Robert Talbert, Ph.D.

FEBRUARY 10, 2023

The computer is a tool for studying mathematical ideas in the same sense that a microscope is for studying biology and a telescope is for studying astronomy. Can anyone seriously imagine banning microscope technology from the biology major, on the argument that biology is a more pure discipline without the technology?

Mathematics 52

Mathematics Computer Algebra Calculus 52

Futurum

FEBRUARY 2, 2023

Pathway from school to environmental geography • Ben recommends studying an undergraduate degree in Earth and environmental science, biology, chemistry or mathematics. If you are more interested in social science, consider studying this as an undergraduate degree and environmental geography as a postgraduate degree. •

Geography 98

Geography Research Research Science 98

Wisconsin Science and STEM Education

SEPTEMBER 7, 2018

Supports conclusions with logical arguments. Supports conclusions with logical arguments. Demonstrates understanding of science concepts. Collects, interprets, and applies data. Grades 4-5 1. Demonstrates understanding of science concepts. Collects, interprets, and applies data. Grades 6-8 1.

Argumentation 40

Argumentation Mathematics Data analysis Sciences 40

Futurum

SEPTEMBER 1, 2022

Through evaluating evidence and mapping out arguments, students can practice this important aspect of scientific communication. Bess says that her broad scientific background in geology, chemistry and biology has helped her career, but notes that ice core scientists can come from a range of backgrounds, including maths and physics.

Geology 52

Geology Energy Communications Research 52

STEM Education Shopping

AUGUST 27, 2023

Critical thinking enables me to analyze information, evaluate arguments, and make informed decisions. For example, during a biology course, conducting experiments allowed me to apply the theoretical knowledge gained from lectures and textbooks. One key element of integrating theory and practice is hands-on experience.

Critical Thinking 52

Critical Thinking Learning Problem Solving Communications 52

Stephen Wolfram

JANUARY 9, 2024

The function Map takes a function f and “maps it” over a list: Comap does the “mathematically co-” version of this, taking a list of functions and “comapping” them onto a single argument: Why is this useful? But we wanted to be able to compute hundreds of different functions to arbitrary precision for any complex values of their arguments.

Computer 100

Computer Calculus Construction Accessibility 100

Stephen Wolfram

SEPTEMBER 9, 2021

Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Chemistry / Molecular Biology. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. There are many.

Physics 67

Physics Science Sciences Mathematics 67

Stephen Wolfram

SEPTEMBER 9, 2021

Events are like functions, whose “arguments” are incoming tokens, and whose output is one or more outgoing tokens. Chemistry / Molecular Biology. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. There are many.

Science 61

Science Sciences Physics Mathematics 61

Stephen Wolfram

NOVEMBER 10, 2021

The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. And we can trace the argument for this to the Principle of Computational Equivalence. But that’s not all there is to it.

Physics 121

Physics Mathematics Computer Construction 121

ED Surge

MAY 7, 2024

The biology teacher went to the mother — and she didn’t even have to use the report — and said that it doesn’t seem like the student wrote it. And we ran it through a [linguistic fingerprint tool] and it produced a report. The report confirmed what we thought that it was unlikely to have been written by that student.

Communications 334

Communications Argumentation Government Biology 334

Stephen Wolfram

AUGUST 29, 2024

The fall of 2021 involved really leaning into the new multicomputational paradigm , among other things giving a long list of where it might apply : metamathematics, chemistry, molecular biology, evolutionary biology, neuroscience, immunology, linguistics, economics, machine learning, distributed computing.

Physics 114

Physics Computer Biology Mathematics 114

Futurum

NOVEMBER 29, 2022

One of the most challenging problems in biology is understanding what motivates animals to perform such behaviours. Philosophers also identify the norms and methods of good reasoning, such as the logical structures of arguments that support drawing true conclusions and avoiding false ones. Let the wisdom of a good mentor guide you.”.

Agriculture 98

Agriculture Biology Research Research 98

Futurum

SEPTEMBER 12, 2023

At the University of Pittsburgh at Greensburg in the US, biologists Barbara Barnhart and Dr Olivia Long are using their Science Seminar programme to ease this transition for first year students studying biology, chemistry and biochemistry degrees. What do students learn from studying this?

Biology 81

Biology STEM Chemistry Critical Thinking 81

Stephen Wolfram

MAY 17, 2021

In the basic definition of a standard cellular automaton, the rule “takes its arguments” in a definite order. RandomGraph[{20, 40}, EdgeStyle -> Gray, VertexStyle -> Table[i -> (RandomInteger[] /. {0 0 -> Hue[0.15, 0.72, 1], 1 -> Hue[0.98, 1, 0.8200000000000001]}), {i, 20}], VertexSize -> 5].

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

JUNE 29, 2022

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. How should we then multiply each element by {1,-1} ? We could do this with: &#10005. In Version 13.1

Calculus 116

Calculus Construction Computer Argumentation 116

Stephen Wolfram

MARCH 5, 2024

of what’s now Wolfram Language —we were trying to develop algorithms to compute hundreds of mathematical special functions over very broad ranges of arguments. Back in 1987—as part of building Version 1.0 In the past, people had painstakingly computed series approximations for specific cases. So why does this work? Mostly we don’t know.

Science 120

Science Sciences Computer Mathematics 120

Stephen Wolfram

JANUARY 31, 2023

But in 1798 Benjamin Thompson (Count Rumford) (1753–1814) measured the heat produced by the mechanical process of boring a cannon, and began to make the argument that, in contradiction to the caloric theory, there was actually some kind of correspondence between mechanical energy and amount of heat.

Energy 91

Energy Physics Argumentation Mathematics 91

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”. This argument is quite rough, but it captures the essence of what’s going on. The Mechanoidal Phase and Bulk Molecular Biology The Second Law has long had an uneasy relationship with biology.

Computer 93

Computer Energy Physics Construction 93

Stephen Wolfram

FEBRUARY 2, 2023

I think Yves Pomeau already had a theoretical argument for this, but as far as I was concerned, it was (at least at first) just a “next thing to try”. People had discussed reaction-diffusion patterns as examples of structure being formed “away from equilibrium”. What kinds of models could realistically be made for these?

Physics 96

Physics Computer Mathematics Science 96

STEM Minds

APRIL 27, 2022

Moral arguments aside, there are also several practical reasons as to why it is in humanity’s best interest to have strong biodiversity. Driving one million species to extinction through our own actions, especially when there are measures we can undertake to prevent this loss, carries a great moral and ethical weight.

Argumentation 52

Argumentation Biology STEM Learning 52

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. and zero arguments: α[ ]. Three that I wasn’t sure about were biology, physics and mathematics. &#10005. &#10005.

Mathematics 119

Mathematics Physics Computer Algebra 119

Futurum

MAY 10, 2023

Dr Lisa Doner and her team from Plymouth State University in the US have developed a programme full of practical activities that allow their students to develop the skills needed for a successful geoscience career. This is often seen as an entirely biological problem, but geoscience elements are also at work.

Geology 52

Geology Critical Thinking Research Research 52

Futurum

FEBRUARY 9, 2023

Pathway from school to forest ecology • Becoming a forest ecologist starts with studying fundamental sciences like biology and chemistry in school. It is inspiring to see the research mainstreamed and the arguments of “is climate changing?” If you feel inspired by any of these questions, forest science might be for you!

Research 78

Research Research Science Sciences 78

STEMe

MARCH 31, 2024

Because of the general skepticism, the argument about whether AI could have a negative or positive impact continues. To solve this problem, the researchers say that the next step is to incorporate other types of information, such as using text and images to show social connections.

Artificial Intelligence 52

Artificial Intelligence Computer Science Architecture Argumentation 52

Stephen Wolfram

AUGUST 22, 2023

Richard Feynman and I would get into very fierce arguments. He relishes calling his parents dopes, but aside from arguments about subjects like how late he should be able to hang out with his buddies, its clear that he doesn’t think we’re dopes. It’s just my nature. Some glide through that period of life without hassle.

Computer 70

Computer Physics Sciences Science 70

Stephen Wolfram

DECEMBER 5, 2024

The last pattern is a bit of an exception; as can also happen in biology, this is a case where for once theres a mechanism in evidence that we can understand.) This is a follow-on to Why Does Biological Evolution Work? A Minimal Model for Biological Evolution and Other Adaptive Processes [May 3, 2024]. So what in the end is going on?

Biology 111

Biology Computer Achievement Physics 111