This is my reply to Leonard Adleman's view on relation between mathematics
and science expressed in Wired magazine in July 1995.  I mailed it to the
Extropian mailing list and to Len Adleman on July 26, 1995.
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     [ Mumbling to myself: Great humans are about as wrong as lay
        humans, but at least they are wrong about *important* things.  ]

 WIRED quoting Leonard Adleman <http://cs.usc.edu:8374/finger?adleman> :

>" "Sciences reach a point where they become mathematized," he [Adleman]
>says, coining a new phrase.  This process begins at the fringes, but, at
>some point, the central issues in the field become sufficiently understood
>that they can be thought about mathematically."

  Let me play with this sentence:

 "The development of Mathematics reaches a point where it can be applied to
a new set of scientific disciplines", says Chislenko...  This process begins
at the fringes of the science, but, at some point, the mathematical methods
become sufficiently developed to offer valuable abstractions for the central
issues of the field."

  Math that was so successfully used during the Renaissance looked nothing
like the math that the modern sciences "grew up for".

  The above passages seem about equally lop-sided.

How about this:  The fringe of the human thought (or the skin of the global
body of knowledge growing up in [my favorite metaphor of] semantic space)
consists of raw observations, phenomenological generalizations and ad-hoc
theories not yet extracting the functional essence of the subject from the
heap of details. After a while, the body of knowledge digests the new field,
makes the necessary distinctions and builds clean abstract theories
(a.k.a. math).

  When an instance of a new structural entity gets uncovered for the first
time, we may claim that we developed a new branch of math  (that's "math
catching up"); when existing abstract instruments are found to be useful
for another subject field, we may claim that "The field ripened to allow formal
theory".  For the whole process it really doesn't matter whether we developed a
theory for one subject, and then figured out that the same theory is applicable
to another subject, or it was the other way round.  The important thing is that
the knowledge organisms keeps expanding and digesting/formalizing its model of
the world.

>
>As biology joins the ranks of other hard sciences, a tantalizing
>prospect opens up for Adleman.  After going through an age of
>specialization, the sciences are now reuniting into a common mode of
>inquiry.  "The next generation could produce a scientist in the old
>sense," he says, "a real generalist, who could learn the physics,
>chemistry, and biology, and be able to contribute to all three
>disciplines at once."
>

  I would claim that the opposite suggestion may better reflect the truth.
From the distance at which the scientific approach looks like "a common mode",
you can hardly see any particular discipline.  Of course, there are some
instruments (like calculus, linear algebra, probability and statistics) that
are applicable to lots of different things. However, there have always
been generic instruments: you can use numbers and rulers to measure both
animals and houses.  Now, not only the shared theoretical toolkit seems
[relatively!] shrinking -- even formalisms used *within one discipline*
diverge to the extent that, for example, the best expertise in DNA modeling
gives you little insight into neural nets or population dynamics.

The diversity of knowledge is definitely running ahead of generalization...

  
  - Sasha The Weeping Generalist