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Show Notes
This is a ~1.5 hour talk + discussion, titled "A Multiscale Logic of Collective Intelligence" by Donald Hoffman ( and Chetan Prakash ( with Robert Chis-Ciure ( and Chris Fields ( and me.
CHAPTERS:
(00:01) Beyond space-time physics
(10:10) Minimal observer participants
(18:49) Recursive trace logic
(35:08) Actions and trace blankets
(43:45) Physics and agency together
(52:32) Causal emergence and joins
(59:52) Contextuality and quantum logic
(01:06:00) Unitarity and positive geometries
(01:16:29) Consciousness-first mind theories
(01:24:39) Testing models together
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Transcript
This transcript is automatically generated; we strive for accuracy, but errors in wording or speaker identification may occur. Please verify key details when needed.
[00:01] Donald Hoffman: A multi-scale logic of collective intelligence, and it's what we call the recursive trace logic. We've had the trace logic for a couple of years, but in the last couple of months discovered a recursive aspect to it that will lead into a notion of agency that's novel. This is different, Chris, than the conscious agent theory. It's a different notion of agency than we've had before. The big topics I'd like to talk about are: can you guys see me? Yeah. Okay. So I'm going to talk a little bit about collective intelligence, our model of collective intelligence, how it involves core screening, which is important to you guys, how it involves generative models, minimizing surprise automatically, bending problem spaces, a recursive notion of agency and self, a new intelligence metric for agents, we'll call lambda sub 2, and its relationship to your measure K. And then how this is all beyond space-time and quantum theory. And I'll start there just briefly about why I'm thinking entirely outside of space-time and quantum theory. The idea is that high-energy theoretical physicists are done with space-time. They say it's not fundamental. So here's Nima Arkani-Hamed at the Institute for Advanced Study. Space-time is doomed. There's no such thing as space-time fundamentally in the actual underlying description of the laws of physics. And he makes it very, very clear that he's saying space-time and anything inside space-time, and that includes anything with unitary evolution, quantum theory in particular. So he's going beyond space-time and quantum theory. And it's not just him, it's because of his success and his collaborators, the ERC has funded a 10 million euro initiative called Universe Plus. And it's all about going entirely beyond space-time and entirely beyond quantum theory and looking for what they're calling positive geometries. And so there's over 100 high-energy theoretical physicists and mathematicians now working on this, and they're finding stuff. And I can talk a little bit about how it's related to what we're finding, but they're finding these positive geometries that give you scattering amplitudes without any quantum theory whatsoever. And you get it much more easily than, and more simply than with quantum theory. So it's clearly quite striking. So I'm stepping entirely inside of space-time. Yeah.
[02:42] Michael Levin: Sorry, just a quick question. Maybe naive, but I just want to understand this idea of space-time being doomed. So on that view, if that were correct, what is the status of, let's say, general relativity? What does it refer? Is it completely different, be supplanted? What is that theory about then?
[03:01] Donald Hoffman: Right, so the idea is that the very notions of space and time, even the combination of them as space-time, is not fundamental at all. So general relativity will go the way of all theories. It will be, like Newton, we still use Newton for certain cases, we'll still use GR for certain cases, but we needed a much deeper theory. The hard fact is that when you bring together GR and quantum theory, you find that space-time has no operational meaning at the Planck scale, 10 to the minus 33 centimeters, 10 to the minus 43 seconds. It simply has no operational meaning. So that means we have to find a deeper foundation. So these are only, at best, approximation theories.
[03:50] Robert Chis-Ciure: So Don, just to be clear, in the obviously Kantian vein in which I know much of your theories, this is not only denamitating the space-time at the empirical level, it's also ejecting it from any transcendental style considerations. It is just a placeholder, until we have something better, but it will die as a concept in our economy of thinking, even about our experience, let alone the empirical physical world.
[04:22] Donald Hoffman: Absolutely. That's the idea that we thought space and time were the fundamental nature of reality. We might have even thought they were a priori true or something, but that's just wrong. That's just plain wrong. And science has a way of forcing us.
[04:37] Chris Fields: If one formulates basic ideas of quantum theory outside space time completely, then there are many routes, which are understudied by huge numbers of people, again, for generating space time as a consequence of basically assumptions about quantum information theory, and also many, many routes for generating Einstein's equations as either approximations or again, outcomes of other kinds of assumptions. So GR turns into something like the status that classical physics has with respect to quantum theory in space time, which is a limiting case, an approximation that's good in some circumstances for doing some things, which is basically how Don just characterized it. So yeah, there's lots and lots and lots of physics underlying this, both in the high energy community and the quantum information community.
[06:07] Donald Hoffman: Right, and what NEMA and the ERC group are doing is even going beyond that because they're saying we're not going to even start with quantum information theory. Anything quantum itself is going to arise joined at the hip with spacetime from something far deeper. So they want to show quantum information theory and general relativity arise together from something that couldn't care less about unitarity at all. So that's what they're after. So there is no locality and there is no unitarity, period, in these new positive geometries. And they don't care about unitarity. And they show that then quantum information theory comes out as an approximation in special case at the same time that you get spacetime. So it's different than the Carlo Rovelli kind of approaches and so forth. So that's the direction you should be trying to go here.
[07:03] Chris Fields: You should actually say that it contradicts most of quantum information theory, because quantum information theory actually has nothing to do with spacetime. So the two arising together would be very unusual.
[07:23] Donald Hoffman: Well, what Nima wants to show is that unitarity and locality together arise from these positive geometries. And then, because you get unitarity rising from it, then you get the foundations for quantum information theory, so that, but we'll see the proof is if you can do it right, so yeah, but I'm just trying to be clear about where they stand with respect to current approaches to trying to build up. As you say, Chris, most approaches that are trying to build space-time are starting with something quantum, and these guys are not. They're saying, we're not even having quantum. We're starting with what they just call positive geometries. So I just wanted to make clear how out of the box their thinking is. So John Wheeler, of course, was trying to think out of the box, and he was saying, you know, someday, this is in 1990, and his wonderful book on gravity and space-time, he says, someday surely we'll find, we'll see a principle underlying existence so simple, so beautiful, so obvious that we'd all say to each other, oh, how could it have, we have all been so blind so long. And so that's what we're looking for. And let's see. I'm not able to, can you guys hear me?
[08:38] Michael Levin: We can hear you, but the slides are not advancing.
[08:40] Donald Hoffman: Let's see. Okay, I guess now advanced. And he said about the same time in his...
[08:52] Michael Levin: Sorry, we're still seeing the type of slide.
[08:56] Donald Hoffman: Okay, let me try this again.
[09:01] Robert Chis-Ciure: We only saw the title page so far.
[09:05] Donald Hoffman: I'll go back and try the... That's weird. So I'll... Let's see. So I'll go back to share. Sorry about that. That's weird. Can you see that?
[10:01] Michael Levin: We can, but it's still in.
[10:08] Donald Hoffman: Yep. Okay.
[10:10] Michael Levin: Yeah, there we go.
Donald Hoffman: Okay, so Wheeler suggested that the notes struck out on the piano by the observer participants of all places and all times, bits though they are, in and of themselves constitute the great wide world of space and time and things. So he was trying to start with what he calls observer participants. And he thought that maybe somehow, and that was in his It from Bit paper in 1989. And he actually, in his paper, cited work that Chetan and I were doing, our book Observer Mechanics. So he was already thinking about the stuff we were doing with observers and participants back then. So what's a minimal observer participant? I'm going to have, we're going to start with just the absolute bare basics. They have experiences, like smell of garlic, taste of mint, and these experiences can change. That's all I'm going to assume. That's the foundation of everything. So my ontology is there are experiences and they can change. So for example, maybe I have four experiences, a very, very simple observer, red, green, blue, and I'll call that yellow, and they change. So now I'm seeing yellow, now I'm seeing green, now I'm seeing blue, and so forth. They keep changing. So a simple, in fact, the simplest and most general way of talking about that is just to talk about Markov chains. So the Markov matrix there, the first row has 0.2, that means if I see red now, what's the probability I'll see red next? The 0.3 is if I see red now, that's a three-tenths chance that I'll get, a 30% chance I'll get green next and so forth. So it's just a transition matrix, probability of seeing the next color, given that I'm seeing the current color. So that's all Markov chains are, there are these matrices. Of course, a lot of complications come out of that. And one aspect of Markov chains is that they immediately instantiate a very interesting kind of goal-directed behavior. No matter what state you start the Markov chain in, it has a target stationary measure. In this case, it's the thing on the left, 0.33, 0.30, 0.16, and 0.21. No matter what state you start this matrix in, it is going to go eventually to that state. And you can perturb it as much as you want. It will resist the perturbation and head back to that target state. So already we have, in the very structure of this, a goal-directed behavior. So, and as you guys in your papers talk about, William James mentions that intelligence is achieving a fixed goal with variable means of achieving it. So, that's the stationary measure, and if you have an ergodic Markov chain, then you will have a stationary measure. Now, the idea is I want to have multiscale collective intelligence, and so we need a notion of scale. So, I'm just going to take an observer that sees a subset of the states that this is. So the first observer I was talking about has four colors, you can see. Let's consider one that has only two. So that's my notion of scale. How many, you know, the subset relationship among the number of experiences that you have. Now, so here's the key idea of everything we're going to be doing now. Suppose I take the matrix on the right as describing, quote unquote, the reality. This is what's happening. And those are the transitions. But this observer on the left only sees two, red and green. What transition probabilities is it going to see? There should be a formula. Given the matrix on the right, there should be some kind of computation we could do to give us a two-by-two matrix for the transitions on the left, just in red and green. Does that idea make sense?
[14:04] Donald Hoffman: Yep. Okay, good. So when you do the mathematics, it turns out that's the matrix. So you get this very two by two matrix. Notice that the numbers are completely different from this matrix, right? It's not just copying, it's the computation that you have to do. And so here are the two matrices. The one on the right is the big matrix. And if you just restrict attention to the red and green, then you get the matrix on the left, induced by the matrix on the right. And this is called the trace, so the matrix on the left is called the trace of the matrix on the right. That's just standard in Markov theory that's been around for more than half a century. So this is not new to me or to us. Now, you can actually, the trace formula is important. I'm going to go through it because it has an important conceptual thing for us. So the way you compute the trace, so I'm going to take this matrix, I want to, I'll call it matrix P, and I want to get its trace on the red and green. So first I'll just notice that we can take this matrix and divide it into four sub-matrices. There's a two by two matrix that has 0.2, 0.3, 0.5, 0.2, that's for the red and green and so forth. That we'll call matrix A, so that's going to be the states that are visible to the trace observer, right? So A is the sub-matrix based on the states that are going to be visible to the sub-observer. C is the sub-matrix relating states that are dark to this new observer. It doesn't see this, so this is all dynamics that's dark to it, okay? B is the matrix that is the exit. This is the exits from what you can see to the dark region. So B is the exits, and D is the re-entrance. This is getting from the invisible world into the visible world. So those are the sub-matrices that we're going to be using, and here is the formula. This works universally. The trace, so the trace matrix on A, which is the visible states, is you just take the original matrix A, so 0.2, 0.3, 0.5, 0.2, and you add this interesting thing on the right. That I is the identity matrix. So you take the identity matrix minus the dark matrix. So I minus C is the identity minus the dark matrix. And you take its inverse. That has the effect of being able to explore all possible paths. There's an infinite number of paths through C that you could take. So you allow I minus C quantity inverse is exploring the infinite number of paths there. And then you pre-multiply by the exits and post-multiply by the entrances. And you add that all up and that's your trace. So that's the idea. You're basically, you get the trace by looking at all the ways that you could go outside of the trace and then coming back into the trace, the trace states, okay? That's the general formula. So that's been around, again, that's not us, that's been around for a long time. So you have hidden memories and controls. B, C, and D are going to be hidden layers of control that the agent A cannot see, but will be influencing their behavior. So that's going to be an interesting hidden memory kinds of possibilities now with B, C, and D. So there's explicit memory changes when you change A directly, but then there's going to be hidden.
[18:00] Robert Chis-Ciure: Don, just one second, can you please go back? In this BCD, so the exits, the entrances, and the invisible, is there any particular mapping to memory or control, or is it more of a blanket category you're using hidden memory or controls? Is memory, for example, C, the dynamics, hidden dynamics in C, or what's the control here? I suspect exits and entrances would be more like control.
[18:27] Donald Hoffman: Well, it turns out that there's different ways to control. You can screw around with B, you can screw around with C, screw around with D, or all of the above in any combination you want. All of them together give you different ways of controlling. So it's really quite fascinating, the possibilities here.
[18:46] Robert Chis-Ciure: Very cool, thanks.
[18:49] Donald Hoffman: So all of that is old, here's the new stuff. We discovered just a couple years ago that the trace relationship gives you a partial order on all Markov chains. That was the discovery, and that's what sort of launched this whole thing. So it's a partial order, which means that there is a logic. So the definition is that the matrix M is less than or equal to a matrix N in the trace order if and only if M is a trace of N. That's it, one trivial definition, but no one saw it before. And it turns out that that definition gives you a multiscale logic of minimal surprise. And the reason it's minimal surprise is because the trace is the zero-surprise view of the bigger matrix. That's the key idea. It is the zero-surprise subset view. And we'll talk about the stationary measures as well. The stationary measure is identical to the, is a normalized restriction of the original stationary measure. So you have minimal surprise in the dynamics. In fact, zero surprise in the dynamics. And in the stationary measure, again, zero surprise. So the trace logic is the logic of minimal surprise for arbitrary dynamical systems. So that's the power of this, because minimizing surprise is, of course, key to intelligence, a key to intelligence. But this is multiscale. So this is the multiscale logic of minimal surprise. So what about this trace logic? The set of all Markov chains form a non-Boolean logic under the trace order. It's non-Boolean. That means that there's no global top, there's no global negation, many matrices do not have meets and joins, or ands and ors. However, so it does have a notion of meet, join, not, and entails generally, but many matrices are not compatible. So they may or may not have meets and joins. So it's a very, very complex logic. However, if you take any particular Markov chain P, and you look at all of its traces, they form a Boolean sub-logic. So I can pick any Markov chain I want to, any one at random, look at all of its traces, all those Markov matrices together form a Boolean logic. So the notion of and, or, not are completely well-defined. And this Boolean logic has 2 to the n members. If there's n experiences, then there are 2 to the n members in this Boolean logic traces. So that's, if you think about it, all we've got right now are, we don't have agency yet, although I showed you that notion of goal-directed behavior, which is sort of like a proto-agency kind of thing. Already, these matrices are going toward their stationary measure, no matter how you perturb them. So already, there is this interesting notion of some kind of agency going on there. But now, here's the key idea. And this is only now two months old, this idea. And that's why, when I had this idea, I realized that it was time to talk with you guys. Once we have the trace logic I've talked about is a logic on observer windows. So it's an infinite space of all possible observer windows. There's this minimal surprise logic on all of it, the trace logic, cleanly well-defined.
[22:53] Donald Hoffman: Now, how do I want to do model agency? And this is the new idea just in the last few weeks. Agency is a matter of changing which window I want to look through. I want to have a policy for how, if I'm looking at the world this way, then how do I want to look at the world next? And how do I do that? Well, another Markov chain. The Markov kernel will say, what's the probability, if this is my current window, that my next current window will be such and such? The way you write that down is, again, a Markov matrix. So what we have is a policy is a Markov matrix on the trace logic itself. So the trace logic is the entire logic of minimal surprise on possible conscious observers. That's what it is. And the first step of agency is to say, let's crawl along the trace logic. That's the first baby step in agency, the first ability to crawl along the trace logic. Now, if we look at the collection of, I'll call those Markov kernels, policies. Each Markov kernel is a policy, it's a first order of agency. And since they're Markov matrices, they satisfy their own trace logic. So we now have a trace, we have the first trace logic of observer windows. Now we start crawling on that trace logic of observer windows. That's our first layer of agency. It has its own trace logic. That's its own, so that's why I call this recursive trace logic. It's recursive now. And you can see we can do this ad infinitum. Once we have the trace logic of policies, I can now crawl on it and get meta-policies. And so I can take agency to whatever layer of complexity I want. We can start with the baby layer. We can start with just the observer windows and explore those. Then study policies and then meta-policies and build up recursively to ever deeper notions of agency. So just at top level, we can think of a policy as simply a path through the trace logic of observer windows. That's the simplest case, right? So I started off with a three-state window, and maybe I moved to a two-state window, and then I moved to a one-state window, and that was what my policy was. And so I've got a Markov kernel that does that. And then a meta-policy would say, I've got thousands and thousands of policies. I now have the flexibility to choose my policies based on whatever goals I might have. So policies can model attention shifts, scale shifts, reparameterizations. It can maybe describe a subsystem that I think is now driving my future decisions, my policies. So the recursive trace logic is the collection of all policies with their trace logics, and then recursed, recursed, recursed again. So it's a whole hierarchy of trace logics. Each trace logic itself is infinite.
[26:57] Donald Hoffman: So we have a choice of policy, meta-policy, meta-meta-policy, and so forth. So we've talked about stationary measures. And there's sort of a minimal kind of notion of goal-directed behavior. We can write down a simple intelligence metric based on Markov chains. So it turns out that for any probability measure pi, there are many Markov chains for which pi is a stationary measure. So if you specify a stationary measure and you ask, what is the Markov chain that has a stationary measure? That's their own question. There's an infinite class of Markov chains that will have that stationary measure, and they vary in very interesting ways. For one, they have different rates of convergence. So some will have this goal-directed behavior where they're going almost immediately to the goal. No matter where you start them, they will go almost in just a couple steps to the goal, and others will converge very, very slowly. So we get to choose, in the trace logic, we can choose how quickly we want to converge to our goal, right? So this is going to be very interesting, because search efficiency is, of course, your measure K is a model of intelligence. So we have a dial here that we can dial the intelligence, and it may be that you might have high intelligence with respect to a goal, but there may be some sub-goals. It turns out that if you go quickly to this stationary measure, you may not do other things intelligently. So we're going to have to be careful which Markov chain we choose, depending on what goals we're trying to get to. So there are many goals that you can get, and I want to talk about that, the possibilities. So there's differing rates of convergence, and the convergence rate is dominated by lambda 2, lambda sub 2, which is the largest eigenvalue of the Markov matrix. You take the Markov matrix and do its eigenvalue analysis. The largest eigenvector has value one. But then you find the largest eigenvalue that's less than one, and that pretty much tells you the rate of convergence for that particular Markov chain. So there are Markov chains with different lambda twos that all have the same stationary measure, and so they converge to it at different rates. So there is then a connection between this Markov notion of intelligence, which is the Lambda 2 convergence, and your metric, which is K. And the relationship is just a simple equation, where T sub M would be essentially R Lambda 2, the rate of convergence. And T blind would be, say, just a random walk that's not smart. Right, so there is a deep connection. But now here's a little trick. We want to have, as you guys talk about, you talk about different layers. It's hierarchical, and higher layers can bend the geometry of the problem space for lower layers. And so how do you model that with Markov chains? Well, it turns out that there... You can have lots of different so-called community structures. So again, for any stationary measure pi, there are an infinite number of Markov chains that have pi stationary, but that have differing community structures. So now a community structure is roughly, is like, you probably know about it, but I'll just say briefly. You could have thousands and thousands of states in this Markov chain, maybe a few hundred are tightly connected over here, a few hundred are tightly connected over there. There's just a few cross-links. The whole thing is ergodic, but basically you might have 10 communities that are tightly knit. Now, within each of those communities, maybe my 100-state community, if I look at it more closely, it itself is composed of maybe three new sub-communities. In other words, you can have an infinite number of communities, sub-communities, sub-communities all the way down.
[31:01] Donald Hoffman: as far as you want, and all having the same stationary measure. So what this gives us is you might have one big goal, reach the stationary measure, but you could have sub-goals, which community, the way you get there is the different communities that you might emphasize as you go down. So it gives you this multi-scale flexibility. And the community structure, it turns out mathematically, is dictated by the eigenvectors. When you do the analysis of the matrix again, the eigenvectors with eigenvalues close to 1 because they involve slow mixing between communities. So the communities themselves mix inside themselves, but they don't mix between the communities very much. So we can have policies then that are trying to focus on stationary measures, community structures, convergence rates, particular dynamical models, and so forth. So policies can be looking at all these things and trying to optimize. And then the meta-policies can explore different policies. We can have meta-policies and meta-meta-policies exploring at different rates. So this starts to give us a recursive notion of agency. And in some sense, the reason I'm bringing this up is here is a framework of mathematical tools that's incredibly simple. There's one definition, the trace. That's the only mathematics there. And then there's one observation, the trace logic. And then the third observation is it's recursive. That's it. And then all the tools, that's it, and all the tools are at your disposal. So meta-policies can explore different policies, and the deeper the recursion that we go, in terms of making deeper and deeper trace logics, we get deeper and deeper notions of agency. So we can actually explore just policies for our simplest notion of agency, and then go to meta-policies to discover deeper notions of agency and so forth. So we can take it one baby step at a time. Now, in terms of how this relates to notions of Markov blankets and the self versus the world, Markov blankets, as you well know, are strictly speaking defined for directed acyclic graphs. And there, they define a boundary between self and the world. And I want to upgrade these notions to Markov chains, right? So the idea of the upgrade is, Markov chains are graphs, but they're not acyclic. They allow cycles. So this is one upgrade. We're upgrading from acyclic graphs to cyclic graphs, and then we're upgrading to labeled cyclic graphs, namely labeled by the transition probabilities. So that's what I mean by upgrade. We're going beyond directed acyclic graphs to something that's far more general. So we have to... So we want to move from the standard notion of Markov blanket to what I would call a trace blanket. And here now, we have to actually construct the self and the world. And we need to, the way we will do that is, and by the way, now, you know, I'm just saying at top level, we have to do a lot of hard work here. But it's going to be policies and meta-policies and what they do. And certain experiences, like experiences of pleasure and pain, will be part of the experiences agents have. And to the extent that certain actions lead to greater hitting of the pleasure centers, the pleasure, the higher stationary measure for the pleasure, then they'll be sought, and to higher stationary measures for the pain, they will be less sought. They will be avoided. And so the idea will be that there'll be pleasure and pain guides, but there will also be, I'm thinking that policies, what policies do is they say, given that I'm looking through this particular observer window, what's the probability that I'll now look through that window over there or that window over there?
[35:08] Chris Fields: Can I interrupt with the question? A couple of sentences ago was the first time you used the word action. And is an action in this framework just a change in policy?
[35:23] Donald Hoffman: So each, it is, but it's not just a change in policy. So a policy itself gives you an action on observer windows because your action is to change observer windows.
[35:37] Chris Fields: Okay.
[35:38] Donald Hoffman: A meta-policy gives you a higher level of action because you're now changing policies, right? And then a meta-meta-policy would be an even higher level of action because you're changing your meta-policy.
[35:51] Chris Fields: Actions are all either changing what you're looking at or changing how you decide what you're looking at.
[36:01] Donald Hoffman: That's right. Recursively.
[36:03] Chris Fields: Great.
Donald Hoffman: That's a recursive notion of action now. Right. So now this, I'm just thinking through this last bit, but it seems like some policies, for example, so now I'm looking at just the smallest level of action. Some policies, if they have certain things that always appear in your observer window. So, for example, in my observer windows, my hands and my body often appear, whereas other things that I call the external world don't appear that often. And I also notice that I seem to be able to directly control my hands and my body. But if I want to have my phone move, I need to move my hand so that I can pick up the phone to move the phone. So what I am going to say is that we really have to, so in the Markov blanket approach, right? The Markov blanket has a clean definition. It's, you know, give me a set of nodes, their blanket is, they're the parents of the nodes, the offspring of the nodes, and the parents of the offspring of the nodes. End of story. That is your blanket, that's your skin. That's your boundary between you and the world. Here, it's much more complicated. Now, I have to use the notion of agency in a non-trivial fashion, and learn probabilistically what features of my sequence of observer windows that I'm having remain there most of the time. My hands are there most of the time. And they're associated, certain actions with my hands are associated with pleasure signals, others are associated with pain signals. So I'm learning to do certain things with my hands and don't stick them in the fire, things like that. Other things are much more contingent. So I can use probabilities of what I'm seeing in my observer windows as a way of starting to construct myself versus the outside world. Plus the pleasure and pain guides.
[38:03] Chris Fields: Don, can I ask another question? Sure. You talked about actions with your hands. What does that mean in terms of changing what you're looking at? Since the only action is changing what you're looking at, what does it mean to control what your hands are doing?
[38:20] Donald Hoffman: Right, so that's a great question, Chris, because what that means is I want an observer window, I have an observer window where my hand is touching my ear. Now I want an observer window in which my hand is touching my leg. And so I transition to that observer. So what's happening is I'm choosing what I want to see in my movie next. And that's what we call moving my hands. It's a completely, you have to really think out-of-the-box now. This is, it's really, it's a choice of what I want to see next, and that's what the actions are.
[38:58] Chris Fields: Okay, okay, great.
[39:00] Donald Hoffman: It's very austere. What I love about it is it's austere. There's only one equation and one logic, and so you have very, very tight guides, and yet the claim is we should be able to get everything out of it. But that's what I love, is a theory that forces you to do it in a principled way. Now, Bayesian inference, we can talk about it more if you want, but I'll just mention briefly, Bayes' rule falls out of the meat and the trace logic. And we can go into how that's the case. It's beautiful and non-trivial, but Bayesian inference is effectively a special case of the meat of the trace logic. And if you want, we can go into that. And you guys talk about bending the option space, and I want to say that, yeah, I'm taking the notion of space. Of course, that was metaphorical when you talk about bending the option space, but there is a real sense in which I want to get space and space-time itself. And what I'm working on quite heavily, and with a couple others, is I believe that we can actually boot up special and general relativity entirely from the trace logic. And so that's the claim, that relativistic space-time can be constructed entirely from the trace logic, and this would be then fulfilling John Wheeler's goal, that starting with only observer participants, that we can build up all of space-time physics. And that's the goal of where we're headed. And I'll just give you, this will be the last thing I do, and then we can have a conversation about it. Just to give you a hint about how that would happen. It's standard in Markov chain theory to have what are called enhanced Markov chains. So you have a Markov chain, but you also have a counter. Every time your experience flips, you change experience, your counter increments. So here I've got a case where I've got the four-color agent, and then there's the sub-agent of just red and green. And notice that there's a counter for the red and green, and there's a counter for all four. And notice the counter on the left is going much faster than the counter on the right because it's seeing more experiences. So the counters go, the counters for sub-agents, or I'm sorry, sub-windows, sub-observers, are going at a slower rate than the ones above them. So if I'm less than you in the trace logic, my time counter is going less than you, than the one. So the trace logic also is giving you a relationship among counters, and that we claim is the time dilation of special relativity and general relativity. That's where it comes from. So it's all about observer windows and their counters. And it turns out that the distances can also be derived. And it turns out that the distances that you will get in the window, the trace window, are different than the distances you'll get in the bigger. And so this is where we're hoping to get general relativity coming out of this. Just simply, there's notions of essentially something like the commute time between states. And similar notions, the commute time, I'll just give you that concretely. It's the expected time of starting at green, getting to blue, and then back to green. What's the expected number of steps? Starting at green, I'll get to blue and then back to green. And it turns out that expected time can be viewed as the square of Euclidean distance. So there are canonical ways of getting Euclidean distances from commute time properties and other. There are Dirichlet measures which are even more to the point, but more complex. I won't go into them. But there are ways of going from, the trace logic gives us effectively the time dilation and length contractions of special and general relativity is the idea. So time runs lower on the trace, gaps between tricks. So I'll just leave it at that. I think that's enough for us to, I'll stop the share so we can talk about it. But I just wanted to give you guys a feel, and I can send you guys some papers on this, but I wanted us to have a little time to talk about this is just, we haven't solved the agency framework, the agency thing. What we've got is a language now that's principled for talking about agency.
[43:45] Michael Levin: Thanks very much, John. That was amazing. Question, a kind of general question. What do you make of the fact that you're apparently pulling out descriptions of physics and descriptions of agency out of the same starting material? Does that surprise you?
[44:03] Donald Hoffman: I think, well, something I've been saying for quite a while is that space-time's just a headset. And we're effectively saying we can build a headset. Space-time is not the reality that's independent of us, and we're little, tiny, little... Our typical view is, Hoffman is this tiny, little, 160-pound thing inside a massive, massive space-time universe. And I'm saying, no, what we call Hoffman is just an avatar inside a space-time headset that's being created by consciousness. And the proof of the pudding is, can we build the headset? So the idea is that space-time, for this approach to go through, we have to be able to show that we can get special relativity, no hand wave, just from the trace logic, and also general relativity and quantum theory. We have to be able to show that we can get entanglement and all of this stuff simply from the trace logic of Markov chain. Now, one objection that someone might have is to say, look, Markov chains, in quantum theory, we have unitary matrices. What are you dealing with? You just have Markov matrices. You don't have these nice unitary matrices. So how are you going to do that? And the idea is most Markov matrices are not unitary, but there are some that are. They are a measure zero subset of the Markov matrices that are unitary. And when you look at the long-term behavior of a Markov matrix, the asymptotic behavior, it turns out that the way that the eigenfunctions, this is now when we go to those enhanced Markov chains. And this is work that Chetan and I did back in 2014. Chetan discovered that the eigenfunctions of the enhanced Markov chains are identical in form to the quantum wave functions of free particles, identical. So the idea is going to be that quantum theory arises as an asymptotic description of a Markov dynamics. So the Markov dynamics gives you a step-by-step-by-step analysis of agency and consciousness. Quantum theory only gives you the asymptotic behavior, not the step-by-step behavior. So that's going to be the connection. Again, this is all a matter of theorem and proof. Either we're right or we're wrong. It's theorem and proof or theorem and disproof. Now, one might say, well, you have the no-cloning theorem in quantum theory. What about that in Markov chains and so forth? And it turns out, if you look carefully at the no-cloning theorem, the proof of it does not require unitarity, it only requires linearity. Markov chains are linear, and they have their own no-cloning theorem. So I see no obstruction right now. We just have to do the hard work. But I see we have a principled notion of agency, and it shows us how the nested community structure can give us nested goals and bending, nested bending of problem spaces. And we can actually not only talk about, metaphorically, about bending the problem spaces, we actually can show, I think we'll be able to show, that we can actually have real space-time curved representations of bending, general relativistic descriptions of bending.
[48:01] Robert Chis-Ciure: Mike, may I share? You remember we were taking this project and embedding it into the variational free energy principle and all that. So may I share now the screen to show Donna and Shetan what we already have. I mean, mind you all, this is work from one year ago. I still didn't get to develop it in full. It's, let's say, maybe 80% done. So on the left, you see this book. This will come soon. It's Carl's book on The Free Energy Principle and the Nature of Things. It's a big monograph of the latest version, I suspect. So we didn't push this paper because I also wanted to have access to the latest form of this before we would push. The synthesis paper had only a few drop names of variational free energy and the decomposable way in which you can assess intelligence and true scale-free quantification and recursive decomposition in that sense. So in this project, we try to do it within the free energy principle framework. So within the variational framework, right? So we take all these problem space operators and embed them into a physical variational physics descriptions. And we also end up on some of the things that you, Yudon and Chetan mentioned, like, for example, when we can have the issue of renormalization and then getting ways in which you can decompose and quantify across scales, additive gains in such efficiency at different scales, and then do it globally for as the whole total of the system, depending on how you would, how efficiency gains are cashed out at different levels. So that can be embedded in the variational logic of the free energy principle for sure. And using the more pedestrian thing in the sense of the all the Ness assumption and the Helmholtz decomposition and building on that, building a minimal Landauer-style floor of cost per unit operator and efficiency gains. So this is not done. But what I want to say is that seeing you present this just now, it is clear to me that you provide a way more finer algebraic structure for us to probe even deeper into this decomposition and then look at what you mentioned, the community structure and all these sort of effects you would get and what would appear to us at the scale and metric of observation as an efficiency gain might come from innumerable ways of tiling that problem space or bending the problem space or just doing, in your terms, just changing the observation frame by communities and certain communities having different policies and then meta policies based on the higher order aggregates and so on. So I think it's definitely valuable even if it was something that's built after this is pushed because this will be finished quite soon. Right. It's definitely worth looking into it. And the connection with physics is certainly impressive for sure. That's the hard work. This is less hard.
[51:41] Donald Hoffman: I would certainly welcome any interactions you guys want to have on this once your current projects are, you get to a certain place. Because I think as I listened to your work, I realized our ideas are really converging quite nicely here. And I think that there's a synergy. The nice thing about the Markov stuff is that it's so well studied. You just look at the eigen analysis of these matrices to get a lot of this stuff. So there are lots of papers out there about the community structure and so forth. So we would just have to do our homework and understand a lot of that stuff we could just then port in here. And it's really quite well understood. The only thing they didn't have was the trace logic and the fact that it can recurse. That's what they were missing to pull this whole picture together.
[52:30] Robert Chis-Ciure: Interesting, interesting. Yeah.
[52:32] Michael Levin: What do you think would happen, or maybe you've already done it, but to apply some of the causal emergence metrics to the dynamics of these things, or some of the stuff that you guys do, Robert, or some of the more conventional stuff that we have. Have you, you know, FID and all that kind of stuff, have you done that at all?
[52:56] Robert Chis-Ciure: You're done.
[52:58] Michael Levin: Don on his stuff. And then if they haven't done it yet, then I'm going to say maybe we should.
[53:03] Donald Hoffman: So say a little bit more about the causal emergence question. I want to make sure I understand that question.
[53:09] Michael Levin: Well, Robert's the better person to speak to it, but there are a variety of newish metrics in information theory that basically try to quantify the important aspects of agency, right? So that the extent to which the whole is in some causally more than its parts, phi, all that stuff.
[53:31] Donald Hoffman: Right, that kind of, exactly right.
[53:33] Michael Levin: That's what I'm getting at. Have you tried any of those metrics on the dynamical path of these things?
[53:39] Donald Hoffman: Well, a lot of that work has been, the motivation between that, Tononi and Coe and so forth, has been to somehow have consciousness be a function of the amount of causal emergence, right? And to the extent that phi is the system with the greatest causal measure. And those are very, very useful. I think they have nothing to do with consciousness.
[54:12] Michael Levin: I'm not making any claims about consciousness. I'm just asking, just step one of getting the measurements and seeing what's going on as far as...
[54:21] Donald Hoffman: Oh, sure, I think that would, as long as there's no claims about that in consciousness, I'm all for it. I think that stuff is really good work, absolutely. What I think is bogus is saying that consciousness has something to do with that. I think that's bogus. But we haven't done that ourselves. So the answer is we haven't gone there yet.
[54:43] Michael Levin: It may be interesting to do, just to get some data and just to do some measurements. I mean, we've been doing it on gene regulatory networks and all sorts of weird things, and there's some really interesting, but we haven't said a word to our consciousness yet with respect to that, but just the data alone, I think, are already interesting, whatever the interpretation.
[55:03] Donald Hoffman: But your data has really inspired me the last few months. I've just really, your work, your whole team has really inspired me. It really forced me to think out of the box about what this thing can do. So thank you. I mean, it's been really quite fun.
[55:17] Michael Levin: Thanks.
[55:18] Donald Hoffman: Your podcast with Lex Friedman, I've listened to it five times or something like that.
[55:25] Robert Chis-Ciure: Don, I mean, on this topic specifically, do you think you could use, not the inverse trace, as a sort of hypothesis generation for this kind of experiments and this kind of data? Because, I mean, it seems like you do the construction sort of in this paper, at least in the paper in this test, we did it mostly forward, but you do have a calculus and an algebra for doing it backwards. So you have, let's say, an observed effective kernel P sub A on the visible states A, and then with the trace chain theorem says that any consistent extension P with the hidden states A prime, was it? Yeah, A prime. Then that must satisfy basically the theorem. So then the ABCD sort of like a tuples is a sort of parameterized hypothesis based about hidden mechanisms. And then it just becomes an inverse problem, right? It's just that. So if that's the case, and we have a lot of data in our synthesis paper, we use the planarian regeneration example, and I don't use the data in that literature, but there is also way more data in GRMs and stuff like that. So do you think we could have a sort of model in the inverse trace that would distinguish between different hypotheses that explain best the data that we see.
[56:47] Donald Hoffman: Yes, in the following sense. So the trace logic, because it's a logic, there is the notion of not only the meet, but also the join.
[56:55] Robert Chis-Ciure: The join, yeah.
[56:56] Donald Hoffman: So I can take two matrices, and if they are compatible, if they're, for example, part of a Boolean sub-logic, then they have a join. Now Chetan has done the hard work of getting a closed-form solution for very special cases. And it turns out to get a general closed-form solution is an open problem. And the interesting thing is, so there can be a join, there can also be, so the join is the least upper bound, right, between two. But you could also have, in some cases, Chetan has pointed out that there could be a whole, say, one-parameter family of minimal upper bounds. So it's going to be very, very interesting. The trace logic, for certain matrices, there may not be a unique least upper bound. There could be a family of minimal upper bounds, and then we may be able to use other factors to choose one that we've got other criteria for what we want. Maybe we want something that's some kind of minimized complexity or maximum complexity or causal structure, greatest causal structure or something like that. So there are all sorts of things that we could do. So we don't know if there is a general closed-form formula for computing the join. Chetan has it for a special case. It's a fair bet that there is not one. That's going to be interesting to, it's an interesting open mathematical problem to study the join of this thing. And I can give you the unpublished paper we have so far, where Jake Don's stuff is there and you can see what we've got so far. And it's open as to how to generalize that, or to prove that it cannot be done, that it cannot be generalized.
[59:05] Robert Chis-Ciure: It's super interesting. I would definitely love to see those papers. And I read some of your stuff and also the latest on traces of consciousness. I went through most of it very...
[59:18] Donald Hoffman: You've seen the trace of consciousness paper, right? So it's in the appendix at the back of that paper that you already have. You'll see Chetan's work on what we have so far in the join.
[59:31] Unknown: Yeah, work in progress.
[59:33] Robert Chis-Ciure: I know of your work because one of my best friends is Robert Prender. So we talk a lot. We just submitted a paper on IAT and conversations theory.
[59:44] Donald Hoffman: Oh, yes, right, right.
Robert Chis-Ciure: One month ago. Yeah.
[59:49] Donald Hoffman: Yeah, of course. I know Robert quite well. Yeah.
[59:52] Chris Fields: So I have a question, John, about the definition of the trace. The trace of any Markov process is also a Markov process, right?
[1:00:06] Donald Hoffman: Yes.
[1:00:07] Chris Fields: Do you have an available model of observations that are, or sequences of observations that are not Markov? So sequences of observations that violate constant probability of switching from one state to the next? So that the probability is not well defined.
[1:00:39] Donald Hoffman: Right, it depends on your time window and how you want to coarse grain the states, right? So one could say, look, there are many, many systems that are, it's not the case that if you look at the states I've given you, that the probability of the next state can be given exactly just based on the current state. You might need to have, look at three states or five states or 10 states or whatever. You have a bigger window to get the probability. But in those cases, you can always then create new states and then turn Markov.
[1:01:19] Unknown: So basically, you can expand the state space, you actually multiply it. There can be a combinatorial explosion, though. You do need to be aware of that possibility. And this only works for finite memory. It doesn't work for infinite memory. But even for finite memory, you do have to be a little careful that the combinatorics can get nuts, which seems to be often the problem in consciousness research.
[1:01:55] Chris Fields: I'm, of course, mainly interested in issues like contextuality and quantum theory, where you have groups of observations for which joint probabilities can't be defined. And so you can't build a single self-consistent hidden variable theory. So I don't know whether the formalism will handle that sort of situation or not, since you do seem to be always assuming well-defined probability distributions.
[1:02:46] Donald Hoffman: Can you say more about the system that doesn't work, Chris?
[1:02:54] Chris Fields: Well, contextuality is defined as a phenomenon: sets of observations for which a joint probability distribution is undefinable, for which the statistics violate the Kolmogorov axioms.
[1:03:24] Unknown: I suspect that the fact that joins don't always work might have something to do with that. That's what I was thinking too. Yeah, that's what I originally thought your question was about, having the same probabilities every time. And of course, you don't need that with Markov chains. They don't have to be homogeneous. But that's not your question. It's much more abstract than that. What I would, my hope would be to somehow find sub-logics which actually look like quantum logics. Right. But if that happens, then we could possibly answer your question in the affirmative. And that would be one way to do it.
[1:04:12] Chris Fields: So another way to think of it in your formalism might be if there are paths, yeah, this would be where it would look like a quantum logic. If you have paths in the trace logic network that don't commute.
[1:04:27] Donald Hoffman: Oh, easily.
[1:04:32] Chris Fields: That may be a way of approaching this join question, then.
[1:04:38] Donald Hoffman: Yeah, that does have no join.
[1:04:40] Chris Fields: To get back to your comment about unitarity at the very beginning, unitarity is really just conservation of information. And Kolmogorov probability is really just conservation of information. So if you don't have situations in which information is actually lost in some global sense, informational singularities, if you will, then the system satisfies unitarity as it's used as an axiom within information theory, which is just conservation of information. So this is where I was trying to emphasize this complete dissociation, actually, of unitarity, any spatial considerations. But anyway, that's sort of an aside. The real question is about contextuality.
[1:06:00] Donald Hoffman: It is striking that Nima Arkani-Hamed and these high-energy theoretical physicists are strident that they're not assuming unitarity. They're saying we don't need it and we'll show that it arises from these positive geometries that are entirely outside of space-time. So they're getting space-time and unitarity together.
[1:06:28] Unknown: I've never seen a demonstration of that fact in itself. What I have seen is they derive scattering amplitudes, which match what's understood from the Feynman approach. That doesn't mean you've derived space-time, and it doesn't mean you've derived unitarity. It just means that you've matched something.
[1:06:56] Chris Fields: Yeah, I think they're referring to.
[1:06:57] Unknown: The principle is absent.
[1:07:00] Chris Fields: Yeah.
Unknown: Sorry.
[1:07:01] Chris Fields: I think they're referring to unitary processes in space-time.
[1:07:06] Unknown: Right.
[1:07:07] Donald Hoffman: That's what they're referring to. Absolutely.
[1:07:10] Chris Fields: That's very different from unitarity as a strictly information theoretic concept.
[1:07:18] Donald Hoffman: And yet the way they wave it around and say, we don't assume space-time or unitarity, right?
[1:07:24] Chris Fields: It's just a disconnect in language, I think.
[1:07:26] Unknown: I mean, it's fine not assuming a collection B when you're doing a collection A. But if somebody like Dyson comes around and says they're equivalent, then you can't say that we don't need space-time. It's just another way of looking at it. So their claim is unfounded as far as I know. I mean, somebody needs to sit down and say, this is how space-time emerges from the ampituvahedron. Otherwise, it's just saying that Schwinger could say I don't need to assume Feynman, and Feynman could say I don't need to assume Schwinger, and they're both right, but they're both equivalent.
[1:08:11] Donald Hoffman: Right now they don't give you space-time, they give you scattering aptitudes. That's what they give you.
[1:08:15] Unknown: Which I think are defined in space-time. Fair enough. It was on a facet of something.
[1:08:28] Chris Fields: I suspect that eventually we'll generally be able to identify amplituhedron-like structures with error-correcting quantum error-correcting codes.
[1:08:48] Unknown: You wrote a paper on that, didn't you, Chris?
[1:08:50] Chris Fields: Well, we have a preprint of it that was revised as of a few months ago, and we're still working on it. But the current available preprint isn't bad. But the hypothesis would be we can go the other way from amplitude hedron-like structures to quantum error correcting codes. And there are many ways to get space-time from quantum error correcting codes. So.
[1:09:28] Donald Hoffman: Interesting.
[1:09:30] Chris Fields: It may be that the inference ends up going in that direction.
[1:09:41] Donald Hoffman: What I'm hoping to be able to show is that some of these positive geometries, like the sociohedron, are sub-polytopes of the Markov polytope. Because the Markov polytope could be describing the probabilities of certain interactive processes that we would think of as scattering processes. If that's the case, then there may be a deep connection between some of these positive geometries and the Markov Hedron, which is itself a positive geometry.
[1:10:14] Chris Fields: Yeah.
Donald Hoffman: Instead of all possible Markov chains is a positive geometry.
[1:10:18] Chris Fields: I suspect that any such structure defined over any space of possibilities or any such dynamics defined over any space of possibilities can be thought of as scattering in some metaphorical, but formally sensible way.
[1:10:52] Unknown: Yeah.
[1:10:53] Chris Fields: I mean, we can think of computation as scattering in interaction space.
[1:11:00] Unknown: Interaction is scattering.
[1:11:03] Chris Fields: Yeah.
[1:11:04] Unknown: I mean, scattering is how interactions look in a physics lab.
[1:11:12] Donald Hoffman: What's surprising is how restricted the scattering events are that you find in physics, right? A very restricted set, and it turns out that something like the standard model gives you all the components that you're ever going to find in a new scattering that you ever do.
[1:11:30] Unknown: We hope.
[1:11:31] Donald Hoffman: So far, that's so far.
[1:11:34] Chris Fields: Well, all the ones that you see with the sorts of things that we call elementary particles.
[1:11:42] Donald Hoffman: What I find interesting is just as when we had the Ptolemaic system, we had all cycles and cycles and cycles, you could get all the orbits of the planets, but it was ugly and just a mess because you had to add all these cycles and correcting cycles to correct those cycles and so forth to do it. And the same thing happens with space-time and scattering. When you look at the Feynman diagrams, it's loop after loop, and you have three or four particle interactions and 500 pages of algebra because you have all these Ptolemaic loop after loop after loop where you're enforcing locality and unitarity. So Feynman is forcing locality and unitarity, and so we have to do all this stuff. And all of a sudden, 400 pages of algebra turns into two terms when you let go of space-time. And also, it feels, again, like we've got this Rube Goldberg machine called space-time. And that's why things look so ugly in space-time and the mathematics. And all of a sudden, we're seeing some hint. I mean, it was a big hint when we went from Ptolemy to Newton. That's, you know, all of a sudden the formulas got a lot. We're on to something much deeper here than Ptolemy was on to. And now when we go from, you know, Feynman scattering diagrams to these positive geometries, once again, we're getting 400 pages of algebra down to two terms. A clear hint that we're on to something deeper beyond space-time.
[1:13:08] Chris Fields: No, space-time's a kluge. I think that's clear.
[1:13:14] Donald Hoffman: What's interesting is that theories of consciousness, all the main theories of consciousness assume otherwise. We start with space-time. We try to figure out what physical systems in space-time could possibly have the right structure to give rise to consciousness. So all of our theories start with the Kluge as the assumption and then try to go from there. So they're doomed, completely doomed to failure.
[1:13:42] Chris Fields: Well, I mean, all of science has done this before about, what, 1970?
[1:13:48] Donald Hoffman: You're talking about the standard model since about 1970.
[1:13:57] Chris Fields: Well, no, I'm roughly dating at least the first things I saw from Wheeler with the notion of observer participants in it.
[1:14:15] Donald Hoffman: In the 70s, right? He saw it. He knew, I mean, he wrote the book on space-time. He wrote the book on gravity. Measler, Thorne, and Wheeler. That is the Bible. And he knew space-time and he knew it was a clue. He was looking for something entirely beyond.
[1:14:35] Chris Fields: Yeah.
[1:14:37] Donald Hoffman: And he was going to call it observer participants. That's what he called it.
[1:14:43] Chris Fields: May I ask something? Yeah.
[1:14:44] Robert Chis-Ciure: Go ahead.
[1:14:46] Chris Fields: I was just going to say good to see you guys again. Good to meet you, Robert.
[1:14:50] Robert Chis-Ciure: Good to meet you, Chris. And I think we will meet in person in Spain, if I'm not mistaken, in July.
[1:14:55] Chris Fields: Yes, hopefully. That sounds very exciting.
[1:14:58] Robert Chis-Ciure: I told them to invite you specifically. Thank you. What was happening in Spain? There will be a workshop organized by some people, the Takena Foundation, and it's a workshop on the known unknowns in our fields of interest. And there will be, yeah, more than one field. So that's why Fields is excellent. And yeah, we'll discuss several things. But Don, I wanted to say that I think this is the biggest myopia in consciousness science. And I work in Anil Seth's lab. I did my PhD with Giulio Tononi. I did a postdoc with David Chalmers. I work with Georg Northoff and the temporal spatiality. I know all the people, and all of them are sort of either physicalists or they still think that consciousness is something you squeeze with enough dexterity at the end of a long tube that you operationally construct. And they really don't get the point that consciousness is the starting point, and everything else must come afterwards. You build everything else from consciousness, not the other way. It's hot. I know the pain.
[1:16:29] Unknown: Do you see the platonic space as having something to do with consciousness in that sense, or being embedded within it?
[1:16:42] Robert Chis-Ciure: That's Mike's answer.
[1:16:45] Unknown: Yeah, that's I'm asking Mike.
[1:16:48] Michael Levin: Okay, so I'm not fundamentally a consciousness researcher. I don't have any strong claims on this yet. But if I had to say right now, I would say that I don't think that from the point of the Platonic space formalism that I'm investigating, I don't think that we are beings that occasionally get visited by Platonic patterns that are something else. I think we are the patterns. And I think these patterns are a wide range of static, dynamic, low agency, high agency things. And I think what we call consciousness is the perspective from the Platonic space outwards into. So what a pattern from the Platonic space experiences when it interacts with the physical world is what we tend to call consciousness. Now, I'm not sure that, like, I don't think that exhausts all the possibilities. I think there are probably lateral interactions within that world. I suspect that when mathematicians think about abstract mathematical objects, what happens is you have two, there are basically two different patterns in residence there, the human one and whatever it is that they're studying. So there may be lateral interactions that don't even require the physical world per se. But basically what I think we mean when we talk about consciousness is what it's like to be a Platonic pattern projecting into a physical world through some interface. So that might be, you know, the sense organs that we have or something completely different and so on.
[1:18:14] Donald Hoffman: So the Platonic patterns transcend our experiential notion of consciousness.
[1:18:21] Michael Levin: In the sense that, say more. What do you mean by that?
[1:18:26] Donald Hoffman: But there's a Platonic realm that maybe we shouldn't describe as conscious, but we perceive, but a human perspective on it is we experience it as consciousness looking at it somehow. So consciousness is just perspective.
[1:18:42] Michael Levin: I ultimately think some version of idealism is probably the more accurate thing. I do think that consciousness is fundamental, but I don't know what to do with that on a practical level right now. I don't have a way of making use of that in the lab or anything like that. What I see is a way to make progress with a somewhat more dualistic version, which I agree that it would be nice to have some kind of simple monism, but what I see right now is that we have different but interacting realms, so to speak, and that model helps us to do new experiments and make new discoveries. So for now, I do think that they're sort of two separate things. But ultimately, if I had to guess, I would say that consciousness is primary. I don't know how to do that reduction right now, so I'm sticking with two because that's what we can handle right now.
[1:19:41] Donald Hoffman: One of our goals is to show that we can actually get space-time, special in general relativity and quantum theory from this theory of Markov chains of consciousness, in which case then we could inherit all the work that's been done in physics, but see it arising from a consciousness first point of view. So that's where I'm headed.
[1:20:04] Michael Levin: I mean, for us, one of the important pieces of our research program is to understand the mapping between the interfaces that we construct, and those are anything from sorting algorithms through cyborgs, through Xenobots, embryos, you name it, all of these stuff, to understand what are the properties of these things that facilitate the ingression of specific patterns from the space. So, what is it about this thing you've made that pulls down this rather than that? And then that allows different degrees of and different kinds of mind state to interact through it and also to quantify. And so we've got some wild stuff that's kind of ripening in the next few months that I'd love to run by all of you. We should all have another meeting so you can see. But we've been trying to quantify one of the things that I think is really important about this Platonic space thing is that it's not just a redescription, and a bunch of sort of useless philosophy that you sprinkle on top of things that work perfectly well. It actually makes very new predictions in the sense that it suggests that what you're getting from that space is things that using conventional theories that we have now of doing the accounting of effort, of computational cost, of physical cost, these kinds of things, that you get free lunches, or at least heavily discounted lunches. You get more than you put in. Our accounting isn't adding up everything that you get. We're missing something very significant. And we now have the ability to quantify how much are we getting, how much free memory, free compute, free whatever. We can, at least in simple toy, sort of minimal models, we can quantify that in biology. You can see it, but it's hard to quantify or prove anything. It's just too complicated. Whereas in these minimal models, we can actually quantify what did we get that we didn't pay for according to the conventional way of totaling up effort. And so that's really important to find out how much and what do you get. Do you just get static patterns? Do you get behavioral propensities? Do you get algorithms? Do you get virtual machines? Do you get free compute that you can do in that space? That's kind of a crazy prediction of mine that I think you can actually get, you can do compute in that space that you don't pay for in this space, so to speak. So that's, you know.
[1:22:31] Donald Hoffman: I've been listening to a lot of your podcasts on this and thinking about it. And I think that there's connection with the hidden states in this Markov system, so that if we just see a trace, most of the intelligence is something you don't see. And so to the trace observer, that's all in a platonic realm, because you literally cannot see it. And yet, what you're seeing is entirely a trace of that world. So your visible world is controlled by this quote unquote platonic space that you cannot see. And so that's why I was thinking, that's what your stuff about the planaria, for example, you cut off the head and cut off the tail and you can change the electric fields and make it have two heads and so forth. I mean, it's just how does it know how to do that? Right, where is that? So I've been thinking, so somehow all we're seeing is the planarian in our trace. We're not seeing beyond what we can see. There's a whole Markov realm of intelligence out there that is projecting down into what we can see, which is just the planarian. So I'd really love to explore with you guys, as this formalism matures, how we might use the formalism in concrete ways to model specific platonic spaces for specific memories, biological memories. Because I think this gives us the tools, right? There are the exits, the dark states, and the entrances. All those tools are part of the platonic space. And if we learn, so we're new to this ourselves, right? We don't know how to use those tools yet, but to learn how to use those tools to model specific things, we might be able to get that platonic space, not just a hand wave, but here is the Markov chain, here's the trace, and this is why it looks like this platonic intelligence that's guiding you. But it would be multi-scale, right? There's going to be multi-scale in the dark space.
[1:24:39] Michael Levin: What might be really fun is, so definitely we should do that with some of the biology examples that we have. In particular, for example, with some of the synthetic things that we have. So, Xenobots, Neurobots, because they raise what I think is perhaps the most interesting part of this is, where do the goals and properties of novel beings come from, where you can't just pin it on selection, eons of selection. I guess where do they come from? So, but I would complement that with, which I think would be even easier, the study of basically applying these things to some of the minimal computational models that we have. Yes. Right, we have sorting. Sorting is one, and there's going to be a bunch of new work on that coming soon. But we have others, we have some really interesting stuff that'll come out soon on giving embodiments to various very weird sources like mathematical objects and making the robots that are driven not by conventional algorithms and sensors and whatever, but their entire behavior is driven by sort of pre-cooked static mathematical constants and watching how those kinds of, or mathematical objects and watching how those things end up navigating a world and adapt, and what cognitive features they end up having and so on. So I think those things are simple enough that we could-- I think we could actually make a pretty tight mapping onto what you have in terms of states and things like that.
[1:26:13] Donald Hoffman: Interesting. Investing. It may be, though, when you get into pure mathematics and sort of a hidden platonic realm that's doing stuff, like sorting algorithms that are doing other things you didn't expect. I'm having my mind stretched to think how Markov chains could do that. It seems like that might be something even deeper somehow.
[1:26:34] Michael Levin: Well, what we could, that was the other thing. I was thinking what is totally doable now is to take your system and apply the tests that we have. So we have a range of assays that basically are taken right out of the behaviorist handbook. Because the one thing I think behaviorists got right is that they weren't worried about what the implementation was. And so it's very easy to apply their tools to anything, right? So we could actually look for habituation, sensitization, associative conditioning, delayed gratification, path planning, illusion, counterfactuals, all this kind of stuff. We have assays now that we can look for all that stuff.
[1:27:15] Donald Hoffman: And it's clear to me that there's always going to be Markov chains that we can build to do that. So it'll be, they're universal Turing machines. Markov chains are universal.
[1:27:28] Michael Levin: So I'm not talking about building ones that do it. I'm talking about finding it in simple or random ones that you don't think should be doing it. That's the trick. We're finding these capacities in very simple and no design, no selection. Usually the three things you think you normally need, you need rational design by an engineer, selection or evolution or learning, right? Those are the three things you need. We're not doing any of that. We're pulling it out of, I don't know, you'll judge for yourself where you think it's coming from, but I think we could do that with random matrices or whatever.
[1:28:13] Donald Hoffman: That's right. We may be able to find matrices in which what we're seeing in the organism is the trace, but the invisible states are having a lot of the intelligence that leads to what you're seeing. And so we write down the matrix that even though the trace, you can't see why it's doing that, but it does it. But in the big matrix, you see why it's doing it.
[1:28:35] Michael Levin: Yeah.
[1:28:37] Chris Fields: I'm going to have to jump off, guys. Great conversation.
[1:28:41] Michael Levin: Thanks, Chris.
[1:28:43] Chris Fields: Good to see you.
[1:28:44] Michael Levin: Thanks, Chris.
[1:28:46] Unknown: Good to see you, Chris.
[1:28:51] Robert Chis-Ciure: Mike, will we have the recording of this?
[1:28:54] Michael Levin: It is being recorded. I'll send you guys a link. If everybody's okay with it, I'll put it up on our center channel. But regardless, you can all have a copy.
[1:29:03] Donald Hoffman: That's fine with me. Yeah.
[1:29:04] Michael Levin: Great.
[1:29:05] Robert Chis-Ciure: Perfectly fine.
[1:29:07] Michael Levin: I think there's a ton of stuff to do. So why don't we go off and think about some specific directions and let's come back. I already have some thoughts, but there'll be lots more in a few weeks when I can send around some pre-prints. I'm having my students write these things up and so then I'll send them out.
[1:29:27] Donald Hoffman: Very good. And if we maybe then pick a particular simple problem system that we can see what the trace logic might do on it and see where we go from there. That would be fun.
[1:29:35] Michael Levin: Yeah, that'd be great.
[1:29:37] Robert Chis-Ciure: And I think a natural extension of our former work after we did the FEP thing is basically try to apply all this stuff to it and see how you can get even deeper, more interesting things you can say about all this computing intelligence across scales in a more fine-grained manner than even the FEP allows.
[1:30:01] Donald Hoffman: I agree that this seemed to be a natural connection with the project you guys are doing right now.
