David Weinberger's Intranet Buzz:
Reed's Law — An Interview
How the Net's Value Comes from Its Enabling of Groups, Not Just of Individual-To-Individual Connections

JOHO: Here are JOHO we like groups. So do you. What do you see as the role of groups on the Net?

One third of a century ago in an article entitled "The Computer as a Communication Medium," J.C.R. Licklider and Bob Taylor wrote

What will on-line interactive communities be like? … they will consist of geographically separated members … communities not of common location, but of common interest. … The whole will constitute a labile network of networks-ever changing in both content and configuration. … the impact … will be very great-both on the individual and on society. … First, … because the people with whom one interacts will be selected more by commonality … than by accidents of proximity.

Licklider and Taylor used this argument to rally a generation of designers including me to join together in research and development of a radical new architecture for communications, which we now call the Internet.

Group forming is, in my opinion, the technical feature that most distinguishes the Internet's capabilities from all other communications media before it. Beyond either the hub-and-spokes broadcast networks of print, television, and radio, or the peer transactional networks of telegraph, telephone, and online financial transactions, the Internet's architecture also supports group-forming networks whose members can assemble and maintain persistent communicating groups.

Though broadcasting of content, catalog sales, and user-to-user messaging and financial transactions easily carry over from old media to the Internet, novel group-oriented functions that did not exist before computer networks have grown rapidly as well. Functions ranging from the "reply-to-all" feature in e-mail, chat-room hosting on AOL, web hosting sites such as GeoCities, auction-hosting on eBay, and buddy-lists in instant-messaging all enable, enhance, and sustain huge numbers of member-organized groups. The key thing about these groups is that they are freely formed — though various institutions, services, and organizations enable the group-forming, the choice of which groups are formed, who participates, etc. is entirely up to the members who organize the group, and the purpose of each group is shaped largely by some common needs of its members.

Contrast the Internet with the telephone network or the commercial broadcast networks. In those networks, which have no architectural features to support groups (save, perhaps, telephone conference call services, and the MCI "Friends and Family" billing group feature), participants never organize, never share, and devote few network resources to sustain their associations. The associations exist — just ask a group of teenagers who check in with all their friends every day — but the network doesn't know it, and certainly doesn't provide services to enhance the natural social tendencies of humans to form groups.

So how do you connect groupiness to economic value? And talk slowly I'm a mathematical idiot-savant, except without the savant part.

Five or six years ago, I was trying to explain what is now popularly called "Metcalfe's Law" to a skeptical engineer. Metcalfe's Law says that the "value" of a network grows in proportion to N², where N is the number of members of the network. The engineer immediately understood that the number of distinct pairwise connections that a network could enable was easily calculated - each of the N members could "call" any of the (N-1) other members, so there are N * (N-1) distinct calls that can be placed. And she also understood that as N gets large, this number grows proportionally to N². But, she said, if you assume that N people make 1 call each day, the number of calls that people make will only be proportional to N, and if you charge so much per minute, you can make money each day that is only proportional to the size of the network, not the square of the size! And of course, she was right…

But rather than run to the New York Times with a breaking news story to the effect that "Metcalfe's Law is wrong" I started thinking about the apparent paradox — wanting to confirm or refute this law on more fundamental grounds. After all, it's certainly possible that by charging "per minute" the phone companies might have just been practicing bad business judgment, and leaving money on the table that could have been captured by a better pricing scheme. Or something else might be going on.

And then it occurred to me that what was really going on was something different. In economics, there is a distinction between what you have to pay (let's call it "price") for something, what it's worth to you (let's call that "value"), and what it costs to produce (let's call that "cost"). Though they are fundamentally different measures, we usually think about them as the same. But to understand "value" in the way that Metcalfe's Law is formulated, you have to think about it quite differently.

In a network like the telephone network, there are two kinds of valuable benefits that a network creates. One kind is capacity - how much stuff it can transport per unit time for each user. The other kind is connectivity - which increases with the number of different destinations a user can choose to contact at any point in time.

The resolution to the apparent paradox results from confusing the two kinds of value. The total capacity used by users of the network does indeed tend to grow proportional to N, if only because the total resources that the users can devote to the network tends to grow proportional to N. But the potential connectivity grows proportional to N² as Metcalfe's Law would predict.

A potential connection is what economic thinkers call an option, which is the right, but not the obligation, to perform an action at some point in the future. The key to understanding a lot of the value of networks is that they create options, and that those options are valued by the users. For another example, consider a cable TV network. Even though you can only watch one program at a time (the capacity), the choice of a hundred channels is worth more to you than the choice of three channels. The more options a network creates, the more value it creates for its users. And since the number of pairwise connection options created in an N member network is N², then if all options are equally valuable, the network's option value tends to grow much faster than its capacity. The example makes this clear is that the value of buying a fax machine depends on the number of other people you want to talk to who have fax machines to connect with. The option value is what drives the value a buyer places on fax machines, not the capacity.

When I had puzzled this out, I started wondering about other kinds of options might be created by network architecture. Much of my career has been devoted to creating applications that focus on groups — information sharing and security, discussion groups, collaboration systems, groupware, email, etc. So it was natural to wonder about groups and option value.

It was one of those Eureka moments. As a student at MIT, I learned that the number of distinct subgroups that can form in a set of N members is 2^N, which means that the number and value of group-forming options grow exponentially as N increases. (I won't repeat the proof of that simple fact here.)

JOHO: Thank you.

So any system that lets users create and maintain groups creates a set of group-forming options that increase exponentially with the number of potential members. And as a function, 2^N dominates N² - which means that even if each individual group-forming option is worth much less than an individual pairwise connection, eventually the total set of group-forming options will have far more option value than the pairwise options.

And I immediately understood why so much Internet traffic was observed to be due to newsgroups, chat rooms, etc. And why AOL's electronic community was much more sticky than CompuServe, despite similar content.

What's exciting to me about this scaling law for group-forming networks, which friends and colleagues have been kind enough to call Reed's Law, is the way it links my long-standing intuitions about the importance and value of group behavior in networks to relatively hard-nosed economic models. To someone who understands the structure of such models, the recipe for designing networks that maximize value for readers, customers, etc. becomes crystal clear. I've discussed some of the implications elsewhere.

Networked communities that support group-forming are growing in scale and reach, and network architectures that enhance group-forming processes are still being invented. Anyone who is serious about the 'net must learn to "get" the power of group-forming communities that Licklider and Taylor inspired.

David has put links to related information on his website at http://www.reed.com/gfn/.