks like challenging puzzles
>(coloring maps, FLT, etc.) - with the flavor of chess. A kind of climbing
>of Mt. Everest in an age of airplanes.

The idea of mathematics as art does explain why FOM is so little appreciated
in mathematical circles: art critics are never much appreciated by the
artists themselves, and little of their work survives as long as the work
they critique does.

Actually, I think there is another sociological parallel for mathematics:
religion.

There are many believers who have learned their beliefs from their culture
without any clear understanding.  they are taking on faith that since most
of the talk in their community makes sense that THIS talk does too.

There are some who try to directly experience what the religion is pushing.
These would be the yogi's of Hinduism, the hesychasts of Orthodox
Christianity, and the graduate students of mathematics.  They practice their
yogic techniques until they "get it".

The one class which seems missing in mathematics (although it is also
missing in some other religious traditions as well) is the class of
prophets: people like Mohammed, Hosea, etc who did NOT ask or try to have
the direct experience of God (or whatever: samadhi, mathematical truth,
etc.) it was simply forced on them.

Can anyone think of mathematical parallels to this group of people?

Michael
>