National Science Foundation

JANUARY 20, 2022

Now, this is usually where I would launch into a well-honed set of arguments explicating the various economic, societal, and moral imperatives which make clear the need for America to tackle issues of equity and inclusion through a systemic transformation approach to cultivate a larger and more inclusive STEMM workforce.

Argumentation 98

Argumentation Biology Achievement Accessibility 98

Futurum

SEPTEMBER 12, 2023

Library and research skills cover areas such as knowing how to reference and cite authors properly, being able to discern between reliable and unreliable sources of information, accessing scientific literature and giving accurate evidence-based arguments when writing scientific essays and reports. What do students learn from studying this?

Biology 81

Biology STEM Chemistry Critical Thinking 81

User Generated Education

JULY 31, 2023

Knowledge Constructor: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others. It begins the first minute of the first day of the first week of school and continues throughout the entire school year.

Schooling 62

Schooling Elementary Communications Argumentation 62

Stephen Wolfram

JUNE 28, 2023

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. It’s the end of a long journey, and a satisfying achievement in the quest to make as much mathematical knowledge as possible automatically computable.

Computer 119

Computer Calculus Construction Mathematics 119

Stephen Wolfram

MAY 23, 2023

And for example doing a very simple piece of machine learning , we again get a symbolic object which can be used as a function and applied to an argument to get a result: And so it is with LLMFunction. By giving a second argument to LLMFunction you can say you want actual, structured computable output. are symbolic objects.

Technology 69

Technology Argumentation Computer Publication 69

Stephen Wolfram

SEPTEMBER 27, 2024

Just like in our original f [0] = 1 case, we can construct “blue graph trees” rooted at each of the initial conditions. Some involve alternate functional forms; others involve introducing additional functions, or allowing multiple arguments to our function f. So what about the behavior of f [ n ] for large n ?

Computer 106

Computer Mathematics Argumentation Science 106

Stephen Wolfram

JANUARY 31, 2023

It began partly as an empirical law, and partly as something abstractly constructed on the basis of the idea of molecules, that nobody at the time knew for sure existed. But, first and foremost, the story of the Second Law is the story of a great intellectual achievement of the mid-19th century.

Energy 89

Energy Physics Argumentation Mathematics 89

Stephen Wolfram

JANUARY 9, 2024

So many discoveries, so many inventions, so much achieved, so much learned. And key to everything we do is leveraging what we have already done—often taking what in earlier years was a pinnacle of technical achievement, and now using it as a routine building block to reach a level that could barely even be imagined before.

Computer 95

Computer Calculus Construction Accessibility 95

User Generated Education

AUGUST 8, 2017

It supports several of the new ISTE NETS for Students: Empowered Learner: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences. Promotes independence and responsibility ( Differentiate Learning With Choice Boards ).

Schooling 116

Schooling Elementary Communications Argumentation 116

PCS Edventures

SEPTEMBER 22, 2021

Learners see the challenges characters face time and again as they work to achieve a goal. Well, in recent years, you may have noticed an increased focus on supporting scientific thinking with written and oral arguments. These stories open their minds to infinite possibilities and, just like engineers, push them to think, “What if?”.

Mathematics 52

Mathematics Engineering Argumentation Science 52

Futurum

OCTOBER 17, 2023

I strongly believe that the world needs engineers with strong critical thinking skills, who know how to ask questions, understand bias, construct and evaluate arguments, and think comprehensively and creatively. My proudest career achievement is the 10 Million Trees project I undertook with Parisa.

Biology 84

Biology Agriculture Engineering Critical Thinking 84

Vivify Stem

NOVEMBER 22, 2022

All are important goals, but to achieve them, we need to make them clear! Are you focused on engineering design such as material selection or problem definition? Maybe the goal is on social skills like teamwork? Or maybe you just want a fun and memorable experience.

Engineering 52

Engineering Science Sciences Earth science 52

Stephen Wolfram

NOVEMBER 10, 2021

It’s yet another surprising construct that’s arisen from our Physics Project. In some ways it’s a bit like our efforts to construct the ruliad. In constructing it, one can imagine using Turing machines or hypergraph rewriting systems or indeed any other kind of computational system. As an analogy, consider the real numbers.

Physics 116

Physics Mathematics Computer Construction 116

Stephen Wolfram

MARCH 7, 2022

When most working mathematicians do mathematics it seems to be typical for them to reason as if the constructs they’re dealing with (whether they be numbers or sets or whatever) are “real things”. And we can think of that ultimate machine code as operating on things that are in effect just abstract constructs—very much like in mathematics.

Mathematics 114

Mathematics Physics Computer Algebra 114

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”. In some types of rules it’s basically always there , by construction. But one never quite gets there ; it always seems to need something extra. But the mystery of the Second Law has never gone away.

Computer 91

Computer Energy Physics Construction 91

Stephen Wolfram

MARCH 5, 2024

A lot of science—and technology—has been constructed specifically around computationally reducible phenomena. Once again, I had no idea this was “out there”, and certainly I would never have been able to construct it myself. There is, however, a subtlety here. Back in 1987—as part of building Version 1.0

Sciences 115

Sciences Science Computer Mathematics 115

Stephen Wolfram

SEPTEMBER 9, 2021

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. It’s not difficult to construct multiway system models. There are multiway Turing machines.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Its key idea is to think of things in the world as being constructed from some kind of simple-to-describe elements—say geometrical objects—and then to use something like logical reasoning to work out what will happen with them. It’s not difficult to construct multiway system models. There are multiway Turing machines.

Sciences 59

Sciences Science Physics Mathematics 59

Stephen Wolfram

AUGUST 29, 2024

Even if I hadn’t been able to imagine quite what could be built on them, I’d been able to construct solid foundations, that successfully encapsulated things in the cleanest and simplest ways. In the end—after all sorts of philosophical arguments, and an analysis of actual historical data —the answer was: “It’s Complicated”.

Physics 110

Physics Computer Biology Mathematics 110

Stephen Wolfram

FEBRUARY 2, 2023

One of the key things that had originally let me start “scientifically investigating” cellular automata is that out of all the infinite number of possible constructible rules, I’d picked a modest number on which I could do exhaustive experiments. Of course, as is typical in the history of ideas, there’s more to the story.

Physics 94

Physics Computer Mathematics Science 94

Stephen Wolfram

MAY 17, 2021

Traditional blockchains achieve consensus through what amounts to a centralized mechanism (even though there are multiple “decentralized” copies of the blockchain that is produced). And for example in 1978 the following “radius 3” rule (operating on size-7 neighborhoods) was constructed (and we’ll call it the “GKL rule”): &#10005.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

JUNE 29, 2022

And for the past four years I’ve been sharing the “behind the scenes” of how it’s achieved—by livestreaming our Wolfram Language design review meetings. we have a new symbolic construct, Threaded , that effectively allows you to easily generalize listability. Why is such a construct needed? In designing Version 13.1 &#10005.

Calculus 113

Calculus Construction Computer Argumentation 113

Stephen Wolfram

AUGUST 22, 2023

He was going for what he saw as the big prize: using them to “construct the universe”. the Vietnam War), whose idea was that it was time to stop the government fighting an unwinnable war, and this could be achieved by having an organization that would coordinate citizens to threaten a run on banks unless the war was ended.

Computer 69

Computer Physics Science Sciences 69

Stephen Wolfram

MAY 20, 2021

1”) releases that deliver our latest R&D achievements—both fully fleshed out, and partly as “coming attractions”—much more frequently. Having this as a single function makes it easier to use in functional programming constructs like this: &#10005. In earlier times we used to release the results of efforts only every few years.

Computer 52

Computer Construction Physics Technology 52