Evaluation of Growth

Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly wrote Metcalfe's Law is Wrong. Please look at the whole thing, especially those with mathematical inclinations:

Imagine a network of 100 000 members that we know brings in $1 million. We have to know this starting point in advance—none of the laws can help here, as they tell us only about growth. So if the network doubles its membership to 200 000, Metcalfe's Law says its value grows by (200 0002/100 0002) times, quadrupling to $4 million, whereas the n log(n) law says its value grows by 200 000 log(200 000)/100 000 log(100 000) times to only $2.1 million. In both cases, the network's growth in value more than doubles, still outpacing the growth in members, but the one is a much more modest growth than the other. In our view, much of the difference between the artificial values of the dot-com era and the genuine value created by the Internet can be explained by the difference between the Metcalfe-fueled optimism of n 2 and the more sober reality of n log(n).

Just another one of those things that might be applicable elsewhere... But I have to admit I'm just not mathematically minded enough; I know when people really get this stuff they can see the whole graph. Anyway, Odlyzko is pretty interesting- you may want to check out some of his other publications.