ILLUSTRATION: SERGE BLOCH

Of all the popular ideas of the Internet boom, one of the most dangerously influential was Metcalfe's Law. Simply put, it says that the value of a communications network is proportional to the square of the number of its users.

The law is said to be true for any type of communications network, whether it involves telephones, computers, or users of the World Wide Web. While the notion of "value" is inevitably somewhat vague, the idea is that a network is more valuable the more people you can call or write to or the more Web pages you can link to.

Metcalfe's Law attempts to quantify this increase in value. It is named for no less a luminary than Robert M. Metcalfe, the inventor of Ethernet. During the Internet boom, the law was an article of faith with entrepreneurs, venture capitalists, and engineers, because it seemed to offer a quantitative explanation for the boom's various now-quaint mantras, like "network effects," "first-mover advantage," "Internet time," and, most poignant of all, "build it and they will come."

By seeming to assure that the value of a network would increase quadratically—proportionately to the square of the number of its participants—while costs would, at most, grow linearly, Metcalfe's Law gave an air of credibility to the mad rush for growth and the neglect of profitability. It may seem a mundane observation today, but it was hot stuff during the Internet bubble.

Remarkably enough, though the quaint nostrums of the dot-com era are gone, Metcalfe's Law remains, adding a touch of scientific respectability to a new wave of investment that is being contemplated, the Bubble 2.0, which appears to be inspired by the success of Google. That's dangerous because, as we will demonstrate, the law is wrong. If there is to be a new, broadband-inspired period of telecommunications growth, it is essential that the mistakes of the 1990s not be reprised.

The law was named in 1993 by George Gilder, publisher of the influential Gilder Technology Report. Like Moore's Law, which states that the number of transistors on a chip will double every 18 to 20 months, Metcalfe's Law is a rough empirical description, not an immutable physical law. Gilder proclaimed the law's importance in the development of what came to be called "the New Economy."

Soon afterward, Reed E. Hundt, then the chairman of the U.S. Federal Communications Commission, declared that Metcalfe's Law and Moore's Law "give us the best foundation for understanding the Internet." A few years later, Marc Andreessen, who created the first popular Web browser and went on to cofound Netscape, attributed the rapid development of the Web—for example, the growth in AOL's subscriber base—to Metcalfe's Law.

There was some validity to many of the Internet mantras of the bubble years. A few very successful dot-coms did exploit the power of the Internet to provide services that today yield great profits. But when we look beyond that handful of spectacular successes, we see that, overall, the law's devotees didn't fare well. For every Yahoo or Google, there were dozens, even hundreds, of Pets.coms, EToys, and Excite@Homes, each dedicated to increasing its user base instead of its profits, all the while increasing expenses without revenue.

Because of the mind-set created, at least in small part, by Metcalfe's Law, even the stocks of rock-solid companies reached absurd heights before returning to Earth. The share price of Cisco Systems Inc., San Jose, Calif., for example, fell 89 percent—a loss of over US $580 billion in the paper value of its stock—between March 2000 and October 2002. And the rapid growth of AOL, which Andreessen attributed to Metcalfe's Law, came to a screeching halt; the company has struggled, to put it mildly, in the last few years.