Log24

Tuesday, June 27, 2006

Tuesday June 27, 2006

Filed under: General,Geometry — m759 @ 10:31 AM
Chinese Jar
Revisited

In memory of
Irving Kaplansky,
who died on
Sunday, June 25, 2006

“Only by the form, the pattern,
Can words or music reach
The stillness, as a Chinese jar still
Moves perpetually in its stillness.”

T. S. Eliot


Kaplansky received his doctorate in mathematics at Harvard in 1941 as the first Ph.D. student of Saunders Mac Lane.

From the April 25, 2005, Harvard Crimson:

Ex-Math Prof Mac Lane, 95, Dies

Gade University Professor of Mathematics Barry Mazur, a friend of the late Mac Lane, recalled that [a Mac Lane paper of 1945] had at first been rejected from a lower-caliber mathematical journal because the editor thought that it was “more devoid of content” than any other he had read.

“Saunders wrote back and said, ‘That’s the point,'” Mazur said. “And in some ways that’s the genius of it. It’s the barest, most Beckett-like vocabulary that incorporates the theory and nothing else.”

He likened it to a sparse grammar of nouns and verbs and a limited vocabulary that is presented “in such a deft way that it will help you understand any language you wish to understand and any language will fit into it.”

A sparse grammar of lines from Charles Sanders Peirce (Harvard College, class of 1859):

The image “http://www.log24.com/theory/images/PeirceBox.bmp” cannot be displayed, because it contains errors.

The image “http://www.log24.com/theory/images/PeirceSymbols1.jpg” cannot be displayed, because it contains errors.

It is true of this set of binary connectives, as it is true of logic generally, that (as alleged above of Mac Lane’s category theory) “it will help you understand any language you wish to understand and any language will fit into it.” Of course, a great deal of questionable material has been written about these connectives. (See, for instance, Piaget and De Giacomo.) For remarks on the connectives that are not questionable, see Wittgenstein’s Tractatus Logico-Philosophicus (English version, 1922), section 5.101, and Knuth’s “Boolean Basics” (draft, 2006).

Related entry: Binary Geometry.

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