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Quantitative causality

A repurposed tool from information theory reveals whether two correlated behaviors share a causal link.

Cause and correlation are two different notions that are often confused. When phenomena A and B are causally related, their time evolutions are correlated. But correlation does not imply causality—an external agent such as an alarm clock, for example, can cause the correlated waking of two sleepers; the two isolated wakings, however, are not causally related. When the dynamics governing A and B are known, an information-theoretic notion called information flow rigorously determines the causal relations between A and B: If the information flow from A to B is zero, A has no effect on B; otherwise, A does affect B. Now X. San Liang of the Nanjing University of Information Science and Technology in China has shown how to obtain the information flow, not from a priori known dynamics but from correlations in the time-series graphs that detail the evolutions of A and B. He applied his result to a problem of practical interest for climate scientists—the relation between El Niño and the Indian Ocean Dipole (IOD), an aperiodic oscillation in sea surface temperature. Liang used correlations between time series—of sea surface temperatures in the Indian Ocean and of an index, called Niño4, that measures the overall strength of El Niño—to calculate the information flow from the IOD to El Niño shown in the figure. For a large swath of the northern Indian Ocean, the sign of the information flow is positive, which, according to information theory, means the IOD causes El Niño to be less predictable. That unusual causal link, suggests Liang, may be the reason climate scientists only recently recognized an influence of the IOD on El Niño. (X. S. Liang, Phys. Rev. E., in press.)

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