Math has never been my strong suit, so far be it from me to get between industry legend Bob Metcalfe and a pair of university researchers as they butt heads over the validity of "Metcalfe's Law."

Actually, it's the academics doing most of the head knocking; Metcalfe is more or less bemused by the attention.

Andrew Odlyzko and Benjamin Tilly of the Digital Technology Center at the University of Minnesota earlier this month dissed Metcalfe's theory but good in a paper titled A refutation of Metcalfe's Law and a better estimate for the value of networks and network interconnections.

Metcalfe's Law posits that the value of a network grows proportionally with the square of its number of users. Meant to be more descriptive than taken literally, it first surfaced in a slide presentation Metcalfe gave in the early 1980s when he was running 3Com and gained acclaim in the late 1990s as justification for "hockey stick" growth projections that propped up many a revenue-barren dot-com.

"The fundamental fallacy underlying [Metcalfe's Law] is in the assumption that all connections or all [enabled] groups are equally valuable," Odlyzko and Tilly argue in their paper.

Even a guy living in a shack out in the woods - without a phone, never mind broadband - ought to appreciate this point, they say.

"The defect in this assumption was pointed out a century and a half ago by Henry David Thoreau. In Walden, he wrote: 'We are in great haste to construct a magnetic telegraph from Maine to Texas; but Maine and Texas, it may be, have nothing important to communicate."

Odlyzko and Tilly do offer an alternative to Metcalfe's Law, suggesting that "the value of a general communication network of size n grows like n log(n)."

In terms even a journalism major can understand, they're saying the value of combined networks do exceed the mere sum of their parts, but by a dramatically more modest amount than Metcalfe's Law has led adherents to believe.

"The problem is that Metcalfe's Law provides irresistible incentives for all networks relying on the same technology to merge or at least interconnect. . . . Yet historically there have been many cases of networks that resisted interconnection for a long time," the Minnesota researchers say. They cite a number of examples, with the most recent being stubbornly proprietary instant-messaging networks that have only recently shown any meaningful willingness to play well with others.

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