Subject: Re: Open letter to those who believe in a right to free software
From: Crispin Cowan <>
Date: Thu, 04 Nov 1999 01:03:40 +0000 wrote:

> Bernard Lang wrote:
> [about my report on how math works]
> ... My wife's field reports on biology, as well as experiences in
> other sciences indicate that this situation is specific to math.  My
> wife can pick up most biology papers, certainly anything in
> molecular and cell biology, and read it.

I would observe that math is special in this regard, because it is one of the
oldest intellectual disciplines.  Math has an almost continuous history of
development going back 5000 years, while most of the hard sciences are really
only a few hundred years old.  Microbiology is a mere youth at 150, and
computer science is a babe at 50, by comparison.

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).

> Furthermore in many
> places, such as the former Eastern Block, this is not a problem.
> In all cases a clear commitment to keep lines of communication
> open is key...

The old Eastern Block could not afford real computers, and so mathematically
inclined individuals had no choice but to study math.  Now that the East can
afford computers, look for their math skills to decline in the coming decades

Crispin Cowan, CTO, WireX Communications, Inc.
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