Why I changed my mind about computational irreducibility with Jonathan Gorard

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 www.wolframphysics.org/people...
• Jonathan Gorard at Cardiff University www.cardiff.ac.uk/people/view...
• Jonathan Gorard on Twitter / getjonwithit
• The Centre for Applied Compositionality www.appliedcompositionality.com/
• The Wolfram Physics Project www.wolframphysics.org/
Concepts mentioned by Jonathan
• Computational reducibility mathworld.wolfram.com/Computa...
• Computational irreducibility mathworld.wolfram.com/Computa...
• General relativity en.wikipedia.org/wiki/General...
• Quantum mechanics en.wikipedia.org/wiki/Quantum...
• Fluid mechanics en.wikipedia.org/wiki/Fluid_m...
• Continuum mechanics en.wikipedia.org/wiki/Continu...
• Solid mechanics en.wikipedia.org/wiki/Solid_m...
• Partition function en.wikipedia.org/wiki/Partiti...)
• Boltzmann equation en.wikipedia.org/wiki/Boltzma...
• Molecular chaos assumption en.wikipedia.org/wiki/Molecul...
• Ergodicity en.wikipedia.org/wiki/Ergodicity
• Distribution function en.wikipedia.org/wiki/Distrib...)
• Chapman-Enskog expansion en.wikipedia.org/wiki/Chapman...
• Stress tensor en.wikipedia.org/wiki/Cauchy_...
• Navier-Stokes equations en.wikipedia.org/wiki/Navier%...
• Euler equations en.wikipedia.org/wiki/Euler_e...)
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Prefer to listen to the audio? Search for The Last Theory in your podcast player, or listen at lasttheory.com/podcast/032-wh...
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[@gergelyadamhorvai3020]

Despite all the advanced concepts that are mentioned, this is such an accessible video on a beautiful a most fundamental insight. How can there be only 2.6k views on this?? My mind is officially blown. I wish the best of luck for Jonathan and also the channel.

[@lasttheory]

Yes, this one really is a fundamental insight from Jonathan. Thanks Gergely!

[@samalvarez1875]

😅😅😅😅😅😅

[@konberner170]

We are too busy watching Luis Fonsi - Despacito, with over 8 billion views ;)

[@anthonypalomba351]

I love these videos! Please keep making them. When you discuss Wolfram Physics in terms of real life problems, you start to see how so much can be easily explained by it.

[@lasttheory]

Thanks Anthony, I really appreciate that! I'll be reaching out to Jonathan again soon to try to bring you more of these conversations.

[@WerdnaGninwod]

Cool insight. What struck me was quite how scale invariant this concept is. Jonathan enumerated examples from quantum mechanics at the nano-scale up to relativity at the macro-scale but always the same pattern of a computational irreducible layer, that in aggregate, presents itself to us as computationally reducible.

[@lasttheory]

Yes, that's one of the most wonderful things about Wolfram Physics: general relativity and quantum mechanics fall out of it in the same way. As you say, from the very smallest to the very largerst scales!

[@stormos25one]

That was an awesome video!! Really helped clear up the picture in my mind! Thank you very much for sharing this interaction!

[@lasttheory]

Thanks! Jonathan is always so clear in his thinking, it's a true pleasure to talk to him!

[@neps4th]

Awesome insight into "another" aspect of physics and the nature of reality.

[@lasttheory]

Yes, this, for me, was a truly revelatory part of my conversation with Jonathan.

[@TheMeaningCode]

This is so great! Very succinctly stated at the end. Thanks, Mark!

[@lasttheory]

Thanks Karen! Jonathan is always so eloquent!

[@wujacob4642]

Genius insight! These guys are really good, continuously pushing our understanding to the universe foward. Mark's summary at the end is precise and helpful. Thank you for presenting this!

[@lasttheory]

Thanks so much for this comment! Yes, Jonathan's insights are great, aren't they?

[@falklumo]

These guys may be really good. But they still fail at publishing their work such that Theoretical Physicists get a chance to look into this. Nevertheless, some criticism was expressed which AFAIK has not been addressed so far. That would be the first thing to do rather than pushing the claims further and further ... To build a YT fan community helps nobody, people with IQ 160+ need to take this serious or it is worth nothing. Theoretical Physics doesn't work by upvoting ideas, fortunately.

[@ericwaraujo]

Just a beautiful beautiful piece!!!

[@lasttheory]

Thanks, I appreciate that! Jonathan is brilliant and concise in his explanations, isn't he?

[@user-hg9xp9xr1i]

hey thanks for this great series. i STRONGLY encourage you and Jonathan to spend time on the work of Ian McGillchrist. He essentially demonstrates that computational irreducibility is an inevitable function of our brain’s structure. as such there is no other conclusion we could draw regarding the relationship between reducibility and irreducibility. we are hard wired to operate this way and navigate the balance between the two. as such you could say that neurologically speaking, it’s a foregone conclusion . i look forward to your reaction to McGillchrist and maybe even an interview with Ian, Jonathan and Wolfram :)

[@lasttheory]

Thanks! I listened to the episode of EconTalk with Iain McGilchrist on the Divided Brain and the Master and His Emissary www.econtalk.org/iain-mcgilchrist-on-the-divided-brain-and-the-master-and-his-emissary/ when that came out. Do you have any other recommendations of how to learn more on McGilchrist's ideas, about computational irreducibility in particular, e.g. a good introductory podcast or KZbin video?

[@barrypickford1443]

I keep thinking this too.

[@Unique-Concepts]

Best channel I have ever found....

[@lasttheory]

Wow, thanks!

[@tomgooch1422]

Excellent analysis! Dr. John Gustafson, in his book, The End of Error, takes a similar approach to the pervasive problem of wasting compute cycles in seeking improved accuracy. His Unum will change the world when it is eventually discovered and adopted by computer architects..

[@lasttheory]

Thanks Tom! I'll have to take a look at The End of Error!

[@Self-Duality]

Beautiful!

[@lasttheory]

Yep, Jonathan never fails to inspire!

[@darrennew8211]

Wow. That was very insightful.

[@lasttheory]

Thanks, Darren!

[@mills8102]

I will say the key word here is scale. It is right on the tip of the tongue but doesn't seem to escape the mouth in this conversation.

[@lasttheory]

Yes, scale is crucial. We don't yet know the scale of the hypergraph relative to the Planck scale (or, to put it another way, the scale of particles relative to the nodes and edges of the hypergraph). It's something I'd love to ask Jonathan Gorard more about in future!

[@mills8102]

@@lasttheory I really like that you show the terms mentioned on screen by the way. Very nice touch for us who are unfamiliar with these concepts. Thank you!

[@konberner170]

Good!

[@farhadfaisal9410]

It seems then that the de Broglie-Bohm version of Quantum Mechanics (QM) goes in the opposite direction of ''un-coarse-graining'' of the usual QM, if it is, as in Gorard's current way of looking at it, a coarse-grained version of a certain computationally irreducible theory.

[@lasttheory]

Thanks Farhad. I'm aware of de Broglie-Bohm, of course, but I'm not deeply familiar with it (I confess I found _Wholeness and the Implicate Order_ mostly impenetrable!) I'd like to ask Jonathan about hidden variables, and how the Wolfram model version of quantum mechanics compares, in my next conversation with him. Thanks for the prompt!

[@glitchp]

Keep making these!!!

[@lasttheory]

Will do... there's so much to explore here. Thanks for watching!

[@glitchp]

@@lasttheory absolutely if you need help with anything please feel free to reach out.

[@rbettsx]

I've got a 1:1 scale map in my knapsack.. but I haven't yet found the occasion to unfold it...

[@lasttheory]

Wait... no... dooooon't!!!!!

[@RonaldoReagan]

EXCELLENT

[@lasttheory]

Yes, Jonathan has such precise insights, it's always a pleasure to listen to him. Thanks for following along!

[@snarkyboojum]

It feels like computational irreducibility is related to discretising continuous theories like GR or Navier Stokes or Quantum theory etc. These theories that have historically given us continuous solutions to predicting how a system will evolve are ‘reducible’ but when you try to model systems computationally you have to come up with discrete algorithms that model the system appropriately and that’s where the irreducibility comes from. It’s a fundamental difference between using continuous functions to describe the evolution of a system c.f. a discrete computational approach. The issue is that you lose the ability to predict from general principles. Instead you just have to calculate quickly. You can do this quickly ahead of the phenomena you’re modelling, but you’re no longer looking for fundamental principles to describe a system, instead your looking for rules that evolve over a series of discrete steps to give you similar behaviour to the system you’re modelling. The main issue here is testability. It feels like admitting defeat to say “well the human mind is computationally bounded and so can never calculate fast enough”. If we lose testability and the ability to make predictions, what do we gain by taking such an approach? It’s almost like the continuous solutions like GR etc are something like fixed points in the evolution of the computationally irreducible discrete complex system underneath it.

[@lasttheory]

Yes, computational irreducibility might be an inevitable liability of discrete models. I think Jonathan's description of General Relativity and Quantum Mechanics as _statistical_ results gives us hope, though. We may never be able to throw enough computational power at a simulation to be able to test the theory, but if we're able to derive continuous equations that operate at a large scale, then we can make testable predictions. That's the hope, at least!

[@faustinus23]

So, starting from Wolfram-physics, how do we get the coarse-grained theory that combines general relativity and quantum mechanics?

[@tgenov]

The picture being drawn here is the theoretical distinction between the intensional (internal? microscopic) and extensional (external? macroscopic) properties of systems. It's a deeply Kantian idea. We have no access to "things in themselves" - we have no access to intensional properties.

[@kvaka009]

But isn't the implication here that things in themselves don't have access to their own intensional properties. A thing in itself is a dubious concept for that very reason, among others.

[@tgenov]

@@kvaka009 Not sure what “having access to own intensional properties” means. Imagine a black box - whatever’s inside it, you can’t look and see. Anything you learn about the contents is via interactions. Any hypothesis about its internal mechanisms is only ever a guess.

[@kvaka009]

@@tgenov precisely. The boundary of a black box (inside/outside distinction) is itself not an intensional property of the black box. It is an extensional feature of the interaction. So the concept of a "black box in itself" is a confused concept if it is assumed to be an ontologically self- supporting object, rather than an ideal object.

[@kvaka009]

@@tgenov and to clarify what I mean by "access to own intensional properties" is a subject, a for-itself, which does have access to its own inner states.

[@tgenov]

@@kvaka009 That’s predominantly because the subject doesn’t know what’s “in” or “out”. Are your thoughts in or out? Relative to what?

[@jonathanlalsiamthara2802]

Computational irreducibility may have to do with states/patterns? that arises from example rule 30 of elementary cellular automata. If one look at the pattern that is generated via this rule after several iteration it forms a bizarre asymmetrical mosaic formed after cellular interactions and there's no way to predict or compute beforehand how the mosaic would look like, even with knowing the initial conditions; unless we run all the iterations step be step.

[@lasttheory]

Yes, thanks Jonathan, you seem to have computational irreducibility right! If a rule produces patterns that are easily characterized, then the system is computationally _reducible,_ because you can take shortcuts to the patterns rather than compute everything step-by-step. If a rule produces chaos, then there are no such shortcuts, and we have computational irreducibility.

[@jonathanlalsiamthara2802]

@@lasttheory Thank you, admin for clarifying! I like the term 'chaos' you've used here.

[@Danhec95]

This helped me understand more where these pockets of reducibility come from… would be cool that this explanation is written somewherre

[@lasttheory]

Thanks, and yes, absolutely. I'm working on a video all about computational irreducibility, which will include Jonathan's unique insights. It'll have an accompanying article giving a written explanation of all this!

[@Danhec95]

@@lasttheory Thats fantiatic. Thanks for this wonderful channel!

[@IncompleteTheory]

This is absolutely fascinating insight from Jonathan. Very often I don't understand a lot what he's saying, but this was very accessible. Two observations: 1) Isn't this another (new?) way of defining emergent behavior? 2) Given that relativity emerges in the Wolfram model as a feature of the the of many individually irreducible hyper-nodes: can this not be used to further track our way towards the often assumed inherent flaw of relativity? Perhaps the issue with relativity breaking down in the singularity already points in this direction; by definition, the singularity should reduce anything with a multiplicity to 1, so it makes sense if the emergence collapses.

[@lasttheory]

Yes, Jonathan really changed my mind on this. 1) Emergent behaviour is a good way of putting it. The analogy with fluid mechanics is a good one, but yes, this is a _new_ kind of emergent behaviour, since it's the coarse-graining of hypergraph evolution (nodes and edges changing over time) rather than of the motion of particles. 2) Yes, I think you're on to something here. Continuous equations that approximate discrete nodes and edges are inevitably going to break down at some point, since those nodes and edges are _not_, when it comes down to it, continuous. Maybe the singularities of General Relativity are just the breaking down of our continuous approximations?

[@IncompleteTheory]

@@lasttheory Exactly! This touches another thought of Jonathan's: even if Wolfram Physics as it is doesn't hold up, it may be that the research on it brings some leads into light that may help to further the existing models.

[@lasttheory]

Yes, exactly, and not just in physics. Jonathan’s Centre for Applied Compositionality is looking at applications of these ideas across many other fields.

[@TurboJon]

Another great video. So if computational reducibility in physics is just a course-graining something that is otherwise computationally irreducible, I have two questions: 1) does computational reducibility exist at all but for the simplest and most obvious of rules/scenarios and 2) does this imply that the ultimate theory of the universe cannot be determined without slogging through 10^100+ steps for all but the obvious dead-end rules?

[@lasttheory]

Great questions, Jonan. 1) I don't know the answer to this, but I, too, fear that computational reducibility simply doesn't happen at larger scales. 2) Yes, it implies that we can't _simulate_ the universe beyond a few steps, but it doesn't mean that we can't _model_ the universe on a smaller scale and find statistical laws that simulate it _roughly._ This, as Jonathan points out, is analogous to the statistical laws of fluid dynamics: they don't simulate the fluid down to the position of every particle, but they _do_ simulate it _roughly_. I need to think about all this a lot more, but I'd like to dig deeper into what these statistical laws might look like, beyond the ones we already know, like general relativity and quantum mechanics.

[@oblivion_2852]

@@lasttheory isn't it the case for dark matter that we have created models that roughly approximate the formation of the universe and found that once simulated the overall structure doesn't match the structure we see in our skies. We may not be able to completely reduce the simulation of the universe but if we can run simulations with our course grained understandings we can more and more closely approximate through probabilistic modeling whether our theoretical models match the real model. Potentially with enough compute and perhaps the help of AI could we not incrementally improve on the functions that we use? (just like Alphatensor)

[@lasttheory]

@@oblivion_2852 Yes, exactly, we probably won't be able to run complete simulations of the hypergraph, but we can run simulations based on our course-grained laws, such as general relativity and quantum mechanics. If Jonathan is right, then these laws are intrinsically probabilistic rather than deterministic, but certainly we have enough compute to simulate them. And your point about AI is fascinating. I've thought about this, too: unleash an AI to attempt to find these course-grained laws based on particular rules. It's a promising approach, I think!

[@danpollard376]

Wolfram does a video where he explains "slice of the universe" ie a computationally bound observer can only reduce a coalesced version of possibilities that they are bound in. IE, we can only observe phenomena we can experience. Think of it like imagine you are a dust mote that has intelligence like an AI tool, the AI experience of the universe and what it can perceive can and will be so outside of what a bound human can experience that it has other realities open to it. Just like a human cant see light light a mantis, we cant understand the universe like an AI existing on another plane could see. Humans are stuck at coarse grain view and we have to infer the rest. Interesting to understand that the math may run out and we will be back to symbols and abstractions

[@lasttheory]

@@danpollard376 Yes, we may indeed be stuck at the coarse-grained level. We certainly have been so far in the history of physics. But there's hope that we'll at least see the _effects_ of the fine-grained level. For example, at what we think of as singularities in General Relativity, such as the collapse of stars into black holes, there may be observable effects of the discreteness of the hypergraph. If we can measure these, we'll not only gain evidence for the Wolfram model, but we may also be able to determine the _scale_ of the hypergraph.

[@generaltheory]

What about individual quants of properties that particles appear to practically have only in interactions with our quants of such properties (not necessarily of other particles)? What are steps up that make reducible constructions that make sense for, ultimately, say, us molecular humans?

[@lasttheory]

Right. It's not obvious how particles arise in Wolfram Physics. A good guess is that particles are persistent tangles in the hypergraph: knots of nodes and edges that, on application of the rules, propagate through the hypergraph while remaining intact. But if this is right, then it could take immense computational resources to simulate even a single particle, let alone interactions between two particles. And, at this stage, this persistent-tangles-in-the-hypergraph theory is entirely speculative. We don't know if it's right, and, if it is, how many nodes and edges might make up each particle (a hundred? a thousand? a million? a billion? more?) Much more to discover here! Thanks for the questions.

[@light8258]

I haven't really studied quantum mechanics let alone quantum field theory yet, but my question would be, what this means for group theory and how quantum fields arise from that. Are these groups also bulk approximations or are they part of the microscopic hypernode rules? And if they aren't, is there at least something in our current physics model, that could give us a hint at the microscopic viewpoint, so that Wolframs theory can be falsified? Very fascinating stuff, and I think Wolfram physics is on the right path, simply because they can explain, how something could arise from nothing, which to my knowledge no other "theory of everything" can do.

[@lasttheory]

I'm afraid your question goes way beyond my understanding of quantum mechanics and group theory! Best I can do here is point you to Jonathan's paper Some Quantum Mechanical Properties of the Wolfram Model www.complex-systems.com/abstracts/v29_i02_a02/ which is a good start on this topic. I'll be looking further into the derivation of quantum mechanics from the hypergraph, and hope to have a better understanding in the future. As you say, finding a way to prove the Wolfram model true or false at a quantum level is important. It _is_ fascinating, and I look forward to future developments here. Thanks for the question!

[@VideoGameWizardry]

Is this sort of the same way we can measure a computationally irreducible algorithm and make general statements about its results, like "It is complex" or "It is sort of random but shows pattern x"? Like of course we can't reproduce or predict the exact results of the computationally irreducible algorithm but we can sort of expect or be unsurprised by future general patterns within its next few steps?

[@lasttheory]

Right, yes, coarse-graining is kinda like that. The clearest example of coarse-graining I know is the behaviour of molecules of water. As you say, we can't predict the next few steps on a microscopic level: in the case of water, the precise positions of those molecules. But we _can_ predict what you call patterns: in the case of water, its incompressibility, its macroscopic flows, etc. Thanks for the question!

[@FutureDJ-wd3im]

The computational irreducibleness always exists but the reducible collections are what in essence shape our reality, that is our brains operate on knowledge and ordering of reducible phenomena that are primarily irreducible when examined. I interpret it as a restatement of the Heisenberg uncertainty principle in that we cannot measure things with ultimate precision. That is why the Wolfram physics is another theory of only the discrete and cannot properly describe ultimate reality which is in essence continuous.

[@lasttheory]

Yes, you're right, everything that happens that we can make sense of with our brains is order somehow reduced from the chaos of the hypergraph. What Jonathan's suggesting, though, it that this might not be a consequence of computational reducibility, more a consequence of statistics. Applying statistics to a chaotic system on a large scale _can_ reduce a discrete model (such as the molecular model of gases) to continuous phenomena (such as the pressure, volume and temperature of gases). Thanks for the comment!

[@jondor654]

Inexpert reflection here. Is it axiomatic that the utility of coarse graining is an acceptance of reduced resolution of the system model in question . Approximation transcends perfection in estimating. And more abstractly is the move to reducability in some way possible due to the indistinguishability of the "atoms" of the system.

[@jondor654]

While admitting of causality (for the most part...) in the physical system , I do not get the attribution of causality in the /a model

[@lasttheory]

Ah, yes, causality. It's a slippery thing. Jonathan Gorard understands causality better than I ever will, I think, but sometimes I wonder whether the Wolfram model's conceptions of causality really match up with what non-physicists are talking about when they talk about causes. Just because one event comes before another event, and is space-like (rather than time-like) separated from it, does that mean it _causes_ the other event? There's so much to say about this, I'm not going to be able to do justice to it here. It deserves its own video, or several videos. Coming soon. Thanks for the comments, Jon.

[@tim57243]

Does the hypergraph model make any predictions? Ratio between electron mass and quark masses, having three large spatial dimensions and one large time dimension instrad of some other number, things like that?

[@lasttheory]

Good question. There are no firm predictions at this stage. Predictions about particle masses are a _long_ way off. In the Wolfram model, particles _might_ be persistent tangles in the hypergraph, but even that's just speculation at this point. Dimensionality seems a lot more likely as a source for early predictions. Obviously, if the hypergraph corresponds to our universe, then whatever rule or rules operate are going to have to give rise to a three-dimensional universe. But it might not be _precisely_ three-dimensional. If we could measure slight discrepancies from three-dimensionality in the universe (e.g. regions that are 2.99999- or 3.00001-dimensional), that'd be a good indication that our previous ideas of space are wrong. Perhaps most likely of all are predictions that could arise from the discreteness of space. For example, if space is discrete at the level of the hypergraph, that could have consequences for extreme events such as the collapse of stars into black holes. We could derive the scale of the hypergraph from the emissions from such events. A long way to go before we have any firm predictions!

[@Youtubelaschool]

does the graph become more complex like a cellular automaton? I mean can we compare the cellular automaton and the hypergraph to a complexification of simple initial conditions? in other words, is the big bang 3 elementary points of the hypergraph for example?

[@lasttheory]

Yes, the graph is very much like a cellular automaton, in that you apply very simply rules to very simple initial conditions, and it becomes very complex very fast. As for the Big Bang, I think it could be even simpler that 3 elementary points. See me video _What is the Big Bang in Wolfram's universe?_ kzbin.info/www/bejne/bXjQiqOBjs-mqbs for how I think it could start from nothing. Thanks for the great questions!

[@Youtubelaschool]

In the case of the wolfram's hypergraph. Can we consider those initial conditions as algorithm ?

[@lasttheory]

@@KZbinlaschool I guess we could consider the initial conditions as _part_ of the algorithm. But it's a small part compared to the applications of the rules to the graph that creates the whole of the rest of the universe. The question of how much the initial conditions affects the evolution of the universe is an interesting one. I hope to do a video on this!

[@kevinvanhorn2193]

It's been 20 years since NKS; has anyone yet put forth a rigorous definition of computational irreducibility?

[@lasttheory]

Another good question, thanks Kevin. This paper arxiv.org/abs/1111.4121 Unpredictability and Computational Irreducibility from Herve Zwirn and Jean-Paul Delahaye suggests a number of formal definitions. Personally, I prefer a more intuitive definition: computational irreducibility is the inability to find simple shortcuts to complex computations. But I accept that more formal definitions have their place too!

[@Spencer-to9gu]

4:51 coarse grain reducibility is a consequence of discrete irreducibility? I get that micro irreducibility can exist alongside macro reducibility, but I don't see how he makes the leap that reducibility depends on/ is a consequence of irreducibility.

[@lasttheory]

Thanks Spencer. I think this is the point Jonathan's trying to make: 1. Coarse-graining depends on randomness (because if, for example, the motion of molecules in a gas weren't random, we couldn't derive laws for the coarse properties of gases, like temperature, pressure, volume, etc.) 2. Computational irreducibility is a kind of randomness (it's not literally randomness, because the computational rules might be fully deterministic; but it's as good as randomness, because if we, as large scale creatures, can't compute the behaviour of a system, it looks to us as if it's random) 3. Therefore, in the context of the Wolfram model, coarse-graining depends on computational irreducibility. I don't know if that helps clarify!

[@Spencer-to9gu]

@@lasttheory thanks for your response! I'm just not sold on point 1. that it's a logical statement of fact. I don't understand why it's considered necessary for things to be "random" in order to get coarse graining. could we get coarse graining from reducibility? I don't see why not, it's just that we wouldn't need it since what we're interested in is already reducible. fwiw, I love that Jonathan and the Wolfram team are tackling this project. I fully support good faith scientific efforts. also thank you for providing this kind of content! it's mentally stimulating and refreshing. much appreciated ❤️

[@lasttheory]

​@@Spencer-to9gu I think point 1. comes from the mathematics. If gas molecules are flying in every possible direction, then we can apply statistics and get the gas laws. If twice as many gas molecules are flying in one direction than in the other direction, i.e. if the molecular motion is _not_ random, than the statistics just don't apply, so we _don't_ get the gas laws. I'd need to brush up on my statistical mechanics to say much more! And yes, absolutely, we could get coherent large-scale behaviour from computational reducibility... _if_ there _is_ computational reducibility. If not, coarse-graining might be all we have to fall back on. Thanks for your kind comments! I find it refreshing, too, that the team are taking such a novel approach to physics!

[@TillerSeeker]

Okay then: Coarse graining in irreducible systems can give us reducible laws!

[@lasttheory]

Yes... well, I'd change the word _reducible_ there, I'd say coarse-graining of computationally irreducible systems can give us _statistical_ large-scale laws. But yes, that's the idea!

[@frun]

I believe, the concept of *Rewriting rules* is immensely important. Can it have a relation to Neural networks or Holography?

[@lasttheory]

I agree, rewriting rules is a surprisingly powerful concept! I don't know much about holography, but I know a little about neural networks. That's a fascinating idea that rewriting rules and neural networks might be combined.

[@frun]

@@lasttheory I see rewriting rules as a kind of backwards coarse-graining. As a kind of field renormalization in reverse. Use a rewriting rule backwards and you get collective excitations instead of atoms. One causal network for atoms and a new rewritten network for phonons. At least that's how i think, it may operate. I believe, SW is right, that time is absolute.

[@frun]

@@lasttheory Yes, that's an amazing idea. The whole neural network may be contained within the rewriting rule, leading to panpsychism. In holography, third dimension arise by consequently applying rewriting rule(coarse-graining). Rewriting rule = renormalization group flow.

[@lasttheory]

@@frun Yes, these are fascinating ideas. Panpsychism is a whole can of worms, strangely related to the question of absolute time. The Wolfram framework does have this concept of absolute time, which I really like. But it also has a more complex concept of time, in which consciousness collapses multiple threads into a single thread of time. Much more to come on this! Thanks for the comments!

[@frun]

@@lasttheory In causal sets, there is a partial order. SW mentioned it many times. Volovik mentioned inner and outer observers, one has an absolute time the other - relative time. The latter uses clocks ⏰ and rods 📏, made of long waves. This probably what rewriting rules do - coarse-grain to waves of longer wavelengths 🌊. Node is not simply a single particle - it is also a collection of them. Infinite ♾️ one, in fact. That's my view at least.

[@tempname8263]

In other words! Chaos and order are both similar. They make systems homogenous. Every piece looks like the other one. Thus, very complicated chaotic systems are similar to ordered simple systems Hence we can simplify chaos using statistics to a set of simple rules

[@timedowntube]

Very cool. Coarse graining seems precisley what the functions of cognition esentially all are. The fact then that cognition is the way to determine coarse grained rules is very circular (spiral really) in that the evolution of coarse grained sensing and responses as cell membrane voltage senistive chanels (computational transitors) has lead to the ability to create coarse grained perceptions of large data streams that are irreducible, find rules and follow rules allowing predictive power for the organism and hence evolutionary fitness in the given fitness landscapes' contingencies. Far out huh..

[@lasttheory]

Yes, that's interesting: evolution = ever more effective coarse-graining.

[@jacksonvaldez5911]

Is my understanding correct? Coarse graining makes statements about high level behaviors that are not derivable from knowledge about rules that govern a system such as the expansion of gas and increase in entropy, and the 2nd law. Computational reducibility makes statements about the exact future state of a system, and *are* derivable from knowledge about the rules that govern a system. And jonathan is saying that the laws of physics are more like coarse graining properties rather than computational irreducible ones?

[@lasttheory]

Yes, exactly: Jonathan is saying that General Relativity and Quantum Mechanics come from course-graining rather than computational reducibility. One change of words: I'd say that these laws of physics _are_ derivable from the rules, it's just that they're derivable _statistically,_ like the laws of fluid motion, rather than _deterministically._ Thanks for the question, Jackson!

[@jacksonvaldez5911]

​@@lasttheorythank you so much!

[@hypercube717]

Interesting

[@lasttheory]

Yep, this is fascinating stuff! Thanks for watching!

[@jamesvafiadis9579]

Are these ideas discussed in a paper I can cite?

[@lasttheory]

Hi James, yes, Jonathan Gorard has a paper _A Functorial Perspective on (Multi)computational Irreducibility_ which you can find here: arxiv.org/abs/2301.04690 Hope that helps!

[@jamesvafiadis9579]

Thanks!@@lasttheory

[@jamesvafiadis9579]

The paper focusses on a formal definition of irreducibility where I was hoping to find a source that discusses the course-graining function of an observer and its role in deriving fundamental laws. Gorard's paper 'Some Quantum Mechanical Properties of the Wolfram Model' touches on this but if you come across any additional sources please let me know. P.S thanks for the content!@@lasttheory

[@lasttheory]

@@jamesvafiadis9579 OK, thanks James. I don't know of anything more on coarse graining beyond _Some Quantum Mechanical Properties of the Wolfram Model._ This is a crucial concept, so I'll certainly keep an eye out for more!

[@konberner170]

I think you are touching on some of the deeper metaphysics that may now be required to proceed in physics. Your points reminded me of this section on page 51 of Chris Langan's CTMU (I don't claim the CTMU is proven, but some questions you are raising will likely require something similar to deal with the important topics you raised). "For example, some proponents of the radical Darwinian version of natural selection insist on randomness rather than design as an explanation for how new mutations are generated prior to the restrictive action of natural selection itself. But this is untenable, for in any traditional scientific context, “randomness” is synonymous with “indeterminacy” or “acausality”, and when all is said and done, acausality means just what it always has: magic. That is, something which exists without external or intrinsic cause has been selected for and brought into existence by nothing at all of a causal nature, and is thus the sort of something-from-nothing proposition favored, usually through voluntary suspension of disbelief, by frequenters of magic shows. Inexplicably, some of those taking this position nevertheless accuse of magical thinking anyone proposing to introduce an element of teleological volition to fill the causal gap. Such parties might object that by “randomness”, they mean not acausality but merely causal ignorance. However, if by taking this position they mean to belatedly invoke causality, then they are initiating a causal regress. Such a regress can take one of three forms: it can be infinite and open, it can terminate at a Prime Mover which itself has no causal explanation, or it can form some sort of closed cycle doubling as Prime Mover and that which is moved. But a Prime Mover has seemingly been ruled out by assumption, and an infinite open regress can be ruled out because its lack of a stable recursive syntax would make it impossible to form stable informational boundaries in terms of which to perceive and conceive of reality. What about the cyclical solution? If one uses laws to explain states, then one is obliged to explain the laws themselves. Standard scientific methodology requires that natural laws be defined on observations of state. If it is then claimed that all states are by definition caused by natural laws, then this constitutes a circularity necessarily devolving to a mutual definition of law and state. If it is then objected that this circularity characterizes only the process of science, but not the objective universe that science studies, and that laws in fact have absolute priority over states, then the laws themselves require an explanation by something other than state. But this would effectively rule out the only remaining alternative, namely the closed-cycle configuration, and we would again arrive at…magic."

[@lasttheory]

Yes, fundamental theoretical physics very quickly turns to metaphysics. I’m not sure I agree that randomness is tantamount to magic. We don’t get to decide the way the universe is: if it’s random, it’s random. It’ll be interesting to see how Wolfram physics lands on this. My suspicion is that it’s fully deterministic, at least in Stephen Wolfram’s formulation. Thanks for the comment!

[@konberner170]

@@lasttheory His claim is that basing any scientific theory on randomness is like basing it on magic, because randomness is, by definition, acausal. Yes, you said it was determined on the fine grain in ways you can't measure, and the measurement can be done on a course grain, but my point is that none of this is getting at the real issue, which is how the fine grain works at all.... at all. To answer this won't be easy.

[@glasperlinspiel]

Then, are these coarse grain structures, rulial domains?

[@lasttheory]

I think coarse-graining and rulial space are separate concepts. For any given set of rules (or, if you prefer, any region on rulial space) there'll be coarse-graining that creatures like ourselves can do to make sense of the hypergraph on a large-scale.

[@glasperlinspiel]

@@lasttheory thx. Hmmm, need a ruliad of category space, imaginary computation. Okay, now my head is spinning 😵‍💫 , well hallucinations die out, I suppose that’s what makes them hallucinations

[@arowindahouse]

I don't think general laws can be obtained "because" of molecular chaos, but rather "in spite" of it. If the micro was completely predictible, the macro would be trivial

[@lasttheory]

Thanks Jorge. Regardless of how the Wolfram model maps on to physics at a large scale, I don't think it's true to say that predictable micro → trivial macro. Take fluid dynamics, for example. Neglecting quantum effects, the micro behaviour of water molecules _is_ completely predictable, yet the macro behaviour of water is far from trivial, it's chaotic except in rare ordered circumstances. I think Jonathan's point is that it's the same for the Wolfram model. Chaos is the norm, but there are rare ordered circumstances in which the chaos averages out to the laws of physics.

[@kingsolomon2571]

🤔

[@gavinlangley8411]

Great insight but isn't it simply a statement that the there is a huge gap between the theory and any practical proof? Computationally irreducible just means too big to calculate. Calling it a formalisation comes from the same issue and, similar to string theory, it just becomes an interesting mathematical exercise?

[@lasttheory]

Thanks Gavin. I like your definition of computational irreducibility: "too big to calculate." It's a good question: is the Wolfram model just an interesting mathematical exercise. Unfortunately, I think the answer is that only time will tell. We _do_ have some pointers, though: the fact that general relativity and quantum mechanics fall out of this formalism so naturally is surely a good sign.

[@dr.bogenbroom894]

What? I thought you meant that when I first heard of computation irreducibility, i guess i understood it right by accident.

[@lasttheory]

You're way ahead of the rest of us: we had to take a wrong turn before getting to the right answer; you just went straight there!

[@dr.bogenbroom894]

@@lasttheory I don't think so, I don't know practically anything about physics, although enjoy trying to learn something from people like Jonathan and Stephen.

[@Ubu987]

Symmetry is a boundary condition, not a foundation. If it looks simple, the underlying phenomenon is too complex to be understood. Viewpoints determined by bandwidth - windows into systems of impossible cardinality!

[@soniahazy4880]

🤩🥰🕴💎🛸

[@falklumo]

When I asked Wolfram a few years ago on his blog about this, he actually never responded back. That was very disappointing. I argued that his branchial space construction is in contradiction with irreducibility. If branchial space (or wave functions better) is now constructed as a reducible coarse grain approximation, the picture changes a lot. To the point that the ORIGINAL idea put forward by Stephen can now be considered debunked. What is your take on this? And why no feedback on this? Another point is that this still does not solve the issue with the Bell inequality for a hidden variables theory such as this.

[@lasttheory]

I do find Jonathan's statistical lens compelling, though the fact that Jonathan himself has changed his mind on this shows that it's not an easy question. Could you say more about why you consider branchial space construction to be inconsistent with computational irreducibility?

[@falklumo]

@@lasttheory To assume causal invariance and computational irreducibility at the same time is odd and requires digging deeper. What Stephen does not do in his original proposal, just handwaving arguments. Which I call an inconsistency.

[@lasttheory]

@@falklumo Thanks, Falk. With causally invariant rules, there's always the possibility of different branches of the multiway graph rejoining. I'm not sure that implies computational reducibility, though. Just because the branches _might_ rejoin, it doesn't mean, as far as I can tell, that it's possible to reduce the computation required to determine, for example, whether they _do_ rejoin. But I, too, need to dig deeper on this: I'm not sure! Thanks for putting this in my mind as something to think about.

[@falklumo]

@@lasttheory Thanks. I don't want to dig deeper here as ultimately, this is over my top. My point is: there are valid concerns to be raised about things where arguments are hand-waving at best. And when asking hard, one is NOT getting satisfactory answers. This doesn't mean the whole thing is bogus. But it is mathematics rather than physics. In its current state, I cannot see how a link to the physical world can be made other than by wishful thinking. Maybe I am wrong. But I need to see the evidence. There are IQ 160+ Theoretical Physicists and so far,, no one seems to endorse Stephen's ideas. Which is odd.

[@lasttheory]

@@falklumo Yes, hand-waving can be frustrating! In case it helps, Jonathan Gorard has done some serious mathematics deriving Einstein's equations from the hypergraph. Take a look at my video _How to derive general relativity from Wolfram Physics_ kzbin.info/www/bejne/Z6XNmXhmipKgncU for more on this. Thanks for the comment thread!

[@williambranch4283]

The universe is analog, not digital. Even digital systems are analog simulations of a man-made system. So reducibility is confusing in terms of digital systems. Computationally, in type theory ... the particular value of a particular element of a particular type is indeterminate by definition ... it only has a partial value (qualitative macro) if you apply a restriction on the variable, and if the type restriction is sufficient you get just one value.

[@annaclarafenyo8185]

This is nonsense. Molecular chaos is NOT computational irreducibility, it's ergodicity. Given chaotic molecular motion, you CAN'T encode a Turing machine into it. It takes a heck of a lot more work to find an irreducibly complex system in the sense of computational irreducibility that Wolfram means.

[@nagualdesign]

Could barely understand the first 30 seconds because of the stupifying background noises. Like having some idiot saying, "BEEP BOOP BOP BLOOP BING BONG...", in one ear while I'm trying to listen to someone talking in the other ear. 🤬

[@lasttheory]

It sounds like the introductory music was too loud for you. Sorry about that! I can certainly lower the volume on future videos. Thanks for the feedback!

[@aaronkuntze7494]

That's your problem! You don't know what the BLEEP you know! Watch the movie WHAT THE BLEEP DO WE KNOW?! And you will know what the BLEEP we know. Any intelligent questions? Education is greater than Opinions and Beliefs combined E>(O+B) =QUANTUM LOGIC It's a fundamental law of physics and philosophy and technology All three at the same time all the time. Got logic?

[@DIPsuicide]

This means that Asimov's Psychohistory is possible.

[@lasttheory]

Yes, it's all about statistics. Though given the difficulty of merely deriving General Relativity from the hypergraph, predicting human behaviour might take a while... Thanks for the comment!