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After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of...
“[Despite] Considerable Effort… [It Proved] Intractable” In the early years of the twentieth century it looked as if—if only the right approach could be found—all of mathematics might somehow...
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What Is Consciousness? Some New Perspectives from Our Physics Project
“What about Consciousness?” For years I’ve batted it away. I’ll be talking about my discoveries in the computational universe, and computational irreducibility, and my Principle of Computational...
View ArticleZX-Calculus and Extended Wolfram Model Systems II: Fast Diagrammatic...
This article presents a novel algorithmic methodology for performing automated diagrammatic deductions over combinatorial structures, using a combination of modified equational theorem-proving...
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The Wolfram Physics Project: A One-Year Update
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Why Does the Universe Exist? Some Perspectives from Our Physics Project
What Is Formal, and What Is Actualized? Why does the universe exist? Why is there something rather than nothing? These are old and fundamental questions that one might think would be firmly outside...
View ArticleFast Automated Reasoning over String Diagrams using Multiway Causal Structure
We introduce an intuitive algorithmic methodology for enacting automated rewriting of string diagrams within a general double-pushout (DPO) framework, in which the sequence of rewrites is chosen in...
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The Problem of Distributed Consensus
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View ArticleHomotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold...
We investigate the algebraic and compositional properties of multiway (non-deterministic) abstract rewriting systems, which are the archetypical structures underlying the formalism of the so-called...
View ArticleHow Inevitable Is the Concept of Numbers?
Based on a talk at Numerous Numerosity: An interdisciplinary meeting on the notions of cardinality, ordinality and arithmetic across the sciences. Everyone Has to Have Numbers… Don’t They? The aliens...
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Even beyond Physics: Introducing Multicomputation as a Fourth General...
The Path to a New Paradigm One might have thought it was already exciting enough for our Physics Project to be showing a path to a fundamental theory of physics and a fundamental description of how...
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Multicomputation with Numbers: The Case of Simple Multiway Systems
table.InCell { margin-left: -0.27rem; } A Minimal Example of Multicomputation Multicomputation is an important new paradigm, but one that can be quite difficult to understand. Here my goal is to...
View ArticlePregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types
How do spaces emerge from pregeometric discrete building blocks governed by computational rules? To address this, we investigate non-deterministic rewriting systems (multiway systems) of the Wolfram...
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The Concept of the Ruliad
The Entangled Limit of Everything I call it the ruliad. Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in...
View ArticleThe Physicalization of Metamathematics and Its Implications for the...
Mathematics and Physics Have the Same Foundations One of the many surprising (and to me, unexpected) implications of our Physics Project is its suggestion of a very deep correspondence between the...
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On the Concept of Motion
How Is It That Things Can Move? It seems like the kind of question that might have been hotly debated by ancient philosophers, but would have been settled long ago: how is it that things can move? And...
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Twenty Years Later: The Surprising Greater Implications of A New Kind of Science
From the Foundations Laid by A New Kind of Science When A New Kind of Science was published twenty years ago I thought what it had to say was important. But what's become increasingly...
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Multicomputational Irreducibility
Multicomputation is the cornerstone of much of the basic science that my teammates and I are doing with Stephen Wolfram. We see an opportunity to metamodel many areas of applied science using the...
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Games and Puzzles as Multicomputational Systems
Humanizing Multicomputational Processes Multicomputation is one of the core ideas of the Wolfram Physics Project—and in particular is at the heart of our emerging understanding of quantum mechanics....
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How Did We Get Here? The Tangled History of the Second Law of Thermodynamics
The Basic Arc of the Story As I’ve explained elsewhere, I think I now finally understand the Second Law of thermodynamics. But it’s a new understanding, and to get to it I’ve had to overcome a certain...
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