Critics have declared Metcalfe’s law, which states that the value of a network grows as the square of the number of its users, a gross overestimation of the network effect, but nobody has tested the law with real data.
Using a generalization of the sigmoid function called the netoid, Ethernet’s inventor and the law’s originator models Facebook user growth over the past decade and fits his law to the associated revenue. [The Web extra is a video interview with Bob Metcalfe about the creation of the first Ethernet local area network 40 years ago at Xerox Palo Alto Research Center.]
…Metcalfe’s law implies a critical mass point in network size, after which network value begins to exceed its cost. That critical mass point is roundly given by the ratio of the cost of the network to the value of network participation. In the Internet, this ratio has been going rapidly to zero. Why?
The asymptotes of various network netoids are moving according to Moore’s law, which states that the number of transistors on an integrated circuit doubles every two years or so. Metcalfe’s law depends on Moore’s law in two ways. Faster and cheaper semiconductor processors and memory are enabling more valuable applications that demand ever-larger bandwidths. Meanwhile, faster and cheaper network ICs are driving down the cost of networking.
Moore’s law is expected to continue for another 15 years. We’ve heard predictions like this before, but since Ethernet’s bandwidth elasticity depends on the continuation of Moore’s law, let’s hope that Moore’s law doesn’t soon hit one of its netoid asymptotes, such as the speed of light, the optical limits of lithography, quantum effects at smaller feature sizes, or overheating.
Of course, Moore’s law isn’t an inevitable law of nature—it’s more a self-fulfilling prophecy that relies on continuing investment decisions at many levels among semiconductor scientists and engineers, chipmakers, and device makers. And so too should we continue investing in Internet/ Ethernet technology and thereby increase freedom and prosperity. Build it, and they will come.