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Gentle folk: vis-a-vis the present discussion, I went back and pulled
out five textbooks on introductory physics from the previous century
(1837- 1895) which were aimed at introductory physics (or natural
philosophy) students. I was fascinated to find that only one had any
algebraic equations at all! All of them did have some mathematical
relationships, but characteristically they described the relationships in
terms of ratio or proportion, and gave the descriptions verbally.
Several of them had quantitative problems based on the verbal
relationships, and example problems. Basically, these texts gave a
qualitative description of phenomena, followed by a verbal description of
the quantitative relationships, and then arithmetical problems involving
the relationships. The selection of texts is an accidental, not a
random, sample but in light of the present discussion I find it
interesting. Of the five books only one explicitly stated 'RULES' for
computation, and even the rules were given in words, but with
arithmetical examples immediately following.
My point is that we need not describe relationships in algebraic terms,
i.e. as formulae, in order to describe them in quantitative terms, and
that there is a middle ground, a quasi-quantitative way of describing
relationships that allows a certain rigor, but may be approachable to
more students, than the abstruse (to some) short hand of algebra.
Bob Morse
Robert A. Morse, Ph. D.
Science Chairman, Physics Master
St. Albans School, Washington, DC 20016
ramorse@cais.com
robert_morse@cathedral.org