[Podcast] Jonathan Gorard on Compositionality, Multicomputation, Ontology, and Functoriality

Timestamps:
00:00:00 Introduction
00:00:31 Jonathan's professional roles
00:02:37 Jonathan's broad theoretical interests and background as a child and teenager
00:07:17 Did Jonathan sense a tension between discrete mathematics and continuous mathematics in his early studies?
00:10:41 What is "compositionality" in the context of (higher) category theory?
00:19:51 Does an ordinary "multiway system" have finitely or infinitely many threads of time?
00:24:03 Can we frame all physical (e.g., chemical, biological, and psychological) systems both as classical systems and multiway systems?
00:28:33 What is a "rulial multiway system"?
00:32:36 What is the "limiting rulial multiway system"?
00:34:27 Is there exactly 1 "limiting rulial multiway system", and if so, why?
00:37:31 Why is 99.9% of computational research focused on Turing-complete computation, as opposed to "hypercomputation"?
00:41:31 How is it that a finitary human being can even formulate an uncomputable function or uncomputable number if the laws of physics do not allow for a finitary system to actually realize "hypercomputation"?
00:45:46 Can the minimal (computable) and maximal (definable) scales of structure be concurrently produced by a "self-generating function"?
00:49:06 Ultimately, is there one unique ontology or an infinite equivalence class of ontologies?
00:54:34 Computational boundedness and heterogeneity of human observers
00:56:52 Uniting abstract syntax and concrete semantics using ∞-category functors
01:04:07 Grothendieck's Hypothesis
01:10:19 At the ∞-category limit, the syntax is functorially equivalent to potential semantic territory

[gnomeculture]

I’ll keep my remark short and sweet:

This is beyond exciting and I’m sure I’m not alone in saying that this new category of content has been eagerly anticipated 🎉

We love your dedication to this work Bernard! ❤️‍🔥 Can’t wait to see how it went!

[TheMemesofDestruction]

Jonathan is one of the most kind and brilliant folks I have had the pleasure of having a conversation with on YouTube. I always learn something. ^.^

[KineHjeldnes]

Not even 30 minutes in, and this conversation is amazing!

[EWischan]

I keep coming back to this discussion. The bit between 37:30 and 41:40 is so good! Put into much better words than I could.

[hamletwinston]

Wow good job for getting Gorard! I wonder if eventually you can convince him of the CTMU? 🧐

[hamletwinston]

Great interview! Gorard is a lovely person, too. Very authentic

[philippweisang]

In my view, Bach is describing the attempt of closing the gap between definability and constructability as the philosophical project of AI. I'm not sure the correspondence is 1:1 though.

[cruiser]

Cannot wait for this my friend, I already know it's going to be a good one. Would love to see you converse with more people in the future too as speaking with another person adds an extra dimension to these topics which can be even more helpful for understanding.

[rysw]

Maybe the most interesting interview I’ve ever listed to. First time watching the channel. Hope there’s more like this!

[muzzington]

Really looking forward to this! Any ideas as to who you're going to talk to next?

[parker]

This is extremely clarifying, and, I think, a good connecting point for analytically inclined people to realize the importance of category theory in physics. I love how generic the concept of thinking about things as a causal network, is, for thinking about complex systems that may be difficult for the reductionists to to reduce. It provides a framework for computer scientists to open the door to physics reframed into their world of computational modeling (or systemic modeling for a physicist).

[NightmareCourtPictures]

I'm definitely in the camp of the Ruliad as a real structure. It's just an object that describes space of all possible things that could exist and like in any other mapping exercise, one is merely mapping functions to and from the Ruliad...and therefor it's this Ruliad that "is" the universe because there only exists this object and things map to it and can't map outside of it. It's like a permutation group of rules, and any morphism is just mapping to the Ruliad up to it's size.

Can think of it like this. you got a 100x100 grid, and a 10x10 grid. The 10x10 grid maps to the 100x100 grid in all the ways that it can, but all configurations of the 10x10 grid, are permutations of 10x10 subsystems of the 100x100 grid. The Ruliad is contained in both of them equivalently (where every mapping exercise can be thought of as a rule), but the space of 100x100 grid has "more" rules because it can construct 15x15 or 30x30 states that the 10x10 grid can only approximate or conjecture it's existence. So the 10x10 grid approximates and conjectures rules of the 100x100 grid, which approximates and conjectures the "ruliad" grid, which could potentially be infinite.

So the Ruliad is the universe, the finite physical universe of 10^400 eames or w.e. map to the Ruliad up to that size...and approach all computable functions, and approximate all non-computable functions. I think this lines up with Gorard's thought on the subject, but just in a different perspective about what the Ruliad could be. I do not think hypercomputation exists...if it did it is like Wolfram would say "exist outside of the event horizon" just like how the 100x100 grid exists outside the 10x10 grid.

Regardless, I love Gorard's take on this stuff though, and i hope they (him and his collaborators) get to agree on something. Cheers,

[GEMSofGOD_com]

Languages and thinking themselves are about composing. The clearer structures are, the more achievable results become.

[novaterra]

+- 27.00 Casually mentions the discrepancy between the way nature operates and our models. My mind is blown mostly by how obvious this is to Jonathan despite the presumed abstract type of issues he deals with on a near daily basis. As someone that found their way into this 'sphere of discussion' from a background of philosophical curiosity and somewhat wanton autodidactic research focused on anything BUT mathematics for the most part thus far, this is great to hear. Despite coming at some of the (implied) topics from what could be considered diametrically opposed vantage points i feel a sense of potential convergence.

All possible worlds has felt like a questionable avenue in philosophy ever since i first encountered it; speaking in terms of potentiality is probably more fruitful, but not really any more clarifying without well defined context (well shit, english, words, all that). Mind was physically blown +-40.00 onwards, i was going to comment in here further but need to rewatch and take notes, no one wants to read several pages of unstructured reflection on the tube.

Going by the timestamps posted i did not expect this to be quite as 'accessible' to someone like me; jack of all trades and a sucker at math. While the deep technicalities are far beyond my current knowledge, i never felt completely disconnected from the discussion. Jonathan seems to have a sense for getting to the core of a subject, summarizing as well as can reasonably be expected (keyword 'whatever' as a courtesy, 'excuse', and a service at once), as well as an overall intuitive kind of intellect that does not blink upon breaking silly modern 'conventions of science'. He's got the skills to be a teacher, and i assume that's part of how you connected.

Great first podcast, great guest, mindbending content that proved not to be quite as arcane as i feared it might be. Lots of food for thought. I'll chime in on the language question after some homework, not for several weeks.

[nodelayfordays]

Regarding the talk at 56 minutes on homogeneity of humans, is it possible that we are evolving toward and just arent there yet and is it also possible that its relative to what's possible?

[alexeyprofi]

Truth is one for all and does not differ depending on the thought processes. It can be clarified by attributing false / true firstly to statements, the meaning of which is obvious to us, moving on to more and more complex

[KaliFissure]

Dude...I would so love a lunch w Jon.
We have like totally different approaches but partially for that reason it would be so interesting no doubt

[chineduecheruo]

Great interview. I share your intuition...Yes defining the minimal and maximal scale, would yield one ontology. The ontology of I AM. Imagination is causality. Jonathan is also right, semantics is in one to one correspondence to causality, because we are attracted to our Imagination. Our objects of meaning. Shiny words. Entangled meaning. Semantics.

[senri-]

Wow this was great, glad to see Jonathan back doing stuff like this, thank you both! Eagerly awaiting part 2.

[-ChrisD]

An amazing conversation! You two mesh well together.