If you drop a spoonful of sour cream into a bowl of borscht, the two liquids will barely mix. But if you stir them, the spoon will drag filaments of cream through the soup. Stir further, and the filaments will stretch and fold. Eventually, if that’s your taste, the cream and soup will blend.

How stirring converts a spatially inhomogeneous state into a homogeneous one seems like the sort of problem G. I. Taylor might have solved in the 1930s. But only in the past 20 years have the mathematical tools become available to build plausible theories.

Those theories have advanced to include components that react with each other. Now, they’re being tested in the lab. Paulo Arratia of the University of Pennsylvania in Philadelphia and Jerry Gollub of Haverford College near Philadelphia have developed an experiment that tracks the progress of a chemical reaction in a stirred solution. 1...

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