Empiricism

The International Prototype Kilogram sat in a vault in Sevres, France, for 130 years. A cylinder of platinum-iridium alloy, 39 millimeters tall and 39 millimeters in diameter, stored under three nested bell jars. It defined the kilogram. Not represented, not approximated — defined. One kilogram was the mass of that object, by decree.

In 1981, a Japanese physicist named Yoshio Koide noticed something about the masses of three particles. The electron, the muon, and the tau are the three charged leptons — three particles that differ from each other only in mass. The electron weighs 0.511 MeV. The muon weighs 105.66 MeV, about two hundred times more. The tau weighs 1777 MeV, another seventeen times larger. Across the three, mass spans a factor of thirty-five hundred. There is no known reason the ratios should take any particular value. The leptons sit there, measured to many decimal places, with three numbers that no theory has derived from anything more basic.