Reed's Law and how multiple identities make the long tail just that little bit longer...

Reed’s Law and how multiple identities make the long tail just that little bit longer… David Cushman, August 2007

Reed’s Law or Group Forming Network Theory as Dr David P Reed* originally and rather modestly called it, is the mathematical explanation for the power of the network.

As with all great ideas it’s breathtakingly simple, easy to understand and enormously enlightening. This paper sets out to explain what Reed’s Law describes and includes more recent understandings of the collaborative power of networks which I hope helps make sense of and gives context to the exponential.

It also suggests that the multiple complex identities we are adopting in multiple communities are not necessarily a ‘Bad Thing’. My contention is that the different modes of thought these actively encourage are to be welcomed when viewed in the context of unleashing the power of self-forming collaborative communities of interest and purpose.

 In the beginning In the beginning we had Sarnoff’s Law – a mathematical description from a broadcast, mass media age.

It was first applied to cinema screens – and latterly to TV. Sarnoff’s law states that the value of a network grows in proportion to the number of viewers.

It’s a straight line. The more viewers, the more value the network has. Most audience measurement techniques have simply followed this ever since. Some (such as unique users/visitor counts) have, inappropriately, continued to apply it to websites and social networks. It’s a serious underestimation when you move out of broadcast models.

Metcalfe’s Law offers a better fit. It offers a better way of measuring the relentless growth of the power of the internet.

This law states that the value of the network grows in proportion to the number of nodes on the network.

For example: One fax machine is useless (1 squared = 0). Two (2 squared = 4), has more utility. And each one that’s added to the network increases the value of all nodes on it (3 squared = 9 etc). So if your website is getting 10,000 more unique users a month more than a rival – the gap between you and them in terms of potential value created is 10,000 squared (100m!). 10,000 more nodes on a network – even linking from one to one - is way more valuable than 10,000 passive viewers of a broadcast (assuming you’ve gone to the trouble of doing more digitally than simply replicating the broadcast model…).

Metcalfe’s N squared value is why the growth of networks used for one-to-one communication (eg phone services, email, IM) follows the pattern it does. Simply, new users will almost always join the larger network because they will reason it offers more value to them. Frankly – it usually does. A tipping point is reached. Floodgates open.

If/when Skype (or one of its many rivals) assumes dominance over our mobile identities as defined by our ‘number’… god help the operators.

Metcalfe’s Law charts an impressive and rapid rate of growth of utility. But even this - according to Reed – is a gross underestimation.

What Metcalfe’s Law fails to take account of is that each of the nodes on the network can choose to form groups of their own, of what ever size or complexity they choose, with near neighbours or distant, initially unrelated, nodes. They can choose small groups, large groups, be part of multiple groups, uber and sub-groups etc etc etc.

Wild growth Add up all of the two-person, three-person, four-person etc groups and the utility is 2 to the power of N. And this represents astonishing, wild growth potential.

Dr Reed quotes the example of the minister who was offered what ever he chose as a reward from his king. He asked for two copper coins on the first square of a chess board, four on the next, eight on the third and so on, following the progression of 2 to the power of n.

The King thought he’d got off lightly… until when they reached the 13th square the number of copper coins had reached 8192. And if he’d had a big enough abacus he’d have discovered that by the 64th square he’d be handing over somewhere in the region of 18 quintillion copper coins – a number rather higher than there are grains of sand in the world.

He didn’t bother. He beheaded the smart arse instead. Not something we can do with our rivals…

Counter-intuitive? There are those who argue that Reed’s Law is counter-intuitive. Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly among them:

“Reed's Law says that every new person on a network doubles its value. Adding 10 people, by this reasoning, increases its value a thousandfold (210). “But that does not even remotely fit our general expectations of network values—a network with 50,010 people can't possibly be worth a thousand times as much as a network with 50 000 people.”

They argue n Log (n) offers a more accurate interpretation of the growth of networks. That’s illustrated in the following diagram from their site. You’ll find their well-reasoned argument at:

Do the Maths Reed has refined his Law in the following mathematical terms.

The number of possible sub-groups of network participants is 2 to the power of N -N -1, where N is the number of participants.

So what Reed’s Law describes is the possible number of sub-groups – and this reveals a potential, not an actual, value. That theoretical value gets closer to being realised if the network is used in a particular way – in a way which I believe is becoming more and more the norm as the digital native generation takes charge.

Groups offer their greatest potential value when they work together to do much more than chat.

Collaboration In charting the possible number of sub-groups Reeds Law reveals the collaborative potential of a network.

When collaboration happens new – often immense – value emerges.

What do we mean by collaboration? JP Rangaswami, on Confused of Calcultta, offers: “collaboration is more than just “working together”… collaboration implies that multiple people produce something that the individuals involved could not have produced acting on their own… “Technology advances have meant that some level of time-shifting and place-shifting is now possible, reducing the simultaneity inherent in the original scenario.”  Flow not focus Stowe Boyd suggests the greatest value unleashed by networks comes when the group is not only one which has self-formed with a collaborative purpose, but one in which people are willing to drop everything to join in the flow as and when they are required to by their connections – ie drop everything to act in real time.

Boyd believes that far from the pipe dream that some may regard this as, this is the natural place our involvement in networks leads to. He asks us to think of attention (ie demand on our time) as being more about flow than focus.

•	“Don't listen to industrial era or information era (the last stage of industrial-ism) nonsense about personal productivity. Don't listen to the Man. •	 “The network is mostly connections. The connections matter, give it value, not the nodes. •	“Time is a shared space -- your time is truly not your own •	“Productivity is second to Connection: network productivity trumps personal productivity.” This belief in the power of the network – and his willingness to subsume personal focus to it is based on the simple notion that: “I am made greater by the sum of my connections – so are my connections.” Don’t just network for networking’s sake When a network is for simple one-to-one communication there is little potential for collaboration (other than between one and another). There is no potential for unleashing the wisdom of crowds**, for tapping into the notion that none of us is as clever as all of us. Ross Mayfield, CEO of Socialtext, offered his own equation for the value created by collaboration, writing in 2003,.

In his Ecosystem of Networks (diagram at he argues that the growth and potential value of a network is not only defined by its freedom to self-form into groups – but crucially by what those groups do. For example. If your blog (your place in the network) is simply about publishing information its value to you and your readers follow’s Sarnoff’s law. If you use Facebook to communicate with your friends, then the value derived follows Metcalfe’s law.

If your node, your place in the network, is used to collaborate with others – to share information, mash-up images… create new ideas, services and products… THEN the value growth can follow Reeds Law.

In other words Reed’s Law reveals the potential value growth in collaborative networks of shared interest and purpose.

And it is in this that the run-away value Reed’s Law describes is found.

It is this which answers Briscoe, Odlyzko and Tilly’s concern: How is a network with 10 more people worth 1000 times more?

Imagine a collaborative network of 1000 scientists who have been seeking the cure for cancer. If 10 more join there are now 1000 more potential subgroups. If just one of the new juxtapositions/mergers/mashings of ideas results in that cure for cancer few would argue that the network had delivered a value 1000-times greater than the network’s previous state.

Of course, not every single potential group will form. Not every new idea will deliver cancer-curing value. This much we know. It’s why simply enabling collaborative networks will never deliver a 100% replica of the Reed’s Law value curve. For each potential group that doesn’t form, a big chunk of subsequent value is lost.

What we find harder to know, or even imagine, is the value emerging from those collaborative groups which do form.

Self-forming collaborative communites of shared interest and purpose It seems to me that the pursuit of that emerging value is the best indicator to where our development and investment efforts should be focused if we wish to create sustainable value.

Networks which allow self-forming collaborative communities of shared interest and purpose WILL create value.

This is the reason networks of collaboration have real power, create value you couldn’t predict and are fast becoming the model for a new way of socio-economic life.

And as networks gain increasing influence on the macro economics of life, they are also having greater and greater influence on our microlife – on the creation of our own individual identities.

Multi-faced identities – we’re all getting a bit complicated Our identities become increasingly complex. The more I collaborate in self-forming groups – the more complex ‘I’ become. It’s all a question of psychological self-determinism – or who the hell do I think I am?

Our identity – whether it carries the label of a name or a number – is a work in progress. Ever-shifting, responding to communities it is part of, your identity is as much (perhaps more) created by those around you as by yourself.

The desire and need for psychological self-determinism is working as a powerful adjunct to the growing influence of global, digital networks.

When communities were fixed in location, your identity was created by your relationships within that fixed community. Your identity was equally fixed.

In terms of Group Forming Network Theory you belonged to just one group. And it was pretty much fixed in size. In a socially-networked world, the creation of your identity becomes a process which is contributed to by more people, more often, and from very varied backgrounds.

The community you exist in shapes your identity from its perspective and from your own. Your identity varies from community to community.

If once you were the blacksmith's son and village blacksmith-in-waiting, now you are a huge variety of identities - depending on the community you are interacting with at any one time.

Our identities become increasingly multi-faceted.

Example - on my blog my identity is relatively serious, thoughtful. On facebook... more playful. I'm displaying a different facet of a complex identity.

The community I feel I am part of when writing my blog joins in the construction of my serious and thoughtful persona (by their comments and expectations).

The community I feel part of on facebook also joins in the construction of my persona there - by the way it acts, by its response to what I do, by the tools it offers me.

The push and pull of the forces forging my identity in all elements of my life are communal. I interact with a community, therefore I am...

Each community creates a different facet of that identity - and in doing so makes a contribution to subtly reshaping the core.

Simple example: Becoming a father changes your personality. You have a new role to play and a new set of relationships - with your child, with your partner (now a mother, too) with other fathers, other parents, grandparents etc etc. Each interaction changes you in small but important ways.

And these result in changes at your core.

This may be an extreme and emotionally-loaded example, but I believe the co-creation of facets of your personality have more than a superficial impact.

Perhaps this is why 'the edglings' that Stowe Boyd decribes, or Generation-C that Alan Moore and Tomi Ahonen describe, have a different set of wants - and aren't satisfied by the norms of mass production/media.

Through new mobile, fluid, co-creating communities they find themselves. And they find they want to share in, to be part of, to engage with.

They are people for whom collaboration and participation is the norm – for whom Reed’s Law is right.

Understanding which facets of personalities you seek to engage with, understanding that you are dealing with personalities created from converged facets... these are real challenges for those marketing and/or creating social media in 2007.

Further, the notion that we want just one digital identity is challenged by the emerging value multiple identities offer.

An adjustment to Reed’s Law? Perhaps there is an adjustment required for Reed’s Law?

If each of us is a node on the network, each time one new node is added the value of the network (assuming the caveats described above) doubles.

But If each node has multiple identities then the potential value must be multiplied by x, where x= the number of identities per node.

This clearly can only add to the value in an uber network – one in which multiple identities apply: The internet itself being the daddy of them all.

What is the value of X? The average number of social networks regularly used by the average social networker is… well, let’s say it’s greater than one. I am a user of five, but a regular user of three. Plenty of people who use them will use just one. Those who use none are not part of any network and are therefore not part of the Reeds Law value value curve creation of the internet. X must equal a factor somewhat larger than 1. Some estimate the average at 2.5.

This then goes some way to restoring some of the value lost to the Reed’s Law calculation when potential groups do not form. This suggests that the actual ‘real’ curve may be somewhere between Metcalfe’s and Reed’s curves.

Of course, if the potential of every group were fulfilled AND we apply the multiple ID factor – then the result must be an even steeper curve than even Reed predicted:

The number of possible sub-groups of network participants becomes 2 to the power of N(x) - N -1, where N is the number of participants and (x) is the average number of identities of each participating node.

The theoretical growth of value in participatory and collaborative networks of multiple identity nodes is greater even than Reed predicts.

It seems reasonable to challenge this identity complication. Why shouldn’t N simply be the value which encompasses the total of N(x)?

I feel it’s worth making the distinction because the N value doesn’t reflect the diversity of thought the multiple identities of one individual node (person) can offer.

The thoughts of my facebook identity may differ from those of my Blogger one. And that’s because my modes of thought, my open-ness, my willingness to think differently in different contexts/communities does vary.

Environment/community counts.

For example, Twitter thoughts may kick the whole long-winded reasoned argument out of the window – resulting in a different set of problem solving thinking, that short-cuts the logical and makes leaps using instinct.

A longer tail Given the notion that the converged identities that make up the network are collaborating to create, it is reasonable to suggest that the supply of what they create should match the demand for what is created. If the network works unfettered it should make only that which there is demand for.

So to discover the demand curve, all we need do is tip Reed’s Law on its side.

And – there’s that long tail. What adding our identity multiple does to Reed’s equation is make the long tail just that little bit longer still. The more identities, the longer the tail.

 Further Reading/References: 1.	That Sneaky Exponential: Dr David P Reed* (http://www.reed.com/Papers/GFN/reedslaw.html ) 2.	Metcalfe’s Law is Wrong: Bob Briscoe, Andrew Odlyzko and Benjamin Tilly (http://www.spectrum.ieee.org/print/4109 ) 3.	Stowe Boyd: Overload shmoverload: http://www.stoweboyd.com/message/2007/03/overload_shmove.html 4.	Communities Dominate Brands: Alan Moore & Tomi Ahonen (http://communities-dominate.blogs.com/ ) 5.	Ross Mayfield’s weblog: (http://radio.weblogs.com/0114726/2003/04/09.html ) 6.	I am part of a community, therefore I am: David Cushman (http://fasterfuture.blogspot.com/2007/08/i-am-part-of-community-therefore-i-am.html ) 7.	Confused of Calcutta: Maybe It’s because I’m a Calcuttan. http://confusedofcalcutta.com/2007/08/31/maybe-its-because-im-a-calcuttan/ 8.	The Wisdom of Crowds ** (http://www.randomhouse.com/features/wisdomofcrowds/excerpt.html) 9.	The Long Tail: Chris Anderson (http://www.thelongtail.com/)