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. It appears that it must some day serve as a universal motor, and be substituted for animal power, water-falls, and air currents.

Energy 88

Energy Physics Argumentation Mathematics 88

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 117

Computer Calculus Construction Mathematics 117

Stephen Wolfram

SEPTEMBER 9, 2021

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). At the level of individual events, ideas from the theory and practice of computation are useful. One is so-called Böhm trees.

Science 65

Science Sciences Physics Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

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). At the level of individual events, ideas from the theory and practice of computation are useful. One is so-called Böhm trees.

Physics 64

Physics Science Sciences Mathematics 64

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). Richard Feynman and I would get into very fierce arguments. Ed was a serious (and, by all reports, exceptionally good) pilot—with an airplane transport pilot license (plus seaplane and glider licenses).

Computer 67

Computer Physics Science Sciences 67

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

NOVEMBER 10, 2021

But what about other models of computation—like cellular automata or register machines or lambda calculus? And we can trace the argument for this to the Principle of Computational Equivalence. We’ve talked about building up the ruliad using Turing machines. A very important claim about the ruliad is that it’s unique.

Physics 122

Physics Mathematics Computer Construction 122