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

NOVEMBER 10, 2021

It’s yet another surprising construct that’s arisen from our Physics Project. And it’s one that I think has extremely deep implications—both in science and beyond. For integers, the obvious notion of equivalence is numerical equality. In some ways it’s a bit like our efforts to construct the ruliad.

Physics 122

Physics Mathematics Computer Construction 122

Stephen Wolfram

MAY 25, 2021

Presumably it’s that we can sample space without having to think about time, or in other words, that we can consistently construct a stable notion of space. No doubt there’ll at least be some “natural-science-like” characterizations of what’s going on. Will there still be “human-level descriptions” that involve numbers?

Mathematics 53

Mathematics Physics Computer Algebra 53