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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The Last Theory is hosted by Mark Jeffery, founder of Open Web Mind