In today’s hyper-connected world, where technology lets us have hundreds (if not thousands) of ‘friends’, people are increasingly interested in understanding what the human limits on maintaining human friendships might be, and why.

Real world relationships have been studied by psychologists, sociologists and host of other ‘-ists’ for decades. However, Dunbar, who works in the area of behavioural brain science, has emerged as one of the most frequently quoted figures, in the blogosphere at least.

Where did Dunbar’s Number come from?

One of Dunbar’s papers, published in 1993, wonderfully titled “The Co-evolution of Neocortex Size, Brain Size and Language in Humans” is cited for something commonly referred to as Dunbar’s number. Shock number one: There isn’t really any such thing as Dunbar’s number, in the sense that people normally refer to it.

The common mythology is that Dunbar said that people can only sustain a network of 150 contacts. Strictly speaking that is not what Dunbar’s paper said. Think of humans as brains on legs for a minute, and put your evolutionary psychology hat on. Dundar argued that, in evolutionary terms, there may be an upper group size that animals can and will live in, determined by cognitive constraints – specifically the processing capacity of the neocortex - and selected for based on various environmental constraints.

Effectively, from an individual animal’s point of view, the neocortex size sets a limit on the number of relationships that can be maintained. That in turn limits the maximum group size for the community that individual lives within, assuming they have the same constraints. At a simple level, if a species is made up of individuals that can only sustain 10 relationships, we might expect to see groups of 10 wandering around. If another member attempts to join the group, the individuals don’t have the capacity to support that extra relationship, and the member wouldn’t be accepted, or the group would fail.

The neocortex size is driven by all sorts of ecological factors that select for group size, but we could potentially use that relationship the other way round to predict group sizes, based on the neocortex. Take one group with a known group size and look at the size of its neocortex. Work out a ratio, then take another species and look at the size of its neocortex and use that ratio to predict how many individuals it would be able to support.

Would the Real Dunbar’s Number Please Step Forward

Dunbar took existing data from a number of primate studies, where typical group sizes can be observed. He then looked at the neocortex size for those primates and projected forwards to the larger human neocortex. His calculations predicted that human group sizes would typically be around 147.8. It should also be noted that Dunbar worked with average group sizes, not maximum sizes.

Now, the maths is much more complex than this summary indicates, but I’ll spare you the detail. Even so, the statisticians out there are probably gagging on their most recent meal at this point. Hang on in there. Some statistical juggling means that confidence limits around this number can be calculated, which ends up giving a range being between 100 to 231, hence my earlier comment about Dunbar’s number not really existing in the way most people expect. Think of it as a range of typical group size, rather than a number limit. Dunbar’s work has been criticised and supported. However, it is interesting to note that his suggested number does seem to match with studies of human group size from other disciplines. I commonly read both military and business books that suggest a number in this range as the typical or maximum size for a group.

Speaking of Language

There is an interesting aside here. Dunbar and others argue that social grooming is important for maintaining relationships, and for sustaining the coalitions that facilitate large group structures. While apes might spend their time picking insects out of each other’s fur, we waggle our tongues and use our voice boxes. Evolutionary psychologists often argue that we evolved language as a very efficient form of social grooming. Well, half of them would. The other half would argue something more along the lines that our brains got so big and heavy we had to do something useful with them, and language turns out to be a rather beneficial thing to have.

Think of it this way: If a large group of apes is only able to be large because they spent their entire time picking nits out of each other’s fur, it won’t be a large group for very long. While they have the advantage of being able to defend themselves and pool resources, they don’t have any time left for finding food. They will be an extinct bunch of apes in very short order.

One of the factors that gives us large group structures is our ability to use language in communication. Language is much more efficient than picking nits out of fur. I can deal with more than one person at once, for a start. That means we can be more efficient about maintaining relationships, using quick bursts of language, rather than all of the time being taken up with social grooming. Personally I find that a great relief. I love communicating with you, but I’d rather not have you dealing with my parasites!

A simpler summary would be that available time, combined with efficiency, determines the number of relationships that can be supported. Language enables us to be more efficient with our time. That in turn enables us to build a larger social world, and still have time to do other things.

Does Social Media Make Us More Social?

One of the (many) aspects of social media of that fascinates me is this: Can it enable us to be more efficient and effective in maintaining relationships? Can computer-based tools enable our brain to cope with more than it would be able to otherwise? If so, that has social ramifications, as well as organisational design ones.

So, if Dunbar’s number (or one of the equivalents from Anthropological studies) is so small, how do we end up with significantly larger groups, like 1,000+ person companies? It comes down to rings of friendships. Think of bands of 30-50, then clans of 100-200, and above that tribal groups of between 500 and 3000. Imagine that I have 30-50 relationships, and those individuals have partially overlapping relationships with others. You can now imagine an inner group and an outer group, with cohesion maintained by those individuals holding relationships across the different bands and within bands.

The way that large groups work is significantly more complex than suggested here so far. Dunbar and others argue for these layers or rings of friendships, with different strengths at each layer. This layered structure enables sustainable group dynamics. The coalitions mentioned earlier are important, since these stronger relationships provide the individual with others to protect them from potential hostility from members of the larger group, by individuals with relationships to both parties.

Bands and clans interact in a way that protects individuals and sustains tribes and population, and reflect different types and strengths of relationship. One of the challenges of today’s social media is that it doesn’t model this subtlety and complexity. Psychologists are still trying to understand the diverse nature of human relationships, and the complex properties that they have.

The Future is Still Social

It may be many years before social media catches up with even today’s understanding, and by then that understanding may have moved on – potentially due to social media itself. Social networking tools let us understand how we maintain relationships, by giving us greater visibility into how people interact, but they also potentially change the way that we do these things, a kind of social version of the schrodinger’s cat problem.

There are still going to be psychological limits on how many relationships we can maintain, whether we fundamentally change them or not. Perhaps technology enables us to have a feeling of maintaining more relationships, or it deepens relationships that have been weakened by our modern life styles. At a more human level, it is raising the question of what we mean by  ’friend‘. It is certainly making qualitative changes to what we know about those around us, and our ability to discover new people to communicate with.

Maybe you’ve worked out your own personal Dunbar number, or found ways of recreating those different circles of friendship with social media? Do you see tribes and bands in action on-line?

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At the time, networks were new and exciting things – they were the web 2.0 of their time. Ethernet, Bob Metcalfe’s technology, had some unusual properties, which are still true nearly 30 years on, now that it connects almost every computer in the average office:

• Everything ON an Ethernet network is connected TO everything on the network (hold that thought).
• All connections are equal, in as much as it didn’t matter where you connected, you got the same.
• Everything on the network receives everything sent to the network (this one has changed slightly).

Compared to point to point or ring based networks most of us fought with at the time, this was revolutionary stuff. Metcalfe asserted that the value of such a network was the square of the number of nodes on it: n^2 (or n x n for the benefit of Windows calculator in basic mode). A picture explains better:

Matcalfe’s law

Matcalfe’s law has been held up along side the likes of Moore’s Law as the foundation of Internet growth, but there are at least a couple of problems with that:

• A. It was never really an empirically proven law.
• B. If it was, we have well and truly broken it.

Alan points to some of the reasons for that, but I’d like to dissect it another way, in thinking about social networks and social media. There are some implicit assumptions in Metcale’s law:

1. All nodes start equal (a node here could be a computer, person, etc…).
2. Every node is equally connected.
3. The interaction of the nodes does not change their value (all nodes stay equal).

If these three things aren’t true for today’s Internet or for social networks, then Metcalfe’s Law probably does not apply. Are they true? Do they reflect a network with people as nodes? One by one:

1. In today’s Internet, as with many things, it turns out that not all nodes are equal. In fact it is often an inverse power law, or a 1/n rule. You see this with blogs, where a small proportion account for the majority of traffic. On most computer networks you have desktop machines (clients) and servers. In people you have introverts and extroverts. Definitely not all equal.
2. The bandwidth or connectivity between nodes is not just about how much is available, it is also about how much is used. We may be able to phone each other, but do we? Also, today’s networks, social or otherwise, have nodes that are connected to more than others – be it Scoble or a Google server. This is the most asymmetric part of social networks and the Internet today.
3. Transactional models have made a huge difference in Psychology. They apply equally well to social computing. The way that nodes (or people!) interact with each other changes their value, and how they interact with other nodes. I start commenting on a blog, I change its value to others. This interaction is one of the very dynamic things in the blogosphere. A complex dynamic, but a key to the value.

A Different Law of Social Media Networks?

By the way, I’m not throwing stones at the law, that would be far too fashionable, as a quick search would show! Two related laws, which Alan picked up on are Sarnoff’s Law (for broadcast networks – their value is proportional to the number of viewers, nice straight line stuff) and Reed’s Law (which is highly exponential, essential saying that Metcalfe’s law understates the value of a network). Somewhere inbetween Sarnoff’s Law and Reed’s Law is the value of a network. Remember, all of these Law’s say that the value is proportional, we aren’t talking absolutes – we can’t say your network is worth “12″ – whatever the units for such a measurement might be.

It was the thinking around uncapped exponential models which caused much of the dot com madness – the myth of infinite scale and near infinite value from huge scale. The reality is that networks actually reach a point of diminishing returns. Some have argued for an inverse of Metcalfe’s law for social sites. It is interesting to think about why this is, at least from looking at computer networks:

• Broadcast noise – this is the reason really big (Ethernet) networks don’t work well. Broadcast packets which go out to everyone, if you get too many devices on the network, sending too many, you end up spending your whole time trying to take it all in. Nodes have no processing power left to get processing done or to send data. This is probably familiar to Twitter addicts! For broadcast media to be two way requires ‘turn taking’ and that gets harder as there are more involved.
• Finite (global) bandwidth. Bandwidth is finite, based on technology and physical infrastructure (if you want to argue this one, go and look at how many under sea cables there are/aren’t). As you add more devices, they share than bandwidth pool, however it is constrained. That means less and less information can be sent. Think of it this way, what happens if you open 100 web pages at once, or if you had 4,000 friends and a single phone was your only means of communication.
• Networks in networks. The Internet provides universal connectivity – pretty much everything is connected to pretty much everything, give or take the occasional blip and governmental intervention. However, the network we experience is not the servers and routers that make it up, it is the applications on them. Web servers running blog software and other applications. These are not universally connected. At the high layers, we revert to point-to-point communication, which puts everything back to a linear model. When the conversation moves from the blog to IM or the phone, others loose out, but at scale that is how it has to be.

Metcalfe’s Law and Dunbar’s Number

This all brings me to Dunbar’s Number, which Alan just had to drag into it! For background see earlier posts on the complete bounds of our social networks: Part I and Part II. Many tout the Dunbar number. I it might be better off throwing around Metcalfe. The law was valid at the time, and in the context, but the way that networks work have changed and evolved means that Metcalfe’s law needs to be evolved accordingly, and many a postgrad is pursuing that one. Likewise with the Dundar number.

Dunbar took research on primates, then scaled the numbers to reflect our larger brains. However, we no longer interact as apes do. Our day to day communication is not just face to face, but increasingly mediated by technology. Ambient communication (like Twitter), blogs, photosharing, Dopplr and Instant Messaging are changing the nature of our communications and relationships.

Welcome to the global beta program, there is no planned release date, little support, no product manager and no uninstall option. We need to take the best that we know, from psychology, systems theory and wherever else we can find, and hold on tight for the ride!

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Paul Graham wrote an essay “You weren’t meant to have a boss” which is really about large versus small companies, and it raises some good questions – if a little controversially.

However, it is Robin Dunbar (now teaching at Oxford) who produced the most famous research, back in 1993. His work was popularised in Malcolm Gladwell’s book ‘The Tipping Point’ – to such extent that many in the social media space talk about “Dunbar’s number“.

Dunbar took research on non-human primate social groups and used some (fairly finger in the air – by his own admission) statistical methods to extrapolate this to humans. Based on our brain’s larger neocortex size, he predicted 150 as the mean size limit for a human’s meaningful social network.

This has been widely used as a sound-bite, even featuring in The Wall Street Journal (article written by Carl Bialik). In a later paper (2003), Dunbar talks about a number range of 100-300 as the number of people in our social world (defined as the people we might turn to in severe stress, or at least approach at the airport if we needed help).

Now that we have social software, we can study people’s social graphs in ways that were very difficult previously. That said, some of the research is a little esoteric, for example Christopher Allen has an interesting post with links to research on the playon blog, looking at data from groups on World of Warcraft (for the non-gamers out there, this is a massively multiplayer on-line role playing game). We have to remember that on-line games and social networking sites like Facebook don’t directly relate to real life relationships – much as the average Facebook addict might find that hard to accept.

Researchers also have the concept of subgraphs – essentially tighter ‘cliques’ that exist within the social graph, as clusters of more tightly meshed relationships, that is individuals who have more mutual friends. In his book ‘Evolutionary Psychology’, Dunbar talks about circles of intimacy – different rings of friendship, with different levels of intimacy. We can map that to our own lives, where we usually have a smaller group of people that we are closer to.

Although Dunbar doesn’t use social networks, his view is that they might help our brains push past this limit. However, on-line networking doesn’t replace the social grooming required to maintain relationships. We still need to meet ‘IRL’ (in real life). He isn’t sold on the idea that social networks make his number outdated. Language may provide a cheaper form of social grooming – it certainly beats picking nits out of your friend’s hair – but it isn’t clear if communication technology provides even greater short cuts. The research, Dunbar says, “made us realize people don’t know what these wretched things called relationships are — and that helps explain why we’re so bad at them”.

Continued in Part II >>

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