The July issue of IEEE Spectrum contained an article called "Metcalfe's Law is Wrong". Bob Metcalfe wrote a response to the article as a blog entry in August. The editorial in the November issue of IEEE Spectrum says that the article raised its own little storm of controversy and solicits further comments. Here are my thoughts.
Metcalfe's Law states that the 'value' of a network grows as the square of the number of connection points to the network. This is usually stated as the number of users where each user is assumed to have their own connection point. The law was popularized in 1993 by Gorge Gilder, writer of Telecosm, the Gilder Technology Report and chief cheerleader of the telecom/internet revolution/bubble. Brisco, Odlyzko and Tilly argue in the IEEE Spectrum article that the actual growth in value is n*log(n) and that the original formulation was bad because it directly led to the speculative excess of the telecom/internet bubble.
Put baldly, Metcalfe's Law says that if I have a network and you have a network, and we connect our networks together, they are worth much more than either network on its own, or even the sum of the two networks. The more networks we connect the more valuable the whole thing becomes. So the point of Metcalfe's Law is that there is a huge incentive for all networks to join together into one completely connected internetwork. This has come to pass, first for telephones and then for computers. Thus my position is that Metcalfe has been proven correct and that it is academic to argue whether the 'value' (whatever that means) of the network grows quadratically or exponentially.
We need to understand the context when looking at Metcalfe's and Gilder's arguments. As Bob Metcalfe says in his blog entry, in 1980 when he devised Metcalfe's Law he was just trying to sell the value of networks and create business for his company 3COM. This was at a time when an Ethernet card cost $5000 and flinty eyed accountants would argue to reduce the size of their network buy while he would argue that they should increase it.
George Gilder is the person who foresaw a single interconnected Internet at a time when there was CompuServe, Prodigy, AOL and thousands of local bulletin board systems. All of these were swept away by the internet revolution except for AOL who managed to ride the wave by co-opting it. So Gilder was correct as well, although he was eventually carried away by the force of his own argument like many who listened to him.