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.

Science 64

Science Sciences Physics Mathematics 64

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 120

Mathematics Physics Computer Algebra 120

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 102

Computer Calculus Construction Accessibility 102

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 122

Physics Mathematics Computer Construction 122

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 92

Computer Energy Physics Construction 92

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. What kinds of models could realistically be made for these?

Physics 95

Physics Computer Mathematics Science 95

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”. The next section is entitled “The Design of a Simulator”, and discusses how such hardware could be constructed, concluding that a 1000×1000×1000 3D grid of cells could be built for $50M (or nearly half a billion dollars today). It’s just my nature.

Computer 68

Computer Physics Science Sciences 68