While the idea of increasing returns—the tendency for what is ahead to get further ahead—has been part of economics since the pin factory, it was long resisted by economists. The reasons were both simple and profound.

For decades, economists had a strong preference for models with a single equilibrium. This preference was incompatible with the idea of increasing returns.

Imagine a farmer choosing whether to use her land to grow food or raise cattle. She begins by planting her most fertile land. When that runs out, she moves into worse land, where the returns for her efforts will decrease. Eventually, the next patch of land is not worth tilling so she dedicates it to cattle instead.

In this story, diminishing returns lead the farmer to allocate land optimally among crops and cattle. It follows that diminishing returns are the secret behind the invisible hand. They imply that economies allocate resources optimally among multiple activities, leading to a strong policy implication: markets find an equilibrium that is both efficient and fair.

The Complexity of Increasing Returns

César A. Hidalgo

NAE Reports, Winter Issue of The Bridge on Complex Unifiable Systems

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Sometimes, it’s easy for a computer to predict the future. Simple phenomena, such as how sap flows down a tree trunk, are straightforward and can be captured in a few lines of code using what mathematicians call linear differential equations. But in nonlinear systems, interactions can affect themselves: When air streams past a jet’s wings, the air flow alters molecular interactions, which alter the air flow, and so on. This feedback loop breeds chaos, where small changes in initial conditions lead to wildly different behavior later, making predictions nearly impossible — no matter how powerful the computer.

Read the full article at: www.quantamagazine.org

Science seeks the basic laws of nature. Mathematics searches for new theorems to build upon the old. Engineering builds systems to solve human needs. The three disciplines are interdependent but distinct. Very rarely does one individual simultaneously make central contributions to all three — but Claude Shannon was a rare individual.

Read the full article at: www.quantamagazine.org