The Last Theory

In the previous excerpt from my conversation with Stephen Wolfram, I asked him how I can remain a single, coherent, persistent consciousness in a branching universe.

In this excerpt, we went deeper into this question. As a conscious observer, I have a single thread of experience. So if the universe branches into many timelines, why don’t I branch into many versions of me?

Stephen’s answer touched on many profound aspects of the Wolfram model.

He started with the failure of the Many Worlds interpretation of quantum mechanics to consider the...

When the universe branches, we branch with it.

Those branches don’t remain forever apart. They come back together.

So we, as conscious observers, are rescued from splitting into an immense number ever-so-slightly different versions of ourselves.

When the branches of the universe – and the versions of ourselves – come back together, we don’t worry that the many paths we took to get there are ever-so-slightly different.

We equivalence all those different paths. We treat all those ever-so-slightly different branches of history as if they were more-or-less the same.

I asked...

The causal graph is at the core of Wolfram Physics.

It’s crucial to the derivations of Special Relativity, General Relativity and Quantum Mechanics.

And if that’s not enough to convince you that you need to know about the causal graph, how about this:

The causal graph is a reflection of the nature of causality, the nature of objectivity, the nature of reality itself.

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Einstein’s train thought experiment

What is the multiway graph? video ⋅ podcast ⋅ article

What precisely is...

Is everything that’s ever going to happen in the universe already determined?

Or does something else – maybe randomness, maybe free will – play a role?

Stephen Wolfram’s answer to this question is straightforward: the ruliad is fully determined.

But there’s a twist. The ruliad is determined, but how we observe the evolution of the universe depends on where we are in the ruliad.

In a fascinating introduction to the role of the observer in the Wolfram model, Stephen touches on some of the deepest philosophical questions in physics, finishing on one of...

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...

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 i...

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...

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 h...

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 begin...

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...

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

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:

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:

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...

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. As...

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

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 expl...

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...

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

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.

Fortunatel...

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 fasc...

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...

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 Wolf...

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 fa...

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’v...

“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 info...

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 thei...

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.

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Stephen Wolfram’s 2010 TED talk in w...

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 Budapes...

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.

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Jonathan Gorard

The pa...

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...

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 Jonatha...

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!

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I rel...

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.

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Dugan Hammock

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.

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.

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I release The Last Theory as a video too! Watch here.

The full article is...

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!

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Dugan Hammock

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...

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?

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I release The Last Theory as a video too! Watc...

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 hy...