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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

But as another example of how this can play out, consider economic systems. But are “numerical prices” the only possible setup for an economic system? Ultimately an economic system is based on a large network of transactions. No doubt there’ll at least be some “natural-science-like” characterizations of what’s going on.

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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. And that term immediately brings to mind wages, economics, etc. This equivalence has many consequences. But plenty is also not.

Computer 105
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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
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

There was one major exception, however, in 1738, when—as part of his eclectic mathematical career spanning probability theory, elasticity theory, biostatistics, economics and more— Daniel Bernoulli (1700–1782) published his book on hydrodynamics. But why should this be true?

Energy 88