Abstract

Ever since Proclus wrote his commentary on Plato's Republic, repeated attempts have been made to find a hidden number of cosmic significance in Rep. 8.546. For the Neo-Platonist it was natural to look for esoteric secrets in ancient works; among the men of the New Learning at the end of the Middle Ages there were enough astrologers and necromancers to ensure respect for the proposition; we are now again enamoured of irrationality. But the scholars who attempted such calculations around 1900 must have considered Plato himself a mystery-monger. In this article I propose: to show why such attempts are mistaken, to discuss what early writers who mention the passage say about its meaning, to provide a mathematician's translation that fits the context, and to comment on it; for the currently accepted explanation is unsatisfactory. ‘There is fairly widespread agreement that the geometrical number is 12,960,000 = 3,6002 = 4,800 × 2,700, but on the method by which this number is reached the widest divergence exists’ or, from an earlier, different guess: ‘…one can, so to speak, state a priori that Plato's number is a multiple of 19 ten thousands’, i.e. the text is approached with a ready-made answer in mind. There are three further objections to the conventional view, It takes the text out of its context as if it had strayed from the Timaeus.