Re-Discovering Cybernetics

rdcybernetics.md

Re-Discovering Cybernetics

@dicey__'s notes about Cybernetics. Probably mostly just paraphrased, quoted, or jacked as a mnemonic exercise. It's not plagiarism because I'm not writing a paper or an article. These are my notes, this is how I actively read, and they're on the Internet for your potential (but by no means guaranteed) benefit.

Source one: "Cybernetics and Second-Order Cybernetics", Francis Heylighen, Free University of Brussels

Provided Glossary:

Variety: a measure of the number of possible states or actions
Entropy: a probabilistic measure of variety
Self-organization: the spontaneous reduction of entropy in a dynamic system
Control: maintenance of a goal by active compensation of perturbations
Model: a representation of processes in the world that allows predictions Constructivism: the philosophy that models are not passive reflections of reality, but active constructions by the subject

This first document describes the history and foundational ideas of Cybernetics. It starts by defining Cybernetics as "the science that studies the abstract principles of organization in complex systems." It is not concerned with what systems consist of, but instead how they function.

Cybernetics focuses on how systems use information, models, and control actions to steer towards and maintain their goals, while counteracting various disturbances.

It's inherently transdisciplinary, and can be used to help understand, model, and build systems of any sort. Second-order Cybernetics focuses on the role of humans in the construction of models of both systems and of other people in those systems.

Historical Development of Cybernetics

Origins

Cybernetics is derived from Greek kybernetes, or "steersman". It was first used by Plato in Antiquity, and then in the 19th century Ampére picked it up. They both saw it as "the science of effective government." Then Norbert Weiner, a mathematician, wrote a book in 1948 called "Cybernetics, or the study of control and communication in the animal and the machine." This was inspired both by the use of people and machines during wartime and Claude Shannon's attempt to develop a mathematical theory of information. Weiner was trying to develop "a general theory of organizational and control relations in systems.

Information Theory, Control Theory and Control Systems Engineering are now separate disciplines, but Cybernetics remains distinct because it emphasizes both artificial and natural systems -- like societies -- and allows for, particularly in the latter case, the components of a system to set their own goals rather than have them be controlled by the creators.

Cybernetics' status as a specific field of study came from "interdisciplinary meetings" in the late '40s and early '50s that included "a number of noted post-war intellectuals": Weiner, John von Neumann, Warren McCulloch, Claude Shannon, Heinz von Foerster, W. Ross Ashby, Gregory Bateson, and Margaret Mead: "The Macy Conferences on Cybernetics". Soon it expanded from machines and animals to minds (Bateson and Ashby) and social systems (Stafford Beer's management cybernetics) and so rounded itself back towards Plato's "focus on the control relations in society".

In the '50s, Cybernetics "came to cohere with General Systems Theory (GST)", which was founded by Ludwig von Bertalanffy, and there was a view of it as an attempt to build "a unified science by uncovering the common principles that govern open, evolving systems." Cybernetics is more specific than GST, though, since it focuses on "goal-directed, functional systems which have some form of control relation." But in general these are all attempts to deliniate a widely-conceived science of systems.

"Perhaps the most fundamental contribution of cybernetics is its explanation of purposiveness, or goal-directed behavior, an essential characteristic of mind and life, in terms of control and information." Negative feedback control loops which try to achieve and maintain goal states could be models for organisms' autonomy, because while our behavior is purposeful, it's not strictly determined by factors that can be pre-modeled. There is "free will" of some kind. This is maybe where the concept of cybernetics as basically just robotics came from, because cyberneticians hypothesized an analogy between autonomous digital systems and brains.

This paper credits cybernetics with "a crucial influence on the birth of various modern sciences: control theory, computer science, information theory, automata theory, artificial intelligence and artificial neural networks, cognitive science, computer modeling and simulation science, dynamical systems, and artificial life." Concepts like "complexity, self-organization, self-reproduction, autonomy, networks, connectionism, and adaptation" were first explored by cyberneticians during the '40s and '50s. Examples: "von Neumann's computer architectures, game theory, and cellular automata; Ashby's and von Foerster's analysis of self-organization; Braitenberg's autonomous robots; and McCulloch's artificial neural nets, perceptrons, and classifiers."

Second Order Cybernetics

After World War II, the engineering of systems, especially computers, gained enormous importance and attention. Related fields like control engineering and computer science could assume, however, that the system designer is in charge of determining what the system will do -- not the elements of the system themselves, like in other kinds of systems.

So once the computer nerds left the building: "the remaining cyberneticists felt the need to clearly distinguish themselves from these more mechanistic approaches" and began to emphasize "autonomy, self-organization, cognition, and the role of the observer in modelling a system." In the early '70s, this new iteration became known as second-order cybernetics.

Second-order cybernetics is focused on the distinction between systems and the models of them that are constructed, and on the fact that models are almost always purposefully reductive, and meant to focus on the aspects of a system that an observer is interested in. Ultimately there is an incontrovertible distinction between the systems and the models. This, these thinkers felt, separated them from engineers working with a mechanical system, whom may not need to make any such distinction, since they are building a system with total knowledge of its components, from the UI down to the transistor. These engineers can act "as if the model is the system."

Such engineers were considered first-order cyberneticists by the second-order cyberneticists, and the latter group believed that the first-order group would resultantly have a domineering approach to the systems they interacted with, since they were "things" to be "freely observed, manipulated, and taken apart", and not agents in and of themselves. When working with organisms or social systems, a second-order cyberneticist would properly not engage in this way, and instead would recognize the system and its components as agents in their own right.

"As quantum mechanics has taught us," the writer writes, perhaps going a bit too far in his transdisciplinarism, but what do I know?, "observer and observed cannot be separated, and the result of observations will depend on their interaction." The observer is also a cybernetic system, trying to model another cybernetic system! Therefore there needs to be a "cybernetics of cybernetics" or "meta-cybernetics" or "second-order cybernetics".

Criticism

While the second-order folks had pretty relevant and balancing ideas in the face of the new focus on electronics and mechanical systems, their resistance to it "may have led them to over-emphasize the novelty" of their approach. The OG cyberneticists like Ashby, McCulloch and Bateson basically agreed that autonomy and self-organization were important and that modelling needed to be considered to be subjective. So to call them "first-order reductionists" is not correct.

Second: the second-order standard-bearers like von Foerster, Pask, and Maturana, were themselves part of developing "first-order" cybernetics. Overall, the writer believes that the field trended towards these "second-order" ideas, which became embedded in all cybernetics at some level, and so there isn't much of a clean break between the two. So as a result the rest of the article doesn't distinguish between the two approaches, considering cybernetics to encompass both.

The author sees an "ideological fervor" behind the second-order cybernetics movement as also having weakened it a bit because the "irreducible complexity of the various system-observer interactions" and the focus on modelling's subjective nature led many cyberneticists to discard math altogether and limit themselves to philosophical or literary discourses. This overall can look like a snake-eating-its-tail kind of effect, where "observers observing observers observing themselves" fosters a "potentially dangerous detachment from concrete phenomena".

Cybernetics Today

• Not well established as an autonomous discipline
• Few, poorly-organized practitioners
• Few research departments and few academic programs

Reasons for this:

• Intrinsic complexity and abstractness of the subject domain
• Lack of up-to-date textbooks
• Ebb and flow of scientific fashions
• The apparent overreaching of the second-order movement

The writer notes, though, that other similar fields like GST are in a similar position. So maybe the primary issue is that it's difficult to cohere such a broad, interdisciplinary field in the wake of the rapid growth of the spin-off disciplines pertaining to computer science. Basically, when fields grow at different rates and in different directions -- and one could argue, when capitalism finds some but not others interesting to pour effort and resources into -- it's hard to keep such a conglomeration together, as "enthusiasm, funding and practitioners" are sapped from the broader field and focused on the subfields of greatest interest.

So, many of the core ideas have been assimilated by other disciplines, where they've remained influential. Others get lost and then rediscovered periodically. Neural networks are an example of a component of cybernetics that was invented in the '40s, then again in the '60s and late '80s. Autonomy was rediscovered in the '90s. And positive feedback effects in computer systems also was rediscovered in the '90s.

"Perhaps the most significant recent development is the growth of the complex adaptive systems movement, which, in the work of authors such as John Holland, Stuart Kauffman and Brian Arthur and the subfield of artificial life, has used the power of modern computers to simulate and thus experiment with and develop many of the ideas of cybernetics." The writer sees this as the closest thing to a holder of the cybernetics 'banner', given that it applies mathematical modelling to complex systems across disciplines, but it largely ignores the issues of goal-directedness and control.

The abstract analysis of systems as defined by their relations, functions and information flows rather tahn by their concrete material components does, the author feels, pervade the modern concept of 'cyber', but only shallowly, and driven more by fashion than understanding. "It seems likely that as the applications of these technologies become increasingly complex, far-reaching, and abstract, the need will again be felt for an encompassing conceptual framework, such as cybernetics, that can help users and designers alike to understand the meaning of those developments."

Other modern cybernetics-related things

Active cybernetics-focused groups include the Principia Cybernetica Project which is interested in cybernetics as evolutionary theory (they're way into transhumanism, I think) and The American Society for Cybernetics, which are into the second-order thing.

The sociocybernetics movement is specifically concerned with a cybernetic understanding of social systems.

There's also continuing cybernetics-focused research on autopoesis (the ability for a system to maintain and reproduce itself), systems dynamics and control theory, with applications in 'management science' (sounds wack) and psychology. There are also 'scattered research centers' in Central and Eastern Europe devoted to specific technical applications: biological cybernetics, medical cybernetics, and engineering cybernetics, though they end up closer to their fields than to cybernetics as a whole.

General Information Theory has become a search for "formal representations which are not based strictly on classical probability theory." According to Wikipedia this branch directly flows from Shannon's work mentioned earlier.

There has been "significant progress in building a semiotic (the study of signs and symbols) theory of information, where issues of the semantics and meaning of signals are at last being seriously considered." Not totally sure what this means.

Finally, "a number of authors are seriously questioning the limits of mechanism and formalism for interdisciplinary modeling in particular, and science in general". Basically, the question of the difference between systems and our models of them -- and ultimately what are the theoretical limits of our models' ability to help us understand the full complexity of the world -- has risen back to focus for 'a number of authors'.

Relational Concepts

Distinctions and Relations

"In essence, cybernetics is concerned with those properties of systems that are independent of their concrete material or components." That's why it can be applied so broadly to so many different kinds of things. It's interested in 'isomorphisms' between them. By focusing on relations -- how parts of a system function, differ, connect, and transform from one to another -- you can abstract a system from its material constituency without losing its essential properties.

Key questions:

• "How do [a system's] components differ from or connect to each other?"
• "How does the one transform into the other?"

High-level concepts used by cyberneticists to approach these questions:

• order
• organization
• complexity
• hierarchy
• structure
• information
• control

"These concepts are relational in that they allow us to analyze and formally model different abstract properties of systems and their dynamics, for example allowing us to ask such questions as whether complexity tends to increase with time."

Also fundamental to all of these concepts: difference or distinction. Of primary concern is the difference between a phenomenon's presence and absence, and how that relates to other phenomena. (Intersectionality, anyone?) The writer traces this back to Leibnitz and believes this principle is expressed "most succictly" by Bateson, who defined information as "a difference that makes a difference."

Any observer starts by making a distinction between the system being studied and the environment in which it occurs.

Then, you go further by distinguishing between the presence and absence of other various properties (AKA "dimensions or attributes") of the systems.

The example given is that of a billiard ball. Properties of a billiard ball: color, weight, position, momentum. Presence or absence of each property can be represented as a Boolean. G. Spencer Brown's book "Laws of Form" details a calculus and "algebra of distinctions" and shows that this is isomorphic to the less simple traditional Boolean algebra.

Variety and Constraint

You can generalize the binary approach to the concept that a property has multiple discrete or continuous values - what color, how much momentum? "The conjunction of al the values of all the properties that a system at a particular moment has or lacks determines its state." I.e.:

var billiard_ball = {
color: red,
position: x,
momentum: p
}

In general, such variables are neither binary nor independent. Example: a berry can be either small and green or large and red, depending on ripeness -- and this recognizes only two states of size and color. So the variables "color" and "size" are completely dependent on each other, and the variety is really one bit rather than the two you get if you treat the variables separately.

More generally: "If the actual variety of states that the system can exhibit is smaller than the variety of states we can potentially ocnceive, then the system is said to be constrained. Constraint C can be defined as the difference between maximal and actual variety: C = Vmax - V.

Constraint provides a reduction in uncertainty and allows for useful predictions. For example: if the berry is small, we know it's green.

Constraint also allows for the formal modelling of relations, dependencies or couplings between different systems, or aspects of systems. "If you model different systems or different aspects or dimensions of one system together, then the join state space is the Cartesian product of the individual state spaces: S = S1 x S2 x ...Sn." (I don't know what this means, yet). "Constraint on this product space can thus represent the mutual dependency between the states of the subspaces, like in the berry example, where the state in the color space determines the state in the size space, and vice versa."

Entropy and Information

Measuring variety and constraint in more general terms can be measured "by introducing probabilities".

If we don't know the precise state of a system s, but we do know the probability distribution P(s) of values of s, you can express the potential variety through a formula "equivalent to entropy, as defined by Boltzmann for statistical mechanics:

H(P) = -∑P(s).logP(s)"

"H reaches its maximum value if all states are equiprobable, that is, if we have no indication whatsoever to assume that one state is more probable than another state." Therefore entropy would, indeed, equal variety (V). H "expresses our uncertainty or ignorance about the system's state". So H = 0 "if and only if the probability of a certain state is 1 (and of all other states 0)," in which case we already know what the state of the system is.

Constraint is that which reduces uncertainty -- "the difference between maximal and actual uncertainty" -- and can be interpreted in a different way -- as information -- and "historically H was introduced by Shannon as a measure of the capacity for information transmission of a communication channel." (So uncertainty is inversely proportional, somehow, to information? That would seem to make sense.) "The information I we receive from an observation is equal to the degree to which uncertainty is reduced: I = H(before) - H(after)." If H(after) = 0, then I reduces to the initial uncertainty/entropy.

Shannon, the author writes, later stopped using "information" to describe this measure because it's "purely syntactic" and ignores the "meaning" of the signal. Still, his theory came to be known as Information Theory. "H has been vigorously pursued as a measure for a number of higher-order relational concepts, including complexity and organization." Entropies, their correlates, and correlates to "such important results as Shannon's 10th Theorem and the Second Law of Thermodynamics have been sought in biology, ecology, psychology, sociology, and economics."

The author also notes that there are other methods of "weighting the state of a system" that don't adhere to the requirement that the sum of the probabilities must be 1. "These methods, involving concepts from fuzzy systems theory and possibility theory lead to alternative information theories". When taken together with probability theory, they are called Generalized Information Theory (GIT). These methods are "under development" however, and so a probabilistic approach to information theory "still dominates applications".

Modelling Dynamics

Once you have such static descriptions of systems, then you can model how their dynamics work and how their components interact.

"Any process or change in a system's state can be represented as a transformation: T: S -> S: s(t) -> s(t+1)."

T is a function that is one-to-one or many-to-one, "meaning that an initial state s(t) is always mapped onto a single state s(t+1)." (Ennh?) "Change can be represented more generally as a relation R ⊂ S x S, thus allowing the modelling of "one-to-many" or "many-to-many" transformations, where the same initial state can lead to different final states."

"Switching from states s to probability distributions P(s) allows us to again represent such indeterministic processes by a function: M: P(s, t) -> P(s, t+1). M is a stochastic process, or more precisely, a Markov chain, which can be represented by a matrix of transition probabilities: P(s_j(t+1)|s_i (t)) = M_ij ∈ [0, 1].

(WTF? Reminding myself, this is an equation that is supposed to model dynamics. ToDo: substitution for this, with something I understand).

Having these representations of "process", we can now study the "dynamics of variety" which is a central theme of cybernetics.

• "A one-to-one transformation will conserve all distinctions between states and therefore the variety, uncertainty or information."
• "Similarly, a many-to-one mapping will erase distinctions, and thus reduce variety..."
• "... while an indeterministic one-to-many mapping will increase variety and thus uncertainty."
• "With a general many-to-many mapping, as represented by a Markov process, variety can increase or decrease, depending on the initial probability distribution and the structure of the transition matrix. For example, a distribution with variety 0 cannot decrease in variety and will in general increase, while a distribution with maximum variety will in general decrease." Apparently there's more explanation of some special cases for "this most general of transformations" later to come.

"With some small extensions, this dynamical representation can be used to model the interactions between systems."

• "A system A affects a system B if the state of B at time t+1 is dependent on A at the state of time t-1."
  • "This can be represented as a transformation: T: S_A X S_B -> S_B: (s_A(t), s_B(t)) → s_B(t+1). S_A here plays the role of the input of B."
• "In general, B will not only be affected by an outside system A, but in turn affect another (or the same) system C."
• "This can be represented by another transformation T¹: S_A × S_B → S_C : (s_A(t), s_B(t)) → s_C(t+1). S_C here plays the role of the output of B."

The outside observer would view B as a process that transforms input into output. If we don't know what the states of B are, and therefore precisely what T and T¹ look like, B is a black box. You can try to figure out what's inside the black box by experimenting with the sequences of inputs (S_A(t), S_A(t+1), S_A(t+2), etc) and observing the sequence of outputs. "In many cases, the observer can determine a state space S_B so that both transformations become deterministic, without being able to directly observe the properties or components of _B." (Is it just me or is that basically the basis of social science? Or at least a very common form of it. "This -> this. Don't know why, but, this -> this. Here are some possible reasons why based on variations on This and this, even though we don't know why, really.")

The writer says this approach is extended to become a full "theory of automata and computing machines" and is "the foundation of most modern computer science." It again illustrates how cybernetic modelling can produce useful predictions via modelling relationships without needing to know the physical components of the system.

Circular Processes

Versus classical, "Newtonian" science, wherein cause -> effect in a linear sequence, cybernetics is interested in processes where cause -> effect -> cause. Circularity is hard for science to deal with and leads to "deep conceptual problems such as the logical paradoxes of self-reference".

Self-Application

Algebraically, circularity is an equation in which some variable or phenomenon is mapped by a function f onto itself:

y = f(y)

Depending on what these variables actually stand for, we can "distinguish different types of circularities." (IOW (I think) the substance of the particular circularity is contained in y and f, which is kind of obvious but maybe worth noting.)

Example given: y is an image, and f is a camera. "y = f(y) would then represent the situation where the camera points at the image shown on the monitor. The image is both the cause and effect of the process; it is both the object and the representation of the object." (Really? Doesn't each y constitute a separate cause, as it is an image containing all the prior images y_n? It's still sort of true, but.) Writer notes that this produces a variety of abstract visual patterns with a lot of complexity.

"In discrete form", the equation changes to y_t+1 = f(y_t+1) -- ok yeah that's what I was saying. "Such equations have been extensively studied as iterated maps and are the basis of chaotic dynamics and fractal geometry." Of course, OK.

Another variation, apparently fundamental to quantum mechanics and linear algebra:

ky = f(y)

k = a real or complex number that is an eigenvalue of f, and y is an eigenstate. Um. The equation here reduces to the more simple statement above if k = 1 (obviously) or if y "is only defined up to a constant factor." Um. " If k = exp (2πi m/n), then fⁿ(y) is again y." Um. "Thus, imaginary eigenvalues can be used to model periodic processes, where a system returns to the same state after passing through n intermediate states."

Gonna need to come back to that whole paragraph. Periodic processes are important.

"An example of such periodocity": the self-referential statement (liar's paradox) "this statement is false." If you assume it's true, it must be false. If we assume it's false, it must be true. Therefore the value can be seen as actually oscillating between the two states -- basically it has the boolean equivalent of an imaginary value. "Using Spencer Brown's calculus of distinctions, Varela has proposed a similar solution to the problem of self-referential statements." OK.

Self-Organization

y ∈ S

This, the author writes, is an equation representing "the most direct application of circularity" where S is a state space and f is the transforming function. (I don't see f). Referring to the prior formula ( ky = f(y) ), it then "states that y is a fixpoint of the function f, or an equilibrium or absorbing state of the dynamic system: if the system reaches state y, it will stop changing."

"This can be generalized to the situation where y stands for a subset of the state space, y ⊂ S. Then, every state of this subset is sent to another state of this subspace: ∀ x∈ y: f(x) ∈ y. Assuming y has no smaller subset with the same property, this means that y is an attractor of the dynamics." Dynamics systems studies attractors in general. Atttractors can have any type of shape or dimension, including 0-dimensional (equilibrium), 1-dimensional (a limit cycle where the system goes through the same sequence of states), and fractal (a "strange" attractor).

"An attractor y is in general surrounded by a basin B(y): a set of states outside y whose evolution necessarily ends up inside ∀ s ∈ B(y), s ∉ y, ∃ n such that fⁿ(s) ∈ y. In a deterministic system every state either belongs to an attractor or to a basin. In a stochastic system there is a third category of states that can end up in either of several attractors. Once a system has entered an attractor, it can no longer reach states outside of the attractor." Therefore the uncertainty (H) about the state has decreased and we know for sure that it's not any state that that's not part of the attractor. This is self-organization -- a spontaneous reduction of entropy (or, "equivalently," an increase in order/constraint).

The claim then is that every dynamical system that has attractors will eventually end up in one of them, losing its freedom to inhabit any other state. This is Ashby's Principle of Self-Organization (sounds also kind of like Murphy's Law, no?) Ashby also noted that if the system is made up of subsystems, the self-organizational constraint implies that the subsystems have become mutually adapted (since they together reach some form of equilibrium).

Example: magnetization. An assembly of magnetic spins with initially maximum entropy end up all being aligned in the same direction (minimum entropy, "or mutual adaptation"). Von Foerster added that self-organization can be enhanced through random perturbations ("noise") of the system's state, which speed up the descent of the system through the basin, and makes it leave "shallow attractors" so that it can reach deeper ones -- the order from noise principle.

Closure

You can extend the "attractor" case to one wherein y stands for "a complete state space". Now, y = f(y) represents the situation where every state of y is mapped onto another state of y by f. (I don't yet understand how this differs from the initial case described upon introducing this equation...?)

"More generally", f could be a "group of transformations" rather than just one.

"If f represents the possible dynamics of the system with state space y, under different values of external parameters, then we can say that the system is organizationally closed" -- it won't vary under any possible dynamical transformation. This requirement of closure is "implicit in traditional mathematical models of systems" -- i.e., the model encompasses all possible states, I think, so that no transformation changes the range of possible states y. All states y will fit into the range of states y.

But cybernetics views closure as a potentially ambiguous state -- a system could be open and closed simultaneously for different kinds of f(). By looking at all the fs however, you should be able to identify the system unambiguously and still make explicit what is inside and what is outside the system.

Self-organization, then, is a way for a system to move towards this concept of closure. If the system is in an attractor subspace, then closure is achieved, as the range of states is unambiguously definable.

Another way to achieve closure is to "expand the state space y into a larger set y* so that y* recursively encompasses all images through f of elements of y: ∀ x ∈ y: x ∈ y* ; ∀ x' ∈ y* : f(x') ∈ y*." Apparently this is "the traditional definition of a set * through recursion," as we frequently see in programming to generate the elements of set y* by iteratively applying transformations to all elements of a starting set y.

Autopoiesis ("self-production") is "a more complex example of closure". This is when a system is able to recursively reproduce its own network of components, thus continuously regenerating and restoring its essential organization. Note: "such organizational closure is not the same as thermodynamic closure"; the autopoetic system can exchange energy and matter with its environment, but it autonomously handles the organization of those resources and of that process. Maturana and Varela have postulated autopoiesis to be the defining characteristic of so-called living systems. Self-reproduction in life can be seen as a special case of autopoiesis (where the system builds another copy rather than restoring itself). "Both reproduction and autopoiesis are likely to have evolved from an autocatalytic cycle". That's "an organizationally closed cycle of chemical processes such that the production of every molecule participating in the cycle is catalyzed by another molecule in the cycle."

Feedback Cycles

In addition to "looking directly at state y" you can look at the deviation ∆y = (y - y₀) for a given state y₀, "and at the "feedback" relations through which the deviation depends on itself". This could be represented ("in the simplest case") as:

∆y(t+∆t ) = k ∆y(t).

"According to the sign of the dependency k, two special cases can be distinguished:"

• "If a positive deviation at time t" -- an increase versus y_0</sub -- "leads to a negative deviation" (versus *y₀) in the next step, the feedback is negative (so k < 0). "In such cases any deviation will end up being suppressed and the system will spontaneously return to equilibrium." So y₀ would be a stable equilibrium, resistant to (these) pressures.

• Example: more rabbits eat more grass, leaving less grass to feed rabbits. Therefore an increase in rabbits -> decrease in grass -> decrease in rabbits. Conversely, a decrease in rabbits -> an increase in grass -> an increase in rabbits.

• "Negative feedback is ubiquitous as a control mechanism in machines of all sorts, in organisms (for example in homeostasis and the insulin cycle), in ecosystems, and in the supply/demand balance in economics."

• The opposite situation: positive feedback, when an increase leads to an increase. (Or, by inverted measurement, a decrease leads to a decrease).

• Example: a virus spreads, and the more it spreads, the more it spreads.

• "An equilibrium state surrounded by positive feedback is necessarily unstable." I.e. "no one infected" is unstable because if one person becomes infected, it will spread.

• "Positive feedbacks produce a runaway, explosive growth, which will only come to a halt when the necessary resources have been completely exhausted". (The virus spreads until it everyone is infected).

• Other examples: arms races, snowball effects, increasing returns in economics, chain reactions leading to nuclear war.

• While negative feedback is the essential condition for stability, positive feedbacks are responsible for growth, self-organization, and the amplification of weak signals. In complex, hierarchical systems, higher-level negative feedbacks typically constrain the growth of lower-level positive feedbacks.

You can generalize the concepts of positive and negative feedbacks to networks of multiple causal relations. A causal link between two variables (A-> B) is positive if an increase in A produces an increase in B, and vice versa. It's negative if an increase produces a decrease.

Each loop in a causal network can be given an overall sign by multiplying the signs (+ or -) of each link. That way we can determine whether each loop will produce either stabilization (negative feedback) or a runaway process (positive feedback). Also, need to take into account any lag between cause and effect. Example of rabbits, the increase happens several weeks after grass increases. "Such delays may lead to an oscillation, or limit cycle, around the equilibrium value."

System Dynamics studies these interlocking loops of positive and negative feedback in a broad array of areas, including biological, social, economic and psychological systems. "Limits to Growth" is a good example of this field, as are games like SimCity and the application Stella.

Goal-Directedness and Control

Goal-Directedness

This is the most important innovation of cybernetics, the writer says: its explanation of goal-directedness or purpose.

Autonomy can be defined as "the pursual of own goals, resisting obstructions from the environment that would make [a system] deviate from its preferred state of affairs."

So goal-directedness implies the ability to regulate perturbations effected by the environment.

Example: a thermostat. Setting defines goal state. Thermostat's job is to minimize effects of perturbations (temperature up/down from environment).

"Basic goal of an autonomous or autopoietic system: survival," or "maintenance of its essential organization." Natural selection, the writer opines, has built this goal of survival into all living systems -- as those not focused on survival were eliminated. The system will have secondary goals -- food, clothes, medicine -- that indirectly contribute to its survival. Artificial systems (like thermostats) "are not autonomous -- their goals are constructed by their designers. They are allopoietic -- meant to produce something other ("allo") than themselves."

"So, goal-directedness can be understood most simply as a suppression of deviations from an invariant goal state." A goal is therefore akin to a stable equilibrium, to which a system returns after a perturbation.

Goal-directedness and stability both have equifinality -- different initial states lead to the same final state, reducing variety/entropy/H. The difference between the two "is that a stable system automatically returns to" equilibrium without performing work or effort. A goal-directed system has to intervene to maintain/achieve its goal.

Is control "conservative"? It does resist "all departures from a preferred state. But the net effect can be dynamic or progressive depending on the complexity of the goal." If the goal is a moving target, suppressing deviation from it means constant change.

A goal can also be a range of states or a subset of the acceptable states - like an attractor. The defining dimensions of these states are essential variables and they must be kept within a limited range compatible with the system's survival.

• Example: a person's body temperature must be kept within a range of approximately 35-40 degrees C. "Even more generally, the goal can be seen as a gradient, or 'fitness' function defined on state space, which defines the degree of "value" or "preference" of one state relative to another. In the latter case, the problem of control becomes one of on-going optimization or maximization of fitness.

Mechanisms of Control

Perturbations can come from inside or outside, but the responses to them functionally are the same.

Three fundamental mechanisms to achieve regulation needed to block their effect on the system's essential variables:

1. Buffering
2. Feedback
3. Feed-forward

(There's a helpful graphic here, and the tooltip is also helpful: in each case, the effectof disturbances D on the essential variables E is reduced,either by a passive buffer B, or a regulator R.)

Feedback and feedforward "both require action" on part of the system to implement -- to compensate for whatever fluctuation is being addressed. I.e.: thermostat acts to counteract drop in temperature by switching on the furnace.

Feedforward:

• will suppress the disturbance before it has had a chance to affect system's essential components/variables
• requires capacity to anticipate the effect a perturbation would have and then correct for it. (OTherwise the system lacks ability to recognize a perturbation or prevent it having an effect).
• So, you need a way to gather early information about fluctuations and then process them.
• Example: apply it to thermostat situation by putting temperature sensor outside of the area being thermostatically-controlled, so that it knows what the environment's effects might be and can prevent them from happening at all.
• Sometimes this is hard to implement or unreliable, because "no sensor or anticipation can ever provide complete information about the future effects of an infinite variety of possible perturbations, and therefore feedforward control is bound to make mistakes." If the system is good, might only be a few mistakes, but eventually the mistakes will accumulate and it will destroy the system.

Feedback:

• The only good way to avoid this accumulation of errors
• Means to compensate for a deviation from a goal after it has happened.
• Also called "error-controlled regulation" since the error determines the control action (like a thermostat in-room reacting to temperature change).
• Disadvantage is it must first allow error to appear before action can be taken; otherwise won't know what action to take
• Therefore by definition imperfect, whereas feedforward could in principle, but not in practice, be made error-free.
• Can still be very effective due to continuity: deviations don't usually appear all at once; they tend to increase slowly, so you can intervene without the effects having already become a problem (again, think about a thermostat)
• Explains why feedforward is still seen as necessary when a perturbation is discontinuous or sudden -- i.e., if someone is pointing a gun at you, you should probably move rather than wait for a bullet to be headed your way before acting.

The Law of Requisite Variety

So, variety: control or regulation is basically a reduction of it.

The system has a range of optimal states. Perturbations with high variety threaten to move the system outside of this range. So you use control or regulation to prevent the transmission of variety from environment to system. This is the opposite of information transmission, where the purpose is to maximally conserve variety. (should come back to that)

Feedback/feedforward requires each disturbance D to be compensated for with a counteraction from the regulator R (a la that graphic above). R needs to be at least as flexible as D, in terms of possible situations -- if R would react the same way to two different disturbances, you'd end up with two different outcomes, so that's not optimal. "If we moreover take into account the constant reduction of variety K due to buffering, it looks like this:"

V(E) ≥ V(D) - V(R) - K

Ashby calls this the law of requisite variety: "in active regulation only variety can destroy variety." This leads to counterintuitive observation that the regulator must have a sufficiently large variety of actions in order to ensure a sufficiently small variety of outcomes in the essential variables (E). Important practical implications of this: "since the variety of perturbations a system can potentially be confronted with is unlimited, we should always try to maximize its internal variety (or diversity) so as to be optimally prepared for any foreseeable or unforeseeable contingency."

Components of a Control System

Zooming in a bit to CONCRETE components of a control system (yay), i.e. a thermostat, complex organism or organization.

These units are functional rather than structural -- as per usual with cybernetics.

Overall: it's a feedback cycle with two inputs: the goal (i.e. the preferred values of system variables) and disturbances (the processes that are not under the system's control but can affect these variables).

1. The system observes variables it needs to control to maintain its preferred state.
2. This perception creates an internal representation of the outside sitch, which is then processed to determine:
3. In what way it may affect the goal
4. What the best reaction is to safeguard that goal.
5. Having determined the appropriate course of action vis a vis the environment, action is taken, affecting the environment and its own complex equilibrium. This affects the variables the system observes to try to maintain its own equilibrium.
6. The change is re-measured, and these steps loop: "interpretation, decision and action". Thus the loop is closed.

Within this scheme might be buffering, feedforward and feedback regulation. "Buffering is implicit in the dynamics, which determines to what degree disturbances affect the observed variables."

Observed variables:

• Must include the variables the system wants to keep under control with feedback in order to avoid error accumulation
• Should also include non-essential variables to function as early-warning signals for anticipated disturbances, which allows implementing feedforward regulation.

The scheme can be as simple or complex as is needed. Example: thermostat:

• simply perceives one variable (temperature),
• has one goal (desired temperature),
• processes one piece of information (whether the temperature is less than the target),
• then acts or does not act on the one controlled variable, the temperature, by applying (or not applying) heat.

So the affected variable is the amount of heat in the room, the disturbance is the amount of heat exchanged with the outside, the dynamics is the process by which inside heating and heat exchange with the outside determine inside temperature.

A more complex example: a board of directors:

• Goal: maximize long term revenue
• Actions: initiatives like publicity campaigns, hiring managers, starting up production, saving on administrative costs
• Environmental disturbances: economy, competitive actors, client needs.
• Together these effect success, defined by variables like # of orders, working costs, production backlog, reputation, etc.

"The board, as a control system, will interpret each of these variables with reference to their goal of maximizing profits and decide about actions to correct any deviation from preferred course."

Note: the control loop is totally symmetric. If you rotate it 180 degrees, environment becomes system, disturbance becomes goal, vice versa. Therefore "the scheme could also be interpreted as two interacting systems, each of which tries to impose its goal upon the other." If they are incompatible, it's model of conflict/competition; otherwise, it could settle into a mutually happymaking equilibrium.

BUT: "In control we generally mean to imply that one system is more powerful than the other one, capable of suppressing any attempt by the other system to impose its preferences." WOAH. "To achieve this, an asymmetry must be built into the control loop: the actions of the system (controller) must have more effect on the state of the environment (controlled) than the other way around".

"This can also be viewed as an amplification of the signal travelling through the control system: weak perceptual signals, carrying info but almost no energy, lead to powerful actons, carrying plenty of energy." This can be achieved by weakening the influence of the environment (by e.g. buffering its actions) and by strengthening the actions of the system (e.g. by providing it with a poewrful energy source). Example of thermostat:

• Walls provide insulation from outside perturbations
• Fuel supply provides capacity to generate heat

Without these two, you can't have a thermostat, because the power dynamic would be flipped. "The same requirements applied to the first living cells, which needed a protective membrane to buffer disturbances, and a food supply for energy."

Control Hierarchies

Claim: "in a complex control system like an organism or organization, goals are typically arranged in a hierarchy -- higher-level goals control the settings for the subsidiary goals." Example is a human being -- you want to survive (primary goal), so you need to maintain your level of hydration, which means that occasionally you need to set a goal of drinking a glass of water. New goal: bring glass to lips. Also involved: don't spill the water, don't smash the glass into your teeth, don't let it get up your nose.

This figure represents "such hierarchical control":

One goal is now seen as a result of an action meant to achieve another goal. Thermostat: has higher-order goal of keeping climate comfortable; you could suboordinate it to a higher goal of not wasting energy. (I.e., use a motion sensor to determine whether people are present, and set to a lower temp.)

"Such control layers can be added arbitrarily by making the goal at level n dependent on the action at level n+1."

Control loops can reduce variation but not eliminate it -- you can layer them to try to eliminate whatever variety is left, tho. The number of layers depends on the efficacy of each, which may reflect limits on the efficacy of your means of control. This is Aulin's law of requisite hierarchy. The weaker your control, the more control hierarchy is needed. BUT increasing the layers of control has a negative effect on the regulatory ability because each layer the "perception" and "action" signals have to go through introduces noise and corruption and delays. (Woah, bureaucracy.) The present trend toward the flattening of hierarchies can be explained by the increasing regulatory abilities of individuals and organizations, due to better education, management, and technological support <-- !!

But if variety gets too great for the current regulation, a higher control level must appear to hold shit down. Valentin Turchin: this is a metasystem transition. He proposed it as a basic unit ("quantum") of cybernetic evolution -- basically he said this is the engine of all evolution and progress. The writer puts it thusly:

"It is responsible for the increasing functional complexity which characterizes such fundamental developments as the origin of life, multicellular organisms, the nervous system, learning, and human culture."

Cognition

Requisite Knowledge

Not only does the regulator have to be capable, it also needs to make the right decision about what to do. The writer maps it thus:

function: D->R

D being disturbance and R being the "appropriate action that will suppress it." So for thermostat:

function: "temp too low" -> "apply heat"

function: "temp high enough" -> "do not heat"

Or:

if condition (perceived disturbance), then action.

This knowledge gets embodied in lots of ways:

• specific designs of artificial systems
• genes in organisms
• culture in humans
• learned connections in neurons

If you don't know, you go the naive approach, until you chance upon a fix. The more potential disturbances, the harder to find the right one via random search, the lower the system's chances of perpetuating itself. So you need more knowledge if there is more variety: this is the law of requisite knowledge. Since all living organisms are also control systems, life therefore implies knowledgE.

IRL in complex control systems the most common action is an educated guess with a good chance of being correct, but no guarantees. Feedback can help correct any errors before crisis. Therefore goal-seeking activity is pretty much heuristic problem solving.

There's a formula for heuristic knowledge -- it's the conditional uncertainty of an action from R, given a disturbance in D: H(R|D). (This is like the first equation with H up above but instead you use P(r|d)).

H(R|D) = 0

...represents complete knowledge / no uncertainty; action is completely determined by the disturbance.

H(R|D) = H(R)

...represents complete ignorance. Aulin shows that you can extend the law of requiste variety to include knowledge vs ignorance by using conditional uncertainty expression ("which remained implicit in Ashby's non-probabilistic formulation of the law"):

H(E) ≥ H(D) + H(R|D) – H(R) – K

This says that the variety in the "essential variables" ( H(E) ) is at least as much as: the possible disturbances to those variables, PLUS the possible disturbances that can result from the actions chosen, MINUS the actual desired effect of your actions to limit the disturbances, MINUS whatever margin of erro?. So you can reduce H(E) by:

• increasing margin of error (buffering K),
• increasing capability to act ("variety of action H(R)"),
• decreasing the uncertainty about the right action ("variety of possible right actions, H(R|D").

The Modelling Relation

Implicitly, the goal figures into the D->R function since a different goal would possibly have a different reaction to the same situation.

A lot of knowledge is independent of goals, though. "Scientific" or "objective" knowledge would be two examples, allegedly. This is important in a system that is higher-order and can vary its goals, because you might want to make predictions in addition to dealing with stuff that happens. Based on predicting outcomes, you can choose better secondary goals.

Modelling this "understanding of knowledge", now. New concept: endo-models: models within systems. Before we were talking about exo-models -- models of systems. This is an endo-model -- a magnification of the feedforward part of the general control system described in Fig 2 -- disincluding the goals, disturbances, and actions.

A model starts with:

• A system to be modeled. Here it's the "world".
• State space W = {w_i}
• Dynamics: F_a: W->W -- these represent the "temporal evolution of the world," similar to Fig. 2, possibly under influence of action a of the system.
• The model itself,
• Internal model states (representations of the world states): R = {r_j}
• A modeling function (i.e. "a set of prediction rules") M_a: R->R.
• They are coupled by a perception function P: W->R. "This maps the states of the world onto their representations in the model."
• A prediction M_a is a success if it correctly predicts what happens to representation R under influence of action a. "This means the predicted state of the model r₂, which equals M_a(r₁) and equals M_a(P(w₁)) *"must be equal to the state of the model created by perceiving the actiual state of the world w₂ after process F_a: r₂ = P(w₂) = P(F_a(w₁)). Therefore, P(F_a) = M_a(P)." IOW: The perception of the result of the function of change should equal the model's expected outcome of the change.

P, M_a, and F_a must commute for M to be a good model to predict the behavior of the world W.

"The overall system can be viewed as a homomorphic mapping" from states of W to states of M, so that the evolution is preserved in both.

"In a sense, even the more primitive 'condition-action' rules discussed above can be interpreted as a kind of homomorphic mapping from the events ('disturbances') in the world to the actions taken by the control system." This is established in Conant / Ashby's 'classic paper' "Every good regulator of a system must be a model of that system." ("Our understanding of 'model' here is more refined," assumes control system can consider various predicted states M_a(r₁) without actually excuting an action a. "This recovers the sense of a model as a representation, as used in section I.B and in science in general, in which observations are used merely to confirm or falsify predictions, while as much as possible avoiding interventions in the phenomenon that is modelled."

A note about epistemology implied here, or "philosophy of knowledge". It might seem that defining a model as a homomorphic mapping of the world implies an "objective correspondence" between objects in the world and their representation as modeled. This leads to "naive realism", or the idea that true knowledge is a perfect reflection of reality independent of the observer. BUT this homomorphism doesn't claim any objective structure of the world -- just the type and order of phenomena that it perceives. A cybernetic system only perceives that which points to potential disturbances of its own goals. Therefore it's intrinsically subjective. It doesn't care about or even have access to the "objective" whole of reality; the outside world only affects the model is in verifying or falsifying its predictions. Since an inaccurate prediction entails poor control, it's a signal to fix the model.

Learning and Model-Building

"Cybernetic epistemology is in essence constructivist: knowledge cannot be passively absorbed from the environment; it must be actively constructed by the system itself." The environment doesn't disprove your models for you; you have that job, in that you must build the model and the apparatus to perceive its correctness. "The environment does not instruct or "in-form" the system, it merely weeds out models that are inadequate, by killing or punishing the system that uses them. At the most basic level, model-building takes place by variation-and-selection or trial-and-error."

Example: a primitive acquatic organism, basically a slightly more sophisticated thermostat. In order to survive, it needs to remain in the right temperature zone to maintain a comfortable temperature, so it has to adjust its depth up and down as appropriate.

• Its perception is a single temperature variable with 3 states X = {too hot, too cold, just right}.
• Its variety of action consists of 3 states Y= {go up, go down, do nothing}.
• Its control knowledge is a set of perception-action pairs, or a function f: X->Y. There are 3³ = 27 possible such functions but "the only optimal one consists of the rules too hot-> go down, too cold -> go up, and just right -> do nothing. The last one could possibly be replaced by either just right->go up or just right->go down," which uses more energy but would still keep organism in a negative feedback loop around the ideal location. All 24 other possible combinations of rules would disrupt this stabilizing feedback, resulting in a runaway behavior that will eventually kill the organism.

Let's say these functions are encoded in genes. Every mutation that produces one of the 24 runaway settings is eliminated by natural selection. "The three negative feedback combinations will initially all remain but" the most energy-efficient will take over eventually. Thus: internal variation of the control rules plus natural selection by the envrionment eventually results in a workable model.

The environment didn't instruct the organism, the organism had to find our for itself. Simple with 27 architectures, but much more complex with more complex organism! Millions of possible models, astronomical variation space. Environment doesn't give specific enough feedback to deal with all of them. So the burden of developing an adequate model is largely on the system itself and will need to rely on "various internal heuristics, combinations of pre-existing components, and subjective selection criteria" to efficiently construct models that are likely to work.

Natural selection is wasteful process for developing knowledge, tho it is source of most knowledge in genes. Higher organisms have developed a more efficient way to construct models: learning!

"In learning, different rules compete with each other within the same organism's control structure." If you do the right thing to achieve your goal, you get rewarded. The things that get the most reinforcement come to dominate the less successful ones. "This can be seen as an application of control at the metalevel, or a metasystem transition," as goal of the model being correct develops, and then the actions taken involve varying the model.

Formalisms to model this process -- Ashby's homeostat, which searched not an option of actions but a choice of sets of disturbance->action rules. Newer methods: neural networks and genetic algorithms.

In genetic algorithms rules vary randomly and incontinuously. Operators: mutation, recombination.

In neural networks rules are "represented by continuously varying connections between nodes corresponding to sensors, effectors and intermediate cognitive structures".

These models originated in cybernetics but have grown into independent specialties: "machine learning" and "knowledge discovery".

Constructivist Epistemology

"The broad view espoused by cyberneticists is that living systems are complex, adaptive control systems engaged in circular relations with their environments." Therefore epistemology (and philosophy) is a natural fit for cyberneticists, as we're dealing with the nature of life, mind, society, etc.

Systems have no access to how the world really is -- just perceptions -- so models are subjective constructions, not objective reflections. Still, our perceptions basically are our environments, as far as our 'knowing systems' are concerned. Perception and hallucination are both patterns of neural activation. To avoid solopsism (inability to distinguish self-generated ideas (dreams, imagination) from perceptions -- complete relativism where all models are as valid as any other -- the requirements are coherence and invariance.

• No observation can prove truth of model, but observations and models can mutually confirm each other, increasing joint reliability
• The more coherent an idea is with other info, the more reliable it is.
• Percepts vary less between observations. I.e., an object can be seen as the aspect of a perception that does not change when POV shifts. Von Foester: "An object is an eigenstate of a cognitive transformation."
• There should also be invariance over observers, hence "reality" of consensus view. "The social construction of reality". Gordon Pask: Conversation Theory is a sophisticated model of how "conversational" interaction ends in agreement over shared meaning.

Constructivism also implies that observers who construct models must also be a part of the model for it to be complete. This is particularly the case if the model-building is affecting the phenomenon being modelled, like if observing perturbs it (as in quantum measurement) or the "observer effect" in social science. Also if the predictions from model can perturb the phenomenon. Examples: self-fulfilling prophecies, where models of systems are applied in steering them, which changes that system and invalidates the model.

Practical illustration: "complexity theorist" Brian Arthur simulated seeming chaos of stock markets by programming agents to continuously model the future behavior of their own system, and to use them as the basis for their own actions. This cancels out their models, and the system becomes intrinsically unpredictable.

To minimize this, you construct a metamodel which represents possible models and how they might affect the observers and the phenomena they observe.

Umpleby: one dimension of metamodel might be degree to which observation affects the phenomenon -- observer independence at 1, quantum observation at 10.

But the metamodel is still a model, so it must represent itself! Basic self-reference. Lars Lofgren: principle of linguistic complementarity, implying all self-reference must be partial -- a model can't completely represent the process by which its representations are connected to the phenomena it describes.

This means no model or metamodel can ever be complete, but a metamodel still proposes a much richer and more flexible method to arrive at predictionsor to solve problems than any specific object model. "Cybernetics as a whole could be defined as an attempt to build a universal metamodel, that would help us to build concrete object models for any specific system or situation."