Talking about Constraints in Cybernetics:

In today’s post, I am looking at constraints with respect to Cybernetics. I am looking mainly at the ideas from Ross Ashby, one of the pioneers of Cybernetics. Ashby wrote one of the best introductions to Cybernetics, aptly titled An Introduction to Cybernetics. Ashby described constraints in terms of variety. Variety is the number of distinct elements that an observer is capable of making. For example, consider the following set of elements:

{a, b, b, B, c, C}

Someone could say that the variety of this set is 3 since there are three letters. Some other person could say that the variety is actually 5 if the lower and upper cases are distinguished. A very common example to explain variety is a traffic stop light. Generally, the stop light in the US has 3 states (Red, Yellow and Green). Sometimes, additional states are possible such as blinking Red (indicating a STOP sign) or no light. Thus, the variety of a stop light can vary from 3 to 4 to 5.

Ashby explained constraints as – when there are two related sets and one set has less variety than the other, we can determine that a constraint is present in the set of elements with less variety. Let’s consider the stop light again. If all the lights were independent, we can have 8 possible states. This is shown below, where “X” means OFF and “O” means ON.

Figure 1 – The Eight States of a Stop Light

Per our discussion above, we utilize mainly 3 of these states to control traffic (ignoring the blinking states). These are identified in the blue shaded cells {2, 6, 7}. Thus, we can say that there is a constraint applied on the stop light since the actual variety the stop light possesses is 3 instead of 8. Ashby distinguishes slight and severe constraints. The example that Ashby gives is applying a constraint on a squad of soldiers in a single rank. The soldiers can be made to stand in numerous ways. For example, if the constraint to be applied is that no one soldier is to stand next to another soldier who shares the same birthday, the variety achieved is high. This is an example of a slight constraint. It is highly unlikely that two soldiers share the same birthday in a small group. However, if the constraint to be applied is that the soldiers should arrange themselves in the order of their height, the variety is then highly reduced. This is an example of a severe constraint.

Another example that Ashby gives is that of a chair. A chair taken as a whole has six degrees of freedom for movement. However, when the chair is disassembled into its parts, the freedom for movement increases. Ashby said:

A chair is a thing because it has coherence, because we can put it on this side of a table or that, because we can carry it around or sit on it. The chair is also a collection of parts. Now any free object in our three-dimensional world has six degrees of freedom for movement. Were the parts of the chair unconnected each would have its own six degrees of freedom; and this is in fact the amount of mobility available to the parts in the workshop before they are assembled. Thus, the four legs, when separate, have 24 degrees of freedom. After they are joined, however, they have only the six degrees of freedom of the single object. That there is a constraint is obvious when one realizes that if the positions of three legs of an assembled chair are known, then that of the fourth follows necessarily—it has no freedom.

Thus, the change from four separate and free legs to one chair corresponds precisely to the change from the set’s having 24 degrees of freedom to its having only 6. Thus, the essence of the chair’s being a “thing”, a unity, rather than a collection of independent parts corresponds to the presence of the constraint.

Ashby continued:

Seen from this point of view, the world around us is extremely rich in constraints. We are so familiar with them that we take most of them for granted, and are often not even aware that they exist. To see what the world would be like without its usual constraints we have to turn to fairy tales or to a “crazy” film, and even these remove only a fraction of all the constraints.

There are several takeaways we can have from Ashby’s explanation of constraints.

  1. The effect of the observer: The observer is king when it comes to cybernetics. The variety of an observed system is dependent on the observer. This means that the observation is subject to the constraints that the observer applies knowingly or unknowingly in the form of biases, beliefs, etc. The observer brings and applies internal constraints on the external world. Taking this a step further, our experiential reality is a result of our limited perceptual network. For example, we can see only a small section of the light spectrum. We can hear only a small section of the sound spectrum. We have cognitive blind-spots that we are not aware of. And yet we claim access to an objective reality and we are surprised when people don’t understand our point of view. We should not force our own views such that we come up with false dichotomies. This is sadly all very prevalent in today’s politics where almost every matter has been turned into a political viewpoint.
  2. Constraints are not a bad thing: Ashby’s great insight was that when a constraint exists, we can take advantage of it. We can make reasonably good predictions when constraints exist. Constraints help us to understand how things work. Ashby said that every law of nature is a constraint. We are able to estimate the variety that would exist if total independence occurred. We are able to minimize this variety by understanding the existing variety and adding further constraints as possible to produce results that we want. Adding constraints is about reducing unwanted variety. Design Engineering takes full use of this. On a similar note, Ashby also pointed out that learning is possible only to the extent that a sequence shows constraint. Learning is only possible when there is a constraint. If we are to learn a language, we learn it by learning the constraints that exists in the language in the form of syntax, meanings of the words, grammar etc.
  3. Law of Requisite Variety: Ross Ashby came up with the Law of Requisite Variety. This law simply can be explained as variety destroys (compensates) variety. For example, a good swordsman is able to fend off an opponent, if they are able to block and counter-attack every move of the opponent. The swordsman has to match the variety of the opponent (the set of attacks and blocks). To take our previous example, the stop light has to have a requisite variety to control traffic. If the 3 states identified in Figure 1 are not enough, the “system” will absorb the variety in the form of a traffic jam. When we think in terms of constraints, the requisite variety should be aligned with the identified constraints. We should minimize bringing in our internal constraints, and watch for the external constraints existing. The variety that we need to match must be aligned to the constraints already existing.
  4. Constraints do not need to be Objects: Similar to point 1, what we tell ourselves in terms of narratives and stories are also constraints. We are Homo Narrans – storytellers. We make sense of the world in terms of the stories we share and tell ourselves and others. We control ourselves and others with the stories we tell. We limit ourselves with what we believe. If we can understand the stories, we tell ourselves or others are telling us, we can better ourselves.
  5. Adaptation or Fit: Ashby realized that an organism can adapt just so far as the real world is constrained, and no further. Evolution is about fit. It is about supporting those factors that allow the organism to match the constraint in order to survive. The organism evolves to match the changing constraints present in the changing environment. This often happens through finding use for what is already existing. There is a great example that Cybernetician and Radical Constructivist, Ernst von Glasersfeld gives – the way the key fits a lock that it is able to open:

The fit describes a capacity of the key, not a property of the lock. When we face a novel problem, we are in much the same position as the burglar who wishes to enter a house. The “key” with which he successfully opens the door might be a paper clip, a bobby pin, a credit card, or a skillfully crafted skeleton key. All that matters is that it fits within the constraints of the particular lock and allows the burglar to get in.

I will finish with Ernst von Galsersfeld’s description of Cybernetics in terms of constraints:

Cybernetics is not interested in causality but constraints. Cybernetics is the art of maintaining equilibrium in a world of constraints and possibilities.

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

In case you missed it, my last post was Deconstructing Systems – There is Nothing Outside the Text:

3 thoughts on “Talking about Constraints in Cybernetics:

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