Subject: Re: Open letter to those who believe in a right to free software
Date: Wed, 3 Nov 1999 20:38:30 -0500

(Crispin's theory connecting age of field to specialization..)
> As to how that pertains to the ability to communicate:  model "knowledge" as
> a 3D sphere.  Total ignorance of a field lies at the origin, and total
> knowledge of the field is the entire volume of the sphere.
> Advances (discovering new things) only happens at the surface.  As a field
> ages, more new stuff is discovered, and the sphere acretes.  New participants
> enter the field at the origin.  Practitioners can wander around inside the
> sphere applying old knowledge to new things.  Researchers (people who
> contribute new results) must *dig* their way (through painful learning) from
> the origin to the surface.
> With young fields (like computer science and microbiology) the shere is
> small, and so a reasonably competent person can be expected to resonably
> comprehend a large chunk of the sphere.  Ancient fields like mathematics are
> so vast that a researcher only has a hope of contributing by focussing on an
> increadibly narrow slice of the sphere, in order to hold the volume of
> knowledge constant.  Naturally, brigher stars in any field can comprehend
> greater volumes of knowledge, and thus contribute in more areas.
> This model seems to exactly predict the observed behavior from the math talk
> story (extremely narrow fields of interest), the observed behavior in
> microbiology (fairly broad fields of interest) and the observed behavior in
> very young fields (open source software development, where everyone knows
> lots about everything).

It fits the evidence.  Many mathematicians would cheer and agree with you.

I personally don't believe it.

I saw active pressure in action against being a polyglot.  I know that
research traditions in other countries somehow managed to keep lines of
communication open and didn't appear to suffer a loss of mathematical
development.  (I would say that a decade ago the USSR was ahead, and what
changed this was that the US since has hired the cream of the Russian crop
of mathematicians.)  And the tradition the US came from appears to have
only really splintered within the memory of mathematicians who are still
alive. (In fact largely since WW II.)

My impression is that preventable social factors play a large part in why
mathematics today looks like it does.  I could see the same thing happen to
software, and I think it is a trap to be aware of and defend against.

But I admit that many mathematicians agree with your analysis and not