Stephen Wolfram

JANUARY 31, 2023

And indeed particularly in chemistry and engineering it’s often been in the background, justifying all the computations routinely done using entropy. There had been precursors of steam engines even in antiquity, but it was only in 1712 that the first practical steam engine was developed. Lazare Carnot died in 1823.

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 118

Computer Calculus Construction Mathematics 118

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). His father ’s university engineering studies had been cut short by the Russian Revolution, and he now had a one-man wholesale electronic parts business. Petersburg; his mother in Odessa ; they met in LA).

Computer 68

Computer Physics Science Sciences 68

Stephen Wolfram

SEPTEMBER 9, 2021

And in general to achieve a “ pathological result ” we’ll typically have to “reverse engineer” the underlying computational irreducibility of the system—which we won’t be able to do with a reference frame constructed by a computationally bounded observer.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

And in general to achieve a “ pathological result ” we’ll typically have to “reverse engineer” the underlying computational irreducibility of the system—which we won’t be able to do with a reference frame constructed by a computationally bounded observer.

Science 64

Science Sciences Physics Mathematics 64

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