Xerxes D. Arsiwalla 2023-09-06 Xerxes D. Arsiwalla 2023-09-06

Ruliology: Linking Computation, Observers and Physical Law

Dean Rickles, Hatem Elshatlawy, Xerxes D. Arsiwalla

Physical laws arise from the sampling of the Ruliad by observers (including us). This naturally leads to several conceptual issues, such as what kind of object is the Ruliad? What is the nature of the observers carrying out the sampling, and how do they relate to the Ruliad itself? What is the precise nature of the sampling? This paper provides a philosophical examination of these questions, and other related foundational issues, including the identification of a limitation that must face any attempt to describe or model reality in such a way that the modeller-observers are included.

Carlos Zapata-Carratalá 2023-07-15 Carlos Zapata-Carratalá 2023-07-15

Hypermatrix Algebra and Irreducible Arity in Higher-Order Systems: Concepts and Perspectives

Carlos Zapata-Carratalá, Maximilian Schich, Taliesin Beynon, Xerxes D. Arsiwalla

Hypergraph and hypermatrix methods are applied to detect irreducible interactions in higher-order systems.

Carlos Zapata-Carratalá 2022-05-01 Carlos Zapata-Carratalá 2022-05-01

Diagrammatic calculus and generalized associativity for higher-arity tensor operations

Carlos Zapata-Carratalá, Xerxes D. Arsiwalla, Taliesin Beynon

Stephen Wolfram 2022-03-07 Stephen Wolfram 2022-03-07

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.