The Last Theory

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

• 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

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

Kootenay Village Ventures Inc.

Causal invariance is one of the most important concepts in the Wolfram model... and one of the most difficult to capture.

So I really wanted to hear Jonathan Gorard’s take on it.

In this excerpt from our conversation, Jonathan addresses the differences between causal invariance and confluence.

Causal invariance means that regardless of the order in which a rule is applied to the hypergraph, the same events occur, with the same causal relationships between them.

Confluence, on the other hand, is the coming-together of different branches of the multiway graph.

Jonathan explores different ways we might determine whether two nodes, two edges or two hypergraphs are the same, and explains that if we identify nodes and edges according to their causal histories, then causal invariance and confluence become the same idea.

I’ve found myself listening to Jonathan’s explanation of causal invariance over and over to make sense of it, but it’s one of the areas where I’m convinced Jonathan has a unique contribution to make.

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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
  • Multiway system

  • Causal structure
  • Causal Set Theory

  • Directed acyclic graph
  • Isomorphic

  • Space-like separation
  • Simultaneity and simultaneity surfaces in relativity

  • Lorentz invariance
  • Poincaré invariance
  • Conformal invariance
  • Diffeomorphism invariance
  • General covariance

  • Confluence
  • Church-Rosser Property

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

Kootenay Village Ventures Inc.

So many of the most complex and most promising graphs and hypergraphs of Wolfram Physics involve loops and self-loops.

They can play a crucial role in the evolution of graphs and hypergraphs... which means that they might play a crucial role in the evolution of the universe itself.

Loops and self-loops matter, because including them in our models reduces the number of arbitrary assumptions we need to make in Wolfram Physics, making it more complete.

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

The full article is here.

Kootenay Village Ventures Inc.

Dugan Hammock lives in the fourth dimension.

As Jonathan Gorard mentioned in our recent conversation on How to draw the hypergraph in Wolfram Physics, Dugan has worked on plotting the evolution of the hypergraph over time.

We get into that in the second part of our conversation, but in this first part, I get to know Dugan as a mathematician and artist.

Enjoy his amazing animations of three-dimensional cross-sections through four-dimensional hypershapes!

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Dugan Hammock

• Dugan Hammock’s videos on YouTube
• Dugan Hammock on Twitter
• Dugan Hammock at The Wolfram Physics Project
• Plotting the evolution of a Wolfram Model in 3-dimensions
• Temporally coherent animations of the evolution of Wolfram Models 

People mentioned by Dugan

• Max Cooper
• George K. Francis
• William Thurston

—

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

Kootenay Village Ventures Inc.

Computational irreducibility means that there are no shortcuts when we apply rules to the hypergraph.

I used to think that our existing theories of physics, such as general relativity and quantum mechanics, were examples of computational reducibility: shortcuts that allow us to make higher-level generalizations about how the application of rules to the hypergraph gives rise to our universe.

Jonathan Gorard used to think this, too.

But it turns out that over the last couple of years, he has changed his mind on this quite radically.

General relativity and quantum mechanics, he now thinks, aren’t examples of computational reducibility, they’re consequences of computational irreducibility.

I truly appreciated this part of our conversation, because it radically changed my mind, too, about this crucial concept in Wolfram Physics.

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Jonathan Gorard

• Jonathan Gorard at The Wolfram Physics Project
• Jonathan Gorard at Cardiff University
• Jonathan Gorard on Twitter
• The Centre for Applied Compositionality
• The Wolfram Physics Project

Concepts mentioned by Jonathan

• Computational reducibility
• Computational irreducibility

• General relativity
• Quantum mechanics
• Fluid mechanics
• Continuum mechanics
• Solid mechanics

• Partition function
• Boltzmann equation
• Molecular chaos assumption
• Ergodicity
• Distribution function
• Chapman-Enskog expansion
• Stress tensor
• Navier-Stokes equations
• Euler equations

—

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

Kootenay Village Ventures Inc.

There are two questions about Wolfram Physics I’m asked a lot:

What’s beyond the hypergraph?

And what’s between the nodes and edges of the hypergraph?

There’s a simple answer to this question.

Nothing.

There’s nothing beyond the hypergraph.

There’s nothing beyond the universe.

But it’s not a very effective answer.

So here’s a deeper response to the age-old question:

What’s beyond the universe?

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

The full article is here.

Kootenay Village Ventures Inc.

The hypergraph is the universe.

So if we want to see the universe, we need only draw the hypergraph.

The question is: how?

The nodes and edges of the hypergraph are determined by the rules of Wolfram Physics. But how we draw those nodes and edges is not determined.

The drawing of the hypergraph is not the universe, it’s just a way of visualizing the universe.

So I asked Jonathan Gorard how we might decide where to position the nodes and edges when we draw the hypergraph, so that we can see what’s really going on in Wolfram Physics.

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Jonathan Gorard

• Jonathan Gorard at The Wolfram Physics Project
• Jonathan Gorard at Cardiff University
• Jonathan Gorard on Twitter
• The Centre for Applied Compositionality
• The Wolfram Physics Project

People mentioned by Jonathan

• Charles Pooh
• Dugan Hammock
• Plotting the evolution of a Wolfram Model in 3-dimensions by Dugan Hammock
• Temporally coherent animations of the evolution of Wolfram Models by Dugan Hammock

Concepts mentioned by Jonathan

• Spring electrical embedding
• Spring embedding
• Layered embedding
• Causal graphs
• Coulomb’s law
• Hooke’s law

—

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

Kootenay Village Ventures Inc.

What is the Big Bang in Wolfram Physics?

There’s a straightforward answer to that question.

It’s the point in the evolution of the universe where the hypergraph goes from nothing to something.

It’s the start of the explosion that eventually yields the uncountable particles, planets, stars and galaxies of our universe.

So that’s pretty straightforward, isn’t it?

Well, yes, except that there’s one phrase above that demands further explanation: nothing to something.

How does the universe go from nothing to something?

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

The full article is here.

Kootenay Village Ventures Inc.

Here’s a slightly technical question:

Does Wolfram Physics really need hypergraphs?

Or could it based on graphs instead?

Jonathan Gorard shares some interesting insights into the evolution of Stephen Wolfram’s model for a fundamental theory of physics.

Wolfram started with trivalent graphs, in which each edge joins two nodes, and each node has three edges.

But when he ran into issues implementing simulations using these simple graphs, he solved the problem by graduating to hypergraphs, in which each hyperedge can join any number of nodes, and each node can have any number of hyperedges.

Here’s how hypergraphs, rather than graphs, came to be the basis of Wolfram Physics.

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Jonathan Gorard

• Jonathan Gorard at The Wolfram Physics Project
• Jonathan Gorard at Cardiff University
• Jonathan Gorard on Twitter
• The Centre for Applied Compositionality
• The Wolfram Physics Project

Concepts mentioned by Jonathan

• Trivalent networks (a.k.a. cubic graphs)
• Mathematica

—

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

Kootenay Village Ventures Inc.

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.