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. And in Mathematica and the Wolfram Language that’s achieved with Integrate. And over the years that’s exactly what we’ve achieved—for integrals, sums, differential equations, etc. And in Version 13.3

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

JANUARY 31, 2023

But, first and foremost, the story of the Second Law is the story of a great intellectual achievement of the mid-19th century. 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.

Energy 88

Energy Physics Argumentation Mathematics 88

Stephen Wolfram

FEBRUARY 3, 2023

Indeed, the Zeroth Law of thermodynamics is essentially the statement that “statistically unique” equilibrium can be achieved, which in terms of energy becomes a statement that there is a unique notion of temperature. 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

JUNE 8, 2022

Here in more detail are the forms of some typical components of branchial graphs achieved at particular steps: &#10005. Imagine that rather than playing a specific game, we instead at each step just make every possible move with equal probability. . &#10005. The Icosian Game & Some Relatives. &#10005. &#10005.

Physics 71

Physics Computer Construction Equality 71

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. &#10005.

Construction 67

Construction Computer Physics Accessibility 67