Archive for May, 2013

The Four Laws of Thermodynamics

May 24, 2013

four_laws_of_thermodynamics0th Law: Heat doesn’t flow between objects of the same temperature.

1st Law: Heat cannot be created or destroyed.

2nd Law: Entropy increases by the flow of heat in a closed system not in equilibrium.

3rd Law: Entropy approaches a constant minimum in a system as temperature approaches absolute zero.

References:

http://www.ridgenet.net/~do_while/sage/v7i1f.htm

http://www.physicsforidiots.com/thermodynamics.html

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

Peter Atkins / Four Laws That Drive the Universe

[*3.169, *7.164]

<>

The Stone Gamut

May 17, 2013

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

[*7.140]

<>

The Archic Philosophers

May 3, 2013

archic_philosophersInspired by philosopher Richard McKeon, I believe that philosophy as a whole is encompassed by four main philosophical stances, exemplified by four ancient philosophers: the Sophists (as a group), Democritus, Plato, and Aristotle. Their four systems of thought lay out principal philosophical directions, much like the compass directions east, south, north, and west lay out a complete set of primary directions.

Of course the compass directions can be subdivided into north-east, or south-south-west, and so on, and similarly each of these philosophical systems can be divided into four parts. This division into a four-by-four matrix is called the Archic Matrix and was written about at length in the separate but complementary works of Walter Watson and David Dilworth.

Watson and Dilworth described the four main philosophical directions to be perspective, reality, method, and principle: perspective for the Sophists, reality for Democritus, method for Plato, and principle for Aristotle. I have written about these philosophical perspectives previously in several ways.

Thus philosophy as a practice goes around and around and revisits the same ideas over and over. Perhaps McKeon thought his philosophical system followed in the footsteps of Aristotle, and probably Watson and Dilworth had a similar view.

Likewise, I believe that my fourfold of Structure-Function represents these four philosophical directions in the following way: Action(s) for the Sophists, Part(s) for Democritus, Structure for Plato, and Function for Aristotle.

structure-function[*6.108]
<>

The Duality of Time and Information, V2

May 2, 2013

The states of a computing system bear information and change time, while its events bear time and change information.

from The Duality of Time and Information by Vaughn Pratt

The most promising transformational logic seems to us to be Girard’s linear logic.

— from Rational Mechanics and Natural Mathematics by Vaughn Pratt

Here we have three duals: information – time, state – event, and bear – change.

References:

Vaughan Pratt / The Duality of Time and Information http://boole.stanford.edu/pub/dti.pdf

Vaughan Pratt / Time and Information in Sequential and Concurrent Computation http://boole.stanford.edu/pub/tppp.pdf

Vaughan Pratt / Rational Mechanics and Natural Mathematics http://chu.stanford.edu/guide.html#ratmech

[*5.170]

<>