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

Stephen Wolfram

We can think of the ruliad as the entangled limit of all possible computations—or in effect a representation of all possible formal processes. Many of these consequences are incredibly complicated, and full of computational irreducibility. But now we can make a bridge to mathematics. So is something similar happening with mathematics?

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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

And in it this computation is going on: &#10005. Let’s change the rule for the computation a bit. But that ignores the phenomenon of computational irreducibility. But it’s a fundamental fact of the computational universe that the result doesn’t have to be simple: &#10005. Imagine you have some sophisticated AI.

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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. And it’s one that I think has extremely deep implications—both in science and beyond. For integers, the obvious notion of equivalence is numerical equality.

Physics 122