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Greece & Rome, Vol. 50, No. 2, October 2003
DROWNING BY NUMBERS
PYTHAGOREANISM AND POETRY IN
HORACE ODES
1.28
By ARMAND D’ANGOUR
“Death is the end, and yet it isn’t. [. . .] IÎm working on something new now.
Will I finish it? Probably not. If immortality exists, I have a certain form of
it. [. . .]
A guy stopped me in the street [and spoke of the impression my
writing had made on him]. P'd touched him. Pd affected this guy anda little
bit of me would stay with him always. If that’s immortality, Ill have it.
Besides, everlasting life would be a nightmare. Each day has meaning
because time is finite.’
Studs Terkel (at age 80), Sunday Times, 10 March 2002
‘The critic, like the poet, can bring only finite resources to an infinity of
discourse.’
Stephen Hinds, Allusion and Intertext (p. 51)
Horace’s ‘Archytas Ode’
Te maris et terrae numeroque carentis harenae
mensorem cohibent, Archyta,
pulveris exigui prope litus parva Matinum
munera, nec quicquam tibi prodest
aérias temptasse domos animoque rotundum
PK¡Sau ANGdOUR YLos
3
percurrisse polum morituro.
occidit et Pelopis genitor, conviva deorum,
Tithonusque remotus in auras,
et Iovis arcanis Minos admissus; habentque
Tartara Panthoiden iterum Orco
10
demissum — quamvis clipeo Trotana refixo
tempora testatus, nihil ultra
nervos atque cutem Morti concesserat atrae,
iudice te non sordidus auctor
naturaeque verique. sed omnes una manet nox
et calcanda semel via Leti.
dant alios Furiae torvo spectacula Marti.
15
exitio est avidum mare nautis.
mixta senum ac iuvenum densentur funera. nullum
saeva caput Proserpina fugit.
me quoque devexi rapidus comes Orionis
IHlyricis Notus obruit undis.
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Author(s): Armand D'Angour
Source: Greece & Rome, Second Series, Vol. 50, No. 2 (Oct., 2003), pp. 206-219
Published by: Cambridge University Press on behalf of The Classical Association
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BY NUMBERS
DROWNING
PYTHAGOREANISM
AND POETRY
HORACE ODES 1.28
By
ARMAND
IN
D'ANGOUR
'Death is the end, and yet it isn't. [.. .] I'm working on something new now.
Will I finish it? Probably not. If immortality exists, I have a certain form of
it. [.. .] A guy stopped me in the street [and spoke of the impression my
writing had made on him]. I'd touched him. I'd affected this guy and a little
bit of me would stay with him always. If that's immortality, I'll have it.
Besides, everlasting life would be a nightmare. Each day has meaning
because time is finite.'
Studs Terkel (at age 80), Sunday Times, 10 March 2002
'The critic, like the poet, can bring only finite resources to an infinity of
discourse.'
Stephen Hinds, Allusion and Intertext(p. 51)
Horace's 'Archytas Ode'
Te maris et terraenumeroquecarentisharenae
mensoremcohibent,Archyta,
pulveris exigui prope litus parva Matinum
munera, nec quicquamtibi prodest
aerias temptassedomosanimoquerotundum
percurrissepolum morituro.
occidit et Pelopis genitor, conviva deorum,
Tithonusqueremotusin auras,
et lovis arcanis Minos admissus;habentque
TartaraPanthoiden iterum Orco
demissum- quamvis clipeo Troiana refixo
temporatestatus,nihil ultra
nervosatque cutemMorti concesseratatrae,
iudice te non sordidusauctor
naturaequeverique.sed omnes una manet nox
et calcanda semel via Leti.
dant alios Furiae torvo spectaculaMarti.
exitio est avidum mare nautis.
mixta senum ac iuvenum densenturfunera. nullum
saeva caput Proserpinafugit.
me quoquedevexi rapiduscomes Orionis
Illyricis Notus obruitundis.
5
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at tu, nauta, vagae ne parce malignus harenae
ossibuset capiti inhumato
particulamdare:sic, quodcumqueminabiturEurus
fluctibus Hesperiis, Venusinae
plectantursilvae te sospite, multaquemerces,
unde potest, tibi defluat aequo
ab Iove Neptunoquesacri custode Tarenti.
neglegisimmeritisnocituram
postmodote natisfraudem committere?fors et
debita iura vicesquesuperbae
te maneant ipsum. precibusnon linquar inultis,
tequepiacula nulla resolvent.
quamquamfestinas, non est mora longa; licebit
iniecto ter pulvere curras.
You were the man who measured sea and earth
and sand beyond number, Archytas:
now offerings of wispy dust confine you near the Matine
shore, and you've gained nothing from assailing the
domains of heaven and ranging with your mind the
circumference of the sky, since you were destined to die.
Even Pelops' father [Tantalus] died, the gods' diningcompanion, and Tithonus who was whisked away to the
winds, and Minos, who was privy to the secrets of Jupiter;
and Hell holds Panthoides [Pythagoras], who descended,
twice, to Orcus - despite proving by the unhooked shield
that he had lived in Trojan times and had yielded up to
dusky Death nothing besides guts and flesh.
In your judgement, he was no mean exponent of nature
and truth. But for all of us one night awaits, and the
road of Oblivion must be trodden but once.
Some the Furies give up to grim Mars for entertainment.
The devouring sea spells destruction for sailors.
The queues of the dead are swollen, mixed with young
and old together. From none does unforgiving Proserpina shrink.
I too was overwhelmed in the Illyrian waves by the driving
South Wind which comes with the setting of Orion.
But you, sailor, do not unkindly begrudge granting
my bones and unburied head a measure of loose sand. In
return, whatever threat the East Wind makes against the
Hesperian sea, may the Venusine woods be battered while
you stay unscathed, and may great bounty from every
quarter pour down on you, from fair-dealing Jupiter and
from Neptune, protector of holy Tarentum.
Are you unconcerned about committing a crime that will
bring harm to your innocent descendants? It may be that
rights withheld and penalties for disdain await you
25
30
35
5
10
15
20
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yourself. I won't be left with my prayers unanswered, and
no atonement will ever absolve you. Though you're in a
hurry, it won't take long. Toss in three handfuls of dust
and you may speed on your way.
35
The musings of a drowned man might seem on the surface to be an
unpromising theme for poetry. But I will suggest that some of the
Ode's interpretative cruces dissolve when we recognize how, with
reference to popular Pythagorean tradition, Horace connects the
notion of drowning to immortality, and immortality to numbers
(hence the title of this paper) . In turn, the notion of numbers,
numeri, connects to poetry itself, and thence to a familiar Horatian
theme of 'poetic immortality'.
The Ode falls into two main sections. An extended apostrophe to
Archytas of Tarentum, the famous fourth-century Greek mathematician, astronomer, and Pythagorean philosopher (1-22), is followed by
an appeal to a passing sailor for burial (23-36). Only when we come to
the final couplet of the first section (me quoque.. .) does the poem reveal
itself to be a monologue uttered by the ghost of a drowned man. Horace
has added few explicit indications of the background or narrative
context, and the poem has raised questions to which scholars have
laboured to find satisfactory answers. What is the imagined scene and
setting, and why has the poet chosen them? What does the selection of
mythical figures signify? Who is the speaker meant to be, and why does
he address his opening reflections to Archytas? What is the poetic
significance of the Ode's Pythagorean undercurrents?
While the apparent change of addressee at line 23 strikes an
unexpected note, commentators have noted that the composition as a
whole exhibits a high degree of formal coherence.2 A handful of
references establish a uniform topographical perspective: litus Matinum
(3), the locus of Archytas in death as in life, is linked to the sailor's
vicinity (29, Tarenti)and to Horace's own native region of Venusia (267, Venusinae silvae).3 In addition, a number of thematic correspondences bind the two main sections of the poem together. The
opening verse rolls out (with appropriate alliterationof r) the impressive
trio of sea, earth and numberless sand; by contrast, the required munera
1 As the titleis not intendedto makeany allusionto the PeterGreenawayfilm so named(UK,
intertext.
1988), perhapsit may qualifyas an exampleof a 'free-floating'
2 R. Nisbet and M.
on HoraceOdesBookI (Oxford,1970), 319, state
Hubbard,A Commentary
'The two partsof the poem do not perfectlycohere';but K. Quinn,Horace,The Odes(Bristol,
1980), 174-5, arguesthat'thetwo halvesof the ode areheld togetherby the reversalof attitudes'.
3 Cf. D. West, HoraceOdesI: CarpeDiem(Oxford,1995), 134.
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209
of sand are parva (3) as specified in final verse (36, ter). The harena
subjected to measurement by Archytas (1) eludes the grasp of the
unburied man (23, vagae .. .harenae).Pulvis now confines the geometer
(3); pulvis is what the speaker demands and entreats for his ritual burial
(36). And shortly after learning of the sea's deadly hunger for nautae
(18), the merchant himself is addressed with the words at tu, nauta (23).
Further verbal and aural echoes abound. Archytas' mind is said to
have scoured (6, percurrisse)the globe; the sailor will resume a humbler
course (36, curras) through the waves. The mathematician, faced with
an infinite quantity of sand, was calculating (3, mensor);the sailor must
not spare (23, ne parce) a few grains. Archytas, moriturus(6), was not
mindful of his mortal destiny; the sailor should take care not to
perpetrate a criminal neglect that is nocitura (30). Death awaits all
(15, manet); dire penalties await the neglectful (33, maneant). Tartarean
realms contain (9, habent)Pythagoras; a few handfuls of dust confine (2,
cohibent) his follower. The former conceded his material body Morti
atrae (13); the Furies make others showpieces torvo Marti (17).
Further suggestive verbal links contribute to the cocoon of correlations. For instance, Orion's descent down the sky (21, devexi) seems to
mirror the philosopher's descent to Orcus (11, demissum).There Minos,
once accepted into the gods' counsels (9, admissus),now acts as judge in
the Underworld; Proserpina too is a judge in Hades, passing harsh
judgement on every caput (20) - a finality keenly sought by one still
unburied (24, capiti inhumato). While the goddess earns the epithet
saeva (20) by sparing none from capital sentence, the sailor is warned
not to earn the epithet malignus (23) by sparing a few grains to ensure
that the speaker can be finally dead and buried. The poet's choice and
disposition of words create unspoken, ironic resonances. Notus is
described as Orion's rapidus comes (21); but Proserpina too, like
Orion, once descended below as Hades' rapta comes. We know that
Minos traditionally sits there as iudex;but when iudex occurs here (14),
it refers to Archytas' mistaken approval of his master's auctoritas.
The notion of threat and punishment is a recurrent theme. Archytas
posed a threat to the gods' aerial haunts (5, aerias temptassedomos);the
winds will threaten to punish the sailor (25, quodcumqueminabitur
Eurus); the speaker finally threatens the passer-by with his curse (33,
precibusnon linquar inultis). The gale whips up the Illyrian billows (22,
Illyricis.. .undis); the sailor, fearful of the Hesperian swell (26, fluctibus
Hesperiis),will be thankful if the woods take the whipping (27, plectantur
silvae).
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The notion of gain or profit supplies a further counterpoint. Pythagoras opted for a kind of immortality (12-13); but is not mortality (1516) a greater gain? The astronomer, assailing heavenly heights in pursuit
of intellectual gain, did not profit (4, nec quicquam tibi prodest); by
contrast, the merchant ploughing the waves may hope for a windfall
from heaven as his reward for dutiful behaviour (27-28, multaquemerces
/ defluat).
The utterances of a drowned speaker invite us to look beneath the
surface. The intricate web of allusions and images adds a mysterious
dimension to the poem's message and hints at a deeper significance. In
probing the depths, we may be able to discover that the poem not only
offers mysteries, but also reveals the solutions to the puzzles it presents.
The perils of immortality
The catalogue of exemplary 'immortals' illustrates how the implications
underlying what is actually said should be allowed to guide our reading.
In setting out to reveal the truth about immortality, the speaker takes
issue with the commonly held, but in his view mistaken, suppositions of
myth:
occidit et Pelopis genitor, conviva deorum,
Tithonusqueremotusin auras (7-8)
Even Pelops' father [Tantalus] died, the gods' dining-companion,
and Tithonus who was whisked away to the winds.
Tantalus and Tithonus were both allegedly accorded immortality on
account of their association with divinities. Here the speaker bluntly
asserts that they are dead: occidit brooks no compromise.4 But one
cannot and should not forget that these particular figures of myth were
paradigmatic for the unhappy, cautionary consequences of their immortalization, rather than for the mere fact of being immortalized. Even the
succinct phrases used to describe them, ironic in their brevity, hint at
those consequences. Tantalus enjoyed the privilege of sharing his table
with gods; but having served his son up for dinner (the locution Pelopis
genitor highlights the grisly tale), he lost all credit for conviviality. The
goddess of Dawn chose to elope with Tithonus to heaven; but he might
have shrunk from her divine favours sooner than, remotusin auras, face
The brusquetrisyllableat the startof the versefillsa singledactylicfoot, withictusand accent
coinciding.
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211
an eternity of growing older.SIn so far as the mere mention of these two
figures inevitably calls to mind their miserable fates, they represent far
from unambiguous exemplars of the boon of immortality which the
speaker seeks to deny.
Rather than wondering at Horace's apparent inattention to detail, we
should embrace the implicit significance of the speaker's roll-call.6 The
horrifying consequences of their 'immortal' status - the endless torments of Tantalus, the everlasting aging of Tithonus - sound a warning
that victory over Death, even were it to be available, would be bound to
leave a bitter taste. The other 'immortals' in the list add weight to the
message. Minos, rewarded for his sober chairmanship of the gods'
councils, is hardly to be envied his royal tenure in Tartarus; we
cannot fail to recall Achilles' opinion.7 Pythagoras, his soul incarnate
in a succession of new bodies, must nonetheless tread the via Leti; only,
in his case, he must do so time and again.8
Instances of the unhappy aftermath suffered by those allegedly
granted immortality could be multiplied.9 To fates such as these, the
finality of the grave with its promise of oblivion (Letumis Greek Lethe,
forgetfulness) must surely be preferred. It seems hardly a coincidence
that the circumstances of other figures mentioned here en passant
resonate with the speaker's disavowal of immortality's privileges.
Proserpina, Hades' divine consort, must spend part of her eternal
portion in the joyless Underworld; reason, perhaps, to be saeva.10
Orion, once a great hunter on earth, now enjoys a less full-blooded
Nachleben in heaven - a constellation whose waning bodes ill for
sailors.11The speaker's fuller purpose comes into view: he means not
5 As well as recalling the goddess's name (Aurora), remotusin auras seems to hint at Tithonus'
familiar fate of dwindling into a cicada, a creature small enough to be wafted by the breezes.
6
Commentators have missed this point. For instance, Nisbet and Hubbard (n. 2), 326: 'It is
curious to find Tantalus in this list of privileged persons who died' and 'Tithonus: in this context
even stranger than Tantalus . . . The crucial piece of evidence does not seem to have been
deployed.'
7 Hom. Od. 11.489-91: 'I would rather be a serf in the house of a landless man on earth, than
king over all the dead departed.'
8 Iterumstrictly implies a second time, but may not preclude the possibility of further travel on
the iter Orco.
9 Other notable victims of
immortality include Sisyphus, Prometheus (cf. Hor. Epode 17.67-9),
Tityos, and Ixion. Calypso thoughtfully proposes to make her lover Odysseus both immortal and
ageless (Hom. Od. 5.136).
10 It might seem more natural for Horace to have written 'no caput escapes Proserpina' But the
inversion reminds us that Proserpina herself once 'shrank from' the notoriously rapacious Hades
(cf. n. 35 below): just as she did not succeed in fleeing him, now she will allow none to escape her
judgement.
" In Odes 3.4, Horace speaks of Orion as the hunter who consorted with gods; like Tithonus, he
was traditionally the beneficiary and victim of Aurora's favour (Hom. Od. 5.120-4).
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just to deny claims to immortality, but to repudiate its false allure. His
catalogue of would-be immortals serves to establish not a single, but a
double-sided conclusion: explicitly, that immortality is a myth; and
implicitly, that immortalityentails a fate worse than death.
Playing with numbers
The introduction of Pythagoras as Panthoides (10) strikes a note of
apparent discord with the assertion of death's finality. Pythagoras is the
speaker'scentral and most extended exemplumof immortalityunattained.
Forerunner and inspirer of Archytas, he boasted that Death had taken his
body but not his soul. He allegedly 'proved' that he had lived an earlierlife
as Trojan Euphorbus, son of Panthous, by recognizing the latter's shield
hanging on the temple wall. The speaker claims to know better, allowing
neither the possibility nor the desirabilityof transmigration.The spirit of
the sage hovers over the Ode, even while the speaker explicitly abjureshis
teachings. Mortal measure is in the end insurmountable, albeit that some
seek to transgress human limit by counting the uncountable. And in the
end, as has been illustrated by the list of would-be immortals, death
should be counted a positive and undeniable benefit.
This conclusion exemplifies on the mortal plane a more abstract,
universal truth: limit (rrepaS) is good, unlimit (arreLpov) bad. This notion
was famously propounded by the philosopher for whom life and
calculus converged.12 Pythagoras' presence is ubiquitous in the
poem's engagement with measurement, calculation, and the play on
numbers which fleshes out the formal antithesis of re'pas and a7TUEpov.
The first line refers to sand without number; the last specifies the
number of handfuls needed for burial. The imagination of genius
leaps across endless space (rotundumpolum, 6); but the path to oblivion
may be trodden but once (semel, 16). The sand is beyond reckoning
(numeroquecarentis, 1) but a little parcel (particula,25) is easily grasped
by hand and mind. Death's simple numerations - one night (una, 15),
three handfuls (ter, 36) - offer a blunt riposte to unutterable magnitudes.
Three, the traditional number of handfuls required for burial, is the
Pythagorean cosmic number par excellence:'For as the Pythagoreans too
say, the Whole and everything in it is comprised by the number 3; for End
7rTepaS and aTretpov head the Pythagorean 'table of opposites' (Arist. Met. 986a22): see
W. Burkert, Lore and Science in Ancient Pythagoreanism(Cambridge MA, 1972), 51. The basic
tenet of Pythagoreans was that 'all is number' (31).
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213
and Middle and Beginning make up the number of the Whole, that of the
triad.'13Human computation may be unreliable:Archytas miscalculates
his advantage(nec quicquamprodest,4) - and he was a /aOq/_LaTtKo. 14
Conversely the merchant, so long as he behaves correctly, may bank on a
big haul (27): in the ethical balance-sheet, profit is conditional on good
behaviour. Debts cannot be avoided by fraus (31), duties must be
honoured (32), penalties for neglect await (33). In the final reckoning,
defaulters will not be forgiven (34). Death is the bottom line, Q.E.D.
Archytas was mistaken in his evaluation of Pythagorean doctrines
about the afterlife (iudice te, 14, suggests a reproving reprise of the
opening te). But the scholar-statesman was more than a misguided
Pythagorean devotee. The speaker's address is respectful, touching off
associations to the range of Archytas' admirable and varied accomplishments. In the fields of astronomy, mechanics, mathematics, and music
Archytas could indeed claim a lasting memorial; even if his soul did not
outlive his body, as he had believed it would, at least the products of his
mind did. As an astronomer, he emulated others who dared to engage
with wind, sky, and stars; as an inventor, he could boast rivalry with
Daedalus by his construction of a mechanical model bird which actually
flew.15He did not shrink from seeking to transcend re'pasand 7Trrepovby
subjecting the infinite to measurement. And while sands may be
numberless, both Pythagoras and his follower famously investigated
numeriof more graspable kind, the measures and proportions of musical
pitch. 16 Ultimately, Archytas' monumentummay not actually be near the
litus Matinum, but in numeri- such as this carmenin which Horace lauds
his memory.
A genius that spanned the cosmos, now confined to a small plot of
ground: the contrast has an obvious and pleasing irony, but the conceit
alone is insufficient to explain the range and focus of the apostrophe to
13
Arist. Cael. 268a10ff.: KaOadrep yap qaal Kat Ol H1v0ayO6pEto, TO Trdv Kat ra rrdavra'TOS rptlav
TrlS rptdSoS. Cf.
dptOfLiOvEXEt TOVTOV 7Tavros, TavTa oE TOv
wpLUTat TeAevZT) yap Kat IfJEov Kat apX~) rTOv
Burkert (n. 12), 265. It would not have been lost on Pythagoras, and perhaps not on Horace, that
the number of the Archytas Ode, 28, is a 'perfect number', a number whose divisors add up exactly
to the number itself (28 is the second perfect number after 6).
14 Pythagoreans were divided into mathematiciand acusmatici;Archytas is identified among the
former (Burkert (n. 12), 198).
15 Aulus Gellius 10.12.9 f. But
percurrissepolum morituroalso raises images of fatal attempts to
fly, e.g. the tales of Phaethon and Icarus.
16 According to Ptolemy (Harmonics 30.9), Archytas 'devoted most attention, among the
Pythagoreans, to music': this would include the development of the mathematical theory of
music (Burkert (n. 12), 384-6). Illyricis, an aural antonym of lyricis, seems to hint that waves
(undis) too are beyond number: the sea is 'illyrical', while poetry (numeri) has music and measure
(modus).
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Archytas. Moreover, in the context of the mise-en-scene gradually
revealed by the poem, the speaker's urgings about death's finality
seem less than watertight. His own soul and consciousness have evidently survived, in some form, his bodily death; and this experience
alone does not entitle him to refute the possibility of transmigration, let
alone immortality.17Indeed, he begs the requisite munera so as not to
remainforeverin his accursed limbo: drowned at sea and deprived of the
chance of due burial, his unburied spirit seems condemned to wander
indefinitely, thus making him a victim of the undesirable kind of eternity
he predicates of other 'immortals'.18How can this be squared with his
categorical repudiation of immortality and his derisive refutation of the
Pythagorean doctrine of the soul's survival after death? The solution to
this mystery seems to lurk within the Ode's centrifugal nexus of allusions
to number, death at sea, limit, and the limitless.
Mortal secrets
The Ode addresses first Archytas, then the nauta: the unifying voice is
that of the mysterious third man, the speaker himself. What he says and
how he speaks seem to lead us, directly or indirectly, towards a
Pythagorean point of departure. First, while Horace offers no grounds
for us to assume a precise identity for the speaker, the accent is
unmistakeably Greek. The epodic metre used here derives from
Archilochus, a poet whose thoughts often dwelt on shipwreck.19The
address to Archytas, with spondaizing vocative, takes us into the genre
of Greek sepulchral epigram: rov TroTEtETrp'qgavTa . . . ('He who once
measured . . .).20 Along with the traditional commonplaces, Grecizing
17 Cf. B.
Frischer, 'Horace and the Monuments: A New Interpretation of the Archytas Ode
(C. 1.28)', HSCP 88 (1984), 102: 'Why does Horace fall into the blatant contradiction of putting a
sermon on the finality of death into the mouth of a dead man?'
18 The impression conveyed by the Ode is that Horace's drowned spirit is addressing the passing
sailor from the watery depths: the final curras(36) imparts a sense that the nauta is in mid-course on
the high seas (Peta Fowler and Alex Hardie independently suggested this to me). While it is usually
assumed that the speaker's unburied body is washed up on shore, the Ode gives no clear warrantfor
this assumption, which derives from the toposof Greek epitaphic tradition and the assumption that
an act of ritual burial would require an actual corpse (though in fact an empty tomb could be
dedicated to a drowned person whose body was irrecoverable, as was related about Hippasus of
Metapontum). We may perhaps credit Horace with imaginative originality in relation to the
standard tradition.
19
E.g. Archilochus 8,13,105 West.
20
Nisbet and Hubbard (n. 2), 318. The 'First Archilochian metre' (dactylic hexameter followed
by tetrameter as used in Odes 1.7) has been interpreted as a technique 'whereby epic material is
self-consciously assimilated into lyric discourse'; see Llewelyn Morgan, 'Metre matters: some
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elements accumulate insistently: words and names (aerias,polum, Minos,
Panthoides, Tartara, Notus, Eurus, Hesperiis), epic-style usages and
epithets (Pelopis genitor, atra Mors, torvus Mars, saeva Proserpina,sacri
Tarenti), metrical devices including hiatus and spondaic verse-end
(capiti inhumato, Orionis).
Secondly, Tarentum was an early hub of Greek commerce and an
enduring locus of Pythagoreanism.21The speaker wishes the merchant
success, the epithet sacri Tarenti suggesting a warmth appropriate to a
native of the city.22But soon his tone changes. Precibusnon linquarinultis
(33), he warns: his vengeful curses will pose no less a risk to the sailor's
safety than the threats of Eurus. The menacing tone takes up notions,
present in Pelopis genitor (7) and crystallized by fraudem immeritis
nocituram (30), of crimes committed against the innocent, and of
lingering punishment (even silvae, 27, may take the rap) for an act of
betrayal or a dereliction of debitaiura (32). We may recall that Tantalus,
in one version of the myth, incurred divine wrath because of his illicit
revelation of divine arcana,a fatal indiscretion and in contrast to the wiser
counsels of Minos lovis arcanisadmissus(9). Arcanahere, raising an echo
of the ironic Horatian phrase Pythagorae.. .arcana renati, 'the mysteries
of Pythagoras the twice-born' (Epod.15.21), completes a circle of allusive
associations, centred on Pythagoras, to secrets entrusted and betrayed,
threats and curses, revenge, and punishment.
Where can this be leading us? To a source, I suggest, lying beyond the
confines of the Ode's own words, which provides a curiously apt point
of departure for meditations on Archytas, death, number, and eternity,
and aligns all these elements with the speaker's stern perspective on the
folly of mortality seeking to transcend its limits. In invoking Pythagorean
doctrine, emphasizing the misery of immortal existence, and laying a
conditional curse on the sailor, the speaker generates images which recall
a particular aspect of Pythagorean tradition. While the narrativeof early
mathematical and geometrical discoveries is notoriously sketchy and
uncertain, reaching back as it does to Pythagorean mystical doctrines
subsequently overlaid by Euclid's authoritative third-century systemhigher-levelmetricalplay in Latin poetry',PCPS 46 (2000), 99-120, n. 55. Here Horace, in
weldingdifferentkindsof sepulchralepigramsinto a singleOde, is doing somethingsimilarwith
elegiacmaterial.
21
George Thomson, The First Philosophers(2nd ed., London, 1961), 249 if. develops the theme
of Pythagoras' connections with the 'merchant class'; Burkert (n. 12), 439-40 suggests that some
Pythagorean number terms (e.g. fractions) were drawn from their use in a commercial context.
22 As David West
(n. 3), 135 argues, 'the passing sailor is a merchant sailing out of Tarentum
(line 30), else why should the guardian god of Tarentum be asked to ensure his prosperity?'
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atization, a memorable legend relates to the early discovery of certain
mathematical mysteries, the attempt to suppress them, and the fatal
consequences of disclosure.23 The discovery and revelation of the
existence of irrational, i.e. 'unlimited', numbers held out the grave
danger of undermining the Pythagorean dictum that 'everything is
number' i.e. the world could be represented by whole numbers.24 It
was related that, as a punishment for betraying the 'secret', the
tia6OzaTKoS Hippasus of Metapontum was expelled from the Pythagorean Brotherhood - and subsequently died in a shipwreck.25A scholiast
on Euclid preserves a brief account of the tradition, offering a plausible
explanation for why the story of Hippasus' watery end might have been
conflated with the disclosure of 'the irrational':
TWV ya4p TIvOayopeL'wv
vava{yip
Ao'yosrOv 7rprTov
rV
TrepLrTeaUev, Kai 'aowS ,3V[rrovro,
Kpv7rTEa6Oat qtIEA' Kat EL rTSatv
qaavepov
TTO
VTO troCa7rTat,
TrrV pTEp rTOVTOVOecopLav
orTv
t
rTO
dAoyov
el'
vXr ETrrotSpatxovaa Tcr TOLOVTw)?Ei'EL TtS
els TOV TrS
V7roE'pe?Tat
7YEVEUEW(S
Eayayovra
Tov3paaves
ev Tro ravTr Kat a7ropov
KaOL veLoeov
7TPOXELtpovKaL
7TOVTOVKai TOLS adTaTrro
T7aVT77)
KAVETerat pevJtaatv.
The Pythagoreans say that the man who first revealed the theory of irrational numbers
perished in a shipwreck. Perhaps they were playing on the idea that anything irrational in
the universe, anything unfathomable or inconceivable, is supposed to remain hidden;
and so if one were to come across an entity of this kind and were to make it readily
available and public, one's spirit would be tossed evermore on the sea of Nature and be
buffeted by its restless currents.
The Ode's points of contact with this account - its engagement with
Pythagorean tradition, the notion of numerical limitlessness, the curse
on the betrayer, the fate of death at sea and the bvXy1
condemned to the
eternal waves - seem remarkably close. Horace's speaker is not
Hippasus, nor meant to be;27but it is clear how the poet's acquaintance
23
The popular furore recently generated by the solution of Fermat's theorem (see Simon Singh,
Fermat'sLast Theorem(London, 1997), suggests that, then as now, knowledge of the mathematical
processes involved in such discoveries may be distinct from the wider and technically uninformed
responses to the accomplishment.
24 Cf.
n. 12 above.
25
Hippasus' indiscretion was associated with another notorious Pythagorean 'secret', the
construction of the dodecahedron, a Pythagorean cult object (Burkert (n. 12), 460). He also
appears to have been involved in early Pythagorean studies of the numerical ratios of musical sound
(ibid., 377-8). Burkert (ibid., 194, 206-7) argues that he was a paO,qtartKKo'.If so, his interest in
music may have caused him to be popularly associated with Archytas, perhaps to the extent of being
thought a contemporary; in fact, Hippasus is dated two or three generations earlier.
26
Schol. Eucl. 417.12ff., as emended by Burkert (n. 12), 458 n. 57.
27
L.A. MacKay, 'Horatiana. Odes 1.9 and 1.28', CPh 72 (1977), 318 suggests that Hippasus is
the speaker of the Ode. But if Horace meant us to identify a specific individual, he would hardly
leave the matter so obscure. As in all the Odes, the speaker is above all Horace's own poetic persona:
Frischer (n. 17), 100.
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with this tradition could have provided the starting-point for his
complex fantasy about a drowned spirit. The topic of numerical
boundlessness may suggest a more remote poetic and historical connection, since the true demonstration of irrationalnumbers was authoritatively ascribed to the mathematician Theodorus of Cyrene:28Cyrene
was a city known to poets for its numberless sand.29
Poetic closure
Iniecto terpulverecurras:the Ode closes by bidding the merchant do his
brief duty and continue on his way. The poet, keenly conscious of the
horrors of death at sea, includes a characteristic ethical message:
reverent action, in this case the performance of a ritual act of closure,
will deflect such punishment, while neglect of duty will invite it. It is an
appropriate message to give to a merchant whose mind is filled with
thoughts of material gain. The pursuit of wealth may obscure the proper
acknowledgement of mortality: he whose gaze is set on multa merces
should take time to linger - non est mora longa- to perform his bounden
duty to those who will be dead for eternity. Money, like sand, is beyond
counting, and boundless wealth may seem to act as a foil or consolation
for the shortness of life. But while desire for money is endless, it must be
bounded by ethical behaviour.30The ocean which entices the merchant
shares these dangerous properties of endlessness and inexhaustibility;3'
a recurrent motif for Horace in the Odes, the sea symbolizes violence,
irregularity,and excess, set against the poet's own oft-expressed preferences for rura, otium, and modus.32
A poem set close by Tarentum, revolving around themes of number and
28
PI. Tht. 147d. Theodorus was a contemporary of Archytas; his visit to Athens, where he made
the demonstration, is dated to 417 B.C.
29
Cf. Catullus 7. 3-4, quam magnusnumerusLibyssaeharenae/lasarpiciferisiacet Cyrenis('as great
a number as that of the Libyan sand that covers silphium-rich Cyrene'), occurring in a poem that
makes play with calculation (da mi quot mihi basiationes . . .). Cyrene was also, of course, the
birthplace of the Hellenistic master of epigram and doctrina,Callimachus.
30 Among the formal properties of money is that it is, in a sense, 'endless', an idea nicely
articulated in Aristophanes' Wealth, 189-93, and cf. Solon 13.71-3; Richard Seaford (work
currently in progress - for a foretaste, see Anon 9.3, (2002)), argues for a deep connection
between the historical event of the invention of money and the evolution of notions in Presocratic
metaphysics such as Anaximander's apeiron.
31 Cf. Aesch. Ag. 958: -arwt Oaaaaa, Ti' be vLV KaraaeroeL; ('There is the sea, and who can dry it
up?')
32 The first seven
poems of Odes I, and numerous other Odes throughout, all make some
reference or suggest some connection to the sea - an element that, unlike poetry, lacks tranquillity,
order, and closure.
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measure, was bound to invoke the memory of Archytas. But in the end the
territoryis, like the silvae of Venusium, unmistakeably that of the poet.33
Through the mouth of the drowned man, Horace reveals a deeper truth
about himself and us. When the speaker asserts that death, in contrast to
the infinite sand, is final, it is Horace the Epicurean who would have us
acknowledge life's closure: morsultima linea rerumest.34 Yet Horace the
vatesalso knows that beyond the 'finish-line of things' something may live
on. While the literalsurvival of the personality as a spectral presence - the
plight of the drowned man - is demonstrably a miserable alternative to
finality,for the poet there is another option: the prospect that that his spirit
will survive through his songs.35 Whereas Pythagoras claimed to have
conceded to Death nothing but his materialresidue, the remains of ink on
paper preserve the texts that perpetuate the divine skill of poets and the
memory of men such as Archytas. Saeva Proserpina does not sit in
judgement over the manifestations of the poet's spirit; clothed in numeri
they live on, inviting only their readers or hearers to judge.
If we sense the spirit of Horace at work in this poem, it is partly
because familiar voices from elsewhere can be heard emerging from the
depths, responding ironically to the Pythagoreans' misguided ambitions.
Horace has no need to scale the rotundumpolum:he tells us at the end of
Book 2 that as the Muses' favourite he takes wing, albus ales, and soars.
He has no need to aspire to the dubious immortality of myth or of
mysticism: he boasts at the close of Book 3 that his carmina are a
monumentumaereperennius,'a memorial more enduring than bronze'.36
We have known all along that if he is but counted among the
constellation of lyrici vates, his head will reach the stars.37This is how
Horace aspires to heaven and to immortality.
Ultimately, to ensure this kind of survival, the vates requires the boon
of closure. He craves and demands boundaries of time and space.38
Limit imposes order, freeing the tormented spirit from the shackles of
33
For metaphorical and metapoetic uses of silva, cf. S. Hinds, Allusion and Intertext:dynamicsof
appropriationin Roman poetry (Cambridge, 1998), 12-14.
34
Hor. Epistles 1.16.79. Commentators who relate this image solely to the chalk line used as the
terminus of a running trackmiss Horace's literarywit (it is, of course, the last line of the epistle as well).
6 7rtVTco / dapTaKTr
35 Cf. Callimachus, Epigram 2, lines 5-6: al 8e reat ~Woovotv
arboveC, aULVw
OVK 'rt XE?pafaAEF.('Your nightingales live on; Hades,who seizes all, will not takethem.')
'Ai`8sr
36
Odes 3.30.1.
37
Odes 1.1.35-6.
38 This formulation recalls its
contrasting incidence in Virgil: his ego nec metas rerumnec tempora
pono:/imperiumsine fine dedi (Aen. 1. 278-9): 'on them I impose no bounds, neither geographical
nor temporal: I have given them an empire without end'. Horace displays a consistent poetic logic.
By virtue of its boundlessness, imperiumis at the opposite pole to the preferred lot of mortals which restrains the lyric poet from tackling 'grand themes' on his imbellislyra (Odes 1.6.10-12).
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eternity.39Blunt spondees in the Ode's second line put the brakes on the
rolling dactyls of the first; three dozen taut lines, with expansive
hexameters pulled back by curtly responding tetrameters, confine
Archytas, the sailor, and their addressee; Archytas is mensor,but homo
mensura ('man is the measure') - that is, human life is measured by
mortality. By means of modus, man both measures and is measured.
Modus alone will allow the poet's voice to resound for posterity.40
Recognizing death as the end, it follows that we can and must live life
to the full. Omnes una manet nox:41 therefore, comes the unspoken
rejoinder, carpediem.42We should, after all, be content that our days are
numbered:43we will all tread the via Leti - just once. But for Horace, as
he bids us go our way (curras),that is not quite the end of the story. Non
omnis moriar ('not all of me will die'), the poet may be pleased to
suppose:44 part of him, a part that ensures his greatness, will avoid the
final reckoning, and will live on to speak to future generations. In this
compact and tightly-constructed Ode, a playful meditation on boundlessness and measure, death and immortality, crime and punishment,
body and spirit, number and limit, he draws attention to his own
(im)mortal achievement. Immersed in a sea of numbers, the poet is
waving, not drowning.45
39 Cf. the Sibyl in Petronius, Cena 48: 'cum illi pueri dicerent2?iPvAAa,
rt 0EAEL respondebatilia
arroOavetvOeAo'. ('When the boys asked her "Sibyl, what do you want?" she replied 'I want to die".')
40
The form of the Ode also teases us about our expectations of closure through its unexpected
combination of otherwise familiar sepulchral forms (Nisbet and Hubbard, loc.cit. n. 20), and with
its final 'run-on' word, curras.
41 The echo of Catullus 5.6 (nox est perpetuauna dorrnienda,'there is one endless night to be slept
through') challenges us to consider the two poets' divergent stances on the matter. Again (cf. n. 38)
the poetic logic seems perfectly consistent: for Horace, life's finiteness dictates that we should live
for the moment, while the impassioned Catullus, by resisting finality (8.2, quodvidesperisseperditum
ducas, 'accept that what you see is over is over!'), risks condemning himself to a life of eternal
torment poised between love and hate (85.1-2, odi et amo .. .sentioet excrucior,'I love and I hate .. .I
feel it and I'm in torment').
42 Odes 1.11.8.
43
Hence we should reject the 'numeri' of astrologers (mathematict):Tu ne quaesieris,scirenefas,
quemmihi, quemtibi Ifinem di dederint,Leuconoe,necBabylonios/ temptarisnumeros(Odes 1.11.1-3):
'Leuconoe, don't seek to know - it's forbidden - what end the gods have in store for me or for you,
and don't engage in Babylonian calculations'.
44
Odes 3.30.6.
45 Versions of this paper were read at the Classics Subfaculty Seminar series on 'The Sea' in St.
Anne's College, Oxford and to the Trinity Group at Guildford Grammar School in February 2002,
and at the Classical Association Conference in Edinburgh in April 2002. Special thanks to Alex
Hardie, Elizabeth Jones, and Chris Kraus for their suggestions on earlier drafts.