Stephen Wolfram

SEPTEMBER 23, 2021

But it really wasn’t physics, or computer science, or math, or biology, or economics, or any known field. The idea not of solving equations, but instead of setting up computational rules that could be explicitly run to represent and reproduce things in the world. What is that science? But at least it would have a home.

Computer 55

Computer Mathematics Science Sciences 55

Stephen Wolfram

NOVEMBER 10, 2021

Because it implies that whatever “computational parametrization” or “computational description language” one uses for the ruliad, one will almost always get something that can be viewed as “computationally equivalent”. But what about other models of computation—like cellular automata or register machines or lambda calculus?

Physics 116

Physics Mathematics Computer Construction 116

Stephen Wolfram

FEBRUARY 14, 2023

It’s not obvious that it would be feasible to find the path of the steepest descent on the “weight landscape” But calculus comes to the rescue. As we mentioned above, one can always think of a neural net as computing a mathematical function—that depends on its inputs, and its weights.

Computer 145

Computer Architecture Mathematics Construction 145

Stephen Wolfram

MARCH 7, 2022

And if we’re going to make a “general theory of mathematics” a first step is to do something like we’d typically do in natural science, and try to “drill down” to find a uniform underlying model—or at least representation—for all of them. From a computer science perspective, we can think of it as being like a type hierarchy.

Mathematics 114

Mathematics Physics Computer Algebra 114