Thursday, 29 December 2016

The contents of the library of Alexandria

Q: 'What is the greatest unsolved mystery of all time?'
A: 'The contents of the Library at Alexandria. Unfortunately that's unsolvable.'
-- opinion discussion on a social forum, 1 Dec. 2016
The 'library of Alexandria' has a very strong brand nowadays. Its image, especially in the English-speaking world, has been shaped by three key moments in modern culture:
  • Edward Gibbon's Decline and fall of the Roman Empire, vol. 5 (1781)
  • Carl Sagan's TV series Cosmos, episodes 1 and 13 (1980)
  • Sid Meier's Civilization video games (1991 to present)
Am I just picking on popular culture? How do I justify picking these events? Well, take a look at how common the phrase 'library of Alexandria' has been in the relevant periods. Here's the Google Ngrams graph for its frequency in the fifty years surrounding Gibbon's work:

The upswing is even more accentuated if you look at a longer time-span, like a century.

The phrase 'Alexandrian library' shows a similar trend, but it also enjoyed more of a vogue before Gibbon came along. In fact it was nearly always the more popular form of the phrase up until recently. References to the 'Alexandrian library' prior to the 1780s, when Decline and fall came out, rarely focus on its destruction: even a 1753 book about Hypatia only mentions the library in passing once. Pre-Gibbon occurrences of 'library of Alexandria' are nearly all caused by a modern publisher called 'Library of Alexandria' which has recently reprinted a number of books from that period.

Here's the graph for the half-century surrounding Cosmos and Civilization:

(The 'combined' line is added by me.) The phrase's increasing popularity is easy to see, but also notice how 'library' gradually acquires a capital L. By the late 1980s, in the wake of Cosmos, capital-L actually becomes more popular than small-l. It's around the same time that 'Library/library of Alexandria' overtakes 'Alexandrian library'. Capital-L drastically increases its lead over small-l, and 'library of Alexandria' over 'Alexandrian library', after the release of Civilization III in 2001 (2 million copies sold by 2003; in-game info sheet) and Civilization IV in 2005 (3 million copies sold by 2008; in-game info sheet). Google Ngrams doesn't present data after 2008. But Civilization V (2010) has sold around 10 million copies on just one sales platform, so don't go expecting the curves to flatten out or decline.

Longer-term graphs show Gibbon's and Sagan's influence in English very clearly, and perhaps surprisingly, also in French. (For the French one you'll have to click the 'search' button after loading the webpage, because of a bug: Ngrams doesn't handle the apostrophe in bibliothèque d'Alexandrie well.) In some other European countries, though, Gibbon had no impact at all: if you look at graphs for German and Russian you can see that there was no interest at all in the Bibliothek von Alexandria or the Александрийская библиотека until the 1980s and 1990s. Gibbon wasn't translated into Russian until 1883, and not into German until 2003, so in those countries the effect is down to Cosmos, Civilization, and increased contamination from the English-speaking world in the internet age.

All three -- Gibbon, Sagan, and Meier -- are responsible for the idea of the library as something uniquely irreplaceable. (And as we've seen in a previous post, that perception is untrue.) Sagan is especially responsible for the modern obsession over the 'destruction' of the library, and for the library's mystique in popular culture. Gibbon is responsible for making the library emblematic of a supposed conflict between Christian anti-intellectualism and pagan scientism, claiming that Christian-pagan violence in 389 CE was the occasion for its destruction. (A lot of sources, like this mostly fictional Wikipedia page, report Theophilus' campaign against pagan temples as happening in 391; Gibbon actually opts for 389, following Marcellinus Comes [see here, under the consulship of Timasius and Promotus.)

In the Civilization games, all the myths pop up simultaneously. Info sheets in Civilization I, II, III, IV, and V all claim:
Religious fanatics destroyed the library in 391 AD, after nearly 700 years of operation. Today, only a portion of the catalog survives, providing us with a mere hint of what treasures the library contained.
'The Great Library' as seen
in Civilization VI (2016)
(Civilization I and V have minor variations.) Not a word of this is likely to true, but it must surely have helped inspire sentiments like the one I quoted at the top. The latest game in the franchise, Civilization VI (2016), has re-written this passage:
Sources differ widely on responsibility for the fiery destruction of the Great Library’s collection of texts; usual suspects listed include Julius Caesar’s troops in 48 BC, Roman Emperor Aurelian c. 270 AD, and others. But it does appear that the last vestiges were burned in 391 at the orders of the Patriarch Theophilus to eradicate pagan influences in Egypt -- not the last time Christians would burn books.
Well ... it's an improvement, of sorts. The idea that the temple of Serapis still housed a library in 391 is doubtful; evidently we're still taking Gibbon at face value and blaming Christianity for the loss of information from antiquity; and here we have even more emphasis on the library's destruction as if it had any impact. However, there are some factual things creeping in too, and the words 'it does appear' are a small concession to the imaginary nature of the story.

Let's move on from the 'destruction' of the library. I want to address the concern raised at the top: the idea that the contents of the libraries are some great mystery.

It certainly would be nice to have a detailed catalogue, not to mention more texts. However, the fact that a lot of information is missing doesn't stop us from forming some very good ideas about it, based on the information we do have. Ancient writers regularly cite each other, and from those citations it's possible to infer an awful lot about what doesn't survive.

Editions of lost texts are a niche industry, but very important to our understanding of antiquity. Here are a few highlights in the modern scholarship --
  • Over 1000 lost authors in the fields of history and geography alone -- the monumental Fragmente der griechischen Historiker, compiled initially by Felix Jacoby
  • 216 lost tragic playwrights, about 170 of them earlier than the fire in 47 BCE -- Snell's 1971 edition of Tragicorum graecorum fragmenta (for the well-known playwrights, their hundreds of lost plays have large editions of their own)
  • Around 80 lost philosophers prior to 400 BCE -- Diels and Kranz' Fragmente der Vorsokratiker
  • About 200 lost epic poems prior to 400 BCE -- spread across several editions
  • Around 90 lost lyric and elegiac poets prior to 300 BCE -- Page's Poetae melici graeci, Gentili and Prato's Poetarum elegiacorum testimonia et fragmenta
Alberto Bernabé's edition
of lost Orphic poems
(1612 pages)
Then there's the Kassel and Austin edition of lost comic poets, in eight large volumes. And I'm not even going to try to count up the later philosophers and poets whose books would have been in Alexandria, as well as in ancient libraries at Athens, Pergamon, Antioch, and elsewhere. And then there are other genres -- mathematics, natural sciences, prose fiction, mythography, technical manuals, and so on. Compared to the vast amount of books that were written in the Hellenistic period, the early ones are small fry. Wehrli's edition of lost Hellenistic philosophers has twelve volumes, and that's just for one school of thought.

The fragments of these lost books are often small. Some authors are just a name. But we do know an awful lot about some of them. Take for example Timaeus of Tauromenion, a tremendously important historian of early Italy. His work is lost, but in the New Jacoby edition, the fragmentary Greek text still adds up to something like 30,000 words. That's more than we've got of some intact historians! One of the most important foundations for the Greek mythological canon, second only to Homer, was a poem called the Catalogue of Women: it's lost, but between 1100 and 2000 lines of it survive, depending on how you count. However you look at it, it's bigger than either of the intact Hesiodic poems!

We don't have the actual texts of most books held in ancient libraries. We don't have much in the way of catalogues (nothing at all, in the case of Alexandria). And no doubt there are many, many more lost authors where no trace survives. But we have so many reports, about thousands of lost books, that we have a very, very good idea about the kinds of things that we're missing out on.
The last remains of the library were destroyed within a year of Hypatia's death. It's as if an entire civilization had undergone a sort of self-inflicted radical brain surgery so that most of its memories, discoveries, ideas, and passions were irrevocably wiped out. The loss was incalculable. In some cases, we know only the tantalizing titles of books that had been destroyed. In most cases, we know neither the titles nor the authors.
-- Carl Sagan, Cosmos, episode 13 'Who speaks for Earth?' (1980)
This is pure romance: invented by Gibbon, popularised by Sagan, and finally embedded by Civilization into a ruthlessly teleological view of the history of knowledge.

'Self-inflicted radical brain surgery'
There's no great tragedy, and not much mystery either. The claim 'The last remains of the library were destroyed within a year of Hypatia's death' is not true. Even if it were true, there's no good reason to suppose it would be important. It makes no sense to weep over Alexandria, nor any other library for that matter, because that's just not how texts got lost. No ancient library ever had the potential to be a repository that could last 2000 years. No modern library either, for that matter: libraries disappearing is just what happens if you wait that long.

In the same way, there's no point wondering or agonising over what arcane secrets might have been in ancient libraries. If you're wondering about the kind of stuff that we've lost, just open an edition of fragments. It's all there. It's there in truckloads.

(Do learn Greek first, though.)

Monday, 12 December 2016

Salting the earth

At the end of that space, a second Scipio, the son of Paulus Aemilius, the conqueror of Perseus, took the city by storm, and destroyed it, razing it to the ground, passing the ploughshare over its site, and sowing salt in the furrows, the emblem of barrenness and annihilation.
-- The New American Cyclopaedia, vol. 4 (1858) p. 479
The setting: the Romans are sacking Carthage in 146 BCE. Supposedly the Roman general Scipio Aemilianus salts the earth to eradicate Carthage for good, making a fertile land into desert.

The destruction wrought by the Romans was absolutely real, and truly horrific: Appian's account of it is real nightmare fuel. The salting-the-earth story, though, is pure myth. There isn't a shred of ancient evidence to suggest that it happened. The story didn't appear until the 1800s.

The myth evaporates easily enough. But it's still a very interesting topic. For one thing, there was such a thing as ploughing over a city and salting the earth -- it's just that it didn't happen to Carthage.

For another thing: when we look closely, it turns out 'salting the earth' isn't about destroying fertile land and turning it into desert. Oh no. The salt is actually meant to be a fertiliser.

Confused? Read on.

Giovanni Battista Tiepolo,
The capture of Carthage (1729; NY Met)
Even some professional ancient historians believed the salt myth until the late 1980s, when it got torn to shreds by a cluster of articles in the American journal Classical Philology. First, in 1986, an article by R. T. Ridley dismantled the myth and criticised scholars who had helped perpetuate it. The earliest example Ridley could find was in a volume of the Cambridge Ancient History from 1930. In 1988 another three authors -- including one Ridley had criticised, B. H. Warmington -- added afterthoughts to Ridley's article (plus an apology in Warmington's case). Between them, they managed to push the date of the salt myth back to an essay published in 1905.

One of them, S. T. Stevens, argued that the myth was an extension of the symbolic act of ploughing the land when founding a city (widely attested) or destroying it (attested in one Greco-Roman source). Long before the salt myth came along, it had been widely believed that Carthage had been ploughed over. Now, the ploughing myth has no foundation either. But it pops up in some eminent historians in the late 1800s; it also appeared in the 3rd edition of the Encyclopaedia Britannica, vol. 4 p. 215, in 1797, and was repeated verbatim until at least the 6th edition in 1823.

In fact the ploughing myth goes back a lot further. In 1299 Pope Boniface VIII personally reported how he demolished the city of Palestrina, as part of his feud with the Colonna family, as follows: 'I subjected it to the plough, following the example of Carthage of old in Africa'. He goes on, 'we also made salt in it, and commanded that it be sown over, so that it should have neither the condition, nor name, nor title of a city.' There are strong connections between the ploughing myth and the salt myth: we'll see more about these connections below.

So the ploughing myth goes back at least to the 13th century. What about the salt myth? Moving on to the internet age, and Wikipedia, we find that it has now been pushed back to 1863. In fact it's a little older still: its earliest appearance is indeed in Ripley and Dana's New American Cyclopaedia, but the volume with the 'Carthage' article dates to 1858 (see link at top).

Most observers agree that the modern idea of salting the earth is inspired by an incident in the Hebrew Bible, in Judges 9:45, where the Israelite king Abimelech 'razed the city and sowed it with salt' at Shechem.

Cover of the 2012 album
Salt the Earth by Carthage,
a deathcore band based in Maryland
In 2007 The Straight Dope covered the myth. There, Cecil Adams tried to estimate how much salt you'd actually need to make land effectively infertile. His estimate: 31 tons per acre. This works out to 7 kg per square metre, or a coating of about 6 mm. In the 3rd edition Britannica and the New American Cyclopaedia, Carthage's walls supposedly had a perimeter of 23 miles (37 km). I haven't tried to find out where they got this factoid from. But assuming they're right, that limits its area to 109 square km. The amount of salt required to make it infertile, then, could be up to 7.63 × 108 kg, or 763,210 tonnes. Standard Roman merchant ships in the Republican era could carry between 70 and 150 tonnes. So to transport this much salt you'd need a fleet of somewhere between 5000 and 10,000 ships, all packed to the brim with salt.

Here endeth the myth. All nice and tidy. There is a little more to talk about, though. And you know what happens when we get into the details ...

First: given that you'd need such a vast quantity of salt to make a place infertile, why then do we find 'salting the earth' going on in the bible, and in Pope Boniface's misdeeds at Palestrina? And second: if it turns out that they're not literally making the area devoid of life, what is really going on?

Ploughing and salting in the ancient Near East

Parts of the answer to the first question can be found in the Wikipedia article I already cited. There's a handful of parallels in mediaeval accounts. But much more interestingly, there's a whole set of parallels for ploughing over cities and salting the earth in several ancient Near Eastern sources. Here they are, all reported by Ridley (1986: 145):
  • a record of the proto-Hittite king Anitta of Nesa (ca. 1720 BCE), who destroyed the city of Hattusa and sowed it with weeds ('and in its place I sowed weeds', pe-e-di-is-si-ma ZÀ.AH-LI-an a-ne-e-nu-un; source. Dörfler et al. 2011: 113-14 interpret the weeds as a bioweapon, suggesting that they might have been bearded darnel, which can devastate wheat production, or greater dodder, which destroys legumes and survives for years in fallow soil);
  • an inscription where the Assyrian king Adadnirari I (early 1200s BCE) destroys the city of Taidu and strews something called kudimmu over it, a plant whose identity is unknown but which may be linked with salt somehow;
  • another Assyrian inscription where Shalmaneser I (mid-1200s BCE) destroys Arinu and strews kudimmu over it;
  • another (Grayson, Assyrian Royal Inscriptions vol. 2 no. 238) where Tiglath-Pileser I (early 1000s BCE) destroys Hunusa and strews something called sipu-stones over it;
  • another where Ashurbanipal (600s BCE) destroys Elam and scatters it with salt and sahlu seeds, where sahlu is an unknown plant;
  • the Hebrew bible, Judges 9:45, written in the 7th century BCE, reporting how Abimelech destroyed the city of Shechem: 'he razed the city and sowed it with salt';
  • and the latest parallel, again in the Hebrew bible, Jeremiah 26:18: 'Zion shall be ploughed as a field; Jerusalem shall become a heap of ruins, and the mountain of the house a wooded height.'
Most of the mediaeval and modern examples owe a lot to the incident in Judges 9. But the blend of salting and ploughing is not a modern invention. It wasn't invented by Pope Boniface VIII either.

Salt = fertiliser

In the Hebrew bible, salt is regularly a symbol of barrenness: see Deuteronomy 29:23, Jeremiah 17:6, and Psalm 107:34. Yet in the other ancient testimony cited above, it's strikingly clear that the salt is not meant to make the soil infertile. Ashurbanipal uses both salt and seeds; Judges 9:45 specifies that the salt is sown (וַיִּזְרָעֶהָ), not dumped in a layer.

Boniface, too, clearly meant his ploughing-and-salting at Palestrina to have fertile results. His exact words were
ac salem in ea etiam fecimus & mandavimus seminari
and we also made salt in it, and commanded that it be sown over
In the 21st century, and back in the 20th century too, most of us are accustomed to thinking of salt as something that eradicates life. If soil is too saline, nothing will grow in it. This is going to be especially on your mind if you're thinking of places like the Dead Sea, or the Bonneville Salt Flats in Utah: both of them salty as all hell, both iconically barren places.

Will Smith drags an alien across the Bonneville Salt Flats
(Independence Day, 1996)
In fact, salt was regularly used as a fertiliser in the past. You have to be much more careful with it than with other fertilisers -- too much will kill off the plants, it only works for some plants, and you don't put it on the roots (according to ancient sources, at least) -- but within those limits, it has been used regularly and, it may well be, very effectively. Plants need salt too. Even in the modern era, there were many experiments with salt as a fertiliser in the 1800s (examples: 1, 2, 3, 4). And yes, we're talking specifically about sodium chloride, not Epsom salt or saltpetre.

Nowadays salt has mostly gone out of fashion. Soil salinity is a real problem. Growers in the past may have had success with salt, but it is really really easy to overdo it. It does still see some use: some cattle farmers use it for growing feed, as cows need a lot of salt. Some organic farmers use it too. But before you try this in your own garden, check the salinity of your soil first.

On to the actual testimony. Greco-Roman witnesses have a fair amount to say on the subject. First, Theophrastus' On effects in plants:
Still, saline water is beneficial even for some vegetables, as cabbage, beet, rue and rocket, ... This improvement occurs, and in a word salinity is good for these vegetables, because they have a certain bitterness in their natures, and the salt water, by penetrating the plants and as it were opening outlets, extracts it (which is why cabbage is best in briny soil) ...
-- Theophrastus De causis 2.5.3-4 (tr. Einarson and Link)
And again:
We said earlier that salinity is also suited to some vegetables, and that soda is used with others. And so it seems we must accept the salinity here too [in pomegranate and almond trees] as appropriate to the plants, since it is evident that the sweetness of these vegetables comes from the saline water and the food.
-- Theophrastus De causis 3.17.8
Elsewhere he repeats that cabbage and purslane grow sweet and have little bitterness in saline soil (De causis 6.10.8); and he claims Egyptian olive oil isn't as good as the Greek stuff because it doesn't get enough salt (Historia 4.2.9).

But he really goes all out when it comes to date palms. Ancient date growers didn't just add a few grains of salt, according to Theophrastus. To borrow a phrase from Quentin Tarantino, they drowned 'em in that shit.
(The date palm) likes a soil which contains salt; wherefore, where such soil is not available, the growers sprinkle salt about it; and this must not be done around the actual roots: one must keep the salt some way off and sprinkle about a hēmiekton (i.e. about 4.3 litres; ca. 5 kg). ... When the tree is a year old, they transplant it and give plenty of salt, and this treatment is repeated when it is two years old, for it delights greatly in being transplanted.
-- Theophrastus Historia 2.6.2-3 (tr. Hort, adjusted)
Elsewhere he mentions that Babylonian date growers use salt but no manure for their fertiliser, and that another method of application is manually applying lumps of salt to the trees (De causis 3.17.1-4; also Historia 4.3.5). Theophrastus' experience must have been with very salt-starved soil. Modern research has shown that date palms do tolerate relatively high salinity, but as with anything, that tolerance has limits. According to this 2015 study, the limit is around 9 to 12.8 dS m-1 (roughly 6-8 g per litre of soil). Modern date growers don't use salt as a fertiliser, even in the region that was once Babylonia.

Theophrastus' enthusiasm about salt isn't quite as visible in other ancient sources. They do mention it though. Pliny the Elder comes up with a rather imaginative explanation -- he obviously doesn't have as much growing experience as Theophrastus --
salsaeque terrae multa melius creduntur, tutiora a vitiis innascentium animalium.
And many (plants) are better entrusted to salted earth, as they are safer from being harmed by animals breeding there.
Pliny is also aware that cattle, sheep, and yoke animals love salty pastures, and that the salt improves their milk and cheese (Nat. hist. 31.88).

A much more striking allusion is in the New Testament, in the gospel of Luke.
καλὸν οὖν τὸ ἅλας· ἐὰν δὲ καὶ τὸ ἅλας μωρανθῇ, ἐν τίνι ἀρτυθήσεται; οὔτε εἰς γῆν οὔτε εἰς κοπρίαν εὔθετόν ἐστιν· ἔξω βάλλουσιν αὐτό.
Salt is good; but if the salt goes bad, in what how will it be used for seasoning? It isn't suitable for the ground or for a manure heap. They throw it away.
-- Luke 14:34-35 (my translation)
As with almost anything in the New Testament, I need to add a caution. These verses are paralleled in Mark 9:50 and Matthew 5:13, but those passages aren't as clear about the use of salt as a fertiliser. As a result, New Testament scholars tend to debate the meaning of the passage in Luke.
Digression: there are two other translation problems here, though neither of them has an impact on the bit about using salt as a fertiliser. I mention them because they are bugging me.
  1. ἐὰν ... τὸ ἅλας μωρανθῇ is more conventionally translated as 'if the salt loses its taste'. That translation is driven by the parallel in Mark, which does mean something like that: ἐὰν δὲ τὸ ἅλας ἄναλον γένηται, 'if the salt becomes unsalty'. But Matthew and Luke use the verb μωραίνω, in the passive, which elsewhere always means 'become μῶρος, become foolish, be stupefied'. There are no parallels to suggest it can ever mean anything like 'lose its taste'. (μωραίνω is a moderately common word; just within the NT cf. Romans 1:22, 1 Corinthians 1:20.)
  2. ἐν τίνι ἀρτυθήσεται is obscure. The verb ἀρτύω means 'to prepare, season, salt', so literally the phrase means 'In with what will (the salt) be seasoned?' My translation above, which takes ἀρτύω as 'to use as a seasoning', strains the syntax a bit. However, the conventional translation 'how can its saltiness be restored?' (NRSV) is much more of a stretch: interpreting ἀρτύω as 'to restore the taste of' is a strain on meaning, not just syntax, and ἐν τίνι cannot mean 'how' or 'with what'. [edit, much later: ἐν does indeed mean instrumental 'with' in New Testament Greek.]
The salt-as-fertiliser reading does however expose another allusion in the parallel in Matthew 5:13 'You are the salt of the earth' (ὑμεῖς ἐστε τὸ ἅλας τῆς γῆς). The idea there isn't just that people are flavoursome, and good for preserving foods -- they're also good for growing things!

So no, Carthage wasn't ploughed and salted, but some other places throughout history have been. It was indeed ecological warfare: the idea was indeed to eradicate a city forever. But not by eradicating all life. Rather, the idea was to turn a once-bustling city into a green space, covered in weeds. And for that purpose, you don't need an outrageous amount of salt at all.


Friday, 2 December 2016

Pythagoras and the beans #2: why ban beans?

We continue directly from last time: now it's time to look at the proposed explanations for the Pythagorean bean ban.

3. The favism theory

People with the genetic condition of glucose-6-phosphate dehydrogenase (G6PD) deficiency can sometimes suffer an illness called favism when exposed to broad beans. Favism destroys red blood cells and is dangerous for young children. The favism theory holds that the Pythagoreans were aware of this condition, and banned contact with beans to prevent it.
  • Those for: Arie 1959; Lieber 1973; Brumbaugh and Schwartz 1980; Katz 1987 (a follow-up to Katz and Schall 1979). (See also older bibliography cited in some of these articles.)
  • Those against: Scarborough 1982; Simoons 1998: 216-249; Dye 1999.
  • Undecided: Garnsey 1998: 219-20.
Proponents cite modern genetic studies showing that 5-6% of the world population has G6PD deficiency, and that the type of G6PD deficiency that can lead to favism is concentrated in the eastern Mediterranean, with incidence as high as 8% to 35% on Rhodes. In principle, you can imagine a high incidence leading to bans for medical reasons. (Katz' argument is slightly different: he believes the ban wasn't consciously intended to avoid favism, but a case of biocultural evolution -- the taboo was a favoured behavioural trait because it prevented favism, and G6PD deficiency is a favoured genetic trait because it assists in preventing malaria.)

World distribution of G6PD deficiency
(source: WHO Working Group 1989: 605)

On the 'against' side, Simoons shows that (1) Pythagoras didn't come from Rhodes, he came from Samos, and on modern Samos the incidence of G6PD deficiency is unexceptional; (2) in Calabria, southern Italy, where Pythagoras established his cult, the rate of G6PD deficiency in the modern population is unusually low (between 0% and 2.7%). The incidence of G6PD deficiency is too variable in different parts of Greece for a figure from modern Rhodes to be at all meaningful.

Dye additionally points out that that's G6PD deficiency, not favism. You have to have G6PD deficiency to get favism, but only a fraction of G6PD-deficient people actually get it. The other determining factors for the disease are poorly understood (Kattamis et al. 1969: 34; WHO Working Group 1989: 608, 610).

Moreover, it's a children's disease. According to the epidemiological studies that Brumbaugh and Schwartz themselves cite (Kattamis et al. 1969; Belsey 1973): (1) only 10-20% of people with G6PD deficiency ever suffer a case of favism in their entire lives; (2) of those, 85-95% are children aged six or under; and (3) they report fatalities only at age four or under.

In light of that, favism doesn't sound quite as momentous. For our purposes, that is: obviously favism remains a critical concern for parents in places that genuinely have a high rate of G6PD deficiency, like Sardinia and Cyprus.

Young children had colossally high mortality rates in antiquity, so when we look at ancient witnesses, it's really only illnesses after early childhood that are going to get any attention. If we assume maximal impact -- that 5.5% of ancient Samians had G6PD deficiency (approximately the modern world average), that 20% of them got favism, and of those, 15% were over six -- then at most 17 in every 10,000 people over six would ever suffer a case of favism. Realistically, it'd be more like half that. If we're talking about Calabria and we assume non-maximal figures, the incidence is going to be more like 2 in every 10,000 people over six. And zero fatal cases.

Does that make a blanket ban a 'common sense injunction' as Brumbaugh and Schwartz believe? Hardly! Against the background noise of other unexplained illnesses, ancient observers wouldn't even notice a disease that is (1) not normally life-threatening for over-sixes, and (2) with a 0.02% chance of ever getting the disease.

Now, if ancient sources showed any awareness of the disease, that'd be different. But they don't. The earliest description of the disease dates to 1843 (Davies 1961: 477).* Ancient herbologists and medical writers are far, far better preserved than any documents relating to Orphic-Pythagorean mysticism, and they do discuss beans extensively -- writers like Theophrastus, Dioscorides, and Galen -- but only as a commonplace food. The only medical caution is that they give you gas. When ancient sources bring up the idea of a prohibition, it is only ever in connection with Orphic-Pythagorean mysticism.
* Note: Davies also cites an 1837 poem by Eduard Mörike which he believes was inspired by a case of favism. In fact the poem is pretty clearly alluding to ancient Orphic mysticism. Mörike was heavily influenced by his study of classical literature, and favism is extraordinarily rare in Germany (Mörike spent his whole life in Baden-Württemberg).

Aristotle points out that the bean 'is destructive' (φθείρει) as one of several possible explanations for the Pythagorean bean ban, and Garnsey thinks this is a point in favour of the favism theory (1999: 88). That's not a strong consideration. The expression appears again in Theophrastus, slightly later than Aristotle --
Let us first deal with beans: applied to the roots and shoots, their pods destroy (φθείρει) not all trees, but only the ones just growing up, since these are weaker. The pods destroy (φθείρει) them by taking the food away by reason of their hardness and dryness, absorbing some of it themselves, and shutting out the rest, for when the trees get no food they perish. The bean pods and the like destroy (φθείρει) the tree by being hostile (as it were) to its sprouting.
-- Theophrastus, On effects in plants 5.15.1-2 (tr. Einarson and Link, corrected)
(Similarly Clement of Alexandria, Stromateis; Geoponica 2.35.1.) Yes, Aristotle calls beans 'destructive'. But apparently he's talking about herbicide, not favism.

The favism theory doesn't amount to a hill of beans. At best it's a mildly interesting speculation. More realistically, it's a piece of speculation that can only be supported by selective treatment of incidence figures, or by ignoring them altogether. The relevant testimony is copious, we would expect to see lots of corroboration there, and yet none exists.

(Katz' form of the favism argument is not completely excluded, though. If the bean ban were an evolved behaviour, as opposed to a medical prohibition -- and that is one hell of an 'if'! -- ancient sources' complete unawareness of favism would be unsurprising. The evolved behaviour idea also sits well with the fact that favism is a children's disease. It's still tenuous: how on earth do we tell when a biocultural explanation is the right kind of explanation for a food taboo? But it's not impossible.)

Herbicide, bringer of sickness, or symbol of human genitals? You choose.

4. Death and reincarnation

The interpretations that are most closely related to genuine Pythagoreanism are those which connect beans with the doctrine of metempsychosis.
Thus quoth the scholar of Greek religion Walter Burkert (1972: 183). To some extent this is borne out by our earliest source on the bean ban, Aristotle:
εἰσὶν ὅμοιοι ἢ ὅτι ᾍδου πύλαις < . . . > ἀγόνατον γὰρ μόνον
(Beans) are like the gates of Hades, for only (the stem of this plant) is unjointed
-- Aristotle fr. 195 Rose
Hypothetically, the unjointed stem might be a symbol for unimpeded progress from the underworld to the living world. However, this is just one of the explanations that Aristotle suggests, and it's not exactly clear.

Reincarnation comes up a lot in 4th century BCE sources, especially Plato, but the terms we throw around for Greek reincarnation -- metempsychōsis 're-ensoulment', metensōmatōsis 're-embodiment' -- are late: neither word is attested before the 1st century. Reincarnation is mainly associated with Epimenides, Pythagoras, Empedocles, and Plato, plus a few more minor names. The jury is out on whether there's any link between Greek and Indian beliefs about reincarnation: I won't touch that today. Herodotus calls it an 'Egyptian' doctrine (2.123), wrongly: that's really just another way of saying it's Pythagorean. An awful lot of Epimenidean-Pythagorean mysticism got spuriously linked to Egypt. Allusions to Egypt were just a way of adding mystique to the mystical. (For another example of faux Egyptianism, see this old post on the 3-4-5 Pythagorean triple.)

In Greek thought, your next life might be determined either by your own choice, or by your moral character. Male and female, human and animal, even plants are potential destinations: one fragment of Empedocles states that in his past lives he had been a boy, a girl, a bush, a bird, and a fish (fr. 31 B.117 Diels-Kranz; also fr. B.127). A substantial discussion in Plato's Republic (book 10, 617e-620d) emphasises that everyone is responsible for choosing their next life. Alternatively, it might depend on whether you're naughty or nice, or on whether you're properly enlightened. Pythagoras supposedly had been a soldier in the Trojan War in a past life, a Trojan named Euphorbus (who appears in the Iliad, naturally): clearly the idea was that he had always been among the great and the good. Empedocles talks about a cycle of reincarnations where the best of the best end up as 'prophets, hymnists, doctors, and front-line fighters' (fr. B.146). This idea shows up in Plato too, in a famous passage casting the mind as the charioteer guiding his horses -- the immortal soul -- through various lives (Phaedrus 246a-254e). Only those with a philosophical inclination get to become human in their next life (249b).

These mystics taught that the cycle of reincarnation is a punishment for some crime committed when your soul was a divinity (daimōn). If you signed up to the parish newsletter, so to speak, you could break free and go back to being a divinity. In Empedocles, salvation takes 30,000 years (fr. B.115.3-8); in Plato, 3000 years (Phaedrus 249a).

We don't know for sure that this has anything to do with the bean ban -- that's why people look for alternate explanations, like the favism theory. The Aristotle fragment quoted above helps, but it doesn't really settle anything. There's also the Orphic fragment we looked at last time:
I tell you, eating beans is the same as eating your parents' heads ...
(the bean) is a path and stairway out of Hades' house
for the souls of the strong, whenever they ascend into the light
-- Orphica fr. 648 ed. Bernabé
Ancient writers tell us that the first line comes from 'Orpheus', but it's attributed to Pythagoras nearly as often. (Bernabé 2013: 123 n. 34; Plutarch Q. conv. ii.635e, 'either Orphic or Pythagorean'.) Some ancient writers explained the bean ban by pointing out that bean pulp under certain conditions changes to resemble human blood or parts of the anatomy, including heads. That suggests someone was taking 'eating beans is the same as eating your parents' heads' very literally. Pliny reports that according to some, 'the souls of the dead are in (beans)' -- but, inconveniently, he explicitly distinguishes this from Pythagorean beliefs (Nat. hist. 18.118).

Roman religion, too, tended to treat beans as a holy symbol and sometimes made a connection between beans and the transition between life and death. In the Lemuria festival, beans were used in a ritual to expel dead spirits from the house (Varro, reported in Nonius Marcellus 135.15 M). Beans played a role in the Parentalia, a festival designed to honour ancestors (Ovid Fasti 2.576); Pliny Pliny NH 18.118). And Roman priests weren't allowed to eat beans (Varro, reported in Pliny NH 18.119); one priest, Jupiter's flamen Dialis, wasn't even allowed to mention them (Aulus Gellius 10.15.12). Some of this is strikingly similar to some things we hear from the Neo-Pythagoreans.

The exact nature of the religious meaning of beans is never made clear, but there does seem to be something here. But if the bean ban was ever framed in terms of some definite purpose, with cause and effect in mind, the purpose was theological, not mundane.

Accordingly, the great theorist of ancient religion Marcel Detienne interprets the Pythagorean treatment of beans as a term in a set of symbols with structured links to one another -- a structuralist interpretation, in other words -- where the taboo on beans is purely religious (1977: 49-59). Beans are a key symbolic term in the Pythagorean system of food classification, Detienne thinks, linked to notions of beast-like behaviour. Beans are quintessentially symbolic of meat-eating: hence the links that some sources draw between beans and raw meat, beans and blood, beans and animal urges. In one story we mentioned last time, where Pythagoras persuaded an ox never to eat beans again, that represented a de-animalising of the ox.

Beanfield in bloom

5. Other theories

You didn't think these two theories were the only two ones, did you? Ancient sources were as confused by the Pythagoreans as we are today. Our earliest source, Aristotle, is among the most confused:
Aristotle says in On the Pythagoreans that (Pythagoras) told them to abstain from beans, either because they are like genitals; or because they are like the gates of Hades, for only (the stem of this plant) is unjointed; or because it is destructive; or because it is like the nature of the whole; or it is oligarchic -- at any rate, (people) use them for drawing lots.
-- Aristotle, reported in Diogenes Laertius 8.34 (≈ Arist. fr. 195 Rose)
So without further ado let's make a complete list of ancient theories on the bean ban.
  1. Because beans are like genitals.
    Aristotle fr. 195; Antonius Diogenes Wonders beyond Thule (reported in Porphyry Life of Pythagoras 44, John Lydus De mensibus 4.42: the bean blossom after being buried in soil for 90 days looks like a baby's head or like female genitalia); Lucian Sale of lives 6 (unripe beans inside the pod look like male genitalia). Cf. Empedocles fr. B.141, with explanation in Aulus Gellius 4.11.9-10.
  2. Because the bean pod has a herbicidal effect.
    Aristotle fr. 195. Cf. Theophrastus Effects in plants 5.15.1-2; Clement of Alexandria Stromateis; Geoponica 2.35.1.
  3. Because the bean 'is like the nature of the whole'.
    Aristotle fr. 195, ὅτι τῇ τοῦ ὅλου φύσει ὅμοιον. Cf. Refutation of all heresies 1.2.14: the bean arose 'at the beginning and composition of all things, when the earth was still combined and sifted together'. Porphyry Life of Pythagoras 44 is parallel, and casts doubt on the reading 'sifted together' in the Refutation; but the Porphyry passage is obscurely phrased. The parallel suggests that the Refutation author, like Porphyry, is paraphrasing Antonius Diogenes' Wonders beyond Thule.
  4. Because beans are a symbol of political engagement, since they are used for drawing lots.
    Aristotle fr. 195; Lucian Sale of lives 6; pseudo-Plutarch On educating children 12f. Cf. Andocides De mysteriis 1.96 ἡ βουλὴ οἱ πεντακόσιοι <οἱ> λαχόντες τῷ κυάμῳ, 'the Council of the Five Hundred allotted by the bean'. (On bean-eating as a social symbol in antiquity see Garnsey 1998: 220-4.)
  5. Because the bean or its blossom transforms into substances or shapes reminiscent of human body parts under various conditions.
    Antonius Diogenes, Wonders beyond Thule (reported in Porphyry Life of Pythagoras 44, John Lydus De mensibus 4.42: chewed bean pulp left in the sun smells like blood, the blossom after being buried in soil for 90 days looks like a baby's head or like female genitalia); Refutation 1.2.14-15 (also based on Antonius Diogenes? see 3. above; chewed bean pulp left in the sun smells like semen, the bean and blossom buried in soil for a few days look like a womb with a baby's head inside it); Lucian Sale of lives 6 (cooked beans left in moonlight turn into blood). Cf. Heracleides fr. 41 (beans buried in dung for 40 days change to look like human flesh).
  6. Because the bean is 'thought to dull the senses and cause insomnia'.
    Cicero On divination 1.(§30).62; Pliny Natural history 18.118. For beans' influence on dreams cf. Plutarch Q. conv. viii.734e-f, Geoponica 2.35.8.
  7. Because the word 'bean' (kyamos) sounds like the word 'pregnancy' (kyēsis).
    Plutarch Q. conv. ii.635e.
  8. Because beans cause sterility in women.
    Clement of Alexandria Stromateis
  9. Because the pattern on the bean blossom contains ill-omened letters.
    Pliny Natural history 18.119; Geoponica 2.35.6.
All these sources are explicit that they are talking about Pythagoras' ban. Obviously there's a lot of overlap between numbers 1 and 5. (Note that some of the sources are less than serious: Lucian is satyrical, and Antonius Diogenes' lost Wonders beyond Thule was a fantasy novel. In item 5, the Lucian passage is almost certainly a satire of Antonius Diogenes.)

It should be pretty obvious that most of these must be purely speculative. No one had any real clue of why the Pythagoreans banned beans, so they were just rummaging around to see what they could dig up. (That's also pretty much how I see the favism theory.)

6. Yes, it's mysterious -- that's the point

I'd better close by repeating that even our ancient sources don't know the reason for the taboo. Aristotle, our earliest witness, and one of the most reliable, lists off five random speculations for want of anything better.

Even in the early period, Pythagoreanism was more a cult than a school. Its teachings were more religious mysticism than anything rationalistic. Alberto Bernabé (2013) makes a thorough catalogue of places where our sources mix up Orphic, Pythagorean, and Empedoclean doctrines. I mentioned above that the line about 'eating beans is the same thing as eating ancestors' heads' is attributed to Pythagoras almost as often as Orpheus.

And the bean ban isn't an isolated bit of weirdness. The Pythagoreans venerated other plants too, like the mallow. Last time we saw that the Eleusinian cult had some kind of link to the Pythagorean bean ban; well, at the Haloa, another Attic festival in honour of Demeter, the list of things you weren't allowed to eat included eggs, fowl, pomegranates, apples, and various other things, as well as beans. The Roman flamen Dialis wasn't allowed to say the word 'bean': well, he wasn't allowed to mention female goats, raw meat, or ivy either.

Some religious doctrines are just not meant to be explained. Sometimes they're symbolic without symbolising anything specific. They exist solely so that they can be revealed to catechumens. That way, advanced initiates get to have access to secret knowledge, but the knowledge doesn't have to be meaningful outside that context.

Remember the story of how the Pythagoreans were caught and killed by soldiers, because they weren't willing to escape through a beanfield? Listen to what happens next:
'Teach me one thing,' (Dionysios) said, 'and you shall go free with a suitable escort.' Myllias asked what he was so eager to learn. 'This,' said Dionysios, 'the reason why your companions chose to die rather than tread on beans.' Myllias promptly replied 'They were prepared to die rather than tread on beans, and I would rather tread on beans than tell you the reason'.
-- Iamblichus, Life of Pythagoras §31.193 (tr. Clark)
Here the entire point of the bean ban is that it's a secret. No one really cares about the reason for the ban: they just want to uncover the secret. Again and again, Iamblichus tells us that everything in Neo-Pythagoreanism has to be hush-hush. Not because of any reasoned danger if the information gets out: it's just that that's what being a Neo-Pythagorean is all about.

You can see this elsewhere too. There's a report on a cult of Demeter at Pheneus, in Arcadia, in the travel writer Pausanias (8.15.3-4). Apparently they had a 'sacred story' (hieros logos) to explain why the locals could eat any kind of pulse except broad beans, which were 'impure'. Will Pausanias tell us this story? No, of course not. It's a secret.


  • Arie, T. H. D. 1959. 'Pythagoras and beans.' Oxford Medical School gazette 11: 75-81.
  • Belsey, M. A. 1973. 'The epidemiology of favism.' Bulletin of the World Health Organization 48: 1-13.
  • Bernabé, A. 2013. 'Orphics and Pythagoreans: the Greek perspective.' In: Cornelli, G., et al. (eds.) On Pythagoreanism. Berlin: De Gruyter. 117-151.
  • Brumbaugh, Robert; Schwartz, Jessica 1980. 'Pythagoreans and beans: a medical explanation.' Classical world 73: 421-422.
  • Burkert, W. 1972. Lore and science in ancient Pythagoreanism. Cambridge, Mass.: Harvard UP. (NB: 180-185 on Pythagorean food taboos)
  • Davies, P. 1961. 'Favism.' Postgraduate medical journal 37: 477-80.
  • Detienne, M. 1977. The gardens of Adonis. Spices in Greek mythology. Princeton: Princeton UP. (Orig. Les jardins d'Adonis, Paris: Gallimard, 1972.)
  • Dye, J. 1999. 'Explaining Pythagorean abstinence from beans.' The Internet Archive (original web publication now deleted).
  • Garnsey, P. 1998. Cities, peasants and food in classical antiquity. Cambridge: CUP. (NB: 214-25 on beans)
  • Garnsey, P. 1999. Food and society in classical antiquity. Cambridge: CUP. (NB: 85-91 on Pythagorean food taboos)
  • Kattamis, C. A.; Kyriazakou, M.; Chaidas, S. 1969. 'Favism. Clinical and biochemical data.' Journal of medical genetics 6: 34-41.
  • Katz, S. H.; Schall, J. 1979. 'Fava bean consumption and biocultural evolution.' Medical anthropology 3.4: 459-476.
  • Katz, S. H. 1987. 'Fava bean consumption: a case for the coevolution of genes and culture.' In: Harris, M.; Ross, E. B. (eds.) Food and evolution. Philadelphia: Temple UP. 133-59.
  • Lieber, E. 1973. 'The Pythagorean community as a sheltered environment for the handicapped.' In: Karplus, H. (ed.) International symposium on society, medicine and law. Amsterdam: Elsevier. 33-41.
  • Scarborough, J. 1982. 'Beans, Pythagoras, taboos, and ancient dietetics.' Classical world 75: 355-358.
  • Simoons, F. J. 1998. Plants of life, plants of death. Madison: U. Wisconsin Press.
  • WHO Working Group 1989. 'Glucose-6-phosphate dehydrogenase deficiency.' Bulletin of the World Health Organization 67: 601-11.

Monday, 14 November 2016

Pythagoras and the beans #1: hands off beans!

Those wacky Pythagoreans! They loved them some numbers: they gave us a famous theorem (actually that isn’t true) and executed people for talking about irrational numbers (that isn’t true either). But at the same time, they were a weird cult, with doctrines about reincarnation, that classes should take place in caves, and about how Pythagoras’ thigh was made of solid gold.

Oh, and they absolutely forbade any contact with broad beans.

Broad beans (a.k.a. fava beans: vicia faba).

Wait, can that really be true? Well, it kind of looks like it is. ‘Abstain from beans’ (κυάμων ἀπέχου) is a widely reported doctrine of the Pythagoreans. In some stories, they weren’t even allowed to touch beans.
The bean ban as a Pythagorean teaching: Aristotle fr. 195 ed. Rose; Callimachus fr. 553 ed. Pfeiffer; Cicero On divination 1.62, 2.119; Pliny NH 18.118; pseudo-Plutarch On educating children 12f; Diogenes Laertius 8.19, 24, 33-4; Iamblichus Life of Pythagoras (24) 109, Protrepticus 21.§37.

Our earliest source on the subject is Aristotle (reported by Diogenes Laertius 8.34):
φησὶ δ’ Ἀριστοτέλης <ἐν τῷ> Περὶ τῶν <Πυθαγορείων> παραγγέλλειν αὐτὸν ἀπέχεσθαι τῶν κυάμων ...
Aristotle says in On the Pythagoreans that he told them to abstain from beans ...
-- Aristotle fr. 195 ed. Rose
(Note: the exact wording is doubtful, but the reference is secure. The title On the Pythagoreans appears only in Andronicus’ list of Aristotle’s works: other witnesses call it by different names. But there’s no doubt about which book Diogenes had in mind, or about the fact that Aristotle was talking about Pythagoras.)

Elsewhere we’re told a story of one of Pythagoras’ miracles: how he persuaded an ox to leave a beanfield ... and it never ate beans again! And that one Zaratas, supposedly a Pythagorean guru of Babylonian origin -- no, there’s no reason to think he was real -- forbade eating beans. And that a group of Pythagoreans, or in some versions, Pythagoras himself, were killed by soldiers because they were unwilling to escape through a beanfield. And the 2nd century CE satirist Lucian frequently mocks the Pythagorean ban on beans.
The ox story: Iamblichus Life of Pythagoras (§13) 60. Zaratas: Hippolytus Refutation of all heresies 1.2.14-15. Beanfield story: Diogenes Laertius 8.39-40, 45; Iamblichus Life (§31) 191-3. Lucian: The dream or the cock 4, Dialogues of the dead 20.3, Auction of lives 6, True histories 1.14, 2.24.

The real question is: why did the Pythagoreans declare that beans were taboo?

When I was a student, the explanation I heard was that it was about Pythagorean teachings on reincarnation. Supposedly, according to the Pythagoreans, eating beans was tantamount to eating the souls of dead people.

Just recently I found out that popular perception tends to go for a different explanation nowadays (though the souls one is still standard among scholars): it’s more hip to interpret the bean ban as a safeguard against favism, an illness that can be provoked by some chemicals in raw broad beans.

Can we dig down and work out what true and what’s just rumour? Yes, we can have a go, but don’t expect a really convincing solution. A complete explanation would require more information, and better information, than we have. Some of the theories floating around are unfounded and tendentious; others are OK, but not compelling enough to persuade someone who’s already a fan of a different theory.

It would take too long today to go through all of the theories that have been suggested, so I’ll split this over two posts. Today is set-up: the introduction I’ve just given, and some methodological points. Next time we’ll move on to actual explanations for the bean ban.

Before we set out, I’d better point out that the vast majority of ancient references to beans are not warnings. They’re just ordinary discussions of a commonplace and nutritious food item. Ancient medical writers and herbologists give us plenty of reports on beans, but those writers make no mention of any taboo, health risks, or any other cautions.

Salvator Rosa, Pythagoras Emerging from the Underworld, 1662
(Kimball Art Museum, Fort Worth, Texas)

1. Non-Pythagorean bean bans

When ancient sources refer to a bean ban, they’re not necessarily talking about the Pythagoreans. So when Heracleides of Pontus, a scholar contemporary with Aristotle, references a ban (fr. 41 ed. Wehrli) but without mentioning Pythagoras, we can’t be sure who laid down the ban: the editor of the Heracleides fragments infers that it’s Pythagoras, but that really isn’t secure. Callimachus, though he mentions Pythagoras’ bean ban (fr. 553 Pfeiffer), makes it clear that he disapproves of eating beans in his own right too: ‘keep your hands away from beans, distressing foodstuff, / I too say, as Pythagoras used to command’ (κἠγώ, Πυθαγόρης ὡς ἐκέλευε, λέγω).

More specifically: some other varieties of mysticism around the 5th century BCE banned beans too, notably Empedocles and Orphic religion.

Empedocles was a mystic-cum-philosopher-cum-miracle-worker who was active in the second half of the 5th century BCE. He’s best known for canonising the ‘four elements’: earth, fire, water, and ... a fourth one. (Number four is traditionally received as air, or aēr, but apparently Empedocles himself had it as the bright aithēr of the upper reaches of the cosmos.) He was not a Pythagorean, himself. But an isolated fragment of his poetry warns against beans --
δειλοί, πάνδειλοι, κυάμων ἄπο χεῖρας ἔχεσθαι
wretches, utter wretches, keep your hands away from beans
--Empedocles fr. B.141 ed. Diels-Kranz
Our information about the Orphic religion(s) is very fragmentary, and refers to religious texts strewn across centuries. Among the surviving snippets we find the following --
ἶσον τοι κυάμους τε φαγεῖν κεφαλάς τε τοκήων ...
ψυχῆ<ι>σ’ αἰζηῶν βάσιν ἔμμεναι ἠδὲ ἀνάβαθμον
ἐξ Ἀΐδαο <δόμων>, ὅταν αὐγὰς εἰσανίωσιν
I tell you, eating beans is the same as eating your parents’ heads ...
(the bean) is a path and stairway out of Hades’ house
for the souls of the strong, whenever they ascend into the light
-- Orphica fr. 648 ed. Bernabé (first line by itself = fr. 291 Kern)
This comes from a lost poem from no later than the 4th century BCE: line 1 is linked to Heracleides fr. 41. (Lines 2-3 may come from a separate poem: they are given together with line 1 in only one very late writer, Eustathius, who may well have got them from a separate source.)

The Orphic bean ban, in turn, is connected to a comparable teaching in the Eleusinian Mysteries. A travel guide links them together in passing:
On this road there is a temple, not big, dedicated to Kyamites (‘beaner’). I can’t say for sure if he was the first to sow beans, or whether they declared someone a hero because they aren’t allowed to attribute the invention of beans to Demeter. (Someone who has seen an Eleusinian initiation or read the Orphic texts knows what I’m talking about.)
It’s a pity Pausanias was so tight-lipped: no one will ever again be able to witness an Eleusinian initiation or read the Orphic texts. So the meaning of his allusion is lost forever.

Pythagoras as hyper-rationalist: detail from Raphael, The School of Athens, 1509-1511
(Vatican City)

2. A dissenting voice: Aristoxenus and Aulus Gellius

According to the 2nd century CE writer Aulus Gellius, not only did the bean ban not exist, the Pythagoreans actually encouraged people to eat beans. He based this view on his readings of Empedocles (see above) and Aristoxenus (4th century BCE), a student of Aristotle who also studied under a Pythagorean, Xenophilus. Here’s his report of Aristoxenus:
sed Aristoxenus musicus, vir litterarum veterum diligentissimus, Aristoteli philosophi auditor, in libro quem De Pythagora reliquit, nullo saepius legumento Pythagoram dicit usum quam fabis, quoniam is cibus et subduceret sensim alvum et levigaret. verba ipsa Aristoxeni subscripsi: Πυθαγόρας δὲ τῶν ὀσπρίων μάλιστα τὸν κύαμον ἐδοκίμασεν· λειαντικόν τε γὰρ εἶναι καὶ διαχωρητικόν· διὸ καὶ μάλιστα κέχρηται αὐτῷ.
But Aristoxenus the musician, a man thoroughly versed in early literature, a pupil of the philosopher Aristotle, in the book On Pythagoras which he has left us, says that Pythagoras used no vegetable more often than beans, since that food gently loosened the bowels and relieved them. I add Aristoxenus’ own words: ‘Pythagoras among vegetables especially recommended the bean, saying that it was both digestible and loosening; and therefore he most frequently made use of it.’
-- Aulus Gellius 4.11.4 (tr. Rolfe; alternative translations 1, 2)
Gellius goes on to conclude that most of what we hear about Pythagorean food taboos is complete bollocks. The Pythagoreans ate beans: they ate meat too, even though the popular image of them is vegetarian. Gellius thinks the bean ban was a result of people mistakenly conflating Empedocles’ teachings with Pythagoreanism.

His idea is worth considering. Ancient sources on Pythagoras have a sharp split: from the 1st century CE onwards, the vast majority of our surviving sources are ‘Neo-Pythagorean’, a movement kicked off by figures like Moderatus of Gades and Apollonius of Tyana, who took a literalist view of pretty much all invented traditions about Pythagoras, and in Apollonius’ case, wrote about him as a vehicle for his own brand of mysticism. Their writings don’t survive intact, but the sources that do survive, like Diogenes Laertius and Iamblichus, draw on them heavily. Most of the surviving testimony about Pythagoreanism -- and about Pythagoras himself -- comes to us through a thick Neo-Pythagorean filter. So Gellius’ focus on early sources like Aristoxenus and Empedocles has a lot going for it.

Like Pythagoras, Empedocles had a persona as a miracle-worker. The story of his death is a good illustration: supposedly, to prove that he could walk on air, he tried to levitate across a volcano crater and was never seen again. Neo-Pythagorean sources co-opt him as a might-as-well-be Pythagorean, along with other miracle-workers like Epimenides (who went to sleep for fifty years) and Abaris (who rode around on a giant magic arrow).

But Gellius’ theory has difficulties. The bean ban is linked to the Pythagoreans long before the Neo-Pythagorean New Wave, in Aristotle and Callimachus. The disagreement between Aristotle and Aristoxenus is a problem. Assuming they were both trying to write honestly, the truth lies with, or somewhere between, these two views:
  1. Early Pythagorean doctrines were, at heart, based on religious practices. Reports that focus on the rational and mathematical aspects of Pythagoreanism are efforts to rationalise away the mysticism and make sense of it. (See Kingsley 1995: 289-316 for an exposition of this view.) In that case, Aristoxenus was acting as an apologist, while Aristotle’s report is more investigative.
  2. Early Pythagoreanism had both mystical and rationalist elements. In that case the difference between Aristoxenus and Aristotle is just about emphasis: Aristoxenus is relatively sympathetic, and Aristotle is just being cynical. (Zhmud 2012 comes pretty close to this view of Aristoxenus.)
These views aren’t hugely different. Either way, Gellius’ theory can’t explain everything: we can’t simply ignore Aristotle’s report. And even if the bean ban did originate with Empedocles rather than Pythagoras, it’d still be nice to know the thinking behind the ban.

So much for the introductory discussion (if you can call something introductory when it’s this long). As I said, next time we’ll move on to what various people, both ancient and modern, have suggested as explanations for the bean ban.


  • Kingsley, P. 1995. Ancient philosophy, mystery, and magic. Empedocles and Pythagorean tradition. Oxford: Clarendon Press.
  • Zhmud, L. 2012. ‘Aristoxenus and the Pythagoreans.’ In: Huffman, C. (ed.) Aristoxenus of Tarentum. New Brunswick: Transaction Publishers. 223-49.

Sunday, 6 November 2016

The Eratosthenes video published by Business Insider: a fact-check

A good myth never dies. A week ago ‘Business Insider’, a prominent online magazine, published to its Facebook page a video called ‘How an ancient Greek mathematician calculated the earth’s circumference’, about Eratosthenes’ calculation of the earth’s size. At the time of writing, the video has 3.2 million views, 29,000 likes, 55,000 shares, and 1200 comments. A lot of people have had their views informed by this video.

Business Insider’s video on Eratosthenes’ calculation of the earth’s circumference (published 28 October 2016)

Now, initially I wasn’t sure it’s a good idea to re-tread old ground: I’ve written two posts relating to this subject before. One was on a myth about Eratosthenes’ calculation, to do with a well at Syene; another was on ancient flat-earthers. But as I watched the video I couldn’t help counting untruths. I found myself thinking about doing a kind of postscript to the earlier posts, just giving a quick list of errors.

On reflection, I decided that a ‘fact-check’ would be a more even-handed way of treating it. And I think it is worth doing: partly because of the number of people this video has reached in one week, partly because my earliest post focused on just one myth. So let’s do that: a fact-check.

In the mid-20th century we began launching satellites into space that would help us determine the exact circumference of the earth: 40,030 km.
True. The earth is slightly oblate, so its circumference from pole-to-pole-to-pole is 40,008 km, and its circumference around the equator is 40,075 km. If it were an exact sphere, with the same volume as the real earth, its circumference would be 40,032 km. I interpret the video’s claim as accurate to four significant figures.
But over 2000 years earlier in ancient Greece,
Mixed. ‘Over 2000 years earlier’ is accurate. Eratosthenes can be considered ethnically Greek, to an extent, but this certainly didn’t take place in Greece: as the video itself goes on to point out, Eratosthenes lived in Egypt. He came from Cyrene, in modern Libya.
a man arrived at nearly that exact same figure by putting a stick in the ground.
Mostly true. His achievement wasn’t nearly as single-handed as the video makes out, but his creative insight was certainly the basis for the finding.
That man was Eratosthenes: a Greek mathematician and the head of the library of Alexandria.
Eratosthenes had heard that in Syene, a city to the south of Alexandria, no vertical shadows were cast at noon on the summer solstice. The sun was directly overhead.
Mixed. It is true that Syene (modern Aswan) was very nearly on the Tropic of Cancer, where the earth’s surface coincides with the plane of the ecliptic at the summer solstice, meaning that the sun is directly overhead at noon. However,

(1) The opening phrasing ‘Eratosthenes had heard’ gives the impression that it was a lucky chance that Eratosthenes found this out. It was in fact a long-standing piece of knowledge, known both to Ptolemaic surveyors and to the native Egyptian population. Egyptian gnomons -- the ‘sticks’ that they used for determining the date of the solstice -- had a bit more to them than just sticking a post in the ground. In fact, specifically to compensate for the shortness of shadows at the summer solstice, Egyptian surveyors adopted the practice of tilting gnomons to the north, so that there would be a shadow to measure (source).

(2) Eratosthenes’ datapoints did not just consist of gnomon readings at Alexandria and at Syene (modern Aswan), but also at Meroë (modern Bagrawiya, Sudan), another 7.15 degrees to the south of Syene. The two distances, Alexandria-Syene and Syene-Meroë, were both reckoned as 5000 stadia. In fact in one key source, Martianus Capella De nuptiis 6.598, Eratosthenes works with only the Syene-Meroë measurement, and ignores Alexandria altogether. (This would improve the accuracy of the calculation: Syene and Meroë are closer to being on the same meridian than either is to Alexandria.)
He wondered if this were also true in Alexandria.
False. He already knew. The practice of taking gnomon readings to determine latitude had been in use since at least the early 4th century, when Pytheas of Massalia took gnomon readings all the way from southern France to a place called ‘Thoulē’ (a.k.a. Thule) somewhere in, or neighbouring, the North Sea. (Source: Martianus Capella De nuptiis 6.595). Also before Eratosthenes’ time, Philon, a surveyor for Ptolemy II, reported gnomon readings at Meroë in a book called the Aethiopica. (Source: New Jacoby 670 F 2 = Strabo 2.1.20.) Eratosthenes, and anyone else who knew anything about geography, knew perfectly well that shadow lengths varied at different latitudes.
So on June 21st
False. It was at the equinox. Multiple sources show that the most important gnomon readings for geographical purposes were those taken at the vernal equinox, not at the solstice. The fact that the sun was directly overhead at Syene at the solstice had nothing to do with the calculation: it just made Syene a significant reference point. The important thing wasn’t the absolute angle of the gnomon’s shadow, but the difference between the gnomon’s shadow at the two latitudes. And for that purpose, it doesn’t matter what time of year you take your readings. The equinox is especially good because you have two of them each year. (Sources: Philon, New Jacoby 670 F 2 = Strabo 2.1.20, specifically discussing Eratosthenes’ measurements; see also Vitruvius De arch. 9.7; Pliny NH 2.74.)

{Correction, Oct. 2018: the time of year does matter, actually. On the equinox, and only on the equinox, the sun’s rays are parallel to the plane of the earth’s equator. That means that at midday on the equinox, the angle between the gnomon and its shadow is exactly equal to the angle of latitude.}

{The ratio between the lengths of the shadow and the gnomon = tan θ = tan (latitude). But ancient writers didn’t have the luxury of modern calculators, so they had no easy way of converting the ratio into an angle. That’s why Pliny reports the equinoctial ratio at Rome as 8/9: because he doesn’t have the means to work out that Rome’s latitude = tan-1 (8/9) = 41.63°.}
he planted a stick vertically in the ground,
and waited to see if a shadow would be cast at noon. It turns out there was one, and it measured about 7 degrees.
False. See above: the basis of the calculation wasn’t a single angle measurement, but the difference between angles in multiple gnomon readings.
Now if the sun’s rays are coming in at the same angle at the same time of day, and a stick in Alexandria is casting a shadow while a stick in Syene is not, it must mean that the earth’s surface is curved.
And Eratosthenes probably already knew that.
True. (Except for the ‘probably’. Of course he already knew that. More than a century earlier, Plato was already taking the earth’s sphericity for granted; it was certainly common knowledge by Eratosthenes’ time.)
The idea of a spherical earth was floated by Pythagoras around 500 BC,
False. The claim that Pythagoras was a round-earther is based on Diogenes Laertius 8.48, but there is no doubt whatsoever that it is false. Diogenes Laertius is unreliable at the best of times, and the passage also ascribes round-earthism to Hesiod and Anaximander, and we know for certain that both of them were definitely flat-earthers.

We don't know for sure who was the first to realise the spherical shape of the earth, but it was probably a Greek in the latter part of the 400s BCE. Dirk Couprie, Heaven and earth in ancient Greek cosmology (2011) p. 169, suspects Oenopides (mid-400s BCE), who is credited as the discoverer of the angle of the ecliptic. The ecliptic is the plane of the earth’s orbit, at an angle to the equator. The fact that the plane of the ecliptic coincides with the Tropic of Cancer at the solstice could well have led Oenopides, or someone shortly after his time, to realise that the ecliptic and the Tropic taken together implied a spherical earth.

(Pythagoras was a flat-earther, but his ideas -- weird as they are, and I’ll be talking about them more next time -- are actually somewhat more remarkable for the fact that he wasn’t a geocentrist. He believed that the earth, along with the sun, moon, and all the planets, revolved around ‘the central fire’, each of them a disc attached to one of many celestial spheres.)
and validated by Aristotle a couple of centuries later.
True. The relevant passage is Aristotle’s On the sky 296b-297b, where he outlines several kinds of empirical evidence for the earth’s shape.
If the earth really was a sphere, Eratosthenes could use his observations to estimate the circumference of the entire planet. Since the difference in shadow length is 7 degrees between Alexandria and Syene, that means the two cities are 7 degrees apart on earth’s 360-degree surface.
Eratosthenes hired a man to pace the distance between the two cities,
False. No evidence exists to suggest this. However, we do have evidence of Ptolemaic surveyors travelling into southern Egypt and Sudan decades before Eratosthenes, and writing books about it, including gnomon measurements taken at Syene and Meroë. Just the ones that we know of: Philon, an official during the reign of Ptolemy II who wrote an Aethiopica recording gnomon readings (New Jacoby 670); Dalion (FGrH 666), who went further south still; and Simonides (FGrH 669), who spent five years in Meroë, apparently as an ambassador of Ptolemy II.
and learned they were 5000 stadia apart,
Mixed. This is indeed the figure used as the basis for the final calculation, but how Eratosthenes arrived at 5000 is one of the more problematic bits of reconstructing what he actually did. (This is going to be a long bit: psych yourself up if you’re planning to read the whole thing.)

In a different context, Eratosthenes used the figure of 5300 stadia for both distances, that is, the distances between Alexandria-Syene and Syene-Meroë:
(Eratosthenes) states that the Nile is 900 or 1000 stadia to the west of the Arabian Gulf, and has a similar shape to a backwards letter N. For, he says, it flows northward from Meroë about 2700 stadia, then turns back to the south and the winter sunset for about 3700 stadia, and it almost reaches the same parallel as the Meroë region and makes its way far into Libya. Then it makes another turn, and flows northward 5300 stadia to the great cataract, curving slightly to the east; then 1200 stadia to the smaller cataract at Syene, and then 5300 more to the sea.
Could 5300 be the distance along the course of the Nile, and 5000 the distance along the meridian? No, that’s not it. In fact the distance measurements may be much older still -- by nearly two thousand years.

Gyula Priskin suggests in a 2004 article that the figure of 5300 stadia is a result of directly converting the traditional measurement of the length of Egypt, 106 iteru (recorded as early as the 1900s BCE in the White Chapel of Senusret I), into Greek units at the rate of 1 iteru = 50 stadia. Priskin emphasises that Eratosthenes was probably not personally responsible for this conversion, but relied on Egyptian measurements expressed in Greek stadia which had been originally based on the 1:50 conversion rate. This fits tidily with another piece of testimony about Eratosthenes’ methods:
Eratosthenes says that he records the distances that have been handed down, but does not validate them, reporting them as they have been received, although at times adding ‘by means of a more or less straight line’.
Priskin goes on to suggest that the variation between the two figures, 5300 stadia and 5000 stadia, comes from substracting the stretch of 300 stadia around Syene where the sun was directly overhead at noon on the solstice. I don’t think that sounds compelling -- though it could be true.

Another possibility is that we’re looking at two different standards for the stadion: there were many different reckonings. The usual standard quoted by ancient sources is 8 stadia = 1 Roman mile. The Greek stadion may have been variable and imprecise, but Roman measurements were precise to between three and four significant figures, so we know the length of a Roman mile very well indeed: 1478 m ± 3 m. (Here’s the classic source on the subject: Hultsch’s Griechische und römische Metrologie (1882), pp. 88-98.) This gives a ‘standard’ stadion of between 184.4 m and 185.1 m. It also coincides well with the Attic stadion of 184-186 m, whose length we know thanks to (1) the length of the racetrack at Athens, and (2) the ancient reckoning of 1 Attic stadion = 600 Attic feet.

Another reckoning of the stadion, Priskin argues, was used in an influential passage in the 5th century BCE historian Herodotus: Herodotus is vague, but Priskin reconstructs the reckonings he used as: 1 Egyptian schoenus (the Greek word for an iteru) = 400 Herodotean stadia = 24,000 Herodotean cubits. This gives a stadion of 175 m. Since Herodotus quotes this reckoning of the stadion in an Egyptian context, could Eratosthenes have been using the same reckoning sometimes? (As it happens, Priskin’s reconstruction coincides tolerably well with a figure quoted by a Byzantine source, Julian of Ascalon, who quotes the ‘stadion according to Eratosthenes’ as 1 Roman mile = 8.25 ‘Eratosthenean’ stadia. This comes out as either 178.3 m or 179.2 m, depending on whether Julian was thinking of the Roman mile before or after 200 CE, when its length changed slightly.)

And it so happens that 5300 × 175 m comes out to 927.5 km, very close to 5000 × 185 m = 925 km. If this is right, it implies that the distances quoted in Strabo 17.1.2, with 5300 stadia, are given in the Herodotean stadion; this would then be the unit that Eratosthenes used in his work the Geographica. And the distances that served as the basis for his calculation of the earth’s circumference, with 5000 stadia, would be in the standard stadion.

Actually I don’t find that very compelling either, even though it does sound good. Basically I don’t buy that the stadion was ever as precise as that. Extant sources that convert stadia to Roman miles quote lengths for the stadion that range between 157.5 m (Pliny NH 12.53, using Dreyer’s conversion rates) and 210 m (the ‘Ptolemaic’ stadion as quoted by Dreyer), or even more. Let’s just say: it’s very doubtful.
which is about 800 km.
False. See above about the imprecision of the Greek stadion. Using the ‘Herodotean’ stadion of 175 m reconstructed by Priskin, 5000 stadia would come out as 875 km; using the standard stadion of 185 m, it would come out as about 925 km. A measure of 800 km presumes a stadion that is 160 m long, much too short to be realistic. On one calculation, Eratosthenes’ stadion according to Pliny works out to 157.5 m, but see above: that is far shorter than any other ancient reckoning available to us. (It’s also incompatible with Eratosthenes’ stadion according to Julian of Ascalon, which works out to ca. 179 m).

More importantly, the traditional calculation of 157.5 m is based on a obsolete figure for the length of the Egyptian schoenus. Dreyer quoted the schoenus as equal to 12,000 royal Egyptian cubits of 0.525 m each. But subsequent scholarship has consistently shown that the schoenus was actually 20,000 royal cubits (see e.g. Priskin’s article). This would make the ‘Eratosthenean’ stadion according to Pliny come out to 262.5 m. 157.5 m is ludicrously low, 262.5 m is ludicrously high. Other measures for the stadion range between 181.3 and 192.25 m (figures quoted by the New Pauly): even the ‘Herodotean’ stadion is suspiciously short for that range. Pliny’s figure is not just suspicious, it’s wildly out of whack with absolutely every other known measure of the stadion. It must simply be wrong.
He could then use simple proportions to find the earth’s circumference. 7.2 degrees is one fiftieth of 360 degrees, so 800 km times 50 equals 40,000 km. And just like that, a man 2200 years ago found the circumference of the entire planet with just a stick and his brain.
Mostly true, aside from the 800 km bit which we looked at already. It’s the bit about ‘with just a stick and his brain’ that’s a problem. That should really say: ‘with (1) a stick marked by carefully measured gauge markings and kept vertical by a system of plumb bobs, (2) nearly two centuries of explorers and Ptolemaic surveyors testing the methodology of taking measurements with these sticks as a measure of latitude (3) and taking measurements at exactly the places he needed, (4) a traditional measure of the length of Egypt dating back nearly two millennia before his time, and (5) his brain’. Yes, it was a remarkable achievement, but he wasn’t a lone genius. He was most definitely standing on the shoulders of giants.

So there we have it. The count comes out as
True: 7
Mostly true: 2
Mixed: 3
Mostly false: 0
False: 6
The Business Insider video is a pretty even blend of truth and falsehood.

Does that sound reasonable? It shouldn’t. Let’s be clear: nearly half false is not a good thing. If I wrote a textbook that was half false, I would rightfully be fired and, I hope, barred from ever teaching in that field. Not good, Business Insider: not good. Maybe Carl Sagan and NASA shouldn’t be your sole sources for ancient history, a topic neither of them knows much about. Just a suggestion.