Stephen Wolfram

JANUARY 31, 2023

But he had a second hypothesis too—based, he said, on the ideas of “that most ingenious gentleman, Monsieur Descartes”: that instead air consists of “flexible particles” that are “so whirled around” that “each corpuscle endeavors to beat off all others”.

Energy 88

Energy Physics Argumentation Mathematics 88

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. Now we can use the path function to make a “spiralling” tour video: College Calculus. In Version 13.1

Calculus 114

Calculus Construction Computer Argumentation 114

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 65

Physics Science Sciences Mathematics 65

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 64

Science Sciences Physics Mathematics 64

Stephen Wolfram

JANUARY 9, 2024

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. Another advance has to do with expanding the range of “pre-packaged” calculus operations.

Computer 102

Computer Calculus Construction Accessibility 102

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[ ]. But if we very roughly imagine that half of every proof is “flexible”, we’d end up with things like variants.

Mathematics 120

Mathematics Physics Computer Algebra 120

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”. 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.

Computer 92

Computer Energy Physics Construction 92