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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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Are there ‘rules’ for conveying emotion through art?

Futurum

Culture and biology “For thousands of years, art has been used to communicate the experiences and emotions of daily life,” says Dr Claudia Damiano, previously a Postdoctoral Researcher at GestaltReVision Lab, KU Leuven, in Belgium, and now Research Associate at Toronto’s Department of Psychology.

Biology 89
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Indoor STEM Activities for Kids

STEM Sport

Focusing on STEM (science, technology, engineering, and mathematics) activities can be an excellent strategy to keep students engaged in winter. This hands-on activity not only introduces the concept of binary code but, visually demonstrates how computers use binary to represent data.

STEM 52
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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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Imaging the invisible: how can research software and imaging techniques help scientists study the things we can’t see?

Futurum

Scientific model — a conceptual or mathematical representation of a real-world phenomenon that allows scientists to study the phenomenon in more detail. Software — a set of instructions, scripts or programmes that are used to operate computers and perform specific tasks. What is research computing? billion lightyears.

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Charting a Course for “Complexity”: Metamodeling, Ruliology and More

Stephen Wolfram

And at first I did so in the main scientific paradigm I knew : models based on mathematics and mathematical equations. But in a quirk of history that I now realize had tremendous significance, I had just spent a couple of years creating a big computer system that was ultimately a direct forerunner of our modern Wolfram Language.

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

Stephen Wolfram

Computational Foundations for the Second Law of Thermodynamics (forthcoming) 2. 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. This is part 3 in a 3-part series about the Second Law: 1.

Energy 88