The Stone Gamut

stone_gamut

Our thesis is that the category Set is the ultimate abstraction of body, and that Set^op, equivalent to the category of complete atomic Boolean algebras (i.e. power sets), which we shall advocate thinking of as antisets, is dually the ultimate abstraction of mind.

— From Chu Spaces: automata with quantum aspects by Vaughn Pratt

Reflecting an era of reduced expectations for the superiority of humans, we have implemented causal interaction not with the pineal gland but with machinery freely available to all classical entities, whether newt, pet rock, electron, or theorem (but not quantum mechanical wavefunction, which is sibling to if not an actual instance of our machinery).

— From Rational Mechanics and Natural Mathematics by Vaughn Pratt

http://en.wikipedia.org/wiki/Boolean_algebra

http://en.wikipedia.org/wiki/Distributive_lattice

http://en.wikipedia.org/wiki/Vector_space

http://en.wikipedia.org/wiki/Partially_ordered_set

http://en.wikipedia.org/wiki/Set_%28mathematics%29

References:

http://boole.stanford.edu/pub/ph94.pdf

http://boole.stanford.edu/pub/ratmech.pdf

http://chu.stanford.edu/

http://en.wikipedia.org/wiki/Chu_space

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One Response to “The Stone Gamut”

  1. Four Transformations of Chu Spaces | Equivalent eXchange Says:

    […] computer scientist Vaughn Pratt’s notions, such as a Duality of Time and Information and the Stone Gamut. Another recent attempt is the diagram above of four transformations that issue out of his analysis […]

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