Let's say I share 1 item/minute x 60 minutes/hour x 24 hours/day x 365 days/year – that's 525,600 items per year, assuming I don't eat, sleep, or do anything else but share. There's clearly a practical limit to how much a single individual can share. The network effect does compound the number of people I share with and could in fact be modeled as exponential growth - as my network grows and my networks' network grows, I share with more and more people. But that's not what Zuckerberg is claiming - he's claiming that the amount of stuff I share will double each year.
From Alexia Tsotsis … Mark Zuckerberg Explains His Law Of Social Sharing [Video]:
Zuckerberg explained that in accordance with Facebook’s data, social sharing functions exponentially, so that the amount of stuff you shared today is twice the amount of stuff you shared a year ago and the stuff that you will share a year from now will be twice the amount you’ve shared today. In Mark Zuckerberg’s Law of Social Sharing, Y = C *2^X –Where X is time, Y is what you will be sharing and C is a constant.
Whether Zuckerberg’s concise prediction of human sharing behavior is accurate remains to be seen. As Chris Dixon points out, it seems kind of absurd that people will be sharing 1,048,576 (2^20) times the items of information they are sharing today twenty years from now.