Institute Output
SetReplace
Max Piskunov
SetReplace is an open‑source Wolfram Language package that executes set‑substitution systems. It evolves user‑defined rules from an initial state and returns structured objects that expose events, causal dependencies, and branching dynamics for analysis and visualization.
Hypergraph rewriting and Causal structure of $\lambda$-calculus
Utkarsh Bajaj
Hypergraph rewriting is studied through categorical frameworks to establish foundational concepts of events and causality in graph rewriting systems. Novel concepts are introduced within double-pushout rewriting in adhesive categories. An algorithm is constructed to determine causal relations between events during λ-calculus evaluation, with extensions developed for arbitrary λ-expressions.
Computational General Relativity in the Wolfram Language using Gravitas II: ADM Formalism and Numerical Relativity
Jonathan Gorard
This paper introduces the Gravitas computational general relativity framework's numerical subsystem, emphasizing its ability to perform 3 + 1 spacetime decompositions via the ADM formalism, handle complex simulations of gravitational phenomena like binary black hole mergers, and leverage adaptive refinement algorithms based on hypergraph rewriting within the Wolfram Language.
The Concept of the Ruliad
Stephen Wolfram
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 all possible ways. 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.
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”.
The Wolfram Physics Project: A One-Year Update
Stephen Wolfram
When we launched the Wolfram Physics Project a year ago today, I was fairly certain that—to my great surprise—we’d finally found a path to a truly fundamental theory of physics, and it was beautiful. A year later it’s looking even better. We’ve been steadily understanding more and more about the structure and implications of our models—and they continue to fit beautifully with what we already know about physics, particularly connecting with some of the most elegant existing approaches, strengthening and extending them, and involving the communities that have developed them.
Exploring Rulial Space: The Case of Turing Machines
Stephen Wolfram
Let’s say we find a rule that reproduces physics. A big question would then be: “Why this rule, and not another?” I think there’s a very elegant potential answer to this question, that uses what we’re calling rule space relativity—and that essentially says that there isn’t just one rule: actually all possible rules are being used, but we’re basically picking a reference frame that makes us attribute what we see to some particular rule. In other words, our description of the universe is a sense of our making, and there can be many other—potentially utterly incoherent—descriptions, etc.
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.
How We Got Here: The Backstory of the Wolfram Physics Project
Stephen Wolfram
I’ve been saying it for decades: “Someday I’m going to mount a serious effort to find the fundamental theory of physics.” Well, I’m thrilled that today “someday” has come, and we’re launching the Wolfram Physics Project. And getting ready to launch this project over the past few months might be the single most intellectually exciting time I’ve ever had. So many things I’d wondered about for so long getting solved. So many exciting moments of “Surely it can’t be that simple?” And the dawning realization, “Oh my gosh, it’s actually going to work!”
Finally We May Have a Path to the Fundamental Theory of Physics… and It’s Beautiful
Stephen Wolfram
It’s unexpected, surprising—and for me incredibly exciting. To be fair, at some level I’ve been working towards this for nearly 50 years. But it’s just in the last few months that it’s finally come together. And it’s much more wonderful, and beautiful, than I’d ever imagined.