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Expression Evaluation and Fundamental Physics

Stephen Wolfram

And if we treat these as equivalent and merge them we now get: (The question of “state equivalence” is a subtle one, that ultimately depends on the operation of the observer, and how the observer constructs their perception of what’s going on. It’s a new kind of fundamentally multiway construct.

Physics 108
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The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

When most working mathematicians do mathematics it seems to be typical for them to reason as if the constructs they’re dealing with (whether they be numbers or sets or whatever) are “real things”. And we can think of that ultimate machine code as operating on things that are in effect just abstract constructs—very much like in mathematics.

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Even beyond Physics: Introducing Multicomputation as a Fourth General Paradigm for Theoretical Science

Stephen Wolfram

If one looks at the history of theoretical science, I think one can identify just three major modeling paradigms that have been developed over the course of scientific history—each of them leading to dramatic progress. Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models.

Physics 64
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Multicomputation: A Fourth Paradigm for Theoretical Science

Stephen Wolfram

If one looks at the history of theoretical science, I think one can identify just three major modeling paradigms that have been developed over the course of scientific history—each of them leading to dramatic progress. Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models.

Science 64
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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 121
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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. In some types of rules it’s basically always there , by construction. But one never quite gets there ; it always seems to need something extra. But the mystery of the Second Law has never gone away.

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Remembering the Improbable Life of Ed Fredkin (1934–2023) and His World of Ideas and Stories

Stephen Wolfram

It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). He was going for what he saw as the big prize: using them to “construct the universe”. “Lick” Licklider —who persuaded Ed to join BBN to “teach them about computers”.