The Sleepwalkers: A History of Man's Changing Vision of the Universe

by Arthur Koestler

Now, at the very beginning of the hair-raising computations in chapter sixteen, Kepler absentmindedly put three erroneous figures for three vital longitudes of Mars, and happily went on from there, never noticing his error. The French historian of astronomy, Delambre, later repeated the whole computation, but, surprisingly, his correct results differ very little from Kepler’s faulty ones. The reason is, that towards the end of the chapter Kepler committed several mistakes in simple arithmetic – errors in division which would bring bad marks to any schoolboy – and these errors happen very nearly to cancel out his earlier mistakes. We shall see, in a moment, that, at the most crucial point of the process of discovering his Second Law, Kepler again committed mathematical sins which mutually cancelled out, and ‘as if by miracle’ (in his own words), led to the correct result.