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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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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. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 88
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Why Choose a STEM Career?

CTE Learning

stands for Science, Technology, Engineering, and Mathematics. On the other hand, physical and biological sciences, mathematics, science technology, and agricultural sciences pay around $50,400 on average. With STEM, customary gender roles are broken, and it gives way to equality in every possible way. The acronym “S.T.E.M.”

STEM 52
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Why Choose a STEM Career?

CTE Learning

” stands for Science, Technology, Engineering, and Mathematics. Mathematics is typically in every activity or occupation we do in life. On the other hand, physical and biological sciences, mathematics, science technology, and agricultural sciences pay around $50,400 on average. So what exactly is a STEM based career?

STEM 52
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Why Choose STEM? The Best STEM Careers for 2018

CTE Learning

stands for Science, Technology, Engineering, and Mathematics. On the other hand, physical and biological sciences, mathematics, science technology, and agricultural sciences pay around $50,400 on average. With STEM, customary gender roles are broken, and it gives way to equality in every possible way. The acronym “S.T.E.M.”

STEM 40
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Games and Puzzles as Multicomputational Systems

Stephen Wolfram

Imagine that rather than playing a specific game, we instead at each step just make every possible move with equal probability. The setup for tic-tac-toe is symmetrical enough that for most of the game the probability of every possible configuration at a given step is equal. The Icosian Game & Some Relatives. &#10005.

Physics 71
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Computational Foundations for the Second Law of Thermodynamics

Stephen Wolfram

And the Second Law assertion that energy associated with systematic mechanical work tends to “degrade into heat” then corresponds to the fact that when there’s computational irreducibility the behavior that’s generated is something we can’t readily “computationally see through”—so that it appears random to us. But there’s even further to go.