Magic numbers

The theory

I'm going to tackle today the second question debated by this organization trying to draw up their constitution. The question for today is: "Should the organization have a register of members?"

The answer I'd give is a clear, resounding "YES", for any organization or group of people that you care to imagine. If you can possibly know who are the people in that group and you have a way of contacting each of them, it will make everything so much easier for everyone. If there is any reason people would like to be anonymous, find ways of keeping them anonymous... but at the very least, count them. There are many reasons for this, so I'll just focus on one of them today. It has to do with working at different scales.

People behave differently in groups of different sizes. Think of a meeting of two people, five people, 50 people, 200 people. People behave completely different in each of those groups. This has to do with practical limitations.

Two people are able to talk comfortably with each other and discuss any topic in any depth that both of them want. Five people can still talk comfortably, but the most introverted among them will say a lot less and may leave lots of things unsaid of what they are thinking, while the most extroverted will dominate unless somebody is trying to compensate this. Fifty people can't possibly engage in a group conversation. Turns have to be respected, people will have to raise hands to ask to speak, and chances are that many of them won't talk at all, unless they are all asked to introduce themselves in order or something like that. The only other alternative for fifty people is to divide into a lot of smaller groups that talk with each other, like in any birthday party. Two hundred is getting to the point that most people wouldn't even be able to remember everybody else they saw in the meeting, even if this was a regular meeting that happened again and again. Many people will keep behaving as if they are among strangers, no matter how many times the meeting is repeated.

If you don't keep a register of members, a lot of the time you won't even know what numbers to expect if you ask for people to come to an event, or to respond to any kind of calling. And it will be impossible to prepare appropriately, because the right preparation will depend on the number of people you get.

When it comes to groups of humans, the two main limits that explain different behaviour in groups of different sizes are:

• People can't listen and speak at the same time. In a group, you can have two kind of situations: either everybody is listening to the same person, and in that case they don't get a chance to speak, or people divide into smaller groups that chat with each other, and in that case they don't get a chance to hear what other groups are saying.
• People's memory is limited. Anybody can remember clearly the names, faces and a couple of personal details of five new people. Fifty new people is a stretch that only a few could manage. Two hundred is a stretch for most people, even if you have repeated chances to see them again.

Other animals are limited in different ways, and that affects in other ways the size of the groups that they usually make. For example, humans often prefer smaller groups because they like to talk, and talk is difficult in big groups. And they want to keep tabs of a lot of information on other people, while most animals couldn't possibly keep all that gossip in their minds. Other apes, such as chimps and gorillas, are able to remember details about their fellow chimps and gorillas, but because their capacity is more limited, their groups aren't ever as big as a human tribe. On the other hand, most animals don't talk or keep tabs on anyone except their closest family, they just keep visual contact with each other and make the ocassional sound that may be somewhat informative to others, but nothing like language. That's why many animals are quite comfortable in big herds, some much bigger than human tribes. But then, most animals don't want too much competition for food, and that is what often limits the size of their groups.

The practice

Experiment 1

Do some bird-watching and compare flocks of birds. Which birds have the biggest flocks? Which birds have smaller flocks? Which are usually solitary? Can you work out why different birds flock in different numbers?

Experiment 2

Think of all the groups of people you belong to, and order them from smallest to biggest. The first one should be only you, the next should be you and your partner if you have one, the next your family. Include anything you can think of: your circle of closest friends, the organization you work in, the team of people you work with, any association you belong to, your neighbourhood, the location you live in, your country. Estimate the number of people in each group. Can you notice things in common in the smallest groups? Can you notice things in common in the biggest groups? In what way are small groups different from big groups? What sizes seem to be the barriers that mark the difference between "small and intimate", "small", "like a big family", "so big I just feel like a number"?