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 https://www.wolframphysics.org/people...
• Jonathan Gorard at Cardiff University https://www.cardiff.ac.uk/people/view...
• Jonathan Gorard on Twitter   / getjonwithit  

• The Centre for Applied Compositionality http://www.appliedcompositionality.com/
• The Wolfram Physics Project https://www.wolframphysics.org/

Concepts mentioned by Jonathan

• Causal invariance https://mathworld.wolfram.com/CausalI...
• Multiway system https://mathworld.wolfram.com/Multiwa...

• Causal structure https://en.wikipedia.org/wiki/Causal_...
• Causal Set Theory https://en.wikipedia.org/wiki/Causal_...

• Directed acyclic graph https://mathworld.wolfram.com/Acyclic...
• Isomorphic https://mathworld.wolfram.com/Isomorp...

• Space-like separation https://phys.libretexts.org/Bookshelv...
• Simultaneity and simultaneity surfaces in relativity https://en.wikipedia.org/wiki/Relativ...

• Lorentz invariance https://en.wikipedia.org/wiki/Lorentz...
• Poincaré invariance https://en.wikipedia.org/wiki/Poincar...
• Conformal invariance https://en.wikipedia.org/wiki/Conform...
• Diffeomorphism invariance https://en.wikipedia.org/wiki/Diffeom...
• General covariance https://en.wikipedia.org/wiki/General...

• Confluence https://mathworld.wolfram.com/Conflue...
• Church-Rosser Property https://mathworld.wolfram.com/Church-...

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Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at https://lasttheory.com/podcast/035-ca...

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