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.
Metcalfe’s Law is Wrong Bob Briscoe, Andrew Odlyzko, and Benjamin Tilly, IEEE Spectrum, July 2006
Metcalfe’s Law says that the value of a communications network that supports pairwise communications grows roughly according to the square of the number of users, N^2. That is faster than Sarnoff’s Law, which says that the value of a broadcast network grows roughly according to the number of users, N. And both are slower than Reed’s law, which says that the value of a group-forming network grows roughly according to the number of users factorial, 2^N.
Metcalfe responded, pointing out the same thing I wrote in my recent book, Risk Management Solutions, that Odlyzko doesn’t get it (either in an earlier paper or in this one), that Metcalfe’s Law isn’t meant to be taken as a literal predictive law; it’s a rule of thumb:
Nobody, including Briscoe, Odlyzko, and Tilly in their SPECTRUM attack, has attempted to estimate what I hereby call A, network value’s constant of proportionality in my law, V=A*N^2. Nor has anyone tried to fit any resulting curve to actual network sizes and values.The same goes for Sarnoff’s Law and Reed’s Law: they’re both vision things, not meant to be taken literally.
As I wrote a decade ago, Metcalfe’s Law is a vision thing. It is applicable mostly to smaller networks approaching “critical mass.” And it is undone numerically by the difficulty in quantifying concepts like “connected” and “value.”
So, if the value of a network does grow as V~N*log(N), I challenge Briscoe, Odlyzko, and Tilly to prove it with some real network sizes and values. In the meantime, I’ll stick with V~N^2.
Guest Blogger Bob Metcalfe: Metcalfe’s Law Recurses Down the Long Tail of Social Networks VC Mike’s Blog, August 18, 2006
The closest Metcalfe can bring himself to mentioning either Sarnoff or Reed is when he talks about the affinity of users on a network. Well, and this:
But that’s not all. The denominator of C/A, the constant of value proportionality, A, has been going up. In the 1980s, Ethernet connectivity allowed users only to share printers, share disks, and exchange emails — a very low A indeed. But today, Internet connectivity brings users the World Wide Web, Amazon, eBay, Google, iTunes, blogs, … and social networking. The Internet’s value per connection, A, is a lot higher now, which means the critical mass size of the Internet, C/A, is a lot lower now, and for two reasons: cost and value.”Social networking; hm, that’s almost like group formation….
Later he notes that Metcalfe’s Law recurses as network users join social networks, er, almost like N factorial, as in Reed’s Law.
Hm, here’s a good point:
Let me leave as an exercise for the reader to develop the formulas for how Amazon’s Long Tail grows to the right as the combination of Moore’s and Metcalfe’s Laws biennially halves the critical-mass size of book audiences. Book buying generally shrinks with time, but I’m guessing that Amazon’s per book critical masses, its N=C/As, have been shrinking faster.What does Metcalfe’s Law have to do with net neutrality?
If a few telcos control content, you don’t get new social networks (or other new applications), growth stagnates, and the value of the network stagnates: everybody loses. Open application competition over a neutral Internet has brought us the World Wide Web, electronic mail, mailing lists, blogs, webcams, anonymous FTP, P2P filesharing, USENET newsgroups, ssh, SSL-VPN, YouTube, google video, VoIP, social networks, and more all the time. Telcos brought us X.25, X.400, and ISDN. Well, and voice mail, 3-way calling, and call forwarding, I suppose.
A small oligarchy of U.S. telcos may think they win, but in the not so long term they lose, too. Japan and Korea already have ubiquitous broadband at speeds much faster than in the U.S., yet at reasonable prices. NTT is already selling 100Mbps FTTH outside Japan, including in the U.S. Gaming the U.S. political system to an oligarchy’s advantage puts the U.S. farther behind in broadband and loses competitiveness for U.S. telcos.
Which is better risk management? Letting a small oligarchy control content? Or getting back to net neutrality?
PS: See also Om Malik’s collection of links on this discussion.