In 1929 an astronomer published a distance that was wrong by a factor of roughly seven. The measurement was careful, the reasoning was sound, and the consequence was a universe calculated to be younger than the rocks it contained. This is, on the face of it, a straightforward embarrassment. It is more usually presented as one. But the episode repays a closer reading, because the error was not a lapse in rigour. It followed inevitably from an assumption that everyone in the field shared, that nobody had reason to question, and that turned out to be false in a way no amount of care at the telescope could have revealed. The assumption concerned a particular class of variable star, used as a distance marker because its brightness varies with a period that can be timed precisely. Time the period, infer the true brightness, compare with the observed brightness, and the distance follows. The method is elegant and, within its assumptions, exact. What nobody knew was that there are two populations of such stars, obeying different relations, and that the calibration had been made on one while the distant measurements were being made on the other. The resulting contradiction is what makes the case instructive. A universe younger than its contents is not a small discrepancy to be absorbed by better statistics. It is an impossibility, and impossibilities are unusually productive. For two decades the field could not proceed as though nothing were wrong, and the effort to locate the fault produced the population distinction, a rebuilt distance ladder, and a considerably better understanding of stellar evolution than anyone had set out to acquire. Had the original figure been merely imprecise, none of this would have followed. An answer that is roughly right invites refinement; an answer that is flatly impossible demands reconstruction. The discipline was fortunate, in a sense, that the error was large enough to be undeniable. There is a temptation to draw a comfortable moral about the self-correcting nature of science. The historical record is less flattering. The correction took twenty-three years, was resisted by several senior figures whose reputations were entangled with the earlier value, and arrived partly because new instruments made the old position untenable rather than because argument prevailed. Self-correction, where it occurs, is frequently a matter of attrition. The more defensible conclusion is narrower and, perhaps, more useful. Errors that contradict something else we are confident about are worth far more than errors that merely sit there. A wrong number in isolation can persist indefinitely; a wrong number that collides with the age of the Earth cannot. What made the 1929 measurement productive was not that it was wrong, but that the field had something solid enough for it to be wrong against. The current value has been stable for some years now. There is a persistent disagreement of about nine per cent between two ways of obtaining it, which several researchers describe, with evident interest, as the most promising problem in the subject.