 Hello everybody and welcome to the Active Inference Lab. Today it's October 26th, 2021 and we're in ACTIMF Livestream number 31.2. Welcome to the ACTIMF Lab. 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 slide. This is a recorded and an archived Livestream. So please provide us with feedback so that we can improve our work. All backgrounds and perspectives are welcome here and we'll be following good video etiquette for Livestreams. We're here in our second group discussion for 31 towards the end of October, so also happy Halloween. And this is our jumping off point to many ideas. So looking forward to this cool discussion. The goal is going to be to learn and discuss this paper by Patricia Palacios and Matteo Colombo, both of whom are with us today. So thanks so much to the authors for joining and feel free to address what you can while you're here and then just leave whenever works for you. And in this discussion, we can take it many different ways because so many topics came up in the dot zero and dot one, but we have all of the formalisms, some big questions, a lot of topics that we raised in the 31.1 video as well. So we can begin with an introduction and warm up section. We'll have the non authors introduce themselves and then just say hello and then we'll pass to the two authors, both of whom are joining for the first time to a stream. So again, thanks for joining and we look forward to the discussion. So I'm Daniel, I'm a researcher in California and to just add something I'm excited about, Matteo and I were just discussing right before we started some of the sociology meets history and philosophy of science. And oh yeah, who could forget about the actual topics themselves. So there's just some cool intersections that we'll be able to talk about. I'll pass it to Dave. Hi, I'm retired from information technology. I'm in the cool dry mountains of the Northern Philippines and now that I don't have to work for a living, I'm getting really busy on learning cybernetics which is one of the things I did back in college and having a great time is fired up about having a complexity weekend ramp up starting tomorrow. So true. And Stephen. We can't hear you Stephen, but you're unmuted. So maybe your audio selection is odd but let's welcome Stephen back. So figured out and let's go to Patricia first. Welcome and happy to hear your introduction. Hello, well thank you for the discussion for the interest in discussing our paper. So I'm an assistant professor in Salzburg. I'm originally from Chile and I work on the philosophy of physics, philosophy of science. And now I'm working more and more in the philosophy of the complexity science. I have done some work on a corner physics and well I'm interested in general in the statistical mechanical applications to other disciplines. Well, statistical mechanical models in economics, biology and well chemistry although I haven't explored that yet. I'm interested on that. And here with Mateo was my, I did my first exploration in the free energy principle. But just to be clear, I'm very interested in the application of statistical mechanics to other disciplines even if we appear to be critical to that in this paper. Thank you, Mateo. Thank you very much for the kind of mutation and also for the spotlight on our paper, completely undeserved. My name is Mateo Colombo. I'm based in Tilburg in the Netherlands. As my accent might suggest, I'm Italian. I'm originally from Milan. And mostly my work lies in the philosophy of cognitive science. I have a special interest in computational modeling, especially reinforcement learning and Bayesian approaches to brain function. And it's been fun to collaborate with Patricia at this project which combined a bunch of interests that already had and helped me to learn something new. Great. Well, maybe we could just start with some of the context of the paper. Like, how did both of you intersect towards this very interesting view on FEP and ACTIV? So were you studying ACTIV inference and then wanted to integrate it with statistical physics or vice versa? I think we heard some of the seeds of that, but it'd be good to clarify. Patricia, shall I go? Yeah, if you want. Yes. Okay, so I think Patricia and I started to chat about these two or three years ago at a conference problem. So my background is in cognitive neuroscience and philosophy, mainly. So I've mastered Simbot and during my work at Edinburgh, as a PhD student, there was actually a co-supervisor by a person, Peggy Serrier, who is an expert in psychophysics. And then she moved slowly to apply tools from Bayesian modeling, reinforcement learning modeling, to psychiatry. And so my other supervisor was Andy Clark. And so it was a good environment for me to learn about ACTIV inference. I think those were the early days of this approach and started to ask questions basically about the approach in terms of actual applications, very limited experience. I suppose that the only serious modeling experience that was during my PhD where with another collaborator, we started to model things in a broad Bayesian framework. This paper came into be, I think, mainly because of my own interest in Bayesian modeling and Patricia's own interest, which she just mentioned, in statistical physics approaches to economics and to other sciences. And so we started to ask, hey, in terms of scientific representation, that's the focus of our paper. Our focus is not so much as also written in the paper on the metaphysics of ACTIV inference, but more about giving this language, this formalism, this scientific representation, and let's ask what kinds of opportunities and challenges this formalism presents when it comes to applying it outside its, say, original field, as in statistical physics. And so we started to chat and we had a back and forth for a while, and then we started to put into focus various opportunities and challenges in applying, say, concepts from thermodynamics and statistical physics to make sense and understand organisms and life science phenomena. And what we found very interesting is this kind of trade-off between the generality of it, that it seems that the machinery of the free energy principle or ACTIV inference, we might have a discussion about the difference between the two. How this machinery allows you to cover at least a model, many types of systems, at least allegedly, but with a sacrifice in our plausibility, what we call realism in the paper. And by itself, this trade-off, we don't think there is anything wrong with going for maximal generality in an approach that might cover, or at least, allegedly, from cells up to cultural phenomena. And that's our paper in a nutshell, that is how these trade-offs might depend on a choice of language or formalism to make sense of allegedly anything. And again, the thing good is one of the key terms, I think, that Maxwell and before him, the car freestone put on the map here. And I think it's a helpful way also to look at our contribution. Again, in a nutshell, I think the framework of thing good might miss out the most interesting properties of the kind of thing, if there are things, say, organisms happen to be. Thanks for that, Patricia. Anything to add? So just to repeat what Matteo said. So my interest in the free energy principle came from my interest in the application of statistical mechanics to all the disciplines. So that's why we start discussing this. And that's why I got so excited about this research. And I agree with the summary of the paper that Matteo just did. This thread of grounding in fundamental physics ideas and then trade-offs or opportunities and challenges really became clear. So maybe one general opening question. What does it mean for a non-statistical physics idea to be grounded in statistical physics? Like, we're intrinsically talking about some interdisciplinary or transdisciplinary or applied scenario. So we're leaving that thing, that field of statistical physics. What baggage, good and bad, do we take with us? And then is it an advantage? Is it a weakness? What does it actually mean for a non-physics area to be grounded in physics? Yeah, thank you for that question. That's one of the questions I have motivated my research in the last years. I don't think there is a unique answer to that. So the more I do research on the applications of statistical mechanics to other disciplines, the more I understand that it varies. So it depends on how it is used, how statistical mechanics is used. And it depends also on the case studies and disciplines and the specific models. So I think that's why it's worth to look at specific case studies, the specific applications of statistical mechanics to the disciplines in order to answer that question, like on a case-by-case basis. I think in some cases, the application of statistical mechanics is well justified, especially when the idealizations are well justified. In some other cases, as I would say, tend to think that it's the case of the free energy principle, the application of statistical mechanics lack justification. So we are not saying or we are not concluding in the paper that that cannot be done or that it doesn't make sense to propose a principle that is based on statistical mechanics, but we just think that there is much more work to be done in the justification, especially of the idealizations that are involved when we use statistical mechanics to formulate a principle like the free energy principle. Classic philosophy, where do we err or miss when we idealize, make ideas of or generalize specific systems or things? And what is the thing concept or the system concept in either Patricia or Matteo in either of your areas? If you mentioned a thing or a system, what would that mean to the disciplines that you're working with, and then how is it being used differently in FEP and ACTIM? And then I see Steve. Matteo, do you want to answer this? Sure. I mean, in a sense, your question is about metaphysics and the question is what's the thing and in what way we can make sense of a thing good with a formalism like the formalism of Marco Blanquets, for instance, or the formalism of statistical mechanics. Just to turn the points like in a different direction, if I may, I suppose the question about thing good and the rule of idealizations on which Patricia just commented on is not just boiling down to the conclusion that, ah, that's difficult, let's move on to apply these tools to a certain system. The challenge we put on the table here is concerning the generality of it, the generality of the ACTIM inference approach. You know, there is excellent work by Philipp Schwantenberg and others using ACTIM inference models in Marco's decision processes with humans, you know, fitting decisions in reinforcement learning or decision tasks with ACTIM inference models. And again, this is just one example of a productive use of the ACTIM inference approach which, you know, resonates with regular approaches like phase-end modeling or reinforcement learning modeling. What we're taking issue with is, look, you're making claims about a maximal scope, okay, maximal scope kind of application of these approach. And to sensibly apply, you know, models at any scale, you know, any scale even outside the life sciences, you know, having to do with economies or thing good, certain assumptions must be in place. And these assumptions, you know, we provide a number of examples which all involve the availability of large data sets that can constrain, say, the application of the model and also background knowledge about the target, the target system and the thing you want to understand. And especially, you know, bridges, conceptual bridges between parameters within your model and features of the actual systems you want to represent. So these are the three, I think, challenges that we put on the map for, again, the large scope or very general scope understanding of active inference or the free energy principle. So these are a bit of a topic. So I didn't really answer your question about thing, but at least these are motivations we had to write this paper, as in making claims about maximal scope come with commitments. And these commitments, at least in the case of many or most biological systems, do not look satisfied or plausible. Thank you. In a way it does, wait, maybe mute a little bit, Matteo, but in a way it does address this question about our models as things and their relationship to other things, perhaps the target of modeling. So Patricia, if you want to add anything, otherwise we can go to Stephen. Just to stress some of the things that Matteo said, because I hear the session offline, I hear the session of last week. And I saw that Maxwell was concerned or pointing out that we didn't take the cases that the applications of the free energy principle to some systems in biology seriously. But the thing is that our claim, we did take them seriously and we mentioned them in the paper, but that doesn't contradict our claim because our claim wasn't that the statistical mechanics cannot or the language of dynamical systems cannot be used to model biological systems. Our claim was about the generality of this principle. So basically we were concerned or where we were casting doubt on the possibility of formulating a general principle like the free energy principle that presupposes that all relevant biological systems can be modeled as random dynamical systems. So just to emphasize that our claim was or our concerns with the free energy principle had to do with generality of this principle and not with the possibility of modeling some biological systems in that way using the language of random dynamical systems. Thank you. So Steven and then anyone in the live chat or anyone with a raised hand here. Yeah, thanks. This is very interesting. Hopefully you can hear me okay. Yes. I'm curious. I know that in the reference you make to the paper that is life as we know it. So there there's that question about suggesting that life or biological self-organization is an inevitable and emergent property of any got it random dynamical system that possesses a Markov blanket. And I know that in some ways I sense that what they've done to try and deflate that claim from 2013 is maybe to go down the mathematical route. And I sense that you're saying the need to maybe also go down the physics route. Would that be something that you would say like in terms of how that statement which has to some extent been couched over the last few years, are you saying that the physics aspects haven't been addressed as much as the statistical aspects? I can say a couple of things and then I leave it to you, Patricia. Yes. Very quickly. So one line of criticism about our paper is that the active inference approach has been evolving over time. And so we're making claims about their Godicity and that which are just obsolete now because from the Costa et al paper, that assumption seems to be dropped and replaced with the assumption of stationarity. But then the question, actually two questions. One question is why should we believe that any life science phenomenon, any organism is stationary? What is the justification for that assumption? And the second observation before I leave it to Patricia is that even within that paper, the Costa et al paper, which is theoretically very rich, they frame the contribution to biology in terms of a metaphor explicitly early on. They're saying, look, what we're saying here is just a metaphorical representation. And so in a sense, that's what we're being arguing for. That is sure you can gain this maximal generality but at the cost of making assumptions by the ergodicity or stationarity now, which might or might not apply to biological systems. Thank you, Patricia. Yeah, so to answer Stephen's concern, I would say yes. So one of the things that we wanted to point out is that we need to focus on the physical foundations of the free energy principle a little bit more than only the statistical foundations of the free energy principle. So we believe we don't claim to be the only one that focus on that, but we believe that there's lack of literature in that sense. And we wanted to contribute to that, to fill that gap, what we call fill that gap. So that's the short answer. Then about, again, the discussion that you had last week, you saw Maxwell, I think as well, was complaining that we focus too much on the older formulations of the free energy principle instead of the new formulations. And he basically said that ergodicity doesn't play any role, it's not even mentioned in the new formulations of the free energy principle. I don't have a biological background or a background in neuroscience and I haven't worked for a long time in the free energy principle, but I do have a background in physics. And I am a little bit puzzled with the idea that ergodicity doesn't play any role in the new formulations of the free energy principle, especially because they explicitly allude to the existence of weekly mixing, random dynamical systems. And to my knowledge, mixing systems require ergodicity, so imply ergodicity. So I'm really not sure, and I haven't seen explicitly how can you drop the assumption of ergodicity in the free energy principle. So I think that if some authors working on the free energy principle could clarify to what extent or why you don't need ergodicity anymore, I think that would be helpful. So we would be grateful for that. We wouldn't consider that as a failure in our project. So we would consider it as a success. So if our paper leads to more clarity in the free energy literature, that would be a success of our paper for us. And I think the fact that Bill et al, also some paper that was quoted in this discussion last week, also allude to the older formulations of the free energy principle, just shows maybe a confusion in the literature between older formulations and new formulations. So I think again, it would be very helpful for people interested in this at least to have more clarity about what has changed in this new framework, in this new formulations of the free energy principle and to have a more consistent framework that one can work with because we were interested in working with the legitimate framework. We weren't against the free energy principle and then tried to look for the weakest argument to attack them. So that was never our strategy. I don't have anything, I am not married against the free energy principle. I don't have anything a priori against freestyle. So the same with Mateo. So we are just generally interested in this application because it can be actually potentially useful or because it has been so, it has called so much attention in biology. So that's why we are interested in this in the first place, not with the idea of attacking the free energy principle. So again, if we could have better understanding of why the new formulations don't require bodicity or about what are the key assumptions in the new formulations of the free energy principle, I think that would save us time. We would be happy to look at that. So I think again, I agree that we focus mostly on the older versions of the free energy principle, but I think it was partially because the papers were clear and not because we wanted to attack the weaker papers. And the same, like the fact that they appeal against the existence of weekly mixing random dynamical systems suggested for me that they still are using a bodicity. And apart from that, a bodicity was not the only argument that we were presenting in the paper. So we also mentioned phase basis and attractors and the new formulations still require phase basis because they need some probability. And they also consider or model homoesthetics or non-equilibrium steady states in terms of attractors. And that again falls into our criticism because we were pointing out independently of the ergodicity assumption. We were pointing out that it's very hard to model in more systems, biological system, even physical system perhaps, station and non-equilibrium stationary states in terms of attractors because attractors imply some asymptotic results and it's not easy to get these asymptotic results. So basically that was our criticism. So we were by no means only focusing on ergodicity. Even if ergodicity doesn't play any role in ergodic formulations, in new formulations which is not clear to me. But even so, I would say the other points still remain and we would like to have a clear answer to that. Even if that means that we have to, I don't know, say that we were wrong in the end, but I insist. So if our paper leads to more clarity in the literature that would be fine, we will consider it a success. Thanks for that and welcome, Blue. So I'll just give one comment and then Steven. So absolutely about the evolution and changes. It's a non-stationary or maybe there's a higher level of a stationarity to the literature but it's one reason why Blue and I and maybe you, if anyone listening wants to contribute seriously to this, are very interested in tracking the nomenclature and which letters are used to refer to internal and external states and which assumptions are implicit or explicit. How does that play out with the evolution of literature in this area? So that's like something that will hopefully we'll be able to point to, maybe it's gonna be version 1.4 in this paper or version 1.4, the English gambit. We can name them like chess openings. Okay, Steven? Yeah, I think you make a good point. I mean, I think also I do agree in the D'Costa paper, stationarity is really given as another way in to some sort of state that gets revisited. It doesn't necessarily take out a good attitude. Maybe add to another potential. So there's this question doesn't, it can't just be answered from a math perspective. I think it's, there's this physics reality and maybe this is where non-equilibrium chemistry starts to come in, although it's a new field. And I think that your points are useful in clarifying some of those questions. I suppose the question that also comes up which is maybe less common in physics is how much can approximation science, how much can a kind of noisy version of ergodicity be enough? And at what point, how many beers is it before I fall over? You know, at what point does the active inferences process come down? And I don't actually think that's necessarily been brought in, but I don't know if physics knows quite how to handle that question. Yes, how stringently do specific realizations or models, especially if they're being evaluated on utility, how stringently must they fulfill some of the underlying frameworks? Like we talked about how the t-test is built around equal variances unless you're using an unequal variance version. And of course those will never be precisely realized, but then how close to being precisely realized must or should things be? Mateo or Patricia, any thoughts? Otherwise the comment that came to mind was, Patricia you mentioned, and it was in your 2018 paper, I think that we looked at in the dot zero about how there's the asymptotic characteristics and the convergence time. So that was very interesting just that there was a, there was, it's sort of this attractor, but there was more to the attractor than just where it was. So maybe unpack that, and then how did you see that grafting into or relating to the comments on FEP and ACTIMF? Yeah. That's my machine address. Sorry I have to leave now. Thank you Mateo. You know, it's been fun. I'm very sorry, you know, it lasted only 30 minutes because I saw some blue joined and I had answers to a couple of their questions in previous sessions about dynamic equilibrium and why we use internal states as active states. Well, we can do 31.3 literally any time. We can do it in a year. So that's why we do decimal notation any time it's right. Just let us know and you're always welcome back for a guest stream presenting on current work. So good luck with your teaching responsibilities in CSUN. Two generous though. Ciao ciao everybody and thanks for paying attention. Cheers. Ciao Patricia. Ciao, ciao Mateo. Okay. Yeah. So yeah, you were measuring my 2018, thank you. Yeah, so I think the question of asymptotics is related to a question of approximation science and I am interested in both questions. And this is basically what I have done independently of the free energy principle in my research in the last years. So basically what I pointed out about asymptotics in the paper that you were mentioning is that in order to make a model realistic, a model that takes asymptotic in order to make that model realistic, we not only have to pay attention to the solutions that you get in the limit when you take a limit, you also have to pay attention to how fast that limit converges. And that time that can be considered relaxation time or that time that the limits needs in order to, or that we need in order to achieve that limit. Needs to be realistic too. So you don't only have to pay attention to the values that you obtain when you take a limit, you also have to pay attention to the rate in which you approach that limit. So that will also help you to understand how realistic is the model that you are using. How would that tie to approximation science? It depends again, some models, like on the models that you are analyzing in the science that you are looking at. So if you are investigating models that use limits then there is a very clear understanding of approximation because limits give you sort of a neat understanding of the approximations that you are using. But approximations are not always in the form of limits. Sometimes approximations can be in the form of similarity and then saying to what extent that model is realistic can be a little bit more obscure. So when your model implies limits then you might have a clear way of understanding to what extent your model is close to the target that you are trying to model. Very interesting. So one thought that's come up in a few different context is it's almost like a vitalism 1.0 and a vitalism 2.0. And the 1.0 was like, is there the Elan Vital? Is there something more to it than chemistry in biology? And the synthesis X vitro, or X vivo should I say of vitamin C for some reasons point to as an example of like demonstrating that biological molecules could arise through chemical synthesis and therefore maybe more than just vitamin C but maybe DNA could also be made in the test tube. And now we're in an area where we're asking, okay, given that grounding of biology in physics and chemistry 1.0, how do we go from that sort of equilibrium into homeostasis and allostasis and more advanced forms of predictive higher level behavior from systems that are also composed of less strategic components. So there's going to be just like there were challenges going from the physics of a membrane into understanding how biological systems deploy membranes. Now we're moving up a level into the cybernetic or into the anticipatory space and asking how those very same biological systems which we've deflated away to be chemical and physical, now will there be another level of deflation or is this a bubble that's a little harder to pop? So Stephen and then Patricia or anyone else with thoughts? Yeah, this is a good point about it being a bit harder to pop because there's a lot of, once you get into the chemistry, there's a lot of hidden states, let's put it like that. There's that assumption that you pass through often maybe a transition state when you go from reactants to products but it's going from equilibrium to equilibrium, even the transition state is looked at in terms of its energy accessibility but that's again a kind of a stable state. So this question about something circling around non-equilibrium or far from equilibrium mixing states which is why I think you can't, I think like you say, ergodicity can't be or something along those lines can't be ignored. Certainly once you get into anything which is more in the liquid contexts. So the question comes up then is when you've got these attractors or these far from equilibrium states which are not necessarily energetically favored alone they may be somehow entropically favored or somehow complexity favored through these attractors. Anyways, that's something around how catalysts are working in the more sort of, if you were to go in at a more detailed level of modeling. So I wonder how your thoughts are around the sort of catalysis processes that might be happening in biological systems and how do these far from equilibrium states facilitate these abilities to minimize free energy. If you have any thoughts on that Patricia, otherwise blue, do you wanna? No, I would leave that to blue who has to work more on the free energy principle. I don't know, I think the assumption that I've worked more on the free energy principle is maybe kind of, I don't know. Not right, I don't really have an answer. Don't let the cat ears deceive you. But cool questions, there's many other avenues we can go but Patricia what is your current research or what do you see following your work now that it came out like where do you go from that state update to your next questions if they're related or not, it's all good. Yeah, actually I'm thinking about applying for a project which it doesn't have to do with free energy principle but it does have to do with applications of statistical mechanics to biology. So I have been working for a few years, I will probably, so I just finish a book on emergence and reduction in physics. So I have been working on a concept of emergence and reduction for physical systems especially thinking about critical phenomena. What I want to do now is to see whether that notion of emergence and reduction that I suggest also works for biological systems but I will focus on biological systems that can be modeled as critical phenomena which means can be modeled using the physics of phase transitions. So this is what I have in mind now. And I intuitively think, so my binary hypothesis is that the same concept doesn't work for biological systems and that one needs to distinguish between them but I think it would be useful to look at specifically at systems that can be modeled as critical phenomena to see the disanalogy maybe between biological systems and physical systems. So that's maybe the reason why I will focus especially on those systems that can be according to to many phases we model and biologists we model as critical phenomena. Interesting. In fact, criticality is perhaps again, the language analysis will reveal in the future but it's not a term that gets brought up in the active and FEP area that much. It's more apt to describe assist although in Friston's work on neural systems there actually is a lot of it. And so there's actually so much in the SPM and dynamical modeling literature that has not made it quite over the hill but I think that there's more to be said we'll look forward to that book, Stephen. Yeah, just that's an interesting point they're making, can I just ask? So is it almost like you think there's a lot of computational processes that can happen purely through phase transitions and statistical processes which is not quite the same as an inference process but is it maybe more like the sort of thing you see when molds find their way to food and things like that. So you're sort of saying there's a kind of a physics explanation for some things which doesn't require an inference process and that could do a lot of the heavy lifting. Yeah, so I will focus on models that use the mathematics of phase transitions with variations or you never use exactly the same mathematics you have to make change depending on the case study that you're investigating but I will focus on models that use the mathematics of phase transitions to understand biological phenomena. An example would be forking behavior, for example. But there are plenty of models that use the IC model or something like the IC model to understand forking behavior which is that behavior of birds that seem to be emerging with respect to the behavior of individual birds. And in other case studies like melding, protein melding that can be modeled as a phase transition. So I'm going to analyze plenty of case studies of research that have been done already in physics or in biology and the idea would be to understand what kind of notion of emergence do you find in biological systems? And the question is whether that is similar to the notion of emergence that appears in physical systems and as I said, I intuitively think that it's not the same but since I will look at similar case studies I think that can show the difference between biological systems and physical systems quite clearly. Cool, Stephen. I'll add one thing to that. Yes, I see the answer. Before I go, I know Piliu's going to say that. I just want to, just one thing that's curious then is it like, because there's this interesting when I'm talking to people who've got maybe more of a chemistry background, emergence is more the emergence of interactions between things, right? And molecules and stuff. And then you get these kind of, and then you've got this more process-based kind of inference, dynamical one. So are you sort of seeing the way of emergence being able to do quite a lot from the kind of perspective of things interacting with each other based on rules rather than a non-linear dynamical approach? Both, actually. So you find both in phase transitions. That's why phase transitions in physics have been considered as the prototype example of emergent behavior. Because you find non-linearity, you find long-range correlations. Well, the interactions in most systems are local, but you still have these long-range correlations that require using some fun elements like the renormalization group methods, for example. So you have some notion of collectivity there in phase transitions in physics, not because of long-range interactions, but because of long-range correlations. So it appears as if the interaction between distant particles would be long-range. It is not, but it appears like that because you have long-range correlations. So I will look at similar cases in biology that have been modeled already using physics. And then I will try to answer with that notion of emergence in terms of non-linearity and so on. What I suggest it's emergence, emergent behavior in physics can also be applied to biology. And I think, well, but this is preliminary. So these are not the results of my research because I will be doing that for the next years. But preliminary thought is you will see a difference, especially with top-down causation that might happen in biology. That doesn't happen in physics. But this is just preliminary. So I will try not to say too much about this because I haven't done the, I just have done the research for the project, but I haven't done the project. So you can wait for this result. Thank you. Lou. So that's super interesting. And again, something that I'm very interested in is this idea of emergence. And when you're studying phase transitions or criticality in physics, like for example, just from a liquid to a gas, it's easy to see on a graph this kind of inflection point of temperature where the phase transition occurs. And I just am wondering what kind of metrics you're using to quantify emergence in your future research in biological systems. That depends again. Sorry that many, many times my answer is the same, that depends on the, I'm not using a specific metric because I'm not proposing a general framework. I'm just studying like different case studies. And depending on the case study on the kind of phase transition that I'm studying is the metric that is attached to it. But I'm not suggesting a general format framework that has a metric in itself. So I'm studying like case by case. So can you maybe provide some examples or you don't want to say yet too much? In biology? Uh-huh. Yeah, the forking behavior. So there are different models that I can, you can send me an email if you want and I can address you to some, to say to you but there are plenty of models of forking behavior. Right, but also- That use models that are already, so that sort of migrate models from physics. So there's some of them use a slightly revised version of the icing model. It makes me think about how the sort of initial target system, let's just say a solid to a liquid phase transition. And then there also are potentially critical dynamics related to information and decision making which comes into play in active inference where you could have a non-linear relationship between information coming in and then it's in policy mode A and then there's a phase transition to policy B. And so it's kind of like, again, that vitalism 1.0, 2.0, there's gonna be a lower bar, a phase transition to talk about, well, the protein folding in the cell, it's gonna be a special surrounding that facilitates it to do special kind of transitions physically, but then how do we think about higher order behavioral properties, especially when they exhibit some tantalizing similarity or analogy or metaphor, like we've been discussing, but can we just take those same models and think that it's gonna be as clean all the way up, blue, and then, Steve. So in the flocking model, for example, like when you're talking about downward causation and something as something that you wish to study, and so I'm sure that you've maybe read the information theory of individuality paper by David Krakauer and the group at the Santa Fe Institute. So there's a point in which this group of birds that's flying around kind of chaotically assembles and forms like a flock and flies together in like a kind of patterned way. And so I'm interested in terms of criticality at what point does downward causation occur, right? And is that the point that then it stops being, like the ensemble becomes a group, a unit that's functional? Like, you know, because there's, like that's a good kind of way to look at emergence, but how do you find that point in which there's the bi-directional information flow? So that's maybe a better way to raise my question. Yeah, so as I, this great to discuss this with you, but as I said, I haven't done the whole research, I am happy to discuss my intuitions here with all of you. But that's it. So one of the hypotheses that I have is that you might find something like downward causation in biological systems. I'm not sure of flocking behavior would be the place to find downward causation, but I'm thinking about downward causation in terms of selection. And it might be that you need some high order properties. So that, sorry, that high order properties explain some fitness. And that in that way, that calls somehow all the way down that at the micro scale, at the micro level, you observe some behavior as a result of that fitness that is sort of coarse grain or higher. So I'm thinking about that work causation in those terms, but you might find other notions of downward causation there and I might found them in doing the research. Now in the flocking behavior, I'm not sure, but you might think that the ability of many birds to go in a particular, to do a particular pattern has some fitness associated to it. And if so, that fitness, which is fitness of a group might explain the individual behavior. So if that's correct, then you might have a notion of downward causation that you don't find necessarily in physics, but these are preliminary intuitions. Thank you, Blu. So like going towards like along those lines and going back maybe to the attractor. So when there is like the emergence of a group, does that like reign all of the individuals in the group like closer to a new attractor state or closer together like tighter, like a tighter cluster around an attractor state or is it like the new attractor state is an emergent property of the group or how do those two fit together? Like in terms of fitness and in biological fitness, you have to be able to maintain this kind of non-equilibrium study state density. So in terms of fitness of a group or a cluster in biological systems, is that like a new attractor or is there, yeah, or just what are your intuitions maybe about that? Yeah, so I wouldn't try to describe the notion of emergence here in terms of attractors, but it might be useful in the end, but I would like to have a notion of emergence that doesn't rely necessarily on attractors because I think that finding attractors is a hard task in biology and some of these models don't work with attractors anyway. So I don't think the notion of emergence needs to be associated necessarily to attractors. Maybe in some case it would be useful to understand emergence in that sense, but I wouldn't think that it's necessary to understand emergence in terms of attractor. And I agree with you, but the coupling of emergence maybe to fitness, to me like I link fitness to an attractor. And so it's hard for me to separate them if fitness is linked to attractor, but fitness is not linked to, or is also linked to emergence, then that draws a line for me between emergence and attractor, if that makes sense. Yes, so that's why I will work with biologists in this project. I'm not a biologist myself, but I think that fitness can be defined also independent on the notion of attractors and I will try to take those notions. I will try to adapt those definitions. So Dave, Jessica's, Yavin asked a question then, Steven. Yeah, one of the reasons that looking for attract, spending too much time looking for attractors associated with emergence is among the things that happens when you get emergent behavior, is there's a more differentiated set of interfaces with the outer world and because of that, there's less duplication and less resemblance among the subsystems already within the overall system. Cool, thank you, Steven. Yeah, that's a good point around the challenge of identifying attractor, especially if you've got this multi-scale nested. I mean, say you've got attractors that are only present for nanoseconds, even if they're there and there's millions and billions of them and then on top of that, so I can imagine that it could be really useful. And I'm curious how you see the freezing of ice and the way that the water becomes more dense and actually about two degrees and starts to get less dense and as it approaches freezing and then you sort of hit this phase transition. And I think there's a real use in that also being learned about for active inference because although in active inference, it doesn't happen directly. In the field of anything to do with entropy, there's this common misconception of neg entropy as if you actually get a negative form of entropy, which is kind of in the kind of common usage, but there's no such thing directly as a neg entropy. There's a neg, there's a change in entropy. There can be a variation in entropy, but it's not a stable state in the same way that you get with energy. But that, I think that can be a misconception that sort of creeps in quite a lot. But I'd be curious if A, effectively, there's a value of entropy that goes down, a spooky value of entropy of which no one quite knows what's going on with the entropy. We know there's a value for entropy that entropy goes changes from ice to water. But even Richard Feynman used to say, well, no one quite knows what's going on there. And maybe this is something that you're trying to sort of get into is what's going on in those phase transitions and these entropic changes, which doesn't have the benefit, like you say, of some agent or driver of the free energy principle to make it happen. So I don't know what your thoughts are, but how that might, even how that might be useful to help people who aren't as heavily into physics, just think about the idea of change and entropy. Because I think it's gonna become something that more and more people are using outside of physics. If you have any thoughts, otherwise just the maximum density is four C for water. And it's super, super slight, but a very interesting pattern. Okay, we can turn to, well, if anyone wants to raise their hand or give a thought. Stephen, you said like that the neg entropy as it might not exist. That was one thing. And there's no such thing as neg entropy. Yeah, I also wanted to, sorry about that. Yeah, I also wanted to stress that in equilibrium phase transitions in physics, you don't use the notion of negative entropy. Of course you just use entropy and standard statistical mechanics plus renormalization group methods. So that might be an asymmetry with some of the case studies that I analyze in biology, but yeah, we'll see. And one of the fundamental trade-offs discussed in the paper was this generality versus the plausibility and the realism do attractors even exist? Or is it just as if a system is moving towards something but does something that is not realized exist? And so this kind of takes us into talking about whether we're describing the system as it is or rather situating the system in a broader space of how it could exist. And that was one of the fundamental points of the paper about the challenges of discovering the appropriate phase space for a biological system. So it's just cool because these are not knockdown punches for FEP and ACTIMF nor are they trivial. They're in that optimally informative or a confusing space between zero and one probability where it does matter and where philosophy comes into play and where the specifics of the situation come into play we can't just simply make arguments without reference to a specific model but then are we trapped to just describing specific models specific papers or are we able to go beyond that ever? I'm just looking through, if anyone wants to raise their hand or any? Yeah, about that, sorry. So we do rise a concern about the existence of attractors. Of course, attractors don't exist in nature because you need taking infinite limits in order to define attractors in a model and you cannot, so infinites are not realistic so we cannot take systems don't take an infinite amount or processes don't take an infinite amount of time and you cannot repeat an iteration in random normalization group transformation infinitely many times in a realistic way. Of course these are all idealizations but in principle I wanted to stress that we don't have a problem with that. So of course any model that uses attractors wouldn't be realistic in a way so you will be using an idealization, that's true but we don't have a problem with that if the idealization can't be justified. I think in many cases, especially for example in the treatment of phase transitions in physics where you use limits, there's a way of justifying those limits and justifying the existence of attractors and therefore even if you miss some realism in the model of your physical system since that idealization is justified that is plausible that model is plausible and it's legitimate. What we are worried about in the paper is that it might happen that sometimes the models that will try to model many systems in terms of attractors are not realistic they cannot justify the idealizations that have been made in order to model many plenty of systems in terms of attractors. So I just wanted to clarify that because we don't disagree in principle with the idea of using models that appeal to attractors even if attractors don't exist in reality our problem is with the possibility of finding attractors in the first place or finding asymptotic solutions and the second is about the possibility of justifying the idealizations that are involved when you use attractors or when you appeal to attractors. Yes and like many other arguments in biology it's a little bit like the anthropic principle or fallacy depending on which side you're on. It's like you mentioned in the paper you have to prove the existence of the attractor as well as as we discussed the time to conversions and then justify why certain attractors denote homeostatic states and one biologists answer is just those are the living systems. If the attractor weren't a homeostatic state or a high fitness state that is not going to be an aunt you see around for long and so we can just say that if there is an attractor and indeed it's as if there's an attractor for persistent systems that's the adaptive one period and the second that it's not that way the system fails to exist. So that's the sort of circular but often impenetrable tautology of selection and persistence of systems blue. So that's a nice transition perhaps into the question that I've had about dynamic equilibrium versus a non-equilibrium steady state density. So I don't know if you want to flip to that side, Daniel but there's several quotes in the paper where I'm not sure exactly what's referred to as a dynamic equilibrium. I'm assuming that it's homeostasis but I just was wondering why because dynamic equilibrium is a reversible chemical reaction and there's nothing about homeostasis that is I mean there may be some things but not everything about maintaining homeostasis is has to do with reversibility. So I just was wondering all biological systems actively maintain a dynamic equilibrium with their environment and what is meant by that? This was a quote from the paper. Oh wait, you're muted, Patricia but if you have any thoughts? Yeah, so sorry, I was missing the screen somehow and it disappeared, everything disappeared. Yeah, so actually unfortunately Matteo wanted to answer that in a neat way. Basically we took this from Freestone himself so he refers in many places and he had the quotations and so on I don't have that at the moment I can try to look at it but you might be right it's not the right way of describing the homeostasis states but I think it's a mistake that Freestone himself does. I think so this is basically what Matteo wanted to say and he had these quotations in the papers where he does that. So if you want to email him he will address you to those works but not so much in our paper it depends on that notion actually so that might be a mistake that we make I think because we took a Freestone but not so much depends on that so basically our criticisms have to do with the idea of modeling all biological states in terms of random dynamical systems in understanding homostatic states in terms of dynamical attractures as they are described in the paper but we don't rely so much on the notion of dynamic equilibrium so that might be just a loose way of understanding homostatic states. So it's referring to homeostasis though not a dynamic property. Okay. Yes, yes, yes, two homostasis, yes, yes. Thank you, Stephen. I mean this could be an interesting area for the ontological work that's happening in the lab because this question of, you know, is it dynamic equilibrium? I think like Blue was saying there can be that kind of backwards and forwards of which there's maybe a bit more of an arrow in one direction. And then you've maybe got the word equilibrium as opposed to non equilibrium. And then you've got this, he has this term dynamic call systems, you know? And as opposed to system dynamics which is the kind of the way that say chemistry like equilibrium work is more system dynamics but dynamical systems. And you've got this interesting thing because you've got this nonlinear dynamical work happening at the sort of the physics level and this emerging property level. And then at some point as it appears from the organism's perspective we might start turning and using the language dynamic equilibrium ecologically, you know, ecological equilibrium. And this shifting the way that the ontologies are present which may be true because as things persist and they're interacted with as entities they appear to be in a different type of dynamic but we are seeing from the active inference so that dynamic may in itself be more dynamical than we perceive. So I don't know, I just thought of mention I don't know if we need an answer to that or maybe Daniel you've got a thought but there's something about this shift between biology and physics at this sort of very molecular stroke, you know, theoretical level and then you've got the idea of what that means for biology and then you've got the idea of what that means for biological organisms. And maybe this is something that we've talked about this pluralistic ontology that needs to be feasible in the field because like I say it depends I think that was a very good point it does depend on where your models are based and grounded. Thanks Matteo has some very interesting work on pluralism in biology and the philosophy of science so I'd recommend people look there. Now, contingent explanations are not necessarily plural one can be an absolutist and say it depends on the particulars and there's only one correct story. So it's an open question to what extent pluralism and particularity will coexist and agreed that at the high level as we mix metaphors, take ideas across different fields we have to be aware of what is gained and lost what are the challenges and opportunities of applying terms from mathematics to physics and from physics to biology and taking us all the way up and down that XKCD comic that we were looking at earlier. One question area Patricia that I had was about action in the loop so maybe there's two parts to it. The first is just we often hear about FEP as being akin to a principle of least action. So just from a physics background what does it mean to be a principle of least action or what would it mean to be like a principle of least action and then how does it change the formalisms or not when we're integrating control of behavior kind of control theory formalisms or cybernetics into ensemble modeling because the actions of molecules are implicit in the phase transition of the ensemble of water but what happens when we actually have a control parameter in our equations like policy? Okay, thank you. So first of all, I did find the papers where Friston uses the notion of dynamic equilibrium so for blue and he uses a synonym of homostasis but I cannot use the chat, can you? Oh, it's on the left side. The bottom left. It says that enter a nickname to use the chat. You can pick the name if you want. Okay, I thought it was kind of fast one. Okay. Call me trim tab. Okay, it was so, I thought it was sort of a password so you wanted to allow everyone to write in the chat. It doesn't require a childhood name but it helps. So these are the papers. Okay, good. These are the papers blue so you can take a look at this. So, but as I said, not so much in our paper depends on that notion of dynamic equilibrium so you might disagree with lack of record there. But yeah, don't blame us for that, we just... Okay, nice. That was interestingly not in a peer review paper. Not that it explains everything but he may be speaking a little bit informally in this Aeon piece. Exactly, I think it's just a more loose way of talking about it and we also use it because it's useful then when you speak about dynamical attractors so if you have a notion of dynamic equilibrium it's just useful but of course we weren't thinking about the proper definition of dynamical equilibrium. No, so good, no. Just return to the action question, yeah. Oh, sorry, go ahead. Okay, so yeah, again, so we are here, sorry that I excused myself of summarizing the work that Friston did but here we are just summarizing so we don't give a proper definition of principle of least action, we're just relying on Friston's own definition and he basically in that paper of 2012 he needs the principle of least action in order to formulate the free energy principle. So the principle of least action is a step, an intermediate step to formulate the free energy principle, nothing more. Then I would be more careful in talking about principles of least action in phase transitions in physics, I think you might not even require any principle of least action there or you might talk about those ground states as sort of relying on a principle of less action but I would be more careful about exporting that notion to the physics of phase transition. Okay. Was that a capo? Yes, so that's the first part about the principle of least action and then just is there something that is changed markedly when we introduced these control theoretic formalisms like policy selection into physical, physically inspired or based models that entail activity like the thermal motion of particles but are not approached from a control theoretic or behavioral regulatory perspective. Are you thinking about social systems, for example? Perhaps different kinds of systems but mainly just a particular system in the way that free energy principle for a particular physics, Friston's 2019 work, like the particle is the blanket and the internal states that's engaging in active inference, let's say. And so it is implementing inference on policy, it's selecting policy, it's behaving. And so is that sort of policy selection latent within non-control theoretic activity based physics models? Again, like the thermal motion of molecules or when we introduce policy inference, does that change some of the qualities of the system? I think, so it's an interesting question. I would need to think about that a little bit more carefully but my intuition is that it does, it changes the way as you understand phase transitions in physics. I think that requires changing formalism and again, it requires important, well, make an important difference in your model with respect to how you model phase transitions in physics. Thanks. I agree, something changes and it's not for a linear time discussion necessarily to unpack but these are the kinds of questions that we're getting at, absolutely. So, Blue? Yes, yes, I think that. So, I just want to reference the articles that you posted in the chat. So the AM thing, they did say dynamic equilibrium but I don't trust op-ed science writers to make direct correct quotations. And in the Ramstead paper that was cited in your paper, the Markov Blankets of Life, it specifies that dynamic equilibrium specifically is not the state of homeostasis. It says the very existence of living systems can therefore be construed as a process of boundary conservation where the boundary of a system is its Markov blanket. That means that the dependencies induced by the presence of a Markov blanket are what keep the system far removed from thermodynamic equilibrium, not to be confused with dynamic equilibrium. So I mean, specifically, it's not dynamic equilibrium, it's far from thermodynamic equilibrium but still dynamic equilibrium is not a part of that. And so that's why that reference was very confusing to me and like they on paper is like, yeah. Yeah, and then we made the same mistake that he made without correcting me. That's the way that Ramstead made it. It can be. So I agree. We were talking loosely there and what we were having in mind was the notion of dynamical attractors. So that's why we found dynamic equilibrium very like a nice term, but we might be talking loosely there. But as I said, so that might be a mistake but not so much in our paper depends on that notion. Well, so and the notion of attractor in the state of homeostasis is specifically a far from equilibrium removed base that a biological system exists in. And so it's just kind of, yeah, confusing to me, I thought. Interesting, it's a challenge to say enough to identify what we're talking about but especially when we're crossing disciplinary boundaries to know which pieces of baggage make it through one border or another. Like dynamical could merely just mean involving time but it also brings on a lot more meaning in different areas. It's a great. Yeah, so we're talking the paper about the possibility of attractors like that change, well, one attractor following another. So we understood that as a loosely as a notion of dynamic equilibrium but you're right when you're seeing the term very grossly probably here. Let's turn in the sort of home stretch of however long we wanna speak to the short and concise conclusion. So in the last paragraph brought up this really interesting point about the FEP as a definition for a system. And so I wondered what else could it be or might we want a framework to be other than a definition? Like what else in the counterfactuals of the way that this paragraph could have been written what else could the FEP or another framework be other than a definition? Is that synonymous or complementary with a description with what other pieces come into play here? Can you repeat the question? I don't know if I understood it. If the FEP is not a definition, what else could it be? Or other than a definition, what do we want for a full pledged model? A principle, what would make it a principle? I think something that can explain life or can explain yeah, why biological systems apparently violate the second law? Why do they stay in that far from equilibrium steady state? I think many defenders or advocators of the pre-NG principle understand this sort of as a principle that explains, that has explanatory power that explains not only the existence, even the existence of living systems, but especially why those living systems stay far from equilibrium or from Maxwell-Boltzmann equilibrium for a long time in a steady state. Great point. So yeah, that's smart. And explanation, which of course goes beyond or is complementary to definition, explanation is one of the key terms and themes in the history and the philosophy of science. And since an explanation is evaluated subjectively or intersubjectively, like was that an adequate explanation? That's a statement about the relationship between a perceiver and the explanation itself. And so it dumps the entire mess back into the lap of almost a psycho-historical perspective on science because good explanation is about the inculturation of the person evaluating how good that explanation is. So Stephen, and then Blue. Yeah, I was just looking up regarding dynamical and dynamics. So dynamical, the adjective means relating to the study of dynamics. So it says a dynamic system is a system exhibiting continual change. So a dynamic system is continual change. A dynamical system is a system relating to the study of the dynamics. So a dynamical system is like a system working with the dynamics of a system. And dynamic itself just talks about the actual fact that there's change happening. So that's kind of interesting. And it'd be interesting as well whether you get dynamical things or there has to be systems. You know, like, is there a, you know, that maybe where there's some sort of interesting play between phase transitions as well. Like maybe there's some, there's a dynamic going on. There's a dynamic that is set in order to the first dynamic in some way. So that's kind of interesting. Yes, things and processes and static versus dynamic and then loose, but acceptable in many cases, use of language. And again, the text modeling will be superlative when we can establish where these adjectives and nouns and verbs are being used appropriately versus inappropriately or at the very least suggesting more precision or less precision than warranted. So blue. Oh, and Dave has a great comment there. Historical, examined by historians using founded methods versus historic, which is like about the event itself like it was a historic victory or something like that. So it's interesting how we give the disciplinary nod with that AL on the adjective. I was just thinking about the difference like linguistically between historic and hysteric. Like what might that be? So my question unrelated to historic and hysterics really goes back to, you know, what Patricia was saying about the second law and touches back to what Stephen was saying earlier about the non-existence of negative entropy. And I'm curious about that because I think, a lot of the FEP is grounded in information dynamics which depend greatly on the existence of negative entropy like the minimization of surprise in the terms of information theory. So I was wondering if physics and information theory are different? Are they one and the same? What are the differences? How do we clarify them? And similarly, you know, one of the claims in the paper is to pay attention to the differences between physics and biology. And what, you know, I've always thought that the laws of physics are universally applicable and perhaps they're not, but I think that they should be and, you know, that this defiance of the second law like are the laws of physics not apply in biology, in biological systems? And is it negative entropy that biological systems do? I mean, Scott David always classically refers to the entropy secretion of, you know, biological systems. And so I just was wondering, how do we reconcile these differences maybe? Do you guys have thoughts? Yeah, great question. Stephen, you wanna go on that topic or? Yeah, I think there's a really good, I think this is important because you see, neg entropy kind of is a bit like negative enthalpy in the way it's formulated. I, but the thing is you have a reduction only relative to a starting state, a starting equilibrium state in terms of entropy. It's might have gone down in terms of a starting state, but it's not actually lower in an, like energy is energy, right? It can't be made, can't be lost, you know, but the entropy, you can have a variation in the entropy and that variation can be noisy going up and down. You can then extract information. You can have things which are more ordered. Now that's fair enough. You can have more order, but neg entropy isn't something which is a value in that way. It's just a convenient piece of temporary mathematics to help see whether you're gonna have a force driving or reducing a reaction, which, so that's where the challenge is because you're getting it from the variations not from something which is an equilibrium state because as soon as you say neg entropy, it makes it sound like it's sitting there with a particular amount of entropy. That makes sense. And it's not really like that. So this is like one of the kind of misunderstandings, I think around entropy. Okay, interesting. One other view, Blue, on your question about information and thermodynamics. We have some very slam dunk info, thermo, synthesis on the processor scale, like the amount of heat that is emitted or absorbed by certain very, very granular atomic in multiple senses, informational transitions. And so it's almost like that's like the stem and we know that there is a connection there, either as if, to be sure, if not in actuality. So map and territory, information and thermodynamics potentially coming together. And part of our curiosity and drive with active inference is whether info dynamics might apply to higher orders of organization and whether we can use some of these models and ideas to describe informational patterns and thermodynamic, eventually even bio energetic patterns and phenomena beyond the CPU. And that's where it's going to be this question of, okay, maybe we generalize and it's useful, but we've lost some reality touch. So the parameter, the temperature parameter on decision-making doesn't refer to the thermometer reading of the brain. I think we're okay with that. So in a way, we are lifting away from the physical grounding because we're using terms like temperature, entropy in their information and not their physical capacity. And as the key questions raised in this paper brought to this discussion, there are opportunities and challenges with making those kinds of generalizations. It's not just a simple win, it's things are gained, things are lost, some things come into resolution, other things become incapable of being resolved. So that's like some of the excellent questions that I think the paper brings to the table and it combines those questions along with just tantalizingly a look at the history and the development of active inference as a framework. And so we can be clear about which papers said what, when and then where are we headed? What would be our preferences for a thermodynamic model of decision-making? Will we only succeed when it's about the temperature of the brain? It might be for some person. However, other people might just say if there's a temperature-like parameter in the sense that that parameter's formalism looks like temperature of water in a test tube, then we have something that's already useful and interesting and that's where the train ends for me and then somebody else may continue to build the rails off towards wondering whether is it metaphysically a temperature of decision-making, all these other areas that people can take it. And so it's this trade-off between realism for generality and utility that we've come to these meta-modeling discussions before in number 14 and beyond. Okay. Anyone wants to ask a question in the chat or raise their hand here. Otherwise, let's see back to our dot one questions and see if there's any threads from dot one that we want to just recap or see if we have a different perspective on and then we can just sort of close the dot two and jump off into the next steps. So in dot one, we started with some questions again from a more history of FEP and ACTIMF about in what ways has physics been used to investigate the FEP? We talked a little bit about how the Dacosta paper that was 26 Bayesian mechanics for stationary processes relates to the ergodicity stationarity discussion or not, we'll see. We talked about then and also a little bit today is the FEP a theory of life? Well, in the conclusion, it was said to be a definition and we talked about some other things it could be, blue. Sorry, I still have to unmute, you'd think. I would learn after all this time. Never learn, don't change. The ergodicity thing, I think maybe you guys discussed that before I got here, but I think like one of the points that was made in this paper, addressing the ergodicity and the fact that biological systems are, I mean, I don't think biological systems can be described as ergodic and this is a discussion that Daniel and I have had many times. I mean, sure, within a very restricted space, like my body temperature, for example, in range from, I mean, what can I survive? Like 105 Fahrenheit probably and maybe 95 Fahrenheit. So I have like this 10 degree range and I'm sure at some point in my lifetime I'll visit all the space within that range because you can't skip over. You don't go from 96 to 100 and skip any of the points in between. So like, it's incrementally like, of course, I'll visit all of that space. And so I do think that that's an important question, but yeah, that was really addressed by Dacosta in that 26 livestream about, you know, homeostasis as a quasi stationary because it's not perfectly stationary, right? It's like a, it's a squishy stationary, but it's not, you know, it doesn't sample the entire, we don't sample the entire state space of say temperature, you know, as a biological system that must maintain a certain temperature. So I think that that was resolved. But did you guys discuss that before I got here? Not the boundedness, per se, but potentially some relevant pieces about arroganticity and stationarity. Yeah, so may I say something? Sorry, I had to turn off the video. I'm with my baby here. Hello, baby. Yeah. Yeah, so we didn't, I agree with you, Blu. I think that's one of the things that we discussed in the paper. So it's very problematic to understand biological systems as a body systems. But in the discussion last week, you were saying or Maxwell was saying that new formulations of the free energy principle don't rely on that assumptions, that they drop that assumption in the new formulations of the free energy principle. And what I was saying before today is that it's still in new formulations of the free energy principle, they rely on the existence of weakly mixing random dynamical systems. And to my understanding, mixing systems require egodicity anyhow. So it's not clear that they have really dropped the assumption in the new formulations. And if so, I would like to see exactly how the framework can work without the assumption of egodicity. I haven't seen that explicitly. I might believe that that can be done, but I would like to see it. And we don't evade requirements just by not mentioning them. So it's about what papers do mention as well as reading between the lines, between the formalisms, between the citations to really what is the bedrock or tautology that the theories rest upon, Stephen. Yeah, I think this also might point to your cybernetics point Daniel, in the sense of where does something happen at this kind of ergodic process of mixing? And where may it happen through a higher level cybernetic mechanism that the organism has that is enabled by sort of ergodic active influence or whatever processes are emerging. The fact that it's emerged from ergodic processes at multiple nested levels doesn't necessarily mean that some of the higher level ways of keeping something within bounds then has to follow that because you can create a system out of all the cells that are doing their thing, so to speak, or being their thing. So this is where it can maybe be that danger that there's an overextension of a certain process. It's like, okay, where does something which is relying on ergodic processes or some other approaches able to give way to another type of control theory? Control theory. Yes, and over short time horizons, is it possible to have sensory motor loops that work whether or not some infinite case is what it rests upon? Blue? So, Patricia, I'm curious to know or to know what you think about if you've read the Dacosta paper about basonary processes for state, Bayesian processes, Bayesian mechanics for stationary processes. There you go. So I'm curious to know if you've read that and what you felt was perhaps lacking from that mathematical description to meet the requirements that you were referring to for mixing systems and ergodicity. Yeah, thank you. I did look at that, but we explicitly wanted to focus on other assumptions not on the Bayesian assumptions of the paper. We didn't also mention the Markov-Blanket assumption, which is a core assumption in the free energy principle. And we left that out deliberately. First of all, because of lack of space, the paper is long enough. Second, because there is much more literature on that than on these other assumptions that we discuss in our paper. So I think in this formulation of, well, I don't have that paper on the top of my head, but I think they again rely on weekly mixing dynamical systems in the paper, right? They don't... We can check. They use that framework. So I think to the extent that they use that framework, if I'm not mistaken, then the same criticism supplied. You need to find space spaces and you need the existence of attractors at least. Cool. I just imagine like these networks of citations like some sort of biological metaphor, some swarm of citations with words being traced between them and connections of the words. And I think we're in the boutique, the artisan, the farmer's market phase of these kinds of analyses. And there will be a time not so far away when these questions can be resolved better, Blue. So yeah, just like the paper aside, I mean, I definitely realize that there are space constraints and also like what was the timing of your paper versus the Dacosta paper? And did you have time to like incorporate all of those, the new like updated version of the maths? So there's not weekly mixing or mixing mentioned in the Dacosta paper. And so I really just would be curious, maybe you wanna follow up via email to know what was missing from that formulation in your mind for it to be plausible. Because for me too, it was very like the foundation of the FEP existing in ergodicity or requiring ergodicity for applicability was very jarring. Like I felt like that can't be right. But I felt that it was really resolved by the Dacosta paper. And so I'm curious if you don't feel the same way what your hesitation would be. So maybe we wanna follow up in a dot three at some point. Yeah, or maybe by email. So I would definitely look at this paper and all their new recent because that was published this year, right? It's very recent. So the papers that we were focusing a little bit more on in the, in our paper was part it out, which is also very new and Princeton 2019 is for this free energy principle for particle physics. And the other papers we look at them very briefly because they were actually out after our paper was accepted or maybe during the review process. So it wasn't part of our research, systematic research, but we did take a look at them. I think we might have even caught that paper. But yeah, so I would like to take a look at that again. I'm not sure whether they use, if they use the notion of information geometry then they probably also rely on weekly dynamical systems, but I would have to look at that again. So we can continue the conversation by email. Counterfactual paper spaces, you know, you have some sort of clause that gets triggered. If something happens in the literature, then this paragraph should be deleted, like pending a future word on this, this could be deleted. In the last little bit, maybe we can just have any thoughts. Just why does this whole discussion matter for the FEP and for ACTIMP? Well, the validity and the adequacy were how it was described by this paper, why it matters. So it's kind of cool because often the citations that we discuss, they don't always lay out on the table why it matters to understand this topic. And I think we got that very clearly from this work. So I really appreciated that. And it also laid out many of the next steps directly, not every next step, but the specific key themes and challenges are addressed. And if there is a obvious or non-obvious response, that'll be a citation that somebody can swoop on. Stephen? Yeah, I think it's important because we are seeing a lot of interest, a huge amount of interest from inactivism and embodied work and physicality and how these things can shape up. And therefore purely mathematical arguments will limit things. I think getting into the nitty-gritty of the physics, which in itself is wrestling with some of this because it's kind of cutting edge for them in terms of that is really important though, I think, because you see some of the criticisms coming around inactivism, trying to get a wrestle on things. And I do think, I will say that I think maybe sometimes saying, go and visit the math, which is ultimately based on the viscosity, which is basically a physics principle as much as a maths principle in terms of how that comes up to be present comes up. So I think this is a really important area that physics and maybe the sort of the areas of applied physics start to come into. Yes, and we'll just send them on the run around. Okay, go to the math and then they'll go to the physics. Okay, now to the philosophers you go and then back to another maybe non-academic department. Is that run around the answer? What if there's a stationarity in the run around? But very good points. It's kind of fun because we've had these questions for a long time, if not the longest time. Yet many of them were explicitly addressed by this paper and by the 31 discussions. So that's kind of cool to see like a sort of, it's not a conclusion on our series but these questions which are often the next step for other papers discussed in the dot two, discussed in the conclusion or the discussion, that's where this work picked up. And so that's a different attribute than we've seen from some of the other literature we discussed. Blue, Dave, do you have any other thoughts? Patricia, would you like to give any final comments? I think I have said, you know, unless you have a last question. What papers? I'm a little bit of fun, I'm sorry, I'm a little bit of fun outside in the free energy principle I must confess but I would like to see how it progress. So as I said at the beginning, we are not against the free energy principle a priori. So if our paper can lead to more research in the free energy principle direction, we would be happy and we would consider it a success. So we are not necessarily enemies of the free energy principle. Then I'm in principle very interested in the application of statistical mechanics and even the language of dynamical systems to biology. So I am in principle interested in this type of research. And also in the active inference of interdisciplinary research. So I would be very interested in see how this evolve. And if we as philosophers can contribute to that by criticizing some points that we find non-rigorous enough then our job is done. So that's basically our goal. Thanks Patricia. Totally agreed. This, hopefully we can enact the kind of dialogue at the micro like a conversation and a disciplinary or scholarly dialogue that plays out over years. And the philosophers have a very important role in that. Blue? So what Patricia was just saying reminds me of, you know, when we discussed Mike Levin's paper in the summer, the computational boundary of a self, it's, you know, there's the instrumentalist view and then the realist view and then the utility axis in that diagram. And so definitely I thought that this paper was useful in provoking dialogue and really kind of, I would like to leverage your vantage point to kind of grind into some of the deeper, maybe more mathematical stuff that's kind of beyond me because it's not really my background but to kind of, you know, dig into that hole and make sure that there's a solid foundation under the hole or is it a hole that pokes all the way through and leads to nothing on the other end? So I think, you know, it's useful for getting at those questions. My last question, Patricia, would be what areas of literature or papers might you recommend that we dive into so that we can have a comprehensive view and know where we're coming from and where we're going? I can mention many, many papers. I can do that better but email again. So if you're interested in literature and some specific research or topic, just send me an email and I can recommend philosophical literature but I would like to especially recommend one paper. So if I can choose. And I don't know the title right now hopefully but it's a paper by Karim Thibault who is called something about imperialism and migration. So I can look at that now because it's a very general paper in philosophy of science where they draw a very nice distinction between migration of models and imperialism of models that I think will be also useful in the interdisciplinary research that you are doing. Because they stress the difference about using the methods or exporting the methods from one discipline to the other in a non-imperialist way which would imply that in the new discipline you have to justify the model, you have to justify the mathematical methods. That's the one, models on the mode, migration and parallelism, brilliant. And they distinguish between that that they call migration of models from imperialism in which you just extrapolate the same models from one discipline to the other and you try to expand your discipline which would be sort of the attitude that was illustrated in the comics that you were discussing last week. So I think that paper is especially useful for people doing interdisciplinary research because it's a very useful distinction, this model is on the move. Thanks for the awesome suggestion. So just to the point about emails or however it goes, just consider the dialogue opened. We really appreciate that both of you came to discuss and also interacted with the .0 and .1 videos. So just awesome work with research and thanks again for helping our lab do what it does. And this is also an excellent suggestion because it's a provocative title but we're talking about provocative ideas and with broad scope. And this kind of takes that map territory discussion to a new place, potentially talking about movements and imperialism and colonization, all these other things that come up in different terms but we've noted this in our upcoming Streams calendar. So after our lab meeting next week, we'll have stochastic chaos and Markov blankets that will complement some of the things that we didn't talk about in 31. We'll talk in 33, thinking like a state with Avel aka Surval and then we'll have two more slots open. So perhaps we'll select one of these that we've already listed or perhaps somebody wants to join if an author wants to discuss. And other than that, I think that brings us to a close today. So again, big appreciation to the authors for their work and engagement with the lab and thanks, Steven, Dave and Blue and everyone else who participated and Maxwell for joining the .1. So good times and we will see you next time. Thank you, thank you very much. Bye.