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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

Already the steam-engine works our mines, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grain, spins and weaves our cloths, transports the heaviest burdens, etc. It appears that it must some day serve as a universal motor, and be substituted for animal power, water-falls, and air currents.

Energy 88
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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. The energy of the particles is indicated here by the size of the “token dots”: Continuing this a few more steps we get: At the beginning we started with all particles having equal energies.

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The Concept of the Ruliad

Stephen Wolfram

For integers, the obvious notion of equivalence is numerical equality. The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. For hypergraphs, it’s isomorphism.

Physics 122