Quotations and history

Quotation isn’t history. But it can be a tool for suggesting history. Like any tool, it can be used -- and misused -- in lots of ways.

Films, books, and games have many tools for evoking a sense of history. In films like Braveheart (1995) and Robin Hood (1991, 2010) the main tool is false archaism: a mash-up of tropes from different historical periods, combined to create a flavour of oldness that has nothing to do with the actual setting. Tolkien’s tool is language: he uses invented languages shaped by historical sound-shifts, similar to ones that happen in real languages, to create a historical backdrop for his novels. In games like Tomb raider (1996) and Prince of Persia: the Sands of Time (2003), it’s about interactive archaeology. Lara Croft is always diving into trap-filled ruins; the Prince starts out in a supposedly Abbasid-era palace, and later descends into an underground ruin with cuneiform-style writing on the walls, suggesting something Assyrian or Achaemenid -- past layered upon past.

Quotations are another tool. Quotations don’t send a story into the past, they bring the past into the present. Often the idea is to claim a kind of inheritance from the past. Sometimes it’s ironic. Sometimes you just want to claim that Abraham Lincoln or Albert Einstein would have been on your side.

Quit, don’t quit -- noodles, don’t noodles -- you are too concerned with what was, and what will be. There’s a saying. Yesterday is history, tomorrow is a mystery, but today is a gift: that is why it is called the present.

-- Master Oogway (Kung fu panda, 2008)

Let’s look at some variants. I’ll stick to two themes: quotations in video games, and Alexander and his conquests.

Entrance to Rapture (BioShock, 2007)

Video games

BioShock

All good things of this earth flow into the city.

-- BioShock (2007)

This quotation is openly political. The line is indirectly based on Thucydides, History of the Peloponnesian War 2.38 -- Thucydides, that hero of alt-righters who either haven’t read him or haven’t understood him. (The Melian dialogue isn’t an instruction manual, guys, it’s a lesson about the immorality of power.)

In BioShock, the line is set over the entrance to Rapture, the underwater city where the game is set. It plays on a double meaning of ‘flow’. First, a boast about Rapture’s affluence, and the supposed superiority of its libertarian economic system; second, a quiet joke on the fact that Rapture is at the bottom of the Atlantic Ocean, and its resources come washing in on the ocean currents.

But the use of a classical allusion also feeds into Rapture’s ideological set-up. The founder of the city in the game, Andrew Ryan, intended the city to be a libertarian utopia. But, when the player actually arrives there, it turns out to be an objectivist nightmare, a monster from the lowest circles of Ayn Rand’s malevolence.

The quotation plays on the way that alt-righters often cast themselves as heirs of Greek and Latin culture. If you see people quoting taglines like si vis pacem para bellum (‘if you want peace, prepare war’, paraphrased from Vegetius), or μολὼν λαβέ (‘come and get them’: Herodotus on the battle of Thermopylae), or Deus vult (a modern Latin motto translated from a mediaeval French one associated with the Crusades), or calling themselves ‘the Spartans’ (Thermopylae again) -- well, then, you know exactly where they sit on the political spectrum. You know what colour their skin is, and what they would like to do to people from the Near East.

So when Rapture’s entranceway quotes Thucydides’ line about Athens at the height of its power and wealth, it seems that the fictional Ryan intended to evoke Athens’ ‘golden age’ and his own politics, both at once.

But it’s a bit of genius from the game’s writers, because it’s also ironic. Athens was obsessed with the purity of its democratic constitution. But if you know your history you’ll know that Athens didn’t owe its prosperity in that period to its democracy, but to its tyrannical imperialism and disregard for the autonomy of other states. The ‘greatness’ of Athenian democracy goes hand-in-hand with ideological puritanism, and flagrant violations of human rights. Just like Rapture.

The BioShock quotation isn’t directly from Thucydides: it comes from the film City hall. There Al Pacino speaks the line, as the mayor of New York: he attributes it to Pericles, as ‘the first and perhaps only great mayor’ --

All things good of this earth flow into the city because of the city’s greatness.

-- City hall (1996)

Thucydides’ wording is more literally ‘because of the size of the city, all things come into it from the whole earth’ (ἐπεσέρχεται δὲ διὰ μέγεθος τῆς πόλεως ἐκ πάσης γῆς τὰ πάντα). The minor distortion ‘good things’ for ‘all goods’ (τὰ πάντα) comes from Rex Warner’s translation of Thucydides --

Then the greatness of our city brings it about that all the good things from all over the world flow in to us ...

-- Thucydides 2.38 (tr. Warner)

I’m guessing the writers of City hall read Rex Warner’s version. Then, later on, BioShock inherited the phrasing.

An Aesop quotation about archery, without any context or relevance to the role of archery in the game (Civilization V, 2010)

Sid Meier’s Civilization

Some entries in the Civilization series (1991 to present) display quotations at moments when the player’s civilisation discovers a new technology or completes a world wonder. Many of them are attributed to ancient sources, and many of them are genuine.

That isn’t praise. Civilization generally has a casual approach to history. The quotations are there precisely to give an appearance of historical content, without any historical method. It’s a veneer of history-flavoured ganache on a dry cake. Some very bad misunderstandings of history have come from Civilization.

I can’t go through all of the quotations because there are too many. Ancient Greco-Roman sources account for sixteen quotations in Civilization VI (2016), seventeen in Civilization V (2010), and fifteen in Civilization IV (2005). Another four appear in the spin-off Alpha Centauri (1999).

As a first impression, generally the older games are the more careful, and pay more attention to nuance and context. The quotations in Alpha Centauri are exact quotations from Plato’s Republic, Symposium, and Aristotle’s Nicomachean ethics, and are chosen to reflect the ideological positions of factions within the game. In Civilization VI, the quotations are a blend of accuracy and inaccuracy, and are chosen merely because they’re roughly related in some way. These quotations are accurate --

‘And first Hephaestus makes a great and massive shield ... And he forged on the shield two noble cities.’ -- Homer (Civ VI, ‘Metal Casting’ technology)

= Iliad 18.478 and 490-491 (tr. Robert Fagles, uncredited)

‘At Rhodes was set up a Colossus of seventy cubits high, representing the Sun ... the artist expended as much bronze on it as seemed likely to create a dearth in the mines.’ -- Philo of Byzantium (Civ VI, ‘Colossus’ building)

= Philon of Byzantium, On the seven wonders §4 (tr. Denys Haynes, uncredited)

-- but the game obviously has zero interest in the purpose of Hephaestus’ shield, or in the irony that the historical Colossus collapsed in just a few decades. And these ones are just wrong --

‘It is the mark of an educated mind to be able to entertain a thought without accepting it.’ -- supposedly Aristotle (‘Education’ tech)

‘I sprang upon the swift ship in the form of a dolphin, pray to me as Apollo Delphinius; also the altar itself shall be called Delphinius and overlooked forever.’ -- supposedly Homer (‘Oracle’ building)

The first one starts out with some real Aristotle, but everything after the word ‘mind’ is made up. The second one isn’t Homer, and if you’re thinking it doesn’t make sense, that’s because they missed out part of the sentence.

It is characteristic of an educated man only to look for precision in each class of things so far as the nature of the subject admits. Getting an argument from likelihood from a mathematician would be like asking for theorems from a rhetorician.

-- Aristotle, Nicomachean ethics i.1094b.23-27 (§1.3)

Since, when I was first seen in the murky sea and I leapt onto the swift ship, I was in the form of a dolphin, so you should pray to me as Delphinian. And the altar will itself be ‘Delphinian’ and ‘Overlooking’ forever.

-- Cynaethus, Hymn to Apollo 493-496

Civilization is, in a limited way, good for the public understanding of history, to the extent that it gets people interested in history. But the game’s overall structure is antithetical to history. Every aspect of gameplay revolves around technologies, and every branch of the ‘tech tree’ is teleological, guiding every civilisation to a pre-determined goal, which looks exactly like the technologies available in present-day western countries -- or, in the ‘futurist’ stage of the game, something that looks like western science fiction.

The whole thing presupposes that anything that doesn’t get us towards modern Mechanized Infantry and Mobile SAM isn’t a valid part of history, and isn’t worth knowing about. The point of history, according to Civilization, is to lead towards us. Ever heard anyone ask ‘What has Africa done for us’? Or ‘Why study the Byzantines, when it’s the western Roman Empire that gave us roads, Vergil, and Catholicism’? I have. And that’s teleological history. Or, to put it another way: not history.

Right to left: Alan Rickman as Hans Gruber, James Shigeta as Joseph Takagi, Alexander Godunov as Karl (Die hard, 1988)

Alexander

Hans Gruber vs. Plutarch

‘And when Alexander saw the breadth of his domain, he wept, for there were no more worlds to conquer.’ {chuckle} Benefits of a classical education.

-- Hans Gruber, Die hard (1988)

The idea behind this ‘quotation’ is to cast Gruber (Alan Rickman) as an opposite to the hero John McClane (Bruce Willis). Gruber is educated, McClane relies on street smarts; Gruber is evil, McClane is good; Gruber wears a suit, McClane looks like a redneck for most of the film; Gruber is European, McClane is John Wayne (‘yippie-ki-yay’).

It’s a pretty straightforward message: education corrupts.

Now, I put ‘quotation’ in scare-quotes, because it isn’t one. ‘Hans baby’ may be an exceptional thief, but I’m afraid his classical education was shonky. In this case, though, I don’t think that’s what the writers intended. This misquotation is more a reflection of America under Reagan than it is of Gruber’s morals. The line echoes something Plutarch wrote (though Gruber doesn’t attribute it to Plutarch, as WikiQuote claims). Die hard gets its version of the line from The Twilight Zone -- ‘he cried because he had no more worlds to conquer’ (‘Of late I think of Cliffordville’, 1963) -- but both of them reverse it: it’s the exact opposite of what Plutarch says.

When Alexander heard Anaxarchos speaking about an infinity of universes, he wept. His friends asked what was wrong. He said, ‘Isn’t it worth weeping if there are infinite universes, and we haven’t yet become the masters of even one?’

-- Plutarch, On tranquility of mind 466d (§4)

Plutarch’s fictional Alexander doesn’t weep because he’s run out of conquests, he weeps because there’s too much to conquer and he can’t get the job done.

(The variation between ‘worlds’ and ‘universes’ is fine, by the way. The Greek word kosmos is just like ‘world’ in English: it can mean the universe as a whole, but also ‘the (human) world’, that is, earth. Plutarch’s Alexander is pretty clearly thinking about conquering the earth, not the entire universe.)

The point of this misquotation isn’t to showcase the laziness of the writers, though: no one cares about that. It’s the notion that education is a sign of moral depravity. And that’s a pretty clear reflection of Reaganism.

‘The Great’

Any time you call Alexander ‘Alexander the Great’, you aren’t doing it because that’s his due title. Because it never was. What you’re doing is supporting the Great Man theory of history.

That’s the theory that the course of history is driven by outstanding individuals, movers and shakers, heroes: Alexander, Caesar, Washington, Napoleon. Historians tend to be very, very hostile to that theory, and for good reason. The famous individuals of history don’t emerge into the limelight because they create limelight around themselves, but because they encapsulate historical ideas and forces that are coming to a head in their lifetimes. That doesn’t mean they aren’t exceptional individuals -- just that history doesn’t revolve around them.

Nowadays the Great Man theory mainly serves to keep the ‘right’ people at the centre of everyone’s attention: it makes sure people talk about rich powerful men. It’s a way to prevent you from thinking about women, minorities, and people who are enslaved or poor.

It’s especially artificial because it isn’t real. Wikipedia names Alexander

Alexander the Great (Ancient Greek: Ἀλέξανδρος ὁ Μέγας ...)

as if it’s a formal title, but there’s nothing to suggest he was called ‘the Great’ during his lifetime. Evidence for the nickname only starts to mount up 250 years after his death, towards the end of the 1st century BCE.

Here’s a whole article on the subject by Professor Catherine Rubincam. She agrees with earlier scholarship that ‘the Great’ was actually originally used for the Seleucid king Antiochus III, around 205 BCE, over 100 years after Alexander died. But after a thorough look at the evidence, she concludes that the popularity of Alexander’s title doesn’t come from Antiochus: its popularity comes from Roman writers talking about Alexander.

Rubincam thinks that process did begin around Antiochus’ time, shown by a reference to ‘great Alexander’ in one of Plautus’ plays (Mostellaria 775-777). I have my doubts. In Plautus it could just be a general term of adulation. Rubincam herself shows that the main support for ‘the Great’ as a title comes from books written centuries later, around the time of Augustus: Trogus, Livy, and Velleius Paterculus. Not that it’s conspicuous that Alexander isn’t called ‘the Great’ any earlier -- I’m just suspicious of granting so much weight to a passing reference in Plautus. Evidence of Alexander being called ‘the Great’ in Greek doesn’t start to pop up until another 200 years later. The earliest references are in Plutarch and Athenaeus, in the mid-to-late 100s CE.

References: Plutarch, Life of Aemilius Paulus 23.5; Life of Pyrrhus 11.2, 19.2; Life of Pelopidas 34.2; On the fortune of Alexander 336e9, 340b4, 341c11; Athenaeus, Deipnosophistae 6.19 p. 231 = FGrHist 76 F 37a. The reference in Athenaeus cites a much earlier author, Douris of Samos, but Douris is lost and Athenaeus’ text is a paraphrase, not a quotation. Another early author, Timaeus, is paraphrased in a similar way with a reference to Alexander ‘the Great’ in Longinus On the sublime 4.2.

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.

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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 3.3.24.3; 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 3.3.24.3; 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 3.3.24.1-2.
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.

References

• 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.

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.)

-- Pausanias 1.37.4

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.

References

• 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.

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.

True.

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,

True.

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.

True.

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.

True.

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.

-- Strabo 17.1.2

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’.

-- Strabo 2.1.41

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.

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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.

Pythagoras and the theorem

a2 + b2 = c2

Chances are you’ve heard this described as Pythagoras’ theorem or the Pythagorean theorem. Mathematicians are perfectly well aware that it’s a misnomer: Pythagoras didn’t prove it, and he didn’t discover it either.

We can be fairly confident that he was aware of the special case of the (3, 4, 5) triangle, which is the one illustrated above: a right-angled triangle with sides a = 3, b = 4 will have a hypotenuse (diagonal) of length c = 5 (32 + 42 = 52). Pythagoras may or may not have been aware that the general case is true. But he certainly wasn’t responsible for proving it.

Alas, we are stuck with the name. It’s probably not going away.

How did his name ever get attached to the equation? Well, it’s thanks to two pieces of ancient testimony. The earliest extant general proof of the theorem is nearly 300 years after Pythagoras, in Euclid’s Elements, book 1 proposition 47 (ca. 300 BCE). Euclid gives a perfectly satisfactory proof. But he doesn’t mention Pythagoras: for that link, we have to wait until more than half a millennium later. In the 200s CE, Diogenes Laertius claims that Pythagoras discovered it. Diogenes is not a reliable source, but we find corroboration in a much more reliable writer, the famous Neoplatonist philosopher Proclus: writing ca. 450 CE, he assigns the theorem to Pythagoras in his landmark commentary on Elements book 1.

So Proclus might be thought to carry some weight. Several other sources attribute knowledge of the (3, 4, 5) triangle to Pythagoras. However, there’s compelling evidence to show that it was that specific triangle that the Pythagoreans were interested in, and their interest was rooted much more in mysticism than in mathematics. In a previous post we’ve seen how Pythagoreanism could sometimes look more like a cult than a school. Here’s how the 2nd century CE author Plutarch describes the (3, 4, 5) triangle:

One might conjecture that the Egyptians hold in high honour the most beautiful of the triangles, since they liken the nature of the Universe most closely to it ... This triangle has its upright of three units, its base of four, and its hypotenuse of five, whose square is equal to that of the other two sides. The upright, therefore, may be likened to the male, the base to the female, and the hypotenuse to the child of both, and so Osiris may be regarded as the origin, Isis as the recipient, and Horus as perfected result. Three is the first triangular odd number: four is a square whose side is the even number two; but five is in some ways like to its father, and in some ways like to its mother, being made up of three and two. And panta (all) is a derivative of pente (five), and they speak of counting as ‘numbering by fives’. Five makes a square of itself, as many as the letters of the Egyptian alphabet, and as many as the years of the life of Apis.

Plutarch, On Isis and Osiris 373f-374a

a	b	c
3	4	5
Osiris	Isis	Horus
male	female	child
origin	recipient	result
first triangular number	first square	pente ‘five’ ~ panta ‘all’

This isn’t mathematics, it’s numerology and wordplay. Worse still, ‘the Egyptians’ is a spurious reference: we know of no Egyptian interest in right-angled triangles. We do know that Pythagorean teachings like reincarnation were often spuriously traced back to faux Egyptian mysticism. Other allusions to the above set of allegories can be found in Aristotle and other writers, and those sources confirm that the allegories originate in Pythagoreanism, not in Egypt (see Burkert 1972: 32-4, 40, 429).

So the attribution to Pythagoras originates with the Pythagorean cult’s investment in numerology, and its allegorical interpretation of the numbers 3, 4, and 5. The Pythagorean cult did have some rationalist offshoots, and their numerological interest extended to things that we would call mathematics, in the hands of intellecturals like Archytas of Tarentum. But evidence about Pythagoreanism in the early Roman era is heavily flavoured by the mysticism of the Neopythagorean movement, embodied by figures like Apollonius of Tyana. In that period, Pythagoras’ mystic interest in the (3, 4, 5) triple was reinterpreted as a more grandiose claim: that Pythagoras was responsible for discovering the general proof. Hence the late story that we find in Diogenes Laertius and Proclus.

So who should get credit for the proof? Reportedly there are getting on for 400 distinct proofs. We’re not going to look at how any of the proofs work: go read the Wikipedia article, it’s great for that kind of thing. There are some pretty simple proofs. (Even the proof given by Euclid isn’t too hard to follow.)

Pythagorean primitive triples for a, b < 700. (The ‘gaps’ would be filled in if we included a subset of non-primitive triples.)

First, a technical term. A Pythagorean triple is a solution to a2 + b2 = c2 such that all of a, b, and c are whole numbers. As it happens, there are infinitely many Pythagorean triples, starting from (3, 4, 5), and going on to (5, 12, 13), (8, 15, 17), (7, 24, 25), (20, 21, 29), and so on. You can trivially generate an endless list of triples by multiplying one of these by a whole number: so (3, 4, 5) can become (6, 8, 10), (9, 12, 15) and so on. But even if we exclude these and confine ourselves to triples that have no common factors, called ‘primitive’ triples, there are still infinitely many. Just for c < 1000 there are 144 primitive triples.

There are two main contenders for the honour of the earliest proof.

(1) Scribes of the Old Babylonian period ca. 1800 BCE were definitely aware of the relationship between the diagonal and the sides of a rectangle. Two tablets, YBC 7243 and YBC 7289, give values for the diagonal of a unit square, with an accurate value for √2 to three sexagesimal places. Other tablets, like BM 96957 + VAT 6598 (text here), contain pedagogical illustrations of how to approximate the diagonal of a rectangle, using a method that Heron of Alexandria was still using for square roots in the 1st century CE. (For more details, see Fowler and Robson 1998.)

Perhaps most famously — or infamously — the tablet Plimpton 322 can be interpreted as giving a table of fifteen Pythagorean triples. Elaine Robson (2001, 2002) has shown that this is a misinterpretation: the tablet is really a set of pedagogical exercises on calculating reciprocals.

The tablet isn’t premised on the idea of the Pythagorean equation, but it still shows awareness of the equation. The table headings refer to the ‘square of the short side’ and ‘square of the diagonal’, implying right-angled triangles. So the Babylonians were well aware of the relationship between this technique and the right-angled triangle.

YBC 6967: This diagram illustrates an Old Babylonian exercise on reciprocals. See Robson 2001: 183-4 for its original phrasing. As Robson has shown, the method also underlies the table in Plimpton 322. Given two reciprocals n and p, and given that the difference between n and p is 7, what are the values of n and p? Note that in Babylonian notation, np = unity can be either 1 or 60, depending on context.

In modern notation we would do this with a quadratic equation: n = p + 7, and np = 60, therefore p2 + 7p – 60 = 0. (The solution is left as an exercise for the reader.)

The Babylonian procedure is geometrical, not algebraic. First mark off the difference, n – p, along the length of n and divide it in two: in this example, n – p = 2q = 7. Then cut-and-paste one of the smaller rectangles to produce the L-shaped figure in the third step. Calculate r = √(O + Q) numerically. The solutions are then n = r + q/2, p = r – q/2.

Plimpton 322 gives figures based on this method. The four columns give values for: (1) R/O; (2) q; (3) r; and (4) line numbers. They are ordered in decreasing value of R/O.

It is easy to mistake the second and third columns of Plimpton 322 for partial Pythagorean triples, since this method has the side-effect of generating the equation O + q2 = r2. As O = unity, it is automatically a square, so this has the same form as a2 + b2 = c2.

The exact same geometrical procedure appears in Euclid, Elements book 10, proposition 29, lemma 1, as a method for generating two squares whose sum is also a square. The only difference is that Euclid does not treat O as unity, and instead posits in advance that n and p are similar plane numbers, i.e. numbers whose prime factors form exact pairs, so that O = np is a square; and n and p have the same parity, so that n - p is even and q is an integer. As a result his equation has the form (√O)2 + q2 = r2.

(2) Euclid, Elements. The Old Babylonians may have been aware of the equation, but no proof of it survives from that era. We also find clear evidence that the equation was known in early India, in the Vedic Śulba sūtras — but still no proof. In Han China, we find proofs for the specific cases of the (1, 1, √2) and (3, 4, 5) triangles; but no general proof for all right-angled triangles.

So our earliest extant general proof is in none other than good ol’ Euclid (who is pre-Han anyway). The relevant section is Elements book 1, proposition 47. It may even be that he’s actually the one who devised the proof. Remember how Proclus attributed the theorem to Pythagoras? Well, pay closer attention to what Proclus actually says. Here’s a translation:

When we listen to people who want to record events of the past, it is possible to find them attributing this theorem to Pythagoras, and calling him ‘ox-sacrificer’ for the discovery. I am impressed by those people who first understood the truth of this theorem, but I admire still more the Elements author: not only because he tied it fast [κατεδήσατο] through a crystal-clear proof, but also because he published a still more general one than this, in irrefutable scientific terms, in book 6.

(The ‘still more general’ proof is book 6, proposition 31, which shows that the relationship holds for any similar rectangle on a, b, and c, not just squares.) Notice what he says? The proof is Euclid’s; only the discovery is attributed to Pythagoras. Though in reality, as we have seen, for Pythagoras the ‘discovery’ was numerology, not mathematics.

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How to decide between these two? Should we simply split the honour, crediting the Babylonians with the discovery, and Euclid with the earliest surviving proof? Any self-respecting historian should bridle at the notion that we have to view the past in terms of how we have benefited by it. And justly so. It’s not as though the only purpose of the Babylonians was to invent theorems for our benefit. Still, if we’re going to use this equation, it kinda makes sense to have a name for it. Splitting the honour seems reasonable to me. The equation is a Babylonian equation; the earliest extant proof is Euclid’s. Either of them strikes me as better than giving Pythagoras credit for something that he neither discovered, nor popularised, nor proved.

References

• Burkert, W. 1972. Lore and Science in Ancient Pythagoreanism. Harvard University Press. (Revised form of the 1962 German edition.)
• Fowler, D.; Robson, E. 1998. ‘Square root approximations in Old Babylonian mathematics: YBC 7289 in context.’ Historia Mathematica 25: 366-78.
• Robson, E. 2001. ‘Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322.’ Historia Mathematica 28: 167-206.
• Robson, E. 2002. ‘Words and pictures: new light on Plimpton 322.’ American Mathematical Monthly 109: 105-20.