The Last Theory

Mark Jeffery

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The Last Theory is an easy-to-follow exploration of what might be the last theory of physics. In 2020, Stephen Wolfram launched the Wolfram Physics Project to find the elusive fundamental theory that explains everything. On The Last Theory podcast, I investigate the implications of Wolfram's ideas and dig into the details of how his universe works. Join me for fresh insights into Wolfram Physics every other week.

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Nov 16, 2023

A toy model of particles with Jonathan Gorard

In this excerpt from my conversation with Jonathan Gorard, he proposes that particles in Wolfram Physics might be persistent topological obstructions in the hypergraph.
He starts with a toy model in which elementary particles are non-planar tangles moving and interacting in an otherwise planar hypergraph.
But he doesn’t stop there.
He explains that there’s an infinite variety of hypergraphs that give rise to such persistent topological obstructions.
These localized tangles behave in ways that look a lot like particle 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
* Utility graph
* Kuratowski’s theorem
* Wagner’s theorem
* Complete graphs – including K_5
* Complete bipartite graphs – including K_3,3
* Robertson-Seymour Theorem
* Graph minor
* Forbidden minor characterization
Image:
* Feynman diagram Feynmann Diagram Gluon Radiation by Joel Holdsworth, public domain
—
The Last Theory is hosted by Mark Jeffery, founder of the Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.

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Nov 2, 2023

How to tell if space is curved

What if you’re inside a universe, and you want to know whether space is curved?
The reason I’m asking is that according to Einstein’s general theory of relativity, our universe is curved, by the presence of matter.
If Wolfram Physics is to be a true model of our universe, then the space represented by the hypergraph must also be curved by the presence of matter.
Which means that determining whether space is curved is crucial to Jonathan Gorard’s derivation of Einstein’s equations from the Wolfram model.
Fortunately, there’s a way to find out that’s so simple that even a crab or a space frog could do it.
Here’s how to tell if your universe curved.
—
Dimensionality:
* How to measure the dimensionality of the universe
* Are Wolfram’s graphs three‑dimensional?
* What are dimensions in Wolfram’s universe?
Space-time:
* Space‑time is dead
Euclidean geometry:
* Euclid
* parallel lines never meet
—
The Last Theory is hosted by Mark Jeffery, founder of the Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Oct 19, 2023

How special is general relativity? with Jonathan Gorard

I asked Jonathan Gorard what it felt like when he realized that general relativity can be derived from the hypergraph.
His answer took us in an unexpected direction.
If the Wolfram model is to be an accurate model of our universe, then it must give us the Einstein equations.
But what if any old model with any old rules can give us the Einstein equations?
What if general relativity isn’t so special?
This is one of the shorter excerpts from my conversation with Jonathan, but it’s a fascinating one.
It takes us to one of the most powerful aspects of the Wolfram model: its ability to answer questions about why our universe is the way it is, questions that were once in the realm of philosophy but may now be within the scope of 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
* Einstein field equations
* Riemannian manifold
* Einstein–Hilbert action
* Causal invariance
* Ergodicity
—
The Last Theory is hosted by Mark Jeffery, founder of the Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.

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Oct 7, 2023

Why scientific theories need not make predictions

In my exploration of Wolfram Physics, I’ve come across one objection more than any other.
Over and over again, people have told me that the Wolfram model must be rejected because it makes no predictions.
I could respond by saying that Wolfram Physics does make predictions. It predicts Einstein’s equations. It predicts Schrödinger’s equation.
But it’s true that it doesn’t make any predictions that differ from those of general relativity and quantum mechanics. At least, not yet.
So here’s my more robust response to the objection: all scientific theories make no predictions when they’re first formulated.
If we dismiss any new theory solely because it doesn’t make any predictions, then we’d dismiss all new theories.
It’s time for academics to learn the lessons of the history of science, and open their minds to bold, new ideas, like Wolfram Physics.
—
Ideas:
* Tycho Brahe
* The paths of the planets are elliptical according to Johannes Kepler
* Philosophiæ Naturalis Principia Mathematica by Isaac Newton
* Astronomers’ test of Albert Einstein’s general theory of relativity
* Against Method by Paul Feyerabend
* The Newtonian Casino by Thomas Bass
Ancient astronomies:
* Egyptian astronomy
* Babylonian astronomy
* Inca astronomy
Images:
* Paul Feyerabend Berkeley by Grazia Borrini-Feyerabend reproduced with permission
—
The Last Theory is hosted by Mark Jeffery, founder of the Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Sep 21, 2023

How to derive general relativity from Wolfram Physics with Jonathan Gorard

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 Jonathan
* Alfred Gray
Research 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 Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.

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Sep 7, 2023

How to derive quantum mechanics from Wolfram Physics with Jonathan Gorard

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 mechanics
* Some Quantum Mechanical Properties of the Wolfram Model
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
* 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 Mind
I release The Last Theory as a video too! Watch here
Kootenay Village Ventures Inc.

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Aug 24, 2023

Peer review is suffocating science

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 review
I first heard Adam’s ideas about peer review in his conversation Adam Mastroianni on Peer Review and the Academic Kitchen with Russ Roberts on EconTalk
Why 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 Mind
I release The Last Theory as a video too! Watch here
The full article is here
Kootenay Village Ventures Inc.

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Aug 10, 2023

Is the universe a tautology? with Jonathan Gorard

“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 Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.

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Jul 27, 2023

What is a particle in Wolfram’s universe?

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 Life
Tools:
* I created an RLE to text converter to convert Run Length Encoded patterns to plain text format
Images:
* 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 Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Jul 13, 2023

One rule to rule them all? with Jonathan Gorard

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 Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.

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Jun 30, 2023

John von Neumann and the art of being there

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 Heise…

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Jun 15, 2023

How to find interesting and plausible rules with Jonathan Gorard

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 Gorard
Concepts 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…

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Jun 1, 2023

Why has there been no progress in physics since 1973?

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 Kelv…

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May 18, 2023

How to find causally invariant rules with Jonathan Gorard

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…

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May 4, 2023

How to knit the universe

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.

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Apr 22, 2023

Animating the hypergraph with Dugan Hammock

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!…

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Apr 8, 2023

Causal invariance versus confluence with Jonathan Gorard

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 Jon…

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Mar 26, 2023

Loops and self‑loops in the hypergraph

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.

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Mar 16, 2023

Living in the fourth dimension with Dugan Hammock

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.

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Feb 23, 2023

Why I changed my mind about computational irreducibility with Jonathan Gorard

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…

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Feb 9, 2023

What’s beyond the universe?

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.
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Jan 26, 2023

How to draw the hypergraph in Wolfram Physics with Jonathan Gorard

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 Hamm…

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Jan 19, 2023

What is the Big Bang in Wolfram’s universe?

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.

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Jan 5, 2023

Graphs v hypergraphs in Wolfram Physics with Jonathan Gorard

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)
* Math…

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Dec 29, 2022

Where I’m going with Wolfram Physics in 2023

I’ve been blown away by your response to The Last Theory in 2022.
How am I going to thank you for reading, listening, watching and subscribing?
Well, by bringing you more Wolfram Physics in the New Year, that’s how.
Here are 7 directions I want to take The Last Theory in 2023.
—
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Dec 22, 2022

Why hypergraphs might be a good model of the universe with Jonathan Gorard

Wolfram Physics is based on hypergraphs.
Why?
What is it about hypergraphs that might make them a better model of the universe than, say, strings of characters, or cellular automata, or Turing machines?
When I asked Jonathan Gorard this question, he gave an answer that was deeply insightful.
It’s such a core question, so fundamental to why we should take the Wolfram model seriously, that I’ve listened to Jonathan’s answer over and over.
—
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
* Roger Penrose
* Rafael Sorkin
* Tommaso Bolognesi
* Causal Set Theory
* Hasse diagram
* Riemannian distance
* Strings (of characters)
* Cellular automata
* Turing machines
* Lorentz invariance
* General covariance
—
I release The Last Theory as a video t…

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Dec 15, 2022

Is Wolfram Physics the next scientific revolution?

For the last few hundred years, all our theories of physics have been mathematical.
If Stephen Wolfram is right, from now on, our most fundamental theories of physics may be computational.
This shift from mathematics to computation feels to me like a scientific revolution.
Recently, I asked Jonathan Gorard, who was instrumental in the founding of The Wolfram Physics Project, whether it feels to him, too, like a scientific revolution.
“I think so,” he said. “I mean, it’s a strong statement, but I don’t think it’ll end up being too inaccurate.”
(If you want to check out that part of our conversation, you can listen here or watch here.)
Here’s why, in my mind, Wolfram Physics is the next scientific revolution.
–
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Dec 8, 2022

Why I took a chance on Wolfram Physics with Jonathan Gorard

Jonathan Gorard admits that it was a risk, for his academic career, to work on the Wolfram Physics project.
In this third excerpt from my recent conversation with Jonathan, I asked him how he thought about that risk and why he decided to take it.
He told me that the opportunity to work with Stephen Wolfram on this new model is a bit like being given an opportunity to work with von Neumann and Ulam on cellular automata, or with Turing, Church and Gödel on computational models, back in the early twentieth century.
So I asked Jonathan whether he thought, as I do, that the reframing physics in terms of computation feels like we’re in a scientific revolution, as important as the reframing of physics in terms of mathematics several hundred years ago.
“It’s a strong statement,” he replied, “but I don’t think it’ll end up being too inaccurate.”
For me, the opportunity to talk to Jonathan about Wolfram Physics feels a bit like being given an opportunity to interview Dirac,…

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Dec 1, 2022

What is the multiway graph in Wolfram Physics?

In Episode 15: Where to apply Wolfram’s rules? (listen to the audio ⋅ watch the video ⋅ read the article) I introduced a radical idea.
When we’re applying a rule to a graph in Wolfram Physics, there are generally many possible places in the graph we could apply the rule, giving us many possible next states of the universe.
Here’s the radical idea: rather than choose one of these possible universes, we choose not to choose. Instead, we keep each of them in mind.
The trouble is, if we choose not to choose, the number of possible universes we have to keep in mind gets extremely large extremely quickly.
To help us visualize all these possible universes, we’re going to need the multiway graph
.
It’s a crucial idea in Wolfram Physics.
The multiway graph will allow us to derive aspects of quantum mechanics from Wolfram Physics.
It’ll lead us to a concept of the observer that promises to resolve issues related to the collapse of the wavefunction that have plagued quantum…

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Nov 17, 2022

From clockwork to computation in Wolfram Physics with Jonathan Gorard

This is the second of a series of excerpts from my recent conversation with Jonathan Gorard, who was instrumental in the founding of The Wolfram Physics Project.
I asked Jonathan why he found the computational approach to physics so compelling.
In his answer, he broached a wide range of fascinating topics in the philosophy of science:
* how we moved from a clockwork paradigm in the age of clockwork to a computational paradigm in the age of computation;
* how saying that the universe is computational is different from saying that the universe is a computer;
* how our adoption of mathematics as the basis for physics has biased us to think of space-time as continuous;
* how the history of science might have been different had Turing been born before Newton;
* how the Wolfram Model can be thought of as a way of building a constructivist foundation for physics.
This led us to discuss a couple of the deeper questions of Wolfram Physics:
* is it possible to know whether the u…

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Nov 10, 2022

Why I don’t like String Theory

In my conversation with Jonathan Gorard about the founding of the Wolfram Physics Project, I said that I don’t like String Theory.
Now, I’ll admit, I don’t really understand String Theory.
It’s highly mathematical. And I’m not much of a mathematician. Actually, that’s an understatement. I’m not a mathematician at all.
So if there’s a problem in the relationship between String Theory and me, it might not be String Theory, it might be me.
Sadly, admitting that I might be part of the problem doesn’t change anything between us. I still don’t like String Theory.
Here’s why.
–
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Nov 3, 2022

The founding of the Wolfram Physics Project with Jonathan Gorard

In 2019, Jonathan Gorard and Max Piskunov goaded Stephen Wolfram into pursuing his ideas for a new kind of science.
This led to the announcement of The Wolfram Physics Project in 2020.
Last week, I talked to Jonathan Gorard about the revolutionary ideas that have come out of the project.
In this first excerpt from our conversation, Jonathan talks about his instrumental role in the founding of The Wolfram Physics Project.
We cover why the time was right in 2020... and why it had been wrong in 2002 when Stephen Wolfram published his book A New Kind of Science.
We talk about how Wolfram Physics might take over from string theory, why Jonathan likes string theory... and why he doesn’t.
It was a true pleasure to talk to Jonathan about what might prove a pivotal moment in the history of science.
—
Jonathan Gorard
* Jonathan Gorard at The Wolfram Physics Project
* Jonathan Gorard at Cardiff University
People and Projects
* The Centre for Applied Compositionality
* The W…

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Oct 27, 2022

Hypergraphs are everywhere

Wolfram Physics models the universe as a hypergraph.
Maybe I’m just seeing things, but it seems to me that hypergraphs are everywhere: physics, chemistry, biology, neurology, ecology, sociology, technology.
What I want to know is:
Why?
Why are hypergraphs everywhere?
—
Molecular structure Styrene-butadiene chain2 by Guido Raos, professor of chemistry, Politecnico di Milano, Italy licensed under CC BY-SA 4.0
Metabolic pathway BRENDA pyrimidine metabolism by BRENDA – The Comprehensive Enzyme Information System licensed under CC BY 4.0
Brain image Neurons & glia by The Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD) licensed under CC BY 2.0
Pelagic food web An in situ perspective of a deep pelagic food web by C. Anela Choy, Steven H. D. Haddock and Bruce H. Robison licensed under CC BY 4.0
Social graph Partitions in my social graph by Matt Biddulph licensed under CC BY-SA 2.0
Internet map Internet map by Matt Britt licensed under CC…

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Oct 13, 2022

How big is the computer that runs the universe?

As you’ll know from Episode 8: Where’s the computer that runs the universe? ( read ⋅ listen ⋅ watch ), I have my doubts about the existence of a computer that’s whirring away, applying Wolfram’s rules to Wolfram’s graphs, performing the computations required to run our universe.
This computer, if it exists, is necessarily invisible to us, and as I warned in Episode 12: Beware invisible things ( read ⋅ listen ⋅ watch ) we should be wary of what we can’t see.
Still, I want to revisit this idea of a computer that runs the universe.
I want to come at it from a slightly different direction.
Rather than adopt the stance of the monkey with its hands over its eyes and insist that if I can’t see it, it’s not there, let’s suppose that there is a computer that runs the universe and ask a simple question:
How big would it have to be?
—
Other episodes I mention:
* Episode 8: Where’s the computer that runs the universe? – read ⋅ listen ⋅ watch
* Episod…

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Sep 29, 2022

Unary, binary, ternary, k-ary hyperedges in Wolfram Physics

Here are answers to some fundamental questions about hypergraphs:
A hyperedge can connect any number of nodes: one, two, three, four, seventeen or any other number.
And a hypergraph can include any of these different kinds of hyperedge, or all of them.
Let’s take a look at what this means for Wolfram Physics... and at some of the beautiful hypergraphs it allows us to generate!
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Sep 15, 2022

What is a hypergraph in Wolfram Physics?

In previous episodes, I’ve been simulating Wolfram Physics using graphs.
But you may have come across simulations of Wolfram Physics using hypergraphs.
What’s the difference?
What is a hypergraph?
—
This epsiode refers to previous episodes on dimensionality:
* How to measure the dimensionality of the universe audio ⋅ video ⋅ article
* Are Wolfram’s graphs three‑dimensional? audio ⋅ video ⋅ article
* What are dimensions in Wolfram’s universe? audio ⋅ video ⋅ article
and previous episodes on space:
* What is space? the where and the how far audio ⋅ video ⋅ article
* The expanse: dimension, separation & explosion audio ⋅ video ⋅ article
—
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Sep 2, 2022

Where to apply Wolfram's rules?

Confession time: I haven’t been entirely honest with you about applying a rule to a graph in Wolfram Physics.
I’ve explained precisely how to apply a rule, but I’ve been strangely silent when it comes to where to apply the rule.
I know, it’s unlike me to be silent, right?
Time to come clean.
It turns out that the question of where to apply Wolfram’s rules is not as easily answered as you might think.
This seemingly straightforward question will take us into the philosophy of time, causality, consciousness, contingency and determinism.
And it’ll lead us towards some of the most important concepts in Wolfram Physics: the multiway graph, branchial space and causal invariance.
Check your breathing apparatus: we’re going deep.
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Aug 4, 2022

Space-time is dead

In his General Theory of Relativity, Einstein combined the three dimensions of space with the one dimension of time in what we now know as Einstein’s equations.
Ever since, physicists have thought of space and time as effectively the same thing: components of four-dimensional space-time.
This might be the biggest blunder physicists have ever made.
Stephen Wolfram, on page 22 of his book A project to find the Fundamental Theory of Physics, calls it the “one ‘wrong turn’ in the history of physics in the past century”.
Space-time is dead.
Here’s why... and how physicists got it so wrong for so long.
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Jul 21, 2022

Is space continuous or discrete?

We’re used to thinking of space as continuous.
A stone can be anywhere in space. It can be here. Or it can be an inch to the left. Or it can be half an inch further to the left. Or it can be an infinitesimal fraction of an inch even further to the left. Space is infinitely divisible.
The graphs of Wolfram Physics, however, are discrete.
If, as Stephen Wolfram proposes, the universe is a graph, then you can’t be just anywhere in space. It makes sense to think about a node of the graph as a position in space. It makes no sense to think about anywhere in between the nodes as positions in space. This space is not infinitely divisible.
It’s as if a stone could be here in space, or here in space, but nowhere in between.
So which is it?
Has every physicist from Leucippus to Einstein been right to insist that space is continuous?
Or is Wolfram right to up-end millennia of settled science and insist that space is discrete?
I release The Last Theory as a video too! Watch here.
The…

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Jul 7, 2022

Beware invisible things

We humans have always been fond of invisible things.
Poltergeists, fairies, unicorns, the Yeti, the Lost City of Atlantis.
Just because you can’t see them, it doesn’t mean they aren’t there.
Scientists, no less than any other humans, suffer from this fondness for invisible things.
Phlogiston, miasma, ether, strings.
Just because you can’t see them, scientists have insisted, it doesn’t mean they aren’t there.
Beware these invisible things.
As I explore Wolfram Physics, I’m aware of certain invisible things that we believe in now, but we’re going to have to let go, if Stephen Wolfram is right.
And I’m also aware of the temptation to replace this old set of invisible things with a new set of invisible things.
Here’s why we’d do well to resist.
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Jun 9, 2022

What are dimensions in Wolfram’s universe?

We know what it means when we say that our universe is three-dimensional: it means that we can move in three orthogonal directions: left-right; up-down; forwards-backwards.
But what would it mean to say that a universe is 2½-dimensional?
Or 3.37-dimensional?
Or 9-dimensional?
When I measured the dimensionality one of Wolfram’s graphs, I found it to be at least 3.37-dimensional.
If Stephen Wolfram is right, then our universe might not be uniformly three-dimensional.
So maybe dimensionality isn’t quite what we think it is.
What, exactly, are dimensions?
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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May 26, 2022

Are Wolfram’s graphs three‑dimensional?

Are Wolfram’s graphs three-dimensional?
In Episode #009: How to measure the dimensionality of the universe – watch the video or read the article – I introduced a mathematically-minded crab, which was able to determine the dimensionality of its universe by measuring how much space it covered moving different distances in every possible direction.
Now I’m going to use the same crabby method to determine the dimensionality of graphs generated by Wolfram Physics.
I’m finally going to answer the question: how many dimensions are there in one of Wolfram’s universes?
And the answer’s going to be unexpected.
Here’s a hint: it’s not two and it’s not three.
Today’s episode includes a lot of visuals, so I recommend you watch the video or read the article rather than listen to the audio.
Kootenay Village Ventures Inc.

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May 12, 2022

How to measure the dimensionality of the universe

Today’s episode includes a lot of visuals, so I recommend you watch the video or read the article rather than listen to the audio.
In Episode #007: The expanse: dimension, separation & explosion – watch the video or read the article – I argued that the graphs of Wolfram Physics are going to have to be three-dimensional to be a true representation of our universe.
But how can we tell whether these graphs are three-dimensional? Many of them are so convoluted that it’s difficult to tell whether they’re two-dimensional, three-dimensional or somewhere in between.
I’m going to make the question even more difficult. We’ve been looking at graphs from the outside, from a God’s-eye view.
In reality, though, we’re not outside the graph. Remember, we’re hoping that the graphs of Wolfram Physics will prove to be a true representation of our universe, and we can’t be outside our own universe.
How could we tell whether a graph is two-dimensional, or three-dimensional, or ev…

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Apr 28, 2022

Where’s the computer that runs the universe?

I’ve been running simulations of our universe, according to Stephen Wolfram’s computational theory of physics.
Where’s the computer that runs these simulations?
Well, it’s right here. This a low-powered laptop in my hand is literally the computer that runs these universes.
It’s natural to ask a follow-up question.
If Wolfram’s right and the real universe evolves computationally in the same way as these simulated universes, where’s the computer that runs the universe?
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Apr 14, 2022

The expanse: dimension, separation & explosion

In the last episode, I introduced two fundamental characteristics of space: position and distance.
Today, I’m going to introduce three more characteristics of space: dimension, separation & explosion.
If it’s to be a viable theory of physics, Wolfram Physics has to accurately model space as we know it, including all five of these characteristics.
Let’s see how it measures up.
—
Today’s episode includes a lot of visuals, so you might prefer to read the article, or watch the video, where they’re animated.
In the episode, I refer back to Episode #006: What is space? the where and the how far. Again, I recommend you watch the video or read the article rather than listen to the audio for that episode, since you’ll want to see the visuals!
Doppler siren by jobro reproduced under CC BY 3.0
Kootenay Village Ventures Inc.

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Mar 31, 2022

What is space? the where and the how far

What is space in Wolfram Physics?
I’ve talked about the basic concepts of Wolfram Physics: nodes, edges, graphs & rules.
I just threw these concepts out there. No explanation. No rhyme, no reason. Nodes, edges, graphs & rules. Take them or leave them.
Naturally, this raised a few questions in some people’s minds.
These questions can be summed up as follows:
Wait... What? Nodes, edges, graphs & rules? Why?
This a deep question.
Let’s get into it.
—
This episode includes a few visuals, so you might prefer to read the article or watch the video.
In this episode, I refer back to Episode #004: Different rules, different universes. This one, too, includes a lot of visuals, so again, I recommend you watch the video or read the article rather than listen to the audio for that episode.
I also refer to a Polynesian stick chart. You can find it here: Micronesian navigational chart.
Kootenay Village Ventures Inc.

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Mar 17, 2022

What is physics? the how and the why

I like being asked questions about Wolfram Physics.
When I try to answer them, though, I often find myself trapped in an infinite regress.
To address a question about Wolfram Physics, I might first need to address another, more fundamental question, about physics.
And to address that question, I might first need to address another, more fundamental question, than might be more philosophy than physics.
Today, I’m going to go to one of those deep questions that need to be asked, if not answered, before I can begin to address many of the questions I’ve been asked about Wolfram Physics.
What is physics?
Prefer to watch the video? Watch here.
The full article is here.
Kootenay Village Ventures Inc.

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Mar 3, 2022

Different rules, different universes

It’s all about the animations.
I’ve been coding coding coding the few weeks to develop my simulations of Wolfram Physics.
So now I’m able to explore a number of simple rules and ask a number of simple questions.
What different rules could be applied to our universe?
What different universes would arise from these rules?
Today, I explore different rules, different universes.
Today’s episode includes a lot of visuals, so you might prefer to read the article, or watch the video, where they’re fully animated.
If you missed Episode #002, Nodes, edges, graphs & rules: the basic concepts of Wolfram Physics, you can find the article here and the video here.

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Feb 17, 2022

Why you’ve never heard of Wolfram Physics

Wolfram Physics might be the most fundamental scientific breakthrough in your lifetime.
And yet you’ve probably never heard of it.
Here’s why.
—
Albert Einstein’s 1905 papers
Stephen Wolfram’s project to find the fundamental theory of physics
Stephen Wolfram’s 2020 announcement
There are maybe half a million physicists in the world
—
Prefer to watch the video? Watch here
The full article is here

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Feb 3, 2022

Nodes, edges, graphs & rules: the basic concepts of Wolfram Physics

Are you ready?
Today, I’m going to dive right into Wolfram Physics.
If you’ve never heard of Stephen Wolfram or his team’s project to find the fundamental theory of physics, don’t worry.
Think of it like this: I’m going to dive right into the fundamental structure of the universe.
And, well, you might not believe that the words “simple” and “physics” can go together, but I’m going to keep it simple.
Today’s episode includes a lot of visuals.
You can find them in the article, or you might want to switch to watching the video, where they’re fully animated.

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Jan 20, 2022

Why I’m writing about Wolfram Physics

I always envy those people who, through a fantastic stroke of luck, find themselves to be exactly the right person in exactly the right place at exactly the right time to seize a once-in-a-lifetime opportunity.
I always ask myself, why can’t that happen to me?
Well, it just did.
Let me explain.
In this week’s episode, I discuss why I’m writing about Wolfram Physics.
I’ll be digging into the details, as well as taking a step back to see some of the philosophical implications, in future episodes.
Prefer to watch the video? Watch at lasttheory.com/channel/001-why-i-am-writing-about-wolfram-physics
The full article is at lasttheory.com/article/why-i-am-writing-about-wolfram-physics

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Dec 26, 2021

The most fundamental scientific breakthrough of our time

Welcome to The Last Theory, an easy-to-follow exploration of what might be the last theory of physics.
In 2020, Stephen Wolfram launched the Wolfram Physics Project to find the elusive fundamental theory that explains everything.
On The Last Theory, I investigate the implications of Wolfram’s ideas and dig into the details of how his universe works.
Join me for fresh insights into Wolfram Physics every other week: subscribe to the free newsletter, podcast or YouTube channel at lasttheory.com
After all, this might be the most fundamental scientific breakthrough of our time.

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