Hypergraphs can have any number of dimensions. They can be 2-dimensional, 3-dimensional, 4.81-dimensional or, in the limit, ∞-dimensional.
So how does the three-dimensional space we observe emerge from the hypergraph-based Wolfram model?
Why is space three-dimensional?
Stephen Wolfram’s surprising answer to this questions goes deep into space, time, computation and, crucially, our nature as observers.
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Stephen Wolfram
People mentioned by Stephen
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.
Stephen Wolfram reveals that his first major wow along the path towards a fundamental theory of physics was his realization that General Relativity and Quantum Mechanics are the same theory, played out in different kinds of space.
Many other dominos have fallen along the way, from the derivation of Einstein’s equations to applications of the ruliad beyond physics.
But the aspect of Wolfram Physics that Stephen Wolfram himself finds maybe the most compelling is this mirroring of the two pillars of twentieth century physics.
Perhaps General Relativity and Quantum Mechanics aren’t as incompatible as they’ve so long seemed.
In this first excerpt from my conversation with Stephen Wolfram, he tells the story of how he came to apply hypergraphs and hypergraph rewriting rules to the universe itself, and arrived at the first traces of a path towards what might be the last theory of physics.
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Stephen Wolfram
People mentioned by Stephen
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.
It feels like everyone has their pet Theory of Everything these days.
So why should you take my preferred Theory of Everything seriously?
Well, give me 5 minutes, and I’ll give you 5 reasons why I find Wolfram Physics more compelling than anything else that’s happened in physics in my lifetime...
...and maybe you’ll want to take it seriously too.
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.
Here’s a question.
Why does the universe exist?
Why is there something rather than nothing?
One of Stephen Wolfram’s boldest claims is that he has the answer.
Let me know whether you’re convinced by his argument!
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Ideas:
People:
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.
Do you know what causality is?
If you do, let me know, because I’m not sure.
I’ve never come across a conception of causality that makes sense to me.
After all, our universe seems to follow simple equations like Einstein’s equations, and there’s no mention of causality in these equations.
It makes me think that there’s no such thing as causality.
Unless...
Well, here’s the thing.
I’m no longer sure that our universe does follow these continuous equations.
I’m beginning to think that at the smallest scale, our universe might evolve through discrete computations.
If that turns out to be true, it allows for a limited conception of causalityafter all.
It’s causality, Jim, but not as we know it.
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References:
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
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 concept in Wolfram Physics.
It’s how we get special relativity from the Wolfram model.
It’s how we get quantum mechanics from the Wolfram model.
So what precisely is causal invariance?
This question will take us deep into the multiway graph, to an even deeper question: what is causality?
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What is the multiway graph? video ⋅ podcast ⋅ article
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.
I’ve heard from many of you that you’d like the whole of my conversation with Jonathan Gorard in a single podcast.
So here it is, the complete first interview.
These three hours are a brilliant exposition of Wolfram Physics from a figure whose contributions to the project are second to none.
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Jonathan Gorard
Jonathan’s seminal papers
Stephen Wolfram’s writings
A complete list of links to the research, concepts and people mentioned by Jonathan is here
Images
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.
You like Stephen Wolfram, right?
I mean, if he’s to be believed, he has reinvented physics, not to mention philosophy.
How could you not like such a thinker?
Well... it turns out that there are plenty of people who don’t like Stephen Wolfram... or his physics... or his philosophy.
Here are four criticisms of Stephen Wolfram I regularly hear...
...and here’s why these criticisms, though they hint at uncomfortable truths, nonetheless miss the mark.
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Stephen Wolfram:
Stephen Wolfram’s claims:
Some of the things Stephen Wolfram created:
Other people involved in the Wolfram Physics Project:
Other people mentioned in this episode:
Brilliant people of the past:
Other episodes of The Last Theory mentioned:
Reference:
Images:
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.
In this final excerpt from our conversation in October 2022, Jonathan Gorard explains how ideas from Wolfram Physics can be applied in fields beyond physics, including biology, chemistry and mathematics.
He describes the concept of compositionality, and digs deeper into why the hypergraph is able to model so much of our universe.
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Jonathan Gorard
Concepts mentioned by Jonathan:
People mentioned by Jonathan:
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.
You know who Stephen Wolfram is, right?
Whether you love him or, you know, don’t love him, there’s no denying that Stephen Wolfram has founded a host of fascinating projects... most of them named Wolfram-something-or-other.
What are all these Wolfram-branded projects?
Who is Stephen Wolfram?
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Some of the things Stephen Wolfram created:
not to mention:
More about Stephen Wolfram:
Stephen Wolfram’s education:
Some of Stephen Wolfram’s special subjects:
Some of Stephen Wolfram’s books:
Other people involved in the Wolfram Physics Project:
Reference:
Image:
Some of my own projects:
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
The full article is here.
Kootenay Village Ventures Inc.
I asked Jonathan Gorard the question I’m asked the most: can the Wolfram model make testable predictions about reality, predictions that differ from those of general relativity and quantum mechanics, predictions that might prove that Wolfram Physics is right?
Jonathan showed how the Wolfram model might shed light on some of the most mysterious phenomena of our universe, from black hole inspirals to quantum entanglement.
He focused on four areas where the class of theories encompassed by the Wolfram model might predict observable phenomena:
1. Cosmological consequences of global dimension change
2. Astrophysical consequences of local dimension change
3. Discretization effects during extreme astrophysical events
4. Quantum mechanical effects such as maximum entanglement speed
These dozen minutes of my conversation with Jonathan were dense with insights into Wolfram Physics, a true pleasure to revisit!
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Jonathan Gorard
Concepts mentioned by Jonathan
People mentioned by Jonathan:
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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.
The Open Web Mind is a protocol for shared human intelligence, based on the knowledge hypergraph.
Take a look at this quick introduction for subscribers to The Last Theory, then jump to the 2-minute trailer on the new channel.
And if you haven’t done so already, make sure to subscribe to the new Open Web Mind channel, podcast and newsletter.
If you’re interested in Wolfram Physics, I think you’ll find Open Web Mind fascinating!
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The Last Theory is hosted by Mark Jeffery founder of Open Web Mind
I release The Last Theory as a video too! Watch here.
Kootenay Village Ventures Inc.
How big are electrons compared to the hypergraph?
Is one electron formed of 10 nodes, or 10100 nodes?
And if it’s 10100 nodes, might it prove impossible to simulate an electron on any computer we can possibly imagine?
When I asked Jonathan Gorard this question, he took us on a tour of the scales of the universe, from the Planck scale to the Hubble scale.
He revealed how the Wolfram Physics Project’s early estimate of the scale of the hypergraph was based on a tower of rickety assumptions.
And he explained how the Wolfram model might connect with particle physics regardless of the disparities of scale.
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Jonathan Gorard
Concepts mentioned by Jonathan
—
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.
What if you’re inside a universe, and you want to measure the curvature of space?
It’s important because getting a measure of the curvature of the hypergraph takes us one step further in Jonathan Gorard’s derivation of General Relativity from Wolfram Physics.
Einstein’s equations relate the curvature of space to the presence of matter. So if we’re going to prove that Einstein’s equations follow from the Wolfram model, we’re going to need that measure of the curvature of the hypergraph.
Once again, a two-dimensional crab comes to the rescue, given us a way to measure the curvature of a universe from inside that universe.
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See Stephen Wolfram’s announcement, under Curvature in Space & Einstein’s Equations, also included as the introduction to his book A project to find the Fundamental Theory of Physics, page 20, for more on measuring the curvature of space
Concepts:
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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.
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.
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Jonathan Gorard
Concepts mentioned by Jonathan
Image:
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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.
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.
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Dimensionality:
Space-time:
Euclidean geometry:
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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.
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.
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Jonathan Gorard
Concepts mentioned by Jonathan
—
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.
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.
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Ideas:
Ancient astronomies:
Images:
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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.
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.
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Jonathan’s seminal paper on how to derive general relativity
Jonathan Gorard
People mentioned by Jonathan
Research mentioned by Jonathan
Concepts mentioned by Jonathan
From A Project to find the Fundamental Theory of Physics by Stephen Wolfram:
Images
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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.
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.
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Jonathan’s seminal paper on how to derive quantum mechanics
Jonathan Gorard
Concepts mentioned by Jonathan
Stephen Wolfram’s books
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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.