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 that 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. What Oenopides discovered, Couprie thinks, 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!

Tuesday, 10 December 2019

Who preserved Greek literature? (Part 1)

In particular: how important a role did Muslim scholars play in the survival of ancient Greek texts?

The answer is ‘they played an important role’ -- but there’s a right way and a wrong way of saying that. You could say, for example, that the modern world might well not be nearly as interested in ancient Greece as it currently is, if not for mediaeval scholarship in Arabic. You could say that modern mathematics and western philosophy would have a very different shape.
An 11th century Greek manuscript of Plutarch’s How to benefit from enemies: one of hundreds of thousands of examples of direct reception. (Vatican Library, MS Barb. gr. 182)
And then there’s the wrong way. Here’s how the Wikipedia article on ‘Transmission of the Greek Classics’ allocates its attention:
  1. Direct reception of Greek texts -- 242 words (6.8%)
  2. Syriac translations -- 95 words (2.7%)
  3. Western Roman Empire -- 717 words (20.2%)
  4. Arabic translations and commentary -- 2501 words (70.4%)
You can probably guess where I’m going with this. The article on Recovery of Aristotle is in a similar vein, giving no hint that Aristotle is still available in Greek.

There’s a popular perception -- not universal, but more widespread than you might imagine -- that ancient Greek texts only survive today because they were preserved in the Arabic-speaking world.

But it’s only lazy people that think that, right? Only people who never check what they’re told? Think again.
... not only the texts but the way that we think about those texts and think about how to read those texts is inherited from the Arabs who passed them down.

... we generally recognize that we have Greek texts today because of the Arab ‘hold’ on these texts ...
-- Adriel Trott, The Trott Line, 14 Feb. 2015

... things might have been much worse had it not been for Islamic scholars. ... the ancient texts, those not destroyed by the guys with the shiny belt buckles and fondness for pre-literate ignorance, were copied and preserved. Had this not happened, we would have lost even more of the advances of antiquity.

These texts preserved and added to by Islamic scholars jump started the renaissance.
-- Rob Dunn, Your Wild Life, 3 June 2015
These aren’t wild guesses by laypeople. They’re both academics. Trott is an associate professor of philosophy and has written two books on Aristotle. Dunn is a professor of biology. If Trott were put on the spot, I’m sure she’d acknowledge you can read Aristotle’s Politics in ancient Greek, without having to rely on Arabic translations. She might possibly be right about how we read Aristotle. But about having Greek texts at all, what she’s written is, at best, gravely misleading.

If you look into the textual transmission of ancient Greek texts that are still commonly read nowadays you’ll find that the proportion of them that are known through ‘direct reception’ is, very roughly, 100%.

Not the 7% that Wikipedia would have you imagine.

There aren’t any mediaeval Arabic translations of Greek literary works or historical works. When you read Homer, Sophocles, or Herodotus, in any language, what you’re reading is something that was transmitted directly. In Greek.
Note: some mediaeval Arabic translations of Greek literary works may have existed at some time. A full Arabic translation of the Iliad didn’t appear until 1904, but here’s a 1956 article that thinks there’s evidence of parts being known in Arabic in the mediaeval period, via a lost 8th century Syriac translation attested by Bar Hebraeus.
Where we do rely on translations into other languages, it’s generally for texts that aren’t read very often, but which are important in some specialised area. They include things like --
  • The history of medicine and mathematics. For these areas, Syriac and Arabic versions can be very important. In some cases -- though still a minority -- they are the only surviving versions of ancient texts.
  • Some non-canonical Jewish and Christian writings. Many were written originally in Hebrew or Aramaic, but some like the Ladder of Jacob appear to have been written originally in Greek, and now survive only in translations into Slavonic, Coptic, Ethiopic, Armenian, or Georgian.
  • Some individual literary and historiographical texts: like the Alexander Romance, a mostly fictional -- but very influential -- account of Alexander’s life. Greek versions survive, but for the earliest recension, Armenian and Latin translations are more important. Or Dictys of Crete, a semi-novelised account of the Trojan War, and one of the two biggest influences on the development of the Troy matter in the mediaeval period, both in the Greek east and the Latin west. Only fragments of the Greek text survive; the most important version is a Latin translation. Or John Malalas’ Chronography, a history dating to the early Byzantine period: the surviving Greek text is abbreviated, and a Slavonic translation fills the gaps.
  • Ancient scholarly commentaries on scientific works, and fragments of certain lost authors.
For literary works, the exceptions are few and far between. Even with the Alexander Romance, the versions you find in modern translations are normally based mainly on Greek versions. (Dictys of Crete is an interesting reversal: nearly all translations are based exclusively on the Latin version, completely ignoring the Greek sources, with just a couple of exceptions.)
A 16th century Armenian copy of the Alexander Romance. The earliest recension of the Romance survives only in a very incomplete form in the original Greek; the Armenian is more complete. (Yerevan, Matenadaran 5472; source:
The idea that Greek texts only survive thanks to the work of mediaeval Muslim scholars is a myth. It’s based on something real. But it’s a complete misrepresentation of that real thing.

Take another look at the Wikipedia article. Here’s the opening:
The transmission of the Greek Classics to Latin Western Europe during the Middle Ages was a key factor in the development of intellectual life in Western Europe.
-- ‘Transmission of the Greek Classics’, Wikipedia, 6 Nov. 2019
(Original emphasis.) Notice the mismatch between the title and the quotation? The article is actually about Greek scientific, philosophical, and mathematical works, and about how they were transmitted to mediaeval western Europe. It isn’t about ‘the classics’. And it isn’t about transmission in and of itself.

Two grotesque biases feed into this myth.
  • Western-euro-centrism. The myth downplays the fact that, throughout the mediaeval period, the texts still existed and were still being read and studied in Constantinople and elsewhere in Greece. It also ignores the fact that translations survived in languages other than Arabic, especially in eastern Europe. The Wikipedia article, in its very first sentence, treats transmission of ancient Greek texts and transmission of Greek texts to the Latin west as the same thing. It’s colonialism pure and simple.
  • STEM-centrism. I don’t just mean the fact that the myth focuses on scientific and mathematical texts to the exclusion of everything else. That is true, but it’s more pernicious than that. The myth sets out to ignore and obscure the work done by modern humanities scholars. When modern editors publish ancient Greek texts, they rely almost exclusively on Greek manuscripts; acknowledging the continuing existence of Greek manuscripts would mean acknowledging research done in the humanities. So it’s probably no coincidence to see a biologist repeating the myth. It meshes neatly with the STEM-centric notion that humanities academics just spend their time listening to Beethoven and reading Shakespeare. (Yes, that caricature really exists: I’m not exaggerating for rhetorical purposes. Here’s Neil deGrasse Tyson saying it out loud.)
The western-euro-centrism manifests in other dangerous ways. The Wikipedia article used to have a section on transmission of Greek texts via mediaeval Armenian scholars. It was never substantial: it only had two sentences. An anonymous editor deleted the entire section in 2015 with this comment:
Has nothing to do with this subject. This article is about the Greek (to Syriac) to Arabic translation movement.
-- anonymous Wikipedian, 15 Aug. 2015
-- as if the title were ‘Translation of Greek scientific works into Arabic’. Which would be a fine idea for an article, by the way. It’s just that the article’s title actually says that it’s supposed to be about transmission, full stop.

For the record, Armenian transmission is important, even if only for a relatively small set of texts. It does warrant a small place in a balanced article on ‘transmission of the Greek classics’.
How the Wikipedia article on ‘Transmission of the Greek classics’ has allocated its attention over the last five years. ‘Arab(ic) translations and commentary’ has never dropped below 70% of the article. ‘Direct reception of Greek texts’ didn’t even reach the 4% mark until late 2016. The deleted ‘Armenia’ section shows up only as a thin red line.
The concerted effort to downplay Greek traditions, in an article that claims to be about ancient Greek literature, is the colonialist spirit in action.

Mediaeval Arab scholars didn’t preserve ancient Greek texts. They did use them as a basis for their own scholarship, and they did disseminate some texts, in a particular period, to a particular audience. It’s unfortunate that people often conflate these things.
... the well-documented role of the Arabic world in preserving the works of Aristotle, among others.

The role of Muslim world in preservation (and spread!) of ancient science is very large.

The Arabs played a very significant role in preserving ancient Greek texts ...
-- Stack Exchange, May 2015
But even ‘dissemination’ is a demeaning way to put it. Arab scholars weren’t just a vehicle for Greek texts to get from point A to point B, from ancient Greece to the mediaeval west. They were innovators, researchers. So were their Byzantine counterparts. Just because you didn’t hear about them at high school doesn’t mean they’re not important. Modern science owes at least as much to Al-Kindi and Averroes as to Aristotle. There’s no doubt that since the mediaeval period, Muslim contributions to human understanding have been actively silenced in many quarters.
Muslim contributions to human understanding are still obfuscated in western thought: the Independent, reporting on a May 2019 survey conducted by Civic Science (source)
If mediaeval Arabic scholarship hadn’t been a thing, of course the world would be greatly impoverished. But purely in terms of ‘transmission of the Greek classics’, the differences wouldn’t be nearly as big as all that.

Yes, the world would be different in many ways. Western European history would look a bit different. The development of mathematics would have followed a very different course. Maybe we wouldn’t be using Hindu-Arabic numerals (yikes!). Aristotle wouldn’t hold such an elevated position as he does.

But Aristotle’s works would still have survived. So would Euclid, and Ptolemy, and Theon. Because they did survive -- in the Greek-speaking world. Figures like Aurispa and Bessarion would still have amassed their enormous libraries of Greek books. They did their book-collecting in Greece because they lived there, not because their reading of Averroes inspired them to pay a visit. There would still have been a tidal wave of publishing ancient Greek books in the 1400s. (Or rather, in the ͵αυs, since we wouldn’t have Arabic numerals.)

The question ‘Who preserved Greek literature?’ has an easy answer. The Greeks did. Lots of other people helped too.

Postscript, two days later

I’ve had more than one comment that, as well as dispelling a myth, I should have told the true story of the survival of Greek literature. This is a very fair criticism.

I have therefore retitled this as ‘Part 1’. Part 2, on the transmission of Greek texts in the eastern empire, and the role played by Byzantine scholars and schools, will follow at some point yet to be determined.

Tuesday, 26 November 2019

The Archimedes palimpsest

The ‘Archimedes palimpsest’ is the most famous manuscript of any ancient pagan text. I’d better explain its title first:
  • A palimpsest is a parchment manuscript that has been recycled and had a second layer of text written on it. The word literally means ‘re-polished’, that is, a parchment that had the original text washed or scraped off. Scholarly publications sometimes use the term rescriptus (‘rewritten’).
  • Archimedes of Syracuse (287-212 BCE) is the most renowned of all ancient mathematicians. He wrote important books on topics like conic sections, the uses of infinitesimals and infinity, combinatorics, mechanical principles, and buoyancy.
Not much of Archimedes’ writings survives, even though he was a revered authority. So the Archimedes palimpsest is a big deal.
Monastery of Mar Saba, West Bank, where the palimpsest was housed in the 1600s. (Source: Jean and Nathalie, cropped; CC BY 2.0)
The manuscript, once catalogued as Metochion of the Holy Sepulchre MS 355, Constantinople, contains
  • Archimedes’ Method, which survives nowhere else;
  • the only Greek copies of On floating bodies and the Stomachion, both of which survived elsewhere in Arabic translations (a fragmentary translation in the case of the Stomachion);
  • other works by Archimedes known from other copies (Planes in equilibrium, Spirals, On the sphere and cylinder, Measurement of the circle);
  • two speeches by the Athenian orator Hypereides, which survive nowhere else (Against Diondas, Against Timandros);
  • an ancient commentary on Aristotle’s Categories.
So far the story is all true. Now we’re going to look at three widespread misconceptions about the manuscript.
  1. The belief that the palimpsest is a potent example of how religion corrupts science: that a 13th century scribe destroyed Archimedes’ text to make a prayer book, and that this is characteristic of the opposition between religious belief and the scientific method.
  2. The belief that the texts in the palimpsest went unread between 1229, when the prayerbook was completed, and 1998, when it was sold at auction.
  3. The belief that modern technology, such as X-ray fluorescence imaging and ultraviolet imaging conducted from 1999 to 2008, bears the sole credit for rescuing the texts in the palimpsest.
OK, there are elements of truth to each of these. But they wildly misrepresent the reality.

It’s true that a 13th century scribe erased Archimedes’ and Hypereides’ text to create a prayerbook. It’s true that modern technology saved texts that would otherwise have been lost.

But it’s false to imagine that this represents a conflict between religion and science. (Who do you think copied out the Archimedes in the first place? Elves?) It’s at most half true to imagine that modern technology was undoing damage wrought by a monk. It’s false that Archimedes’ Method went unread until 1998, and it’s false that the Method was saved by modern imaging techniques.

The illicit antiquities trade

This isn’t a story of the scientific method triumphing over religious ignorance. The bigger story is about the trade in stolen antiquities.
The Archimedes palimpsest. Where is it now? Officially, no one knows.
Over the last few years there’s been heavy attention to the fact that sales of ancient -- and mediaeval -- manuscripts often take place without any attention to provenance or legal ownership. This has been in the news just recently thanks to a fiasco surrounding an early papyrus of the New Testament gospel of Mark, owned by the Egypt Exploration Society. In 2013 the papyrologist Dirk Obbink secretly tried to sell it and three other New Testament papyri, without the EES’s knowledge or consent, to an American company, Hobby Lobby. Hobby Lobby is a prominent supporter of Christian evangelicalism, and has a reputation for rapaciously acquiring ancient Christian manuscripts without the slightest concern for where they came from. It has since turned out that Obbink ‘sold’ eleven other EES-owned papyri to them in 2010 -- and possibly to other buyers too.

At the time, Obbink was the general editor of the EES’s Oxyrhynchus papyri collection. He held that position until the EES got wind of his activities.
In August 2016 the EES did not re-appoint Professor Obbink ... primarily because of unsatisfactory discharge of his editorial duties, but also because of concerns, which he did not allay, about his alleged involvement in the marketing of ancient texts, especially the Sappho text.
-- EES press release, 14 Oct. 2019
As it happens, the Mark papyrus and ‘the Sappho text’ mentioned here are both very relevant to the case of the Archimedes palimpsest.

In 2014 Obbink published some new fragments of Sappho. Obbink has been nearly as secretive about where they came from as he was about the New Testament papyri. His initial publication stated only that the Sappho was ‘now in a private collection, London’, without a word about where it came from or how it was found.

He has since stated that the Sappho was bequeathed to the University of Mississippi (sometime around 1960, apparently) then sold at auction by Christie’s in 2011. Rather conspicuously, the Sappho also has a past with Hobby Lobby: see research by Brent Nongbri (Dec. 2018, Apr. 2019).

Where is the Sappho papyrus now? Only Obbink knows.

(Well, officially. Most likely it’s in the hands of Mahmoud Elder, a collector who once ran an antiquities trading company with Obbink, and who has also sold papyri to Hobby Lobby.)

What has that got to do with Archimedes? Well, several experts have pointed out recently that classicists have been eager to leap on the text of newly found manuscripts, while ignoring the secretiveness -- and often illegality -- surrounding the physical objects.
... the BMCR review of the 2016 edited volume devoted to the newest Sappho poems omitted any discussion whatsoever of questions of provenance, save a brief comment that the editorial board felt “obliged” to insert as a header. The “recovery” of even the slightest scrap — let alone a trove including a nearly complete, previously unknown poem — is, so the reasoning seems to go, to be celebrated no matter the means by which it is achieved.

The scope of Obbink’s alleged activities on the antiquities market would seem to put the lie to this reasoning.
-- Sampson and Uhlig, Eidolon, 6 Nov. 2019

I would personally avoid publication if documents are lacking, but anyone who decides otherwise must be very clear about why, though documents are missing, they think the papyrus was legally acquired. ...

In other words, dear Classicists, especially those among you who have commented and written pages and pages on the new Sappho poems, we have completely lost track of the only extant copy of the verses in question, verses otherwise unknown and unattested. Leaving aside the problems connected to the very unclear provenance of this “elderly” gentleman’s fragment, to me this seems a remarkable illustration of the unfair conditions of access that come with private collections.
-- Mazza, Eidolon, 8 Nov. 2019
Exactly the same reservations apply to the Archimedes palimpsest. Like the Sappho papyrus, no one knows where it is -- except for the people who published it. And, again like the Sappho, its location is only a secret officially. Everyone knows the Archimedes palimpsest is at Jeff Bezos’ house.

But in the case of the Archimedes, we can say with 100% certainty that it is stolen property.

When Anne Guersan sold the Archimedes palimpsest to Jeff Bezos, all attention was focused on the price, the text, and the conservation efforts. Some people did pay attention to where the physical object came from and where it was going -- but these things weren’t part of the popular story.

The false narrative

Read up on the palimpsest, and you will mostly find praise of the conservators, imaging specialists, and philologists who have studied the manuscript since 1998. I don’t exactly want to condemn their work: they aren’t the ones who stole it. And we have seen real discoveries about Archimedes and Hypereides. Would I have acted differently, in their shoes? I don’t know.

But, as with the Sappho, the scholars have been careful to avoid looking a gift horse in the mouth. They are effusive in their praise of ‘Mr. B.’ In public discussions they tend to avoid drawing too much attention to the palimpsest’s history between 1908 and 1998. A 2007 popular book on the palimpsest lays so much emphasis on the auction -- ‘a huge day for the history of science’ -- that if you stopped reading before chapter 7, you might well come away thinking the palimpsest was completely unknown beforehand.
A team of scientists used a special x-ray imaging technique, called x-ray fluorescence (XRF) imaging, to finally unlock these scientific secrets, hidden from view since antiquity on a goatskin parchment manuscript.
-- California Council on Science and Technology, July 2006

(The project leader) assembled a team of some of the world’s best imaging experts to recover as much as possible of Archimedes' text from the Palimpsest that no eyes had seen in modern times.
-- Scientific American, Sep. 2011
Well, the 1998 auction was a huge day, but not for science. It was a terrific day for trading in stolen antiquities. The huge day for science was 91 years earlier, in 1907, when the Method was published by Johan Ludvig Heiberg, a Danish expert on Archimedes. The popular story keeps so quiet about this that the authors of the above snippets simply never knew it.
Archimedes’ Method, published by Heiberg in 1907. Here’s a translation-cum-paraphrase from 1912.
The popular story also tends to create an imaginary timeline --
  1. the text was written by Archimedes,
  2. then a monk damaged it, illustrating the perniciousness of Christianity,
  3. then it was rescued by 21st century secular technology.
If you listen to this TED talk, given by the project leader in May 2012, you may notice how he directs his audience’s attention. He spends nearly a minute describing how a monk tore apart seven unique texts and erased them (1:05-1:58). Then he spends 9 seconds on the damage done by 20th century looters and forgers (2:28-2:36) -- without ever mentioning that they were looters. He even says (2:40),
It’s the sort of book that you (would have) thought would be in an institution. But it’s not in an institution: it was bought by a private owner in 1998 ...
Well, it was in an institution, actually. And it was kept in pretty good condition, all things considered. Until it was stolen from that institution sometime around 1920.

So, here are a few counterpoints to the beliefs I outlined above.
  • The palimpsest didn’t go unread between 1229 and 1998. Johan Heiberg published the Method all the way back in 1907. Heiberg’s equipment was a magnifying glass and a camera. A German translation appeared the same year, an English translation-cum-paraphrase in 1912, then another critical edition in 1913.
  • Between 1999 and 2011 a barrage of careful and high-tech conservation efforts were aimed at the palimpsest. These efforts certainly revealed more of the text than Heiberg had been able to read, especially the diagrams. But, contrary to what is claimed in a 2007 popular book about the palimpsest, the important parts of the Method were known since Heiberg.
  • Conservation efforts weren’t primarily aimed at fixing damage inflicted by a Christian monk. Yes, the manuscript was damaged by the 13th century monk. Some of the text was illegible to Heiberg, and Heiberg didn’t even try to transcribe the Hypereides speeches. But the main focus of the conservation efforts were to rescue the book from damage done by thieves, forgers, and illicit collectors in the 1900s, after it was stolen.
The discovery of the Archimedes palimpsest in 1907: front page coverage. (New York Times, 16 July 1907, page 1)
You have to treat this story pretty selectively to make it a story of religion versus science. Yes, the 13th century scribe made Archimedes’ text harder to read. But it was Christian monks that made the Archimedes manuscript in the first place. And the damage done in the palimpsesting process pales in comparison with the reckless treatment of the manuscript over the last hundred years --
  • Some damage was probably done when the palimpsest was stolen after the end of World War I.
  • Much worse damage was inflicted by Salomon Guerson, Marie-Louis Sirieix, and Anne Guersan, who had the palimpsest at various points in the 1900s:
    • Guerson removed seven leaves, got a forger to erase the text and paint fake illuminations on four of them, and reinserted those four leaves (the other three leaves are lost).
    • Sirieix and possibly Guersan kept the palimpsest in a damp cellar where it grew mouldy.
    • One of them, or maybe all of them, put rusty objects and Blu-tack inside the palimpsest’s pages, and tried to ‘fix’ the book with layers of PVA glue.

The real history of the palimpsest

The most thorough history is one written by John Lowden (2011). Most of the following is a condensed, streamlined version of his report.
Note. I do have reservations about some aspects of Lowden’s account. As a team-member in the 2000s research project, Lowden has a vested interest in casting the current ownership of the palimpsest as legitimate. He suggests the mould on the manuscript may not be Sirieix’s fault; his closing paragraph tries to give the impression that the 13th century scribe is equally as culpable as the 20th century looters and forgers; he casts Jeff Bezos’ purchase of the stolen book as something ‘that can be unequivocally praised’; he says Bezos himself has ‘heroic generosity’. (Try telling that to Amazon employees.) It’s very tendentious. Still, his investigations into the history of the forged illuminations, and his interview of Elie Behar, make his account indispensable.
The Archimedes manuscript was made by Christian monks in the 10th century. In the 13th century a scribe recycled the manuscript into a prayerbook -- making it a palimpsest -- and completed his work in 1229. During the 1600s the palimpsest was housed in the Mar Saba monastery, in what is now the West Bank, about 9 km south-east of Jerusalem.

In the early 1800s the Patriarchate of Jerusalem took over the monastery’s collection. They relocated a number of books to Constantinople (as it then was), to a sort of embassy monastery that they had there, the Metochion of the Holy Sepulchre.

In the 1840s the biblical scholar Constantin Tischendorf visited the monastery, and secretly cut out one leaf and stole it. He knew it was a mathematical text, but he probably didn’t know it was Archimedes. He bequeathed the page to Cambridge University Library, and the stolen item is still there, catalogued as MS Add. 1879.23.

In 1899 Athanasios Papadopoulos-Kerameus catalogued the Metochion’s holdings, and published a description of the manuscript, including an insert that showed that it had come from Mar Saba. He also transcribed a passage of the palimpsest.
The Metochion as it appears today. (Balat, Istanbul)
Heiberg realised that Papadopoulos-Kerameus’ transcription was Archimedes, and travelled to Constantinople in 1906 and 1908. He studied the manuscript as carefully as he could, took photographs, and published the Method and the Stomachion in 1907. Between 1910 and 1915 he published a complete new edition of Archimedes’ works.

It was probably in the hubbub following World War I that the palimpsest was stolen from the Metochion. The people who worked on the palimpsest between 1998 and 2011 insist the palimpsest was bought, not stolen, and they point to one other manuscript being bought from the Metochion in the 1920s. They have a vested interest in that belief. If the palimpsest is stolen property, that would compromise every aspect of their work.

Even if it was bought, we know that Patriarch Damianos of Jerusalem wrote to the Metochion in 1923 with strict instructions not to sell any manuscripts. Whether it changed hands for money, or it was seized by a French soldier in the occupation force, it went without the knowledge or consent of its actual owner.

If money did change hands, the situation is identical to that of the Oxyrhynchus papyri that Dirk Obbink sold to Hobby Lobby. Just like the papyri, the palimpsest is stolen property.

After this point, there are two versions of what happened.

Story number 1 is the story given by Anne Guersan, the seller of the palimpsest in 1998. Her father Marie-Louis Sirieix (1884-1956) was a French soldier who served in Greece in World War I, and acquired the palimpsest in the early 1920s. This is the story she gave to a New York court when the Patriarchate of Jerusalem sued to prevent the sale in 1999, but with no evidence of how Sirieix acquired it.

Story number 2 is that Sirieix didn’t get the palimpsest until 1942. Prior to that it was held by Salomon Guerson (1872-1970), a carpet dealer who moved his business from Istanbul to Paris in the 1920s, and who is known to have been trying to sell mediaeval manuscripts to various museums and libraries between 1926 and 1934. In 1942 Guerson fled Paris to escape the Nazis, and at that point he sold the palimpsest to Sirieix, who was in the Resistance. This is the version given by Guerson’s grandsons, Elie Behar and Salomon Guerson, according to H. Brandt Corstius, who phoned Guerson in 2007, and John Lowden, who was in contact with Behar in 2010. After the war Salomon’s and Sirieix’s children, Robert and Anne, married in 1946. (The variation Guerson-Guersan comes from transliteration differences when the family moved from Istanbul to Paris.)

In addition, we know that in 1932 Guerson showed one folio of the palimpsest to the curator of the Huntington Library in Los Angeles -- probably Reginald Haselden -- who identified it as Heiberg’s Archimedes text. Subsequently Guerson offered it to collections in Paris, Oxford, and Chicago. These details come from a letter that Guerson wrote to Harold Willoughby at Chicago University in 1934, naming the price as $6000.

Guerson’s 1934 letter is pretty much a guarantee that story number 2 is the true one. Anne Guersan’s testimony at the 1999 trial was false.

Between 1938 and 1942 Guerson arranged to have illuminations forged and painted over some pages. Lowden documents Guerson’s track record of faking illuminations into manuscripts that passed through his hands. We know this happened after 1938 because the paint contains phthalocyanine green, a synthetic pigment, and that’s the year that it became commercially available. It’s likely that three further leaves, which vanished from the manuscript between 1908 and 1998, were also taken out to have illuminations forged on them, and never reattached.

According to Anne Guersan’s testimony -- though based on what we’ve seen, we should doubt every word of it -- Sirieix passed the palimpsest on to Anne in 1947. The information about what the palimpsest actually was didn’t make it as far as her: she claims that she began asking people for advice about the manuscript in the 1960s, following Sirieix’s death in 1956. She had it identified -- so she says -- by Abraham Wasserstein, a specialist in ancient science who during the 1960s was at Leicester University and the Hebrew University in Jerusalem, and Père Joseph Paramelle, a hellenist-byzantinist at the CNRS in Paris.
Note. A 1976 review written by Wasserstein discusses the palimpsest without giving a particular impression that he was aware of its whereabouts.
In the early 1970s the Guersan family started trying to sell the palimpsest. This may have been prompted by Salomon Guerson’s death in 1970; alternatively it might be that she was feeling pressure in the wake of the 1970 UNESCO agreement on the trade of cultural property. She got expressions of interest from various American universities -- Yale, Texas, and Pittsburgh -- but none of them was rich enough for her taste.

Finally in the 1990s she tried Christie’s in New York. And there she struck gold.

Just one snag: it was stolen property, and everyone knew it. Christie’s informed the Greek government of the situation in August 1998, two months before the auction. In September they listed the sale publicly. The Patriarchate of Jerusalem, to which the Metochion belonged, notified Christie’s a week before the auction that they believed the manuscript was theirs.

But the palimpsest was already in the US. In 1999 a New York court ruled that the sale was legal. There’s zero chance of the decision being overturned.

Given that the Patriarchate responded to news of the auction so quickly, it may sound crazy that the court ruled that they had delayed unreasonably. It was the right call, actually. The court pointed out
... if the Patriarchate was able to retain counsel with impressive speed to bring this action the night before the Christie’s auction, it could have retained counsel to search for the Palimpsest, or at least make some inquiries, at some point during the previous seventy years.
-- Greek Orthodox Patriarchate v. Christie’s, Inc. 1999, at *31
For further legal discussion see Reyhan 2001: 999-1002; Carver 2005; Ray 2015. Carver thinks the Patriarchate would have had a stronger case with different arguments -- but she also concludes that the case probably can’t be relitigated.

So the judgement is final. It may even be just: the Patriarchate admitted at the trial that they hadn’t taken much interest in the fate of the Metochion’s manuscripts before 1998. And it’s not clear that the palimpsest’s condition would be improved by going back to Jerusalem.

Still, the fact remains that the stolen palimpsest stays in Jeff Bezos’ keeping. Bezos has allowed detailed publications and open access information about the palimpsest. But an important cultural object is lost forever -- not only to the Patriarchate, but to the whole world.

More importantly, Bezos has set a potent example. The enormous amount of money he has spent on buying and conserving it is a huge encouragement to the trade in stolen antiquities. The incident certainly didn’t discourage Christie’s from auctioning the Sappho papyrus in 2011. It isn’t going to put them off other similar deals in future.