Notes on The Good Regulator Theorem:

In today’s post, I am looking at the Conant-Ashby theorem, “The Good Regulator Theorem”, named after Roger C. Conant and W. Ross Ashby. Ashby is one of the pioneers of the Cybernetics movement. This theorem states that:

Every good regulator of a system must be a model of that system.

A really good version of this theorem comes from Daniel L. Scholten, who says – Every good key must be a model of the lock it opens. The key must match the lock in order for it to open it. As Conant and Ashby put it:

Any regulator that is maximally both successful and simple must be isomorphic with the system being regulated… Making a model is thus necessary. The theorem has the interesting corollary that the living brain, so far as it is to be successful and efficient as a regulator for survival, must proceed, in learning, by the formation of a model (or models) of its environment.

The one to one relationship (isomorphism) is between the desired states of the system being controlled and the states that can be achieved by the regulator controlling the system. If we are to successfully manage a situation, we should have a model of the situation in our mind. The need to create a model is to identify the essential variables that we have to manipulate in order to get the desired results. Let’s consider an agent (person of interest who is doing the regulation) in an environment. In Cybernetics terms, the agent has less variety than the environment. In order to stay viable in the environment, the agent has to have a model of the environment so that the variety of the environment can be successfully met with.

One of Ashby’s examples is that of a swordsman (agent). The swordsman has to counter every attack that the opponent is making. For that to happen, the swordsman has to anticipate the opponent’s move. In other words, the swordsman has to have a model of the opponent – the moves they might make, their strengths and weaknesses etc. Some points to consider here is that the swordsman does not need an exact model of the opponent since that will be too much variety to handle. Thus, the swordsman only cares about certain states of the opponent and ignores the rest of the states that are not useful for his survival. In Cybernetics terms, this is termed as attenuating or filtering unwanted variety. When the swordsman is able to match the selected variables or states of the opponent, he is able to survive. What the opponent does next is the information that the swordsman really wants. The uncertainty is best reduced when the internal model matches the opponent. This is also how Conant and Ashby set out to prove their theory out. They identified that the entropy is reduced maximally when there is a one-to-one relationship between the possible states of the regulator and the selected states of the system.

An important point to keep in mind here is that the ability to generate a successful model depends entirely on the swordsman or the agent or the observer. If the swordsman is not able to distinguish the key states of the opponent, then the model will not have the required variety to aid the swordsman to survive the attack. This is also another theorem or law that Ashby is famous for called, “the law of requisite variety”. This says that only variety can absorb variety.

This also leads to one more important point to keep in mind – the agent has to consider himself or herself in the model. This is an important aspect for the agent to keep learning. This self-reflexivity is very well addressed in the second order cybernetics or the study of observing systems, as the great Heinz von Foerster put it. The notion of self-reference is generally frowned upon in logic. But the notion of self-reference/circularity is the backbone of second order cybernetics. Second order cybernetics points out that an objective access to the external world is not possible. What we have access to is the world as perceived by our perceptual network. We construct a world based on this and we react to it. This idea is very much like the great philosopher Immanuel Kant’s idea of Noumena and Phenomena. Kant said that we do not have access to the real world out there, which he called as the Noumena. What we have access to is the perceived world. Kant called this the Phenomena. Kant also said that we have categories of mind that influence the Phenomena. This idea has been referred to as Kant’s spectacles. To loosely put it, we are all born with a pair of spectacles that we cannot take off. We see the world through the spectacles, and thus what we see is influenced by the spectacles. In some regards, we can say that the structure of what we perceive has the structure of the perception network or the spectacles. This is very much like the isomorphism idea of Conant-Ashby theorem. The structure of model has to match the structure of the system being regulated in order to be successfully regulated. We can go further with Kant’s idea and state that the structure of our knowledge (what we have learned) has the structure of our learning framework. More on this on a future post.

All this brings me to my corollary to the Good Regulator theorem:

We do not manage the situation. We can only manage the model of the situation.

I make this statement based on the ideas noted above. What we are reacting to is the world that we have constructed internally. Cybernetically speaking, how good we can construct the model of the system to be regulated is determined more by the limitations of our perception or learning framework. If we have to update our internal model, we have to be aligned with the environment, and be perceptive to the changes happening around us. We need to be mindful of Kant’s spectacles and that we don’t have access to the objective reality. We will never have the same amount of variety as the external world, however, all we have to do is to have requisite variety. And for that we need to have a model of the situation. As another great cybernetician Stafford Beer put it:

If the law of requisite variety is to be handled intelligently, and not just by leaving nature to find the variety balance (which of course can be nasty for us humans), then it follows that the regulative forces must not only dispose requisite variety—which is a number of possible states; they must also know the pattern by which variety in the system is deployed. On the journey to work we need to have enough options open; we also need to know the pattern of the highways—where they run, what the control points are like, what other drivers habitually do. In the process of putting the children to bed we need several variety amplifiers at our command; but we also need to know (as we do, but let’s make it explicit) the likely behavior pattern of the children. Without these known patterns, proliferating variety looks even more threatening than it really is, which is bad enough.

What I have been calling a pattern is what a scientist calls a model. A model is not a load of mathematics, as some people think; nor is it some unrealizable ideal, as others believe. It is simply an account—expressed as you will—of the actual organization of a real system. Without a model of the system to be regulated, you cannot have a regulator.

Please maintain social distance and wear masks. Stay safe and Always keep on learning…

In case you missed it, my last post was Pluralism and Systems Thinking:

3 thoughts on “Notes on The Good Regulator Theorem:

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