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The Economist, July 2002:

IT WAS an essential ingredient of dotcom business plans and conference slide-shows: Internet traffic, went the industry's favourite statistic, doubles every 100 days.... Unfortunately for the telecoms firms that rushed to build networks to carry the reported surge in traffic, it wasn't true.

So where did the claim come from? According to Andrew Odlyzko...the short answer is WorldCom.

Technorati founder Dave Sifry, August 2006:

The blogosphere has been doubling in size every 6 months or so. It is over 100 times bigger than it was just 3 years ago.

(Okay, let's be fair, Sifry says the growth will eventually slow. Right after Technorati gets sold to Fox or Viacom.)

The power of WorldCom's puff [Economist]
State of the Blogosphere, August 2006 [Sifry's Alerts]
Kevin Burton: The Numbers Don't Lie [OnoTech]