Math and Science

© 1995 Alexander Chislenko

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.
[ 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:
" "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

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