When today we conjure up the name of Pythagoras (ca. 570–495 B.C.), most of us suppose his fame to rest on the discovery of a mathematical theory about right-angled triangles that we remember being taught in school. Perhaps we also recall being told that he was the first person to make the connection between number and musical harmony. As with so much that one learned in school, neither of these statements is true. Both observations were made by the Babylonians many hundreds of years before Pythagoras. The Chinese may have demonstrated a proof of the first as long ago as the eighth century B.C.

In his wise, wide-ranging, and exceptionally well-produced book on Pythagoras, When the Dog Speaks, the Philosopher Listens, Nigel McGilchrist readily acknowledges these facts, pointing out that the earliest sources identified his subject as neither a mathematician nor a musician.¹ But as with the Turin Shroud, the abandonment of a simplistic or ingenuous belief makes room for something more interesting and complex.

Our understanding of this entire period is impeded by the lamentable fragmentariness of what has survived.

The book is set in the earliest phase of classical antiquity. Our understanding of this entire period is impeded by the lamentable fragmentariness of what has survived. It is an era nearly all of whose original productions have been reduced to dust. We cannot gauge the impact of the celebrated Aphrodite of Knidos, for instance, since we have access