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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. 3 The Metamodeling of Axiomatic Mathematics. 4 Simple Examples with Mathematical Interpretations. 15 Axiom Systems of Present-Day Mathematics. 21 What Can Human Mathematics Be Like? Graphical Key.

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Numbers and networks: how can we use mathematics to assess the resilience of global supply chains?

Futurum

Numbers and networks: how can we use mathematics to assess the resilience of global supply chains? At Brigham Young University in the US, Dr Zach Boyd is using his mathematical skills to determine how best to protect our supply chains. BUILDING MATHEMATICAL MODELS. FIELD OF RESEARCH: Mathematics. Published: July 13, 2022.

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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. And it’s one that I think has extremely deep implications—both in science and beyond. (And—it The full ruliad is in effect a representation of all possible computations.

Physics 117
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Behind the screens: the crystals that flow like rain down a windowpane

Futurum

When was the last time you looked at a computer, TV, phone or tablet? Mathematically, a sphere is the shape that minimises the surface area of a fixed volume, explaining why small water droplets on a flat surface take the shape of a spherical cap. JOSEPH’S MATHEMATICAL MODELS. COMBINING EXPERIMENTS AND MATHEMATICAL MODELS.

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What Is ChatGPT Doing … and Why Does It Work?

Stephen Wolfram

See also: “Wolfram|Alpha as the Way to Bring Computational Knowledge Superpowers to ChatGPT” » It’s Just Adding One Word at a Time That ChatGPT can automatically generate something that reads even superficially like human-written text is remarkable, and unexpected. But how does it do it? And why does it work?

Computer 145
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Will AIs Take All Our Jobs and End Human History—or Not? Well, It’s Complicated…

Stephen Wolfram

And all I’ll be able to do here is give a snapshot of my current thinking—which will inevitably be incomplete—not least because, as I’ll discuss, trying to predict how history in an area like this will unfold is something that runs straight into an issue of basic science: the phenomenon of computational irreducibility.

Computer 103
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Mechanical Hand Made of Cardboard

Scientix

CC-BY, Unsplash Introduction This educational activity was carried out during the skills workshops, in the context of the natural science lesson as well as in the IT lesson. Then, with the help of a computer, they programmed the wheel to move clockwise and counterclockwise to open and close the fingers.

Primary 52