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On the Nature of Time
Stephen Wolfram
Time is a central feature of human experience. But what actually is it? In traditional scientific accounts it’s often represented as some kind of coordinate much like space (though a coordinate that for some reason is always systematically increasing for us). But while this may be a useful mathematical description, it’s not telling us anything about what time in a sense “intrinsically is”.
Observer Theory
Stephen Wolfram
We call it perception. We call it measurement. We call it analysis. But in the end it’s about how we take the world as it is, and derive from it the impression of it that we have in our minds.
Aggregation and Tiling as Multicomputational Processes
Stephen Wolfram
Multiway systems have a central role in our Physics Project, particularly in connection with quantum mechanics. But what’s now emerging is that multiway systems in fact serve as a quite general foundation for a whole new “multicomputational” paradigm for modeling.
Expression Evaluation and Fundamental Physics
Stephen Wolfram
It is shown that way the Wolfram Language rewrites and evaluates expressions mirrors the universe’s own evolution: both proceed through discrete events linked by causal relationships, form “spacetime-like” structures and branch into multiway histories analogous to quantum superpositions.
Multicomputation with Numbers: The Case of Simple Multiway Systems
Stephen Wolfram
Multicomputation is an important new paradigm, but one that can be quite difficult to understand. Here my goal is to discuss a minimal example: multiway systems based on numbers. Many general multicomputational phenomena will show up here in simple forms (though others will not). And the involvement of numbers will often allow us to make immediate use of traditional mathematical methods.
Multicomputation: A Fourth Paradigm for Theoretical Science
Stephen Wolfram
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 our physical universe works. But what I’ve increasingly been realizing is that actually it’s showing us something even bigger and deeper: a whole fundamentally new paradigm for making models and in general for doing theoretical science. And I fully expect that this new paradigm will give us ways to address a remarkable range of longstanding central problems in all sorts of areas of science—as well as suggesting whole new areas and new directions to pursue.
The Problem of Distributed Consensus
Stephen Wolfram
In any decentralized system with computers, people, databases, measuring devices or anything else one can end up with different values or results at different “nodes”. But for all sorts of reasons one often wants to agree on a single “consensus” value, that one can for example use to “make a decision and go on to the next step”.
Fast Automated Reasoning over String Diagrams using Multiway Causal Structure
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
ZX-Calculus and Extended Wolfram Model Systems II: Fast Diagrammatic Reasoning with an Application to Quantum Circuit Simplification
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
After 100 Years, Can We Finally Crack Post’s Problem of Tag? A Story of Computational Irreducibility, and More
Stephen Wolfram
For Post, the failure to crack his system derailed his whole intellectual worldview. For me now, the failure to crack Post’s system in a sense just bolsters my worldview—providing yet more indication of the strength and ubiquity of computational irreducibility and the Principle of Computational Equivalence.
Multiway Turing Machines
Stephen Wolfram
Over the years I’ve studied the simplest ordinary Turing machines quite a bit, but I’ve barely looked at multiway Turing machines (also known as nondeterministic Turing machines or NDTMs). Recently, though, I realized that multiway Turing machines can be thought of as “maximally minimal” models both of concurrent computing and of the way we think about quantum mechanics in our Physics Project. So now this piece is my attempt to “do the obvious explorations” of multiway Turing machines.
ZX-Calculus and Extended Hypergraph Rewriting Systems I: A Multiway Approach to Categorical Quantum Information Theory
Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
Faster than Light in Our Model of Physics: Some Preliminary Thoughts
Stephen Wolfram
“So you think you have a fundamental theory of physics. Well, then tell us if warp drive is possible!” Despite the hopes and assumptions of science fiction, real physics has for at least a century almost universally assumed that no genuine effect can ever propagate through physical space any faster than light. But is this actually true? We’re now in a position to analyze this in the context of our model for fundamental physics. And I’ll say at the outset that it’s a subtle and complicated question, and I don’t know the full answer yet.
Event Horizons, Singularities and Other Exotic Spacetime Phenomena
Stephen Wolfram
In our models, space emerges as the large-scale limit of our spatial hypergraph, while spacetime effectively emerges as the large-scale limit of the causal graph that represents causal relationships between updating events in the spatial hypergraph. An important result is that (subject to various assumptions) there is a continuum limit in which the emergent spacetime follows Einstein’s equations from general relativity.