etyCan you deal with it?

Deal originates from divide. It initially meant only to distribute. Now it also means to cope, manage and control. We manage things by dividing them. We eat an elephant piece by piece, we start a journey of a thousand miles with a single step, and we divide to conquer.

(This is the second part of a series on the concept variety used as a measure of complexity. You may want to read the previous part before this one, but even doing it after or not at all is fine.)

That proved to be a good way to manage things, or at least some things, and in some situations. But often it’s not enough. To deal with things, and here I use deal to mean manage, understand, control, we need requisite variety. When we don’t have enough variety, we could get it in three ways: by attenuating the variety of what has to be dealt with, by amplifying our variety, or by doing a bit of both when the difference is too big¹There yet another way: to change our goal..

And how do we do that? Let’s start by putting some common activities in each of these groups. We attenuate external variety by grouping, categorising, splitting, standardising, setting objectives, filtering, reporting, coordinating, and consolidating. We amplify our variety by learning, trial-and-error, practising, networking, advertising, buffering, doing contingency planning, and innovating. And we can add a lot more to both lists. We use such activities but when doing these activities we need requisite variety as well. That’s why we have to apply them at different scale²Some may prefer to put it more technically as “different level of recursion”.. We learn to split and we split to learn, for example.

What about the third group? What kind of activities can both amplify ours and attenuate the variety of what we need to deal with? It could be easy to put in that third group pairs from each list but aren’t there single types? There are. Here are two suggestions: planning and pretending.

With planning, we get higher variety by being prepared for at least one scenario, especially in the parts of what we can control, in contrast to those not prepared even for that. But then, we reduce different possibilities to one and try to absorb part of the deflected variety with risk management activities.

Planning is important in both operations and projects, and yet, in a business setting, we can get away with poor planning long enough to lose the opportunity to adapt. And that is the case in systems with delayed feedback. That’s also why I like the test of quick-feedback and skin-in-the-game situations, like sailing. In sailing, You are doomed if you sail off without a plan, or if you stick to the plan in front of unforseen events. And that’s valid at every planning level, week, day or an hour.

The second example of activity that both amplifies and attenuates variety is pretending. It can be so successful as to reinforce its application to the extreme. Pretending is so important for stick insects, for example, that they apply it 24/7. That proved to be really successful for their survival and they’ve been getting better at it for the last fifty million years. It turned out to be also so satisfactory that they can live without sex for one million years. Well, that’s for a different reason but nevertheless, their adaptability is impressive. The evolutionary pressure to better resemble sticks made them sacrifice their organ symmetry so that they can afford thinner bodies. Isn’t it amazing: you give up one of your kidneys just to be able to lie better? Now, why do I argue that deception in general, and pretending in particular, has a dual role in the variety game? Stick insects amplify their morphologic variety and through this, they attenuate the perception variety of their predators. A predator sees the stick as a stick and the stick insect as a stick, two states attenuated into one.

Obviously, snakes are more agile than stick insects but for some types that agility goes beyond the capabilities of their bodies. Those snakes don’t pretend 24/7 but just when attacked. They pretend to be dead. And one of those types, the hognose snake, goes so far in their act as to stick its tongue out, vomit blood and sometimes even defecate. That should be not just convincing but quite off-putting even for the hungriest of predators.

If pretending can be such a variety amplifier (and attenuator), pretending to pretend can achieve even more remarkable results. A way to imagine the variety proliferation of such a structure is to use an analogy with the example of three connected black boxes that Stafford Beer gave in “The Heart of Enterprise”. If the first box has three inputs and one output, each of them with two possible states, then the input variety is 8 and the output is 256. Going from 8 to 256 with only one output is impressive but when that is the input of a third black box, having only one output as well, then its variety reaches the cosmic number of 1.157×10⁷⁷.

That seems to be one of the formulas of the writer Kazuo Ishiguro. As Margaret Atwood put it, “an Ishiguro novel is never about what it pretends to pretend to be about”. No wonder “Never Let Me Go” is so good. And the author, having much more variety than the stick insects, didn’t have to give his organs to be successful. He just made up characters that gave theirs.

• 1
  There yet another way: to change our goal.
• 2
  Some may prefer to put it more technically as “different level of recursion”.

The cybernetic concept of variety is enjoying some increase in usage. And that’s both in frequency and in a number of different contexts. Even typing “Ross Ashby” in Google Trends confirms that impression. In the last two years, the interest seems stable, while in the previous six – it was non-existent, save for the lonely peak in May 2010. Google Trends is not a source of data to draw serious conclusions from, yet it confirms the impression coming from tweets, blogs, articles, and books. On the one hand, that’s good news. I still find the usage insignificant compared to what I believe it should be. Nevertheless, little attention is better than none. On the other hand, it attracts some interpretations, leading to a misapprehension of the concept. That’s why I hope it’s worth exchanging more ideas about variety, and those having more variety themselves would either enjoy wider adoption or those using them – more benefits, or both.

The concept of variety as a measure of complexity had been preceded and inspired by the information entropy of Claude Shannon, also known as the “amount of surprise” in a message. That, although stimulated by the development of communication technologies in the first half of the twentieth century, had its roots in statistical mechanics and Boltzmann’s definition of entropy. Boltzmann, unlike classical mechanics and thermodynamics, defined entropy as the number of possible microstates corresponding to the macro-state of a system.

Variety is defined as the number of possible states in a system. It is also applied to a set of elements. The number of different members determines the variety of a set. It can be applied to the members themselves, which can be in different states, and then the set of possible transitions has a certain variety. This is the first important property of variety. It’s recursive. I’ll come back to this later. Now, to clarify what is meant by “state”:

By a state of a system is meant any well-defined condition or property that can be recognised if it occurs again.

Ross Ashby

Variety can sometimes be easy to count. For example, after opening the game in chess with a pawn on D4, the queen has a variety of three: not to move or move to one of the two possible squares. If only the temporary variety gain is counted, then choosing D2 as the next move would give a variety of 9, and D3 would give 16. That’s not enough to tell if the move is good or bad, especially keeping in mind that some of that gained variety is not effective. However, in case of uncertainty, in games and elsewhere, moving to a place that both increases our future options and decreases those of the opponent seems good advice.

Variety can be expressed as a number, as it was done in the chess example, but in many cases, it’s more convenient to use the logarithm of that number (in case that sounds like a distant memory from school years, nowadays there are easy ways to refresh it in minutes). The common practice, maybe because of the first areas of application, is to use binary logarithms. When that is the case, variety can be expressed in bits. It is indeed more convenient to say the variety of a four-letter code using the English alphabet is 18.8 bits instead of 456 976. There is an extra bonus. When the logarithmic expression is used, varieties of elements are combined by adding instead of multiplying.

Variety is sometimes referred to and counted as permutations. That might be fine in certain cases but as a rule it is not. To use the example with the 4-letter code, it has 358 800 permutations (26 factorial divided by 22 factorial), while the variety is 456 976 (26 to the power of 4).

Variety is relative. It depends on the observer. That’s obvious even from the word “recognised” in the definition of state. If, for example, there is a clock with two hands that are exactly the same or at least to the extent that an observer can’t make the difference, then, from the point of view of the observer, the clock will have a much lower variety than a regular one. The observer will not be able to distinguish, for example, 12:30 and 6:03 as they will be seen as the same state of the clock.

This can be seen as another dependency. That of the capacity of the channel or the variety of the transducer. For example, it is estimated that regular humans can distinguish up to 10 million colours, while tetrachromats – at least ten times more. The variety of the transducer and the capacity of the channel should always be taken into account.

When working with variety, it is useful to study the relevant constraints. If we throw a stone from the surface of Earth, certain constraints, including those we call “gravity” and the “resistance of the air”, would allow a much smaller range of possible states than if those constraints were not present. Ross Ashby made the following observation: “every law of nature is a constraint”, “science looks for laws; it is therefore much concerned with looking for constraints”.

There is this popular way of defining a system as something which is more than the sum of its parts. Let’s see this statement through the lens of varieties and constraints. If we have two elements, A and B, and each can be in two possible states on their own but when linked to each other A can bring B to another, third state, and B can bring A to another state as well. In this case, the system AB has certainly more variety than the sum of A and B unbound. But if, when linking A and B they inhibit each other, allowing one state instead of two, then it is clearly the opposite. That motivates rephrasing the popular statement to “a system might have different variety than the combined variety of its parts”.

If that example with A and B is too abstract, imagine a canoe sprint kayak with two paddlers working in sync and then compare it with a similar setting, with one of the paddlers rowing while the other holds her paddle in the water.

Yet, “is more than the sum of” can be retained but then another modification is needed. Here’s one suggested by Heinz von Foerster:

The measure of the sum of the parts is greater than the sum of the measures of the parts. One is the measure of the sum; the other is the sum of the measures. Take, for example, the measurement function “to square,” which makes this immediately apparent. I have two parts, one is a, the other b. Now I have the measure of the sum of the parts. What does that look like? a + b as the sum of the parts squared, (a + b)² gives us a² + 2ab + b². Now I need the sum of the measures of the parts, and with this I have the measure of a (= a²) and the measure of b (= b²): a² + b². Now I claim that the measure of the sums of the parts is greater than the sum of the measures of the parts and state that: a² + b² + 2ab is greater than a² + b². So the measure of the sum is greater than the sum of the measures. Why? a and b squared already have a relation together

Heinz von Foerster. The Beginning of Heaven and Earth Has No Name (Meaning Systems) (p. 18)

And now about the law of requisite variety. It’s stated as “variety can destroy variety” by Ashby and as “only variety can absorb variety” by Beer, and has other formulations such as “The larger the variety of actions available to control system, the larger the variety of perturbations it is able to compensate”. Basically, when the variety of the regulator is lower than the variety of the disturbance, that gives high variety of the outcome. A regulator can only achieve the desired outcome variety if its own variety is the same or higher than that of the disturbance. The recursive nature mentioned earlier can now be easily seen if we look at the regulator as a channel between the disturbance and the outcome or if we account for the variety of the channels at the level of recursion with which we started.

To really understand the significance of this law, it should be seen how it exerts itself in various situations, which we wouldn’t normally describe with words such as “regulator”, “perturbations” and “variety”.

In the chess example, the power of each piece is a function of its variety, which is the one given by the rules and reduced by the constraints at every move. Was there a need to know about requisite variety to design this game? Or any other game for that matter? Or was it necessary to know how to wage war? Certainly not. And yet, it’s all there:

It is the rule in war, if our forces are ten to the enemy’s one, to surround him; if five to one, to attack him; if twice as numerous, to divide our army into two.

Sun Tzu, The Art of War

Let’s leave the games now and come back to the relative nature of variety. The light signals in ships should comply with the International Regulations for Preventing Collisions at Sea (IRPCS). The agreed signals have a reduced variety to communicate the states of the ships but enough to ensure the required control. For example, if an observer sees one green light, she knows that another ship is passing from left to right. If she sees one red light, it passes right to left. There are lots of states – different angles of the course of the other ship – that are reduced into these two, but that serves the purpose well enough. Now, if she sees both red and green, that means that the ship is coming exactly towards her. That’s a dangerous situation. The reduction of variety, in this case, has to be very low.

The relativity of variety is not only related to the observer’s “powers of discrimination”, or those of the purpose of regulation. It could be dependent also on the context. Easop’s fable “The Fox and the Stork”comes to mind.

Fables, and stories in general, influence people and survive centuries. But is it that do you need a story instead of getting directly the moral of the story? Yes, it’s more interesting, there is this uncertainty element and all that. But there is something else. Stories are ambiguous and interpretable. They leave many things to be completed by the readers and listeners. To put it in different words, they have a much higher variety than morals and values.

That’s it for this part.

And here is the next.