Institute Output

Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity
Research Paper Jonathan Gorard Research Paper Jonathan Gorard

Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity

Jonathan Gorard

This paper introduces the Gravitas computational general relativity framework's numerical subsystem, emphasizing its ability to perform 3 + 1 spacetime decompositions via the ADM formalism, handle complex simulations of gravitational phenomena like binary black hole mergers, and leverage adaptive refinement algorithms based on hypergraph rewriting within the Wolfram Language.

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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics
Computational Essay Stephen Wolfram Computational Essay Stephen Wolfram

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

Stephen Wolfram

One of the many surprising (and to me, unexpected) implications of our Physics Project is its suggestion of a very deep correspondence between the foundations of physics and mathematics. We might have imagined that physics would have certain laws, and mathematics would have certain theories, and that while they might be historically related, there wouldn’t be any fundamental formal correspondence between them. 

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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