Stephen Wolfram

JUNE 28, 2023

And, yes, when you try to run the function, it’ll notice it doesn’t have correct arguments and options specified. also includes a number of advances in the core machine learning system for Wolfram Language. It’s a process similar to machine learning training. And, yes, it’s taken a while, but now in Version 13.3

Computer 119

Computer Calculus Construction Mathematics 119

Stephen Wolfram

DECEMBER 14, 2022

Almost any algebraic computation ends up somehow involving polynomials. can be manipulated as an algebraic number, but with minimal polynomial: &#10005. And all of this makes possible a transformative update to polynomial linear algebra, i.e. operations on matrices whose elements are (univariate) polynomials. &#10005.

Astronomy 75

Astronomy Computer Construction Algebra 75

Stephen Wolfram

MARCH 7, 2022

One can view a symbolic expression such as f[g[x][y, h[z]], w] as a hierarchical or tree structure , in which at every level some particular “head” (like f ) is “applied to” one or more arguments. So how about logic, or, more specifically Boolean algebra ? We’ve looked at axioms for group theory and for Boolean algebra.

Mathematics 114

Mathematics Physics Computer Algebra 114

Stephen Wolfram

AUGUST 29, 2024

I later learned that a century earlier many well-known physicists were beginning to think in a similar direction (matter is discrete, light is discrete; space must be too) but back then they hadn’t had the computational paradigm or the other tools needed to move this forward. There was still much to do (and there still is today).

Physics 110

Physics Computer Biology Mathematics 110

Robert Talbert, Ph.D.

MAY 19, 2023

So I’m writing this article as a “read this first” guide for journalists and anybody else wanting to learn about ungrading, and all forms of alternative grading, and tell its story. This typically happens when the student does not produce evidence of learning that rises above a minimum threshold. What is ungrading?

Publication 73

Publication Communications Construction Academic Standards 73

Stephen Wolfram

JANUARY 9, 2024

So many discoveries, so many inventions, so much achieved, so much learned. Of course one of our great achievements has been to maintain across all that functionality a tightly coherent and consistent design that results in there ultimately being only a small set of fundamental principles to learn.

Computer 95

Computer Calculus Construction Accessibility 95

Robert Talbert, Ph.D.

APRIL 15, 2022

How it traditionally works In traditional, points-based grading systems, the evidence that students present about their learning is almost always in the form of one-and-done assessments: Tests, exams, homework, presentations, and the like. One-and-done assessment is clearly a terrible way to measure student learning.

Academic Standards 52

Academic Standards Communications Calculus Algebra 52

Robert Talbert, Ph.D.

APRIL 1, 2022

Here's what I've learned about how to do it. In fact because of Butler and Nisan, there is a good argument to be made for decoupling marks from feedback and then throwing out the marks, basing the course grade just on feedback, student portfolios, and self-evaluations. First, you do not have to give marks at all.

Primary 52

Primary Mathematics Algebra Argumentation 52

Stephen Wolfram

MARCH 5, 2024

But here for the most part I’m going to adopt a narrower definition—and say that AI is something based on machine learning (and usually implemented with neural networks), that’s been incrementally trained from examples it’s been given. In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be.

Science 115

Science Sciences Computer Mathematics 115

Stephen Wolfram

AUGUST 22, 2023

He used to like to tell people I’d learned a lot from him. 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). And in fact I think it was only in writing this piece that I even learned he’d grown up in Los Angeles (specifically, East Hollywood).

Computer 69

Computer Physics Science Sciences 69

Stephen Wolfram

SEPTEMBER 9, 2021

Because what we seem to be learning is that in fact our whole universe is operating as a giant multiway system. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. But I suspect there’s even more to learn by looking at something closer to the underlying token-event graph.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Because what we seem to be learning is that in fact our whole universe is operating as a giant multiway system. Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. But I suspect there’s even more to learn by looking at something closer to the underlying token-event graph.

Science 59

Science Sciences Physics Mathematics 59

Stephen Wolfram

MAY 17, 2021

And perhaps there is some way to extend the cellular automaton to a neural net with continuous weights, and then use machine learning methods to iteratively find minimal places where weights can be changed. In the basic definition of a standard cellular automaton, the rule “takes its arguments” in a definite order.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

MAY 20, 2021

we’re connecting to “Descartes-style” analytic geometry, converting geometric descriptions to algebraic formulas. Given three symbolically specified points, GeometricTest can give the algebraic condition for them to be collinear: &#10005. Tree takes two arguments: a “payload” (which can be any expression), and a list of subtrees.

Computer 52

Computer Construction Physics Technology 52