Tuesday, 30 November 2021

Unique words in Odyssey 24

Homer scholars have often argued that the last part of the Homeric Odyssey is spurious, added by a different poet. One of the main arguments is that its language is somehow distinctively different from the rest of the Odyssey.

An 1816 book by F. A. W. Spohn made this argument, claiming that the ‘epilogue’ — the last 624 lines of the epic, Odyssey 23.297 to 24.548 — has lots of language in it that doesn’t appear elsewhere in Homer. Spohn’s complaint is that it has lots of unique words.

Odysseus reunited with Penelope (terracotta relief, Melos, ca. 450 BCE; NY Met)

At this point in the Odyssey, Odysseus has slaughtered the suitors and reunited with his wife Penelope. In the epilogue, the suitors’ ghosts arrive in the underworld, Odysseus is reunited with his father Laertes, and his conflict with the suitors’ families is resolved. Spohn’s argument was prompted by two ancient glosses:

Aristophanes [of Byzantium] and Aristarchus make this the end-point of the Odyssey.
sch. M,V, Vind. 133 on Od. 23.296

Aristarchus and Aristophanes say that this is the conclusion of the Odyssey.
sch. H, M, Q on Od. 23.296

Why they said this, and what exactly they meant by it, are open questions. (I have my own ideas: see Gainsford 2015: 123–124.) What we’re looking at here is what Spohn says in support of these glosses (1816: 156–157, my translation):

There are numerous words in the Iliad that are not used in the Odyssey; conversely there are many in the Odyssey which are missing in the Iliad. ... But in this last part of the Odyssey, the number of hapax legomena we find is huge for its length; and it contains many forms which show that the language and style have developed.

‘Hapax legomena’ is Greek for ‘things uttered once’: unique words.

Many later scholars repeated this central claim. Page (1955: 101–136) gives an updated list of supposed anomalies in the language of the epilogue. He identifies 37 features that are unique in Homer, another 19 that are uncommon, and asserts that all such features are by their nature non-Homeric. Others have rejected Page’s argument, dismantling his anomalies one by one (Erbse 1972: 177–229; Wender 1978).

But no one ever questioned the reasoning, or the basic premise:

  • Unique language means it’s spurious.
  • The epilogue has lots of unique words.

Both of these are the purest nonsense.

Unusual language, therefore spurious?

[I]t may be confidently asserted that there is no other passage of comparable length in the Homeric poems in which linguistic evidence of relatively late composition is to be observed in such profusion.
Page 1955: 102

Stylometrics alone will not demonstrate the spuriousness of the Epilogue, though we can point to a selection of oddities which must trouble its defenders.
West 1989: 120

The epilogue has linguistic ‘anomalies’: well and good. That is a single datapoint. A compilation of these anomalies demonstrates that they exist. But that conveys no information at all about how typical or atypical the datapoint is. Anomalies exist everywhere. What matters is how frequent anomalies normally are, and whether the epilogue falls outside the usual parameters.

In other words, Spohn, Page, and West totally ignore the importance of statistical significance. Spohn’s argument was tendentious, but he had a partial excuse: statistics as a field didn’t exist in his time. More recent scholars have no excuse.

When Erbse and Wender demolished Page’s list of anomalies, they missed the point too. They explained the anomalies away, one by one, until there were none left. But in doing so they attacked only the data, not the methodology. The methodology itself was nonsensical. A single datapoint cannot demonstrate a discrepancy.

If a discrepancy were demonstrated, it would also be important to show that the discrepancy was statistically significant. One attempt at a stylometric analysis of the epilogue by Norman Postlethwaite falls down catastrophically here too. His metric is the frequency of certain kinds of noun-epithet phrases in the epilogue. But his control consists of another single datapoint, Odyssey 2.1–434, along with a passage from the Iliad. And that’s totally useless. We need to know not just a typical rate for stylometric features, but also the variance in their rate. Postlethwaite comes so close to confronting variance in the control, but misses: a couple of stats classes at school would have made all the difference.

The scatter figures for the two control passages of Homer are ... sufficiently alike to suggest that a figure in the neighborhood of these represents the normal frequency ...
Postlethwaite 1981: 182 (my emphasis)

Hapax legomena

Hapax legomena are words that appear with a frequency of 1, as I said above. Scientists working on stylometry have sometimes taken an interest in hapaxes. They aren’t a highly-regarded measure of authorial style these days, but they aren’t useless either.

Here’s the really important thing. Every text, of every length, has hapax legomena.

And here’s the really counter-intuitive thing. The ratio of hapaxes to total vocabulary is roughly constant, no matter how large the text corpus is.

Take a moment to digest that. No matter how large. You’d expect that as the size of a text corpus increases, more words get repeated, and so hapaxes as a proportion of the total vocabulary would drop.

You’d expect that. But that isn’t what happens. Hapaxes do get less frequent as corpus size increases — they make up a smaller and smaller proportion of the corpus. But as a proportion of the vocabulary, they stay pretty much constant. Here are some examples from English-language corpuses:

  • Lewis Carroll’s Alice in Wonderland is 26,505 words long, and has a vocabulary of 2651 words. Of those, 1176 appear only once. That is, 44.4% of the vocabulary in Alice is hapaxes.
  • Mark Twain’s Tom Sawyer is 71,370 words long; 49.8% of its vocabulary is hapaxes.
  • Kierkegaard’s collected works have 2 million words; 43.6% of the vocabulary is hapaxes.
  • A ‘representative’ 103 million word corpus of American English studied by Brainerd has a vocabulary with 44.7% hapaxes.
Note. For Alice, see Baayen 2001: 2–12; for Tom Sawyer, Fan 2010: 3; for Kierkegaard and the 103 million word corpus, Brainerd 1988: 14.

Scientific models of vocabulary distribution are forced to assume that the available vocabulary is literally infinite. One study has shown that the proportion of vocabulary that appears twice — dis legomena — hovers around 15.0% to 15.6% for corpuses up to 400,000 words; but above that size, their proportion starts to decline as more and more words are repeated. We can conjecture that for an extremely large corpus, on the order of over a billion words, we might start to see a similar effect for hapaxes ... then again, we might not.

Note. Infinite vocabulary: Baayen 2001: 56 ‘This definition explicitly requires S to be infinite while requiring that the hapax legomena constitute a non-negligible proportion of the vocabulary.’ Dis legomena declining for corpus-size over 400,000 words: Sichel 1986: 53–57.

What about the Odyssey? First, be aware that in ancient Greek it’s important to apply ‘stemming’. A regular Greek verb can have over 400 distinct forms, and there’s no value in treating all of them as separate vocabulary items. ‘Stemming’ means we treat λύω, λύεις, and λύει as a single vocabulary item.

With that in mind, here are the figures for Homeric hapaxes:

  Odyssey Iliad both epics combined
size of corpus 87,092 tokens 111,711 198,803
vocabulary 4856 types 5448 6807
hapax legomena 1606 types 1771 1962
hapaxes as % of vocabulary 33.1% 32.5% 28.8%
hapaxes as % of corpus 1.84% 1.59% 0.987%
hapaxes per 100 lines of verse 13.3 per 100 lines 11.3 7.06

These figures are based on the Northwestern University dataset, available through the WordHoard application and The Chicago Homer website. Some classicists found Homeric hapax rates surprisingly high when they first read about them, in Michael Kumpf’s 1984 book Four indices of the Homeric hapax legomena:

In a total of around 9000 lexical items ... used by Homer, [Kumpf] has found 2692 hapaxes, a number that is astonishing at first sight in the context of the formular style, where repetitions are much more numerous than in literary texts of the post-Homeric era.
Ruijgh 1987: 178 (my translation)

As you’ll have noticed, these proportions aren’t high at all: they’re actually lower than in the English corpuses mentioned above.

Note. Kumpf’s figures are different from mine for four reasons. (1) Kumpf includes proper names. (2) Kumpf uses the OCT edition for his text, while the Northwestern dataset uses Murray’s Loeb text. (3) The Northwestern dataset is more generous with stemming: for example, Kumpf counts Od. 1.328 ὑπερωιόθεν and 2.193 ἀσχάλλω as hapaxes, while the Northwestern dataset treats them as forms of ὑπερώιον and ἀσχαλάω. (4) Kumpf includes rejected readings from the OCT critical apparatus.

The linguist George Kingsley Zipf (1935) found that if you order words in a corpus by frequency, and plot their frequency on a graph with a logarithmic scale, you end up with a nearly linear graph. Formally, what that means is that if z = Zipf rank and V(z) = frequency, then Zipf’s Law states

log V(z) ≈ log (V(1)/z)

Zipf’s Law works just as beautifully for Homer as it does for modern English corpuses, formular style be damned. Here are the top Zipf-ranked words in the Odyssey:

Zipf rank Frequency Word
1 4506 δέ
2 2486 ὁ, ἡ, τό, etc.
3 2435 καί
4 1772 τε
5 1558 ἐγώ, με, etc.
6 1051 εἰμί, εἶ, ἐστί(ν), etc.
7 995 ἐν
8 958 σύ, σε, etc.
9 815 μέν
10 812 ὅς, ἥ, ὅ, etc.

We don’t start getting to nouns until Zipf rank 25 (ἀνήρ, frequency 449). Plot frequency vs. Zipf rank, and you get an absolutely typical Zipf curve:

Zipf graph of Odyssey vocabulary. The most frequent word, δέ, is plotted as the dot at the top left: Zipf rank 1, frequency 4506. The line of dots at the bottom right represents hapax legomena, Zipf ranks 3251 to 4856, all with frequency 1.

Now, remember that any given chunk of text is going to have hapaxes, and there are lots of them. If you want to make a claim like ‘the number of hapaxes we find is huge’, you need to know how many hapaxes you should expect to find.

If you plot the number of hapaxes per book of the Odyssey, it quickly becomes obvious that there’s nothing very special about book 24. There isn’t even anything special about the Laertes scene (Od. 24.205–412), which Page regarded as especially objectionable for its unique language.

Hapaxes in the Odyssey by book, and in the epilogue by episode. ‘Domain: Homer, Hesiod, Hymns’ represents words that appear once in the entire corpus of early hexameter; ‘Domain: Odyssey’ represents words that appear once in the Odyssey. With the larger domain there are fewer hapaxes, because many Odyssey-hapaxes get repeated elsewhere.

It turns out that the bit of the Odyssey that actually has the highest rate of unique vocabulary is in books 5 and 6: specifically, Odyssey 5.402 to 6.128, a passage with a rate of 32.3 hapaxes per 100 lines (71 hapaxes in 219 lines). The hapax-rate in the Laertes scene is half that, a mere 16.3 per 100 lines (31 hapaxes in 208 lines).

Hapaxes are just a small slice of the linguistic pizza, of course. Modern stylometric analysis is much more sophisticated than counting hapaxes. Once upon a time I’d planned to write this discussion up into a journal article; but hapaxes are too trivial, by comparison with what the real experts do.

And we can’t quantify the other kinds of anomalies that Spohn and Page listed: many of them relate to mythological conceptions that don’t appear elsewhere (Hermes as ‘Cyllenian’; ‘nine’ Muses), or unusual morphology (ἠριγένειαν as a substantive; πρου- in the arsis of a foot; contracted genitive Ὀδυσεῦς). These are very diverse, and they can’t really be quantified on the scale of the epic as a whole.

Hapaxes, however, can be dealt with quite straightforwardly. And with respect to hapaxes, Spohn and his followers couldn’t have been more wrong.


  • Baayen, R. H. 2001. Word frequency distributions. Dordrecht, Boston, London.
  • Brainerd, B. 1988. ‘Two models for the type-token relationship with time dependant vocabulary reservoir.’ In: Bernet, C.; Thoiron, P.; Labbé, D.; Serant, D. (eds.) Études sur la richesse et la structure lexicales. Paris. 13–22, 165–172.
  • Fan Fengxiang 2010. ‘An asymptotic model for the English hapax/vocabulary ratio.’ Computational Linguistics 36.4: 631–637. [MIT Press link]
  • Gainsford, P. 2015. Early Greek hexameter poetry. Cambridge. [CUP link]
  • Kumpf, M. M. 1984. Four indices of the Homeric hapax legomena. Hildesheim, Zürich, New York.
  • Page, D. L. 1955. The Homeric Odyssey. Cambridge.
  • Postlethwaite, N. 1981. ‘The continuation of the Odyssey: some formulaic evidence.’ Classical Philology 76: 177–187. [JSTOR link]
  • Ruijgh, C. J. 1987. Review of Kumpf 1984. Mnemosyne 40: 178-80. [JSTOR link]
  • Sichel, H. S. 1986. ‘Word frequency distributions and type-token characteristics.’ Mathematical Scientist 11.1: 45–72. [Applied Probability link]
  • Spohn, F. A. W. 1816. Commentatio de extrema Odysseae parte. Leipzig. [Internet Archive link]
  • West, S. 1989. ‘Laertes revisited.’ Proceedings of the Cambridge Philological Society (now Cambridge Classical Journal) 35: 113–143. [JSTOR link]
  • Zipf, G. K. 1935. The psycho-biology of language. Boston.


  1. > and it contains many forms which show that the language and style have developed

    What is this explained by, and is this better proof for different authorship?

    (Not being in any way a linguist, I assume this is something like doth --> does, or some evolution in suffixes that I can't think of an example of at the moment. Please tell me if I'm incorrect)

    1. If you follow the link you can take a look at his examples -- they're in Greek of course, but you're not going to get discussion of Greek language that doesn't use Greek. Spohn's own list wasn't great; Page makes the same argument, and his list is an all-round improvement (for what it is). I mention a few examples of the kind of things he picks out in my second-last paragraph.

      But no, it's not a good argument. It's a terrible argument.

      In the first place, the statistical value of citing examples of 'developed' forms - anomalies, in other words - isn't possible to quantify. (a) There are anomalies everywhere; (b) anomalies other than hapaxes are very diverse, by their nature, so you can't do statistical analysis on them.

      There's a more fundamental problem, which I didn't touch on above. Someone with experience in stylometry pointed it out to me. And it is this: focusing on the rarest linguistic features is going to give you the smallest amount of data.

      Real stylometrists work especially hard on the commonest linguistic features, because you get heaps of data out of them. Put another way, quantifying the use of δέ, καί, and τε is going to give you far more information than quantifying the use of ἐπιβρίθω, αὐχμέω, and βρότος. Looking at rare features means you always have the worst possible data.