Twitter and Metcalfe's Law don't seem to have much in common, at first.
Metcalfe's law describes how the value of a network is affected by the number of nodes it has (specifically, how the more users a network has, the more connections are created by each new user), and the whole point of Twitter is that it isn't a network.
It's just a way for people to communicate.
But Twitter has turned into a sort of network of its own.
People use Twitter to talk to one another, or to search for new trends, and they integrate other services with it.
Metcalfe's Law comes into play when you look at what happens every time Twitter adds a new service, or a new user.
At that point, Metcalfe's Law and Twitter come into collision: a new Twitter user can use any of the new services, or contact any existing user, or be contacted by any existing user.
If there are ten million users, each new user creates ten million potential conversations.
This means that each new user increases the value to the next user.
The math of Metcalfe's Law and Twitter gets even more complicated when you look at applications that use Twitter.
Take Foursquare, for example: every new users of Foursquare makes Foursquare more popular within Twitter.
And when that happens, Twitter becomes more attractive to new users-some of whom may end up using Foursquare! Twitter and Metcalfe's Law interact in an unpredictable way to make Twitter grow even faster than Metcalfe's Law would predict.
You can't analyze a phenomenon like Twitter without think of Metcalfe's Law.
But just running the numbers isn't enough.
You also have to understand the reasoning behind them, which shows that the numbers only tell the whole story if you know how to use them.