Hello, everyone. Welcome to the Active Inference Lab. We're here on August 17, 2021, in livestream number 26.2, on the second discussion that we're having as a group on the paper, Bayesian Mechanics for Stationary Processes. Welcome to the Active Inference Lab, everyone. We are a participatory online lab that is communicating, learning, and practicing applied active inference. You can find us at the links here on this page. This is recorded in an archived livestream, so please provide us with feedback so that we can improve on our work. All backgrounds and perspectives are welcome here, and we'll be following video etiquette for livestreams so we can use the raise hand feature in JITSEE. This short link has the upcoming livestream discussions. Here we are on August 17th in our last discussion on this paper, 26.2. Next week, we'll be heading into a new paper, and we still have some openings in the coming weeks. So if anyone has a suggestion or an author to contact or wants to discuss their own paper, just let us know, and we can try to make that happen. Today in Active Stream number 26.2, the goal is to continue learning and discussing and unpacking this awesome paper that we've been thinking about for the last few weeks, Bayesian Mechanics for Stationary Processes, and we're really appreciative that the first author is here to join with us and co-learn with us, have fun with us. And this video is just going to be wherever we want to take it, so we have some questions prepared, but especially if anyone in the live chat has questions that'd be awesome and we can definitely address them. So we can just start with a quick introduction round and feel free just to say hello or to answer one of these questions like what's something that you liked or remembered about the paper and what's something that you're wondering about or want to have resolved by the end of today. So I'm Daniel, I'm a postdoctoral researcher in California, and something that over the last week made me excited to have this discussion was I was speaking with a physicist friend, someone who's working with lasers and oscilloscopes and stuff. And I brought up this paper and it turned out that they actually were using PID control in their research on a day-to-day basis, but actually it was new for them to hear about how it was connected to some of these broader topics. But as soon as I brought out the physical printed paper, then they were just so excited and it was cool to see how they had all this practical experience working with PID, and then they instantly just saw that there was kind of this crossover point into some broader questions that also they were curious about, but the day-to-day practice actually hadn't brought them to those general questions. So I learned a lot about PID control and about actually how it plays out with the knobs and everything like that. I'll pass to Dean. Yeah, good morning. Yeah, I came away from the paper again trying to figure out how to create some sort of a coherent narrative around the physical math and the statistical math. That part for me really got me going away and thinking a little bit because I think they go in different directions, but I do think that they can work in concerts. So yeah, I'd be really interested to see how that might play out in terms of what our guest here thinks the directions this might be able to go. I'll pass it to Stephen. Hello, I'm Stephen, based in Toronto. I work a lot with community development and sort of spatial meaning making, so inferences of different kinds. I'm curious how some of the ways that the mathematics have been done on this paper can help broaden some of the questions around ergodicity and non-ergodicity. That's a bit of a thorn, sometimes a weapon in the inactivist, active influence dialogue. So yeah, and that's something I'll be interested in and I'm going to pass this over to Dave. So I think Dave doesn't have audio, but Dave, thanks for joining and any questions in the YouTube live chat is awesome. So thanks to everyone who's joined and pass to Lance. Thanks Daniel and thanks for inviting me again. So I'm Lance. I'm a PhD student at Imperial and UCL and I'm really excited to be here and to engage in this discussion. I'm really looking forward to feedback about the paper, seeing what's interesting to pursue in future work. So yeah, really looking forward to share this paper with you and talk about it. So maybe one lead in question before we jump to the content. What stage in your PhD are you and is this like the meat and potatoes chapter one? Or is this a little cul-de-sac that you found yourself having to explore in the course of another research project? Yeah, great question. So I'm right in the middle of my PhD. I'm two years in to still have two years to go. And ideally, I would like to pursue this work. But so I have two supervisors. One is a mathematician. Another one is a neuroscientist. And so really the goal is to have some kind of mathematical theory of how adaptive systems work. So I think this is really the first chapter. I want to push that further. But then there are also other projects that take up my time. So I'm trying to make all that work together. Awesome. So for this dot two, we have some questions prepared, some topics that we know we want to talk about. But anyone who asks a question in a live chat will definitely have time to address that. The paper that we've been talking about is this Bayesian mechanics for stationary processes paper. And in the dot zero and the dot one, there's more information on the primary aims and claims. So check those out if you haven't already. We're just going to take one more look at the roadmap where we've been, where we're going. Remember, we were talking about Markov blankets and Bayesian mechanics. How does active inference have similarities and differences from other ways to model dynamical systems? And let's just go straight to the first question that we have, which is going to help us review where we've been. And then also as a jumping off point for some of these extended questions that we've already written. So a colleague asked me and said, I think it would be good to expand on the differences of the paradigms in section three. And those are section B, C and D related to a posteriori estimation after the fact, predictive processing and variational base. So perhaps Lance first and then anyone else who wants to give a take or ask a follow up question. What are the similarities in the differences here and why were they structured in this order? Is this the chronological order? Is this most specific to least specific or what is the ordering and the meaning here? Right. So it goes from the simplest to the most sophisticated. So a posteriori estimation is a special case of predictive processing, which is a specific special case of variational base. And so the idea is if you receive some piece of data, so for example, if you see an image with your eyes, you're going to try to infer what's going on outside in the environment. And so if you do a posteriori estimation, what you're trying to guess is what is the most likely thing that's going on in the environment. So it could be if you see an image of a chair, you would say, oh, it's a chair, but you wouldn't encode any kind of uncertainty. Oh, it might be like an armchair, for example, or something a bit different. So in a posteriori estimation, you try to guess what's going on outside, but there's no uncertainty. Then predictive processing, you encode the uncertainty. So mathematically, that's called the variance or the precision. And then variational base, it's more sophisticated. So you actually encode an arbitrary distribution on external states. So it could be, oh, it's very likely that it's an armchair, and it might also be very likely that it's a cat, so that this example doesn't make sense where you could imagine that there's two things that are very different that could be equally likely. So for example, if you see an illusion, it could be something, but also something very different. So you would imagine these two things are having a high probability of being there and then other things are having low probability. So this is really the most general thing. And also as a side comment, so variational base, like a lot of machine learning algorithms, you can see them as special cases of variational base. So I think this is really the most general way to think about inference. And this is really at the heart of the free energy principle. And I think this is why people have been describing the brain as performing variational base, because it's really the most general way to think about this kind of problem of inference. Awesome. Well, before I give a comment on that, what made you say that it was at the heart of the free energy principle? Right. So the free energy principle says that the brain is doing variational base. And then all this work, I mean, this paper in particular, but like the last decade, people have been trying to justify why would the free energy principle apply actually? And so this paper is part of a line of work where we try to examine physical systems or adaptive systems and see whether we can describe them as performing variational base. Great. So first, Steven, with a question and then anyone else with a question. Thanks. That's really helpful, that explanation. I was wondering, is it a case then that you can go only so far with say predictive processing and then to get to variational base and to bring in that uncertainty, that you kind of need a free energy principle solution to be able to bring in these more unknown models and to go beyond variational base at some point. That's when you'd have to bring in the active inference to it. Would that be a kind of the way you would think about it? Yeah, yeah, I would think about it like this. I would say, like loosely speaking, the term predictive processing, I think is also meant to refer to variational base. By this variational base, there's like a proper mathematical definition of what it is. And then predictive processing, it's more like, oh, we're predicting something. So it's not that clear how, I mean, there's no clear definition of predictive processing. But in this paper, predictive processing is meant as predictive coding. As in like the papers by Rao and Ballard where they looked at the visual system and then they looked at neurons in the cortex as forming predictions and suppressing prediction errors. So yeah, if you only do predictive processing in this sense, I think you're limited. And variational base and active inference is really like the next generation because you can accommodate all sorts of models. And yeah, I don't think it, I mean, I cannot see at least how you would go beyond that. Thank you. So Dean with raised hand, and then anyone else? I was curious. So it seems like the math is able to help us understand the difference between something that's really highly defined. So that kind of a posteriori and then sort of the fuzzy where the variational base part sort of gives us something a little less defined in terms of the edges. And so I was just curious, does the brain kind of go back and forth to some degree mathematically speaking between that which is really clear and really has a hard edge mathematically and those things which statistically seem to distribute within the parameter set? Yeah, I mean, I think all these three, like a posteriori estimation as well as variational base, there's this plausible explanations for how the brain would implement them. Okay. And so the idea, the idea for variational base or predictive processing is that so the brain would be encoding some kind of uncertainty. And so in the literature, people say that the mean firing rate of a neural population would encode the posteriori estimates. So what you think is actually out there. And then the variance of the firing rates would encode your uncertainty. So I think, so I think there's plausible, plausible theories for how the brain would implement all of these things. And then I think the, that's the nice thing, at least with active inferences that we try to develop models that are consistent with our understanding of the brain. And as our understanding of the brain evolves, we kind of like refine these models. So I think we're definitely working towards models that do explain, at least I mean so far it's very coarse grain and very simplistic, but we're working towards models that could be implemented in the brain. So I think like these very abstract, very general form of variational base could be implemented in the brain. One quick follow up is you mentioned how the mean firing rate corresponds to this first a posteriori estimation, which is a mean estimation, and then there's the variance in the firing rate. So what measurements or what does it look like to implement variational base in the brain? Like what measurements are we making? What kinds of analyses would we make on those just like mean invariance? Well, so the idea, I mean the very simple idea is that you would get some sensory stimulus.  And then the premise is that your brain has embodied a generative model of its environment. So it's able, it has learned how to recognize, how to infer things in the environment from its sensations. And so the stimulus that would be, that would go into V1 and all these other parts of visual cortex. And then the neurons in the visual cortex would align their mean firing rate with respect to oh, it's an armchair or it's something different. So maybe there's a neural population that encodes armchair and there's a neural population that encodes something else. There's also a lot of studies for specific neurons like one neuron encoding one particular stimulus.  So you can be very specific. And yeah, and so if it's uncertain that it's Bill Clinton, your Bill Clinton neuron would like fire, yeah, I guess would have a lot of variance in its firing rate. Okay, awesome. So welcome, Blue, with a raised hand, go for it. And then we'll continue and also Stephen, so go ahead, Blue. Hi, I am Blue Knight and I'm an independent research consultant from New Mexico. And I have a question on your paper and it's kind of something that I've been questioning a lot lately with regards to the free energy principle and the requirement for ergoticity.  And so I'm wondering how these stochastic dynamics relate to ergoticity, if at all, and if that fulfills the requirement for ergoticity necessary by the FPP. Right. Yeah, that's a great question. Yeah, I think Stephen also wanted to talk about that. So it's great that you bring this up. So, yeah, so the idea of these stochastic dynamics is that we don't assume that dynamics are deterministic and it makes sense because you can describe planets as having deterministic dynamics. But when you talk about biological systems, things are a lot more messy. And if you're not modeling them at the molecular level, which you never are, things are stochastic. So then the assumption on our system is that it's stationary. And this is really what it means to be adaptive. So you're preserving some kind of steady state, but we never assume ergoticity. So there's actually a deep, so stationary and ergoticity are not the same. So we assume stationary, but we don't assume ergoticity. And so if Daniel, you could go to appendix B, there's a figure, I think, which would be the best way to illustrate a bit below. Yeah, perfect. So here in this appendix, we illustrate some dynamics that are ergodic and some dynamics that are not ergodic. So if you look at the top left and bottom left panels, these dynamics are ergodic. And so I guess the intuitive definition of ergodicity is that here you have the steady state in blue. So regions that are very blue are regions of high probability mass under the steady state. So regions where your dynamic is likely to be in and regions that are less blue, you're less likely to be in. Now ergodicity means that if you start your dynamic anywhere and you let it run for a sufficient amount of time, so you observe your biological system for a very long time, your dynamic would basically sample the whole distribution. If you give it enough time, it would go really far away, and then it will come back and it will do all sorts of things, as you can see in the bottom left and bottom right. So this is ergodic. Now in the top left and bottom left, it's ergodic, and then in the bottom right, it's not ergodic. And so as you can see, if you start the dynamic on the bottom right anywhere, it will go around the orbit. They won't sample the whole distribution, so it would still come flying to a small region. So the paper still applies for these kind of dynamics. So yeah, I don't know, does that help or was that not very clear? So to follow up, the paper does apply in situations where it's not ergodic, that's what you said, right? Right, yeah, we don't need ergodicity. Well, so even within a steady state, so biological systems operate within homeostates, but it's a range, right? So it's not like a constant, it's not like, you know, purely we're not at 37 degrees all the time, right? So there's some fluctuation all the time within that steady state. And so I just wonder kind of how you rectify those concepts. Is it like a restricting of the state space or how does that work? So this idea of homeostasis, that's really the steady state assumption. So for example, in the state space maybe you would have one coordinate that describes the temperature of your biological system. And if it's a human, then it would have regions of very high probability. So here regions in blue around 37 degrees and then regions that are less blue, like a bit further away. And so the dynamic, I mean, your system can evolve in all of these regions. Just like on average it will be more often around 37 degrees just because that's how we are. But sometimes it will be higher and sometimes it will be lower. And so this is all allowed. And so I guess this ergodicity assumption. So then if you assumed that the biological system was ergodic, then this would imply that if you leave the biological system like run for a sufficiently long time, like you observe it for a very long time, it will basically, it will sample your whole distribution of temperatures. So maybe like the temperature that a human body is allowed to have are between like 36 and 39. Let's just say for simplicity. And so ergodicity would say, yeah, if I observe my biological system for a sufficiently long time, I would see my biological system at all these temperatures. And I think maybe that would happen. So maybe temperature is like we're ergodic with respect to temperature. But maybe there's other things in which we aren't ergodic. And I think the previous papers on the pre-engined principle, for simplicity, they always assumed some kind of dynamic and it turned out to be ergodic. And so in here we're not making that assumption. So I'm sorry, I'm going to just follow up with one more question, Daniel, is that okay? Yeah. So, you know, it's great, right? If you're talking about one human system, right? Like my mark of blanket, the petitions like internal and external states. And so I have my one human system or even multiple human systems that will operate in the same kind of steady state based range. But if we're talking really about, you know, collections and how kind of collective dynamics and overlapping markup blankets, do you think it's mathematically possible to extend the state space? Like I can operate, you know, from 35th to 39th, that's an okay temperature for me. But like a reptile has a very different kind of temperature range. But clearly, like we have some interaction. I have interaction with the reptile. And so there's some, some emergent dynamic between me and some reptile feature, right? Right. So can we define a state space? Like would it be mathematically like acceptable? Or is it like offensive mathematically like impossible to define a state space where I'm allowed to sample all of these temperature ranges with my markup? Like if it's some other feature in some kind of collective dynamic is not like they have a different. Is that still a revisiting? Because it's not, clearly, I'm not sampling the entire state space. I'm sampling my state space. But like, is that confounding in some way?  That's why I'm asking. Yeah, that's a really good question. So this is all fine. So we can do everything you just said. And so when we, so actually when, when we say, oh, we, so we, we always sample a distribution. We're not, I mean, and then the distribution is on the state space. So we're sampling the state space. But like, if your distribution is confined to a region of state space, so let's say, as a human, I cannot possibly have any bodily temperatures below 36 degrees. Then you're, then you would sample only things are above 36 degrees. So I think you would have your own steady state, your own stationary distribution with temperatures around 37 degrees. And then if there's a, if there's a snake also in the, in this environment that you're modeling, then we'll have a, another very different steady state. And so I think it really, your question really speaks to the possible extensions of these, of this work. Because in this paper, we just say, oh, there's like an internal state space, which would be what's inside. And then there's an external state space, which would be what's outside. But then really what, what people would need to do now is to say, oh, but my, actually there's a lot of very interesting things in my environment. There may be snakes, there may be other kinds of animals, and they all have their own mark of blanket and they all have their own steady state. So then what you can do is to partition your external state space into all of these things that might be around you. And then instead of having some kind of performing some kind of simple inference as we have in this paper, you would have some more structured inference, a more structured inference because part of your inference would be about what's just in front of you, part of your inference would be about your dog that's right over there. And you would have a lot of, by carving your external state space into different things with their own steady state, you would actually have an inference that's much more structured because you would infer all these things, all these different things that are in your environment. So this can all be accommodated in this paper, but it would definitely need another paper to like make that explicit and say some really interesting things, because yeah, this is really the way to go. But the mathematics doesn't need extension. It's just like, yeah, it would just be like partition the state space and then we can have all that you spoke about. Great. And also one piece of then Stephen's question is it's not as if something being ergodic or not is equivalent to it being easy or simple or tractable. Like looking at these distributions or trajectories here, the one that you characterized as non ergodic not sampling basically across the state space, the bottom right. This one is the one that in the caption, it says purely conservative dynamics lower right panel are reminiscent of the trajectories of massive bodies whose random fluctuations are negligible. So it's actually not like it's maybe this will speak to Stephen's questions about what is a thorn and what's a rose because this is a non ergodic system that's massively predictable. You can do it with a gear. So maybe that relates to some of these criticisms about, well, we're only working with a limited set of ergodic processes. It's like, okay, but that's the squiggly one that's dancing everywhere. The stochastic process that we care about, whereas including non ergodic processes, some of these non ergodic processes might just be going around in an oval. So it won't be a challenge for the math at all. Something that works on the stochastic squiggle is going to have actually an easier time on this oval one. So Stephen, and then anyone else with a question? Yeah, thanks. Yeah, I suppose actually tying into what you just said there, Daniel, there's this question with how much we need to be able to sample over big state spaces. So it might well be that, I don't know, the chemicals of a cell with molecules vibrating millions of times a second. And there may be a quick ongoing way to get a feel for the ergodic state space. Now, if you watch a cricket ball come towards you, you don't get that chance to do that. But you might want to maintain some sort of trajectory that can still be tractable, I suppose. So I think this is this is actually quite, quite useful. I suppose the question then comes in is how what's the sort of in-betweens? Where does approximation science come in more and more to allow us to sort of work with not knowing and work with something like these solenoid or flows in a more fuzzy way? I'm assuming that if you've got less chances to sample your state space, solenoid or might be more useful to get towards something tractable. Or maybe I'm wrong, but I wonder what your thoughts are on that. So actually solenoid, I mean, so in this figure here on the bottom left you have like no solenoid or flow. And then the bottom right is just solenoid or flow. So I would say all of these two like very special cases, they don't look like biological systems at all. And they're also the simplest ones to understand mathematically and to study mathematically. And actually when it gets really interesting and when it looks a lot more like a biological system is on the top left. And that's harder to assess mathematically. And so as you can see it's quite, I mean, I think the dynamic on the top left is quite nice because on the one hand you have dissipation, like you have some squiggly lines, you have randomness. On the other hand, thanks to the solenoid or flow you have some kind of exploration. And also some kind of like circular patterns. So for example, and this is actually how you characterize what's called a non-equilibrium steady state. But without going into the details, as humans and as animals we have a lot of circular patterns that are not purely deterministic. For example, we all have a circadian rhythm and we all have all sorts of other circular patterns. And I think to account for that you really need to be on the top left. So I think one of the next steps to this research is right now we just assumed that the dynamic is stationary. And so this applies to like a humongous range of dynamics. And a lot of them don't look like biological systems at all. And I think the next step would be to respect ourselves to dynamics that look a lot more like biological systems. And then see what else can we say. And I bet there's some dynamics that look a lot like very intelligent systems. And some that also look like maybe lifelike systems that are not so intelligent. So then the question is what kind of parameters, what kind of dynamics do you need to characterize something that explores its environment. Something that makes decisions and all sorts of things. Yeah, and that's going to be a challenge. Also, I mean just speaking about biological systems, I think biological systems have a lot of solenoidal flow. And they do have dissipation, but they don't have so much dissipation. So you would have something like the top left, but with like huge, yeah, huge like a lot of exploration. Like you would go a lot further than that in your state space. And then you would have a bit of, I mean, you would have a lot of squiggly lines. But it would be, yeah, there would be a lot more like exploration than there is dissipation. Yes, Stephen, go for it. Yeah, and you have both can combine, so gradient and solenoidal flow can kind of be playing at the same time. I'm wondering if someone was to bring attention to a goal or a type of attention, maybe a more pragmatic attention or an epistemic attention or a risk averse attention. Whether it might be that rather than trying to deal with the whole state space, maybe that general process carries on. But it tries to introduce a solenoidal type of flow, which in some ways you could imagine being more tractable to a biological system if it's like bioelectricity, the types of dynamics which maybe are more tractable around a certain trajectory than some. So are you seeing that these dynamics could combine in different regimes of attention? Yeah, definitely. And I think to properly account for attention, we need to go beyond these continuous state spaces and do what people and basically extend to these standard models of active inference where in addition to have some continuous state space, maybe like for movements and this kind of thing, you also have a discrete state space. And then you will have a dynamic evolving in your discrete state space and maybe like some states would be, oh, I'm attending over there and some other state would be I'm attending over there. So I think attention is really something that can be modeled with a discrete state space. And then it would, I don't think it would be so hard. I mean, at least seems doable to extend all the math here to like models. Yeah, that have some like continuous state space maybe for movement or other kinds of things like maybe like blood glucose concentration is also something that evolves on a continuous scale. There's also a lot of things in our mind that are discrete. So is this red yes or no? Is it raining yes or no? And to account for all that, we need a discrete state space as well. Awesome. Thank you, Lance. Welcome, Scott. I see your hand raised. So go for the question and then anyone else for the raised hands. Thank you. I came in a little late. My apologies. It's fascinating. The solenoid will flow when that gets set up. Is it possible that you have multiple state spaces and might because of the solenoid will flow might it have a periodicity in each of the state spaces so that you might be able to use Fourier transforms to unpack multiple state spaces in a biological system. So could you use to having that periodicity? Does that allow for a Fourier type analysis to start to unpack state spaces potentially when you have multiple state spaces and you're trying to distinguish them? Yeah, that's a that's a really good point. I know I know a paper actually that that analyzes the solenoid will flow in terms of the Fourier transform. I haven't really really thought about it. I think I mean if you if you get rid of the dissipative part if you get rid of the swigly lines and you're just in the bottom right, then you can definitely use Fourier transforms. But then also the dynamic on the bottom right is not is not representative of biological systems. So then what you can do when you're on the top left, which is really the interesting case is analyze the time irreversible part so the solenoid will flow with a Fourier transform. And then so you so you do this households decomposition that we're talking about in the appendix. You decompose your dynamic into. Yeah, so it's the equation a to. Yeah, perfect.  So B is the direction which your dynamic is moving on average into reversible and irreversible parts. The irreversible part is the solenoid will flow which you can analyze using Fourier transform. But then you need to like figure out how to accommodate the reversible part with it. So I can share I can share the paper. It's interesting. But yeah, it seems like they're they're able to to like do do some things with that technique. But it's also pretty pretty involved to be honest. A question on the time reversible and irreversible. What does that mean? And in a world where it seems like we're moving forward to time only. What exactly does that mean that there's something that's invariant under time reversible? Versus something that changes sign under time reversible? Like if we can't get the time machine or put the process in a time machine, why does it matter that it's time reversible or how does that fall out of the equations? Right. Well, yeah, so so all this is really to emphasize that we're not assuming the dynamic to be time reversible.  If you go back to the figure just below, so the movement of planets is really something that's irreversible. I mean, the earth turns around the sun in one direction. And if you are to rewind time, it will turn around the sun in the other direction so that so in this case, you can really tell the difference between time as time goes forward and as time goes backward. And that's really what's meant by time irreversible. But now if you look like at a cup of coffee and the coffee is still, the molecules, the coffee molecules or whatever molecules you have in that cup, they're still bouncing with each other. And that's that's something that's time reversible because if you look at the cup of coffee, if you if I give you a movie of the cup of coffee sitting still, you can watch the movie as time goes forward or backward and you wouldn't be able to tell the difference. So that's something that's reversible. And so as you can see from this example, actually things that are reversible aren't interesting at all from at least a biological perspective. And there's there's so much literature about I mean, one of the fundamental things of being alive is being time irreversible. It's about like eating and producing waste. It's about consuming energy. All that kind of thing. All that kind of stuff produces entropy and is time irreversible. But then time so time irreversibility, it's something that's necessary to be alive, but it's not it's not sufficient. So for example, if I give you a convection cell, though that would be time irreversible, they won't it won't be alive. So any any kind of cycle that's more or less periodic. So maybe if you if you see like a cyclone, a cyclone is time irreversible because it's like spinning one way and not the other. So if you run on time, it would be spinning the other way. It's different. So it's time irreversible. But that's not alive. And so there's many, many things like that time irreversibility, creation of entropy. There's a few things like that that characterize biological systems. And I think as we as we go on with this work, we'll try to like specialize to only those dynamics that satisfy all these requirements and eventually things like oh, we need systems that are able to reproduce, for example, like a Markov blanket that is able to divide into two Markov blankets. For example, when a cell decomposes into into two cells. So so this is really the beginning. And in the next years, I think this community is really going to be able to to like address all these challenges and like all these characterizations of living systems to gradually evolve towards models that are more realistic. Awesome. So I'll have more to say on it. But Scott, go for it. So a couple of things. There's a book called Life's Ratchet, which is kind of interesting just on that idea of that irreversibility and that value of that. And the idea is that life kind of ratchets in these forms that work with the externality. I haven't revisited that since I've been exposed to active inference, but it might be interesting to take another look at Life's Ratchet. Also, one of the things that I like that discussion of living forms and what's necessary prerequisites to living forms. One of the working definitions I'll share that I'm using now, and I think then let me tell you why I'm using it, is that life is auto-catalytic and entropy secreting. Now, my kids claim, I just wanted to say secretion in my definition because it's gushy. That was what my kids used to say. But auto-catalytic and entropy secreting. So notice, I didn't say it had to be embodied in a specific form or a specific matrix or context. It could be a market. It could be a Markov, you know, a lot of different things. So the reason I share that here, it's interesting because active inference, we have this definition of life like Corollus Linnaeus. You look at it and you see if it has feathers and you see if it has blood and stuff like that. But now we're going towards mathematical definitions of living things. And that's going to be very interesting because I think when we have a working definition that works for biologic forms. So again, my working definition right now is auto-catalytic and entropy secreting. Then I can start to say, okay, if that worked for biologic forms, let's say that did work and maybe there's problems with that. But if it works, then you can start to say, okay, what other systems happen to be auto-catalytic and entropy secreting and therefore we shall now call living and maybe we can start to look at them and make observations about those systems. And what I'm thinking about, I'm a guy who's a lawyer and in finance for years. So I'm looking at this and saying, okay, you look at these systems. Biological systems came up with these markets and these other systems that we have to do things in the world. Maybe these systems are describable with biological framings. And so that's why the kind of work you're doing feels like as it starts to reveal some more general definitions of living forms, taking those definitions and then reapplying them back out into the world and saying, okay, are there living forms that have escaped our detection as living forms? And basically, is there scale independence? Are there fractal elements? Are there things that we can now describe in those things that we previously had not thought of as biology but in fact are describable as biology? That's very exciting to me. So I just wanted to say that the kind of things you were describing there and that kind of working way back down into a model of life based on time irreversibility is very interesting, I think. Thanks. And a very interesting paper overall. I'm looking forward to diving into this and the other paper you were mentioning also. Thank you. Cool, yeah. Yeah, thanks a lot. That's really great. So to tie this from the some of the physical examples we've been talking about like the diffusion processes to the physics of information and information flows. The big thing we've been talking about is this statistical physics and this Bayesian mechanics. And we heard a little bit earlier how we could talk about the moments like the first moment, the simplest form, the a posteriori estimation was the mean. And then the second moment of a statistical distribution is the variance. And there's also higher statistical moments that describe higher and higher aspects of an informational distribution. There's also the concept in physics of moments like the position and the velocity in higher and higher physical moments. And so the mapping is that potentially these physical moments that would describe components of a physical flow that could also be decomposed using the Helmholtz decomposition might also apply to some of these informational flows and decompositions. So we could use those analogies like the coffee mixing and the steady state of the coffee and then think about how a statistical distribution is playing by similar rules. And so it's also interesting, Scott, about instead of going from the non-living systems and then looking for that pattern and pattern matching to biological systems, we can kind of start up on the top left with or something even more biologically fleshed out and then look for those patterns and pattern match outside of systems that have, you know, a vertebra and a central nervous system because that shouldn't be the card to get into the club of information processing systems or entropy secreting systems. So any thoughts on this? Yeah, I mean, yeah, I think that's really interesting. I mean, the real challenge here is to make the link between the physics and the information. And the more I've been working on this, the more I realized that actually a lot of physics or at least a lot of statistical physics, you can explain with properties of information. So for example, entropy increasing is also information being lost, not stochasticity. Stochasticity, so the inability to predict the future exactly is exactly the same as entropy being lost over time. Information being lost over time and entropy increasing. So I think there's very deep connections between information, physics, inference, and some of them have been fleshed out, but it hasn't really been put together at least as far as I know in this context, in the context of Markov blankets, in the context of how can we have a theory of how adaptive systems work, and can we describe adaptive systems as performing inference? So I think this is really exciting. And also as you can see from this paper, so the dynamics that we're considering, they're extremely general. And for these dynamics, for all of them, we're able to derive some kind of inference. So this is to say that this inferential description it applies to many systems, and so it means that on the one hand it's very ubiquitous, but then on the other hand it's not that useful because maybe the things that didn't look at all like biological systems can still satisfy this kind of pre-energy principle or Bayesian mechanics so I think what's really exciting is to be able to, in the future, to specialize to those dynamics that look more like biological systems and then really look at these informational properties. And I think a big one is how much exploration do we have? And exploration is really something, exploration and curiosity. It's really something that characterizes intelligent systems as we know it. And yeah, so there's some discussions in the literature of how we would be able to use things like information length and concepts for information theory and information geometry to quantify things like memory and itinerancy, curiosity and so on. So one question from the live chat where you continue. The question is what is the explicit definition of information flow and also maybe in that if you want to describe a little bit about this other paper like what is information flow? What is information geometry and how does it relate to what we're talking about here? Right, so this is all the idea of, as an organism you're always encoding some beliefs about your environment. So we talked about maximum posteriori and variational inference. So the idea is that we're always receiving sensations and then making some inferences about the outside. Now if you're making some inferences about the outside implicitly or mathematically you're parameterizing a distribution about things in the environment. And so information geometry then comes into play information geometry quantifies the extent to which beliefs about the environment are different from each other. So it doesn't make sense. So for example, let's say that, I think Daniel's eyes are blue, let's just say. And then I have some uncertainty around the real color. So that would be like one kind of belief I could hold. And then another type of belief would be Daniel's eyes are brown and then I would have some other kind of uncertainty. Now the way, now a question you could ask me is how different are these two beliefs? And if I had a different belief about the color of his eyes would that belief be more different than the beliefs I initially had? So then information geometry enables you to answer these questions it enables you to say how two beliefs are different from each other by quantifying the distance between them but also even more interestingly as I, let's say I've never met Daniel before let's say I haven't seen his picture before now you give me a picture of Daniel.  So from being initially completely agnostic I'm going to move my completely agnostic belief to a belief that says oh maybe he has brown eyes. So this is to say that as we make inferences and sample the world, our beliefs evolve and so information geometry enables you to quantify how much your beliefs evolved and what kind of trajectory did they take because I mean I'm assuming at least our beliefs they evolve in a continuous manner as we sample more information and then it becomes interesting to see what kind of trajectories did my beliefs take and was that trajectory efficient? If it wasn't efficient maybe I lost some energy there that I could have used somewhere else so my inference wasn't very optimal from that perspective and then so there's a paper about this actually an active inference that uses information geometry to see whether inferences in active inference are efficient from a metabolic point of view so that's something that you can look at with information geometry Thanks just to follow up from the chat and then we'll return to our colleagues here Do we have or more precisely do we hope to have a definition like an electromagnetic flux in field theory for information flows, information flux? Yes Yes so information flux is the movement of beliefs and so you can you can write that down mathematically so yeah I mean a belief is a probability distribution about things that are going on in the environment and as you sample information you would change probability distribution so it would be like a motion on the space of probability distributions that's really the meaning of information flow but maybe the question was about can we derive some kind of like Maxwell's equation some kind of law about how information flow happens like maybe an equation for information flow and I would say that that would be the aim that would be what people are working towards in theoretical neuroscience like some kind of equation that explains how we make inference Awesome so a few raised hands Scott first then Blue then Steven go ahead Scott A couple of things that was fascinating little bits there so on that last piece on the information flows two points the embodiment I'm thinking of embodiment of information so I'm thinking of a farmer that's deciding what crops to plant so they look and they get information from the newspaper and they look at the weather reports and they gather information then they decide on what seeds to plant the seed itself is an embodiment of information they put the seed in the ground the results with their farming the markets then respond so there were seeds as information farmers processing information markets processing information and one of the things is kind of interesting here so a lot of the work I'm doing now is in food chains and trying to figure out how to de-risk food chains and just food generally and that efficiency question just asked is really interesting what are the losses and conversions that happen when information is embodied in those different aspects of the decision process through which something gets converted from a need of society to have a certain amount of corn at a certain time of year through all those chains of seeds and selections of farmers processing those things it's kind of interesting to look at the system as both each piece of it is living the seed is arguably living although there's a question of whether seeds are living among people who are biologists but anyway they're kind of stasis but anyway that's one I'll ask both then turn my voice here so the embodiment question is one kind of that notion that just talked about an overall formula maybe there's an overall embodiment characterization that's made possible using those landscapes and looking at a multi-faceted landscape and looking at those conversions that happen from one embodiment of information to another and efficiencies there but the other one is you said something about curiosity before maximum exploration, maximum curiosity that really struck me because one of the things we've been advocating for I did a lot of cyber scouting work a number of years ago and people were coming out of the military and we were saying oh hey you ex-military guy you got to learn more critical thinking and I was kind of insulting them because they were senior people and one of the things I started to say is don't tell people they have to have critical thinking they have to be more curious and it's kind of interesting that we're getting now to the system having a maximum exploration possibility a maximum efficiency in some ways with curiosity to me that really informs a lot of teaching because if you have people who develop a curiosity over their lifetime they take care of being educated they continuously are learning and so that notion of exploration and curiosity seems like it could fundamentally through active inference affect how we do teaching and much less of rote teaching and much more of a curiosity based teaching because of the power you'll never know what you're going to encounter out there in the world and so telling your children hey be curious will intrinsically serve them versus teaching them a rote series of things that respond to their environment so just a couple of comments that I thought were fascinating thank you yeah that's really interesting so as you said and I think we all agree information or maybe 70 years ago or 80 years ago we didn't have any kind of information theory information theory wasn't a thing computers weren't a thing and we didn't really think about information even though it was there in books I mean everywhere around us advent of computers and information theory just information became a big thing and people realized that it was important and now everyone thinks about everything in terms of information and I think that's the right way to look at things I mean it seems to be yeah information can encode just about anything by definition and so physics or at least our descriptions of the world the matter was the most important thing matter and waves this is how it all started and then information geometry and information theory came into play and people started looking at these things in terms of information as well but I think matter remained a big thing but more and more people are looking at information in terms of like the the most important concept the root concept from which you can encode or explain everything else and so yeah information geometry came around and it enables you to see how information is flowing over time and how that relates to heat and things like that and now people are looking at how information may be encoded by things about other things and this is really Bayesian mechanics Bayesian mechanics the root of the word is beliefs about things that are held by other things and I think this is yeah I mean Bayesian mechanics I guess started out I mean in a way it started out long ago with like Bayesian inference but Bayesian inference started out as an abstract statistical concept and now people are trying to relate that to physics and yeah so I think we're moving towards a physics that's information based and based about yeah based about beliefs about things encoded about other things so this is really Bayesian mechanics information geometry and then what you said about curiosity was also really interesting and so yeah definitely I mean in AI people are tuning curiosity so yeah they're trying to optimize curiosity of agents with respect to different environments in a paper that we have called active inference on discrete spaces a synthesis we in one of the appendices we justify the expected free energy objective that people use for to explain decision making biological agents and we actually show that we could have so the expected free energy for those who don't know it's basically ways exploration and exploitation so exploration is really the curiosity so he has these two terms and in general I mean these two terms are put on the same footing but actually in the appendix of that active inference synthesis paper we show that you could weigh them in a different way and it would and I mean the yeah the agent would still work somehow we'll have a different behavior so it could be a lot more curious less curious and that would be really interesting to quantify in terms of like concepts of information geometry but so this is to say that you can actually tune that and have agents that have different curiosities and also make me think about what you said about things from computational psychiatry where people explain diseases like computational diseases as people having like different priors in their genetic model and seeing how that would affect behavior so you can explain like suboptimal optimal and suboptimal behavior with like the same principles just by changing the model and we also have a recent paper on the Bayesian brains and the reny divergence we're basically showing that by changing doing variational inference a bit differently you can actually account for agents that are optimal that make like the right decisions and agents that maybe are a bit suboptimal in terms of curiosity and so on so I think there's a like a lot of exciting computational work to be done in terms of characterizing different behaviors and I think we're really at the beginning and ultimately all these things we'll be able to I mean people will be able to account with information geometry I think that's the right framework thank you Lance just quick follow up Scott go for it yep quick follow up two things when the Bayesian mechanics when you say beliefs about things that are held by other things that feels nice with my example of the farmer in the seeds because it's an embodiment each thing that embodies something is the embodiment is a belief in a sense right because it's holding a seed doesn't have a belief itself but it's embodying information and so it's interesting to think about belief of things and then the embodiment of information in the thing intrinsic affordance that the thing offers right that is that what's the relationship between belief and intrinsic physical affordance that's in a system that is the result of an earlier information system that's one follow up then the second follow up is the way I soften people up when you talk to older people and you're like oh it's all information it's not physical we're information beings the way I soften them up just to share is I say to them do you have a 401k or retirement plan you most older people starting to think about that and then they they say yeah and I say do you think it's a pile of groceries waiting for you to do retire because it's not it's just data in a system and if that system goes away you got nothing so it's that idea of getting people to understand how much we depend upon information and then people start thinking oh wow I guess I really do depend upon all sorts of other systems in my life it's something that as physical beings it's hard for us to realize how much we are information beings and that's again as part of that rhetorical exercise to get people in the headspace of saying wow maybe things really are information that I thought were solid like my retirement plans but really they're just totally dependent on systems and the information output of the system thanks nice Scott thank you so Blue with the question go for it go for it so you mentioned a paper that you well I don't know if it was really about information geometry and active inference is it this one that's mark up blankets information geometry and stochastic thermodynamics is that the paper you're talking about no that's not this one so if you're referring to the one about how inference is efficient like quantifying efficiency of inference and how much like energy you need to do a kind of inference so that's not this paper it's not a paper called neural dynamics under active inference something that so I have some questions and I don't know anything about information geometry I mean just a little tiny bit so it's something that I'm definitely starting to get very interested in because I think that it's going to be maybe like the next level of where active inference goes maybe I mean I just have this sufficient so when when you have information and in an information geometry like in an information flow I've been reading other papers about information flow in channels right so like when you and I mean it makes sense because when you have when you know something about the current state I mean it's just like basic inference like your belief about the next state of the world is based on the state of the world right now right so I mean it doesn't make sense that you would think you know all of a sudden I'm going to be like unfleudable based on my kind of information and so it does is information geometry or do the channels appear when you look at inference and information geometry like does it appear to be like a trajectory that's a good question so I think information geometry is more general like you don't need to have a channel it's really about at the heart of it it's really about having different probability distributions and these are actually beliefs about stuff and looking how they differ from each other and like movement how probability distributions change over time these kind of problems but then so you're right to say that information theory started out with the study of channels communication channels between different things and you have yeah there's a lot of work on information theory and channels and still today with in engineering so I would guess there's a lot of work also on information geometry with channels but that would be like a subset of the whole field of information geometry and I would say it's it would be yeah I would say that people contributing to that literature would be mostly from the from engineering or around engineering thanks blue anything there yeah go for it so so I know like about information theory and like the flow of information in the channel stay like a telephone line or whatever like some direct method of communication but like the way I don't know if I'm thinking about it in the wrong way because when I try to search for like information flow in a channel and maybe it's the same but I think about it in a different way like I think about the channel flowing from like the present into the future right so like there's only so many like next states that are possible right like based on my present state and so is it incorrect or is it correct to think about like not a direct channel as in I'm speaking to you over this internet information channel but like the channel from now into some future state is that the same kind of like mathematical engineering information channel yeah that yeah you're catching me off guard because I don't know about channels so I mean what you say sounds plausible and I would say yes but I wouldn't be able to say for sure just because I don't know that literature thanks well I'm sure come back to this in the weeks and years to come so Steven go for it yeah I'm really interested by the these different tie in these bits together you know why I suppose that sort of come up we've got this sort of information geometry that I suppose can come from an ergodic space or a state space and then you've got solenoidal flows within maybe an isocontour of that or potentially I suppose it doesn't have to be solenoidal it could be like an isocontour flow if it was more complex I mean and when you've got that potential to go and have a solenoidal type flow to sample would that be a slightly more of a second order sampling approach that something might use so you've got you know the distribution could just emerge from a steady space steady state sort of ergodicity process and you would maybe somehow systematise a flow or a way of engaging that information and I could imagine that would then make sense of some of the entropy consuming potential of a living system which is that it can kind of go up grade in descent and the solenoidal flow then gives Scott's sort of entropy secreting option it seems a bit more viable then because maybe I could choose multiple solenoidal samplings of information geometries and secrete the ones which aren't as good if that makes sense so I'd be curious in terms of how you know that the ability to go to more second order understandings within a system and within the dynamics might be offered by the solenoidal sampling maybe even taking into account things like the landscape used on the mountain car problem you know that landscape if you can't sample the whole landscape ergodically could you have lots of solenoidal samples or something like that around the landscape yeah yeah it's a really good point so there's deep connections between solenoidal flow and information geometry and mostly in the context of the as you pointed out the sampling literature so in so the idea is that if you start a stochastic process somewhere and you have solenoidal flow it will converge to its steady state a lot faster than if it didn't have solenoidal flow so then you can quantify that in terms of information geometry maybe taking a shorter path to the steady state and things like that so then there's also a really nice new paper actually called is there an analog of Nesterov Acceleration for MCMC and so that paper shows that that paper really does a nice job of illustrating some deep connections between stochastic processes and information geometry and so the idea is that if you start with a very simple a very simple process called overdamped non-japan dynamics then you can show that actually the dynamic in information space is doing the process is doing a gradient descent on KL divergence to reach the steady state so the target distribution so this process is exactly doing standard variational inference but then if you add some solenoidal flow you actually make that convergence happen faster so it's like an accelerated method and so in terms of biology you can say that if you have solenoidal flow it just happens faster so you're able to infer things a lot faster so in a sense more intelligent I think we talk about it in one of the figures in the part of the paper and so in that paper that I just mentioned they show that with a particular stochastic process actually implements some kind of accelerated variational inference so yeah there's some literature about that and it would be interesting to see those processes that perform inference very fast whether when we put them in the Bayesian mechanics contest whether we can say oh these actually can be seen to correspond to biological systems that we've been studying, things like that Can I just ask one quick question on that when you say adding solenoidal flow is that adding it in the sampling methodology or is it somehow maybe could it be thought of physically or how does that work yeah definitely so the solenoidal flow is really this time irreversible part so intuitively it's this kind of like stirring or mixing the system so maybe if you have a really nice example if you have a cup of coffee and you pour milk in it now what you could do is just wait for the milk and the coffee to mix together and this would be no solenoidal flow because you're not mixing anything like it's just happening on its own and you have a dynamic like in the figure that we saw before like on the bottom left so it would be time reversible and this would like actually converge the steady state pretty slowly in terms of information geometry you would have a slow dynamic to the steady state in terms of statistics you would have a slow variational inference because you reach your target distribution very slowly now what you can do is adding in solenoidal flow so this would be I take my spoon and I'm going to stir the coffee and the milk together then we all know then that this is going to allow the system to mix and to actually become uniformly mixed a lot faster so mathematically it means that we reach the target distribution of the steady state faster so as of information geometry we're also faster in terms of statistics you can interpret that as doing variational inference faster now this interesting thing about adding in solenoidal flow is that in physics it's called breaking detail balance and breaking detail balance is about you actually probably need to input energy from the outside so this is the physical meaning of the time irreversible part of the dynamic when there is some time irreversible part it means that there is actually energy coming in from the outside and this is also like it ties in nicely with biological systems we know that biological systems consume energy from the outside so we know that they have to be that they need to have some kind of this irreversible dynamic thanks Lance so anyone else in the live chat who wants to ask a question this would be a good time to go for it and then Dean and then anyone else let's be gentle on me I don't know about that I just feel really vulnerable but I'm going to throw it out there anyway so lots of chatter about the encoded aspect of this and I think we all understand what that means so I'm going to raise a metaphor kind of a around negative space and the idea of threading a needle which is if you think about it as a distributed exercise is plenty complex like there's a lot of math in terms of being able to just do that thing that's hard hard enough so if I'm trying to explain to somebody else a Bayesian manifold and what that represents can I say that it's both a barrier and a filter at the same time can I say that it acts kind of like a sieve meaning that it's mathematical structure it acts as a ground to the physical things that we are inferring are going on in the world so I guess what I'm asking is statistical mechanics serving to allow us to understand what negative space is as a non-form within all as part of all the forms that we're seeing the edges of the liminal understanding until we get to the very limits of what and the high definition of what that means so does the statistical manifold allow us to go in around and pass through zero it doesn't allow us to reverse the spin of the solenoid but it does allow us to get away from zero and move closer to what the known is because if we continue to kind of go back and forth between the physical math and the statistical math I know why we have to kind of talk both at once like we have to have two hands to clap but I think it's I think what ends up happening is in this conversation the encoding and the physical piece tends to dominate and then and the non physical stuff the statistical stuff maybe that ground that the statistical manifold allows for doesn't it hasn't maybe been fully pushed out in a way that helps me help explain it to other people who aren't as far along in this journey as you are and I'm hoping to get to a place where I can translate it for them so maybe you can just talk to that a little bit about what is the statistical manifold is just the hard stuff that we see or should we be paying attention to maybe the spaces between all of those data points right yeah so that's a really interesting and actually a hard question to answer but just to start with the easy part the statistical manifold is the mathematical object that says these are all the beliefs all the different beliefs that you could hold about your environment right and so as time as time evolves and you're gathering the information your what your brain is doing is moving on this statistical manifold your beliefs are changing over time and then in terms of explaining it to people so the way the way that I try to explain it is that this this like information talk things encoding things encoding information about other things is just a different description of the world so we have a description that takes like matter and waves and forces and things like that and then we have a different description that looks at information and I think these two descriptions are equivalent it's just two different ways to talk about the same thing on the other hand this way of talking about the world in terms of information flows and information processing I think it might be more general in the sense that instead of needing to have like matter and all these different concepts different kinds of particles and it gets really messy maybe it would be possible to unify more with the concept of information because with information you can explain what a proton is and what what a proton is and and you name it so it would be more more unified and maybe more mathematically simple at the end of the day but that remains to be seen interestingly so does this guy go from the computational engine go from alpha so this guy is actually a physicist I didn't know that until very recently but he has been doing some really interesting work over the past few years working towards a theory of everything that is based on the concept of information so information and computation is the the thing he starts with and I think he's managed to he basically postulates that the the world evolves in time according to some kind of computation that's recursively applied to itself so you could think of it in terms of a dynamical system but so it's like the way he thinks about it is a bit more general but it would be like maybe you give a number to a program and then the program outputs a number and then so that would be one time step and then you reapply the program to that number that would be another time step and so he and so he postulates that the universe in that way evolves according to like discrete steps with a repeated program and the program would be the laws of physics it's like kind of an abstract informational way to look at it and so the so yeah so he he makes this very abstract approach to physics and also very simple I mean very kind of unified approach to physics and I think he's managed to derive approximations to the equations of relativity just with that so with a certain kind of program I mean anyway he's been doing some really interesting work trying to unify known physics with the concept of information and he's written a very nice article like a blog post about it I think if you google like a Wolfram theory of everything you might come up but yeah it's I mean it's not technical I mean it is technical somehow but it's not like there's no equations it's conceptually I think conceptually hard what he does but the way he explains it is nice so yeah I think we're moving to this kind of information based physics but it doesn't mean that the physics that we know with matter and so on should be discarded it's just like different levels to talk about it just like we have psychology that talks about the brain from a like very overall perspective and then we have like talking about like maybe biases our biases decision making so that would be one description of the world and then we have molecular dynamics that would look at the brain from a very from a basic molecular level and all these descriptions have to fit together somehow and I think depending on what we're trying to ask one description would be more fit than the other so if I'm studying a human psychology is probably much more useful than molecular dynamics thanks Lance one quick comment on the information is it allows us to drop into a mode of matter and organization as information which is still within the objective stance but also it allows us to model ourselves and our beliefs and thinking about them informationally about other beliefs or about matter which is a way of mathematically complementing the relational stance so it also moves us towards Wolfram's vision of what new science would look like because we actually have quantitative relational techniques that help us deal with our uncertainty and about the way that we interact with the world actively interfering and measuring and manipulating not just like us walled off as the investigator trying to get to the most exact framing of a system so it's really interesting developments so we have time for some more questions so Scott and then after that we'll go to Steven so go ahead Scott couple of little thoughts on that last bit so that multiple dynamics that you're talking about very interesting you've got me thinking about that coast of England problem from fractals where if you measure the coast of England with a one mile yard stick versus a one inch yard stick if it's a one inch yard stick the coast of England is longer because you're measuring more of the nooks and crannies in the fractal coast so that scale dependence when you're talking about the dependency we see nature and see biology through different lenses it's kind of interesting if we have a unifying lens maybe you start to have a fractal and scale independent descriptors then we'll pop out of that because you'll start to have things that'll anyway it feels like this we're coming at descriptions of systems as you're saying from different in different ways they're the same system ultimately and so there'll be an interesting analysis on the way in which they come together I guess is that this one piece another thing the mention about information and the that kind of a Wolfram idea that expansion one of the things I had a conversation with a couple of astrophysicists and I was talking to them about Seth Lloyd out of MIT part of his book called Programming the Universe he talks about the idea that all interactions since the Big Bang have increased exponentially just the number the volume of interactions and I was talking to somebody about it and they said well if the universe is made of information then the exponential increase in information maybe that's what dark energy is we perceive dark energy that expansion force as being with something but really what it is is the universe expanding out exponentially because it's made of information and so something just to think about it kind of leaps around there between physics and information theory but there's that's one other piece of it and then the other piece of it was this idea the outside energy you were talking about before the need for outside energy one of the things that I've been fussing around with is whether in fact and in 2013 I did a presentation MIT called entropy accounting and then the year after they did something called entropy engines and the idea that was that was that in information theory in Carnot's equation you need a hot and cold differential to perform work Carnot's equation those differentials are identical to arbitrage differentials you need for a market to perform to move if there's no information differentials you don't have trading in markets and so one of the questions is Roger Penrose wrote a book recently about the time before the Big Bang what he talks about is we had the yellow light of the sun come in and the infrared light go out we don't overheat except for climate change and carbon dioxide blankets because the net energy energy gain is zero right energy and energy otherwise we'd overheat he said what we gain is neg entropy because the yellow light of the sun has a higher information carrying capacity than the red light that goes out plants construct themselves from the yellow light of the sun create neg entropy and then we now projecting forward are now burning that fossil fuel that stored up that neg entropy and releasing disorder in the form of now climate change disorder political and social disorder so I'm jumping around there is suggesting that disorder accounting and entropy accounting when you have von Neumann and Shannon's link of physics and information and other links like we have here that maybe when we're talking about entropy as disorder we can talk about it not by analogy but direct application to social contexts and start to use information and understand disorder in society and in markets as amenable to the same kind of math that we find in some of these biological systems thanks just a few thoughts thanks Lance if you want to add anything sure yeah that was interesting and yeah so I want to add actually that all this the thing that we talk about like reality can be described at different scales and I think there's a nice extension to this work that speaks to that you could if you look at a human I mean it's composed of a lot of cells and each cell has its own boundary and these cells form organs that themselves have their own boundary so there's the street this recursive aspect of like mark of blankets being assembled together at different scales and I think I think it would be interesting interesting to impact that because I think that's how biological systems are formed both societies are formed as collections of multiple different individuals that are themselves that themselves form organizations that that talk to each other and form together a society there's really this recursive aspect and being able to hopefully use the same kind of math to talk about all these different aspects and also I mean people it's true like a lot of people in the past maybe 10-20 years maybe more they've used the same kind of dynamical models that we have in this paper and so very standard models to model for example interactions between people and in particular models of opinion formation so for example maybe let's say we're in the US and some people are Democrats some of our Republicans some cannot really make their mind yet and so they would talk to each other they would interact and then they would converge onto a steady state where some yeah some some people would be die-hard Democrats in that steady state so they would kind of stay in that area some people would be die-hard Republicans and some people would like yeah flop to it, flop to it in the middle so I think we can use I mean this math about stochastic processes and information is really the yeah the the ground I mean the the good framework or useful framework to model many kinds of things but then I think what a lot of these models are missing is really this belief based aspect so a lot of these models of opinion formation there they just say oh I'm a particle you're a particle and we interact just like particles in physics would interact so it's quite simplistic so I think once you I mean things are very small maybe we can describe them in a very simple way but as you as like Marko Blank it's self-organized at different scales and as you as you go to larger and larger scales things become a lot more complex and I would say maybe we are the scale at which things are most complex or molecules tend to be quite simple we tend to be quite complex and then if you go up and up again maybe to planets then things start to become really simple again because all these random fluctuations are kind of averaged out and then we have Newtonian mechanics where everything kind of looks deterministic so I think there's this like sweet spot we're in where we're not too big and not too small and interesting things happen there and that's where I would say that's where I would say Bayesian mechanics is hoping to fit in in terms of explaining and describing what's going on so Stephen go for it yeah that idea again that brings us back to embodiment I suppose because we're embodied at a particular size and scale and they sort of say if you go right down to the smallest scale of like and then right up to the biggest scale we are kind of in the middle ironically but so I was wondering how sort of following on from what you were saying and bringing in the computational psychiatry piece that you sort of alluded to this is if we say that we've got everything that we perceive even the physicality of the world we actually only have access it through information anyway even if we are actually accessing the true physical world so we've got this process of sense making that we're doing to make that idea of what is our consensus reality so if our kind of working space that we're in is our consensus reality what's interesting is that with psychology and social sciences you can almost say psychology is a bit like the predicted processing model of the world it's like these are predicted ways that are out there that have been chosen as the models in particular sort of discreet spaces and those are externally managed so it's like an externally managed system there could be an entropy secreting system where it looks like there is although entropy is not actually a substance to secrete per say and you could say that it's externally managed information geometry that the social sciences as well with their averages and the psychometrics that they reference to they're all kind of housed out there in the world and you've kind of got the kind of what we see as our reality and the phenomenology of our experience as kind of the boundary but what your works doing and what computational psychiatry does and which we're not able to do without those tools is it allows us to go into that neurobiology and the actual like the internal internally managed statistical dynamics of our own models so to speak so not the ones that we make out there to be our perspective on which we try and reduce free energy around but just what is the models that we're doing what you could call entropy consuming i.e. we're actually just swimming in that entropy and finding the variations right and so I'm curious like that ability for this type of work to contribute to a new kind of way of knowing about what it is to be in the world and go into our internal models rather than be reliant on these external psychological and social science models what's your thoughts on how this might link into developing that field so are you talking specifically about the link between all this physics and the psychology or is your question a bit more general maybe the boundary between the kind of like the scales of basically the boundary of going for externally making models of the world and standing models like psychologists are doing and social scientists are doing and psychometrics and the ability to actually go into our own models our own phenomenological neurobiological models and just say okay what are the dynamics that are alive not what are and how are we actually managing not how do we manage our models of what we think they are which is kind of what happens in our kind of niche but we're able to probe our own phenomenology so I was wondering how you see that tying into that yeah that's a really good point so as you point out now models in like psychology and computational psychiatry I mean they're driven by intuition they're driven by experiment and they're driven also by your own biases and our observations about yeah patients who suffer some some kind of yeah some kind let's say schizophrenia and so we know schizophrenic patients behave like this and like that and so we try to create models that kind of reproduce that and then we try to to validate these models by saying oh maybe I can simulate some kind of action potentials of some neurons and then I'm going to check whether actually these organisms that I'm studying have this same kind of action potentials or same kind of electrophysiological responses and so I think that I mean I think that's really good and the research is doing a lot of progress but then this kind of work not this paper but this line of work would be able to to like go the I mean I mean takes a different perspective and would be able ultimately hopefully to describe mathematically what thinking like a human is what is being human mathematically and of course there won't be like a definition of this is a human but there would hopefully be in the future a mathematical description of how we make decisions and what class of models are we implementing to make sense of the world and how can we characterize these models in terms of and hopefully the community will get to that through physical experiments but also through like just mathematical conceptualization I think using mathematics you can you cannot get you cannot just get there without any experiment but you still can there's still quite a few constraints that we have on that we know that humans have for example breaking detail balance creation of entropy all these things we know we know humans satisfy like I mean they have a lot of characteristics and we can incorporate that in the physics and I think this really constrains the model space that then people in psychology can go and look into so it just feels like when you're digging a tunnel and psychology would kind of dig in one way and basic mechanics would be digging from the other direction and at some point they will meet in the middle hopefully but I don't think they have met really yet and it will take a while awesome what a fun discussion and it's so cool how this paper it's almost like there was a few stairs we explored some basic ways to frame how nodes on a Bayesian graph insulate other sets of nodes and then how that conditional independence can be finessed for these increasingly developed and elaborated networks that do as we talked about expectations over external states all the way up to variational base and then it's like we at the top or at the middle of that staircase started taking it in a lot of other directions so this was really a fun discussion just in the last few minutes maybe we can any and all of us think like what are we going to continue working on for some of us that's probably a research project others that's I don't know lunch or something else just how are we going to keep on learning about this and start to apply it in our own work or research so I have a really good question Lynn are you working on the next paper where you're going to partition the external database or having started or it's just like looking on a back burner somewhere it's not cooking yet so you can you're more than welcome to go ahead and start plowing it's at the farmers markets the ingredients are still out there and Dave also raised in an email some really interesting questions about other partitionings and basically philosophical threads that might be translated into different possible partitionings within internal states or other ways of partitioning because it was the partitioning of the blanket states from kind of one set of blanketing states into incoming sensory and outgoing active states that allowed for this perception as inference action planning as inference step and it's not that that's the end game of node partitioning so there's so many ways that these partitions can continue Steven yeah I'm going to be I'm trying to see how the two tunnels or whichever way maybe it's a whole load of like insect warrens or whatever it is trying to meet and so psychology and bringing together some of these processes so I'm going to try and bring that together maybe more actually not so much from a clinical perspective but maybe more from a community psychology and psychosocial psychosocial methodologies that might be used so I'm going to be chewing on that as best I can so maybe if I ever stuck it might I might fire you an email if that's okay yeah there's many ways we can continue and also I think all along our trails we dropped a few little notes for some other pieces that could come into play if anyone else wants to raise their jitzy hand we can take a last thought otherwise though just in closing Lance this was awesome and Connor as well for joining the first live stream this was a great development we all learned a ton so I hope those watching live or in replay also got something out of this paper you're always welcome back anytime you want to jump on a guest stream or be a participant just always welcome thank you so much Daniel and thank you everyone for the discussion I really enjoyed it okay see everyone see everyone next time thanks bye great times thanks everyone