Abstract
We describe innovation in terms of a generalized branching process. Each new invention pairs with any existing one to produce a number of offspring, which is Poisson distributed with mean . Existing inventions die with probability at each generation. In contrast with mean field results, no phase transition occurs; the chance for survival is finite for all . For , surviving processes exhibit a bottleneck before exploding superexponentially—a growth consistent with a law of accelerating returns. This behavior persists for finite . We analyze, in detail, the asymptotic behavior as .
- Received 30 March 2010
DOI:https://doi.org/10.1103/PhysRevLett.105.178701
© 2010 The American Physical Society
Synopsis
Explosive innovation
Published 18 October 2010
A microscopic model of innovation tells us how human progress occurs in fits and starts.
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