Jonathan Gorard: 'Fast Diagrammatic Reasoning and Compositional Approaches to Fundamental Physics'

29th of April, 2021. Part of the Topos Institute Colloquium.
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Abstract: The Wolfram Model — a discrete spacetime model based upon hypergraph rewriting — can be naively formalized as a conventional double-pushout rewriting system over a partial adhesive category of (directed) hypergraphs. However, the abstract rewriting structure of the model also permits an elegant interpretation in terms of dagger compact categories, with considerable formal analogies to FdHilb and the foundations of categorical quantum mechanics, yet with an additional causal semantics definable in terms of a second symmetric strict partial monoidal structure (such that the entire system can be formalized, for instance, in terms of a double category or a weak 2-category). In addition to potentially defining a general categorical semantics for discrete models of quantum gravity, this formalism presents a fundamentally new approach to performing efficient diagrammatic reasoning over combinatorial structures, by suggesting various generalizations of the standard deductive inference rules of resolution, superposition, paramodulation and factoring in the Knuth-Bendix completion approach to automated theorem-proving, and by making more explicit use of the causal structure of the abstract rewriting system in the choice of which inference rules to apply. We show how this approach can be applied to the problem of enacting fast diagrammatic simplification of circuits in quantum information theory, as well as (time-permitting) the problem of efficiently discretizing the Cauchy problem in numerical general relativity, showcasing comparisons against some existing software frameworks and algorithms.

[Self-Duality]

I love this presentation and discussion! Amazing job to all involved, especially J. Gorard - deep respect and admiration 😌💭☘️💖

[Achrononmaster]

Everyone who comes up with a new isomorphism to a universal Turing machine thinks they've reinvented physics. But if they cannot even get an electron interacting with photons, without inserting it in by hand (finding a rule for it), they've got no physics, it's a delusion.

[NightmareCourtPictures]

The biological analogy at the end is accurate. The network theories of biology is the way to think about how biological systems work but what’s key here is that the network is the emerging structure of a deterministic…systematical array of the elements. The network thus creates the next level of systematic array of elements, so the networks are in a sense the same thing as the elements. Like xerses points out it depends on the level at which you look at these systems.

Fundamentally it’s Newtonian, but the elements in these networks are themselves made of networks too. Both are inseparable and thus the network theory way to describe biology is necessary. The wolfram model allows the two to be United in a single structure and complexity theory has always subscribed that this is the case.

The fact that physics gave such a push back against network theories is and always was a huge mistake. Probably the only thing holding physics back.

I’m addition, biological evolution has many similarities in terms of its relation to network theory and in many ways can be though of as computational. You can model evolution as you would a primitive computation of winning/losing (surviving and dying) as binary elements that make up a multi-way/casual evolution graph, performing a computation of “who wins” so to speak.

[johnalley]

10 < Living humans that can follow Jonathan through this stuff in realtime <100

[GEMSofGOD_com]

Dear Jonathan Gorard / anyone really, what the heck is Alephs, please strategize a periodic table of cardinalities and stuff OR I WILL

[tarkajedi]

It has taken me a year to catch up to a basic understanding of the maths and model and it is surprising, insightful and it will change the way all of us do physics it is that significant. To watch it unify and work with GR, SR and QM it is truely astonishing. Once you understand the ideas and maths you will become excited !!!

[tarkajedi]

If you haven't heard of the Wolfram Model or the pioneer Jonathan Gorard then where have you been the last year? The Wolfram Model is the most ground breaking work since GR, SR and QM! It is fantastic to also see his coauthors here! Brilliant minds working on an incredible new Model. I believe that Wolfram, Jonathan, and everyone working on this are heading for a Nobel Prize!

[drdca]

A nice talk :) .
However, I'm not sure that I understand the practical use of finding proofs of equivalence of proofs of equivalence of two different proofs of a certain theorem? Like, one level up, in order to work to improve the algorithm for finding shorter equivalent proofs for a given proof, it sounds reasonable that that is beneficial, but it would surprise me that going up many more levels of meta had a practical benefit? Maybe it is just meant to be theoretical after going up more than [some small number] levels?
There's the joke that when there is an infinite hierarchy of strategies in a particular competitive game, in practice the optimal strategy is at most 3 levels up, "because have you ever met a person".

The chat replay for this video doesn't seem to be working properly for me?