I have been meaning to focus on this aspect of mathematics for some time. It is a topic I elaborated in my “Angular Momentum” post. But I also think it has something to do with the difficulties that normal folks have with elementary math, in particular, numbers. I thought I would dub it the Cheshire Cat Paradigm, involving the Cheshire Cat’s grin.
See the Cheshire Cat Paradigm.
(Updates 6/7/2025, 7/19/2025, 7/20/2025) Contra Concrete Algebra, James Tanton Videos, Imaginary Numbers Continue reading
Years ago (1963) I got the paperback The Calculus:A Genetic Approach, by Otto Toeplitz, which presented the basic ideas of the differential and integral calculus from a historical point of view. One thing Toeplitz did at the end of his book that I had not seen in other texts was to show the equivalence of Kepler’s Laws and Newton’s Law of Gravity. (Since 1963 David Bressoud has developed this theme in his excellent 1991 text.) I thought I would try to emulate Toeplitz’s approach with more modern notation (vectors) and arguments in hopes of extracting the essential ideas from the clutter.