Donald Hoffman Meets Stephen Wolfram For the First Time on TOE

The Ruliad—the abstract object representing all possible computational rules—is the fundamental substrate of reality, from which physics, mathematics, and space-time emerge as observer-dependent projections rather than intrinsic features of existence.

“the ruad is just an abstract object and you know the fact and it is my uh sort of assumption perhaps but it's working really well that sort of everything that exists is somehow part of the ruad which means we are too which means that the ruad is sort of a substrate for everything that we are”

Time is not fundamental but emerges from computational irreducibility in the Ruliad; without computational irreducibility, the passage of time would be meaningless because one could jump directly to final states without traversing intermediate steps.

“the fact that the passage of time is Meaningful is a consequence of computational irreducibility if it wasn't for computational irreducibility the you know the leading of our lives would be there would be nothing that was actually happening it would just be oh we could jump to the end and say the answer is 42 or whatever”

The laws of physics—general relativity, quantum mechanics, and the second law of thermodynamics—are derivable from the Ruliad combined with two critical observer assumptions: that observers are computationally bounded and that observers maintain a persistent, single thread of experience through time.

“the thing that's been very exciting to me and was not something I saw coming at all was the way in which one can given the idea of the ruad the way in which one can derive the know laws of physics and that's something that you know if you'd asked me five years ago even would there be a way to derive general of derive quantum mechanics I would have said well there might be an underlying Theory from which those emerge but I don't think that there would be any way to for that would make those theories necessary”

Leibniz's mill argument—that examining the gears of a physical system cannot explain consciousness—remains valid because physical explanations cannot bridge the explanatory gap between mechanism and subjective experience, making it logically impossible to derive consciousness from unconscious physical substrates.

“liets was right with his argument from the mill and and that right now the the work that's been done in in cognitive Neuroscience on the models of Consciousness these are all my friends and colleagues that are working on this I always ask them okay you're proposing a neurobiological mechanism so what mechanism gives rise to the taste of mint... I I think there's a significant feature of us as observers that we have this concept that we have this belief that we have a single thread of experience”

No physicalist theory of consciousness can currently explain any specific conscious experience such as the taste of chocolate, smell of garlic, or taste of mint, despite three decades of intensive research by brilliant colleagues working on integrated information theory, global workspace theory, and orchestrated collapse of quantum states in microtubules.

“physicalists have been trying to give theories of Consciousness quite strongly now for the last three decades right so we have integrated information Theory uh Global workspace Theory orchestrated collapse of quantum states of microtubules and so forth but and I I know that the players and they're brilliant people and their friends and I they know what I'm going to ask them every time I talk with them or get on stage with them is what specific conscious experience can your theory explain Taste of chocolate the smell of garlic the the taste of mint... what I I you know we're in we're interested in scientific theories that explain specific conscious experiences what experience can you give me humans can experience around a trillion different experiences so it's should be like shooting fish in a barrel there's a trillion experiences which ones have you done and the answer is zero”

An observer that has no conscious experiences is not meaningfully described as an observer; consciousness is constitutive of observation rather than being an incidental feature that might be present or absent.

“an observer with no conscious experiences um is nothing I don't know what that means exactly”

Leibniz is claimed to have a key distinction over earlier idealism in that he could not imagine a way for consciousness to arise from non-consciousness, requiring all substances (monads) to begin as conscious or mind-like.

“Leibniz...could not imagine a way that mind could arise from non-m mind and I think you think the same thing that is you can't imagine a way that mind can arise from non-m mind”

Simple computational systems produce remarkably complex emergent behavior that contradicts intuitions about what simple rules can generate; after 40-45 years of studying cellular automata and computational systems, Wolfram finds he is constantly surprised by how much complexity and sophistication emerges from minimal initial specifications.

“I mean you know it's amazing that even after all these years you know I I do these experiments on different kinds of systems and I keep on being wrong and I keep on thinking you know this thing is somehow too simple to do anything interesting and my my intuition keeps on you know even though I think I've now developed much better intuition about this it is remarkable the extent to which sort of things much richer things than you might imagine can emerge from simple causes so to speak”

The persistence of a single, unified thread of conscious experience—the sense that 'I' am experiencing one continuous stream of events rather than multiple simultaneous conscious streams—is a distinguishing feature of human consciousness and may be critical to defining what consciousness is for observers like us.

“a critical feature of of our typical conscious experience is that we believe we are persistent and we have a single thread of Consciousness we think definite things are happening in the world we think definite things we think that we are thinking definite things you know forget about what's happening in the outside world but we imagine that we have a definite train of thought so to speak we do not imagine that we have kind of oh there are a superposition of a hundred thoughts that I'm having right now”

The central question in any investigation of consciousness is: what definition of success would satisfy the theory? In other words, what specific predictions or experimental tests would demonstrate that a theory of consciousness is correct rather than merely speculative?

“so so my question will be you know if you can define a notion of success for you know for Consciousness as experienced by you and as extrapolated by you as experienced by me and other humans and so on then the question is what you know that that definition of success of of did you manage to derive that can I then is that definition of success transportable enough that I can really apply it to an llm”

The S-Matrix approach in particle physics—describing only initial and final states without worrying about internal mechanisms—was developed by Heisenberg partly because attempting to treat space itself as discrete while maintaining consistency with relativity kept failing.

“the um you know one of the things that's relevant to you know my efforts to understand fundamental physics is the question of you know what's discret what's continuous you know back in Antiquity you know people are arguing about everything you know is matter discreete or continuous and so on that fin got resolved at the end of the 19th century basically and yes you know matter is discreet as made of molecules we can see brownan motion all those kinds of things and then very soon after you know light is consistent with being thought of as being discreet at the time 10 and something years ago most of the oos physicists were convinced that space was also discreet but they kept on trying to make that work from a mathematical point of view and particularly make it compatible with relativity and they kept on failing and Heisenberg as I recently leared was kind of in the middle of that whole effort when he said I just can't make this work and he said forget it all I'm not going to try and describe the mechanism I'm not going to describe what's happening in space I'm just going to set up the S Matrix and say you know this is given this initial configuration what you know how will that translate to final configurations”

Markovian matrices provide a computationally universal framework for modeling consciousness when interpreted as transition probabilities between conscious experiences, allowing the theory to capture essentially all possible conscious dynamics.

“so the first though I would bring up um something called the theory of computational equivalence that that that I agree with you on and it's a simple thing to point out that Marian kernels are computationally Universal it's trivial so so the problem is as soon as you've got probability in the picture you're no longer dealing with pure computational rules probability is a statement”

Electrons and other particles can be understood as carriers of pure motion through physical space—they maintain identity through space-time—analogously to how concepts are carriers of pure motion through 'idea space' in the computational substrate.

“when you have a particle like an electron or a photon a quark or something like this one of the things it's doing is it is a it is a carrier of existence through space and time that is the electron is a thing that you can identify as being the same electron when it moved to another place or another time and that's sort of similar to this idea that concepts are also sort of transportable things I mean in in our view of the way this works you know an electron is a something capable of pure Motion in physical space a concept as something capable of motion of pure Motion in Ral space”

The notion of truth is a derived and complicated human concept rather than a foundational notion in mathematics or physics, and the Gödel incompleteness theorem's appeal to truth as something transcending proof reflects platonist assumptions that computational approaches should reject in favor of constructivist frameworks.

“I think this the problem is this notion of Truth is a complicated derived human concept and I don't think it's the right thing to think about as a foundational thing I think that constructive constructing things is a much more useful foundational idea”

The equation of space-time with time by Minkowski—treating spatial and temporal dimensions as equivalent in a single spacetime manifold—is a conceptual error; time should be understood as progressive application of computational rules, while space is a structure we construct to describe the universe's content, making them fundamentally different categories.

“I think it it has not helped the progress of of a lot of kind of physics that people have sort of had this idea that space and time are the same kind of thing which is kind of I think you know in terms of doomed ideas that is a doomed idea that was that was a thing that you know Einstein didn't have that idea that idea came in when makovski said it's really cool that there's this quadratic form that we can write with space pieces in A Time piece and they all sort of fit together and that's how kind of this concept of space time was was born and I think it's it's sort of a mistake because I think that you know time as I see it is this kind of progressive application of computational rules and space is this thing that uh you can you can reasonably construct as a way to describe what's in the universe”

Mass of a particle can be understood as a projection of the entropy rate of a communicating class of Markovian kernels, spin is a projection of the determinant, and momentum is a projection of the number of asymptotic events in the communicating class, building a dictionary between particle physics and Markovian dynamics.

“we're proposing that particles in SpaceTime are projections of communicating classes of Markov kernels the entrop and the notion of mass of a particle is a ection of the entropy rate of the communicating class and the spin is a is a projection of the determinant and the entropy the momentum is a projection of the number of ASM totic events inside the communicating class”

Consciousness is fundamental and space-time is a perceptual interface or 'headset' that consciousness uses to interact with other conscious agents, analogous to a pixel display on a screen that creates an interface to underlying reality without being conscious itself.

“I think that our experience of space and time and physical objects is um just a headset so it's it's my Consciousness is is created a headset to interact with other consciousnesses and so when I look at you on the screen for example all I see is pixels and the the pixels on the screen are I wouldn't want to say are conscious but through the pixels I'm getting a portal into I think your Consciousness”

One can describe the world in terms of either mechanisms and underlying structure, or in terms of what is achieved (action principles), but these are complementary descriptions not contradictory, as demonstrated by Lagrangian mechanics.

“can describe things by mechanism or you can describe things by kind of what's achieved in the end so for example if we're doing mechanics we can describe the equations of motion for something you know a ball going through the air we can describe we can say there's an equation that says what the B will do at the next moment in time or we can say we're using an action principle and there is an overall constraint that the motion of the ball should minimize the you know the the action quantity”

There is no physical evidence or property inside the brain that can distinguish which neurons are 'conscious' neurons versus non-conscious substrate, and even if one could map every neuron and synapse, this would not answer the question of why those physical details give rise to subjective experience.

“if we could observe everything about the system its entropy would always be equal to one zero rather because there's only one possible state of the system is it state of the system future state of the system and so what leads to our perception of the increase of entropy is that we are not observing every detail of the system”

A prediction of Hoffman's theory is that massless particles (where mass = entropy rate = 0) must correspond to Markovian kernels with zero entropy rate (containing only 0s and 1s with one 1 per row) and maximum speed, which matches the known requirement that massless objects travel at the speed of light.

“when if we Define the entropy rate the mass to be a projection of entropy rate then that that forces us to make certain predictions so a mass zero would correspond to an entropy rate of zero and that would correspond to a Marian Matrix that has only zeros and ones in it a single one in each row and all has zeros and well so we know that in SpaceTime massless objects must move at the speed of light so it better fall out of our theory that you get the maximum travel speed in our theory for the things that are have zero entropy rate and it turns out if you look at the the What's called the commuting time between states and a Markov Colonel the the maximum commuting time the fastest commuting times you s so the smallest Community times the fastest travel times are for the ones with have zero entropy rates”

Local realism is false; particles only exist in the act of observation and do not exist when unobserved, and this undermines the entire line of questioning about whether a molecular copy of a brain would preserve consciousness because the original assumptions about physical continuity are incorrect.

“maybe an even prior question is do we believe in local realism in SpaceTime so I would want to argue that local realism is false and that and and even stronger that that in fact particles only exist in the act of observation and otherwise don't so to be really out there I'll say neurons only exist when they're perceived and neurons do not exist when they're not perceived so local realism is false”

Time emerges as a subjective experience for observers who lose information through projection; the full dynamics of the whole consciousness is stationary (no entropy increase), but projections of that consciousness necessarily exhibit increasing entropy and hence the experience of temporal progression.

“what what I'm imagining is that the the full dynamics of the whole Consciousness um is stationary but I am a projection of that so you I'm a trace so I'm a projection so I've lost information and it's it's a theorem pretty easy to prove that when you take you a projection Say by conditional probability where you lose information the projected chain will have increasing entropy so I'm proposing that there is no time for the whole Consciousness and time emerges as well as space as an artifact of the loss of information and projection”

Energy is most fundamentally understood as the flux of causal edges through space-like hypersurfaces in the Ruliad, and momentum is the flux of causal edges through time-like hypersurfaces, providing a geometrically natural definition of these quantities.

“one of the things that surprised me a lot was the very easy interpretation of what energy is so it turns out that energy is basically the amount of activity in this network I mean more formally if you make the causal graph it's the Flux Of causal edges through space likee hypersurfaces momentum is the Flux Of causal edges through time like hypersurfaces”

Consciousness operates through Markovian dynamics where conscious agents have qualia kernels (products of decision, action, and perception kernels) representing probabilistic transitions between experiences, and these kernels can be combined through a newly discovered partial order logic on Markovian kernels.

“we have a theory we call the theory of conscious agents and we have some papers that we've published where we have a mathematical model it uses marvian Dynamics um in the model and what we're what we're doing right now right is to try to answer your question”

A single observer cannot construct an external model of the world (the ruliad requires multiple observers to generate meaningful physics); the interaction and partial incompatibility between observers creates the scaffold necessary for building scientific theories of external reality.

“I claim if there's only one conscious agent that no Grist there's no there's nothing you can do to kind of build up that external model of the world just as I don't think you can tell in the solipsistic view of things you can't really tell whether there's any external whether there's anything out there”

The concept of a conscious experience (the taste of mint, the smell of garlic) is itself the starting point for a scientific theory of consciousness, not something that needs to be reduced to or explained by non-conscious processes; this is more parsimonious than theories that must both explain consciousness and explain away the initial evidence.

“if we don't know if we don't have a en description of the target it's very hard to answer that question...and you ultimately have only one instance of that which is what's happening inside you you don't even know that I have that same conscious experience”

Observers cannot be fully described or understood from within a single observer's perspective due to fundamental limitations in communication between different types of observers; humans can infer other humans are conscious through similarity but cannot achieve equivalent understanding with radically different observers like the weather or cats.

“the thing to to understand is this is you know it's a classic issue in in lots of areas of science you can describe things by mechanism or you can describe things by kind of what's achieved in the end so for example if we're doing mechanics we can describe the equations of motion for something you know a ball going through the air we can describe we can say there's an equation that says what the B will do at the next moment in time or we can say we're using an action principle and there is an overall constraint that the motion of the ball should minimize the you know the the action quantity by by the trajectory it chooses”

Probability in physical theories indicates the boundary of explanation; probabilities are the endpoint of mechanism, and introducing probability into a foundational theory admits incompleteness rather than solving the underlying problem, requiring a deeper theory to eliminate the probabilistic component.

“so so absolutely I agree that probabilities are the end of explanation and so when probabilities appear in my markovian dynamics of Consciousness I'm saying this is where my explanation stops we'll need a deeper if you want to get rid of these probabilities you're going to need a deeper Theory than the one I'm offering you right now”

One cannot easily jump between arbitrary points in the ruliad without a connected path; understanding novel regions of the ruliad requires gradual exploration following continuous mathematical principles rather than random leaps.

“we we to build up something which we can have a real experience of or something I'm not sure if experience is the right word we kind of have to go in steps like first we understand this we get familiar with that then we go to this and so on we're not we're not able you know if we're just thrown out there anywhere in Ral space it's just totally disorienting”

The universe is computationally irreducible and deeply wasteful of computational resources, generating vast numbers of different computational histories most of which have nothing to do with observers like us.

“the universe is an unbelievably proplate waster of computational resources and you know I had always imagined that there would have to be a definite history in the universe that it couldn't be the case that the universe is just sloughing off these immense numbers of different histories most of which are completely irrelevant to us”

In Hoffman's framework, there is no top element (no omniscient unified consciousness) and no bottom element, forming a non-Boolean lattice where consciousnesses can only combine when their overlapping states have identical probability measures.

“you can't combine consciousnesses unless where where they the states overlap they have the same Trace you have to have the same trace on your overlapping states to allow consciousnesses to combine”

Nematodes with 302 neurons are potential candidates for testing consciousness theories because their fixed, well-mapped neural circuit allows precise correspondence between neural states and subjective experiences, unlike humans where neural mapping is ambiguous.

“one might think even if I could accurately measure kind of the electrochemistry of the nematode that I would capture kind of that's the whole story or do you believe that there's something that is kind of beyond the physical...a nematode sort of interesting thought experiment could one nematode communicates scientifically to another nematode its internal experience of the taste of mint because after all the nematodes have a fixed set of nerve cells”

The dimension of space-time (3+1 dimensions) is not fundamental but emerges from observer properties; there is likely some obvious feature of how we observe that forces us to perceive three spatial dimensions and one temporal dimension, but observers with different sensory and cognitive properties could construct different dimensional structures.

“I'm sure the answer is no right and you know my guess is that there is some totally obvious feature of the nature of the observations that we make that leads us to believe that the universe is 3+1 dimensional”

The history of science shows that many phenomena previously thought to require vital or non-mechanical explanations (life, heredity, etc.) eventually yielded to mechanical explanations, yet consciousness remains stubbornly resistant to such explanation despite centuries of effort.

“so physicalists have been trying to give theories of Consciousness quite strongly now for the last three decades right so we have integrated information Theory uh Global workspace Theory orchestrated collapse of quantum states of microtubules and so forth but and I I know that the players and they're brilliant people and their friends and I they know what I'm going to ask them every time I talk with them or get on stage with them is what specific conscious experience can your theory explain”

A person taking a molecule-by-molecule copy of their brain might not preserve consciousness because protons or other physical particles might have consciousness-dependent properties that are lost in copying, similar to how computer memory only executes as a program when there is a program counter advancing through it.

“it is not obvious that if I copy a proton for example that it could be the case that there's a special proton that is a proton in a conscious mind that is different from proton from other protons and it could be that when I copy the proton it it is no longer a conscious proton”

The set of possible conscious experiences that humans could have is measure-zero compared to the infinite set of all possible conscious experiences in the mathematical space of consciousness; researchers should not extrapolate from their own limited experience to conclusions about what is or isn't possible in consciousness.

“the set of experiences that you've had is measure zero compared to the set of experiences that are out there so so don't make the the the the silly uh mistake of taking your own experiences as as comprehensive of all experiences really in some sense use your experiences to get going but then follow the math don't follow your experiences”

The Occam's Razor principle itself is not fundamental to reality but rather a feature of how human minds work; it is a subjective preference for simplicity that emerges from observer properties, not a law of nature.

“I don't know why aam's Razer is true I mean it's it's an interesting Criterion it's um in a sense the ruad denies oam's Razer because the ruad has everything all these kinds of things going on in it at some level from the point of view of of abstract Aesthetics the ruad is lovely because it assumes nothing but you know from the point of view of of you know is it saying oh the the description of what's happening for example let's take an aram's razor argument about what happens in a fluid okay the arham's razor argument would probably be if the fluid is Flowing from here to there all the molecules inside it must be flowing in exactly that direction that would be wrong”

The fact that matter is now understood to be discrete (atoms and molecules) after centuries of debate shows that intuition about what is fundamental is often wrong, suggesting skepticism about current intuitions that consciousness cannot emerge from non-conscious elements.

“you know if you'd asked me in 1980 do I disagree with liet's intuition I would have said um I don't know I don't know how you would get a mind-like thing to arise from a a non-m mind-like sort of uh origin but then by 1981 I was starting to do all kinds of computer experiments and so on about what you know what simple rules can actually do right and it really surprised me in other words what could emerge from something that seemed like it was too sterile to generate anything interesting I was completely wrong”

The notion of experience itself—whether subjective sensations like the taste of mint—consists of stable, transportable patterns that persist across time and can be compared across observers, whereas fleeting neural activations that appear and disappear without being robust patterns are not genuine conscious experiences.

“it is a non-trivial fact if it's true that that is a transportable thing through time that there is a consistent persistent thing that is the engram or whatever it is that represents that that concept and that it is robust and I think that that if you you know the version of it that's locked inside your brain at some moment in time I don't think that's transportable I don't think that's scienz I think that's a thing that you would say it is I mean if if we were thinking about it in terms of an llm it would be some little you know some some activation of some neuron at some moment and you know then it's gone”

The relationship between discrete and continuous mathematics mirrors the historical relationship between discrete matter and continuous fluids: what appears continuous at one scale (fluids) is actually discrete at another (molecules), suggesting continuous mathematics may be emergent from discrete computational structures.

“back in Antiquity you know people are arguing about everything you know is matter discreete or continuous and so on that fin got resolved at the end of the 19th century basically and yes you know matter is discreet as made of molecules we can see brownan motion all those kinds of things and then very soon after you know light is consistent with being thought of as being discreet”

Wolfram's Physics Project claims that general relativity can be derived more readily than proton structure from observer properties, and therefore the pathway to testable predictions should focus on spacetime structure rather than particle-level details like momentum distributions of quarks.

“you won't get there that that won't work but but I think you'll go if you can you you will probably be able to get from from this kind of formalism my guess is that you will be able to get basically the ruad and then you know then it's I'm all in favor of more people pushing to get from the ruad to the momentum distribution...that's a heavy lift I don't think we're going to see that in a short time”