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

Stephen Wolfram

We can think of the ruliad as the entangled limit of all possible computations—or in effect a representation of all possible formal processes. Many of these consequences are incredibly complicated, and full of computational irreducibility. But now we can make a bridge to mathematics.

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Indoor STEM Activities for Kids

STEM Sport

Below are five engineering activities that use everyday items: Popsicle Stick Bridges: Use popsicle sticks and glue to construct bridges. This is a fun way to explore geometric shapes and stability in construction. Homemade Pendulum: Construct a simple pendulum by suspending a weight from a string.

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

Stephen Wolfram

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. So for me it was obvious: if I couldn’t figure out things myself with math, I should use a computer. Computation theory.

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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? He uses these key factors to construct mathematical models that capture the key physical effects of nematic behaviour. If you are interested in soft matter, it would also be good to study another science, such as chemistry or biology.

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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 simulations — an advanced type of computational model that not only represents a real-world phenomenon, but aims to predict how the phenomenon might change under different conditions or parameters. Software — a set of instructions, scripts or programmes that are used to operate computers and perform specific tasks.

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How Inevitable Is the Concept of Numbers?

Stephen Wolfram

And in it this computation is going on: &#10005. Let’s change the rule for the computation a bit. But that ignores the phenomenon of computational irreducibility. But it’s a fundamental fact of the computational universe that the result doesn’t have to be simple: &#10005. Imagine you have some sophisticated AI.

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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. 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. This is part 3 in a 3-part series about the Second Law: 1. How Did We Get Here?

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