Re: Lessons From The Cantor Transfinite Thread

>>From Osher Doctorow

I think that an important lesson from the Cantor Transfinite thread is
the importance of History including the History of mathematics,
physics, engineering, psychology, biology, and the USA and the world.
Cantor's role in history as compared with Kronecker's is certainty
important, but here I'll mention two other important items: Sir Isaac
Newton's and Leibniz' roles, on the one hand, and the difference
between Garrett Birkhoff of Harvard and Saunders MacLane of Chicago.

Sir Isaac and Leibniz are credited with discovering Calculus by
"history", but actually it was discovered by Archimedes and by Pierre
De Fermat in large part. What seems to have struck the mathematics
historians was partly the physics discoveries of Sir Isaac and partly
the discovery of differentiation and integration as inverse operations
by Sir Isaac and Leibniz.

The word "operations" is a clue word into the mentality of Saunders
MacLane in the second half of the 20th Century, who following Lawvere
pioneered the algebra-inspired Category Theory that has become the fad
in large sections of the Ingenious Imitators in both mathematics and
physics. To be more precise, MacLane has decided that the operation
of Composition of functions, functors, and whatever else is "key", that
the word Objects should replace Sets without "necessarily generalizing
them," whatever that means (it's his idea if not his words), and that
commutative diagrams unite all quantitative disciplines that he knows
of which seems to include at least mathematics and physics.

Why did the man Garrett Birkhoff of Harvard, who by the way was a
Nonconformist who broke with his father's Nazy sympathies (his father
was also a Professor) and who advised Saunders to study in Germany
(which Saunders MacLane did for his Ph.D.), not go the way of Category
Theory and the composition operation but instead in the direction of
Dimensional Analysis and Hydrodynamics and Differential Equations?

I think that it has to do with the Composition operation (composition
of functions for example), which is so general that it provides almost
no clues to anything, but I'll have to try to continue this next time.

Osher Doctorow

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