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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 23 The Physicalized Laws of Mathematics. 29 Counting the Emes of Mathematics and Physics. 1 | Mathematics and Physics Have the Same Foundations. 3 The Metamodeling of Axiomatic Mathematics. Graphical Key.

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Charting a Course for “Complexity”: Metamodeling, Ruliology and More

Stephen Wolfram

So for me it was obvious: if I couldn’t figure out things myself with math, I should use a computer. And so when it came to complexity, it was natural to try to do the same thing. Mathematical physics. Computation theory. The Emergence of a New Kind of Science. It had worked out very well for the language.

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The Concept of the Ruliad

Stephen Wolfram

Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways. It’s yet another surprising construct that’s arisen from our Physics Project. And it’s one that I think has extremely deep implications—both in science and beyond.

Physics 122
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What Is ChatGPT Doing … and Why Does It Work?

Stephen Wolfram

And for example the concept of “temperature” is there because exponential distributions familiar from statistical physics happen to be being used, but there’s no “physical” connection—at least so far as we know.) In this particular case, we can use known laws of physics to work it out.

Computer 145