Remove Algebra Remove Construction Remove Elementary Remove Natural Sciences
article thumbnail

The Physicalization of Metamathematics and Its Implications for the Foundations of Mathematics

Stephen Wolfram

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.

article thumbnail

How Inevitable Is the Concept of Numbers?

Stephen Wolfram

Instead, what happens is that the universe evolves by virtue of lots of elementary updating events happening throughout the network. 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. But there is a subtlety here.

article thumbnail

The Concept of the Ruliad

Stephen Wolfram

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. In some ways it’s a bit like our efforts to construct the ruliad. The whole continuum of all real numbers is “from the outside” in many ways a simple construct.

Physics 122