Asymptoting towards zero…

September 18, 2007

Nearly ten years ago Hal Vari­an wrote a paper called Mar­kets for Inform­a­tion Goods. It’s none too eleg­antly expressed, but it has what you might call “pro­found” implic­a­tions:

I would like to coin a “Malthus’s law” of inform­a­tion. Recall that Malthus noted that num­ber of stom­aches grew geo­met­ric­ally but the amount of food grew lin­early. Pool (1984)* noted that the sup­ply of inform­a­tion (in vir­tu­ally every medi­um) grows expo­nen­tion­ally where­as the amount that is con­sumed grows at best lin­early. This is ulti­mately due to the fact that our men­tal powers and time avail­able to pro­cess inform­a­tion is con­strained. This has the uncom­fort­able con­sequence that the frac­tion of the inform­a­tion pro­duced that is actu­ally con­sumed is asymp­tot­ing towards zero.

*Ith­iel De Sola Pool, Hiroshi Inose, Nozomu Taka­saki, Roger Hur­witz. Com­mu­nic­a­tions flows: a census in the United States and Japan. Elsevi­er Sci­ence, New York, 1984.

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