Exploration and Exploitation

I love going to jazz festivals. Listening to good jazz at home is a pleasure, but what’s missing are the vibes during a live performance. And it’s not the same when you listen to a recording of a concert. Everything changes when you are actually there, immersed, experiencing directly with all your senses. I guess it’s similar with other types of music. But what makes the difference between listening to a recording and being at concert even bigger for jazz, is that it is all about improvisation. And then the experience of single concerts versus festivals is also different. With concerts, you immerse yourself for a couple of hours into a world of magic and then go back to the normal world. But with jazz festivals, you relocate to live in a music village for a couple of days. This doesn’t only make it a different experience, but also calls for different kinds of decisions.

Previously, when I learned of a new jazz festival or read the line-up of a familiar one, the way I decided whether to go was simple. I just checked who would be performing. If there were musicians that I liked, but hadn’t watched live, or some that I had, but wanted to see again, then I went. If not, I usually wouldn’t risk it.

Once I chose to go, this brought more things to consider. Jazz festivals usually have many stages, with parallel performances during the day and into the night. Last time I went to the North Sea Jazz Festival, there were over 80 performances in only a few days. So, there is a good chance that some of those you want to watch will clash, and you are forced to choose. And I kept applying the same low-risk strategy for choosing what to watch as I did for deciding if I should go at all.

Then one day, I arrived late to a festival just before two clashing sets were about to begin. I dashed into the closest hall with no clue as to what I would find. And there I experienced what turned out to be the best concert of the whole festival. I hadn’t heard of the group, and if I had read the description beforehand, I would have avoided their performance.

I realized then, that by only choosing concerts with familiar musicians, I was over-exploiting and under-exploring. My strategy was depriving me of learning opportunities and reducing the overall value I got from the festivals.

What happened at that festival changed the way I decide whether to go and which performances to see. Now I not only attend many more concerts of musicians previously unknown to me, but not having a familiar name in the line-up does not determine the decision to buy tickets.

However, when the whole line-up of the festival is completely unknown, then going is all exploration. That’s highly risky. When there are no familiar musicians, I listen to recordings of previous concerts of some of the groups. If I like at least two of them, then I usually go to the festival, and once there, I will still check out a few acts I don’t know. That’s another way to balance exploitation and exploration.

When I am in control, “I restrict the world to what I can imagine or permit”, writes Ranulph Glanville. He gives the example of going to a restaurant with friends. If it’s always him who chooses the restaurant, the group will only go to the restaurants that he knows. They are limited to his taste and knowledge, or rather – as he admits – by his ignorance. Letting go of control by letting others choose, not only expands his knowledge but would often give a better experience for everyone.

Having the wrong strategy when it comes to jazz festivals and restaurants reduces the pleasure, but in these examples, the decisions make such a small impact that they may not show how important this balance is. Yet, we make similar choices all the time. For example, you might decide to invest your time in getting better at what you currently do well while not allocating time to trying out new things. This may put you in a very unpleasant situation in times when there is no more demand for what you are skilled at, or when you need a change but have difficulty choosing because you haven’t tested many alternatives.

Throughout our lives, many of us realize that when making choices, we should have a balance of exploration and exploitation. We should let go of some control and not limit ourselves to what we already know. And that’s an important first step, but it’s not enough. It takes a greater effort to keep this awareness awake. And somehow, it’s also easier at a personal level. How so?

We live our lives and are experiencing every minute of every day. We absorb sounds, tastes, smells, and light and feel the air on our skin. Through evolution we are well equipped to receive a signal when there is even a small problem. We get a scratch and react right away. That’s not the case with organizations. They might be missing a whole limb or – and here the metaphor will fail to produce a feeling of exaggeration – a head, without noticing for years. And even if we have learned how to balance exploitation and exploration in our lives, the chances are we are working in organizations that haven’t. It’s not easy even to imagine what maintaining this balance means for an organization. We can’t really step into the shoes of one. What we can do instead is study this phenomenon a little closer, try to understand it better, and then, armed with a new pair of glasses, make the best of that knowledge while we keep learning from what happens. To understand how the balance between exploration and exploitation works in organizations, we’ll start with the problem of resource allocation, and then move to more complex situations. Continue reading

Productive Organisational Paradoxes

It is often said that organisations are full of paradoxes. But this refers to contradictions and tensions. It is understood as something that needs to be taken care of. When organisations are looked at as social systems, however, it becomes clear that they are only possible because of paradoxes, and particularly paradoxes of self-reference. Understanding how these paradoxes create and maintain organisations is an important skill for practitioners trying to make sense of what’s going on and improve it. The basic generative organisational paradox is that of decisions. It brings new light not only on decision patterns and dependencies, but also on understanding the nature of objectives, power, and relations with clients.

Here are the recording and slides from my talk at the SCiO open day in London in January 2019.

Most of this story, but told gently, is in Chapter 5 of Essential Balances.

What can Social Systems Theory bring to the VSM?

In 2015, when the Metaphorum was in Hull, I tried to kick off a discussion about potential contributions from cognitive science, and particularly from the Enactive school. I shared some insights and hinted at other possibilities. This year the Metaphorum conference was in Germany for the first time. It was organised by Mark Lambertz and hosted by Sipgate in Düsseldorf. I saw in the fact that the Metaphorum was in Germany a good opportunity to suggest another combination, this time with the Social Systems Theory of Niklas Luhmann.

These are the slides from my talk and here you can also watch them with all animations.

Related posts:

The Mind Of Enterprise

Redrawing the Viable System Model diagram

Productive Paradoxes in Projects

SASSY Architecture

Notes on Stability-Diversity

To be healthy, organisations – like human beings – have to operate in balance. Going temporarily out of balance is OK, but if this goes on for too long, it’s dangerous. Just like riding a bike, the balance is the minimum organisations need to be able to move forward.

What kinds of things need to be balanced? There are three essential balances. The first one is between autonomy and cohesion, the second is about maintaining both stability and diversity, and the third is balancing between exploration and exploitation. The important thing to recognise here is that the nature of each balance will differ between organisations. And what needs to be done to restore balance will change over time. So we can’t be prescriptive or learn “best practice” from others. We can only give people the glasses to see what is going on and the knowledge that will help them maintain the balances in their organisations.

I’ve been doing the Essential Balances workshop for four years now. During the workshop, all three of them seemed relatively easy to get yet a bit more difficult to work with and create a habit of.  Based on the feedback I received from people using in practice these glasses for organisational diagnosis and design, the first and the third balance, Autonomy-Cohesion and Exploitation-Exploration, come more naturally (with certain difficulties in the fractal dimension), while the second one, Stability-Diversity, creates problems. All three of them and a few more will be explained in detail in the forthcoming book Essential Balances, but until then, I’ll make some clarifications here. I hope it will also be of use for people who are not familiar with this practice.

Stability and Diversity. At first glance, it might be difficult to see it as a balance. In fact, it covers three dynamics. So, it might be easier to see it as three different balances. Different, yet somehow the same. And the key to it is exactly in these two words: different and same. Continue reading

The Mind Of Enterprise

I should have shared this presentation in November 2015 but anyway, better late than never. Here it is as static slides…

… and if your browser allows, you can play the original:

There is also a video, but due to a technical problem, only the first few minutes were recorded.

What’s Wrong with Best Practices?

That is a question I get very often from people who know that I keep away from prescriptive approaches. I’ve been giving some quick responses, but it would be better if next time I can point to a more elaborated answer. And here it is.

While I have a lot of sympathy for those that object to ‘Best Practice’ as a name — even more — to those that object it as a claim, my uneasiness is somewhat different. I’ll focus here on that.

Some best practices are very useful. In fact, most mature and well-applied best practices for carrying out some technical tasks, from taking a blood test, painting a wall or repairing an engine, to building a factory or a ship, are indeed valuable (as long as they don’t suffocate innovation).

The real problem is when best practices are applied to people and social systems. I call this a ‘problem’, but it is in fact a huge opportunity for many. Most contemporary non-fiction books, especially management and self-help texts, have been seizing this opportunity extremely well. It’s not easy to find a best seller in this category or a popular article, that doesn’t provide some sort of prescriptions and advice, often numbered, on how to achieve or avoid something. Maybe it is a best practice for best sellers. Let’s give it a try then:

 

Four Reasons Why You Should Be Cautious When Applying Best Practices:

 

1. Correlations.

How do Best Practices come about? Some individuals or organisations, become known or are later made known by the actions of the best practice discoverers and proponents, as successful according to some norms. Let’s call these individuals or organisations ‘best practice pioneer’. Then one or more observers, the ‘best practice discoverer’, studies the pioneers to find out what made them successful. The discoverer first takes certain effects, and then selects, by identifying commonalities, what she or he believes were the causes. That is followed by a generalisation of the commonalities, from which point they begin their life as prescriptions, regardless if they are called ‘best practices’, ‘methodologies’, ‘techniques’, ‘recipes’,’templates’, or something else. Later they are tested and based on feedback, reappear in more mature forms and variations, in some cases supplied with scalability criteria and conditions for a successful application. The successes and failures of those that apply them give birth to Best Practices on applying Best Practices.

The problem is, that the discoverers select common patterns among the observed successful pioneers, and infer causal relation between these commonalities and those that were the criteria to select that set of pioneers in the first place. Then such correlation leads the discoverer to select what to pay attention to, and every pattern that supports the hypothesis based on the selected commonalities would be preferred over those that don’t.

2. The risk of over-simplification.

Best practices help us deal with external stimuli, when they are too many to handle, by prompting which ones to pay attention to and how to react to them. The only way to deal with a situation is when the number of responses is higher than the number of the stimuli, within a given goal set (Ashby’s law). Or in other words, best practices are tools for reducing external variety. But not only that, they also provide means for amplifying internal variety in a special way – coupled with those stimuli that you are advised to pay attention to. So if that assumption was wrong, and it often is, neither the external variety is reduced, nor the internal is amplified.

3. Assumptions about the application context.

I used to be a practitioner of PRINCE2. What I still appreciate is a few smart techniques and in fact – the name itself. The name is the important disclaimer I’m missing in most methodologies and other types of best practices: they only work in controlled environments. They work when most of the conditions of the design-time if you allow me the IT jargon, are unchanged in run-time. This is rarely the case and is increasingly less so. This brings another interesting phenomenon: the same conditions that make the world less predictable also help quickly productise and spread best practices. They come with better marketing and with more authority in a world in which less of what has happened could prepare you for what will.

4. The habits created by Best Practices.

The worst is when people hide behind the authority of best practices or their proponents. If not that, best practices create habits of first looking for best practices, instead of thinking. And then, there is the alternative cost: the more time people spend on learning best practices, the less time they have for developing their senses for detection of weak signals and for developing their capabilities for new responses.

In summary, if you are sure that certain best practice is useful, and it’s not based on wrong inference and does not lead you to dismiss important factors, and the situation you are in is not complex, and it doesn’t weaken your resilience, then go ahead, use it.

 

The Pathologies of Silo-fighting

The division of labour has been the main principle for structuring organisations in the last two centuries. That is still the dominant approach for allocating resources, information and power in companies and public institutions. The new dynamics in a connected world have revealed a rich spectrum of problems related to these structures ranging from ineffective coordination to turf wars. This gave birth to the stigmatising label ‘silos’ and a whole industry of silo-fighters armed with silo-bridging or silo-breaking services, methods and technologies.

Here I will point out the two most prominent organisational pathologies brought by such silo-fighters. I’ll split the silo-fighters’ strategies into silo-bridging and silo-breaking – an oversimplification – to make the illustration of the two pathologies more clear.

‘Bridging the silos’ is not a strategy based much on appreciating their role and thus opting for bridging over breaking.  It’s mainly due to silo-fighters’ insufficient resources and power. If they manage to sell successfully the story of the bad silos, coming with a rich repertoire of metaphors such as walls, chasms, stove-pipes, islands and such like, then they get permission to build – as such a narrative would logically suggest – bridges between the silos.

Now, the problem with bridges is that they are either brittle and quickly break, or they are strong enough to defend their reason to be. They break easily when they fail to channel resources for a longer time than the patience over their initial failures would allow. However, identity formation switches on viability mode. The bridges start to grow out of a network of decisions supporting their mission, now turned into an ongoing function. If the reason the bridges exist are silos, and the bridges want to keep on bridging, then the silos have to be kept healthy and strong as they are what the bridges hang on to.

The bridges reinforce and perpetuate themselves up to a point, in which they are recognised as silos, and the problem is solved very often by building new bridges between them. This is how a cancerous fractal of bridges starts to grow. As attractive as this hyperbole is, I have witnessed repeatedly only two levels of recursion, but isn’t that bad enough?

In contrast, the silo-breaking strategies want nothing less than the destruction of silos. There, the silos are seen only in their role of a problem. Nobody asks what kind of problems this problem was а solution to. Instead, these silo-fighters start waging exhausting wars. The wars can end up in several ways. A common one is resource depletion. Another is with the silos withstanding, or with the silo-fighter being chased away or transformed. And then of course it could be the case of victory for the silo-fighters. And this is when the disaster strikes. Having the silos down, the silos fighters are faced with all the problems being continuously solved by the silos during their lifespan. Usually, they have no preparation to deal with those problems, neither they have the time to come up with and build alternative structures.

When discussing these two pathologies, it is very attractive to search for their root cause and then, when found, fix it. But that would be exactly the fuel these two types of silo-fighters run on. It takes a deeper understanding of the circularity of and in organisations, to avoid this trap. By ‘understanding’, I mean the continuous process, not the stage, after which the new state of ‘understood’ is achieved. And it takes, among other things, the ability to be much more in, and conscious of it, and at the same time much more out, but only as a better point for observation, not as an attempt for excluding the observer.

 

Redrawing the Viable System Model diagram

I’ve been arguing repeatedly that trying to get the Viable System Model from overviews, introductions and writings based on or about it, can put the curious mind in a state of confusion or simply lead to wrong interpretations. The absolute minimum is reading at least once each of the three books explaining the model. But better twice. Why? There are at least two good reasons. The obvious one is to better understand some points and pay attention to others that have been probably missed during the first run. But there is also another reason. Books are of linear nature, and when tackling non-linear subjects, a second reading gives the chance to better interpret each part of the text when having in memory other parts which relate to it.

Still, one of the things that are expected to be most helpful is in fact, what brings about either confusion, aversion or misuse: the VSM diagrams. They clearly favour expected ease of understanding over rigour, and yet often they fail in both. Here is my short list of issues, followed by a description of each:

  • Representation of the channels
  • Confusion about operations and their direct management
  • Notation and labelling of systems
  • They show something between generic and example model
  • Hierarchical implication

Representation of the channels

Stafford Beer admitted several times in his books the “diagrammatic limitations” of the VSM representations. Some of the choices had to do with the limitation of the 2D representation and others, I guess, aimed to avoid clutter. Figure 26 of “The Heart of Enterprise” is a good example of both. It shows eleven loops but implies twenty-one: 3 between environment, operations and management, multiplied by 3 for the choice of showing three operations, then another 9 = 3×3 for loops between same-type elements and finally 3 more between operation management and the meta-system.

Confusion about operations and their direct management

Depending on the context, System One refers either to operations or to their direct management. In some diagrams, S1 is the label of the circles, and in others – of the squares linked to them. Referring to one or the other in the text, depending on which channels are described, only adds to the confusion. That is related to the general problem of

Notation and labelling of systems

All diagrams representing the VSM in the original writings and all interpretations I’ve seen so far suggest that circles represent System One, and triangles pointing up and down, represent System Two and Three* respectively. Additionally, most VSM overviews state exactly that in the textual description. My assertion is almost the opposite:

What is labelled as S1 and what is shown as circles are both not representing S1.

That might come as a shock to many, and yet, now citing Beer, System One is not the “circles” but:

The collection of operating elements (that is, including their horizontal and vertical connexions)

The Heart of Enterprise, page 132

Strictly speaking, a system is a system because it shows emergent properties so it is more than the collection of its parts1that is by itself a popular but problematic statement. but even referring to it as a collection reveals the serious misinterpretation of taking only one of its parts to represent the whole system.

They show something between generic and example model

Communicating such matters to managers trained in business schools wasn’t an easy task. And it is even more challenging nowadays. There is a lot to learn and even more to unlearn. It is not surprising then that even in the generic models typically three operations are illustrated (same for System 2).  Yet, I was always missing a true generic representation, or what would many prefer to call “meta-model”.

Hierarchical implication

It can’t be repeated enough that the VSM is not a hierarchical model, and yet it is often perceived and used as such or not used especially because of that perception. It seems that recursivity is a challenging concept, while anything slightly resembling hierarchy is quickly taken to represent one. And sadly, the VSM diagram only amplifies that perception, although the orthogonality of the channels serves an entirely different purpose. Stafford Beer rarely missed an opportunity to remind us about that. Nevertheless, whatever is positioned higher implies seniority and the examples of mapping to actual roles and functions only help in confirming this misinterpretation.

 

There are other issues as well but my point was to outline the motivation for trying alternative approaches for modelling the VSM, without alternating the essence of the governing principles. Here is one humble attempt to propose a different representation (there is a less humble one which I’m working on, but it’s still too early to talk about it). The following diagram favours circular, instead of orthogonal representation which I hope achieves at least destroying the hierarchical perception. Yet, from a network point of view, the higher positioning of S3 is chosen on purpose as the network clearly shows that this node is a hub.

GenericCircularViewOfTheViableSystemModel

System One is represented by red colouring, keeping the conventional notation for the operations (S1.o) and their direct management (S1.m). As mentioned above, apart from solving this, the intention is to have it as a generic model. If that poses a problem for those used to the hybrid representation, here’s how it would look if two S1s are shown:

 

Circular Netwrok View Of The Viable System Model-2operations

I hope this proposal solves fully or partially the five issues explained earlier and brings a new perspective that can be insightful on its own. In any case, the aim is to be useful in some way. If not as it is now, then by triggering feedback that might bring it to a better state. Or, it can be useful by just provoking other, more successful attempts.

 

  • 1
    that is by itself a popular but problematic statement.

Variety, Part 2

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.

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.

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

Variety, Part 1

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.RossyAshby_as_seen_by_GoogleTrends 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.

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 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.