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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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The Concept of the Ruliad

Stephen Wolfram

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. In the language of our Physics Project, it’s the ultimate limit of all rulial multiway systems. For integers, the obvious notion of equivalence is numerical equality.

Physics 116
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Indoor STEM Activities for Kids

STEM Sport

As winter begins, keeping kids both physically and mentally active becomes a challenging task for parents and educators. This activity introduces concepts of structural engineering and the physics of weight distribution. Plastic Cup Towers: Stack plastic cups in various formations to build the tallest or most stable tower.

STEM 52
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The Unknown Particles of the Universe

STEMe

The Standard Model of Elementary Particles was developed fairly recently in the early 1970s and has explained myriad phenomena related to quantum physics. Thus, the Higgs boson, the last particle in the Standard Model of Particle Physics, was theorized.

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

Stephen Wolfram

But by the end of the 1800s, with the existence of molecules increasingly firmly established, the Second Law began to often be treated as an almost-mathematically-proven necessary law of physics. 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 89
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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

The history of physics might make one think that numbers would be a necessary part of the structure of any fundamental theory of our physical universe. But the models of physics suggested by our Physics Project have no intrinsic reference to numbers. We discussed above the example of fundamental physics.

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Will AIs Take All Our Jobs and End Human History—or Not? Well, It’s Complicated…

Stephen Wolfram

(For about three centuries it seemed as if mathematical equations were the ultimate way to describe the natural world—but in the past few decades , and particularly poignantly with our recent Physics Project , it’s become clear that simple programs are in general a more powerful approach.) How does all this relate to technology?

Computer 102