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 108

Computer Mathematics Argumentation Sciences 108

Stephen Wolfram

MARCH 5, 2024

Three centuries ago science was transformed by the idea of representing the world using mathematics. A lot of science—and technology—has been constructed specifically around computationally reducible phenomena. And that’s for example why things like mathematical formulas have been able to be as successful in science as they have.

Sciences 116

Sciences Science Computer Mathematics 116

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

Stephen Wolfram

JUNE 28, 2023

They’re mathematically more complex, but each one we successfully cover makes a new collection of problems accessible to exact solution and reliable numerical and symbolic computation. 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

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. There were still mathematical loose ends, as well as issues such as its application to living systems and to systems involving gravity.

Energy 89

Energy Physics Argumentation Mathematics 89

Stephen Wolfram

SEPTEMBER 29, 2023

And if we treat these as equivalent and merge them we now get: (The question of “state equivalence” is a subtle one, that ultimately depends on the operation of the observer, and how the observer constructs their perception of what’s going on. It’s a new kind of fundamentally multiway construct.

Physics 101

Physics Computer Argumentation Construction 101

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

STEM Education Shopping

AUGUST 25, 2023

Logical thinking serves as the foundation of problem-solving and innovation within the diverse realms of science, technology, engineering, and mathematics. As a student pursuing a degree in Science, Technology, Engineering, or Mathematics, I have experienced firsthand how logical thinking forms the foundation for success in these fields.

Data analysis 52

Data analysis STEM Problem Solving Critical Thinking 52

Stephen Wolfram

DECEMBER 5, 2024

And indeed it now seems that the foundations of both physics and mathematics aremore than anythingreflections of this interplay. As I discussed when I introduced the model , its possible to construct a multiway graph that represents all possible mutation paths. And now it seems thats true of biological evolution as well.

Biology 108

Biology Computer Achievement Physics 108

Stephen Wolfram

AUGUST 29, 2024

Pleasantly enough, given our framework, many modern areas of mathematical physics seemed to fit right in.) I had realized that one of the places the ideas of the Physics Project should apply was to the foundations of mathematics, and to metamathematics. And now the responsibility had fallen on us to do this.

Physics 111

Physics Computer Biology Mathematics 111

Computing Education Research Blog

JULY 12, 2021

Computational thinking and modeling which describes how data and algorithms are used to construct digital solutions and artifacts. computer systems, networking) used to construct digital solutions and artifacts. Technological knowledge and skills which describes the tools (e.g., programming languages) and infrastructures (e.g.,

Computer Science 40

Computer Science Computer Curriculum Sciences 40

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. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Physics 65

Physics Sciences Science 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. In the mathematical paradigm one imagines having a mathematical equation and then separately somehow solving it.

Sciences 60

Sciences Science Physics Mathematics 60

PCS Edventures

SEPTEMBER 22, 2021

While sciences and mathematics may take center stage, literacy skills have always been waiting in the wings, ready to make their debut. Mathematics and Literacy. Well, in recent years, you may have noticed an increased focus on supporting scientific thinking with written and oral arguments. We can’t forget literacy in math!

Mathematics 52

Mathematics Engineering Argumentation Sciences 52

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

JANUARY 9, 2024

Then for each function (or other construct in the language) there are pages that explain the function, with extensive examples. One new construct added in Version 13.1 —and And now there’s a way to specify that, using Threaded : In a sense, Threaded is part of a new wave of symbolic constructs that have “ambient effects” on lists.

Computer 96

Computer Calculus Construction Accessibility 96

The Science Penguin

AUGUST 11, 2023

The DCI states, “Support an argument that plants get the materials they need for growth chiefly from air and water.” At the end of the unit, students construct explanations using evidence collected from the activities, investigations, and readings to answer this question: How can we use maps to reduce the impact of natural disasters?

Critical Thinking 52

Critical Thinking Argumentation Engineering Science 52

Wisconsin Science and STEM Education

SEPTEMBER 7, 2018

The second target connects to several science and engineering practices, with clear mathematical connections. It’s notable that their system aims to connect to literacy and mathematics learning while focusing on meaningful science practices. Supports conclusions with logical arguments. Collects, interprets, and applies data.

Argumentation 40

Argumentation Mathematics Data analysis Sciences 40

Stephen Wolfram

FEBRUARY 2, 2023

It’s a story I’ve told elsewhere , but one of the important elements for our purposes here is that in designing the system I called SMP (for “Symbolic Manipulation Program”) I ended up digging deeply into the foundations of computation, and its connections to areas like mathematical logic.

Physics 94

Physics Computer Mathematics Sciences 94

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. I love mathematics, problem solving and logical thinking. This goes hand in hand with ethical thinking.

Biology 84

Biology Agriculture Engineering Critical Thinking 84

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

Wisconsin Science and STEM Education

DECEMBER 4, 2018

. · Investigating and Building Evidence – This category combines the practices of Planning and Carrying Out Investigations and Analyzing and Interpreting Data, with Using Mathematics and Computational Thinking. Further, they employ mathematical thinking as they design plans for collecting quantitative data and make sense of data sets.

Sciences 40

Sciences Science Argumentation Energy 40

Vivify Stem

NOVEMBER 22, 2022

Practices include: Asking questions (science) / Defining problems (engineering) Developing and using models Planning and carrying out investigations Analyzing and interpreting data Using mathematical and computation thinking Construction Explanations (science) / Designing Solutions (engineering) Engaging in Arguments from evidence Obtaining and evaluating (..)

Engineering 52

Engineering Sciences Science Earth science 52

Robert Talbert, Ph.D.

APRIL 15, 2022

Those assessments can take on various forms, and in well-constructed courses they do have varying forms, corresponding to different levels of Bloom's Taxonomy. An argument for traditional grading goes like this: Sure, a single assessment might have a grade on it that doesn't accurately reflect student understanding.

Academic Standards 52

Academic Standards Communications Calculus Algebra 52

PHYSICS! BLOG!

JULY 6, 2017

Experimentally, graphically, and mathematically determine the mass, volume, and density of a substance. Explain energy ideas in words and construct arguments that use diagrams as evidence. Represent substances and changes in substances at the particle level that are consistent with the Law of Conservation of Mass.

Chemistry 40

Chemistry Energy Physics Math 40

Stephen Wolfram

MAY 17, 2021

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. But in the 1980s a complicated cellular automaton was constructed that it was possible to prove would not show such behavior. But it turns out that this isn’t true.

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

AUGUST 22, 2023

He was going for what he saw as the big prize: using them to “construct the universe”. It explains that III has four divisions: Mathematical and Programming Services, Behavioral Science, Operations, and “New York”. So what happened is Marvin [Minsky] and I basically fleshed out the idea of a mathematical thing.

Computer 69

Computer Physics Sciences Science 69

Stephen Wolfram

MAY 20, 2021

Having this as a single function makes it easier to use in functional programming constructs like this: &#10005. But sometimes it’s much more convenient to get the subgraph (and in fact in the formalism of our Physics Project that subgraph—that we view as a “ geodesic ball ”—is a rather central construct). So in Version 12.3

Computer 52

Computer Construction Physics Technology 52

Stephen Wolfram

JUNE 29, 2022

we have a new symbolic construct, Threaded , that effectively allows you to easily generalize listability. You can give Threaded as an argument to any listable function, not just Plus and Times : &#10005. we’re adding SymmetricDifference : find elements that (in the 2-argument case) are in one list or the other, but not both.

Calculus 113

Calculus Construction Computer Argumentation 113