Monday, September 27, 2021


 Almost every year I find some excuse to run one of my favorite quotes ever from a math volume, a bit of linguistics and recursive philosophy from provocateur David Berlinski in "The King of Infinite Space" (about Euclid). Berlinski is nothing if not an artiste of wordplay, and recently finishing "Shape" by Jordan Ellenberg's (no slouch at wordsmithing himself; though a bit more fun), simply reminded me of it once again:

"Like any other mathematician, Euclid took a good deal for granted that he never noticed.  In order to say anything at all, we must suppose the world stable enough so that some things stay the same, even as other things change. This idea of general stability is self-referential. In order to express what it says, one must assume what it means.

"Euclid expressed himself in Greek; I am writing in English. Neither Euclid's Greek nor my English says of itself that it is Greek or English. It is hardly helpful to be told that a book is written in English if one must also be told that written in English is written in English. Whatever the language, its identification is a part of the background. This particular background must necessarily remain in the back, any effort to move it forward leading to an infinite regress, assurances requiring assurances in turn.
"These examples suggest what is at work in any attempt to describe once and for all the beliefs 'on which all men base their proofs.' It suggests something about the ever-receding landscape of demonstration and so ratifies the fact that even the most impeccable of proofs is an artifact."

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