Stephen Wolfram

SEPTEMBER 9, 2021

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Many would say that modern exact science was launched in the 1600s with the introduction of what we can call the “ mathematical paradigm ”: the idea that things in the world can be described by mathematical equations—and that their behavior can be determined by finding solutions to these equations.

Science 64

Science Sciences Physics Mathematics 64

Futurum

FEBRUARY 9, 2023

Simulation and statistical models (SSMs) are types of mathematical models used in ecology. 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?”

Research 78

Research Research Science Sciences 78

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. Chemistry as Rule Application: Symbolic Pattern Reactions. We could do this with: &#10005.

Calculus 114

Calculus Construction Computer Argumentation 114

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 95

Physics Computer Mathematics Science 95

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? You need to be able to easily define mathematically complicated boundary conditions. are Comap and ComapApply.

Computer 102

Computer Calculus Construction Accessibility 102

Stephen Wolfram

AUGUST 22, 2023

In 2015 Ed told me a nice story about his time at Caltech: In 1952–53, I was a student in Linus Pauling’s class where he lectured Freshman Chemistry at Caltech. It explains that III has four divisions: Mathematical and Programming Services, Behavioral Science, Operations, and “New York”. And it was agreed that we would do it.

Computer 68

Computer Physics Science Sciences 68

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”. How does one tie all this down with rigorous, mathematical-style proofs? 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 92

Computer Energy Physics Construction 92