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Expression Evaluation and Fundamental Physics

Stephen Wolfram

And it’s all based on ideas from our Physics Project —and on a fundamental correspondence between what’s happening at the lowest level in all physical processes and in expression evaluation. And this is where we can start making an analogy with physics. And now there’s a deep analogy to physics.

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

Stephen Wolfram

1 Mathematics and Physics Have the Same Foundations. 2 The Underlying Structure of Mathematics and Physics. 23 The Physicalized Laws of Mathematics. 29 Counting the Emes of Mathematics and Physics. 1 | Mathematics and Physics Have the Same Foundations. 3 The Metamodeling of Axiomatic Mathematics. Graphical Key.

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

Stephen Wolfram

One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how our physical universe works. 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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The Concept of the Ruliad

Stephen Wolfram

It’s yet another surprising construct that’s arisen from our Physics Project. In the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. And here is a rulial multiway system made from hypergraph rewriting of the kind used in our Physics Project , using all rules with signature : &#10005.

Physics 121
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The Story Continues: Announcing Version 14 of Wolfram Language and Mathematica

Stephen Wolfram

Then for each function (or other construct in the language) there are pages that explain the function, with extensive examples. So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. But even now there are still frontiers.

Computer 102
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Launching Version 13.1 of Wolfram Language & Mathematica ??????

Stephen Wolfram

we have a new symbolic construct, Threaded , that effectively allows you to easily generalize listability. Why is such a construct needed? Now “characters” could be 16-bit constructs, with nearly 65536 possible “glyphs” allocated across different languages and uses (including some mathematical symbols that we introduced).

Calculus 114
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics

Stephen Wolfram

It began partly as an empirical law, and partly as something abstractly constructed on the basis of the idea of molecules, that nobody at the time knew for sure existed. The theory of heat will hereafter form one of the most important branches of general physics. physics) in Glasgow—began to be curious about.

Energy 88