Note 50 — Chapter II · THE MEANING OF NUMBERS

One may be permitted to add that according to legend, both Hippasus who took to himself public credit for the discovery of a sphere of twelve pentagons, viz., the regular dodecahedron (regarded by the Pythagoreans as the quintessence—or æther—of a world of real tetrahedrons, octahedrons, icosahedrons and cubes), and Archytas the eighth successor of the Founder are reputed to have been drowned at sea. The pentagon from which this dodecahedron is derived, itself involves incommensurable numbers. The “pentagram” was the recognition badge of Pythagoreans and the ἄλογον (incommensurable) their special secret. It would be noted, too, that Pythagoreanism was popular till its initiates were found to be dealing in these alarming and subversive doctrines, and then they were suppressed and lynched—a persecution which suggests more than one deep analogy with certain heresy-suppressions of Western history. The English student may be referred to G. J. Allman, Greek Geometry from Thales to Euclid (Cambridge, 1889), and to his articles “Pythagoras,” “Philolaus” and “Archytas” in the Ency. Brit., XI Edition.—Tr.