Stephen Wolfram

MARCH 7, 2022

And in what follows we’ll see the great power that arises from using this to combine the achievements and intuitions of physics and mathematics—and how this lets us think about new “general laws of mathematics”, and view the ultimate foundations of mathematics in a different light. So how about logic, or, more specifically Boolean algebra ?

Mathematics 120

Mathematics Physics Computer Algebra 120

Stephen Wolfram

MARCH 5, 2024

In 2000 I was interested in what the simplest possible axiom system for logic (Boolean algebra) might be. Here’s how the “loss” evolves (over the course of 100 generations) for a collection of paths: And what we see is that there’s only one “winner” here that achieves zero loss; on all the other paths, evolution “gets stuck”.

Science 122

Science Sciences Computer Mathematics 122

Stephen Wolfram

MAY 17, 2021

Traditional blockchains achieve consensus through what amounts to a centralized mechanism (even though there are multiple “decentralized” copies of the blockchain that is produced). In both these cases, the rule successfully achieves “global consensus”. So what other cellular automaton rules achieve consensus like this?

Computer 52

Computer Achievement Mathematics Physics 52

Stephen Wolfram

DECEMBER 11, 2023

But in observer theory what we want to do is just characterize the equivalencing that’s achieved. Sometimes then the crucial step of equivalencing different detailed inputs is achieved by simple “numerical aggregation”, most often by accumulation of objects (atoms, raindrops, etc.) or physical effects (forces, currents, etc.).

Physics 120

Physics Mathematics Computer Communications 120

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Chemistry / Molecular Biology. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. There are many.

Physics 64

Physics Science Sciences Mathematics 64

Stephen Wolfram

SEPTEMBER 9, 2021

Part of what this achieves is to generalize beyond traditional mathematics the kind of constructs that can appear in models. Chemistry / Molecular Biology. But in thinking about molecular computing it may be crucial—and perhaps it’s also necessary for understanding molecular biology. There are many.

Science 64

Science Sciences Physics Mathematics 64

Stephen Wolfram

NOVEMBER 10, 2021

The global structures of metamathematics , economics , linguistics and evolutionary biology seem likely to provide examples—and in each case we can expect that at the core is the ruliad, with its unique structure. For sure, the “sensory apparatus” that we effectively use is different in different cases. But that’s not all there is to it.

Physics 121

Physics Mathematics Computer Construction 121

Stephen Wolfram

MAY 16, 2022

My stated goal at the beginning of A New Kind of Science was to go beyond the mathematical paradigm, and that’s exactly what was achieved. All of these ideas rest on what was achieved in A New Kind of Science but now go significantly beyond it. In traditional chemistry, things like this generally aren’t “observed”.

Science 63

Science Sciences Mathematics Physics 63

Stephen Wolfram

AUGUST 22, 2023

Ed was never officially a “test pilot”, but he told me stories about figuring out how to take his plane higher than anyone else—and achieving weightlessness by flying his plane in a perfect free-fall trajectory by maintaining an eraser floating in midair in front of him. Then McCarthy started to explain ways a computer could do algebra.

Computer 67

Computer Physics Science Sciences 67