BMCR 2007.03.34

Archytas of Tarentum, Pythagorean, Philosopher and Mathematician King

, Archytas of Tarentum : Pythagorean, philosopher, and mathematician king. Cambridge: Cambridge University Press, 2005. 1 online resource (1 volume). ISBN 0511113412 $175.00.

We have here another blockbuster offering from Carl Huffman (hereafter H.), who has already put us in his debt by a definitive (and similarly vast) study of Philolaus ( Philolaus of Croton, Pythagorean and Presocratic, Cambridge, 1993). This work will serve in turn to establish Archytas as a philosopher in his own right, and not simply a footnote to Pythagoras, as has all too often been the case hitherto.

The book is divided into three parts, which are really best read more or less simultaneously since they throw light on each other. In Part I (pp. 3-100), H. discusses, first the life, writings and reception of Archytas, then an overview of his philosophy, and lastly, and more briefly, ‘the authenticity question’ — an issue of basic importance to his project. In each case, constant reference forward to both of the later parts is desirable. Part II (pp. 103-252) covers the genuine fragments — just four of them — in each case giving the text, translation and a copious commentary, both general and detailed. Part III (pp. 255-594) presents the genuine testimonia, 25 in all, divided into (i) life and writings; (ii) moral philosophy and character — mostly anecdotes of varying degrees of revelatoriness; (iii) geometry — specifically the duplication of the cube; (iv) music; (v) metaphysics; (vi) physics; and (vii) miscellaneous — comprising the topics of Archytas’ dove (an ingenious construction), and Aristotle’s books on him. There follows one appendix on the spurious writings and testimonia, and another on the form of his name.

There is a staggering amount of material assembled here, regarding a man about whom, really, precious little is known. To take Part I first, we derive a surprisingly lively, if rather impressionistic, picture of Archytas’ rule in Tarentum from the mid-380’s to the mid-350’s. He seems to have presided over a form of democracy — he is said to have been elected general seven times, but not necessarily consecutively — not much like the general image of earlier Pythagorean-run oligarchies. Indeed, Archytas comes across as a highly unusual Pythagorean, who wears his allegiances lightly. On the more trivial level, he loved children (and possibly invented a mechanical clapper to amuse them — A 10); was unwilling to beat his slaves while angry with them (A 7); and, when he felt like cursing, preferred to write rude words down on a wall than to pronounce them (A 11). More seriously, he was a most successful general, and under him Tarentum led the Italian League (A 2), and he gave considerable thought to establishing true political harmony between rich and poor by balancing the recognition of the privileges of wealth with the acceptance of the duty of the well-off to relieve the hardship of the poor (Fr. 3).

An important source for our knowledge of Archytas the man is the Life composed by his fellow-citizen and student of Aristotle, Aristoxenus of Tarentum, certain portions of which are preserved in Athenaeus and in Iamblichus’ Pythagorean Life. One significant anecdote (A9) concerns a disputation he held with a Syracusan called Polyarchus., who proposes a view of life similar to that of Callicles in Plato’s Gorgias, that self-aggrandizement and the pursuit of pleasure should be the aim of life. This may well be in its surviving form a literary composition by Aristoxenus, but H. is doubtless right that it is not just a re-hash of Plato, but goes back to something authentic. He is probably also justified in linking to it a passage of Cicero, De Senectute (A9a), which seems to constitute Archytas’ reply.

Philosophically, Archytas’ chief contributions would seem to be in the area of harmonics and mathematics (which he calls logistic). The four surviving fragments all concern various aspects of these topics, though with Fr. 3 straying interestingly into politics as well, as we have seen. H.’s commentaries on these — as indeed on many of the testimonia — are masterful and exhaustive. H. most persuasively inserts λογίζεσθαι in l. 5 of fr. 3, as it serves to tie the two parts of the passage together, and much improves the sense. His detailed commentary on the fragment contains mini-treatises on such topics as logismos, pleonexia, and isotas, all 5 pages each.

And so it is for the testimonia as well. His discussion of the evidence for Archytas’ solution to the problem of doubling the cube (A14-15), which continues for nearly 60 pages (342-401), is an extraordinary tour de force — I now at last understand how the doubling of the cube comes down to the finding of two means between two given lines, the second being double of the first. Remarkable also is his exposition of Archytas’ division of ‘the genera and the tetrachords’ (A16, from Ptolemy’s Harmonics). H. has plainly mastered the arcana of Greek geometrical and musical theory, and expounds them as lucidly as can be done.

Archytas had views on other aspects of philosophy and science as well, such as optics and the theory of motion, as well as some suggestions of a theory of first principles, and all of these H. expounds with great fullness. One can only salute his immense industry, while wondering how many punters are actually going to get through the 620 pages of text. Those who do, however, will be well rewarded, learning much, not only about Archytas himself , but about many other areas of antiquity as well.