Why this
Everyone knows the story
Everyone knows the story. Wolfgang Petersen's Troy put Achilles on a hundred million screens in 2004; Christopher Nolan's Odyssey is in cinemas as I write. You can have the plot of either poem in an hour from any of a hundred good sources, several of them listed at the end.
I learned Latin as a boy and Greek a little later, and I grew up on Árpád Szabó's retellings — A trójai háború and Odüsszeusz. Szabó was a historian of Greek mathematics, and it was through him that I first felt the pull between mathematics and philosophy that led me to Plato, and from Plato to a life in linguistics and philosophy. That is one child, one set of tales. These two have done the same for millions of readers across nearly three thousand years.
What is genuinely hard is not the story but reading Homer. In the original it is hard because the Greek is archaic, dialectal, and formulaic. In translation it is hard in a different way: every translation is an argument, and reading one well means reading the argument too.
Counting is a third way in. It has nothing to say about why book 24 is unbearable, but it answers questions reading is bad at. Which words does one poem hoard? Who actually speaks to whom? Where does the map run out?
Where the words come from
Standing on giants' shoulders
The text is the Perseus edition of each poem, in TEI, from the Scaife Viewer. περσεύς has been doing this since before the web was a normal place to put a library. Both poems come in their inherited 24 books: 15,687 lines and 12,107 lines.
Counting words in Greek means deciding what a word is. ἄειδε, ἀείδειν and ᾄδω are one verb wearing three faces. Getting from the face to the verb is called lemmatisation, and it is the step where a project like this usually goes wrong.
Here it does not, because the work is already done. The Ancient Greek Dependency Treebank hand-annotates 99.97% of the Iliad and 99.59% of the Odyssey — 199,985 tokens, each with its lemma and part of speech checked by a human. No model stands between the text and the numbers. Classicists did the hard part, decades ago, and published it.
Two more debts. DICES marks every direct speech in Greek and Latin epic with who speaks and who is spoken to: 1,370 of them across the two poems. ToposText is a gazetteer, a geographical index that ties place-names to coordinates, covering the ancient world: 8,068 places, each with a location, a Pleiades identifier, and, crucially for us, an honest rating of how confidently it is placed.
All three cite the same canonical line references, so everything joins on (epic, book, line) without any guesswork.
What each poem hoards
Proper nouns first, themes second
Set each poem against the other and ask which words one uses far more often than chance allows. That is keyness: a measure of the gap between the count you would expect and the count that is there, which is why a common word can rank below a rare one.
The Iliad's list opens as you would guess: Ἕκτωρ, Τρώς, Αἰνείας, Σαρπηδών. Then the war kit: θώραξ breastplate, φάλαγξ battle-line, αἰχμή spear-point, ἡνίοχος charioteer.
The Odyssey's is its mirror: μνηστήρ suitor, Πηνελόπεια, Φαίαξ, συβώτης swineherd, Κύκλωψ. And its own vocabulary of domestic trouble: ξένος guest-stranger, μέγαρον hall, πτωχός beggar, οἶκόνδε homeward.
Two of these deserve a pause. κορυθαίολος, “of the glancing helm”, is Hector's formulaic epithet; περίφρων, “circumspect”, is Penelope's. Nobody told the method about epithets. It found them by arithmetic.
Read the two columns again and the strongest signals in both are proper nouns. The poems separate by cast first and by theme second, which is the opposite of the order in which we usually describe them.
Now the third tab: lockwords, the vocabulary the two poems hold at the same rate. Most are the particles τε, μέν, γάρ, ἀλλά, the metrical mortar of hexameter. And among them, ναῦς. The ship.
The Odyssey says ship about as often as the Iliad does. Anyone calling the Odyssey the sea poem on the strength of its vocabulary should stop there and account for that. Over 8,820 distinct lemmas the poems share 3,883, and the rank-turbulence divergence between the two rankings is 0.3416, on a scale where 0 means the two poems rank their words identically and 1 means they share nothing. They are speaking one language.
What each poem is doing
21.3% of the Odyssey is open water
Keyness works on totals, so it has no way to say what a stretch of poem is about. We cut both poems into 574 passages of 50 lines, none of them crossing a book boundary, and factorised the lot at once with non-negative matrix factorisation. A topic here is a cluster of lemmas that keep turning up in the same passages. One model covers both poems, so each topic means the same thing in each.
The number of topics is a real choice and we did not want it to be a taste. Fitting every value from 10 to 14 and scoring each by how reliably its topics' words share passages, the best is 13. The score peaks inside the range and falls away at both ends of it, which is what makes the sweep worth running.
Each poem is wound onto a spiral, book 1 at the centre and the last line at the rim. The Iliad's largest topic leads 20.6% of it: Τρώς, Ἕκτωρ, μάχομαι, Αἴας, τεῖχος, the battle line.
Open water — πόντος, θάλασσα, ἄνεμος, κῦμα, νῆσος — leads 21.3% of the Odyssey and 0.6% of the Iliad. One coil fills with it; the other has two scraps.
This answers the ναῦς problem from the last scene. Both poems say ship at the same rate, and only one of them is ever at sea. The Iliad's ships are beached furniture: something to argue beside and something to defend. The Odyssey's are something you are in, with the water all round. A word count sees one lemma. The topic model sees the company it keeps, which is where the difference was hiding.
The longest arc in either poem is the Odyssey's opening: 14 consecutive passages, roughly 700 lines of books 1–2, all led by Telemachus and his father. Of the 574 passages we measured, no other stretch of either poem holds one topic for so long. The spiral draws it as a single unbroken stroke, and the poem has not reached Odysseus yet.
The Iliad's longest is 10 passages of The battle line across books 12–13, the fighting at the wall. Shorter, and the poem takes twelve books to get there.
This is the received reading, confirmed and quantified. Of 13 topics, 8 lead at least 10 times more of one poem than of the other, and 3 lead nothing at all in the other. Reassign passages until one poem's topic profile matches its neighbour's and you will have moved 0.821 of the poem.
Then look at the common ground, which is domestic. Fathers, mothers, children — παῖς, πατήρ, μήτηρ, δάκρυον — and Gold, wine, and the well-made house are the only two topics with real weight in both. Together they are about a tenth of the Iliad: the tenth with Andromache in it, and Priam, and the cup Achilles will not share.
Both poems know what a household is. They disagree about where to put it: at the centre of the story, or at the edge of it, waiting.
Who speaks to whom
The small world of Greek heroes
Because DICES records the addressee of every speech, we can draw the poems as social networks without guessing: a link from each speaker to each person spoken to. The figure is yours to drive: switch poems, colour, and measure with the controls.
Start on the Iliad. It is a crowd. Achilles is the largest node and only just: he holds 6.1% of the poem's connections, with Agamemnon, Hector, Nestor, Odysseus, Diomedes and Zeus close behind him. It is a network of peers arguing.
Switch to the Odyssey and the shape changes at once. Odysseus holds 14.5% of the connections, more than twice Achilles' share of his own poem. Degree centralisation, which measures how far one node dominates the rest on a 0-to-1 scale, goes from 0.24 in the Iliad to 0.44 in the Odyssey.
Change the sizing measure and the ranking barely moves: whether you weight nodes by raw connections, by betweenness, or by PageRank, Odysseus stays first. His centrality is not an artefact of one way of counting.
This is the part of the received reading that survives cleanly, and by a factor you can put a number on. Two checks that it is real. Set the toggle to named individuals: about a tenth of the participants are collectives — “the Greeks”, “the gods”, “the companions of Odysseus” — and dropping them leaves the gap intact. And the colours are Louvain communities, the clusters that talk among themselves: the Iliad splits into councils and battlefields, the Odyssey into one large household around Odysseus and a scatter of episodes.
Both networks have the shape found in real human communities: dense local clusters, short paths between them, and hubs that prefer to talk to non-hubs. In the Iliad any two speakers are 2.9 steps apart on average, the clustering coefficient is 0.21, and small-worldness σ is 7.5 against a random graph of the same size. Degree assortativity is -0.21 in the Iliad and -0.25 in the Odyssey: both negative, meaning hubs attach to non-hubs. Kydros, Notopoulos and Exarchos found the Iliad small-world and disassortative too, in 2015, building their network from name co-occurrence rather than from who addresses whom.
The edge of the map
The Catalogue and the wanderings
Every capitalised noun in the treebank was offered to the gazetteer, and the gazetteer decided what was a place. Then each place was sorted three ways: securely located, uncertain, or, the interesting case, named by the poem and locatable by nobody.
Start with the count, which is the opposite of what the received reading predicts. The Iliad names 209 distinct places. The Odyssey names 91.
One book does almost all of it. The Catalogue of Ships, Iliad 2, names 151 distinct places on its own, more than the entire Odyssey. Take that single book away and the Iliad names 104 to the Odyssey's 91: level.
The poem that never leaves one plain is the poem that recites the whole Greek world. It just does it in one enormous list.
The Odyssey's places are fewer and further apart. Measured from each poem's own centroid, the Iliad's sit a mean 233.5 km out, with nine in ten inside 380.7 km. The Odyssey's average 339.4 km, with nine in ten inside 718.8 km, and its western edge is Mount Atlas at 7.9° west.
Fewer places, flung twice as far. The received reading is right about the dispersion and wrong about the count.
Then the poems part company completely. 16.5% of the Odyssey's place-mentions are to places no gazetteer holds, against 3.2% of the Iliad's.
These are absent rather than uncertain. ToposText has no entry of any kind for Ogygia, Scheria, Thrinacia, Aeolia or Laestrygonia. They are listed beside the map because they cannot be put on it, and the silence is itself the finding.
The Iliad's only unlocatable places are Ocean and Erebus, the edge and the underneath, which both poems share. Its divine geography is otherwise perfectly findable: Olympus is a real mountain in Pieria, and it is the most-named place in the poem.
A closing admission, because two thirds of the places were once people. The first version of this map was rubbish, and it is worth saying how.
Its three most-named “places” in Homer were a sanctuary of Zeus in Crete, a shrine of Athena, and a town in Egypt called Menelaos.
ToposText files a cult site under the bare name of the god it belongs to, so Ζεὺς is literally the Greek name of a Cretan temple, and every Zeus in both poems matched it. Separately, real Hellenistic towns were named after Homeric characters centuries later: a Menelaos in Egypt, a Laertes in Pamphylia, an island Helene, a river Iris. Homer means the people. Together these accounted for about two thirds of everything that first pass called a place.
The fix was two filters. Exclude the built environment, since a temple or a tomb or a theatre is a building rather than a toponym. Then apply a short, auditable blocklist naming each person-place collision and the reason for it. Both are version-controlled, and both are wrong in ways someone can argue with, which is the point.
Two limits remain, and we would rather state them than bury them. Choosing between same-named places — which Thebes? whose Pylos? — is a real scholarly question, and our tie-break simply prefers securely-located places near the Aegean. And gazetteers have holes: there is no ToposText entry for Mount Ida in the Troad, so the Iliad's mountain resolves to a Thracian town of the same name. It is flagged uncertain, and it is still wrong.
An exercise in authorship
The tenth book
One more question, and a frankly speculative one. The classic case in computational stylometry is the Federalist Papers: in 1963 Mosteller and Wallace settled a dozen disputed essays between Hamilton and Madison not on their arguments but on their function words — how often each writer reached for by, to, upon. Those little words are chosen below the level of intention, so they stay steady across subjects and fingerprint the hand.
The Iliad has its own disputed passage. Book 10, the Doloneia — a night raid that sits oddly in the poem — was doubted in antiquity: a scholion reports it was composed apart and only later inserted. Can counting see the seam?
Here are all 48 books of both poems, each placed by its Burrows's Delta distance from every other: the standard stylometric measure turns a book's profile of word-frequencies into a position. The toggle chooses which words: function words for the authorial signal, content words for the subject.
Two honest cautions first. The two epics barely separate: on function words the average distance between an Iliad book and an Odyssey book is only 1.083× the distance within a poem. Homeric diction is a shared, formulaic, sung tradition, and it shows. This method cannot cleanly tell the poems apart, let alone prove a hand.
And yet. On function words — the signal that ought to track authorship — the Doloneia is the 4th most distinctive of the Iliad's 24 books, out near the edge of its own poem. Switch to content words, the signal of mere subject, and it falls to 15th, unremarkable.
That contrast is the whole result. Book 10 stands out for how it is written, not merely for what it is about, which is the shape a later insertion would leave. It is not proof; the sample is tiny and the tradition formulaic. But the counting, asked the question philologists asked on other grounds, gives the same faint answer.
Read it yourself
Better things than this essay
The Scaife Viewer gives you both poems in Greek with a word-by-word dictionary under the cursor, free. The Chicago Homer aligns Greek and English and marks the formulae. Both are better uses of an hour than most things.
In English, Richmond Lattimore is the close one, Robert Fagles the loud one, and Emily Wilson's Odyssey and Iliad are the ones to read if you want to feel the poem move. In Hungarian there is only one real answer: Devecseri Gábor.
For a companion to read alongside the poems, Thomas A. Szlezák's Homer oder Die Geburt der abendländischen Dichtung is the best I know — patient, close to the text, and unfashionably sure that the poems are the work of a poet. No English translation exists yet; there is a German original and a Hungarian one.
And if you can get hold of Árpád Szabó's A trójai háború and Odüsszeusz — do. They were written for children and they are not childish.
Colophon
How this was made
Text from Perseus and the Scaife Viewer; lemmas from the Ancient Greek Dependency Treebank; speeches from DICES; places from ToposText and Pleiades; coastline from Natural Earth. All of it open, all of it cited, none of it ours.
Keyness and rank-turbulence divergence with keyflux, networks with kenon, topic model with chronowords, visual grammar from lexograph.
The ornament is generated with Python, in the vocabulary of the Greek Geometric period — roughly 900–700 BC, the century the poems themselves were taking shape in. The ornament and the epics are contemporaries. The code is on GitHub.