Theories of Everything with Curt Jaimungal - Karl Friston: The Most INTENSE Theory of Reality Explained

Episode Date: August 16, 2024

Karl Friston is a leading neuroscientist and pioneer of the free energy principle, celebrated for his influential work in computational neuroscience and his profound impact on understanding brain function and cognition. Karl is a Professor of Neuroscience at University College London and a Fellow of the Royal Society, with numerous awards recognizing his contributions to theoretical neurobiology. Watch on YouTube: https://youtu.be/uk4NZorRjCo Become a YouTube Member Here: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) Join TOEmail at https://www.curtjaimungal.org LINKS: - Karl's Previous TOE Episode: https://www.youtube.com/watch?v=2v7LBABwZKA Timestamps: 00:00 - Intro 01:05 - Lecture Overview 05:53 - Schrodinger’s Question 08:48 - Markov Blankets (The Brain) 16:16 - Quick Crash Course in Physics! 29:30 - Different Temporal Scales 35:38 - Markov Blanket (Continued) 01:06:16 - Outro/Support TOE Support TOE: - Patreon: https://patreon.com/curtjaimungal (early access to ad-free audio episodes!) - Crypto: https://tinyurl.com/cryptoTOE - PayPal: https://tinyurl.com/paypalTOE - TOE Merch: https://tinyurl.com/TOEmerch Follow TOE: - NEW Get my 'Top 10 TOEs' PDF + Weekly Personal Updates: https://www.curtjaimungal.org - Instagram: https://www.instagram.com/theoriesofeverythingpod - TikTok: https://www.tiktok.com/@theoriesofeverything_ - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs - iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-with-curt-jaimungal/id1521758802 - Pandora: https://pdora.co/33b9lfP - Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e - Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything Join this channel to get access to perks: https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join #science #biology #physics Learn more about your ad choices. Visit megaphone.fm/adchoices

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Keep it fresh at Michigan.org. Professor Carl Friston, it's wonderful to speak with you again. I think this is the fifth time that we've spoken on this channel. We've also spoken in person off air in London. That was beautiful to meet you. Where was it? The Royal Society? It was the Royal Society.

It was wonderful to see you. Yes, it was wonderful. You said, meet me at, where did you say it was some statue? It was the- But I thought it was a pub. Yes, I remember. It was the Duke of York steps. Yes, yes.

You said, meet me at the Duke of York. And I looked online, Duke of York. Oh, that's a pub. Okay, it's 10 minutes away or five minutes away. And I'm running and I think it was drizzling at that time. Yeah, anyhow, it was great. Great to see you. Why don't you start your presentation, sir?

Sure. But just as context for the audience, this is for a lecture series on theories of everything called Rethinking the Foundations of Biology. What lies beyond Darwin is the question. In this episode, Karl Fersen is just taking more of the Rethinking the Foundations of Biology itself. So please. Thank you. Indeed I am. And for a reason. That reason is, I'm going to appeal here to

Chris Fields, that there is no bright line between physics and biology, psychology, and what could even argue philosophy. So the foundations of biology should, by definition, therefore be the foundations of physics and everything else. And I'm going to leverage the notion of everything else by just thinking about the nature of things, a foundation of thing-ness, the story I'm gonna tell is a characterization of what it is to be some thing and the behaviors that that thing must possess. So this is a slightly deflationary foundation account of existence in the sense it just describes those things

that persist in time over a suitable time scale. The other aspect of this foundational account, I refer to it here as the physics of sentience. It's really just the physics of things that self-organize technically to a set of characteristic states or attracting states and attracting set. The other aspect of this is that there's no new physics here, there's no new biology here, and there's probably no new psychology. It starts basically with the foundations that are shared by all of physics, ranging from quantum physics, quantum mechanics, through to stochastic or statistical mechanics,

right through to classical mechanics. We're just gonna start right at the beginning and ask the question, what is it to be a thing? And having answered that question. So the story here is what it is to be a thing and what characteristics must this kind of thing be. And I reiterate the physics interpretation of this is not new and it's actually almost tautological.

The final point I want to make is I did notice that there was beyond Darwin in many senses, the account that I'm going to briefly rehearse over the next few minutes is very closely allied with Darwinian thinking at two levels. First of all, it shares the same almost tautological aspect in the sense that we are just describing things that exist and that existence is defined in terms of things that are there. The other point of contact is that what arises or emerges from this approach is a mechanics

that you could say was the very mechanics of Darwinian selection. So I'm not gonna go beyond Darwin, I'm going to meet Darwin and effectively tell selection. is divide this discussion into three parts. First part is going to be just a consideration of the statistics of life with a special focus on Markov blankets and the ensuing Bayesian mechanics. I'm then going to tell the same story

but using the rhetoric and concepts that a neurobiologist or a psychologist, cognitive scientist might bring to the table, specifically unpacking the mechanics that has been established in the first bit in terms of particular coding neural networks. And then if we've got time, sort of move to a consideration of different kinds of things, different kinds of particles, different kinds of people, different kinds of institutions, and draw a distinction between certain things that do not have an authentic kind of agency and other things that might have a natural intelligence or agency and try and articulate that

distinction in terms of in fact Markov blankets. Okay so the first bit then I'm going to start with a question posed by Skrodinger. How can the events in space and time which take place within the spatial boundary of a living organism be counted for by physics and chemistry? Now I'm not going to answer that question but I am going to draw attention to the notion of a boundary. The boundary I think is essential in terms of individuating or distinguishing something from everything else, or indeed nothing, or no thing. And I got to read that boundary as a statistical object, specifically a Markov boundary or Markov blanket.

So what's a Markov blanket? Well, imagine we had a little universe where these cyan circles represent states and the arrows or the edges represent a causal influence. So this state influences this state. And if I identified some set of states, say my internal states, then the Markov blanket comprises the parents, the children, and the parents of the children and the role of this set of states this blanket plays is that it separates me statistically from all the other states in the universe if i

wanted to know the dynamics of my internal states given everything else in the in a putative universe then i'd only need to know my blanket states. In other words it provides a statistical veil or insulation that surrounds and shrouds my internal states and separates and individuates my internal states from my external states. Technically it just means that the dynamics on the inside are conditionally independent of the dynamics on the outside, given the blanket states. I'm going to make a further move here.

I'm going to introduce a bipartition of the blanket states into sensory states and active states, where the sensory states influence but are not influenced by the internal states, while the sensory states influence but are not influenced by the internal states, while the active states influence but are not influenced by the external states. So we've got this interesting, very simple partition of the states of any universe from my perspective in terms of blanket states comprising sensory and active states that together with my internal states can be regarded as the states of a particle so it could be a small particle it could be a person or as you've been to make it an institution.

It doesn't matter that the rules or the causal structure and the mark of blanket should apply in a scale invariant and possibly even scale free sense. And just to provide you with a couple of examples of different scales, here's my favorite system, the brain, where we can regard the internal states of the brain as my neuronal dynamics, my connectivity that influence the active states that then change external states that could include my body that in turn reciprocate by influencing the sensory space my sensory epithelia that then the cause changes in my internal states briefly professor the difference between scale and variance and scale free means what. scale invariance and scale free means what? Technically your renormalization group flow or your RG flow has some quantitative conservation as you move from scale to scale as opposed to the functional form of the dynamics as described by the Lagrangian or indeed the functional form of the dynamics as described by the Lagrangian

or indeed the functional form of the equations of motion just being conserved. So yeah, scale-free if you like is a sort of special case of scale invariance where there are extra constraints on what is conserved as you move from one scale to the next scale. And also just briefly, conditional independence for the Markov blanket is different than being completely independent.

Absolutely, and this is quite crucial. So clearly if two sets of states were independent in the sense that they never influenced each other, you'd be describing two separate universes. And you would only be interested in focusing on one universe or the other universe so you're only interested in terms of systems that or states that can be distinguished, individuated, via conditional independences. So if you like it, it's an open boundary. So if you take yourself, it's an open boundary. So if you take yourself back to your schoolboy physics,

what we're talking about now is what constitutes the heat bath in a sort of classical physics view of, say, a canonical micro-ensemble. What's interesting is what's beyond the heat path and indeed how do we communicate through a heat path which we can now treat as a Markov blanket to what is beyond that. So we're talking specifically, another way of foregrounding the importance of a Markov blanket is we're moving away from 20th century physics in the sense of equilibrium into the world of non equilibria that definitively require the system to be open so where's the open to say what the openness here is the openness of the system. through a vicarious exchange with the outside where the, if you like, the conditional independence is maintained by this two-way traffic. So the inside

influences the outside through the sensory states and the inside influences the outside through the active states. So the system is open and therefore when we're talking about self organization of these open systems we are talking not about equilibrium we are talking about non equilibrium steady states and i'll straight one of those in the next slide just to give a bit more intuition to this so this is all about sort of self-organization of non-equilibrium, Fafn equilibrium systems that are open, but open in a way that allows you still to preserve the difference between the thing, the internal states of the thing and the state's external or outside that kind of thing. And this is just another example here, say a single cell organism with its interestacellular states

will be the internal states. The actin filaments would be the active states that push the cell surface on sensory states into the external milieu that reciprocates by changing cell surface receptors that changes the intracellular states. So just another example of the preservation of these conditionally dependencies and thereby the functional example of the preservation of these conditionally

dependencies and thereby the functional form of the dynamics and thereby making this effectively apt for application of the apparatus of the renormalization group, which brings us back to the scaling variant aspect of this, this kind of partition. So you said the filaments are the active states, but why do you call them active states and not an active part of the organism? What I mean to say is that, look, a state I imagine is the entire organism, but then you would say that this part is active.

You don't call that an active state, at least just in the terminology that I'm familiar with. Sure. So I'm using states here in the context of a state space. So an organism would be a collection of a very large number of states, so that the state of an organism would be a point in a high dimensional state space. So states here are collections of multiple different states and this Markov blanket effectively is providing a partition of these multiple states in a particular way that allows you to distinguish. So you certainly could say that the active states, for example, could comprise a list

of the particular position of all my actuators or my muscles. The reason I mentioned actin filaments is in the actin filaments of cells are the things that sort of push the cell surface around, they actually cause movement. So normally speaking, your active states are simply those that afford the capacity to move of the kind that you would expect to see in biotic motion, for example. Is that distinction quite clear?

Or is there some ambiguity between what's an active and an inactive state? Right, well, the definition of active states is only in relation to this Markov blanket partition. So you can label the notion of an inactive state introduces a different kind of semantics to it, which doesn't exist at this stage. So you can certainly have an active state or an internal state that is for a certain period of time around an unstable point attractor, so it's not moving. So you could say, from a dynamical perspective, it's inactive because it's not changing.

But at this stage, I'm just using the phrase active states just to denote a subset of ways of states in some state space that has this particular dependency relationship or influence relationship, and specifically here, the kind of states that influence the rate of change of external states. So this is explicitly as a dynamical formulation. Bumble knows it's hard to start conversations. Hey. No, too basic. Hi there. Still no.

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if you're given this little diagram here. So this is a starting point for everything that follows. And in fact, let me ask you now to forget about the Markov blanket for a moment. What we'll do now is just do a 101 crash course in all of physics and then what we're going to do is put the Markov blanket back into play and see what emerges. So this in effect is a reflection of what I was saying in the introduction that the kind of physics that I'm going to describe here is no different from any other kind of

physics other than it is committed to a careful distinction between the states of something and the states of everything else that is not part of that thing, not a particular state where the particular states include the Markov-Banke states and the internal states. But if we just start where one could argue all of physics starts, including quantum mechanics, with a random differential equation or a description of a random dynamical system in terms of its motion, which is some lawful function of where it is in state space plus a random fluctuation, then we can sort of cartoon the system. So I've just got two states here, along the X and the Y axes. And as the system develops, it is traces out a trajectory or a path in this two dimensional state space.

And again appealing to the sort of scaling brand aspect this can be any scale you want so for example it could be. Electric chemical oscillations in a single cell in my body it could be my cardiac cycle during the heartbeat, different aspects of the state of my heart. It could be me getting up in the morning, doing my emails, having a cup of coffee and so on. It could be Christmas, Easter. The key thing is at any scale or for any description of the universe at the scale in terms of some state space the object in question here means that the system i will keep revisiting at any scale states that i have once been in so that's the kind of thing that i am trying to describe technically

So that's the kind of thing that I am trying to describe. Technically, a random dynamical system that possesses an attracting set or a limit set that itself is a random variable, namely a pullback attractor. So I'm interested in systems in which things can exist in virtue of there being this tendency to revisit states that you were once or the system was once in. Is that clear?

Yeah, so anything that you do on repeat, whether it's your heart that has a beat or you're drinking a cup of coffee, either in the day or in multiple sips within the same five minute period. Now, what I don't get is what is a pullback attractor compared to a regular attractor? Well a regular attractor if one should exist Normally is read as an attracting or limit set for a deterministic system

But as soon as you introduce random fluctuations on into the equations of motion or the dynamics because this thing itself is a random variable. The limit set is again itself a random variable. Intuitively you can think of winding back in time and then winding forwards again given a particular realization of these random fluctuations to produce these pullback attractors. And I'm sure that doesn't help. What I often read is for technical reasons,

we refer to a pullback attractor. But I think in spirit, you can regard this just as a, as an attractor in the vernacular sense. It's just a set of states that effectively the system looks as if it is attracted to in virtue of the dynamics bringing you back to this manifold. But this manifold can be very, very space filling and incorporate the itinerant dynamics that you were just referring to. So that repetition, I think, is probably more crucial than one might realize when one first articulates it like that.

Because we're talking about things that will have, well, certain things that will have biotic aspects to them. So we're talking, for example, about things that have oscillations in them. And I'm using the example of a single cell, electrochemical cell in my brain. I could regard this as a description of fast camera oscillations, for example, in my hippocampus. But we can also read this tendency to revisit this particular kind of itinerancy that is associated with these pullback attractors as biorhythms and you can even go as far as life cycles and just sort of bring you back to the you know the title of your series Beyond Darwin. Replication is just another facet of the behaviors that these kinds of systems have to possess. So this is another, if you like, perspective on,

we don't need to go beyond Darwin. Darwin had everything that was necessary. Just reproduction replication is just one way that this kind of itinerancy on a pullback attractor is manifest. Interesting. Okay. Let me see if I got that correct. In life, you reproduce or you replicate. And this replication you can see as an oscillation in the same way that you would drink the same cup of coffee

multiple times. Absolutely. I mean, what you've just described is a lovely illustration of the scaling variance of the mechanics at hand. And all you're saying is that there has to be an attracting set, and this attracting set is a set of states in a system that is open,

and the openness comes along with the Markov blanket, which we'll get to in a second. Sure, and I also assume that in the same way your heart doesn't beat the exact same way every single time, even though it looks identical to us with our eyes. Yeah, it has in a slight variation. Maybe there is no such thing as two heartbeats in the same way. There's no such thing as two snowflakes that are exactly akin, but sorry, that are exactly equivalent. They are akin.

Absolutely. So I assume and we don't have to get to the details, but I assume that in your model, it doesn't have to be exact repetitions. There can be some variation. Absolutely. Otherwise, you don't have Darwinianism. Absolutely. Yeah. And in fact,

it can never be exact. You can never revisit. I should have said the neighborhood. So you revisit the neighborhood. And that is, if you like, the essence of this pullback attractor that inherits from these random fluctuations. So okay, you just understood. Yeah, you just you're just you're you're revisiting regimes of state space. That can

be described probabilistically. So unlike a point attractor, you know, classical attractor, or indeed even milliner attractors, we're not talking about being attracted to the same spot, we're talking about to the vicinity, in the neighborhood of. So this is where the probabilistic perspective comes in because I can now interpret this pullback attractor as where the density of the trajectories that are never coincident, they never converge, they never cross, or perhaps they do cross, we're probably

getting into gauge theory now, but we can interpret the density of these trajectories, these paths, as a probability that you will find me in this state at any one particular time, if you sampled me at a random time. So, and you know, exactly your observation that a man never steps in the same river twice, there aren't two snowflakes are never the same, is accommodated by this probabilistic perspective on these

pullback attractors. And that's effectively the root or the basis of the move that gives rise to this basic mechanics. Because once you've got in mind a description of the system in terms of the probability density of the system being in any state you can now disappear to all of physics to describe the evolution not have the state in state space but of the probability distribution. of the probability distribution. And this boils down to something really, very simple and really interesting. Because we've just said that there is effectively a pullback attractor, we could also describe this as a non-equilibrium steady state. It's not equilibrium because we're talking

about open systems, but there is a steady state in the sense that this repeating this replication, this itinerant revisiting of neighborhoods there is a steady state in the sense that this repeating this replication, this itinerant revisiting of neighborhoods means that the density, the probability density reading of this object is itself unchanging. So I can just go along and take off the shelf your favorite density dynamics. This could be Richard Feynman's pathological formulation, it could be a master equation and kinetic models, it could be the Fokker-Planck equation, whatever

you like, they're all at this level, expressions of the same thing. They just basically express the rate of change of this probability density in terms of the amplitude gamma of random fluctuations and the flow, the flow through state space at any point in that state space. So I've just written that down in terms of the Fokker-Planck equation. But note, because we want to describe things that possess this attracting set or have a non-equilibrium steady state solution, the rate of change of this probability distribution is zero, which means I can now solve the density for the density dynamics. Perhaps I should just say that this is also one expression of a time independent Schrodinger equation. So I can just get the solution to that. And that allows me to do something quite

interesting. It allows me to express the dynamics, the flow of the states as a function of where I am in state space as a mixture of gradient flows on the gradients subtended by the log of this probability, basically a potential of erosion Um, in my world, we'll, we would call this self-information, uh, which is nice because it's all about self-organization also called by people like tribus, um, surprise or more simply surprise or the negative of it is surprise or surprise and self-information. Um, this, um, partition of these two kinds of flows here is due to or a generalization of the Helmholtz decomposition. And all it's saying is that the flow at any one point on

this attracting set, this pullback attractor, this manifold can be divided into two parts. One is a gradient flow, up log probability gradients or down potential gradients, and one which circulates on the iso potential or probability So often called solenoidal flow in virtue of that or divergence free flow or conservative flow, whereas this part is the dissipative dynamics of flow and has curl free aspects to it. So that circular flow, I think I sort of highlight that simply because of our discussion previously about the importance of replication, repetition, revisiting the neighborhood of states that we were once in, those states that are characteristic of the kind of thing that I am. This rests upon the non-neuralities in these systems, these random dynamical systems that manifest as this seronoidal circular flow. So I think that's quite important,

although it wasn't something I was going to foreground in this. You do realize we're not going to do this in 30 minutes or an hour. So you're going to have to stop me at the designated time. We'll keep going as long as you can keep going, and then the audience will have questions. Anyhow, we can always come back for part two. I think we're going to have to come back for part two. At this rate, it's going to probably be part three. I think we're going to have to come back for part three.

Right. Because you're drilling down some of the really key issues. it's going to probably be part three. I think we're going to have to come back for a part three. Cause you're drilling down some of the really key issues, um, um, which, you know, I speak to the nature of the, of the kind of systems that we're trying to account for. So not only do we have this sort of solenoidal aspect and this itinerancy and the randomness that is underwritten by pullback attractors, but also what we implicitly have spoken about is the fact that these systems exist in multiple scales and each scale provides a context in the scale below.

And they all have this sort of itinerant non-equilibrium steady state aspect, but the steady state is never actually attained, but is slowly going towards these solutions at different timescales. So an important aspect of this construction is that there is a scale above. So we're talking before about my, this being my heartbeat. That scale is going to be much, much longer and larger than the scale associated with the depolarization of the myocardium and or any particular cell in my myocardium that could be responding to inputs and outputs that are much faster timescales, say oscillating very, very fast frequencies, much more quickly than the slow second-to-second evolution of the system at

the level of the heart itself. And what that means is that from the point of view of one cell, then the context in which it is operating is largely unchanging, you know, by appeal to an adiabatic approximation, which means that there is a solution at that temporal scale of the single cell to its fast dynamics. So it can attain its particular attracting set at this phase in the cardiac cycle. However, of course, the phase of the cardiac cycle is itself slowly changing. So the pullback attractor from the point of view of single cell is slowly moving all the time. And of course, exactly the same maths underwrites Darwinian selection.

So you've got your phenotype, which is the single cell, you know, from the point of view of evolution or transgenerational dynamics, from the point of view of the phylogenetic time course or time scales. The organism is changing very, very quickly as it grows and behaves and acts and decides and develops and dies. But from the point of view of the phenotype, the change in the genotype is so slow that's irrelevant. So the phenotype, the creature, the organism at a very small scale, now can be described as if it is conforming to its own little pullback attractor. The states that I described before about getting up and doing my emails and having my cup of coffee. That's only true while I am alive,

or why I am in a position to read emails and drink my cup of coffee. So that attractor, that manifold, has a, if you like, an expiry date on it. But because of the adiabatic approximation, we can assume that at any given scale, the scale above is changing so slowly that we can assume the existence of the solution

to these dynamics and therefore apply the solution of the Fokker-Planck equation. So I'm wittering on about that because I think there's a beautiful connection with Darwinian thinking here. Once you put this density dynamics of the kind that you would pursue in terms of quantum mechanics,

if you read this as a Schrodinger equation, you can pursue this. And what you end up with is a Schrodinger equation. You can pursue this and what you end up with is a variational or a density dynamic approach to natural selection in and of itself. A lot of people have written about this and it's certainly a current theme as far as I know in theoretical biology, reading things like say the replicator equation as

effectively exactly the same mechanics that people doing inference and basic filtering would use. So there's an opportunity here to have a completely distinguished, just talking about the mathematical and formal correspondences between the story I was going to tell about Bayesian mechanics and the story that somebody taking a Bayesian perspective on Darwinian dynamics would tell. It's the same story basically. But anyways, in order to tell that story, I have to make a link now between this sort of universal dynamics

expressed in terms of a Helmholtz decomposition, which we can read as an admixture of gradient flows up not probability gradients, up adaptive fitness or marginal likelihood if you like, and this circular replicator-like dynamics that is associated with the conservative or the divergence-free flow or dynamics. How does that read as inference and Bayesian filtering or sentient behavior? Well, that's where the Markov bucket comes in. So if we now go back and just remember that previously we'd just been talking about any arbitrary and exceedingly large state space X. Now we come to partition X into the external, internal and intervening blanket states. And furthermore just focus on two of those subsets, namely the internal states of any given two of those subsets, namely the internal states of any given system, say me, and my active states. And then by construction, if you remember, the unique thing about the internal

states and the external states is that they are not influenced by the external states. However, that Helmholtz decomposition still has to be present, which means that I can write down the dynamics of my internal states, say, or my neuronal dynamics, and my motion of my actuators, my active states, my muscles, and autonomic reflexes, as in terms of this Helmholtzky composition where the gradients are supplied by exactly the same potential. So the log of the probability of some sensory sector of my Markov blanket given that particular Markov blanket partition. And the reading of this, and it is just an interpretation, is in terms of perception and action respectively. And the perception part now yields to an interpretation

in terms of sense-making and Bayesian inference, which is why I was talking about the emergence of Bayesian mechanics from the master equation or the time independent Schrodinger equation or the Fokker-Planck equation if you're given the Markov-Plancket petition. In other words, if something exists in the sense that it possesses this distinguishing aspect in terms of possessing a Markov blanket, then it must comply with its internal and active states, sometimes referred to as autonomous states of this particle or person, must conform to this dynamics here. So now the game is how would one interpret this?

How will you describe this to your students or your professors or your children? And there are lots of ways that you can do that. So I've just listed a few here. I'm sure you will have come across all of these. But just to, again, reinforce this point that this is foundation in the sense that it is assumed or described by many. There is of self organization and the particular accounts of behavior things and actually move so. What is this quantity log probability of my sensory states given a Markov blanket.

Well, we've just said that these states belong to an attracting set. The pullback attractor. So these are the sensory states that are attractive to me in the surviving phenotype given I've got this pullback attractor and it is permitted by the context in which or the universe in which this attractor is manifest. So it just scores the attractiveness or the value to me of being in this particular sensory state here or the value in this sensory state space. So all this equation is saying is that both perception action is going to try and maximize value and that can now be read as reinforcement learning. If I was an engineer it would be called optimal control theory and if I was an economist it would just be expected utility theory where the reward the control objective or the utility just is this log probability of being in a state that

is characteristic of the kind of state that I find myself in. The negative of this thing is what I was referring to before which is the self-information also known as surprise and surprise. So this equation says that I'm trying to it looks as if I am trying to minimize my surprise or self-information. And from that, we can read off the principle of maximum mutual information or the Infomax principle. It could have been the minimal redundancy principle

of Horace Barlow and the free energy principle. So where does free energy principle get into the game? Well, the variational free energy is a proxy for, in fact, it's actually an upper bound on the self-information. So when people talk about the free energy principle as systems trying to minimize their free energy, what they mean is basically systems that conform to this foundational Helmholtz decomposition of their dynamics, where you've

just substituted the free energy for the Lagrangian, the potential self-information or the surprise of Just a moment. Sorry, Professor, you keep saying before we explain this to our children, some non-trivial task to put it lightly. You keep saying given a Markov blanket. Now what's giving us the Markov blanket? Is it the causal structure of the universe? Is it our internal versus active states? Or does the Markov blanket give rise to those instead? I understand there's some interplay. I understand that. But what gives us initially the Markov blanket? Right, well, I think you're now touching upon the tautology that I introduced right at the beginning.

So when I say given, I just mean technically conditioned upon. So that bar in the notation in my world just means given or conditioned upon something. the I think is slightly deeper than that. I am the answer is very clear all we are doing. Is describing the dynamics of any system that possesses a mark off blanket. So this is a little bit like it's deflation in the following sense so what what the free energy principle is saying is not that in order to survive, you must maximize value or adaptive fitness or marginal likelihood. That's not what the free energy principle is saying. What it's saying is if you survive in the sense of possessing a pullback attractor, then you will always be described as if you are maximizing value, adaptive fitness or marginal likelihood. So that is the tautology

that I was appealing to in the Darwinian sense. So we're assuming all we're doing is trying to invent a physics, basically what this ends up being is a variational principle of least action that can be applied to something where the thing in question is very carefully defined technically in terms of a Markov blanket. So by saying that something exists, then the free energy principle applies simply because the thingness is defined stipulatively by being able to differentiate. The time average of this self-information is entropy,

which means that these equations can also be read as the holy grail of self-organization in the sense that they look as if on average they're trying to minimize entropy and then from that you can elaborate synergetics of the kind that Herman Haken has established. It's just an expression of homeostasis. It's just keeping your essential variables, your physiological variables within viable bounds that are valuable for me, that are characteristic of my particular states. So resisting the dispersion of the random fluctuations by these gradient flows that look as if I tried to minimize self-information or on average trying

to minimize the entropy of my sensory states. And there's a final interpretation which licenses the rhetoric of basic mechanics. So if I was a statistician, what i would look at what i would describe this quantity is just the probability of some sensory data. Given condition to pon my mark off blanket that i can now read as a model so my my blanket and my internal states now can be read as a model of the external states. So I can now equivalently describe this Helmholtz decomposition of the dynamics in terms of the Bayesian brain hypothesis or evidence accumulation,

and a popular one in the neurosciences and cognitive sciences is predictive coding. So this has been taken even further in philosophy that you can read these equations as essentially doing a gradient descent on model evidence. Model evidence is also known as a marginal likelihood. Why marginal? Well, because you've marginalized out all the causes of your sensory states or your sensory data, your sensory impressions, the impressions of the sensory sector of your Markov blanket,

by which I mean those causes that are the external states are not part of this probability density. So you've effectively integrated out or average away or marginalize them. So this is also known as the marginal likelihood or the model evidence, the likelihood of these data given me as a model of the world, the external states that caused these data. And that has been described or summarized in philosophy as self-evidencing. So I'm minimizing my self-information

just is acting and perceiving in a way where perceiving is associated with my internal dynamics in a way that maximizes the evidence for my model of the world or the external states. Put that another way, this self-evidencing just means that it looks as if I'm going around gathering evidence for my model of the world that just is me. So I'm just gathering evidence for the fact that I exist. So that's the most deflationary but poetic reading of this Bayesian mechanics. So that gives you just a flavor of the different ways in which you can understand

ways in which you can understand ways of describing the dynamics of things where the thing in virtue of its existence cannot have any other dynamics. That can be neatly summarized in terms of the existence of a particle implies a partition of the system's states, the systemic states into internal blanket comprising sensory and active and external states that are hidden behind the Markov blanket from the point of view of the internal states. Because the active states change but are not changed by the external states, they look

as if they're going to reduce the entropy of the blanket states. And this means that action will appear to maintain the structural and functional integrity of the Markov blanket. And one can read this in terms of self-assembly in computational chemistry or in biology as self-creational or autopoiesis, some of a very elemental form. Finally, internal states appear to infer the hidden causes of sensory states by increasing Bayesian evidence or model evidence or marginal likelihood and actively influence those causes. And in my world, we refer to this as active influence,

taking this self-evident perspective afforded by the interpretation of the underlying self-information as effectively the log of the or the negative log of model, Bayesian model evidence. So that was the first half of the talk. I now notice that we've been well over our allotted time. I'm going to suggest that we stop here and then you can wax a lyrical and ask questions for a few minutes.

And then we should rebook part two to tell the same story, but now just using the concepts and the rhetoric and the constructs from neurobiology and psychology. Okay, so then this is actually a natural stopping point because the latter half of the talk is using the first half of the talk to explain neurobiology and psychology. Absolutely. Yeah, we're just gonna basically interpret the same gradient flow, Helmholtz decomposition, but through the lens of somebody looking at electrophysiology

and sense making in animals and indeed psychology or possibly even neurophilosophy. Yeah, absolutely. Okay, so one of my questions was this Fokker-Planck equation. I'm unsure what you're saying is the relationship between that and other density equations like in quantum mechanics Schrodinger's equation or the Feynman path integral. Are you saying that you can derive the Feynman path integral from the Fokker-Planck equation or that the Fokker-Planck equation is a density equation of the same sort that follows the calculus of variations?

Like is that what unites them? Yeah. Just that they're minimizing something or maximizing something? Yeah, well I think the latter expression, there's just ways of articulating the same thing. So you can either write down the dynamics in terms of a random dynamical system, in terms of a large one equation, specify the equations of motion

in terms of these flows and the statistics on random fluctuations. And then it is a fairly trivial matter to move to either a Fokker-Planck description of the implicit probability densities of this random dynamical system that can be articulated either in terms of a pathological formulation or in terms of a Fok formulation or in terms of a Vocaplank equation. Okay, so then it's the claim that the Langevin equation is the ultimate equation that gives rise

to the other equations. I think in terms of what is the seed that gives birth to the rest? I think, well, for me, I mean, you know, if you spoke to other people, you may get a different answer, but certainly for me, the seed is the large-band equation. It is just a description of a random dynamical system. It's random because you've got these random fluctuations that in my world, distinguish themselves from movements in state space in virtue of just being very, very, very fast,

so fast that they cannot be observed. So you can't actually observe them. All you can do is write down a probability distribution, say the mean and variance. So for me, we'd start here. Given that, I can then write down the Fokker-Pank equation. So specifically, the amplitude, the statistics, the sufficient statistics of the random fluctuations

just are the gamma here, and I know F. So if I know the statistics of the random fluctuations and I know F. So if I know the statistics and random fluctuations and the flow, then I can now just articulate this in terms of the Fokker-Planck equation that is just a function of the statistics and random fluctuations and the flow. And from that, you can,

or you could express it in terms of a pathological formulation. So that, you know, that's the, that is the seed. And then we move to the Fokker-Pank equation and then make a very, very simple and important move. The move is that this is equal to zero because the things that we want to understand are possess a solution to the Fokker-Planck equation that they have a solution to the density dynamics in the same way that the time independent Schrodinger equation, which would be the equivalent

if you were working, well, perhaps I can just show you what I meant by that, which will be the equivalent in quantum mechanics. You're just looking at the solutions with a little preview of what we might have the opportunity to go through in sessions three. But what I wanted to show you, this is just another intuition as to the importance of this Helmholtz decomposition in terms of self-organizing systems, countering the random dispersion due to random fluctuations, by imagining somebody dropping a blob of ink into a cup and the ink molecules gathering themselves up by flowing up the concentration gradients. But you also have this sort of solenoidal component

very much like we are all aware of when we're looking at sort of water flowing down the bath, the bath hole, but also doing it solenoidal thing. But what I wanted to illustrate, so the Fokker-Planck, the special cases of this, the solution to the Fokker-Planck equation, that obtain when the amplitude of the random fluctuations

goes away, you're just left with a solenoidal flow, and that's just classical mechanics. So that's just things where, you know, there are lawful relationships between, you know, position and the velocity and mass and the like that emerged just because this circular solenoidal conservative dynamics, or the random fluctuations can get so big when you get very, very small, because you're under the renormalization group or

your random fluctuations haven't yet been averaged away because you're too small. Then you get thermodynamics where it's all about the gradient flow and from that you can derive fluctuation dissipation theorems and statistical or specifically stochastic mechanics. For if you wanted to go quantum, you just factorize this probability density in terms of complex roots and you get from this the time independent Schrodinger equation. Who was the first to point this out? See these three different colors that you have here, the three different derivations. Who was the first to point out that they're all reflections under different assumptions for actually that they're all under the the Langevin equation, which is then decomposed

in various ways. I did my trading. I'm sorry. Yes, just qualify. This is the Bayesian mechanics that is exactly the same as these things, but you've just now split your Xs into internal and active states. So I've shown the fourth one

because the Bayesian mechanics is just as famous as that. I don't know, the last time I was sitting in a lecture theatre doing physics was at the Cavendish Laboratory at Cambridge some 40 years ago. So you've at least independently stated this? Oh yeah, but I'm assuming it's common knowledge. Certainly. Okay. I mean, you'll know better than I will. Certainly the equivalence between the pathological formulation

and the Fokker-Planck equation and the time independent Schrodinger equation. While I say common knowledge, I have certainly referred people to technical papers in the literature just to substantiate the observation that one can't derive everything from the Langevin equation. Sorry, sir. To maximize on the time as this is a pun actually at the time that we have left, I want to talk about maximization or minimization. You said that, let's take Darwin as an example.

Survival of the fittest sounds like if you're the fittest, you will survive. But then you said, well, if you were to survive, it would appear as if you were the fittest sounds like if you're the fittest you will survive. But then you said, well, if you were to survive, it would appear as if you were the fittest and those two aren't the same statements. And rather what's happening is the latter. So help me understand how those two sentences are different. I think they're only different in the sense that the notion that I survived because I have a high adaptive fitness implies a teleology. So you can have a completely teleologically or telonomy or teleology free account of self-organization under the free energy principle and also quantum mechanics and stochastic and classical mechanics. Okay, so you weren't saying that let's say we take this cup and if I was to let go it

would just fall and it would fall because it's minimizing action. Now for people who are listening who don't understand what action is, let's say it's minimizing energy. We don't need to concern ourselves with the difference between two different types of energy being action. It's minimizing something, whether it's energy or action. So that's one way of saying it, that this cup minimizes its action. But then another way from what I understood of what you were saying is that I will only perceive objects that minimize their action. In other words, this cup could have done plenty of other actions or there could be many other cups, but my perceptual system, for whatever reason, is only tuned to what minimizes.

And therefore it's not that what survives is the fittest is only that I'll see what's maximizing the fitness as surviving. Or I'll only see this cup move in this direction because it minimized something. I think that's, I think that's absolutely correct. But I think sort of makes it more- Okay, so that sounds loony to me. So explain to me how that's correct. Now, what I'm saying, things out there conform to a path of least action

because they exist. there conform to a path of least action because they exist. Therefore, we will perceive them as pursuing paths of least action. That's all the free energy principle is saying. It's just saying that we pursue paths of least action. What could one apply that to? Well, adaptive fitness, for example. So, you know, Darwinian thinking. Adaptive fitness is just the thing that supplies the potential in the action, which is time times potential. So, you're maximizing the adaptive fitness

or you're minimizing the negative adaptive fitness. The nice point of content that comes into the way you perceive the cup though, I think reflects the fact that when you put the Markov blanket in place, so don't forget about doing that, you can't talk sensibly about perceiving apples unless you've got an observer and something that's being observed. So you've immediately invoked a Markov blanket. So if you're talking to Stephen Wolfram, you know, he calls this the observer problem.

To solve the observer problem, to even talk about it, you've got to have a Markov blanket. So there has to be distinction between the observer and the observer. The measurement problem, the same thing in quantum physics mechanics. You have to have the Markov blanket explicitly in play. once you got the market in play then the adaptive fitness is just the measure of synchrony. I'm alright some offers them between the inside and the outside so literally if you take this space in the counts perspective the adaptive fitness is the ability of you to fit into your environment, by which I mean the

sensory impressions provided by your environment, the feedback that the environment is giving you was the most likely for the kind of thing that you are, the phenotype that you are. So adaptive fitness is just the marginal likelihood of the environment, providing that sensory, the way that the environment influences you by the sensory states is the measure of adaptive fitness. And it's just the fit of your model, the ability of your model to fit this world. So it all I think it does actually come back to you say, I can only perceive falling apples

because apples only fall. Yes. If I lived in a universe where apples did, which did not comply with a principle of least action, which is not impossible. You know, I couldn't live in a very small universe where random fluctuations cause things to depart enormously from paths of least action.

And I would still be able to model that. But, you know, in this instance, I would be able to perceive random fluctuations of the apple, you know, or itinerant dynamics which violated, say, conservative dynamics. So I have one more question. I know you have to get going. If the free energy principle is true by definition of tautology, then why is there so many papers published on it? There has to be something more to the free energy principle than just being a tautology. So in other words, Kant has analytic truths, but there must be something here that's synthetic.

Otherwise I don't understand how it can be rich if it's not purely analytic. Well, I never said it was rich. I know you're not saying it's rich. The fact that we've even spent over an hour on it, and that there's more than one slide, and that there are papers and that you're the highest cited neuroscientist in the world implies that it's rich. So help me understand that. I can. There is an answer. But given I've only now got three minutes left, I think that's an excellent place we should start. I'll give you a clue. You can use the free energy principle in the same sense you can use Hamilton's principle of least action to design automobiles, trajectories,

physical artifacts that do stuff. You can leverage the free energy principle to write down your pullback attractor. You can write down the states to which a system should self-organize and then just solve the free energy flows or the basic mechanics to reproduce self-organization and in principle, intelligent kind of self-organization. So you can create and simulate self-organization because you know the principles that underwrite the dynamics. So that's a clue, but I can unpack that in more detail the next time. Let's uncompress it next time. And I see Hamilton's equation as synthetic, not just analytic, but we can talk about the distinction next time, sir.

Okay. This was so much fun. It went by like that. Thank you. I love talking to you. So I'll see you hopefully in a few days or weeks, depending upon your itinerary. Yes. Okay.

Brilliant. Thank you, sir. Firstly,. Okay, brilliant. Thank you, sir. Firstly, thank you for watching. Thank you for listening. There's now a website, curtjymongle.org, and that has a mailing list. The reason being that large platforms like YouTube, like Patreon, they can disable you for whatever reason, whenever they like. That's just part of the terms of service. Now a direct mailing list ensures that I have an untrammeled communication with you. Plus soon I'll be releasing a one-page

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