Metcalfe was an optimist
Chris pointed out that he had heard on the Cryptography list about a paper by Odlyzko and Tilly that calls into question Metcalfe's Law. Metcalfe said that the value of a network is proportional to the square of the number of users of the network, because the number of possible conversation partners is n(n-1)/2. Odlyzko and Tilly say that not all possible conversation partners are equally valuable to everyone -- including a great discussion of Thoreau's comment on Maine and Texas -- and conclude that there are reasons to think that the value of a network grows more slowly than the square of the number of its users.
By the way, apart from saying that the value of networks grows quickly as they get larger, Metcalfe isn't actually that much of an optimist.
