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What Ultimately Is There? Metaphysics and the Ruliad
Stephen Wolfram
“What ultimately is there?” has always been seen as a fundamental—if thorny—question for philosophy, or perhaps theology. But despite a couple of millennia of discussion, I think it’s fair to say that only modest progress has been made with it. But maybe, just maybe, this is the moment where that’s going to change—and on the basis of surprising new ideas and new results from our latest efforts in science, it’s finally going to be possible to make real progress, and in the end to build what amounts to a formal, scientific approach to metaphysics.
P vs. NP and the Difficulty of Computation: A Ruliological Approach
Stephen Wolfram
“Could there be a faster program for that?” It’s a fundamental type of question in theoretical computer science. But except in special cases, such a question has proved fiendishly difficult to answer. And, for example, in half a century, almost no progress has been made even on the rather coarse (though very famous) P vs. NP question—essentially of whether for any nondeterministic program there will always be a deterministic one that is as fast. From a purely theoretical point of view, it’s never been very clear how to even start addressing such a question. But what if one were to look at the question empirically, say in effect just by enumerating possible programs and explicitly seeing how fast they are, etc.?
Quantum Operators From Wolfram Model Multiway Systems
Furkan Semih Dündar, Xerxes D. Arsiwalla, Hatem Elshatlawy
Using Wolfram Model multiway rewriting systems we have found that by using multiway systems one can construct representations of quantum circuits, showing that one can encode the Hadamard gate, the π/8 gate and the CNOT using multiway rewriting systems. This suggests the possibility of universal quantum computation using multiway rewriting.
Quantum Gates from Wolfram Model Multiway Rewriting Systems
Furkan Semih Dündar, Xerxes D. Arsiwalla, Hatem Elshatlawy
We show how representations of finite-dimensional quantum operators can be constructed using nondeterministic rewriting systems. In particular, we investigate Wolfram model multiway rewriting systems based on string substitutions.
What’s Special about Life? Bulk Orchestration and the Rulial Ensemble in Biology and Beyond
Stephen Wolfram
It’s a key feature of living systems, perhaps even in some ways the key feature: that even right down to a molecular scale, things are orchestrated. Molecules (or at least large ones) don’t just move around randomly, like in a liquid or a gel. Instead, what molecular biology has discovered is that there are endless active mechanisms that in effect orchestrate what even individual molecules in living systems do. But what is the result of all that orchestration? And could there perhaps be a general characterization of what happens in systems that exhibit such “bulk orchestration”?
The Ruliology of Lambdas
Stephen Wolfram
It’s a story of pure, abstract computation. In fact, historically, one of the very first. But even though it’s something I for one have used in practice for nearly half a century, it’s not something that in all my years of exploring simple computational systems and ruliology I’ve ever specifically studied. And, yes, it involves some fiddly technical details. But it’ll turn out that lambdas—like so many systems I’ve explored—have a rich ruliology, made particularly significant by their connection to practical computing.
“I Have a Theory Too”: The Challenge and Opportunity of Avocational Science
Stephen Wolfram
Most physicists term people who send such theories “crackpots”, and either discard their missives or send back derisive responses. I’ve never felt like that was the right thing to do. Somehow I’ve always felt as if there has to be a way to channel that interest and effort into something that would be constructive and fulfilling for all concerned. And maybe, just maybe, I now have at least one idea in that direction.
A Functorial Perspective on (Multi)computational Irreducibility
Jonathan Gorard
This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding category of (1-dimensional) cobordisms.
Games and Puzzles as Multicomputational Systems
Stephen Wolfram
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. But how can one get an intuition for what is initially the rather abstract idea of multicomputation? A good approach, I believe, is to see it in action in familiar systems and situations. And I explore here what seems like a particularly good example: games and puzzles.
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.
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”.
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.