Okay, we're back, so whenever you want to start, I'll just edit it. Sure. So I was just talking about the orthodoxy of this kind of approach to life phenomena, to biology. that basically it's still, when you look at, you know, philosophy of science, philosophy of biology, you see that there are still these kinds of views dominant. And in fact, when scientists come up with, biologists come up with kind of trying to explain what they are actually doing.
doing and you know they basically you can see the traits of these orthodoxies still preserved in their approaches so the consequence of orthodoxy for biology is that either life is radically reduced to simple chemical mechanisms and then to apply traditional physics or it has to be taken outside the paradigm altogether and asserted as metaphysically so generous both were and are in plausible positions these are undoubtedly the early theory building stages through which any science has to go you
know as you know in order to assemble better understanding and this is something that we We will come back to it later. And people who are familiar, I have recommended one of the best books that talks about basically this kind of theory building, especially for life phenomena, is Giuseppe Longo and Francis by physical singularity of life. So possibly this was itself intuitively understood by many scientists.
Even so, there was enough dogmatic conviction in science and certainly in philosophy of science that the results were not pleasant for basically descendants. who were denied a hearing and research finding and, you know, often ostracized. And basically, this is still a continuation. And this is something that, you know, for example, I had a conversation with Longo, and he was saying that, you know, when probably, when basically they want to fund, for example, cancer research, you know, still these kinds of genetic, cellular, you know, linear, you know, theory making
is still in fashion. And, you know, any person, for example, tries to look into, you know, the kind of macro-level complexity and micro-level complexity, for example, that there is no such a thing as this kind of clear-cut hierarchical system, hence hierarchical theory. Oh, God, I don't know what... What is it, Tony? Sorry. Is everything okay? Yeah, no, no, no, it's just... I'm having a website thing to get it online. It's still recording, we're good. Okay. I apologize. So, basically, he was saying that, you know,
people who are trying to do, approach the problem of, for example, you know, cancer, you know, for example, in terms of hormonal pathways, you know, the kind of diverse and complex nonlinear hierarchy of, for example, you know, dynamics behind, you know, cancerous growth, they don't get research funding because the people who actually provide funding are the ones who are, for the most part, are actually still retaining the kind
of classical orthodoxy. So back to our introduction. So, yet all the while, scientific work itself was quietly and often unintentionally laying the groundwork for suspending this orthodoxy, both scientifically and philosophically. understand why this might be so one has only to contemplate what the previous paradigm excludes from consideration namely all irreversible far from
equilibrium thermodynamic phenomena this comprises the vast majority of the subject matter of the subject of interest to science everything from you know kind of super galactic formation in the early cooling of the universe down to the planet formation, all or most of our planets drew climatic behavior, all phase change behavior, natural to the planet or not, and of course all life forms since these are irreversible far from equilibrium systems. What all of these phenomena exploit is this equilibrium, a spontaneous instability, a
symmetry breaking, specifically non-local irreversible symmetry breaking to form increased complexity. So this is starkly clear for, you know, for example, cosmic condensation in physics. universe begins as a super hot super symmetric expanding point sphere but as it expands with cools differentiates breaking its natal supersymmetry the
fundamental forces differentiate out their nonlinearities amplify the smallest fluctuation of differences into, you know, kind of ever-increasing structural features. So it's not surprising that from early on, or even, you know, while the elegantly simple mathematics of the symmetry, stability, equilibrium paradigm were being developed, and striking successes explored, scientists sense the difficulties of remaining within its constraint, albeit in scattered, kind of hesitant forms.
Maxwell, who formulated modern electromagnetic theory in later 19th century and sought to unify physics drew explicit attention to the challenge posed by instability and failure of universality for formulating scientific laws. His contemporary Henri Poincaré spearheaded an investigation of both nonlinear differential equations and in and in stability especially you know geometric methods for their characterization by the 1920s is that a static dynamic and a
structural equilibria and in the stability's had been distinguished in engineering for example non-linearity and emergent dynamics appeared in an analytically tractable manner with with the entry of feedback and development of dynamical control theory Maxwell in you know 1868 provided the first rigorous mathematical analysis of a feedback control system by the early 20th century general systems theory was developed you know by fun Bertel and and others with notions like feedback, feed forward, homing in, homeless status, and other
basis. Later cybernetic was constructing basically emerged from control engineering as its applied counterpart. control theory which became a disciplinary paradigm by the 1960s forms the basis of the use of dynamical system models in many contemporary systems application in 1887 And Poincare had also become the first person to discover a chaotic deterministic system,
later introducing ideas that ultimately led to modern chaos theory. And we are basically today, we are going to a little bit going into this. Meanwhile, Hadamard, 1898, studied a system of idealized billiards and was able to show that all trajectories diverge exponentially from one another. Sensitivity is basically sensitivity to initial conditions, which we talk about today. the positive Lipunov exponent. I will later talk about these concepts.
However, it was only with the advent of modern computers in the late 1960s that investigation of chaotic dynamics developed. For example, for atmospheric dynamics, Lorenz, by the mid-1970s, chaos had been found in many diverse places, including physics, both empirical and the theoretical work on turbulence. Chemistry, biology, logistic map population dynamics, for example, and the mathematical theory behind it was solidly established. Since then, the story is one of exponential explosion of an increasing complexity in content.
Complexity is slowly uncovered in sensitivity to initial conditions and chaos in systems. Meanwhile, the identification and understanding of self-organized emergence shows no sign of global consensus yet. and we'll get to this subject next session and probably the third session especially because it's very fashionable especially both in the continental side and kind of more avant-garde philosophy of science
all the talks about self-organization you know a strong emergentic behavior so on and so forth while many philosophers early on preferred change in exclu in excluple though from constituents and the like scientists prefer something less human dependent but without much agreement commencing from the most general features and Narrowing down there are first the common appeals to a spontaneous symmetry breaking and failure of linear superposition. I will talk about this. Followed by expresses logical depth.
That's Charles Bernan's concept. We will introduce it next session. And again, in the second module, when we are talking about computational complexity. Better global system predictability, which is basically introduced by James Crutchfield and his colleagues. Again, we'll talk about this very briefly when we are talking about computational measures, and in the second module, we'll talk about computational complexity. exhibiting downward causation by, for example, Asperi and Campbell, relatively micro-cut and
strained formation, Collier and Hooker. So these last three being cousins if the better predictability is because of the emergent constraints on the system. Optimal prediction is simulation or reproduction as the amount of past information required to predict future system estates. Basically these are the characteristics of emergent behaviors which we talk about. So we probably went too much into these kind of future concepts that we are going to talk
about. So returning back to the kind of larger narrative, this historical account itself of how basically complex science emerged. You know, kind of is, first of all, is very rudimentary, but unavoidably selective. Nevertheless, it sufficiently indicates the slow buildup of an empirically grounded conceptual break with a simple symmetry of stability equilibrium orthodoxy, and a corresponding background, you know, a murmur of doubt and difficulty within the foundational philosophical tradition. However, the new approach often still remains superficial to the cores of the sciences themselves.
In physics, this is for deep reasons to do with the lack of a way to fully integrate its instability processes, especially structural instabilities, into the fundamental dynamical flow framework, for example, the lack of integration of irreversibility into fundamental dynamics and the related difficulty dealing with global organizational constraints, for example, in flow characterization. For biology, all that had really developed was a partial set of mathematical tools applied to a desperate collection of isolated examples that were largely superficial to the then core principle
and developmental dynamics of the field. Nonetheless, by the late 1970s, it's clear in retrospect that science had begun to pull together many of the major ideas and principles that would undermine the hegemony of the simple symmetry equilibrium orthodoxies. Inestabilities were seen to play crucial roles in many real life systems. They even confer sometimes valuable properties on those systems, emergent properties, such as sensitivity to initial conditions, structural liability in response.
These ininstabilities broke symmetries, and in doing so, produced the only way to achieve more complex dynamical conditions. The phenomenon of deterministic chaos was not only surprising to many, to some extent, it pulled apart determinism from analytic solutions, and so also from prediction in that positivistic sense, and hence also pulled explanation apart from prediction, again, in the kind of positivistic framework that was the dominant. It also emphasized a principled, as opposed to a merely pragmatic role for human finitude in understanding the world.
And this is something that we will talk about in terms of computational cost, but also in terms of problems with modeling of complex systems. So I don't want to go too much into basically this history. But it is, I mean, what I wanted to just emphasize that basically the very rough sketch of this is that complexity science really emerged from these
observational anomalies that the dominant scientific frameworks couldn't explain. And once they tried to explain them, basically that led to kind of like a series of this kind of chain reaction, both in mathematical formulation, in physical theories, in life sciences, so on and so forth. Another thing that I think before moving to our actual discussion is that we can see basically
another way to define this divergence is this kind of way of looking at systems. The black box system, which basically you have the linear interaction between hypothetical components of the system, and then you try to basically apply the kind of positivistic theory of induction to this black box. And the other one is basically a kind of multilevel, non-positivistic approach to nonlinear interaction
between components of the system. So, which of course, you know, this brings us to basically the main ideas behind the entire seminar. Basically, all we are trying to look into is can be boiled down to two dominant concepts as studies by sciences and scientific frameworks
before the rise of complexity theory and afterwards. And what are these two concepts? Behavior and interaction. And this is something that we talk about this in the first module in terms of complexity, but we can't really get into the kind of detailed framework of how to basically really understand what a behavior is and what interaction is until the second module and the third module. So let me share this screen.
I can see your mouse, but nothing at all. Can you see anything from the screen? No, I'm talking about it. Okay, one second. Are you in full screen? Back to you. There we go.
Yes? Yup. Okay. So, the best way to start looking into complexity sciences and the concept of complexities to kind of get rid of a few common misunderstandings, which I'm
sure all of you are familiar. But nevertheless, if not they themselves, their varieties are dominant in philosophy, philosophy of science, but nevertheless, you can see these kinds of approaches very often in continental philosophy especially. The first five general problematic interpretations of complexity that we should avoid from the beginning, moving forward.
one is that complexity means intricacy, or complex system is a complicated system. Systems that have intricate parts may actually exhibit simple behaviors. The second one is that complex systems are those that have many components. More components means more complex behavior. But even a three-point-like, blizzard-like system can exhibit complex behaviors. The third one is that complex systems are systems with interconnected components. Hence, more interactions between components means more complex behavior. Systems with many linear interactions don't show complex behaviors.
And conversely, systems with few nonlinear interactions can show complex behaviors, you know, as in the billiard ball three-point body example. again we often especially like in kind of this continental philosophy approach to complexity of phenomena we come across these kinds of you know claims that everything is complex everything is network everything this and everything is that but the thing is that you know
This kind of approach to what actually complexity is yields zero descriptive explanatory value, not to mention that it aligns the distinction between complexity at the level of models and complexity at the level of causes or properties of the actual system. The fifth problematic thing is to say that there is a unified theory of complexity. The bad news is that of course neither there is a unified theory nor there are similar metrics. In fact, there are over 50 different metrics of measuring complexity.
And even though at the surface level they might have commonalities, but when you look into them, they actually quite verge from one another. So these five ones were the most basic things that we should absolutely rule out before starting to talk about what complexity is. There are also three problematic methodological approaches to complexity that we should basically move out of the picture. One, that only selecting few characteristics, usually just chaos randomness, and ignoring
the rest when we are defining complexity or complex systems. The second one is that models of complexity are context-independent and can be neatly applied to real-world phenomena. This is a quite popular view, for example, when you see that the policymakers or economists or even in biology, they apply different models of complexity without any kind of discrimination to real world phenomena.
A good example of, for example, people who are very interested in this economic modeling in terms of all this stuff, especially if you are interested to follow this seminar in in conjunction with some of these new topics in philosophy about accelerationism or the kind of complex approach to politics, it would be great to read this article, the one that's Rafael Scholl's confession
of a complexity skeptic, which raises a few powerful challenges to this kind of application of, basically, complexity sciences to policymaking and economy. The third problematic, methodological problematic, is that models of complexity can be applied all the way down or up, regardless of their level of abstraction. This is something that is unfortunately is prevalent even among the people who
are aware of the kind of details about complexity theory. In fact, we can see that it's quite dominant in philosophy of science and philosophy of biology especially. So we talked about the general one, the methodological problematic and the metaphysical epistemic assumptions about complexity and complex systems that are problematic and require careful examination. And we are going to, in this session and next session, talk about these two, metaphysical and epistemic assumptions, by giving, you know, kind of a starting from, you know, basically
some of the basic concepts and talk about, you know, the kind of epistemic metaphysical assumptions and interpretations that are given based on these concepts. One is that chaos and complexity lead to a radical revision in or even obsolescence of our conception of determinism. The second one is that chaos and complexity means that, you know, and this is less in basically actual science but in kind of a philosophical interpretation. has different varieties from forget predictability to impossibility of predictability in a specific
framework and as we see basically this kind of approach, this kind of interpretation that complexity and chaos means forget predictability or impossibility of predictability and certain modeling framework leads to actually kind of overcompensating interpretations about, that basically we can come up and solve the problems arise in modeling of complex systems
by a kind of statistical modeling pluralism, simply applying varieties of a statistical approach to complex phenomena in order to be effectively modeling them. So, starting with the metaphysical epistemological issues, A number of metaphysical and epistemological issues are raised by the investigation and behavior of complex systems. Before treating some of these issues, a characterization of nonlinear dynamics and complexity needs
to be provided, and that's what I'm going to do. with this background some folklore folklore about chaos and complexity will be discussed although some claim that chaos is ubiquitous and many take the signal feature of chaos to be exponential growth in uncertainty these examples of folklore turn out to be misleading They give rise to rather surprising further folk interpretation that chaos and complexity espel the end of predictability and determinism. Some have argued that chaos and complexity lead to radical revisions in our conception
of determinism, namely that determinism is a layered concept. But such arguments turn on misunderstanding of determinism and predictability and their subtle relations in the context of nonlinear dynamics. When the previously mentioned folklore or folk interpretation is cleared away, the relationship among determinism, predictability, and nonlinearity can be seen more clearly. still contains some subtle features. In addition, the lack of linear superposition in complex systems also has implications for confirmation, causation, reduction, and emergence. And natural
laws in nonlinear dynamics, all of which raise important questions for the application of complex nonlinear models to actual world you know phenomena I will begin with a distinction that is immediately relevant to physical descriptions of states and properties known as the antique epistemic distinction in philosophy of science roughly antique estates and properties are features of physical systems as they are when nobody is looking whereas epistemic estates and properties refer to features of physical systems as accessed empirically an
important special case of antique estates and properties are those that are deterministic and describable in terms of points in an appropriate state space whereas an important a special case of epistemic estate and properties are those that are describable in terms of probability distribution on some appropriate estate space the anti-epistemic distinction helps eliminate eliminate of confusion confusions which arise in the discussion of nonlinear your dynamics and complexity as we will see.
Complexity and chaos are primarily understood as mathematical behaviors of dynamical systems. Dynamical systems are deterministic mathematical models. Where time basically can be either a continuous or a discrete variable. You know, a simple example of this would be, you know, just the equation describing a pendulum swinging. Such models may be studied as purely mathematical objects or may be used to describe a target system, some kind of physical, ecological, or financial system. Both qualitative and quantitative properties of such models are of interest to scientists.
The equations of a dynamical system are often referred to as dynamical or evolution equations describing the change in time of variables taken to adequately describe the target system. A complete specification of the initial state of such equations is referred to as the initial condition for the model.
While a characterization of the boundaries for the model domain are known as the boundary conditions. A simple example of the dynamical system would be the equations modeling a particular chemical reaction, where a set of equations relates the temperature, pressure, amounts of the various compounds, and their reaction rates. The boundary condition might be the container walls maintained at a fixed temperature. The initial conditions then would be the starting concentrations of the chemical compounds.
And the dynamic system would be taken to describe the behavior of the chemical mixture over time. The dynamical systems of interesting complexity studies are nonlinear. A dynamical system is characterized as linear or nonlinear depending on the nature of the dynamical equations describing the target system for example consider a
different a differential equation system dx over dt equals fx where the set of variables you know X1 X2 Xn might represent positions momenta chemical concentration or other key features of the target system suppose that X sub 1 of T and X sub 2 of T are solutions of our equation system if the system of equation is linear it is easy to show this is also a solution where a and b
are constants this is known as the principle of linear superposition very rudimentary of speaking what is linear superposition linear superposition basically describes two basic features. One is homogeneity and one is additivity plus, shift invariance for special cases of basically linear systems. Homogeneity is that if an amplitude change in the system results in an identical amplitude change in the output.
For example, resistors. If the input to the system is the voltage across the resistor V and the output from the system is the current true resistor I , the system is said to be homogenous. Additivity, you know, a system admits additivity if added signals pass through the system without interacting. A very intuitive example of this is that listening to a phone conversation between Levi and Nathan at different locations, having conversation with one another.
What we hear is the sum of the conversation between the two. What we hear is basically in the sense that we hear Levi and Nathan having conversation. We do not hear it as they have been added together, basically, as a third person. Now, in addition to the additivity and homogeneity, we have also a special kind of, basically, relation, a property. And this only holds for a special kind of linear systems.
this is shifting invariant shifting invariance it roughly goes like this that if a shift in the input signal will result in nothing more than an identical shift in the output signal a system is said to be shift invariant again an An intuitive example would be you stimulate, or a person stimulate your ear once with an impulse, measure the electrical response. Then you stimulate it again with a similar impulse
at a different point in time. And again, you measure the response. If you haven't, you know, basically ruined your ear, the first impulse, the second impulse basically, sorry, the second impulse should expect to be yielding the same measurement. the second impulse has occurred later in time would be you know in terms of time
would be invariant to the basically the first impulse now Additivity and homogeneity basically define the core characteristics of linear superposition property. if the principle of linear superposition holds then roughly a system behaves such that any multiplicative change in a variable for example say factor alpha implies a multiplicative or
proportional change of its output by alpha for example again kind of very similar to this kind shift invariance but different if you start with your television at low volume then turn the volume control up you know one unit the volume increases one unit then if you turn on the control up two units the volume increases two units this is basically an example of linear response in a nonlinear system this linear superposition and hence this linear behavior fails and a system need not change proportionally to the change in
variable for example if you turn your volume control up two units the volume you know increases tenfold this is you know an example of a nonlinear response Dynamical systems involve a status space. You know, roughly speaking, a state space is an abstract mathematical space of points where each point represents a possible state of the system.
An instantaneous state is taken to be characterized by the instantaneous values of the variables considered crucial for a complete description of the state. When the state of the system is fully characterized by position and momentum variables, often symbolized by Q and P respectively, the resulting space is often called a phase space. A model can be studied in a state space by following its trajectory, which is basically a history of the model's behavior in terms of its estate transitions from the initial state to some chosen final state.
The evolution equations govern the path, namely the history of the state transitions of the system in a state of space. Now, there are some little noticed yet crucial assumptions being made in this account of dynamical systems and status spaces. And what's that? is that the actual state of a target system is accurately characterized by the values of the crucial state-space variables and that a physical state corresponds via these values to a point in a state-space.
These assumptions allow us to develop a mathematical model or mathematical models for the evolution of these points in a state of space and to consider such models as representing basically the target systems of interest. You know, that's called basically various schemas of isomorphisms or, you know, kind of from rudimentary forms of isomorphisms to more complex relations. In other words, we assume that our mathematical models are faithful representations of target systems and that their status spaces employed faithfully represent a space of actual possibilities
of target systems. This package of assumptions is known as the, you know, basically faithful model assumption. In its idealized limit, the perfect model scenario license the slide between model talk and system talk. know whatever is true of the model is also true of the target system and vice versa I will talk about this a little bit further down the line now back to you
know, the consequences of loss of superposition property. And that's where we are getting back to, you know, this idea, the problems with this idea, interpretation of models and faithful modeling and model confirmation in complexity sciences. Now, one striking feature of chaos and complexity is their sensitive dependence on initial conditions, the property of a dynamical system to show possibly extreme different behavior with only the slightest changes in initial conditions.
A very popular measure of the sensitive dependence involves, that involves basically the exclusive growth of the smallest uncertainties in the initial conditions of a nonlinear system is called positive Lipunov exponent, positive global Lipunov exponent, not local. And this is an important distinction, a global exponent rather than a local exponent.
This explosive growth is often defined as an exponential parametrized by the largest global Lipanov exponent. Measure the growth rates of generic perturbations in a regime where their evolution is ruled by linear equations, basically a linearized approximation. So first, what is exactly a Lipanov exponent? I think the best idea is to give a little bit of an intuitive example.
idea behind lipon of exponent is that if we imagine a small ball of initial conditions around a certain point in a status space where each point on the ball represents a small displacement or perturbation basically perturbation beneath the measure the threshold of measurement and these displacements are you know basically from the central point the evolution equations will act on this ball to change its shape the ball will stretch or shrinks in each
direction depending on whether the dynamical system acts to magnify or reduce a small displacement. For a three-dimensional system, the deformation of the ball can be approximately described by three numbers corresponding to the formation along the trajectory of the central point and along two directions perpendicular to it. These three numbers are basically the Lipanov exponents. Now if the exponent in a certain direction is negative, any small displacement in that direction will exponentially shrink as the system evolves. If it is zero, the displacement will roughly remain at the same magnitude. But if the exponent is positive,
Any small displacement, namely perturbation, will grow exponentially. The presence of a positive Lyponov exponent means sensitivity to initial conditions. Its size provides a measure of how quickly and uncertainty about initial conditions grow to make predictions impossible. Now, global Liponov exponents measure growth rates of generic perturbations. It's basically a measure for the total predictability of a system in a linearized approximation.
These exponents arise naturally out of linear stability analysis of trajectories of nonlinear evolution equations in a suitable status space. The infinite time limit plays an important role in this analysis, indicating that global Lypunov exponents represent time-averaged quantities so that transient behaviors has decayed. Again, back to our example. Imagine a small ball of points in a state of space around the initial conditions for
any number delta greater than zero and for every slightly different initial condition y zero in this small ball exponential growth means the initial uncertainty of this, you know, at both X and Y, at basically the smallest uncertainties, will evolve such that at basically at infinite time, this is important, this is the whole
point of the global exponent concept is that it's the assumption is infinite time framework basically the stability that basically the the behavior of the system shifts according to this basically measurement rate this this is that this lambda is basically the positive global Lyponov exponent. Lambda is interpreted and is taken to represent the average rate of divergence of neighboring
trajectories issuing forth from points very nearby basically the smallest uncertainty if London is positive then the growth in uncertainty is exponential as we talked about if the system is bounded in a space and in momentum there will be limits as to how far nearby trajectories can diverge from one another now when you know the classical way of that you know this positive global Lyponov exponent is interpreted is that is interpreted as
that it shows that basically sensitivity to initial conditions means you know basically impossibility of prediction precisely because of you know this explosive growth of the smallest uncertainties over you know infinite time framework and you know basically this is really these interpretations are at the core of the more kind of you know mainstream interpretations basically
chaos or you know kind of complexity behaviors means you know basically lack of or or the impossibility of prediction now there are problems with this kind of interpretation with this you know interpretation of defining sensitive dependence and hence characterizing chaos and complexity using global Lyponov exponent. One problem is that the definition of global Lyponov exponent involves
the infinite time limit. As strictly speaking you know the measure the global exponent only characterizes growth in uncertainties as t increases without bounds not for any finite time at best this would imply that sensitive dependence characterized by a global Lupinoff exponent can only hold for the Large time limit. And this would further imply that chaotic phenomenon can only arise in this limit, contrary to what we take to be our best evidence.
Furthermore, neither our models nor physical systems persist for infinite time. But an infinitely long time is required to verify the presumed exponential diversions of trajectories issuing from infinitismally close points in a state of space. The standard physicist assumption that an infinite time limit can be used to effectively represent some large but finite elapsed time will not do in the context of nonlinear dynamics either. when the finite time liponov exponents are calculated they do not usually lead
to on average exponential growth as characterized by the global liponov exponents this is because you know roughly speaking the propagator namely an operator evolving the uncertainty in some ball of points in a status space forward in time varies you know from point to point in a state of space for any finite times the propagator is a function of the position X basically small point in a state of space and only approaches a constant in the infinite time limit so local finite time Lyponov exponents vary from point to point in a
state space whereas global Lyponov exponent do not therefore trajectories diverge and converge from each other at various rates as they evolve in time so that the uncertainty usually does not vary uniformly in the chaotic region of of the status space. And this is the most important thing. So basically it comes down to this idea that the global Lyponov exponent, the basic concept behind the kind of popular interpretation of explosive growth of uncertainty in complex systems has basically an idealized timeframe work.
And that idealized time frame work basically implies a uniform growth of uncertainties. As a basically a bound, you know, Lyponov exponent means that these growth of the uncertainties in its complex systems are not uniform. They diverge as much as they converge.
I will just go over a little bit more on this and then we can either have a break in questions and answers. So what does this mean? Basically, what is exactly the implication of this, you know, that actual complex systems, you know, can't be seen through the lens of global Lyponov exponent. It means that on average exponential growth in uncertainties is not guaranteed for chaotic dynamics.
Linear stability analysis indicates when nonlinearities can be expected to dominate dynamics. And local phenotype Lipanov exponents can indicate regions on an attractor where these nonlinearities will cause all uncertainties to decrease, cause trajectories basically to converge rather than to diverge, so long as trajectories remain in those regions. to summarize this first problem with the kind of default interpretations of chaos and complex systems that trajectories issuing forth from neighboring points in some ball in a status
space are guaranteed to diverge on average exponentially in a chaotic region of a status space is false in any sense other than for infinitesimal uncertainties in the infinite time limit." Basically, that kind of uniform explosive growth that the folk interpretations of this kind of theories present is that it only happens in infinitesimal local regions of
of a state, a space of systems. Whereas in the global level, we see that basically the growth of the uncertainties, as I said, is not uniform. form it can decrease or it can basically increase and this is the whole point that the global liponof exponent the application of global liponof exponent
to basically as a kind of a core concepts of dynamic nonlinear dynamic systems gives a false interpretation of basically growth of uncertainties in system perturbations of displacements in the system the second problem with you know
this interpretation based on global Lyponov exponent is that there is simply no implication that finite uncertainties will exhibit an on average growth rate characterized by any Lyponov exponents, local or global. Now as I said, the linearized dynamics used to derive global Lyponov exponents presupposes infinitesimal uncertainties. But when uncertainties are finite, linearized dynamics involving infinitesimals does not appropriately characterize the growth of finite uncertainties aside from telling us when nonlinearities should be expected to be important.
Infinitesimal uncertainties can never become finite in finite time except through super exponential growth. And even if infinitesimal uncertainties became finite after finite time, that would presuppose the dynamics is basically unconfined, unbounded. However, the interesting features of nonlinear dynamics usually take place in subregion of the state of space. For example, particularly energy surfaces or in regions where attractors exist. Presupposing an unconfined dynamics then would be inconsistent with the features
we are trying to capture in modeling, basically, complex systems. In practice, however, all finite uncertainties saturate at the diameter of the attractor. I will talk about the attractors and the concept of attractors in the next session. But for now, I assume that more or less everyone is familiar with the rough definition of an attractor. The uncertainty reaches some maximum amount of a spreading after a finite time and is not well quantified by measures derived from
global Lyponov exponents. So the folk interpretation that on average exponential divergence of trajectories characterizes chaotic dynamics and complexity is misleading for nonlinear systems. Therefore, drawing an inference from the presence of positive global Lyponov exponent to the existence of an average exponentially diverging trajectories for a dynamical system is shaky at best. As I said, basically, you know, global Lyponov exponent is linearized approximation.
And once you, once basically the underlying assumptions of these measures basically don't hold for basically nonlinear, nonlinearly interacting components in the system, basically a nonlinear dynamic system. So before moving further, I think it would be just a good idea to stop and have some
discussions and some talks. was just a very very super rough super rudimentary stuff about you know you know kind of like at least in terms of you know one of the core concepts behind you know defining uncertainty and you know nonlinear dynamic behaviors and you know that it basically that using that concept is problematic it is much more restricted than usually it is interpreted so we had this you know
rudimentary introduction about the history about you know the stuff that we should rule out we should disregard you know the common interpretations and then we move to basically you know and this is what we are going to talk from now on and the second session you know the kind of epistemic and metaphysical assumptions and interpretations behind you know the core concepts of nonlinear dynamic systems and complex systems so before moving forward with you know
defining features of complex systems. It would be fantastic to just open this whole thing up and just talk a little bit about, very casually, about different things that we have discussed so far. Tony, can you hear me? Hello? Hi, Reza. I can hear you fine. Oh, okay. Sorry, I thought that basically I lost the connection.
No, no, no. I'm not sure. I'm not sure. I'm not sure. I'm not sure. I'm not sure. I'm not sure. I'm not sure. I'm not sure. I'm not sure. No, no, no. You haven't been talking to an empty mic for half an hour or anything. So, I don't have a necessarily very deep response, but it was interesting that all this question about instability or inconsistency of physical laws, sort of onogenic and epistemic states, There's a novel called The Three Body Problem which has been getting some attention recently, which is also very much in this territory, but it's a novel.
I wonder if it's something that you've related to. I am actually, a friend of mine suggested this to me. Is this the one that's about making computers out of the Chinese army? Yeah, it's even, yeah, there's one thread in it. It's by a man called Lucis Cien. Yeah, and there's a whole sort of... I haven't read it. No, I haven't read it, but I have, a couple of people have mentioned it to me. I mean, I know I think it won an award. No, I'm not familiar with the novel, unfortunately. what is exactly you know the the core concept in relation to the you know and
body problem yeah I I am in the recap I don't know how many spoilers out it I should give that the the concept of instability of physical laws or inconsistency of physical laws is definitely a thread and then it also gets tied into like an alien relationship and then sort of this interaction between observability and and and the way that things change it it just seems very much on this territory it's uh which is interesting it's a good novel sure i will check it out um definitely but yes we will actually get
next session to basically when we are talking about today I'm going to just talk about you know I talked about the lippin of exponents I will talk about a what it means a what this what what the failure are basically linear superposition principle means for modeling I will talk about this and then next session I will talk about the you know kind of deterministic scenario problem you know with determinism causation laws yes thank you very much any any other suggestion thoughts discussion question
I guess this is something that we'll probably cover later, but just also sort of as a framework, because the lead into this class is talking about how social sciences really need to be reconceptualized around this concept of complexity and a proper understanding of it. And you were going into a little detail how these concepts are being applied without sort of a full understanding and sort of some of the misconceptions that can come in. Do you have like a good set of examples of people doing this kind of work that you think has a good grasp on it or is forward-looking or sort of more of a framework of how we might want to apply this kind of stuff? Yes.
Actually, when we are talking about modeling, especially kind of, you know, probability modeling a statistical, sophisticated statistical modeling. I have actually a suggestion. I have actually put the link on the PDF, which I'm going to screen share. So you will see it. Yes. I have at least one example in this session about the kind of people who are doing a good job. Although it's technical a little bit, but you can still follow the discussions. And also I will talk about basically some of these problems about this idea that, you
know, the loss of, as I said, the loss of linear superposition property has, leads to a lot of problems about how to model a complex system. I will talk about this today. The idea that basically this is one of the things that I talked about, the idea of the faithful model and confirmation model. In fact, the loss of linear superposition makes this whole idea of a canonical model,
not as a model, a canonical theory of modeling very problematic. Reza, you might want to jump out and jump back in. We're getting some sort of feedback. Sure, sure, sure. But yeah, I will talk about this I will give an example of a couple of good folks in the way. For example, people who are doing kind of physics biology stuff and also people who are more doing public policy and economy stuff, modeling, or complex behaviors.
So if there is no questions, we can go on with talking about formal features of complexity. Can you see the EFDF again? Hello? Hello? Yeah, you can see it. But yeah, your mic is still giving the feedback.
Okay, please tell me my voice is getting glitchy. So, although several formal definitions of complexity have been proposed for characterizing and other forms of complex behavior, there is no consensus on which is the best definition,
nor do these basically different definitions agree in picking out the same categories of behaviors. And that's where I talk about the kind of methodological approaches. And we see that basically not only we don't have a unified theory of complexity, nor- Reza? Yes. Can you please try to reconnect on something? We hear you, I hear you very bad. Okay, sure, sure, definitely. Thank you.
Is it better? Yes, much better. Okay. So I was saying that we don't have a unified theory of complexity. We don't have, you know, basically agreeing and harmonious measures of complexity.
Nor do we have basically a set of common features of complexity. There is some evidence to suggest that different measures are useful for characterizing interesting behaviors of different systems for different purposes. Now, perhaps, sorry, one second, I think I, okay. this is not too surprising as it can be argued that complexity is just the kind of feature requiring a complex basically set of tools and measures
however most of these complexity measures provide no intuitive access to the to the issues of emergence causation at working complex systems some dynamical measures applicable in particular circumstances are exceptions And I talked about the base, and also measures of complexity are quite context-sensitive, context-dependent. This is because most measures of complexity are formalized in terms of probabilities with no explicit reference to physical system variables. Again, dynamical measures are exceptions in this scenario. physical variables are implicitly involved in probabilistic measures because such variables are required to define the state space over which probability
measures are defined often often is more informative to characterize complex systems phenomenologically some of the most important features in these characterizations are sorry I have forgotten to put the first one in the slides I assume that you guys have access to the slides now I mean can you see it Hello? Yes. Okay.
Thank you. Sorry, I can't see any of you because I only see the screen. That's why I'm kind of afraid that I might have lost the connection. So the first feature, the phenomenological feature of complexity and complex system, is many-body systems. Some systems exhibit complex behavior with as few as three constituents, while others require a larger number of constituents. The second feature is broken symmetry. various kinds of symmetries such as homogeneous arrangements in space may exist before some parameters reach as a critical value
but not beyond a good example of very detailed look into the consequences of broken symmetries is the work of Giuseppe Longo and Francis Bailly, the one that I said, but also his more recent book on complexity in biology. You can easily type it in Google. It's called Physical Singularity of Life. The third one is hierarchy.
There are levels or nested structures that may be distinguished, often requiring different descriptions at different levels. For example, larger scale motions in fluid versus the smaller scale fluctuations. Or for example, hierarchical level at the level of molecules, and at the level of cells, or at the level of organs. Now, there are different criteria of differentiation of hierarchies. We will get into this in the third session, hopefully. Again, a good example of looking into the study of hierarchies in relation to complexity sciences is a book that I will,
basically, let me just bring it, is this book. It's considered to be the most classic text in the study of hierarchies, but also one of the most classic texts in the study of complexity. But very classical text. complexity, hierarchical structures, and scaling in physics. So, back to the features. The fourth feature is irreversibility. Distinguishable hierarchies usually are indicators of or result from irreversible processes.
For example, diffusion-effusion. again Longo is a very good book to at least in particular context for example in the context of biology you know see the ramifications of the irreversibility of processes relations systems constituents are coupled to each other there will be some kind of relation. So are not mere aggregates like sand-bredden piles. Situatedness, and this is something that is going to be one of the central themes in the second module about computation and also the third module about cognitive complexity.
The dynamics of the constituents usually depend upon the structures in which they are embedded, as well as the environment and history of the system as a whole. There are many, many books on situatedness in different contexts, from embodied cognition, situatedness in embodied cognition, to situatedness in dynamic processes, to situatedness in computation. I will give references to different contexts as we move forward.
But a good book kind of like about, you know, basically the ramification of situatedness for modeling and model-based reasoning is Lorenzo Mainani's Echo, I think. it's a book about abduction and abductive reasoning I've forgotten the title is it ecocognitive abduction I think something like that you should be able to find it on Google the next feature is integrity
systems display an organic unity of a function which is absent if one of the constituent or internal structure is absent or if relations among the structures and constituents is broken. Then next feature is integration. Various forms of a structural functional relations, such as feedback loops, couple of the components contributing crucially to maintaining system integrity. So integration is usually also tied back to the talks about hierarchies. We will get back to this again, hopefully, in the third module. And integration, again, means it can mean basically functional integration of different hierarchies
or basically a structural integration of different hierarchies, which is usually studied in terms of mechanisms and mechanistic integration. The next one is intricate fluctuating behavior. System behavior lies somewhere between simple order and total disorder, or it basically fluctuates between orderliness and randomness, such that it is difficult to describe and does not merely exhibit randomly produced structures.
A good text on this is, and this is generally one of the best essays on complex systems, It's called What is a Complex System by J. Imes, Ladyman, and Lambert. Stability. The organization and relational unity of the system is preserved under small perturbations and adaptive under moderate changes in its environment. A good example of this, people who want more to look into this, would be Rona Thoms' Structural Stability. It's probably one of the best books on the issue of stability,
both functional and structural in complex systems and complexity-driven phenomena. The last one is observable relativity. This is something that we talk about, would be one of the focus of our discussions, and it's one of the people behind this, distinguishing this feature is James Crutchfield. Now, it means that the complexity of system depends on how we observe and describe them.
Measures of and judgments about complexity are not independent of the observer and her choice of measurement apparatus. Discussion about observer dependency is especially, you know, tied to computational cost of the observer. And, you know, general notion of computational cost in cognitive processes, but also in studying complexity, in basically looking into the complex behavior. That itself has a computational cost. And what is exactly a computational cost?
We'll talk about this, but roughly speaking, it's like this idea that, for example, when we have this kind of multilevel complex systems with different hierarchies of complexity, as the observer moves up the hierarchy, because the structures and functions are situated on top of one another to a phenomenon called generative entrenchment. Basically, one needs to be in place for the other to be basically functioning properly. This creates an
increasing basically hierarchical complexity. And as the observer moves up the hierarchy, the computational cost of the observer to look into this complexity grows. Its internal model keeps growing. For example, for a biological organism, it means that it has to devote more computational resources, more cognitive resources, physical resources, metabolic resources, to make predictions about basically how the behaviors at each level of hierarchy evolve.
So, such features of complex systems make the development of context-free measures of complexity unlikely. This can be illustrated by focusing on the nature of hierarchies in complex systems. systems. And it seems that we are running out of time, but nevertheless I will talk about this, and then hopefully we can go into modeling. The concept of hierarchy in the context of complex system is of particular note. In some systems, the hierarchy of physical forces and dynamical
time scales provide ontologically distinguishable levels of structure. In some cases, the lower level constituents may provide both necessary and sufficient conditions for the existence of and behavior of the higher level of structures now in complex systems however levels of a structure are often only epistemically distinguishable in terms of dynamical time scales furthermore these levels are coupled to each other in such a way that at least some of the higher level structures are not fully determined by and even influenced or constrained by the behavior of constituents in lower level structures. That is, the lower level constituents provide
necessary but not sufficient conditions for the existence and behavior of some of the higher level structures in addition the lower level constituents may not even provide necessary and sufficient conditions for their own behavior if the higher level structures and dynamics dynamics can constrain or otherwise influence the behavior of lower level constituents this latter kind of hierarchy is called a control hierarchy control hierarchies are basically distinguished from merely hierarchical structure like sand grain piles to the kinds of control they exert the kind of influence they exert on lower level
structures and dynamics now it's different that these influences are not necessarily taken to be causal influences like you know the idea of downward causation but they are simply functional constraints that's basically they push the lower level hierarchies to adjust readjust their structures the functional constraint on a top level drive a lower level hierarchy to readjust modify and sometimes you know fundamentally change its structure.
In complex systems control hierarchies affect lower level constituents primarily through constraints the most important example of constraints actively change the rate of reaction or other processes of constituents relative to the unconstrained situation is you know switches and catalysts for example these constraints control lower level constituents without removing all of the latter's configurational degrees of freedom in contrast for example to of simple crystals. These top-down constraints may be external due to the environment interacting with the system,
or such constraints may arise internally between the system due to collective effects of its constituent or some other higher level structural feature. Typically, fundamental forces like gravity and electromagnetism are not explicitly identified with these layer internal generated constraints. Now, the notion of hierarchy and sensitive dependence that we talked about allow us to formulate a more qualitative distinction between linear and nonlinear systems. Though this characterization can also be made empirically precise, linear systems can be straightforwardly decomposed into and composed by subsystems,
a consequence of the principle of linear superposition that we talked about. For a concrete example of the principle of linear superposition, consider a linear harmonic vibration of a string which can be analyzed as a superposition of normal modes. These normal modes can be treated as uncoupled individual oscillators. The composition of the strings vibration, also these component vibrations, is then analogous to aggregating these parts into a whole. The linear behavior of such systems in these cases is sometimes called resultant or in contrast to emergent feature.
In nonlinear systems, by contrast, this straightforward idea of composition and decomposition fails. Why? Because of the loss or the failure of linear superposition property that we talked about. When the behaviors of the constituents of a system are highly coherent and correlated, the system cannot be treated even approximately as a collection of uncoupled individual parts. The tight coupling between constituent and nonlinear systems is related to the non-separability of the Hamiltonian. roughly speaking the latter is you know the Hamiltonian is a function which
corresponds to the total energy of the system and is related to a system's time evolution a Hamiltonian is said to be separable if there exists a transformation carrying the Hamiltonian describing a system n coupled constituents into N equations each describing the behavior of an individual system constituent otherwise the Hamiltonian is said to be non separable and interactions within the system cannot be decomposed into interactions among only the individual components of the system so to sum up linear systems can be decomposed into their constituent parts because of linear superposition property and the
behavior of each component can be changed independently of the other components which will then respond to the change introduced nonlinear systems often exhibit collective behavior where an individual system component cannot be isolated and its behavior changed independently of the rest of the system modification of behaviors in a null in your system may have to take place at some higher hierarchical level or even at the level of total system so that's why you know started to talk about hierarchy so basically it you know you know the core
fundament of this nonlinear dynamic systems of complexity can be and the kind of complexity of behaviors can be understood as basically the difference between you know the hierarchical model of linear systems and the hierarchical model of or hierarchical structure functions of nonlinear systems where basically the interaction between the components of the system are nonlinear. The mathematical modeling of physical systems requires us to make distinction between variables and parameters as well as between systems and their environments. But when linear superposition is lost, systems can be exquisitely sensitive to the
smallest of influences, smallest of perturbations. A small change in the parameter of a model can result in significantly different behavior in its time evolution, making the difference between whether the system exhibits chaotic behavior or not basically quite highlighted quite discernible parameters like the heat on a system surface due to its environment may vary over time leading to white variations in the time evolution of the system variables as well as temporal change in parameters. In such cases, the distinction between model variables and parameters tends to break down.
Similarly, when a nonlinear system exhibits sensitive dependence to initial conditions, even the slightest change in the environment of the system can have a significant effect on the system's behavior. In such cases, the distinction between system and environment breaks down now distinction between system and environment is still preserved because it's preserved because of the you know it's pragmatic usefulness in analyzing the behaviors it's basically is a kind of a pragmatic analytic solution All these subtleties raise questions about identity and individuation for complex systems.
For instance, can a complex system somehow be identified as a distinct individual from its environment? Can various hierarchies of a complex system be individuated from one another? Asking these questions presupposes both that a distinct entity can be identified as well as individuated from other entities. Now, classical views of identity and individuation, you know, based on, for example, Leibniz's principle identity of indiscernibles might be of some use in the pragmatic projects of identifying complex systems and their components. However, these would only yield identification and individuation, a kind of objective ontology
of distinct things, hence many of our judgments about identity and individuation in nonlinear dynamics are epistemic rather than untick. Whether the kinds of features associated with complex systems imply that there are no rigid designators and hence complex systems represent a case of contingent identity and individuation is still an open question. But also, more importantly such features also raise questions about our epistemic access to complex systems the question of modeling obviously some kind of cuts between observer and the observed between system and the environment has to be made along
with this difficulty there are clear epistemic difficulties confronting the measurement and a study of complexity one epistemic difficulty is the mismatch the incongruity between the accuracy or level of fine-grained access to the dynamics of the complex system and its underlying states and properties for example if a particular measurement apparatus only samples some even relatively fine-grained partition of the dynamical states states of a complex system, the result will effectively be a mapping of perhaps infinitely many system states into a much smaller finite number of measurement apparatus states.
This is an argument made by Crutchfield. Such a mapping produces an apparent complexity, epistemic dynamical states in the measurement apparatus projected the space that may not faithfully represent the complexity or simplicity of the system's actual dynamics, namely ontic estates. Another epistemic difficulty is that any measurement apparatus used to ascertain system estates
necessarily will introduce a small disturbance into complex systems that in turn will be amplified by sensitive dependency condition. No matter how fine-grained the measurement instrument, no matter how tiny the disturbance, this perturbation will produce an unpredictable influence on the future behavior of the system under study, on the system being modeled, resulting in limitation on our knowledge of a complex system's future. Along with the disturbance introduced the complex system being measured, there is also a small uncertainty in the measurement apparatus itself. So the apparatus must also measure both itself and its disturbance perfectly
for full accounting of the exact state of complex system being studied. Now this in turn leads to an infinite regress of measurements, measuring, measurements, measuring, requiring the storage of the information of the entire universe state within a subsystem of it, namely the measurement instrument, because a system exhibiting sensitive dependence is involved and any measurement uncertainty will be amplified. An infinite amount of information is stored in the measurement apparatus is required, which is basically physically impossible. So long as the uncertainty in ascertaining the initial state of a linear system remains infinitesimal,
there are no serious limitations on our ability to predict future state of such systems due to rapid growth in uncertainties. In this sense, it is not the present, it is not basically the existence of a positive global Lyponov exponent that signals predictability problems for nonlinear systems per se. But it is rather the loss of linear superposition property that leads to possible rapid growth in finite uncertainties in the measurement of initial estates. When the disturbance of the initial estate due to the act of measurement is included, rapid growth in the total uncertainty in the initial estate
places impossibly severe constraint on the predictability of individual trajectories of a system or their components or various time scales. Now, we are running really short on time, so I won't be able to get into the implications of these for modeling, modeling complex systems and you know observing complexity in actual target systems but we get you know the kind of a for kind of a one of the underlying problems the underlying that the modeling itself not only has internal
disturbances but also at the level of mapping there are the modeling and the actual system can be mismatched and that mismatch of mapping also increases uncertainty of modeling, not to mention the measuring instrument would add to the disturbances. So with this whole idea of this kind of, because complexity behavior, both at the level of modeling and at the level of physical system, make the idea of faithful modeling or perfect modeling problematic and this is something that I will get into in much more details
in the next session. So any questions? You said earlier, real briefly, that you made a differentiation between imposing functional constraints on a lower level of the hierarchy and causal influences running from a hierarchy Because Cardinal influences usually is that kind of a strong emergentic downward causation, which presupposes that, for example, you know, Jake Won Kim has this...
I'm not saying that there is no such thing as downward causation, but downward causation needs to be approached very carefully. And a good discussion, challenge to this topic is given by Jake Won Kim. The idea that, you know, means that this down-to-one causation means that basically the upper level must have causal properties that simply the, basically the lower level hierarchy shouldn't have. And that's because if the lower level hierarchy actually causes the upper level hierarchy to emerge in the first place. Yeah. Yes, it basically means having also the same, the lower level,
basically the downward causation wants to have it both ways. Basically imposing the basically causation downward, but also emerging from the upward causation. Right. Yeah, I guess my question was, I mean, is imposing or if it's just transmitting functional constraints, whether because they come from the environment or they come from the history of the upper level system or whatever it is, I mean, is that transmission of the effects of functional constraints like a sort of a legitimate formulation of downwards causation? I mean, it's sort of semantics that I'm asking about,
but like it would just be, Do we very much want to say that that's not a kind of causation? And if so, then what is our definition of causation? Yes, yes. I think that's a very good point. Yes. I think when we are talking about, you know, and Jay Wong King, when they talk about downward causation, they mean it at the level of a structure, mechanisms, generative mechanisms. And function... Sorry? I said you broke up at like a crucial point. Oh, sorry. Yes, sorry. I said when Jake Wonkin, for example, talks about downward causation, he specifically means it in terms of generative mechanism at the level of a structure,
basically the mechanistic account of causation. Functional constraints are different. And now, yes, functions also can be mechanistically interpreted, which, again, brings back to a different, you know, variation of the kind that you just mentioned. But also they can be independently talked about. Functions as basically decoupled, functional description decoupled from the structural description. Okay, so it's descriptively reducible still with functional constraints. Like it doesn't have to be integrated into the causal structure of that system. You can still talk about those functions as if they were simply. Yes, yes, yes, yes. But now this also, of course, so many mechanistic philosophers like Bechtel, William Bechtel, think that this is not possible.
But my thoughts is that this is in fact possible, and in fact we should differentiate different accounts of functional description. And this is something that we get into the computational description of functions. You know, the kind of basically functions that basically the interaction of processes. Whereas... Would that be linear operators? No, no, no. No, no. No, the difference would be between this computational description of function, the canonical mathematical function, which is, you know, usually modeled by lambda calculus, the canonical mathematical function, which is the sequential algorithm,
sequential state transitions, which is, you know, the inductive predictive account of computation. as different from the computational picture of non-sequential interaction between processes that is given by a wholly different model of computation which is no longer sequential. It's not a theory of computability and hence irreducible to canonical mathematical functions. function this is something we will talk about when we get it sorry you can't it's not expressible and like statements in the lambda calculus yes it's not expressible yes because it needs basically a a a formal theory of
processes now they are getting ahead of ourselves but yeah in computer science there is something they call it a 700 syndrome of algebra various algebra processes, but there is no canonical definition of processes in computer science. That's one of the most interesting things. And we try to get into these kinds of stuff when we are talking about semantic of information processing. Okay. Thank you. I think that goes most of the way towards it. That gets me a step ahead in the question. And as I said, one of the things, you know, and it comes, you know, this is one of the
questions that, you know, comes again and again in our discussion is, as I said, is this anomalies in behavior and anomalies in interaction and various accounts of interaction and various accounts of behavior. And basically, this whole idea of complexity versus complex system versus, sorry, nonlinear dynamic systems as in contrast to linear dynamic systems is basically this boils down, as I said, to this idea of interaction and behavior and how you model it and how you formalize it, basically what it means to really formalize behavior, what it means to formalize interaction.
To some extent, like psychology, I mean anything is a good example, like if being able to characterize behavior means you have to be able to control the system to isolate, to be able to isolate control groups or index values to hold certain things the same, then you're imposing a kind of functional constraint which is theoretically generalizable isn't it the whole problem behind behaviorism behavior is functionalism classical behavior is functionalism is precisely a kind of this cycle psychologistic accounts of observable functions which basically are modeled on our
practical reasoning account of fun what functions and what malfunctions basically these are all analogically driven but also very observable observer dependence and you know basically this also you know gives rise to this we talk about the computation gives rise to this account of of a functional description, for example, of the mind that is basically you can simulate it because you can easily decouple it from the structure precisely because of this artificial constraint that you have put on differentiating behavior from the actual system.
Hence, it can be reproduced flawlessly and then turned into algorithms, sequential algorithms, so on and so forth. Okay, so which is, at least in terms of speculating, the ability to simulate it, and then which means acting it out part way in these models in real life, it's kind of like they're positing what they've already presupposed. By separating behavior from structure in the first place, they've already presupposed that you can do such a thing to simulate it, and then they just make the step again. Yes, but also it has something to do with the way that they formalize behavior too. But also it has something to do with observable behaviors. That formalisms of behaviors, and especially in computational theories of the mind,
are formalized or formalistic theories of observable behaviors. And observable behaviors are very different from those processual internal behaviors of the system. Right. And basically simulation technically, I mean the technical definition of simulation is, you know, replication of observable behaviors relevant to, you know, for example, a, you know, a specific portion of the system. So treating it like a black box, like a replica, yeah, okay. I'm actually kind of lost in like the last few questions that I've asked him where we've gone
that I don't know where the point is circling back to, but that was really interesting. Thank you. That was helpful for sure. Sure. We will get to these. I mean, the whole thing is just stepping, I mean, the stuff that I talked today, you know, It looks like, you know, kind of like, you know, different stuff. But as we move toward these hierarchies, also through our different modules, we see that they come together and they become a completely different nature of so many different things, so many different complexes at the level of function, at the level of structure, modeling function, modeling the structure, formal system for modeling these functions and formalizing structures.
Yes, we get into all of these topics down the line. Cool. Kind of sounds like all of physics and math, not math necessarily, but all of physics all over again, in terms of just like sheer diversity and scope of methods and objects and sort of differentiation among what you're doing depending on what system you're looking at? Yes, well, this also comes down to this very, as I will talk in the second module, comes down to a very fundamental problem. It's a still open question. It's that idea of, you know, computation.
And by computation, I don't mean like, you know, theory of computability. Computation in general. Is it an observer-dependent, basically, thing? Or is you can give actually an observer-independent account of information processing? Because you see, the whole idea of complex systems that came from prior physics was really look into the information of the system and how basically they drive the tendency of the system, the behavior of the system.
So it's important, and this basically, you know, the whole, you know, computational measures of complexity look into the computational, basically, structure or infrastructure of this information. Which is kind of like what, like the virtual machine that it has to be hosted on, like what's required to interpret or implement it, like based on the structure that it has. Yes, and I see a link here, understanding the brain by creating the brain toward manipulative neuroscience. I mean, probably I'm wrong, but the title sounds like an emulative rather than a simulative scenario.
This is more of an emulation kind. where basically you have, you kind of reproduce the relevant structure in order to replicate the behavior. But also emulation is highly constrained and problematic at some level. We will talk about this. Because usually these kinds of emulated structures are situated because they nonlinearly interact with the environment, which means that not only you need to have simulation and emulation strategies, but also you need to have the strategies of reenactment, basically create the parameters responsible for the situatedness of the system within its environment. The study does control for environment to reproduce certain behaviors, so it's actually causal.
Sorry? The paper that I linked to, it was... Oh, okay. They do control for confounders when they sort of produce stimuli to figure out where are these sentiments coming from within the brain or where these images are. It's not just correlational. Okay. Yes. I mean, well, I'm just, I mean, to give a very, like, a brief, you know, what I'm really interested in all of these topics is you know really artificial intelligence and you know the philosophical ramifications of this especially and one of the things
that I think that you know yes brain can tells us a lot about you know how to construct you know for example robust stronger artificial intelligence but But I see that there are huge problems in terms of these kinds of scenarios about emulation, simulation, reenactment of brain at the level of cause, at the level of function. Precisely because cognition is not just the brain. And this is what we are talking about in the third module. that in fact
and this is I take side with Kant that the core component of cognition is really linguistic practices with them being a different form of computation covering different classes of computational complexity or complexity than those basically described by canonical or classical accounts of computation and complexity. And this is something that actually I have seen that has been only recently taken very
seriously by a range of computer scientists and logicians who have looked more carefully into linguistic phenomena, linguistic behaviors, linguistic practices, but also into fundamental philosophical arguments behind these objections. Really I think some of the most interesting computer scientists who are working today, one of them is Samson Abramsky. Samson Abramsky and basically his model of computation allows to, you know, basically tries to capture language
as a specific form of computation that is not that cannot be basically modeled that cannot be constructed by way of those kinds of computational descriptions of you know basically causal estates Questions, talks? So by causal states, do you mean like equivalence classes of histories?
that could produce the present state of the system, like in whatever it was called, computational mechanics? Yes. OK. Yes, that's exactly what I meant. And thank you for bringing it up. I sat in for a couple of classes last time, so I remember that one. And so if it's not, could you just like unpack, I know we have to, everybody's got to go, me included, but like just sort of unpack what it would mean for something not to be susceptible to differentiation into that. like is it is your qualitatively unable to group histories into equivalence
classes or there's no way to calculate what different histories produced in terms of their next state of the future state without having enacted them in real time well I would say that all of the above in some respect yeah but it's fundamentally I mean the kind of computation that involves in linguistic behaviors in you know and basically link the linguistic scaffolding of cognition rather than the kind of a neuroscientific scaffolding of cognition are compute qualitatively different and their complexity is also
qualitatively different. They are basically you can and this is what I think is a kind of a good way to put it that and for you know the kind of you know a strong artificial intelligence scenario we need to understand these kinds of you know causal structures and talks about causal states you know a statistical account of causation, computational mechanics, all of this stuff, emulation, situatedness as necessary but not sufficient conditions for reproduction of cognition or reconstruction
of cognition. Necessary but not sufficient. And were the missing, so language or something about the causal structure of language being this missing element or being its implementation for us? Like beyond these necessary but not sufficient? Yeah, what is basically those accounts of causal states, causation, structure, are missing something to reach to that level, to that level of basically robust, strong cognition.
in a generative framework of cognitive practical abilities, for example, in AI. And what exactly is missing is what we are talking about in the third module, which is what is exactly language. I mean, there are so many philosophies of language. There are so many arguments about centrality of language. but what is missing in all of these things is that language itself in these pro-arguments pro-centrality of language for example in Sapiens why we need to look carefully into it for construction of a strong AI
is that language is usually understood as some sort of symbolic medium or some sort of social communicative discourse or some sort of syntax regime with some semantic features thrown on top. But no, what we are going to talk about is actually a qualitatively different computational regime behind the picture of language itself, which cannot be decoupled from its interactional infrastructure. And that's why we are talking about the interactive paradigm of computations, semantic of information processing in terms of interaction between processes.
Okay. Reza, do you mind not screen sharing really quickly so we can see you for the last few minutes? Oh, I thought that I... Because right now we just see your screen of whoever you're speaking. Oh, sorry. Sorry. You should just be able to. How do I do this? Sorry, I have no idea about these things. Thank you. It's no problem. Is it? Do you have it? No, we had you before. I saw you for a second, then I went to the screen share. Oh, OK. So now you're back again. Now I have you. Now we're screen sharing again.
Why does it keep going back on a minute? Don't worry about it. We'll figure it out after the next session. Sorry, I'm completely illiterate about this. Yeah, it's quite interesting that it keeps going back. I think if you just click the screen share button on the left, it should just turn it off, right? And it's off. OK, I see you. So any questions, any discussions, any observation, comments, suggestion?
I would just ask what would be sort of the most important things to read for next week? Or just like, because we like covered sort of the whole broad focus of what we'll be doing over the next time? Yes. So what? Sure. Basically, for the next session, I think Ladyman's
what is the complex system is a really good entry text. You can easily find it online. But also, since we are going to talk about the measures, probably not that much because massive amount of material left from today's session. For the measures, computation measures, the text that I forwarded to Tony and Mo, it's called How to Define Complexity in Physics and Why. I think it should be in the Google Classroom. Yeah, if it's not, I'll post it right now.
Yeah, and what is a complex system? You can easily find it online. Sharing the slides from today in the classroom. Also, that would be really helpful. Oh, sure, sure. I think I only missed one of the people you mentioned as being people to look at. Like, I got J.Cole and Kim and Bechtel, but you said Abramsky? Samson Abramsky. Samson? Samson Abramsky, yes. At Oxford?
Yes. Alright, cool. Okay, I guess with that then we could, if nobody has any further questions, we could wrap up. I don't know if I might have just oh no you're back Chris I thought you froze for a second so residue any final comments final comments no but I see that they're so like a few new faces who didn't introduce themselves and didn't give any background information about themselves that would be great if I know more about
you guys okay so that was Jake and Victor and Aaron and also Jessica's around she's here and Juan so we can start with Juan are you there? Juan? Can you speak? Do you have a mic? Okay well Erin do you want to introduce yourself? I'll just go through. Well, I believe I'm not new, but yeah, we've met but to everyone else.
I'm Aaron, I'm in New York. My background is much more intellectual history and political science, so I'm sort of trying to grasp this in an implied way and sort of crash coursing it. So I'm going to throw myself at a lot of introductory material would be helpful also. But yeah, any sort of applied studies I think would be a good guess for me and an interesting place to sort of then kind of like work backwards to the theory. Sure, yeah. Yes, definitely I will talk about, I mean, next session I will talk about, you know, basically this, what I said, you know, that the combination of the hierarchical, you know,
feature of complex systems and also the sensitive dependency create problems and ramifications for modeling. And I will talk about a little bit of, for example, what does it mean for public policy making, these ramifications. Because as I said, these kinds of, especially so fashionable that everyone is saying that everything is complex or we are very conscious of complexity of the situation. But what does that mean really? Especially when you are trying to model complexity, it's not so straightforward. Neither the confirmation of the model nor tracking the behavior of the target system, actual system.
I will talk about these complications next session. Okay, so Jessica, are you available to come in and say a little bit? Yes. Yeah, I'm here. Hi. Hello, how are you? Good, how are you? Thank you for having a great class. I took the New Rationalism class last year, and it had a really, really strong impact on my thinking so that I better do this one as well I so I I guess my and my interest right now is this dynamical system approach I trying to sort out
something that's like an attempt to you take the political ideas that are in there but to really illuminate illuminate them in a more aesthetic sense because for one I'm a musician and composer and working a lot with the voice and text and space so I feel like all of these kind of points I was really happy you brought up the image of the string and hierarchies related to to sound actually I think will be very interesting to to think about but because I'm not well read in these areas I
I take a lot of it on a poetic level and but I am excited to to read a lot of these these suggestions as well and to see see kinda where where that takes me in in writing and in composing and just getting to know know all of you and how you approach these kind of subjects. Excellent. Thank you very much. No, the great thing about this class is that I was more thinking of, you know, and that's why I kind of like started with very, very basic rudimentary, considered to be basic rudimentary in these kinds of technical topics because I assume, you know, that they are diverse
from art, from philosophy, I stick to the kind of approach, trying to keep it at the introductory level, but also with an eye on more nitty-gritty parts of the discussions and arguments. But I'm very glad about diversity, and I'm very glad that there are people among the attendants who are familiar with these or have background in computer science, programming, mathematics, biology. I think Victor, if he's around, if he's the last to introduce himself.
Sure, can you hear me? Yes. I'm Victor, I'm an anthropologist. I'm based in Scotland, soon I'll be starting a postdoc in Denmark, and I do field work in the Amazon in Ecuador, and I'm interested in this for various reasons, partly because complexity, the idea of complexity and complex systems were sort of important about 10 years ago in anthropology in the Amazon. stuff has been written on that by interesting people and trying to understand what it means, what they were trying to do and what that means now. And it's sort of about cognition and sort of about social life.
So some of it is around this. And then I am generally interested. Thank you very much. Thank you. No, I will actually, I mentioned that I will, if the time allows, I will talk about the ecology, modeling climates, modeling basically regional ecologies. And one of the, I think, would be, if you are interested in this, kind of like associations between complexity theory and hierarchical structures and with the kind of climate-oriented anthropological discussions, One of the good books that also I suggested, and I have suggested in the previous session, is William Wimsatt's Reengineering Philosophy for Limited Beings.
It's considered to be a classical text, and it is quite astonishing monument. Cool, I'll have a look. Thank you. Welcome. Okay. Juan doesn't have a microphone, so... Yes, I can see it. Thank you very much. Thank you. Thanks. Thank you. Thank you. Thank you. Goodbye, everyone. Thank you. Bye-bye. Bye.