Sunday, 16 February 2020

Did Roman engineers stand under bridges?

Did Roman engineers or architects have to stand underneath their bridges, to prove that they were properly built? This story sounds weird, and it’s totally implausible. (Bear in mind that the Romans built bridges to go over water.)
Hmmm, thinks: if I were a Roman engineer, where would be the best place for me to stand under this bridge so it can be tested? (The Ponte di Tiberio, Rimini, dating to the principates of Augustus and Tiberius, early 1st cent. CE)
If you haven’t heard the story before, I’ll grant that it is niche. But like so many myths about antiquity, it does pop up all over the place. Here’s Nassim Taleb in a 2012 book:
First, never get on a plane if the pilot is not on board. ...

The first heuristic addresses the asymmetry in rewards and punishment, or transfer of fragility between individuals. Ralph Nader has a simple rule: people voting for war need to have at least one descendant (child or grandchild) exposed to combat. For the Romans, engineers needed to spend some time under the bridge they built -- something that should be required of financial engineers today. The English went further and had the families of the engineers spend time with them under the bridge after it was built.
-- Taleb, Antifragile (2012), chap. 23
We shouldn’t expect Mr Taleb to be very accurate about the Romans, mind. In 2017 he infamously had an online shouting match with Professor Mary Beard, the eminent Roman historian, in which he insisted tenaciously (and falsely) that there was racial purity within each province in the Roman empire.
I’d better grant that later in the same chapter Taleb adds a couple more snippets about the Romans which are at least partially accurate. (1) Roman soldiers had to swear a military oath on joining the army (apparently Taleb believes other armies don’t do that); (2) there existed an extremely rare military punishment called decimatio, the random execution of 1 in every 10 or every 100 soldiers (Taleb comments that ‘putting more than 10 per cent to death would lead to weakening of the army’ -- apparently a 10% casualty rate wouldn’t do that). It’s clear he gets his ancient history mainly from popular culture.
Taleb didn’t invent this story, but I do wonder if it’s because of his book that the notion entered popular culture.
Predictable aswer alert! (QI, ‘Keys’, 2013)
Stephen Fry. In Roman times, they’d get the constructor of the arch to stand right under the arch when the support scaffolding was taken away, just to show that he had faith enough in his own, er ...

Tim Minchin. Well, it’s natural selection of arch-builders, isn’t it. Is that guy any good? Well he’s still here!

Isy Suttie. I like that idea of getting people to test things. It’s like going to a barbecue and getting someone to try the sausage.
-- QI, series 11 episode 8 ‘Keys’ (first broadcast 25 October 2013)
Notice how Stephen Fry spots the problem with having this as a story about bridges: he makes it about arches instead. There’s no basis for that either, just some imaginative rewriting, to try to get the story to make some kind of sense.

It wasn’t QI or Taleb that invented the story. The oldest version I’ve found is a signature line used in a USENET post back in 2004:
"When Roman engineers built a bridge, they had to stand under it while the first legion marched across. If programmers today worked under similar ground rules, they might well find themselves getting much more interested in Ada!"
-- Robert Dewar
-- Preben Randhol, post to comp.lang.ada, 11 Feb. 2004 (alternate link)
Robert Dewar was a computer scientist who ran a company involved with the Ada programming language. Is he the ultimate origin of the myth? Who knows.

But I will say this: to me, it sounds awfully like the kind of thing you might hear from a tour guide.

I have a sneaking suspicion that the story really originates with the Pons Fabricius, in central Rome. It’s about 10 minutes’ walk from the Forum and from the Circus Maximus, and just around the corner from the Theatre of Marcellus. It was built in 62 BCE, and it’s still in use for pedestrians and cyclists to cross between the east bank and the Isola Tiberina.
The Pons Fabricius, a.k.a. Ponte Fabricio
Not that Fabricius had to stand underneath his bridge while the legions marched across! No no, I have in mind something much more mundane. It’s a simple misinterpretation. You see, there are inscriptions on the side of the bridge recording who built it and who restored it. Things like

L(ucius) Fabricius G(ai) f(ilius), cur(ator) viar(um) faci<e>ndum, c<u>ravit

Lucius Fabricius, son of Gaius, curator in charge of making roads, supervised (the building of the bridge)
But in separate places, the following gets tacked on:

idemque probavit

and the same man (i.e. Fabricius) approved it
(Don’t mind the spellings, that’s just what Latin looked like when Caesar was in his 30s.)
The thing is, the word probavit is ambiguous. Probare can mean ‘approve’, but it can also mean ‘test, demonstrate’. The same ambiguity can be seen in two English words derived from probare: ‘approve’ and ‘prove’, with ‘prove’ in the sense of test (as in, ‘the exception proves the rule’).

The modern Italian derivative, ha provato, is more specific. It’s almost always going to mean ‘he tried, he demonstrated, he tested’. So if someone like a tour guide were explaining or describing the inscriptions, I’m imagining they might well give the the meaning as ‘test’.

And just to show how plausible this is, here’s an ancient history website set up by an Italian family that reports the inscription exactly like that.
A latin inscription above the arch, on both sides of the bridge reminds us that it was built by Fabricius curator viarum (warden of roads) and that "idemque probavit" - he personally tested it.
-- ‘Ancient Roman Bridges’,, May 2006
I suggest we’ve got three stages in the development of the myth:
  1. The original: ‘Fabricius supervised the bridge, and the same man (idem) approved it (probavit).’
  2. An intermediate version, like on the MariaMilani site, with the mistranslations: ‘Fabricius built the bridge and personally (mistranslation of idem) tested it (mistranslation of probavit).’
  3. The misinterpretation of the mistranslation: ‘Fabricius built the bridge and personally tested it by standing underneath it.’
When tourists in Rome want to walk across a real, ancient, Roman bridge, they’re going to be crossing the Pons Fabricius. It’s nice and central, ten minutes’ walk from the Forum, as I said. So this is a misinterpretation that stands a good chance of going viral.

Of such things are myths made. Even ones as small as this.

Monday, 10 February 2020

The Epic Cycle wasn't as popular as you think

The Epic Cycle is perhaps the most famous group of lost texts of all time. They haven’t existed for at least 1500 years. Yet, when people studying Greek myth nowadays learn that they once existed, they’re often inexorably drawn to the lure of what has been lost -- what might have been.

What is the Epic Cycle? For those lucky people who are about to learn this for the first time, the Cycle was a group of eight early epic poems about the Trojan War -- the legendary war over Helen, fought between the city of Ilion or Troy, and an alliance of Greek heroes. Together the eight epics formed a complete poetic account of the war.
The wooden horse in the film Troy (2004). The horse used in the film is now by the waterfront in the nearby city of Çanakkale.
The two surviving Homeric epics, the Iliad and Odyssey, were reckoned among the eight. For the other six we have titles, summaries, author names. Of the poems themselves, we have only a few isolated snippets of text.
  • Kypria. This epic covered everything from the wedding of Thetis up to the start of the Iliad, in the ninth year of the war. (Some scholars like Jonathan Burgess think it originally covered the whole war. That’s more than just speculation, but we don’t have time to talk about it today.)
  • Iliad. This one survives.
  • Aithiopis. This covered two major episodes: the arrival of Penthesileia and her Amazons, and her death at the hands of Achilles, then the arrival of Memnon and his Aithiopes, and his death at the hands of Achilles. (Memnon’s Aithiopes are kind of linked to the real Ethiopia, but only kind of.) And then Achilles dies too.
  • Little Iliad. This covered various prophecies that had to be fulfilled before Troy could be defeated, like the theft of the Palladion and the story of Philoctetes. Also, the wooden horse gets built.
  • Sack of Ilion (or Iliou persis). The wooden horse goes into action, and Troy is razed to the ground. (Incidentally, the historical Troy was inhabited continuously through the end of the Bronze Age until about 950 BCE. The traditional date for its destruction is 1184 BCE. The real Troy survived after that date for about as long as the USA has existed.)
  • Returns. The homecomings and/or deaths of the major Greek heroes ...
  • Odyssey. ... except Odysseus, who gets a whole epic to himself.
  • Telegony. Another one with two episodes, synthesising inconsistent traditions about Odysseus’ later career and death, in northwest Greece and in central Italy.
See the ‘further reading’ list below for the surviving summaries and other material: they can be found in West 2003.
By the way the Brad Pitt movie, Troy (2004), uses material from the Iliad, but none of the others. The non-Iliadic bits of the film -- some of the Iliadic bits too -- are based on original material, combined with some other ancient sources.

What if we had even one of these epics? How great would it be to have the story of Achilles’ death? What literary glories are we missing out on?

These are the questions that tantalise Cycle fans. Let’s boil the questions down into slightly more academic terms:
  1. How different were the Iliad and Odyssey from the rest of the Cycle?
  2. What about the Theban cycle?
  3. Why did only the Iliad and Odyssey survive?
  4. When was the Epic Cycle lost?
The fall of Troy: the oldest surviving visual depiction, a Cycladic vase from Mykonos, ca. 670 BCE, roughly contemporary with the Iliad. Centre: the wooden horse, with peepholes for the Greek soldiers inside. Right: the death of Astyanax, son of Hector, perhaps being thrown from a tower by Odysseus, while the child’s mother Andromache reaches out her hands to plead for his life.

1. How different were the Iliad and Odyssey from the rest of the Cycle?

It’s best to withhold judgement on this, because it’s just too speculative. We have Aristotle’s opinion that the Kypria and the Little Iliad weren’t as good as Homer. But it’s a bit tendentious. The Little Iliad seems to have had much more unity of plot than he lets on. Around Aristotle’s time ‘cyclic’ became a generic word for tiresome, rambling storytelling. But we don’t know exactly how it came to have that sense. The Greek word kyklikos literally means ‘circular’, but it has other metaphorical meanings too; and there’s testimony linking kyklikos as a literary term to Antimachus, an epic poet who lived a few decades before Aristotle.

We can assume the lost epics weren’t as good as Homer. Anything more than that is speculative. There’s a famous article condemning the literary qualities of the Cycle, mostly because of its fantastic elements (Griffin 1977) -- but bear in mind that we’d be raising eyebrows at the Iliad, too, if only a summary survived. Just imagine: ‘Achilles’ horses talk to him, then a river chases him across the battlefield.’ You can’t judge literary quality from a summary.

2. What about the Theban cycle?

There’s no such thing as a Theban cycle. It never existed.

Poems about Thebes did exist! But no cycle. Modern scholarship has often grouped together four lost epics, the Oidipodeia, Thebaid, Epigonoi, and Alkmaionis, but there’s no reason to imagine they were grouped together in antiquity. No source, anywhere, ever mentions a ‘Theban cycle’. The idea was invented in the 19th century by the scholar Friedrich Welcker.

Some ancient sources do refer to a ‘cyclic Thebaid’. Others assign stories that may have belonged to Theban poems to ‘the cyclic (ones)’ -- poets? summarisers? mythographers? Who knows. The most robust interpretation is that ‘cyclic’ could be used as a catch-all term for any early epic that wasn’t the Iliad or Odyssey. Or maybe they’re references to Antimachus’ Thebaid. Either way, there’s no suggestion of a group of four epics.

One of the Tabulae Iliacae -- miniature carvings depicting Greek heroic legends, made in the early Roman principate -- lists the Oidipodeia and the Thebaid together, and mentions a ‘cycle’ shortly afterwards. But it still isn’t a Theban cycle. The tablet also lists two other epics, the Danais and the Titanomachy, which are totally unrelated. Plus, the word ‘cycle’ seems to be the next item in the list, not an umbrella term for the other titles.

Two poems do get grouped, but only sometimes, and never as a ‘cycle’. The Thebaid and Epigoni both get assigned to Homer by two early sources, Herodotus and (probably) Alcidamas. Also, the first line of the Epigoni survives, and its wording suggests the existence of a previous story. So these two may have gone together as a pair -- sometimes. But no group of four.
  • ‘The cyclic Thebaid’: Thebaid fragments 2, 3, 6 ed. West. Theban-related stories ‘in the cyclic (writers)’: Thebaid frs. 9 and 11 West; Epigoni fr. 3 West.
  • Titanomachy, Danais, Oidipodeia, and Thebaid listed together in conjunction with a ‘cycle’: Tabula Iliaca 10K ed. Sadurska, the ‘Borgia tablet’ = Cyclus Epicus fr. 2 Bernabé. Note that ‘Titanomachy’ is a supplement for ]μαχίας.
  • Thebaid and Epigoni assigned to Homer: Epigoni fr. 1 (from the Contest of Homer and Hesiod, quoting the first line of the Epigoni, probably based on Alcidamas) and fr. 5 (= Herodotus 4.32) ed. West.
In particular, no ancient or mediaeval source ever mentions a ‘Theban cycle’, contrary to what some people claim.
Sure, it’d be great to know more about the Theban epics. I’d love to have the Thebaid in particular! The Iliad has a few odd features that seem to be inspired by Thebaid material. For example, the fact that Agamemnon sometimes lives in Argos instead of Mycenae. Also, the Homeric formula anax andron Agamemnon ‘Agamemnon lord of men’ sounds like it was designed with Adrestus, anax of Argos, in mind: Agamemnon is a basileus, not an anax.

That doesn’t mean I have to assume the epics were ever a tetralogy. It’s high time to abandon that invention. There never was a Theban cycle.
The wooden horse imagined in Lego by ‘Brickman’, Ryan McNaught (‘Let’s go build’ exhibition, Te Papa, Wellington, Dec. 2017. Photo by T. Schaefer.)

3. Why did only the Iliad and Odyssey survive?

We’re damned lucky they did survive. It wasn’t a foregone conclusion. The Homeric poems didn’t hit the big time until the late 500s BCE, maybe a century and a half after the Iliad was composed. Until that moment, they might easily have gone the same way as the Thebaid and the Cycle.

We have only a couple of mentions of Homer in settings earlier than 500 BCE, and there it’s pretty clear that the name referred to epic poetry in general -- a bit like using ‘Hollywood’ to refer to all films regardless of where they’re made. In one story, set in the early 500s, it’s clear that ‘Homer’ means the Thebaid, not the Iliad or Odyssey:
For when Cleisthenes (tyrant of Sicyon) made war against the Argives, firstly he banned rhapsodes in Sicyon from competing in (performing) Homeric epic, because Argos and the Argives get praised so much all the way through. And second, there is a hero shrine to Adrestus, son of Talaos in the marketplace of Sicyon, and Cleisthenes wanted to cast him out of the country because he was Argive. ...

(Unable to ban the cult of Adrestus directly,) he introduced (a shrine to) Melanippos, on the grounds that he was Adrestus’ archenemy, since he had killed Adrestus’ brother Mekisteus and his son-in-law Tydeus.
-- Herodotus 5.67
The Iliad does have lots of references to all the Greeks as Argeioi, ‘Argives’. But this story is entirely about things from the Thebaid -- Adrestus, king of Argos, which made war on Thebes; Melanippus, one of Thebes’ defenders.

The fame of the Iliad and Odyssey suddenly skyrocketed with the advent of performances at the Panathenaia festival in Athens. After that they never lost their popularity. From about the 520s BCE onwards, their survival was guaranteed. The Cycle just didn’t get as lucky.

4. When was the Epic Cycle lost?

Look, the Cycle was never popular. It never enjoyed any prestige. It never had a wide readership. We have plenty of citations of it, sure, but only in antiquarian material -- scholars citing obscure words from an early text, abstruse mythological details, that kind of thing.

But even with scholars, hardly any of them knew the Cycle firsthand. They repeat odd facts and words without any context. Often it’s obvious that they've only encountered the material in earlier scholarly works. We can literally count on one hand the ancient writers who claim to have read any of the actual poems: Herodotus, Aristotle, and Pausanias. That’s it.

Pausanias is the latest. He’s a travel writer, living in the 2nd century CE. He states explicitly that he has read the Kypria and the Little Iliad. (Some scholars doubt even that this is true.) In one passage (10.29-10.30) he cites the Returns, so he may have known that poem as well. It isn’t impossible that some other late authors might have known some of the poems -- maybe Athenaios, maybe Porphyry -- but they don't say outright that they knew them, so we can't be sure.

Does this sound overly sceptical? Let’s put it in the context of which early poems people were actually reading. We have thousands of fragmentary literary papyri from Egypt, mostly Roman-era. The best represented author is Homer, unsurprisingly: there are hundreds of copies of the Odyssey, well over a thousand of the Iliad. If we look at lost authors, we see some of the big lyric poets -- Archilochus; Simonides; Sappho’s poetry was still a school text in the 7th century CE. For lost epics, the big name is Hesiod: we’ve got around sixty fragmentary copies of the Hesiodic Catalogue of Women (more than either of the surviving Hesiodic poems).

Here’s the question you should be immediately be thinking of. How many papyri of the Epic Cycle do we have?

If you guessed ‘none at all’, then congratulations, you are an excellent guesser of papyrus quantities. This doesn’t necessarily mean the Cycle had already disappeared completely. But it does show that it was way less popular than any other early poetry we know of.
Note. For completeness, I’d better note that one papyrus does appear in Bernabé’s edition as Little Iliad fr. 32. But no one believes it’s genuinely from the Cycle: Bernabé himself catalogues it as a ‘doubtful fragment’.
So if no one was reading the Cycle, how did the stories survive? In the Hellenistic and Roman eras there was a fashion for mythological manuals, encyclopaedias of myth, and prose summaries of myth. That’s how we know about the Cycle: the summaries that have survived were apparently copied from one of those manuals. The summariser makes it clear that the poems weren't popular in his own time:
... the poems of the Epic Cycle are preserved and have many people interested in them, no so much because of their merit, but because of the continuity of the material in it.
-- Proclus, Chrestomathy §20 ed. Severyns
The material also had a vogue in the visual arts. There are some Megarian ‘Homer cups’ from the 3rd-1st centuries BCE. And I’ve already mentioned the Tabulae Iliacae miniatures, from around the time of Augustus. These adapt many scenes that we know of in the Cycle summaries, but without trying to copy the poems or their summaries slavishly.
The most famous of the Tabulae Iliacae: tablet 1A, the Capitoline tablet (Rome, Musei Capitolini, Sala delle Colombe inv. 316). The left side of the tablet is missing. The panels down the right side illustrate books 13 to 24 of the Iliad, summarised in tiny writing on the pillar to their left. The central panel shows the destruction of Troy. At bottom centre are scenes relating to lost Cyclic epics. Perhaps the most striking thing about this tablet is its size: it’s tiny. It’s just 28 cm wide.
Several tablets mention Cyclic epics: tablet 1A has captions mentioning the Aithiopis, Little Iliad, and Sack of Ilion; 2NY and 6B mention the Sack of Ilion alongside the Homeric epics; 9D mentions the Iliad, Aithiopis, and Sack of Ilion; 7Ti mentions the Little Iliad and Sack of Ilion, and refers to events from the Aithiopis.

But these weren’t working directly from the poems either. They’re using summarised forms, the kind of thing you get in an encyclopaedia. One giveaway is that though the artists clearly spoke Greek perfectly well, they don’t use the spelling that you’d find in an early epic: their spelling is phonetic. They write Αἰνήας for Αἰνείας, Ποσιδῶν for Ποσειδῶν, Ἰλίας μεικρά for Ἰλίας μικρά, that kind of thing. If they’re not familiar with the spellings used in early epic, that means they weren’t reading early epics.

Another giveaway is the phrase used for the wooden horse. Tablet 1A calls it the δούρηος ἵππος (again phonetic, for δούρειος ἵππος). But that phrase could never have appeared in an epic poem. It doesn’t scan. Whatever the Little Iliad called the wooden horse, it wasn’t that. When Homer mentions the wooden horse in Odyssey 8, he calls it the δουράτεος ἵππος.

But guess what we find when we look at the summary of the Little Iliad? Yup: δούρειος ἵππος, just like in the tablet.

No one was reading the Epic Cycle. People lapped up Cyclic material in secondhand accounts instead.

It’s possible Pausanias is telling the truth, and that he found intact copies of the Kypria and Little Iliad in a library in Athens. But even if he is, they must have been among the last copies still in existence. We don’t know if the poems ever even got to Alexandria. And no ancient writer ever claims to have seen a copy of the Aithiopis or the Telegony. I’d bet those poems were lost even before the Roman conquest. (Which is a pity -- those are the most interesting ones!)

Even if the poems did survive, they were very obscure. When Roman poets like Vergil and Ovid went looking for Cyclic material, it’s most likely that they got hold of summaries, in Rome, rather than making a research trip to Athens like Pausanias did.
Note. The last part of this post is based on a paper I gave at the ASCS 41 conference in Dunedin in January 2020, titled ‘The Aeneid and the Epic Cycle’. Abstracts can be found here, and the slides I used here.

References and further reading

  • Bernabé, A. 1996. Poetarum epicorum graecorum testimonia et fragmenta vol. 1, 2nd ed. (1st ed. 1987). Teubner.
  • Burgess, J. S. 2001. The tradition of the Trojan War in Homer & the Epic Cycle. Johns Hopkins University Press.
  • Davies, M. 2001. The Epic Cycle, 2nd ed. (1st ed. 1989). Bristol Classical Press.
  • Davies, M. 2014. The Theban epics. Harvard University Press.
  • Fantuzzi, M.; Tsagalis, Ch. (eds.) 2015. The Greek Epic Cycle and its ancient reception. Cambridge University Press.
  • Gainsford, P. 2015. Early Greek hexameter poetry. Cambridge University Press.
  • Griffin, J. 1977. ‘The Epic Cycle and the uniqueness of Homer.’ Journal of Hellenic Studies 97: 39-53.
  • Huxley, G. L. 1969. Greek epic poetry from Eumelos to Panyassis. Faber and Faber (London).
  • Sadurska, A. 1964. Les tables iliaques. Państwowe Wydawnictwo Naukowe (Warsaw).
  • Sammons, B. 2017. Device and composition in the Greek Epic Cycle. Oxford University Press.
  • West, M. L. 2003. Greek epic fragments. Harvard University Press (Loeb 497).
  • West, M. L. 2013. The Epic Cycle: a commentary on the lost Troy epics. Oxford University Press.

Thursday, 23 January 2020

Detecting the earth’s curvature

How did ancient observers work out that the earth is (very nearly) spherical?

It’s pretty well-known these days that the spherical shape of the earth was discovered by ancient observers. As I wrote in an older post, the turning point seems to be a little before 400 BCE in Greece. Before that date, all reports have the earth as flat; after 400, round-earthers pop up quickly, and there are only a handful of flat-earthers. Flat-earthism has never been anything more than a fringe opinion since then, in any place that had access to their findings.

What’s obscure, though, is this: how exactly did the Greeks discover it? What was the key piece of evidence?
A ship receding over the horizon. (NB: This is not how the ancients discovered the shape of the earth.) Notice the distortion caused by refraction. Source: ‘Mathias Kp’, preview image for ‘Ship sailing into the horizon’, YouTube, Feb. 2016.
Ancient sources don’t tell us directly. Let’s jump straight to academic opinions. Here are some lecture notes from a reputable astronomy professor. This is what Ohio State University astronomy students have learned since at least 2004:
Ancient Greek philosophers argued earth was a sphere, on several grounds:
  • Sphere a "perfect" shape.
  • Ships disappear over horizon.
  • Positions of constellation above horizon change as one goes north or south.
  • Earth casts round shadow on moon during a lunar eclipse.
-- Prof. David Weinberg, Ohio State, A161 lecture notes
The big myth here is the thing about ships going over the horizon. It doesn’t appear in any ancient Greek source. Weinberg’s fourth point does appear in surviving ancient accounts, Aristotle and Ptolemy. The third point isn’t precisely what the ancient sources say, but close enough. But the thing about ships is a distortion of a report of a low-quality Roman source who didn’t know what he was talking about. As for the first point, that’s completely imaginary: ancient writers who discuss evidence for the earth’s shape talk about matter falling towards local minima in the earth’s surface, not about ‘perfection’.
Note: The lecture notes have some other errors too, especially in the bit about Eratosthenes. Most of them are copied from Carl Sagan’s inaccurate treatment in Cosmos (1980): I’ve dealt with that in an earlier post. The thing about the well is untrue. Two more specific points: the angular distance between Eratosthenes’ cities was 7.2°, not 7.5°; and his calculated circumference was ca. 46,600 km, not the 39,300 that Weinberg states. The standard Greek stadion was 185 m, plus or minus a metre. It’s true there’s some confusion over the length of the stadion, thanks to some variations, and some misreporting in the early 20th century, but the 185 m standard really is unproblematic: see here for more discussion. Anyway, Eratosthenes’ high figure comes from the fact that he didn’t have great figures for the distances between cities. His data seem to have been based on traditional measures of Egypt dating back to well over a thousand years before his lifetime.
Ships going over the horizon get brought up very, very frequently when people think about how ancient people detected the earth’s shape. You’d think it’s something people observe every day. I wonder how many people have actually seen it. Of them, I wonder how many saw it without a telescope or a really good camera.

The problem is that it doesn’t actually work very well. Not because it’s false! Ships do indeed descend past the horizon.

It’s because human eyesight isn’t good enough. Sure, with a really good zoom, or a telescope, it’s possible to observe the phenomenon. But most people’s eyesight can’t resolve details that fine.
A Nikon P900 can see this, but your eyes might not be up to the task: the schooner Denis Sullivan, photographed from Frankfort, Michigan, 2 July 2016. The ship is apparently about 18 km offshore, judging from how much of it is concealed. The height is 29 m. I assume that about a third of it is concealed by the horizon, and camera height at 2.5 m above sea level. At that distance, the angular size of what’s visible here would be about 0.06°, less than an eighth the diameter of the moon. According to Wikipedia, someone with 6/6 vision (20/20, for American readers) can discern contours 1.75 mm apart at a distance of 6 m. That’s an angular size of 0.0167°. The sails appear 3.6 times larger than that, so the feat is technically possible. But only about a third of people have 6/6 vision. Calculations are based on Walter Bislin’s Advanced Earth Curvature Calculator, and account for atmospheric refraction. Photo source:


When Aristotle discusses empirical evidence for the earth’s shape, in On the sky 297a-298a, the evidence that he actually mentions is as follows:
  • Gravity -- or as Aristotle puts it, ‘the nature of mass to be borne towards the centre’ (τὸ φύσιν ἔχειν φέρεσθαι τὸ βάρος ἔχον πρὸς τὸ μέσον) -- ensures that all parts of the earth come to rest at a local minimum, so the resulting shape must be roughly spherical.
  • The earth’s shadow on the moon during a lunar eclipse is always circular, and only a sphere has a shadow that is invariably circular.
  • Even a relatively short journey to north or south changes which stars are visible.
By ‘short journey’, he may mean as little as a twelfth of a degree of the earth’s curvature, since that’s the precision in latitude we find reported in Ptolemy’s Geography. That’s just 9.27 km -- a couple of hours’ walk.
From all this, then, it is clear that not only is the earth’s shape curved, but also that it is not a huge sphere. Otherwise people would not be able to see it so quickly, when they move only a short distance. ... All the mathematicians who try to calculate the size of its circumference say that it is about 400,000 (stadia, i.e. 74,000 km).
-- Aristotle, On the sky 298a.6-8, 15-17
Even that figure is too high, obviously, and a century later Eratosthenes came closer.


Ptolemy’s evidence for the earth’s shape, Almagest i.1.14-16 (ch. i.4), is a bit different:
  • Lunar eclipses take place at the same time for all observers, but they are reported at an earlier hour by observers further east, and at a later hour by observers further west; and the difference in hour is proportional to the east-west distance separating the observers.
  • Alternative shapes for the earth -- concave, plane, polyhedral, cylindrical -- are ruled out by various astronomical observations (omitted here).
  • Travelling north or south changes which stars are visible in the sky, and the change is proportional to the north-south distance travelled.
  • Observers on a ship moving towards a mountain see the mountain gradually rising up out of the sea as they approach.
The last point comes within spitting distance of the ships-going-over-the-horizon trope, but it’s far more realistic than the popular idea. A trireme 20 km away may be too small to make out properly, but mountains are a much bigger target.
Samothraki seen from Thasos, 75 km away. Photo by Borislav Angelov. Source: Google Maps.
Here’s an example from the Greek world: Mt Fengari, on the island of Samothraki, seen from the shore of Thasos, 76 km away. Fengari is the highest peak in the Aegean Sea, at 1611 m.

The photo is taken from the edge of the shore, so let’s assume eye height at 2 m. A basic geometrical calculation would have it that the bottom 394 metres of the island are concealed by the earth’s curvature. However, we also need to account for atmospheric refraction. The vertical distortion from refraction actually reduces the effect of the earth’s curvature, so that distant objects are more visible.
Diagram illustrating the relationship between a distant object’s actual location, and the place where it appears as a result of refraction. Source: Walter Bislin’s Calculator.
With the standard refraction figures used by the Advanced Earth Curvature Calculator, created by Walter Bislin, a Swiss engineer, it turns out that the actual portion of Samothraki that is concealed by the horizon is the first 322 metres. That’s 20% of the mountain’s height. The angular size of the visible part of the mountain is just under 1°, double the apparent diameter of the moon, so the effect ought to be noticeable for someone who knows the shape of the island well.

Now, when I said mountains, you probably thought of Mt Olympus, the highest peak in Greece at 2917 m. Actually, Olympus doesn’t work well for this. But let’s do the calculation anyway.
Mt Olympus seen from Sani, Halkidiki, 80 km away. Source: Sani Resort website.
Using Bislin’s calculator again, this time assuming 3 m eye height, it turns out that the first 349 metres of its height are concealed: more than a tenth of the mountain’s height. But the effect is going to be harder to see. The land at Olympus’ base is higher than 349 metres, so the skyline is still above the horizon. The apparent shape of the land wouldn’t be very different from how it looks up close.

Basically, for best results, sail towards islands.


There’s just one ancient writer who mentions the trope of ships going over the horizon: dear old Pliny the Elder.
It is the same reason why land is not seen from ships, but is visible from ships’ masts. Also, when a ship is sailing far away, if a shining light is attached to the top of the mast, it appears to go down gradually and is finally concealed.
-- Pliny, Natural history 2.164
So, this line is the ultimate source of the myth. It isn’t hard to imagine that this is an experiment that someone might actually have tried.

But notice the difference. In the popular myth, you’re supposed to discern the contours of a distant ship, unaided. In Pliny’s version, it’s the light that you’re supposed to observe descending into the sea. That’s much easier to believe: a light-emitting source is way, way more visible than distant contours.

Still, I’m pretty sure Pliny isn’t the source that professors teaching the history of astronomy are getting it from. (If they were reading ancient sources, they’d know Aristotle doesn’t talk about spherical ‘perfection’.) I’m betting the modern myth is filtered through a much more recent source: Copernicus.
It is understood by sailors that waters also press down into the same shape (a sphere): for land which is not visible from (the deck of) a ship is regularly seen from the top of the mast. Conversely, if something shining is placed at the top of the mast as the ship is moved away, it seems to people remaining on shore to go down gradually, until at last it is hidden as if setting.
-- Copernicus 1543: 1b (ch. i.2)
Weirdly, Copernicus bases the structure of his introduction on Ptolemy, but his arguments are inspired by Pliny -- the worst possible choice, out of the three ancient sources we’ve looked at so far.

Because Pliny is not a good source of evidence for the shape of the earth. OK, yes, he does say it’s a sphere. But most of his ‘evidence’ is ridiculous. He thinks mountains in the Alps are over 50 Roman miles high, that is 74 km (NH 2.162); he thinks the earth’s shape is demonstrated by the shape of drops of water; that a convex meniscus on a liquid surface is a consequence of the earth’s curvature; that heavy objects placed in a cup of liquid don’t cause it to overflow, because the surface acqures a convex curve (NH 2.163).

If you’re looking for empirical evidence for the earth’s shape, Pliny should not be your main resource. Copernicus, I’m afraid, gets C+ for treatment of textual evidence.


Cleomedes’ discussion of the earth’s shape is similar to Ptolemy’s, in that he spends time rejecting alternative shapes, then at the end he tacks on the appearance of mountains when approaching them by sea. This is slightly odd given that he never cites Ptolemy, but let’s not get into that. His exact arguments are (Circular motions of heavenly bodies 1.5, = pp. 72-86 Ziegler):
  • The length of time between sunrise and sunset is different in different places.
  • Eclipses are observed at different hours in different places.
  • The celestial pole has a different azimuth in different places.
  • Different stars appear in the sky depending on how far north or south you are.
  • When you approach mountains by sea, they appear to gradually rise up out of the sea.
However, this is already some way into his treatise: he invokes a number of arguments for sphericity earlier on in his book, too. More about that in a moment.

We still haven’t got to the root of the question. How did the person who worked out the earth’s shape do it?

One thing we can be absolutely sure of is this: they didn’t work it out by looking at ships or mountains. They were looking at the sky. All of the evidence cited by Aristotle, Ptolemy, and Cleomedes is based on astronomy, not geography. Ptolemy and Cleomedes only tack on the thing about mountains as an afterthought, to make it easier for readers to accept.

Here are two theories. First, Otto Neugebauer:
... [I]t seems plausible that it was the experience of travellers that suggested such an explanation for the variation in the observable altitude of the pole and the change in the area of circumpolar stars, a variation which is quite drastic between Greek settlements, e.g., in the Nile Delta and in the Crimea.
-- Neugebauer 1975: 576 (more generally see 575-578)
And second, Dirk Couprie:
Several sources ascribe the discovery of the ecliptic (or the Zodiac) to Oenopides, who lived about one century after Anaximander and was a younger contemporary of Anaxagoras (DK 41A7). This makes Oenopides a serious candidate for the discovery of the sphericity of the earth as well, as the ecliptic must be thought of as inclined to the celestial equator, which is the projection of the equator of a spherical earth on the celestial sphere.
-- Couprie 2011: 169 and 201-202
Couprie’s theory about Oenopides and the ecliptic may take a little explaining.
Left: the ecliptic plotted on a celestial sphere. Right: the ecliptic plotted on a rectilinear map of the stars as seen from earth.
The ecliptic is a path against the fixed stars, which the sun, moon, and planets stick close to at all times. On a rectilinear map it looks like an S-shape, but plotted onto a spherical sky it is a circle at a fixed angle to the celestial equator. That angle is 23.5°, but it wobbles slowly: in Eratosthenes’ time it was closer to 23.9°. The Greeks called it hēliakos ‘the sun’s (path)’, ekleiptikos ‘(the path) of eclipses’, or zōidiakos ‘belt-like’, since it is a circle around the earth. That of course is where we get the name for the constellations along the ecliptic, the zodiac.

Now, that’s the geocentric point of view. In reality, the ecliptic is the plane in which the earth and other planets revolve around the sun. The earth’s equator is at an angle to that plane, and that’s what produces the phenomenon.

Couprie’s idea is this. The astronomer Oenopides is said to have discovered the ecliptic, but we know that’s not true. It was well known to Babylonian astronomers a millennium earlier. However, the ecliptic implies a spherical geometry for the sky. So, Couprie thinks, what Oenopides really discovered is that that somehow implies a spherical geometry for the earth too.

It doesn’t imply that all by itself, mind. It does tend to imply that it’s the earth that’s rotating, not the stars -- but ancient testimony is pretty hostile to that theory (Aristotle On the sky 296a.26-27; Ptolemy Almagest i.1.24-25 = ch. i.7).

However, if you take it in conjunction with Neugebauer’s point about Greek colonists in Ukraine and Libya noticing different astronomical phenomena, then you get a line of reasoning that looks very similar to the opening chapters of Cleomedes’ work. Cleomedes doesn’t present the earth’s shape as a premise. He works his way up to it.

Cleomedes starts off by establishing the spherical geometry of the sky; he describes the celestial equator, tropics, and arctic and antarctic circles, and how these have corresponding zones on earth; then he moves on to the planets and their motion relative to the ecliptic, and how the ecliptic is at an angle to the celestial equator; and then he gets to the key point that
The Earth is spherical in shape, and thus [located] downwards from every part of the heavens; as a result its latitudes do not have an identical position relative to the zodiac, but different ones are located below different parts of the heavens.
-- Cleomedes 1.3 = p. 36.21-26 Ziegler (tr. Bowen and Todd)
This is basically the conjunction of the spherical cosmology, the ecliptic, and Neugebauer’s point about the angle of the celestial sphere being different depending on how far north or south you are. Cleomedes carries on in exactly this way, talking about how ‘the heavens slope’. Only later on does he get into explicit arguments to support the earth’s sphericity.

It’s pretty likely that his manner of exposition is very close to the original reasoning. It isn’t a certainty. The ecliptic doesn’t come up in Aristotle’s or Ptolemy’s discussions of evidence for the earth’s shape. But I think the beginnings of the idea must have followed something like Cleomedes’ reasoning.

I want to add, as a postscript, that though Greek thinkers prior to 400 were all flat-earthers, including beloved names like Thales and Democritus, their work wasn’t a waste of time. Anaximander, in particular, can be credited with the important realisation that the earth isn’t the base of the cosmos, but is suspended in space. He was wrong about why it is suspended -- pre-Socratic philosophers thought it must be held up by air pressure -- but it was a crucial step. Without that notion, I doubt the spherical earth could have been discovered until many centuries later.


  • Bowen, A. C.; Todd, R. B. 2004. Cleomedes’ lectures on astronomy. University of California Press.
  • Copernicus, N. 1543. De revolutionibus orbium coelestium. Ioh. Petreius (Nürnberg).
  • Couprie, D. L. 2011. Heaven and earth in ancient Greek cosmology. Springer.
  • Neugebauer, O. 1975. A history of ancient mathematical astronomy (2 vols). Springer.

Wednesday, 1 January 2020

Top posts of 2019

Another year has passed, and who knows what the new one will bring? More illicit papyrus sales? An intact Hellenistic library in a cave in Afghanistan? A new Bronze Age shipwreck? More refined techniques for detecting ancient ink inside carbonised scrolls from Herculaneum?
But ‘Romans go home’ is an order, so you must use the ...?
We’ll find out as we go. 2020 isn’t hindsight -- not for another year, anyway. With that in mind, here are the most popular posts from 2019.
  1. Learning Latin: why conjugations? (5 September). Memorising a single pattern with two exceptions is way easier than memorising four separate patterns. But do note the criticism someone left about how I conflated thematic vowels with other kinds of epenthetic vowels. Technical, but true. I erred.
  2. Titans and Olympians (14 June). The Olympians overcoming the Titans aren’t a symbol for the Mycenaeans overcoming the Minoans. The two groups are very much baked into Greek mythology. Still, here’s something interesting: the succession myth is Mesopotamian in origin, but the ‘two families of gods’ thing seems to be Indo-European. Or maybe we should just give up on treating Titans and Olympians as separate families.
  3. Why maps have north at the top (31 July). Yes, there is a reason, and his name is Ptolemy. (Which direction was up on the maps made by Eratosthenes and Marinus? We may never know.)
  4. Bad Latin in the movies: Constantine (2005) (13 June). John Constantine’s demons speak Latin. Bad Latin, at that. Silly film writers! Everyone knows real demons speak Klingon. (I’ve heard rumours Keanu would like to do a sequel: maybe, for that, they could switch to bad Hebrew. Or maybe they’ll do that for the new Bill & Ted.)
  5. Upward attribution and ‘Go tell the Spartans’ (20 February). Simonides didn’t write ‘Go tell the Spartans’: he’s the punchline to a just-so story. Upward attribution strikes again -- and it’s such a pervasive thing that it really ought to take off as a technical term in literary criticism. Let’s make 2020 the year of #UpwardAttribution!
  6. Bad Latin in the movies: Life of Brian (1979) (21 June). Brian’s Latin lesson from a grouchy centurion has inspired many generations of anglophone Latin students. I’ve still got no idea whether versions of the film dubbed into other languages have had a similar effect. (If your Latin is good enough to spot what’s wrong with the centurion’s explanation of domum, in any language, then give yourself an A.)
  7. The ‘FCM’ scandal: a timeline (2 July). How do you solve a problem like Dirk Obbink? / Where do you buy a papyrus of the Bible? / How do you find the word that means Dirk Obbink? / I’d better not write the next line because of libel.
  8. The golden ratio (27 February). Who’d have thought it -- Donald Duck, responsible for a really widely believed myth about ancient Greek architecture. I hope it was obvious that all the illustrations in this post were in golden ratio proportions. Hey, maybe there’ll be another Donal Duck cartoon one day that claims Hippasus was murdered by his fellow Pythagoreans for revealing the existence of irrational numbers. (For reference, I covered that one back in 2015. That story’s false too, but it is at least an ancient story.)
Some artists have used the golden ratio -- just not Pheidias, even though the golden ratio was named φ for him. Left: Salvador Dali’s Last supper (1955), which uses the golden ratio and Fibonacci numbers in several ways. Right: Leonardo da Vinci’s illustration of a hollow dodecahedron for Pacioli’s Divina proportione (1509; plate xxviii), the book that ignited interest in the golden ratio in the modern era.
  1. Who preserved Greek literature? (10 December). Arab scholars were integral to the development of mathematics, medicine, and western philosophy. But they shouldn’t have a big role in the story of how ancient Greek texts were preserved. This post never did get around to explaining the true story of how ancient Greek texts were preserved, and some people called me out on that -- quite rightly. So it’s now re-titled as ‘Part 1’. Stand by for Part 2 in the new year.
This number two post squeaked in right near the end of the year, but it never really stood a chance of catching up with this year’s runaway winner --

(drum roll)
  1. Shanties in Assassin’s Creed: Odyssey (31 January). People really like finding out what their ancient Greek sailors are singing. I do find it sad that the writers of the shanties didn’t talk to someone who could have pointed them to copies of the Anacreontea and Homeric Hymns without typos, but I still respect the effort. I mean, they translated the title song into ancient Greek too, to the same tune as the English version -- and with fewer grammatical errors than you might expect.
On to 2020. Excelsior!