Stephen Wolfram

JUNE 28, 2023

Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

JANUARY 31, 2023

Already the steam-engine works our mines, impels our ships, excavates our ports and our rivers, forges iron, fashions wood, grinds grain, spins and weaves our cloths, transports the heaviest burdens, etc. He introduced the Boltzmann Transport Equation which allows one to compute at least certain non-equilibrium properties of gases.

Energy 88

Energy Physics Argumentation Mathematics 88

Stephen Wolfram

JUNE 8, 2022

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

Physics Computer Construction Equality 71

Stephen Wolfram

FEBRUARY 3, 2023

Once one has the idea of “equilibrium”, one can then start to think of its properties as purely being functions of certain parameters—and this opens up all sorts of calculus-based mathematical opportunities. That anything like this makes sense depends, however, yet again on “perfect randomness as far as the observer is concerned”.

Computer 92

Computer Energy Physics Construction 92

Stephen Wolfram

NOVEMBER 10, 2021

For integers, the obvious notion of equivalence is numerical equality. Then (by the assumed properties of equality) it follows that. But what about other models of computation—like cellular automata or register machines or lambda calculus? For hypergraphs, it’s isomorphism. Imagine that you’ve proved that and.

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

DECEMBER 13, 2021

When you do operations on Around numbers the “errors” are combined using a certain calculus of errors that’s effectively based on Gaussian distributions—and the results you get are always in some sense statistical. Also in the area of calculus we’ve added various conveniences to the handling of differential equations.

Construction 67

Construction Computer Physics Accessibility 67