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

Sometimes textbooks will gloss over everything; sometimes they’ll give some kind of “common-sense-but-outside-of-physics argument”. 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.

Computer 92

Computer Energy Physics Construction 92

Stephen Wolfram

AUGUST 22, 2023

It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). But I think at least in the later part of his life, Ed felt his greatest achievements related to cellular automata and in particular his idea that the universe is a giant cellular automaton.

Computer 68

Computer Physics Science Sciences 68

Stephen Wolfram

NOVEMBER 10, 2021

But what about other models of computation—like cellular automata or register machines or lambda calculus? In other words, we’re concerned more with what computational results are obtained, with what computational resources, rather than on the details of the program constructed to achieve this. But ultimately there’s only one ruliad.

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).

Science 64

Science Sciences Physics Mathematics 64