The Last Theory

Here’s a masterclass from Jonathan Gorard.One of the most compelling results to come out of the Wolfram Physics is Jonathan’s derivation of the Einstein equations from the hypergraph.Whenever I hear anyone criticize the Wolfram model for bearing no relation to reality, I tell them this: Jonathan Gorard has proved that general relativity can be derived from the hypergraph.In this excerpt from our conversation, Jonathan describes how making just three reasonable assumptions – causal invariance, asymptotic dimension preservation and weak ergodicity – allowed him to derive the vacuum Einstein equations from the Wolfram model.In other words, the structure of space-time in the absence of matter more or less falls out of the hypergraph.And making one further assumption – that particles can be treated as localized topological obstructions – allowed Jonathan to derive the non-vacuum Einstein equations from the Wolfram model.In other words, the structure of space-time in the presence of matter, too, falls out of the hypergraph.It’s difficult to overstate the importance of this result.At the very least, we can say that the Wolfram model is consistent with general relativity.To state it more strongly: we no longer need to take general relativity as a given; instead, we can derive it from Wolfram Physics.—Jonathan’s seminal paper on how to derive general relativity Some Relativistic and Gravitational Properties of the Wolfram Model; also published in Complex Systems Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project People mentioned by JonathanAlfred GrayResearch mentioned by Jonathan The volume of a small geodesic ball of a Riemannian manifold by Alfred Gray Tubes by Alfred Gray Concepts mentioned by Jonathan Hausdorff dimension Geodesic balls, tubes & cones Ricci scalar curvature Ricci curvature tensor Einstein equations Einstein–Hilbert action Relativistic Lagrangian density Causal graph Tensor rank Trace From A Project to find the Fundamental Theory of Physics by Stephen Wolfram: Dimension Curvature Images Spinning and chargend black hole with accretion disk by Simon Tyran, Vienna (Симон Тыран) licensed under CC BY-SA 4.0 Альфред Грэй в Греции by AlionaKo licensed under CC BY-SA 3.0 —The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

Here’s the first of two crucial excerpts from my conversation with Jonathan Gorard.The core idea of Wolfram Physics is that we can model the universe as a hypergraph. If we want this idea to be taken seriously, we’re going to have to derive physics from the hypergraph.The twin pillars of physics, as we know it, are quantum mechanics and general relativity.In this episode, Jonathan explains how quantum mechanics can be derived from the Wolfram model, indeed, how quantum mechanics unexpectedly fell out of the model.It’s a fascinating story.We start with the role of the observer. According to Jonathan, it turns out not to be necessary to narrow our focus to only causally invariant rules.Why not? Because macroscopic observers like ourselves impose causal invariance through our coarse-graining of the hypergraph. In other words, by squinting at the universe, seeing only its large-scale features and glossing over the finer details, we reduce multiple paths through the multiway graph to a single timeline, and, in the process, impose causal invariance.Jonathan goes on to explain that this coarse-graining can be modelled with completion rules. These are fake rules, similar to the true rules of Wolfram Physics, but posited solely to model the coarse-graining of the hypergraph by the observer.And here’s the thing. According to Jonathan, these completion rules are formally equivalent to the collapse of the wavefunction in quantum mechanics. In other words, we finally have an explanation for how the observer causes the collapse of the wavefunction, reducing Schrödinger’s half live, half dead cat to one that’s either dead or alive.If Jonathan’s right, then this is a true breakthrough, not just in quantum mechanics, but in the philosophy of physics.In the next episode, we’ll move on to the other pillar of physics: Jonathan will explain how to derive general relativity from the hypergraph.There’s much more to explain about each of these derivations, but we’re finally getting to the crux of Wolfram Physics, the question of whether it can, after all, model our universe.—Jonathan’s seminal paper on how to derive quantum mechanicsSome Quantum Mechanical Properties of the Wolfram ModelJonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project Concepts mentioned by Jonathan Causal invariance Computational irreducibility Celestial mechanics Molecular dynamics Space-like separation Heisenberg’s uncertainty principle Heisenberg’s microscope experiment Quantum entanglement Bell’s inequalities Multiway system Coarse-graining Schrödinger equation Unitary operator Hermitian operator Conjugate transpose operation Time reversal Wavefunction collapse Quantum interference Quantum tunnelling Stephen Wolfram’s books A New Kind of Science A project to find the Fundamental Theory of Physics —The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch hereKootenay Village Ventures Inc.

You know peer review, right?It’s the way academics check each other’s research papers.It ensures that only the good ones are published and prevents the bad ones from getting through.Right?Wrong.Peer review does precisely the opposite of what you think it does.It prevents the good papers from being published, and ensures that only the bad ones get through.Peer review is suffocating science.If we want to reverse the stagnation of science over the last 50 years, then we’ve got to get rid of peer review.—I highly recommend you read Adam Mastroianni’s splendid article The rise and fall of peer reviewI first heard Adam’s ideas about peer review in his conversation Adam Mastroianni on Peer Review and the Academic Kitchen with Russ Roberts on EconTalkWhy has there been no progress in physics since 1973? article audio video Scientific papers: The journal Nature began to require peer review in 1973 Millions of academic articles are published every year Some scientists simply make stuff up Fraudulent studies make it into respectable journals like Science, Nature and The Lancet Physicists: Isaac Newton Albert Einstein’s four papers published in 1905 Max Planck’s principle that science progresses one funeral at a time The Wolfram Physics Project: Stephen Wolfram Jonathan Gorard My projects: The Last Theory Open Web Mind Image of Adam Mastroianni by permission from Adam Mastroianni—The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch hereThe full article is hereKootenay Village Ventures Inc.

“Sorry, this is now getting very metaphysical,” says Jonathan Gorard part way through this excerpt from our conversation.We start by talking about applying more than one rule to the hypergraph to create rulial multiway systems.This takes us part way towards applying every possible rule, in other words, towards the ruliad.We move on to the idea of measuring the complexity of a structure in terms of the minimum amount of information needed to express it.Jonathan applies this idea to the ruliad, pointing out that it takes almost no information to express, since it encompasses all possible rules.Since he believes, however, that there is some content to the universe – that it is not a tautalogy – this leads Jonathan to reject the idea of the ruliad.We dig into why he has this intuition is that the universe is not a tautalogy.Jonathan invokes theologians like John Duns Scotus, who promulgated the idea the the world is neither completely reducible nor completely irreducible.He follows the scholastics in steering a middle path, suggesting that there’s enough content in the universe that it’s interesting, but not so much content that we can’t write down well-defined laws of nature.This brings us, for the first time, to the role of the observer in the Wolfram model.Again, Jonathan steers a middle path between placing the computational burden entirely on the universe and placing the computational burden entirely on the observer.I find this 9-minute exposition fascinating. It gets to the heart of some of the philosophical differences between Jonathan Gorard and Stephen Wolfram, and to the nature of the universe and our role as observers.—Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project People mentioned by Jonathan John Duns Scotus Xerxes D. Arsiwalla Hatem Elshatlawy Research mentioned by Jonathan Homotopies in Multiway (Non-Deterministic) Rewriting Systems as n-Fold Categories by Xerxes D. Arsiwalla, Jonathan Gorard, Hatem Elshatlawy Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types by Xerxes D. Arsiwalla, Jonathan Gorard Concepts mentioned by Jonathan Rulial Multiway System ∞-category ∞-groupoid (∞,1)-topos Grothendieck’s homotopy hypothesis Algorithmic complexity theory Algorithmic information theory Kolmogorov complexity Einstein field equations Curvature invariant Qualia —The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

It’s pretty easy to see how three-dimensional space might arise from Wolfram Physics.The hypergraph kinda looks like space, and, for some rules, it kinda looks like it’s three-dimensional.But our universe isn’t just empty three-dimensional space.It’s mostly empty space, but there are also particles moving through that space: photons, neutrinos, electrons, quarks.Sometimes, these particles interact, annihilating each other and producing new particles.If Wolfram Physics is to be a successful model of our universe, it must, of course, model these elementary particles and their interactions.So where are the particles in the hypergraph?What is a particle in Wolfram’s universe?—Animations: Thanks to Alan Dewar for permission to use his excellent implementation of Conway’s Game of Life for many of the animations in the video Thanks also to Chris Rowett for permission to use his Life Viewer, a beautiful implementation of Conway’s Game of Life, which I used for the greyship animation in the video and image in the thumbnail Another implementation of Conway’s Game of Life, which reproduces the Life Lexicon from ConwayLife.com, is at playgameoflife.com Sources:Talking of ConwayLife.com, that’s another incredible resource for information on Conway’s Game of LifeTools:I created an RLE to text converter to convert Run Length Encoded patterns to plain text formatImages:  John H Conway 2005 by Thane Plambeck licensed under CC BY 2.0 Sounds: Crickets choir by Serg Childed licensed under CC BY-SA 4.0 —The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

In the early days of the Wolfram Physics Project, Stephen Wolfram seemed to be seeking a single rule that, when applied to the hypergraph, could generate our universe.More recently, however, Wolfram has promoted the idea of the ruliad, the application of every possible rule to the hypergraph.So I asked Jonathan Gorard, who was instrumental in the founding of the Wolfram Physics Project, whether all rules might be applied to generate our universe, or whether he was searching for one rule to rule them all.—Stephen Wolfram’s 2010 TED talk in which he said he was committed “to see if within this decade we can finally hold in our hands the rule for our universe”.Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project Concepts mentioned by Jonathan Equivalence class Congruence class Lagrangian mechanics Hamiltonian mechanics Teleology Ontology Axiomatic view of mathematics – top-down Constructivist view of mathematics – bottom-up Domain of discourse Intuitionism Algorithmic information theory —The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

John von Neumann might be the most important figure in Wolfram Physics prehistory.Whenever any of the most important prerequisites to Wolfram Physics were happening – quantum mechanics, Gödel’s theorem, Turing machines, electronic computers, cellular automata – John von Neumann always seemed to be there.How did John von Neumann always come to be in the right place at the right time to contribute to some of the most significant developments in physics, mathematics and computation history?For this, another high-budget, big-hair episode of The Last Theory, I flew all the way to Budapest, where John von Neumann was born, to point to a plaque and get some answers.—I took inspiration and information for this episode from Ananyo Bhattacharya’s biography of John von Neumann: The Man from the Future Buy it in the US Buy it in the UK Buy it in Canada Buy it in Australia People John von Neumann Albert Einstein Erwin Schrödinger Werner Heisenberg Kurt Gödel Alan Turing Seth Neddermeyer J. Presper Eckert John Mauchly Stephen Wolfram Jonathan Gorard Max Piskunov Stanisław Ulam Father Strickland Concepts Hilbert space Gödel’s incompleteness theorems Universal Turing machine Turing’s proof Von Neumann architecture The Manhattan Project Cellular automata Computers IAS machine ENIAC EDVAC IBM 701 Images Image of John von Neumann from the Los Alamos National Laboratory, which rather pointlessly requires that this rather ponderous statement be reproduced here: “Unless otherwise indicated, this information has been authored by an employee or employees of the Los Alamos National Security, LLC (LANS), operator of the Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396 with the U.S. Department of Energy. The U.S. Government has rights to use, reproduce, and distribute this information. The public may copy and use this information without charge, provided that this Notice and any statement of authorship are reproduced on all copies. Neither the Government nor LANS makes any warranty, express or implied, or assumes any liability or responsibility for the use of this information.” Turing Machine Model Davey 2012 by Rocky Acosta licensed under CC BY 3.0 Animation. 1200 iterations of the ‘Rule 110’ Automata by Mr. Heretic licenced under  CC BY-SA 3.0 Bundesarchiv Bild183-R57262, Werner Heisenberg by an unknown author (Bundesarchiv, Bild 183-R57262) licensed under CC BY-SA 3.0 DE Turing in 1935 by Tomipelegrin licensed under CC BY-SA 4.0 Gospers glider gun by Lucas Vieira licensed under CC BY-SA 3.0 —The Last Theory is hosted by Mark Jeffery, founder of the Open Web MindI release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

The Wolfram model allows an infinite number of rules.Some of these rules generate interesting universes that are complex and connected, some of these rules generate plausible universes that look a little like our own, and others... go nowhere.In this excerpt from my conversation with Jonathan Gorard, I ask him how to find rules of Wolfram Physics that are both interesting and plausible.—Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project The paper referred to by Jonathan Algorithmic Causal Sets and the Wolfram Model by Jonathan GorardConcepts mentioned by Jonathan Causal invariance Manifold Causal graph Space-like separation Causal cone Dimensionality Curvature Discrete differential operators Discrete Laplacian —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

The twentieth century was a truly exciting time in physics.From 1905 to 1973, we made extraordinary progress probing the mysteries of the universe: special relativity, general relativity, quantum mechanics, the structure of the atom, the structure of the nucleus, enumerating the elementary particles.Then, in 1973, this extraordinary progress... stopped.I mean, where are the fundamental discoveries in the last 50 years equal to general relativity or quantum mechanics?Why has there been no progress in physics since 1973?For this high-budget, big-hair episode of The Last Theory, I flew all the way to Oxford to tell you why progress stopped, and why it’s set to start again: why progress in physics might be about to accelerate in the early twenty-first century in a way we haven’t seen since those heady days of the early twentieth century.—Eric Weinstein’s claims that there has been no progress in physics since 1973: BigThink The Joe Rogan Experience Lord Kelvin— I release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

Causal invariance is a crucial characteristic for any rule of Wolfram Physics.According to Wolfram MathWorld, if a rule is causally invariant, then “no matter which evolution is chosen for a system, the history is the same, in the sense that the same events occur and they have the same causal relationships.”Causal invariance is one of the assumptions Jonathan Gorard needs to make to derive the equations of General Relativity from the hypergraph. That’s how crucial it is! Given that not every rule of Wolfram Physics is causally invariant, I asked Jonathan how we find the ones that are.Here, in another excerpt from our recent conversation, is his answer: how to find causally invariant rules.—Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project People and concepts mentioned by Jonathan Stephen Wolfram Max Piskunov Causal invariance Wolfram Function Repository Wolfram Engine Wolfram Mathematica Wolfram Programming Lab CausalInvariantQ TotalCausalInvariantQ Associative Commutative Automated theorem proving Undecidable problem —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

Now that I’ve introduced you to the different kinds of edges that might make up a hypergraph – unary, binary and ternary edges, as well as loops and self-loops – we can have some fun.Some of rules in the Wolfram model give rise to fascinating universes.Today, I’m going to show you a few rules that seem to fabricate space itself in much the same way as knitting needles might fabricate a blanket.And if you think that knitting is a far-fetched analogy, just wait until you see my animations!–I release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

Dugan Hammock creates beautiful animations of three-dimensional cross-sections through four-dimensional spaces.But his animations aren’t mere mathematical abstractions. He has also applied his geometrical skills to animating the hypergraph of Wolfram Physics, in such a way that it doesn’t jump from frame to frame.In this second part of my recent conversation with Dugan, we talk about his extending spring-electrical embedding into an additional time dimension......and we show some of the beautifully smooth animations that come out of it.—Dugan Hammock Dugan Hammock’s videos on YouTube Dugan Hammock on Twitter Dugan Hammock at The Wolfram Physics Project Plotting the evolution of a Wolfram Model in 3-dimensions Temporally coherent animations of the evolution of Wolfram Models  People and concepts mentioned by Dugan Coulomb’s law Hooke’s law Spring-electrical embedding Charles Pooh —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

Causal invariance is one of the most important concepts in the Wolfram model... and one of the most difficult to capture.So I really wanted to hear Jonathan Gorard’s take on it.In this excerpt from our conversation, Jonathan addresses the differences between causal invariance and confluence.Causal invariance means that regardless of the order in which a rule is applied to the hypergraph, the same events occur, with the same causal relationships between them.Confluence, on the other hand, is the coming-together of different branches of the multiway graph.Jonathan explores different ways we might determine whether two nodes, two edges or two hypergraphs are the same, and explains that if we identify nodes and edges according to their causal histories, then causal invariance and confluence become the same idea.I’ve found myself listening to Jonathan’s explanation of causal invariance over and over to make sense of it, but it’s one of the areas where I’m convinced Jonathan has a unique contribution to make.—Jonathan Gorard  • Jonathan Gorard at The Wolfram Physics Project  • Jonathan Gorard at Cardiff University  • Jonathan Gorard on Twitter  • The Centre for Applied Compositionality  • The Wolfram Physics ProjectConcepts mentioned by Jonathan  • Causal invariance  • Multiway system  • Causal structure  • Causal Set Theory  • Directed acyclic graph  • Isomorphic  • Space-like separation  • Simultaneity and simultaneity surfaces in relativity  • Lorentz invariance  • Poincaré invariance  • Conformal invariance  • Diffeomorphism invariance  • General covariance  • Confluence  • Church-Rosser Property—I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

So many of the most complex and most promising graphs and hypergraphs of Wolfram Physics involve loops and self-loops.They can play a crucial role in the evolution of graphs and hypergraphs... which means that they might play a crucial role in the evolution of the universe itself.Loops and self-loops matter, because including them in our models reduces the number of arbitrary assumptions we need to make in Wolfram Physics, making it more complete.–I release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

Dugan Hammock lives in the fourth dimension.As Jonathan Gorard mentioned in our recent conversation on How to draw the hypergraph in Wolfram Physics, Dugan has worked on plotting the evolution of the hypergraph over time.We get into that in the second part of our conversation, but in this first part, I get to know Dugan as a mathematician and artist.Enjoy his amazing animations of three-dimensional cross-sections through four-dimensional hypershapes!—Dugan Hammock Dugan Hammock’s videos on YouTube Dugan Hammock on Twitter Dugan Hammock at The Wolfram Physics Project Plotting the evolution of a Wolfram Model in 3-dimensions Temporally coherent animations of the evolution of Wolfram Models  People mentioned by Dugan Max Cooper George K. Francis William Thurston —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

Computational irreducibility means that there are no shortcuts when we apply rules to the hypergraph.I used to think that our existing theories of physics, such as general relativity and quantum mechanics, were examples of computational reducibility: shortcuts that allow us to make higher-level generalizations about how the application of rules to the hypergraph gives rise to our universe.Jonathan Gorard used to think this, too.But it turns out that over the last couple of years, he has changed his mind on this quite radically.General relativity and quantum mechanics, he now thinks, aren’t examples of computational reducibility, they’re consequences of computational irreducibility.I truly appreciated this part of our conversation, because it radically changed my mind, too, about this crucial concept in Wolfram Physics.—Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project Concepts mentioned by Jonathan Computational reducibility Computational irreducibility General relativity Quantum mechanics Fluid mechanics Continuum mechanics Solid mechanics Partition function Boltzmann equation Molecular chaos assumption Ergodicity Distribution function Chapman-Enskog expansion Stress tensor Navier-Stokes equations Euler equations —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

There are two questions about Wolfram Physics I’m asked a lot:What’s beyond the hypergraph?And what’s between the nodes and edges of the hypergraph?There’s a simple answer to this question.Nothing.There’s nothing beyond the hypergraph.There’s nothing beyond the universe.But it’s not a very effective answer.So here’s a deeper response to the age-old question:What’s beyond the universe?–I release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

The hypergraph is the universe.So if we want to see the universe, we need only draw the hypergraph.The question is: how?The nodes and edges of the hypergraph are determined by the rules of Wolfram Physics. But how we draw those nodes and edges is not determined.The drawing of the hypergraph is not the universe, it’s just a way of visualizing the universe.So I asked Jonathan Gorard how we might decide where to position the nodes and edges when we draw the hypergraph, so that we can see what’s really going on in Wolfram Physics.—Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project People mentioned by Jonathan Charles Pooh Dugan Hammock Plotting the evolution of a Wolfram Model in 3-dimensions by Dugan Hammock Temporally coherent animations of the evolution of Wolfram Models by Dugan Hammock Concepts mentioned by Jonathan Spring electrical embedding Spring embedding Layered embedding Causal graphs Coulomb’s law Hooke’s law —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.

What is the Big Bang in Wolfram Physics?There’s a straightforward answer to that question.It’s the point in the evolution of the universe where the hypergraph goes from nothing to something.It’s the start of the explosion that eventually yields the uncountable particles, planets, stars and galaxies of our universe.So that’s pretty straightforward, isn’t it?Well, yes, except that there’s one phrase above that demands further explanation: nothing to something.How does the universe go from nothing to something?–I release The Last Theory as a video too! Watch here.The full article is here.Kootenay Village Ventures Inc.

Here’s a slightly technical question:Does Wolfram Physics really need hypergraphs?Or could it based on graphs instead?Jonathan Gorard shares some interesting insights into the evolution of Stephen Wolfram’s model for a fundamental theory of physics.Wolfram started with trivalent graphs, in which each edge joins two nodes, and each node has three edges.But when he ran into issues implementing simulations using these simple graphs, he solved the problem by graduating to hypergraphs, in which each hyperedge can join any number of nodes, and each node can have any number of hyperedges.Here’s how hypergraphs, rather than graphs, came to be the basis of Wolfram Physics.—Jonathan Gorard Jonathan Gorard at The Wolfram Physics Project Jonathan Gorard at Cardiff University Jonathan Gorard on Twitter The Centre for Applied Compositionality The Wolfram Physics Project Concepts mentioned by Jonathan Trivalent networks (a.k.a. cubic graphs) Mathematica —I release The Last Theory as a video too! Watch here.Kootenay Village Ventures Inc.