Sunday, October 3, 2010

Search for the Basic Picture

Filed under: General,Geometry — m759 @ 5:01 PM

(Click to enlarge.)


The above is the result of a (fruitless) image search today for a current version of Giovanni Sambin's "Basic Picture: A Structure for Topology."

That search was suggested by the title of today's New York Times  op-ed essay "Found in Translation" and an occurrence of that phrase in this journal on January 5, 2007.

Further information on one of the images above—


A search in this journal on the publication date of Giaquinto's Visual Thinking in Mathematics  yields the following—

Thursday July 5, 2007

m759 @ 7:11 PM

In defense of Plato’s realism

(vs. sophists’ nominalism– see recent entries.)

Plato cited geometry, notably in the Meno , in defense of his realism.
Consideration of the Meno 's diamond figure leads to the following:

The Eightfold Cube and its Inner Structure

For the Meno 's diamond figure in Giaquinto, see a review—


— Review by Jeremy Avigad (preprint)

Finite geometry supplies a rather different context for Plato's  "basic picture."

In that context, the Klein four-group often cited by art theorist Rosalind Krauss appears as a group of translations in the mathematical sense. (See Kernel of Eternity and Sacerdotal Jargon at Harvard.)

The Times  op-ed essay today notes that linguistic  translation "… is not merely a job assigned to a translator expert in a foreign language, but a long, complex and even profound series of transformations that involve the writer and reader as well."

The list of four-group transformations in the mathematical  sense is neither long nor complex, but is apparently profound enough to enjoy the close attention of thinkers like Krauss.

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