作者：潘岔迕 发布时间：2019-03-15 08:14:01

By Jacob Aron A curious mathematical crime-fighter has just boosted our confidence that the galaxy is brimming with alien worlds. The statistical phenomenon, called Benford’s law, has been shown to fit existing data on both confirmed and candidate exoplanets. The results suggest that of the thousands of planetary candidates, the majority will turn out to be real worlds and not errors in the data. Initially a mere mathematical oddity, Benford’s law states that the first digits of the numbers in certain sets follow a pattern of probability. For the numbers in a variety of data sets, 1 is the leading digit about 30 per cent of the time. Higher digits are less frequent: on average, just 4.6 per cent of numbers in such sets begin with 9. It turns out that this numerical quirk is rife in nature with phenomena from the lengths of rivers to the depth of earthquakes all following the law. It also works on various forms of financial data and has been used to detect fraudulent attempts to cook the books with fake transactions, which usually fail to fit the pattern. The law works whether you measure the same rivers in feet or kilometres, or the same monetary transactions in pounds or dollars. Thomas Hair at Florida Gulf Coast University in Fort Myers wondered if Benford’s law would hold true even beyond the solar system. “I became intrigued with the idea that exoplanet mass might fit,” he says. Hair examined data from the online catalogue exoplanets.org, which lists 755 confirmed exoplanets and nearly 3500 planet candidates, many of them found only in the past few years by NASA’s Kepler space telescope. Masses are given in multiples of Earth’s or Jupiter’s mass. He found that the figures closely fit Benford’s law for both units. Previous efforts at matching exoplanets to Benford’s law showed a discrepancy, but that was with a sample of just 400 planets, and the larger data set we have now is more statistically valid, he says. The latest results show our cosmic accounting is sound, Hair says. Other work has suggested that 90 per cent of the known candidates will turn out to be planets, and that billions of habitable worlds are strewn across the Milky Way. “The close fit with Benford’s law gives a confirmation to experts’ belief that most of the candidates are valid,” says Hair, who will present the work in January at the Joint Mathematics Meeting in Baltimore, Maryland. This mathematical tool probably won’t help astronomers find more planets, cautions Christoph Mordasini of the Max Planck Institute for Astronomy in Heidelberg, Germany. Benford’s law is not a law in the physical sense, like Newton’s laws, but a consequence of how we represent numbers, he says. “However,

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