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

Stephen Wolfram

2 The Underlying Structure of Mathematics and Physics. But what our Physics Project suggests is that underneath everything we physically experience there is a single very general abstract structure—that we call the ruliad —and that our physical laws arise in an inexorable way from the particular samples we take of this structure.

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Multicomputation with Numbers: The Case of Simple Multiway Systems

Stephen Wolfram

With arbitrary “symbolic” this (“free multiway system”) tree is the only structure one can get. It’s worth noting that the specific setup we’re using here avoids quite a lot of the structural complexity that can exist in multicomputational systems. What can we say about this structure? . &#10005. &#10005. &#10005.

Physics 52
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Twenty Years Later: The Surprising Greater Implications of A New Kind of Science

Stephen Wolfram

And these ideas build crucially on the paradigm of A New Kind of Science. But pretty soon I was swept up in the building of Wolfram|Alpha and then the Wolfram Language, and in all the complicated and often deep questions involved in for the first time creating a full-scale computational language.

Science 63