Stephen Wolfram

JUNE 29, 2022

Needless to say, you can do this computationally—though the “calculus” of what’s been defined so far in Unicode is fairly bizarre: &#10005. And in addition to adding a great deal of flexibility, this also means that the toolbar immediately works on all platforms. (By Fractional Calculus. . &#10005. &#10005.

Calculus 114

Calculus Construction Computer Argumentation 114

Robert Talbert, Ph.D.

JUNE 15, 2023

This is a four-credit course primarily intended for students in engineering that combines topics from these two gigantic areas of mathematics. You'll find versions of this course at many universities that offer engineering degrees, and it's clear that many profs who teach it don't quite know what to make of it.

Engineering 52

Engineering Math Algebra Calculus 52

Futurum

JULY 26, 2022

CONCEPTUAL ENGINEERING – a method philosophers use to try to find and fix places where ideas from science (or everyday life) are confused or unclear. I think this work requires a lot of flexibility. INTERDISCIPLINARITY – the collaboration of two or more branches of knowledge. WHO OR WHAT INSPIRED YOU TO BECOME A PHILOSOPHER?

Biology 52

Biology Research Research Science 52

Stephen Wolfram

JANUARY 9, 2024

And we’ve been steadily doing the engineering to let AIs call on Wolfram Language as easily as possible. So did that mean we were “finished” with calculus? Somewhere along the way we built out discrete calculus , asymptotic expansions and integral transforms. And in Version 14 there are significant advances around calculus.

Computer 102

Computer Calculus Construction Accessibility 102

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

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. I know of a few perhaps-closer approaches to our conception of multiway systems.

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. I know of a few perhaps-closer approaches to our conception of multiway systems.

Science 64

Science Sciences Physics Mathematics 64

Stephen Wolfram

FEBRUARY 14, 2023

I should say at the outset that I’m going to focus on the big picture of what’s going on—and while I’ll mention some engineering details, I won’t get deeply into them. It turns out that the chain rule of calculus in effect lets us “unravel” the operations done by successive layers in the neural net.

Computer 145

Computer Architecture Mathematics Construction 145

Robert Talbert, Ph.D.

APRIL 15, 2022

be the primary measure of success in a course, and some measure of grace and flexibility will be included along with high standards and "rigor" And for other instructors, this concept raises more questions than answers. For some instructors, it provides hope that student growth will (finally!)

Academic Standards 52

Academic Standards Communications Calculus Argumentation 52

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. But what if we’re more flexible in what we consider the objective of the demon to be?

Computer 92

Computer Energy Physics Construction 92