Elsewhere

Metcalfe’s Law, Reed’s Law, Boyd’s Law: A Post From 2003

[originally posted on Aug 20, 2006. I dug out of the archives because of the Knight News Challenge on Networks, which refers to Reed’s Law. It’s still topical reading.]

Back in 2003, at my old, old blog, Timing, I wrote a post, that laid out the basis of Reed’s Law, which is now relevant because of the of the recent IEEE Metcalfe’s Law brouhaha. Fred Wilson recently noted that he wished that Metcalfe had enlarged his arguments to include Reed’s Law. So I unearthed this from the time vaults:

[from Re: Social Disutility and Competition in Network Ecosystems]

Tim Oren writes about Ross Mayfield’s thoughts on ecosystems of networks.

First of all, this seems to all have grown from David Reed’s “Sneaky Exponential” piece, where he introduces Reed’s Law, and contrasts the various stages of value as the network grows. I wrote about this at some length in a recent tissue of Message.

Finding the Value of the Network: Communities

The conventional wisdom about the value of a communication network is embodied in Metcalfe’s Law, named after one of the founders of the Internet. He said that the value of a communications network grows as the square of the number of people using it, or 2 to the Nth. Metcalfe’s Law is focused on the point-to-point, pair-wise communications between individuals. It is a linear model of growth.

But this model seems wrong, and does not account for the non-linear effects of social groups. David Reed is a well-known exponent of the observation that the value of a communication network grows with the number of groups it supports.

“Reed’s law is the assertion of David P. Reed that the utility of large networks, particularly social networks, can scale exponentially with the size of the network.

The reason for this is that the number of possible sub-groups of network participants is 2N, where N is the number of participants.

This grows much more rapidly than either

  • the number of participants, N, or
  • the number of possible pair connections, N(N+1)/2 (which follows Metcalfe’s law)
so that even if the utility of groups being available to be joined is very small on a per-group basis, eventually the network effect of potential group membership can dominate the overall economics of the system. (Wikipedia, www.wikipedia.org)

Stated another way, any communication network’s value is best estimated by the number of groups that exist in the population of users. The value of a network like the Internet, Reed is telling us, can not be effectively measured by the number of financial transactions it can support, or the number of messages being sent through its millions of routers, or even the number of people using it at any time. The only reasonable way to measure its value is to count the number of groups that it supports, or so he asserts.

Accelerating Collaboration: Communities of Purpose

While its wonderful that Internet-enabled fans of the newest heavy metal band can swap gossip, MP3s and revealing photos, and this may enrich western civilization in some way, it may seem a long way from the factory floor or the pressing realities in the CEO’s suite. But it is exactly this sort of social interaction that forms all groups, even the most practical and purposeful, like those within the enterprise.

Turning Reed’s Law into a tool to enhance value for the enterprise may seem to some to be a bit out there, a bit too new age, like bringing in a Feng Shui geomancer to avoid building the new corporate headquarters in the wrong orientation to the Cosmos. But it is simply pragmatic. Obviously, work gets down by groups, Obviously, you want to harness the value of closer, more productive relationships with partners, suppliers, and customers. And, yes, it is becoming obvious that any significant enterprise performance improvements will require interactions with people – and applications – outside the enterprise.

Tim Oren’s final observations — that people generally contribute significantly to around 2.5 groups, and that groups hit size limits (the Dunbar 150 person max rule) — return to the core theme of social groups and network value. Size does matter. People can only meaningfully be involved with a limited number of groups, and groups lose group cohesion after some ceiling is reached.

But the value of the network is a function of the number of groups supported, even if the membership of each group is bounded. The flexibility associated with group transience is an additional factor — so it’s not just a static equation, its a non-linear flow equation. All of the laws that Reed compares — Sarnoff, Metcalfe, and Reed — are statically defined.

In a recent report I wrote for Cutter (now in production) I argue that real-time groups create value for companies as an extension or corollary of Reed’s Law, which I humbly have dubbed Boyd’s Law. Ahem.

As companies seek to increase their individual responsiveness and decrease the impacts of volatility in their markets, they will increase their synchronous communications with partners, but the net effect will be an increase in asynchronous operations of the meta-enterprise.

This seeming paradox is simply explained. A real time enterprise will have more frequent communication with its partners – passing information from application to application, or conducting real time communication between members of real time communities – and as a result, the latency in information transfer decreases.

This means that companies in the meta-enterprise are free to act on this lower latency information earlier, increasing overall performance across the meta-enterprise. Or put another way, decreasing latency in the individual communication events translates into higher probabilities of increased parallelism in the overall network. This emergent property of increased real time communication in networks is exactly the value creation David Reed was getting at.

In human terms, and leaving the queuing theory aside, this value increase grows from the power of social groups. It’s not quasi-mystical chaos theory – it’s just practical.

So, you have to look at other factors, not just size, or even who is a member, but things like the tools being used to communicate in order to understand the components of value arising from social interaction.

And today, in 2006, it’s even stranger to see some IEEE article attempting to peg the value of a network on some sort of stock market economics, as opposed to the utility of the network in practice: the value created for individuals, groups, and the network denizens as a whole.

[And today, in 2012, I am totally unsurprised that folks are still referring back to statically defined rules instead of something like what I was poking at in 2003: Boyd’s Law. I would now define it this way, taking the perspective of the value of a person in a social network:

The value of any new node in a network — and in social networks, a node is a person — can be characterized as the increase in network-wide parallelism caused by the connections the new node establishes.

Nine years later.]

Zuckerberg Proves He’s No Math Whiz

Alexia Tsotsis, Mark Zuckerberg Explains His Law Of Social Sharing

Zuckerberg explained that in accordance with Facebook’s data, social sharing functions exponentially, so that the amount of stuff you shared today is double the amount of stuff you shared a year ago and the stuff that you will share a year from now will be double the amount you’ve shared today. In Mark Zuckerberg’s Law of Social Sharing, Y = C *2^X — Where X is time, Y is what you will be sharing and C is a constant.

Holding that most people intuitively misunderstand the profundity of exponential growth, Zuckerberg provided the example of a piece of paper folded upon itself 50 times. “If you took a piece of paper and folded it on itself 50 times, how tall would it be?” He continued, “Most people would say a few feet … Turns out it goes to the moon and back 10 times … I mean it’s 2^50 * the height of the paper. It’s a small base doubling many times.”

Whether Zuckerberg’s concise prediction of human sharing behavior is accurate remains to be seen. As Chris Dixon points out, it seems kind of absurd that people will be sharing 1,048,576 (2^20) times the items of information they are sharing today twenty years from now.

It’s impossible.

However, there is a curious power law of social sharing lurking in the nets somewhere, probably something that parallels Reed’s Law, which states that the value of a network increases as a function of the number of groups that are formed in the network. Perhaps, updated to a function of the number of productive relationships each member of the network has?

My bet is that overall sharing in the network increases as a function of both content, specifically the salience and distinctiveness of what people see, and context, which includes both the features of the tools we use to access and communicate through the network, and the nature of the relationship to the person who is the source of information.

The combination of these factors is generally misunderstood. I am much more likely to share information that is unique and timely, and the likelihood of that is principally a function of who I am following. The single greatest factor in information sharing is quality of sources: the more they provide distinctive and compelling messages, the more likely I am to pass those messages along. And therefore by extension, the more likely I am to influence those that follow me to do the same.

So Zuckerberg is wrong to suggest that social sharing will increase without regard to our choices, like the way the universe expands uniformally, as discovered by Edwin Hubble.

On the contrary, sharing increases as a function of our connection to each other.

Damon Centola has shown that increasing social density increases the likelihood and rate at which ideas can travel through social networks. So the factors that increase social density — better social tools, urbanization, ubiquitous connectivity — come to bear directly on this.

It’s not like Hubble’s constant, but a variable, depending on us and the tools we build and use. And most importantly, on the people we chose to follow.

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