Stimuli and Responses

Understanding the Law of Requisite Variety

Many essays here will refer to the Law of Requisite Variety. Some readers will be familiar with it. Others may try Wikipedia, ChatGPT, Gemini, or simply read chapter 11 of An Introduction to Cybernetics by Ross Ashby or his paper Requisite Variety and Its Implications for the Control of Complex Systems. Time well spent, for sure. If you don’t have the time or if you find these sources too technical, here’s a gentle guide that might be useful. I tried to make it as accessible as possible. A second objective was to give many and diverse examples. Hopefully, they will show the universal applicability of the law and help in creating a thinking habit.

This article is a modified excerpt from the fourth chapter of Essential Balances and is, so far, my best attempt at explaining the Law of Requisite Variety. I’ll avoid technical jargon and will simply render the law in terms of stimuli and responses.

The concept of variety is commonly used to refer to different types. However, there is a broader way to use variety¹. It was first proposed by Ross Ashby in 1950s. He came up with a law that he called the Law of Requisite Variety (LORV). It says that “variety destroys variety.” Stafford Beer rephrased it as “only variety can absorb variety.” But what is variety in this context?

One way to calculate variety is to count the number of different elements. The word cuckoo has six letters, but only four of them are different. It has a variety of four. If we rewrite it with a capital C and if the difference between uppercase and lowercase letters matters, then Cuckoo has a variety of five.

Fruit attack

Now, imagine the following game.

Somebody throws a melon at you, and you have to catch it. You do. Then she tosses a second melon your way. You happen to have excellent melon-catching skills, and you succeed in holding on to it. You now have a melon in each hand. She pitches a third melon. You are not allowed to let a melon fall on the ground. Can you keep hold of what you have and grab the incoming fruit? Oops! You drop the second one while trying to grasp the third. With four or more lobbed your way, there will be an ever-growing sticky pile of broken melons at your feet since you won’t be able to catch all of them.

As far as catching melons goes, you can cope as long as their number matches the number of your catching devices: your hands. To succeed, your responses should match the stimuli.

You want to catch melons with your hands. If no more than two melons are thrown, you can catch them. You can only succeed if the variety of the stimuli matches the variety of the response. Two melons against two hands. So far, you can count your variety by counting your hands.

But now you have a new fruity threat looming. This time, your assailant comes at you hurling lemons, one by one. You must not allow a lemon to fall on the ground.

Photo by Marije Woudsma

Let’s assume that you are as adept at catching lemons as you were with melons. You might be able to catch and hold four lemons, two in each hand. In this case, you succeed as long as the lemon-holding capacity of your hands matches the number of lemons thrown at you. If we apply the law, your capacity alone determines your variety.

While we catch our breath before another inevitable fruit attack, let’s measure the variety of words again. The variety of cuckoo was four. If your goal is to count the variety of a word, as long as you can distinguish these letters, you have enough variety to achieve this goal. But what about the variety of melon and lemon? It’s five for both of them. If these are two hands of five playing cards, they are exactly equal in strength. But that doesn’t mean there won’t be a winner. The cards will be played in a certain order. Only the order of the letters helps us distinguish between melon and lemon. We see now that the different types of letters, sizes, and order may all participate in measuring the variety of a word. If the font or the color of letters is different, there might be other criteria for distinction, depending on whether it matters for your goal. For example, we assumed that the elements of a word are the letters, which is a common and fair assumption. But if our goal is to print them clearly, then we are more interested in the number of pixels.

Heads up! Incoming cherry assault. This time, once you have both your hands full of cherries, you can start catching them with your mouth. Remember, the goal is to keep the cherries off the ground. Then, your variety will be equal to the sum of the cherry-holding capacities of your hands and mouth. And not only that. If you happen to be wearing a skirt or a dress, you could stop a lot of cherries using the upper part of your body and then trap them in your lap.

For the nature of this game, what matters most is the size of the fruit. But no less important are your reflexes and agility. So, a lot of things can contribute to variety: reaction time, speed and precision of movement, capacity, what clothes you are wearing, your decision about which hand to use when, and so on.

All these factors contributing to variety are relative. They depend on what you want to achieve. If your goal is to catch only one piece of fruit, then you may succeed regardless of the size of the melon. For lemons and cherries, you may also do something else in parallel. The variety of the responses that matters depends on your goal. The same is true for the variety of stimuli. Some of it might be safe to ignore. The variety of stimuli that you can potentially register will also depend on the limits of your perception.

Like gravity, LORV is omnipresent. Whenever there is purpose and interaction, it’s there. It has been in every story² so far. Remember, for example, the story of Ferenc? Every situation there can be seen through an LORV lens. But we are not going to go through that now. Instead, let’s see how Emma’s morning went on that day.

Emma’s Morning

Emma woke, glanced at her clock, and saw that it was a bit after six. Then she realized it was only half-past midnight. She had misread the clock, which had hands almost the same size. Luckily, she was soon sleeping again.

When it was actually six, she was already about to make herself a coffee. She had woken up some minutes earlier with a stiff neck. Now, waiting for the coffee machine to warm up, Emma tried stretching her neck by gently pulling her head and shoulder in opposite directions.

She was thinking about the mail she had to write to Ferenc. She had forgotten to invite him for the meeting at two and now she also needed to tell him that the evaluation report had a new, probably impossible, deadline. She was frowning at the thought when the indicator showed the coffee machine was ready. Emma pressed the button. She pulled her smartphone from the pocket of her nightgown to check the weather. The screen was dirty. The machine announced with a beep that the coffee was ready. She took out the cup, then tried to wipe her phone screen with a dry napkin. That didn’t work. She successfully cleaned it with a slightly wet tissue. She forgot what she needed the phone for and started checking her agenda. After a few sips of coffee, she went to take a shower.

What she had seen on her agenda wasn’t pleasant. More things were due that week than she had thought. While thinking about that, she was failing to get the shower to the right temperature. The water was either too hot or too cold.

The temperature outside was going to vary as well. This was what she found out when she finally checked the forecast some minutes later. She had an initial idea for what to wear today, which she was going to ditch for a layered alternative. But then she remembered that she was mostly going to be in the office the whole day, and when she wasn’t, she would be in her car. So, she decided to stay with her original clothing plan.

Half an hour later, Emma was driving to the office. She missed the green light at the first big intersection by a second and had to stop. No cars were passing on the crossing street while the queue was growing behind her. It was stupid, she thought. Intersections like that shouldn’t be controlled with traffic lights. A roundabout would have been much more suitable. The throughput would be based on the traffic, not on the mindless cycle of the traffic lights.

She had read about the Magic Roundabout in Swindon, UK. Five mini-circles surround a sixth bigger one, creating a configuration of seven roundabouts: an outer circle and five mini-roundabouts going clockwise, and the inner circle going anticlockwise. It sounds like a nightmare, and many drivers think it is. Yet, it’s been there since 1972, and statistics show it’s both faster and safer to go through compared to other similar junctions.

She got a green light and pressed the accelerator, her thoughts moving to a project for which she badly needed a green light as well. On the highway, she drove for less than five minutes before she was halted by congestion. Surrounded by cars, she considered what kind of arguments she could bring and what kind of support she could get for the project. Her thoughts were interrupted by occasional honking. Honking reminded her of baby cries. Babies want to communicate various emotions, but when they try, it comes out as one and the same cry. Well, not to their mums, I guess, Emma thought.

The traffic on the other side of the highway was light. She saw an exotic vintage car approaching. As it passed, she watched it to the point allowed by her neck, which was still stiff and painful.

Emma arrived at her desk just after eight-thirty. She answered a couple of emails. Then she wrote that message to Ferenc and right after forwarded him the invitation for the meeting in the afternoon. Then it was time to leave for her first meeting.

There were five people in the meeting. They had all arrived earlier and were already discussing the situation with the new competitor, which is what the meeting was about. During the 90 minutes of the meeting, several options from different perspectives were discussed. In the end, it seemed there were two ways to deal with it: either increase their product range to match the competitor’s best-selling lines or merge with the competitor. The latter was appealing. It had the additional advantage of eliminating one competitor. But it posed other issues.

Were you able to spot how many times the LORV was at play in this story? The answer is ten. Let’s go through them one by one.

First is the misreading of the clock. We want a clock to show us the time. For everyday use, if we can distinguish minutes, that’s good enough. An analog clock shows 12 hours. That makes 720 minutes. Then, the variety of analog clocks is 720. We tell the time by the position of the two hands. They should have 720 positions that we can distinguish. But there are some fancy analog clocks that compromise that to look nice or original. And it seems this was the case with Emma’s clock. When the clock hands are of similar size, then they don’t clearly communicate the variety of the clock mechanism. Two different times, such as 12:30 and 6:03, can look almost the same.

The dry napkin wasn’t much use when Emma tried to clean her smartphone screen with it. It didn’t have requisite variety. The wet tissue, as expected, did. Physics comes with a theory of cohesive and adhesive forces, surface tension, and suchlike to explain why this is the case. It is a useful theory. But unlike the Law of Requisite Variety, it can’t be applied to other situations. The wet tissue brought the needed variety that the dry napkin was lacking. This made the variety of the response (cleaning) sufficient to match or exceed the variety of the stimuli, the dirt on the phone screen.