Some historical context.
The most prestigious prize in mathematics, the Fields Medal, is awarded every four years and so reckoned to be four times as grand as the Nobel. On that gold medal is engraved the following Latin phrase: TRANSIRE SUUM PECTUS MUNDOQUE POTIRI, translated in the website of the International Mathematical Union as, “To transcend one’s spirit and to take hold of (to master) the world.” The phrase, save the slight change of suum for the original tuum, is line 392 of the Fourth Book of a long poem, Astronomica by Marcus Manilius, written in the first years of our era under the reign of Augustus. It seems to be the first extant treatise on astrology, from which Montaigne frequently quoted and on which the poet A. E. Housman spent many years of philological work.
Not to pick a bone with the IMU Webmaster, translating suum pectus as “one’s spirit” in this particular context is not quite adequate, even though the early Stoics pretended to have proved that the rational soul resided in the breast (pectus), not in the head. In the Loeb edition of Manilius (page 253), G.P. Goold translates tuum pectus by “your understanding,” which is no better. The Fourth Book of the Astronomica starts by reminding the disciple and the reader that we are all subject to fate, that everything that happens to us from conception to death is foreordained. Major heroes of Roman history, from Aeneas to Caesar and Pompey, are then paraded for review: all were under the yoke of destiny and the stars, of the destiny encoded in the stars. After which Manilius proceeds to explain how destiny is encoded in the stars – the zodiacal signs, the houses or temples, the usual astrological kit – until the disciple complains that things are becoming too hard for him and excessively obscure. To this the master responds grandly, starting at line 390: “What you are searching for is God, no less. You are trying to climb all the way to the skies, and even though your birth was governed by fate, you want to understand fate’s law, and thus to transcend your human condition and make yourself the master of the world.”
I have chosen to translate pectus as “human condition,” but will go along with “mortality”. What the master astrologer is saying is that in spite of your birth and your pectus you are trying to reach divine knowledge, a divine knowledge that can only be acquired by the spirit and the understanding, not in spite of them. One must transcend one’s birth and one’s pectus or mortal condition—one’s body—not one’s understanding or spirit. Besides, pectus has kept, even when close to our term “understanding,” much of the original meaning related to the breast, the heart and the emotions. Thus Manilius’ Latin verse, engraved on the Fields medal, is an exhortation to leave behind all that is contingent, earthly and historical – your home, parentage and childhood, your fears and passions, this whole particular world, this handful of dust traversed by this beam of sunlight –, to dare to jump over that chasm which, much later, Gotthold Lessing would call ein garstig, breite Graben, a loathsome wide ditch, and reach, reach with all your might for the eternal realm of necessary truths: for the realm of mathematics, that is, which for the ancients comprised astronomy or astrology, harmony or music, geometry, and the science of number.
The ethical, metaphysical and religious conviction behind Manilius’ exhortation is called Pythagoreanism: it runs like a river, sometimes above-, at others underground, through all Greek thought, and having flowed uninterruptedly for two-and-a-half millennia, in our own time it has become a flood. Here a single illustration must do. Xenocrates, the third head of the Academy after Plato and Speusippus, taught, in the Pythagorean spirit, that the soul is “self-moving number”: arithmòn kinoûnth’ heautón. Aristotle, a contemporary and rival of Xenocrates, recounts this in On the Soul 408b-409a, and with rare acerbity calls it the most unreasonable of all theories; for first, he says, the soul doesn’t move, second, it cannot be number, and third, how can number move? In our own days, however, when consciousness, or the soul, is widely assimilated to a computer, consider that the model of all computers is the Turing machine, and then remember (or check it in Google) that the Turing machine consists of a reading/writing head and an infinite tape divided into cells, on which the head can read/write zeros and ones and cause the tape to move one cell to the right or to the left. What is that if not self-moving number? Bravo Xenocrates.
Two-and-a-half millennia, though, is a bit much of history of Pythagoreanism to handle: we shall concentrate on or around the principate of Augustus, and provide a brief context for Manilius’ hortatory lines, and for Horace’s Ode I. 28. Above all, we must keep in mind that Manilius was not alone in his hubris. His contemporary Eudorus of Alexandria likewise declared that the aim of Platonic-Pythagorean wisdom was to become like god – god in the singular, mind. At about the same time, Philo the Jew Pythagorically attributed the biblical creation in six days to six being the first perfect number (the sum of its divisors, save itself – 1, 2, 3 – is equal to 6; the next perfect number is twenty-eight). Nigidius Figulus, friend of Cicero, was an astrologer who, it is said, foretold the future greatness of Octavius; he was mentioned by St Jerome in a letter, three centuries later, as a Pythagorean and magus. Apollonius of Tyana the miracle worker, Philostratus, and Moderatus of Gades all belong to one or two generations later. And there were many others. The neo-Pythagorean temple at Porta Maggiore in Rome, discovered in 1917, attests to the revival of Pythagorean cults around the time of Augustus. Finally, and for my purpose most importantly, the major philosophical schools, with the exception of the Epicureans, had by this time adopted Pythagoras as their founding figure or topmost patron, even above Socrates, hence above Plato, Aristotle, and Zeno the Stoic.
The difficulties and depth of Horace’s Ode.
Of all Horace’s poems, Ode I. 28, the so-called “Archytas Ode,” has proved to be the most resistant to interpretation. One huge tome at least for each of the major European languages could be filled with the preposterous stuff some of the most famous scholars wrote about this poem.
In Spanish, Marcelino Menéndez y Pelayo, Horacio en España, Madrid, 1885 (3 volumes), reveals that from the Renaissance up to that time our ode was avoided by most Spanish translators or imitators, being among the least favored and understood of Horace’s works. The best Spanish translation, in the judgment of Menéndez y Pelayo, was by Javier de Burgos (Madrid, 1820). And how did don Javier, the Gallicized Spanish hidalgo who imitated Horace in poems like “Oda a la razón y al porvenir”, deal with I. 28? He crowned it with the absurd title: “A sailor is introduced who pokes fun at Archytas, having come across his unburied corpse. The philosopher asks the sailor not to leave before burying him.” The first six lines are given by Don Javier to the sailor, the remainder of the poem to Archytas; in the commentary notes, Horace is upbraided for his sarcasms: “to be sure, metempsychosis is an absurd doctrine, but Archytas was a praiseworthy, respectable philosopher who deserved better treatment.”
Indeed, Archytas of Tarentum was a respectable philosopher and a first-rate mathematician: his solution of the Delian problem – how to double the volume of a cube, or in other words, given a segment of length one, to build a segment of length cubic-root-of-two – is one of the most ingenious constructions we have from ancient geometry. Friend of Plato and teacher of Eudoxus, Archytas was thus at the origin of the long struggle the Western spirit has kept up with that monster, infinity, in response to the Eleatic challenge – a struggle that is still going on, albeit not with turtles and arrows but with weapons more abstract. During the period on which we are focused, first centuries BC and AD, Archytas was Pythagoreanism personified (Pythagoras himself being felt to be more a legend than a person, and a Ionian, not a native Italian like Archytas)(1). So when Horace (or his drowned sailor) apostrophizes Archytas, the poet is speaking ad doctrinam rather than ad hominem, and he views as his target the currently successful neo-Pythagorean salvation cults.
The initial taunt to dead Archytas is an ethical statement, and it goes directly against the spirit of Manilius’ hubristic injunction and the Fields Medal boast:
Te maris et terrae numeroque carentis harenae
mensorem cohibent, Archyta,
pulveris exigui prope litus parva Matinum
munera, nec quicquam tibi prodest
aërias temptasse domus animoque rotundum
percurrisse polum morituro.
(Archytas, you who measured sea, land and the uncountable sands, are now confined by a lowly gift of a mound of dust near the flanks of Mount Matinus, and nowise does it help you that you explored with mortal soul the ethereal realms or traversed the celestial vault).
It is a curious fact among many curious facts in the critical history of this ode that translators tend to separate the two words, animo and morituro, which together – mortal soul, or intellect – are the equivalent of Manilius’ tuum pectus, your human condition. Horace’s point is that, pace Manilius and his proud and powerful ilk, we should not try to transcend our mortal condition and master the world.
That is the beginning of our ode; further down, the drowned sailor beseeches the sailing passer-by not to be mean and to bestow a bit of shifting sand on his unburied head and bones:
at tu nauta, vagae ne parce malignus harenae
ossibus et capiti inhumato
and still further down, here are the last two lines:
quamquam festinas, non est mora longa; licebit
iniecto ter pulvere curras
(even if you are in a hurry, the delay won’t be long; three handfuls of dust, and you may speed along).
The sands, which at the beginning are cosmic, too numerous for numbers and the occasion for a formidable challenge to the sharpest minds (we know they were so for Archimedes: recall his Sand Reckoner), become, in the second half of our ode, a handful or a tiny bit, the humble gift the piety of a passer-by is beseeched to bestow, to spread ritually over head and bones. We went from an abstract idea to something eminently tactile, from the universal sand to this particular sand here in your hand. Dust, which is said to stifle and confine Archytas in the first half of the poem, becomes the drowned sailor’s object of vehement desire in the second.
Partly on the basis of these contrasts, numerous commentators and editors have divided I. 28 into two separate poems, the first containing lines 1-20, the second, starting from line 21, “Me quoque devexi …”, to the end. That is the case with the obsolete Loeb edition (C. E. Bennett, first printed 1914), but the recent one (N. Rudd, 2004) sticks to the contemporary consensus that the ode should not be divided, and that it is a monologue spoken by a drowned sailor. The consensus, however, is not total. Bernard Frischer(2) has this to say, based partly on the fully unpersuasive argument that Horace, being an Epicurean, should not have endowed dead souls with speech:
“In the first part of the poem, we hear Horace’s sarcastic reaction to the funerary iconography and inscription on Archytas’ tomb; in the second part, we hear Archytas’ only “response” to Horace’s taunts in the form of his epitaph, which falls into the category of epitaphs in which a dead man addresses a passerby to convey information about his death and to request a favor.”
Being dead, Archytas can only respond by means of his epitaph. Thus Frischer retreats all the way back to Don Javier de Burgos.
Recent opinions on the artistic merits of our ode are neither unanimous nor heartening. E. Fraenkel(3) devotes to it half-a-footnote: “I am inclined to regard it as a sign of a certain immaturity … that in the Archytas ode (i. 28, in epodic form) it is not until ll. 21 ff. that we learn that the whole opening speech belongs not to the poet but to a dead man.” P. V. Callahan and H. Musurillo(4) argue for unity on the thematic basis of grains of sand: “the sand motif in both sections is truly striking.” They start their note by: “The so-called Archytas ode is one of the most enigmatic in Horace’s entire collection”, and conclude with a back-handed compliment: “The ode for all its obscurity is on the whole quite successful. It obviously belongs to an early stratum of Horace’s poetic creativity...” David West(5) ignores the social and religious context in which Horace wrote, reduces everything to a bare-bones “carpe diem,” and writes, “Archytas of Tarentum … is chosen partly because of the irony of the contrast between his cosmic achievements and his insignificant end.” If so, why didn’t the poet choose, say, Alexander of Macedon, whose physical afterlife – his end – was insignificant too, meaning also reduced to dust?
Of the commentaries I have seen, the one by R. G. M. Nisbet and M. Hubbard(6) comes closest, if somewhat obscurely, to what I believe is at stake in I. 28:
“The Ode to Archytas is often dismissed as a chaotic youthful experiment, but such a view is unconvincing. The poem is undeniably bizarre in conception, but it is original and imaginative as few other Latin writings. The long rambling sentences catch the variety and impetuosity of the living voice better than the congested involutions of Horace’s maturity. … The tempestuous dactyls evoke the wind beating on the woods of Horace’s childhood, or blowing the sand about a drowned man on the Calabrian shore – the sand that Archytas once had counted, and which now stifles him. Anybody who likes this poem has discovered something about poetry.”
Right, and the “something” touches on the essence of poetry. If it is true that there is no science but of the general, no math but of the universal abstract, it is no less true that only poetry can grasp the ephemeral particular. In math, the higher we go in levels of generality and abstraction, the more and the farther we see; but in poetry, we must go down all the way to the particular, the seemingly unimportant individual object, to grasp the whole—as if the entire soul crystallized around a single particle. That opposition, the two sides of Lessing’s loathsome ditch, which are the lips of our spiritual wound, is the “something” enacted in Horace’s poem.
1. Cicero mentions Archytas at least eleven times, the elder Pliny six times, Propertius, Varro, Vitrubius, Valerius Maximus, Quintilian, and Columella each refer to him at least once.
2. Bernard Frischer, “Horace and the Monuments: A New Interpretation of the Archytas Ode (C. 1. 28)”, Harvard Studies in Classical Philology, vol. 88, 1984, pp. 71-102.
3. Eduard Fraenkel, Horace, Oxford U. Press, 1957, page 74.
4. Paul V. Callahan and Herbert Musurillo, “A Handful of Dust: The Archytas Ode (Hor. Carm. 1. 28),” Classical Philology, vol. 59, 1964, pp. 262-69.
5. David West, Horace Odes I: Carpe Diem, Oxford U. Press, 1995, pp. 132-5.
6. R. G. M. Nisbet and M. Hubbard, A Commentary on Horace: Odes, Book I, Oxford U. Press, 1970, pp. 319-320