Variety – part 2

‘Can 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 sequence devoted to the concept variety used as a measure of complexity. It’s a good idea to read previous part before this one but even doing it after or not at all is fine.)

And that indeed proved to be a good way of managing 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 variety1Strictly speaking, we can also manage and control things by changing our goal but here we focus on 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 big.

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.

Attenuate and amplify variety

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.

Variety – part 1

The cybernetic concept of variety is enjoying some increase in usage. And that’s both in frequency and in number of different contexts. Even typing “Ross Ashby” in Google Trends confirms that impression.RossyAshby_as_seen_by_GoogleTrends In the last two years the interest seems stable, while in the previous six – non-existing, 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 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 that none. On the other hand, it attracts some interpretations leading to misaplication 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 usually 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 pawn on D4, the queen has 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 variety of 9, and D3 would give 16. That’s not enough to tell if the move is good or bad, especially having in mind that some of that gained variety is not effective. However, in case of uncertainty, in games and elsewhere, moving to a place which both increases our future options and decreases those of the opponent, seems a 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, nowdays 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. And then, when the logarithmic expression is used, combining varieties of elements is done just by adding instead of multiplying. This has additional benefits when plotting etc.

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 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.

Clock with indistiguishable hands

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 important 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 inference out of this: “every law of nature is a constraint”, “science looks for laws; it is therefore much concerned with looking for constraints”. (Which is interesting in view of the recent claim of Stuart Kauffman that “the very concept of a natural law is inadequate for much of the reality” and that we live in a lawless universe and should fundamentally rethink the role of science…)

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 the similar setting but 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 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 profound 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 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 that 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

But let’s leave the games for a moment and remember the relative nature of variety. The light signals in ships should comply with the International Regulations for Preventing Collisions at Sea (IRPCS). Yes, here we even have the word “regulation”. Having the purpose in mind, to prevent a collision, the signals have 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, and  – from right to left – if she sees red light. There are lots of states – different angels of the course of the other ship –  that are reduced into these two but that is serving 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 dependant also on the situation, on the context. An example that first comes to mind is the Easop’s fable “The Fox and the Stork”.

Fables, and stories in general, are interesting phenomenon. Their capability to influence people and survive many centuries is amazing. But why is that? Why 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, interpretable. They leave many things to be completed by the readers and listeners. And yes, to put in different words, they have much higher variety than morals and values.

That’s it for this part. Stay tuned.

Requisite Inefficiency

In his latest article Ancient Wisdom teaches Business Processes, Keith Swenson reflects on an interesting story told by Jared Diamond. In short, the potato farmers in Peru used to scatter their strips of land. They kept them that way instead of amalgamating them which would seem like the most reasonable thing to do. This turned out to be a smart risk mitigating strategy. As these strips are scattered, the risk of various hazards is spread and the probability to get something from the owned land every year is higher.

I see that story as yet another manifestation of Ashby’s law of requisite variety. The environment is very complex and to deal with it somehow, we either find a way to reduce that variety in view of a particular objective, or try to increase ours. In a farming setting an example of variety reduction would be building a greenhouse. The story of the Peruvian farmers is a good example of the opposite strategy – increase of the variety of the farmers’ system. The story shows another interesting thing. It is an example of a way to deal with oscillation. The farmers controlled the damage of the lows by giving up the potential benefits of the highs.

Back to the post of Keith Swenson, after bringing this lesson to the area of business process, he concludes

Efficiency is not uniformity.  Instead, don’t worry about enforcing a best practice, but instead attempt only to identify and eliminate “worst practices”

I fully agree about best practices. The enforcement of best practices is what one can find in three of every four books on management and in nearly every organisation today. This may indeed increase the success rate in predictable circumstances but it decreases resilience and it is just not working when the uncertainty of the environment is high.

I’m not quite sure about the other advice: “but instead attempt only to identify and eliminate “worst practices”. Here’s why I’m uncomfortable with this statement:

1. To identify and eliminate “worst practice” is a best practice itself.

2. To spot an anti-pattern, label it as “worst-practice” and eliminate it might seem the reasonable thing to do today. But what about tomorrow? Will this “worst-practice” be an anti-pattern in the new circumstances of tomorrow? Or something that we might need to deal with the change?

Is a certain amount of bad practice necessarily unhealthy?

It seems quite the opposite. Some bad practice is not just nice to have, it is essential for viability. I’ll not be able to put it better than Stafford Beer:

Error, controlled to a reasonable level, is not the absolute enemy we have been thought to think of. On the contrary, it is a precondition for survival. […] The flirtation with error keeps the algedonic feedbacks toned up and ready to recognise the need for change.

Stafford Beer, Brain of the firm (1972)

I prefer to call this “reasonable level” of error requisite inefficiency. Where can we see this? In most – if not all – complex adaptive systems. A handy example is the way immune system works in humans and other animals having the so called adaptive immune system (AIS).

The main agents of the AIS are T and B lymphocytes. They are produced by stem cells in the bone marrow. They account for 20-40% of the blood cells which makes about 2 trillion. The way the AIS works is fascinating but for the topic here of requisite inefficiency, what is interesting is the reproduction of the B-cells.

The B-cells recognise the pathogen molecules, the “antigens”, depending on how well the shape of their receptor molecules match that of the antigens. The better the match, the better the chance to be recognised as antigen. And when that is the case, the antigens are “marked” for destruction. Then follows a process in which the T-cells play an important role.

As we keep talking of the complexity and uncertainty of the environment, the pathogens seem a very good model of it.

The best material model of a cat is another, or preferably the same, cat.

N. Wiener, A. Rosenblueth, Philosophy of Science (1945)

What is the main problem of the immune system? It cannot predict what pathogens will invade the body and prepare accordingly. How does it solve it? By generating enormous diversity. Yes, Ashby’s law again. The way this variety is generated is interesting in itself for the capability of cells DNA to carry out random algorithms. But let’s not digress.

The big diversity may increase the chance to absorb that of pathogens but what is also needed is to have match in numbers to have requisite variety. (This is why I really find variety, in cybernetic terms, such a good measure. It is relative. And it can account for both number of types and quantities of the same type.) If the number of matches between B-cell receptors and antigens is enough to register “attack”, the B-cells get activated by the T-cells and start to release antibodies. Then these successful B-cells go to a lymph node where they start to reproduce rapidly . This is a reinforcing loop in which the mutations that are good match with the antigens go to kill invaders and then back to the lymph nodes to reproduce. Those mutations that don’t match antigens, die.

That is really efficient and effective. But at the same time, the random generation of new lymphocytes with diverse shapes continues. Which is quite inefficient when you think of it. Most of them are not used. Just wasted. Until some happen to have receptors that are good match of a new invader. And this is how such an “inefficiency” is a precondition for survival. It should not just exist but be sufficient. The body does not work with what’s probable. It’s ready for what’s possible.

(Note: This is the mainstream explanation of how the immune system work. There are other theories, and some of them  – this one for example – I find way more convincing, especially when  comes to the self/non-self problem. However, in all explanations the phenomenon of requisite inefficiency is equally prominent. )

The immune system is not the only complex system having requisite inefficiency. The brain, the swarms, the networks are just as good examples. Having the current level of study, the easiest systems to see it in are ant colonies.

When an ant finds food, it starts to leave a trail of pheromones. When another ant encounters the trail, it follows it.  If it reaches the food, the second ant returns to the next leaving trail as well. The same reinforcing loop we saw with the B-cells, can be seen with ants. The more trails, the more likely the bigger number of ants will step on it, follow it, leave more pheromones, attract more ants and so on. And again, at the same time there always is a sufficient amount of ants moving randomly which can encounter new location with food.

The requisite inefficiency is equally important for social systems. Dave Snowden gave a nice example coincidently again with farmers but in that case experiencing high frequency of floods. Their strategy was to build their houses not in a way to prevent the water coming in but to allow the water to quickly come out. He calls that “architecting for resilience”:

You build your system on the assumption you prevent what can fail but you also build your system so you can recover very very quickly when failure happens. And that means you can’t afford an approach based on efficiency. Because efficiency takes away all superfluous capacity so you only have what you need to have for the circumstances you anticipate. […] You need a degree of inefficiency in order to be effective.

It seems we have a lot to learn from B-cells, ants and farmers about how to make our social systems work better and recover quicker. And contrary to our intuition, there is a need for some inefficiency. The interesting question is how to regulate it or how to create conditions for self regulation. For a given system, how much inefficiency is insufficient, how much is just enough and when it is too much? May be for the immune systems and ant colonies these regulatory mechanisms are already known. The challenge is to find them for organisations, societies and economies. How much can we use from what we already know for other complex adaptive systems? Well, we also have to be careful with analogies. Else, we might fall into the “best practice” trap.

(See also More on Requisite Inefficiency)