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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

Let’s say that we’re trying to achieve the objective of having an efficient transportation system for carrying people around. No doubt there’ll at least be some “natural-science-like” characterizations of what’s going on. Ultimately an economic system is based on a large network of transactions. One person wants to get a cookie.

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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. He introduced the Boltzmann Transport Equation which allows one to compute at least certain non-equilibrium properties of gases.

Energy 88
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The Concept of the Ruliad

Stephen Wolfram

For integers, the obvious notion of equivalence is numerical equality. Then (by the assumed properties of equality) it follows that. But it’s a fundamental claim that we’re making—that can be thought of as a matter of natural science—that in our universe only computation can occur, not hypercomputation.

Physics 122
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Will AIs Take All Our Jobs and End Human History—or Not? Well, It’s Complicated…

Stephen Wolfram

One of them is that one can expect to make something equally computationally sophisticated out of all sorts of different kinds of things—whether brain tissue or electronics, or some system in nature. Processes in nature—like, for example, the weather—can be thought of as corresponding to computations.

Computer 105