• Otávio Santiago

The Three-City Problem of Modern Life

NASA CAN LAND a probe on Saturn's largest moon, 764 million miles from Earth—yet no one has been able to mathematically demonstrate the exact positions of the Earth, sun, and our own moon at a given point in the future. Scientists can make estimates, but these all rely on simplifications.

Two-body problems, like mapping the movement of one planet around one star, are solvable. These binary orbits are easy to predict. But a serious complication arises if a third body is introduced. Our moon, which has the gravitational forces of both the sun and the Earth acting upon it simultaneously, is part of an infamous three-body problem.

Trying to solve for the movement of three large bodies in one another’s orbit creates a circular logic. The calculations rely on the initial positions of the three bodies, but these initial positions are unknowable over time because the bodies always affect one another in unpredictable ways. In the 300 years since Isaac Newton outlined the dilemma in his Principia, diligent physicists have only been able to offer special-case solutions for restricted versions of the problem. “In a nonlinear system like the chaotic three-body problem,” writes Caroline Delbert for Popular Mechanics, “all bets are off, and our intuitions are scrambled.”

The three-body problem is the best metaphor I’ve found for a social complexity that affects us all today—a problem resulting from the interaction of three major centers of gravity. This dynamic is scrambling our intuitions and making us long for order in what feels like an increasingly chaotic world. We’re caught on the inside of a three-city problem.

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