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

by Arthur Koestler

Yet the last step which had got him out of the labyrinth had once again been a faulty step. For it is not permissible to equate an area with the sum of an infinite number of neighbouring lines, as Kepler did. Moreover, he knew this well, and explained at length why it was not permissible.21 He added that he had also committed a second error, by assuming the orbit to be circular. And he concluded: ‘But these two errors – it is like a miracle – cancel out in the most precise manner, as I shall prove further down.’22 The correct result is even more miraculous than Kepler realized, for his explanation of the reasons why his errors cancel out was once again mistaken, and he got, in fact, so hopelessly confused that the argument is practically impossible to follow – as he himself admitted. And yet, by three incorrect steps and their even more incorrect defence, Kepler stumbled on the correct law.23 It is perhaps the most amazing sleep-walking performance in the history of science – except for the manner in which he found his First Law, to which we now turn.