Metcalfe's Law is really, really wrong … still

Say what you will about Metcalfe's Law, but this much we know for certain: It hasn't gotten any better in the past year-and-a-half.

Even Bob Metcalfe would agree.

We point out the obvious because the July issue of the IEEE's Spectrum magazine carries an article headlined "Metcalfe's Law is Wrong," authored by Andrew Odlyzko, Benjamin Tilly and Bob Briscoe.

In March 2005, Network World carried a 'Net Buzz column headlined "Metcalfe's Law … ain't" -- we're not quite as formal as Spectrum -- written by yours truly and based on a paper entitled "A refutation of Metcalfe's Law." The paper was authored by the very same Andrew Odlyzko and Benjamin Tilly, then researchers at the University of Minnesota (Odlyzko's still there, Tilly's moved on to, and Briscoe, whose name was not on the "refutation" paper, works for Networks Research Centre, BT.)

The academic paper received press coverage elsewhere, too, and seemed to exhaust whatever "gotcha" value the subject possessed -- at least until this month's Spectrum article attempted to rekindle things. 

Metcalfe's law, which dates to the early '80s, holds that the value of a network grows proportionally with the square of its number of users. Odlyzko and Tilly argued in last year's "refutation" that the value of a network actually grows at a much less dramatic pace. They offered their own alternate theory. … They do both again, with Briscoe's help, in the latest Spectrum.

What's Metcalfe's defense -- then and now? I didn't have the heart to contact him again and ask why the theory he concocted a quarter of a century ago hasn't gotten any better in the year and half since these critics first called him out. But here's what he told me last year:

"I am delighted that Metcalfe's Law keeps getting all this attention," he said. "Unlike Moore's Law, which has been numerically true since 1965, Metcalfe's Law has never been numerically true, unless you allow me to adjust the constant of proportionality to fit each case."

"One trouble is that the 'value' of networking is very hard to measure," he added. "So now that Metcalfe's Law is debunked, what is the exact formula for the value of a network?"

 I'm pretty sure it was a rhetorical question then … and would guess it remains one today.

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