Pythagorus

by Kitty Ferguson

  Aristoxenus, like Dicaearchus, did not toe the Pythagorean line precisely. He dismissed the idea of the soul being more than a harmony of the body’s various components, and his music theory took a different direction from Archytas’. The information Porphyry and Iamblichus attributed to Aristoxenus probably came from his biography of Pythagoras – thought to have been the first written – but neither Porphyry nor Iamblichus ever actually saw Aristoxenus’ and Dicaearchus’ books.[12] The information they took from them came indirectly, through other writers who lived during the centuries in between.

  After Aristotle there were no attempts in antiquity to draw a distinction between pre-Platonic Pythagorean doctrine and Plato. Beginning with Plato’s pupils Speusippus and Xenocrates, no one for centuries would make a distinction between Platonism and Pythagoreanism at all. Almost without exception, everyone would accept what Plato taught in his Timaeus and his ‘oral doctrine’ (reported by Aristotle) as the teaching of the early Pythagoreans. In the eyes of the educated world, Plato was a Pythagorean.

  By the turn of the century in 300 B.C., the world of classical Greece, of Plato and Aristotle, and of strong and often warring city-states like Athens, Sparta, and Thebes had ended.12 The rise of a power from the north – the kingdom of Philip the Great of Macedonia – was heralding a new era. Less than forty years after Philip had become king of Macedonia in 359, his son (traditionally Aristotle’s pupil) Alexander the Great had conquered not only Greece but also Egypt and the entire Persian empire to the east, as far as present-day Afghanistan, Pakistan, and the Indus River. The culture and learning of Greece and its colonies and of the conquered peoples mixed and, to an impressive extent, enriched one another.

  After Alexander died in 323 B.C., though the city-states had not vanished entirely and change was slow in remoter regions such as Magna Graecia, his short-lived and sprawling empire became three ‘successor states’ under his former generals and associates. Mainland Greece became part of Macedon. The Seleucid dynasty controlled Syria. Egypt was ruled by the Ptolemies, the dynasty that would later include Cleopatra. At the time of Alexander’s death (and Aristotle’s, for he died a year later, in 322), Athens was still the hub of the intellectual world, but Alexandria, with the wealth of the Ptolemys lavished on literature, the arts, mathematics, science, and a library and museum would soon rival and eventually eclipse her.

  Around 300 B.C., Euclid, who lived in Alexandria, gave mathematics and geometry a new form of life, surpassing all others in antiquity for putting the power of numbers to use in a truly significant and comprehensive manner. Euclid personified the Pythagorean intellectual and philosophical conviction that mathematics was a precious guide to truth, and he was even known to use a Pythagorean aphorism, but he did not consider himself a Pythagorean nor did he belong to a Pythagorean community.[13]

  Euclid in a sixteenth-century engraving

  Euclid’s Elements is one of the premier intellectual achievements of all time, foundational for later mathematicians and geometers. It was both a comprehensive summary and treatment of what had been discovered before him, and wondrously original, and Euclid did not clearly distinguish between what was new and what was old. He knew the Pythagorean theorem and included it in Book I as ‘Proposition 47’, never referring to it as ‘Pythagorean’ but also never claiming it was his own discovery or mentioning another origin. His knowledge of early Pythagorean mathematics and astronomy appears to have come mostly through Archytas, though modern experts who have analysed the Elements believe that many of the results which appear in it13 predated Archytas, and that some of the material was extremely old.14 Archytas had previously built on some of this earlier work, and his discoveries, particularly his number theory, were incorporated by Euclid in the Elements Book VIII.

  By Euclid’s standards, a feeling of inevitability and a few examples did not constitute a ‘proof’. The so-called Pythagorean mathematics of his own contemporaries did not fall in happily with his higher abstraction.15 That tradition nevertheless wheezed along and proved tenacious beyond all expectation. Iamblichus preferred it:

  Pythagorean mathematics is not like the mathematics pursued by the many. For the latter is largely technical and does not have a single goal, or aim at the beautiful and the good, but Pythagorean mathematics is preeminently theoretical; it leads its theorems toward one end, adapting all its assertions to the beautiful and the good, and using them to conduce to being.16

  Though Euclid was translated into Latin and not unknown in the Middle Ages, the premier mathematical textbook of those later centuries would be in the ‘Pythagorean’ mathematical tradition, not his.[14] However, and in spite of Iamblichus’ opinion, Euclid’s Elements resonates with joy and appreciation for the beauty of the subject he was exploring as no one had before. Though modern mathematicians still carry forward the ancient Pythagorean/Platonic belief in the beautiful rationality of numbers, and even tend to be suspicious of anything claiming to be mathematical truth that is not beautiful, it is Euclidean technical rigour that guards the gate of beauty.

  [1]The classical scholar Walter Burkert thought that the way Aristotle ‘occasionally plays off the Pythagorean doctrines against the Academy’ makes ‘the conclusion unavoidable that he was using written sources without Academic colouring. Therefore he must have had at least one original Pythagorean document’ (Burkert, 47).

  [2]The three surviving books in which he included material about the Pythagoreans are Metaphysics, Physics, and On the Heavens.

  [3]For the ancient Greeks, including the Pythagoreans, 1 was neither even nor odd, and it was not a number. Number implied plurality – more than 1.

  [4]What emerged as a Platonic idea, the ‘Indefinite Dyad’, was not a Pythagorean concept. Aristotle spoke of no very important role for ‘Twoness’ in Pythagorean doctrine.

  [5]The table of opposites was probably not meant to imply good (the left column) and evil (the right), though other, later such tables did. For example, for Plato’s Academy, ‘good’ led off the left-hand column, and still later, Platonists, neo-Pythagoreans, and pseudo-Pythagorean writers rearranged the columns. Plutarch’s table was thoroughly Platonised: ‘Good’ was on top and ‘Dyad’ replaced plurality.

  [6]A modern major or minor scale.

  [7]Plato did not call them that, though he was using them in the most Pythagorean-inspired of his dialogues.

  [8]Recall that the regular solids each fit neatly into a sphere, and the fifth is close to being a sphere.

  [9]Many called him Empedocles the Pythagorean, but except for agreeing about reincarnation, his ideas ran far from Pythagorean thinking.

  [10]Scholars such as Kahn think these men were not fictional and that their words reflected a much older line of Pythagorean speculation.

  [11]Copernicus would point to Heracleides Ponticus as an ancient precedent when he presented his hypotheses in the sixteenth century. The Earth also rotated in Plato’s Timaeus, and the idea was probably not original with either man, for Philolaus and possibly earlier Pythagoreans thought part of the apparent movement of the heavens was caused by the movements of the earth. Copernicus also referred to Hicetas and Ecphantus of Syracuse.

  [12]In search of the source of Iamblichus’ lists of Pythagoreans, Burkert believed he had narrowed down the possibilties, conclusively, to Aristoxenus (Burkert, p. 105, n. 406).

  [13]When someone asked what the practical use of one theorem was, Euclid turned aside to his slave, sniffed, and muttered, ‘He wants to profit from learning, give him a penny.’ The Pythagorean aphorism was ‘A diagram and a step (an advance in knowledge), not a diagram and penny’.

  [14]The Elements was translated by Boethius in about A.D. 480, but not until A.D. 1120, when Athelhard of Bath translated it again, this time from Arabic into Latin, did mathematicians begin
to appreciate its worth.

  CHAPTER 11

  The Roman Pythagoras

  Third, Second, and First Centuries B.C.

  In Rome in the second and first centuries B.C. there was a popular legend that Numa, the wisest and most powerful of Rome’s ancient kings, had been a disciple of Pythagoras. This was not possible. Dates in the city’s early history were under debate, but no amount of fuzziness or fudging could change the fact that Numa died at least 140 years before Pythagoras came to Croton. The Roman lawyer and orator Marcus Tullius Cicero made that clear in his Republic:[1]

  MANILIUS: It is generally supposed, Africanus, that King Numa himself was a disciple of Pythagoras, or, at least, of the Pythagorean school; we have often heard this from our forebears and we believe it is widely held by the common people, although it does not appear clear from the public annals.

  SCIPIO: Indeed Manilius, it is altogether false, not only a fiction, but an ignorant and obscure fiction. Such a lie is not to be endured, for it is not only not a fact, but we may observe that it could not possibly have been so, for Pythagoras reportedly came to Sybaris, Crotona and other cities in that part of Italy in the fourth year of the reign of Lucius Tarquinius Superbus. His arrival was during the 62nd Olympiad, as was the beginning of the reign of Superbus. By numbering the years from the kings, it is possible to calculate that Pythagoras first reached Italy nearly one hundred and forty years after the death of Numa; nor is this left in any doubt by those who have most diligently studied the annals of the times.

  MANILIUS: Ye Gods! What a ridiculous mistake is that?1

  Nevertheless, Numa’s discipleship made a good story and represented widespread wishful thinking – that Rome could claim a direct link with Pythagoras. Cicero himself liked the idea:

  For who can think, when Magna Graecia flourished in Italy with most powerful and populous cities, and when in these the name, first of Pythagoras himself, and then of the Pythagoreans afterwards, sounded so high, that the ears of our own countrymen were closed to the most eloquent voice of wisdom? Indeed I think it was because of their admiration for Pythagoras, that Numa the king was reputed to be a Pythagorean by posterity; for, knowing the system and institutions of Pythagoras and having from their ancestors the renown of that king for wisdom and integrity – but ignorant, through distance, of ages and times – they inferred that, because he excelled in wisdom, he was the disciple of Pythagoras.2

  Cicero was avidly interested in Pythagoras. That a great man of mathematics and philosophy had also reputedly been an effective civic leader – though no specifics were known about his leadership methods or activities – was particularly appealing. Cicero was a prolific author but considered writing a poor second to his active public career.

  The connection with Numa was by no means the only bit of fiction and semi-fiction about Pythagoras that was current in Cicero’s Rome. The Roman vision of Pythagoras was an amazing mixture of Plato with unfounded legends and assumptions – undergirded by blatant forgeries – and various shades of interpretation and misinterpretation. Pythagoras’ name had been familiar to the Roman public at least since the early years of the third century B.C. In the years 298 to 290 B.C., Rome was struggling for the third time to conquer the Samnite tribes in the central and southern Apennine mountains that form the spine of the Italian peninsula. The Samnites were tough warriors desperately defending brutally rugged terrain that was their familiar home ground. When the conflict was going particularly badly for the Romans, they cunningly adopted the military formation that their enemy were using so successfully, a checkerboard pattern in which solid, tight squares of soldiers alternated with square empty spaces.[2] They also consulted the Oracle at Delphi, which told Rome to honour the wisest and bravest of the Greeks. Responding to this rather insulting order, the Romans chose two figures who were not exactly those a Greek would have chosen: Alcibiades, a notoriously opportunistic military and political genius who had once been a student of Socrates and had often been a thorn in the flesh to the Greeks of his era; and Pythagoras, whom Rome preferred to regard as more Italian than Greek.[3] The oracle must have been satisfied, for Rome subdued the Samnites. The statue of Pythagoras in the Forum stood for two centuries, until the construction of a new Senate necessitated its removal, probably when Cicero was in his late teens.3

  By the mid-second century B.C., Rome controlled the entire eastern Mediterranean, and in Greece, Egypt, and Asia Minor, Romans were encountering some of the highest and most ancient cultures in the world. To their credit, for the most part they did not look upon these as the outdated, easily dismissed, quaint cultures of conquered inferiors, but rather chose to regard the older societies as guardians of a valuable legacy to which Rome had now become the heir.

  The most significant and long-lasting influence was from the Greeks. The Roman military brought home works of art, slaves who were much better educated than they, and a new thirst for knowledge and ideas. Before long, upper-class Romans were avidly reading Greek works in translation and even in the original, for many were becoming bilingual. Roman parents sought out educated Greek slaves to tutor their children, and young men travelled to Greece for part of their schooling. Cicero studied philosophy and oratory in Athens and Rhodes. Authors, artists, sculptors, philosophers, and architects who could match the standards of Greek achievements, or at least do a fair job of copying them, were in high demand. Though state business continued to be carried on in Latin, hardly any part of Roman life escaped this peaceful, sophisticated counterconquest. In the midst of what was rapidly becoming not a Roman but a Greco-Roman culture, Pythagoras, an almost homegrown ancient intellectual giant, of mythical stature throughout both the Greek and Italian world, was a Roman treasure. This was ‘Italian’ philosophy. Aristotle himself had called it that.

  The poet Ennius – whom later generations would call the father of Latin poetry – also helped provide Rome with a much-needed cultural self-image that involved Pythagoras. One of Ennius’ immensely successful poems and dramas was a lengthy historical epic called the Annales, purporting to trace Roman history to the fall of Troy. In it, Ennius presented his credentials as the successor to Homer by describing a dream in which that great Greek poet appeared to him on Mount Parnassus and told him that in a former life he, Ennius, had been Homer himself. This dream was symbolic and symptomatic of Rome’s vision of herself as the heir to Greek culture, but it did not represent orthodox Roman or Greek doctrine regarding the afterlife. It was instead a nod to Pythagoras and the doctrine of reincarnation. In a satirical poem, Epicharmus – the name was that of a Sicilian Pythagorean comic poet – Ennius described another distinctly Pythagorean dream about what would happen after his death, in a place of divine enlightenment.

  Ennius was a member of the staff of the Roman consul Marcus Fulvius Nobilior, which gave him yet another Pythagorean connection. Fulvius had returned from military campaigns in the eastern Mediterranean with a passion for Greek culture and laden with captured artistic treasures. He authored a work called De Fastie that was probably the original source of a passage claiming to be ‘what Fulvius reported from Numa’, implying something genuinely Pythagorean since Numa, of course, was the early king who was supposed to have studied with Pythagoras. Fulvius’ book in fact owed a great deal to Plato’s Timaeus, which at the time was almost universally regarded as Pythagorean doctrine.

  At the time of Ennius and Fulvius, a cult appears to have existed in Rome and/or Alexandria whose members followed what they believed were the ritual practices and lifestyle of the acusmatici. A book had appeared entitled the Pythagorean Notebooks, prescribing that lifestyle, and the claim was that Pythagoras had written it himself, though in truth it dated from little earlier than the cult. Nonetheless, Diogenes Laertius later quoted from it in his biography:

  Virtue is harmony, health, universal good, and god, on which account everything owes its existence and preservation to harmony. Friendship is h
armonic equality. Honours to gods and heroes should not be equal; gods should be honoured at all times with pious silence, clothed in white garments, and keeping one’s body chaste; but, to the heroes, such honours should not be paid till after noon. A state of purity is achieved through purifications, washings, ablutions and purifying ones self from all deaths and births and any kind of pollution; by abstaining from all animals that have died, mullet, blacktail fish, eggs and egg-laying animals and from beans and other things forbidden by those who have charge of the mysteries in the sanctuaries.4

  In second-century-B.C. Rome and Alexandria, many such ‘pseudo-Pythagorean’ books and writings appeared. The semi-historical tradition regarding Pythagoras, fragmentary and confusing as it was already, would be tainted irretrievably by this large body of fiction pretending to be fact.

  Cato the Elder, who brought Ennius to Rome and sponsored his introduction to Roman society, read a book called Pythagoras on the Power of Plants, a work in the genre of natural and supernatural botany in which he found information about a species of cabbages, Brassica pythagorea. Cato included them in his own book De Agricultura, a compendium of practical advice for owners of mid-sized agricultural estates, featuring recipes, prescriptions, religious formulae, and high praise for cabbages, especially the Pythagorean variety, leaving little need to grieve for beans. Pliny the Elder, in the next century, like Cato a man of impressive learning and intelligence, nevertheless also failed to discern that Pythagoras on the Power of Plants was a forgery and alluded to it in his Naturalis Historia, a thirty-seven-volume encyclopaedia of every bit of information available to him about animals, vegetables, minerals, and humans.[4] ‘Nature, which is to say Life, is my subject’, he had declared.5