The Emerging Math/Rules of Social Networks – Magic Numbers
by Rob Paterson
If we are to use the power of the network effect to gain more leverage – I think it will be essential to understand the underlying math. For like all things in the natural world – such as say Gravity – there is a mathematical framework that underlies their operations. When Newton could describe how Gravity worked, the modern world took off. When we can do the same for social networks, we will be on our way to solving the great dystopia of our time – that we have succumbed to a machine model.
The power of the social world is like gravity or light. It seems mysterious. It is easy to wax mystical about it. But I think that what is emerging via observation – just like all good science – is the math. What is ironic is that this math is well known and has been part of human knowledge for millenia. It just has never been applied to the social world before.
It is of course the Fibonacci sequence – the sequence that nature uses to order all relationships if they are to reach their full potential. You may know of the key number that seems to be the limit of Trust for humans of about 150 – called the Dunbar Number after Robin Dunbar.
Many in the Blogosphere have been working on this. Many have seen the sequence emerge naturally in say Guilds in Gaming. Some like Stowe and Valdis are seeing this in the power use of Twitter.
Here is a summary post I made on my own blog 2 years ago that pulled together the field of knowledge that existed then. It is my hope, I am a Historian, that people with a sharper brain than I can add much more to this in the future. I am more convinced than ever that the true potential of the power of social media to get important things done will be revealed once our understanding of how all of this works improves.
Not just marketing and media – but the ideal groupings for work, for learning for health, for credit, for families and for all of our lives. A world reset to our natural design versus a machine world.
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Dave Snowden posted this recently – I could not get Cognitive Edge to accept my comment so I post them here after his post and then add some comments and list of useful links that add to the topic.
Log(N) = 0.093 + 3.389 log(CR) (1) (r2=0.764, t34=10.35, p<0.001)
Recognise it? Well of course, it’s the best-fit reduced major axis regression equation between neocortex ratio and mean group size for the sample of 36 primate genera taken from Dunbar’s 1992 paper which was popularised, and not unduly trivialised by Malcolm Gladwell into a natural limit on human group size of 150 (or 147.8 to be exact). The idea is a simple one. The human brain has co-evolved with social conditions and as a result there is a natural limit on the number of social relationships we can maintain. Dunbar linked the number to village, nomadic and military size over time. The number is exercising several people on the ever idea-stimulating value networks list serve. The argument there relates to if this is or is not a natural limit on a network or a virtual community.150 is not the only natural number. There are two others, so I could have titled this post The rule of 5,15 & 150. All of those numbers, plus a need to think more about identity than about individuals, should influence either evolutionary or engineering approaches to community/network design.What I plan to do is elaborate the numbers and their origins. I then want to look at the way in which the debate around Dunbar’s law is limited by atomistic ontology. This all too common assumption, found in the anglo-saxon world assumes self sufficiency and moral autonomy of the person, and sees communities as assemblies, voluntary or otherwise of individuals. Moving away from social atomism allows to take a different view on communities, their limitations and possibilities, but that will be tomorrow’s blog.
- Five is linked to the natural limits on the short term memory. This was first put forward by Miller’s 1956 paper and relates to time more than items (it is a common urban myth to see it as items). This means that it will vary a bit by language, different languages can compress more or less data into a defined time limit. If you have ever spoken through simultaneous translation then you will know that it takes 30% longer to say something in Spanish that it does in English. Given that the Welsh generally speak english 30% faster than the norm, this can present problems! Translation aside, the number is useful and it relates to common sense experience (always helpful). Think about how many directions you can remember, or how we organise telephone numbers. Another way to validate this is to think about models, or lists and see how many elements they have. More than five and you need a crib sheet. One of the reasons I restrict models in my own work to five elements is because of this. Less then five and they pass the paper napkin test which means they are sense making models as they can be drawn from memory, which means they can be used operationally without reference back to authority.
- Fifteen comes from anthropology and relates to natural levels of deep trust. I define deep trust here as the ability to tolerate a degree of betrayal. The number varies a bit based on the average size of the extended family in a society and is probably an habituated pattern of behaviour learnt during key periods of plasticity for the human brain. Now readers might be able to help be here. I got this number from two sources several years ago. The number was actually an upper limit of thirty but I reduced it to fifteen for alliterative purposes as well as accepting the realities of modern civilisation compared with the tribal systems from which the number originated. Unfortunately I have lost the reference and I am trying to re-discover it to reference in the book. All help appreciated! Again this manages a common sense test. Think about the social groups to which you belong and which pass the relaxation test. This test is a simple one, its who do you feel able to relax with, without worrying too much how your are seen. I realise that this does not always apply to families! However other than in pre or post divorce situations the ideas is that it should. The size there is definitely under fifteen, and more typically is a small number of groups of around eight or nine on average.
- One hundred and fifty is Dunbar’s law and in effect is the number if identities that you can maintain in your head with some degree of acquaints that an individual can maintain. It does not necessarily imply that you trust them, but it does mean that you can know something about them and their basic capabilities. In other words you can manage your expectations of their performance and abilities in different contexts and environments. For the moment lets consider this in terms of individuals (the switch to identity is for tomorrow’s blog). Consider your work groups and the size of your organisation. How many people do you know by name? How many people would you invite to a party? Again you can see the common sense experience coming though in the number. Now the assumption in Dunbar’s working and subsequent writing is that this level of knowledge requires physical proximity. However we now live in virtual as well as physical worlds so the nature of interactions change. The natural limit is probably in place, but its form, and the nature of its creation will have new variants for a new environment
Now these three numbers, 5, 15 & 150 have an alliterative quality which helps us remember and use them. They also have some fairly immediate and practical implications for communities and networks. That is what I want to look at in tomorrow’s blog which will come from Hong Kong. I am shortly leaving for the KMAP2006 conference at which I am keynoting for the second year, and I will also run workshop on uses of narrative in knowledge management. Hopefully I will meet up with some old friends and make some new ones, the conference has an interesting mix and looks less academic that last year when it was held in Wellington, New Zealand.
Great to find more discussion about these numbers. My bet is that by thinking only mechanistically we have “forgotten” their power and organize without any socially valid reason. This may surely be why so many organizations are so dysfunctional such as schools with say 1500 kids and no sub units. Why hospitals that merely have shifts of individuals are so unhappy. Why there is so much “stress” in most workplaces when the work itself is mundane.
The military however still keeps to these numbers. They have to – the task before them demands the full expression of what an organized group of people can do – they tend to use 8 as the base (8 men in a tent in the Roman army = a section) Sections “shrink” to 5 very quickly in action. Below 4, they are not very capable.
My bet is that 5-8 seems to work as the core unit of intimacy. Most sports teams fit this range. It enables you to pass the ball to a space knowing that the person will be there. It enables uspoken flow. It must have been the ideal hunting size.
Dave talks also about the limits to memory. You can remember a 7 number phone number but longer numbers, unless broken into sections of 3 and 4, are very hard to recall.
I recall other material suggesting that most “Tribes” in the hunter gatherer world (our cultural base) were about 35. 8 men and 8 women plus 16 youths and younger children. 35 is the platoon in the military which is the core organizing unit to get any serious work done. The Company would be about 200 as an paper ideal but would shrink in action to the 150 number which is the operational ideal.
VC friends of mine tell me that they get very concerned when they see new companies reach these staffing milestones of 8 -15 – 35 – 150. The hardest one being 15 -35 when you have to introduce some formal communication mechanisms. Complexity obviously does grow exponentially along a log scale.
Other work on gene pools suggests that 500 is the optimal number to keep enough variety. Hence tribal meetings for festivals etc that acted as genetic mixers as well.
What if these hard social numbers were brought back into formal prominence? What would happen to organizations? We see this with blogging now. My blogging social world has settled out along this gradient of 8 close intimates – about 16 close – about 35 reasonably close and a maximum world of 150. My test is my bloglines aggregator. I pay attention along the gradient.
I have also found that I can be assured that those that fit inside the 8 really do fit. I have worked with 2 of them before we ever met face to face.
So is this just an interesting topic or might it lead to an OD revolution? I add some good supporting links in the follow on:-
- Here is Ross Mayfield with his perspective of how these numbers work in the world of social media
- Here is a link to Robin Dunbar’s book – Grooming and Gossip that expands on his paper quoted by Dave
- Here is a link to a piece on the maths of genetics – that we need a population of 500 to ensure enough genetic diversity
- Here is John Robb talking about magic numbers and how terrorist cells are best organized
- A link to a brief survey of mine on the work of John Pfeiffer, author of the Emergence of Man (Out of print) on the numbers of conflict – why groups over 150 have to drive friction
- Ton Zijlstra weighs in here
- Here is I think the most comprehensive summary by Christopher Allen. I find his comments on Guild size compelling
Chris makes the point that while guilds have these total group numbers, it is rare to have more than 40 online at any one time. More on guilds by Chris here
He goes deeper and deeper into the friction that we feel inside organizations today because we do not consider the fall out from not understanding how these numbers work. I find this diagram very helpful -
This confirm my VC friends observation that going from a group of 7-8 to 50 plus is exceptionally difficult. Moving beyond 150 is also a chasm -
I’ve already noted the next chasm when you go beyond 80 people, which I think is the point that Dunbar’s Number actually marks for a non-survival oriented group. Even at this lower point, the noise level created by required socialization becomes an issue, and filtering becomes essential. As you approach 150 this begins to be unmanageable. Once a company grows past 200 you are really starting to need middle-management, but often you can’t afford it yet. Only when you get up past that, maybe at 350-500 people, does middle-management start really working, primarily because you’ve once again segmented your original departments, possibly again reducing them to Dunbar-sized groups.
- Chris also asks in this age of social networking software “Is there an effective limit to the size of your personal network. He adds a comment by a VC friend of his -
Venture Capitalist Jeff Nolan relates similar concerns:
“It strikes me that the social networking theory holds that the more volume you have, the bigger your network will become by introducing degrees of separation roughly along the lines of Metcalfe’s Law. I disagree, human networks do not grow in value by multiplying, but rather by reduction. For me, it’s the quality of relationships that enhances my professional and personal life, not the sheer numbers.”
If you know of other good links please let me know.
