Friday, 14 June 2019

Titans and Olympians

The twelve Olympians are the most important gods in the Greek pantheon. There’s some variation in their membership, depending on who you read. But there are generally twelve, and they’re always headed by Zeus, along with his brothers Poseidon and Hades, each associated with a third of the cosmos (sky, surface, underworld).

Greek myth has other bunches of divinities too. Some are minor local divinities: river gods, nymphs, and so on. Some can be just about as important as the Olympians, like the Dioskouroi (Castor and Polydeuces) or the Great Gods of Samothrace. And then there’s the Titans.

With the Titans, it can be tempting to think we’ve got two orders of gods: elder gods and younger gods, Titans and Olympians.
The Disney version of the Titans (Hercules, 1997)
No no no, not like the Titans in the Disney Hercules. Not like Clash of the Titans either -- a film that’s rather conspicuous for not actually having any Titans in it. (That applies to both the 1981 original and the 2010 remake, by the way.)

If it’s a popular depiction you want, you’ll find a closer match in Rick Riordan’s series of Percy Jackson novels. There, as in ancient Greek myth, the Titans are the arch-enemies of the Olympians, but they’re also the Olympians’ ancestors and parents.

Titans and Giants

Actually there’s one area where the Disney Hercules does represent ancient sources very well. It does an excellent job at steering around a confusion between Titans and Giants -- a common confusion among ancient writers.

The Titans and Giants were both colossal beings who fought the Olympians. The Titanomachy is the primordial war between the Olympian gods and the Titans, cosmic order vs. cosmic chaos. After ten years of fighting the Olympians finally win, aided by the Cyclopes and the Hundred-Handers, and they banish the Titans to the eternal void of Tartaros, the bottomless pit at the bottom of the cosmos, beneath even Hades. The Gigantomachy is the battle between the Olympians and the Gigantes or ‘earth-born ones’, spurred to attack Olympus by their mother Gaia: this time the Olympians are aided by the hero Heracles.

So we’ve got one battle at the beginnings of time, and one in the relatively recent legendary past, just one generation before the Trojan War. And yet ancient writers regularly mix them up. Several sources refer to a ‘Titanomachy’ poem as a ‘Gigantomachy’; in Orphic myth, Dionysus is sometimes killed by Titans, sometimes by Giants; one source glosses the Titans as 'Giants beneath the earth’ (sch. Eur. Hec. 471).

The general impression is that the Titanomachy was at root a poetic narrative, while the Gigantomachy belonged more to the visual arts. There were at least three Titanomachy poems: they seem to have had limited success, and the complete poems have all been lost, but we still have an episode in the Hesiodic Theogony dealing with the story. The Gigantomachy, by contrast, had no poetic treatments that we know of, but it was central to the decorations of two of the most important temples in the Greek world: the temple of Apollo at Delphi, and the Parthenon in Athens.

If you know the Disney film you’ll see how it navigates this ancient confusion. Zeus has imprisoned the Titans in Tartaros, as per the Titanomachy; but they get released, and Hercules intervenes to defeat the bad guys and save the Olympians, as per the Gigantomachy. The film synthesises both variants without ever dragging attention away from its main story. Rather well thought out, really.

Which Titans?

Most of the Titans aren’t even particularly evil. The trio of Kronos, Iapetos, and Okeanos are generally grouped together as the ones opposed to the Olympians. The Homeric Iliad groups Kronos and Iapetos together, imprisoned in Tartaros:
                  ... the nethermost extremes
of earth and sea, where Iapetos and Kronos
sit and never enjoy the rays of Hyperion the Sun,
nor the winds, and deep Tartaros is around them.
-- Iliad 8.478-481
But you notice Hyperion isn’t imprisoned with them? -- even though he belongs to the same generation of divinities. So: are only some Titans imprisoned? Or do only some divinities of that generation count as ‘Titans’? That’s not how Hesiod thinks of it (Theogony 205-6 makes them all ‘Titans’; at 424 Hekate seems to be counted as an ex-Titan).

There are plenty of Titans moseying around outside Tartaros. Elsewhere in Homer we find Phoibe, the moon, shining in the sky too. Dione appears on Olympus in Iliad book 5. Mnemosyne (‘Memory’) regularly gets invoked by poets. In Hesiod, Prometheus and Epimetheus are obviously still kicking around after Zeus becomes king of the universe -- though Prometheus goes on to be imprisoned too, in a separate story. Hekate gets to keep the prerogatives she had from the Titans.

Even Kronos himself wasn’t always the bad guy. Or, at least, not simply the bad guy. Athens and Rhodes celebrated festivals in honour of Kronos -- and, given that these two places belonged to distinct ethnic groups within the Greek world, that kind of suggests a pretty widespread observance. There were occasions, separate from the festivals, when cakes were offered to Kronos in Athens and in Elis. We know there were temples dedicated to Kronos at Athens and Olympia, both of them in precincts of Olympian Zeus.
For the Kronia festival in Athens and temples of Kronos, see New Pauly s.v. ‘Kronos’. For the Rhodian festival see Theodoret, Cure of the Greek maladies 7 (p. 108,46 = p. 294 Gaisford).

Van Dongen 2010: 192 thinks that Kronos and co. were originally separate from the Titans, pointing out that the Titans aren’t named in the Hesiodic Titanomachy. I don’t buy that. First, the idea of separating a single myth into two distinct ‘original’ myths is too close for comfort to the ‘two cultures’ interpretation I look at below. Second, the story is stable enough across both Hesiod and the Iliad (cf. Il. 5.897-898, 8.478-481, 14.278-289, 15.225) to point solidly to a much earlier origin.
Why celebrate Kronos, the arch-nemesis of Zeus? Not an easy question. Some modern theorists go for an agricultural explanation: the Kronia was a harvest festival, the Titans were harvest gods, and that’s why Kronos uses a sickle to cut off Ouranos’ genitals. Well, supposedly. I’m skeptical: I have a sneaking suspicion that some theorists have been taking their ideas about Kronos from Saturn, his Roman counterpart.

There are other ways you could interpret a festival in honour of the enemy of the gods. It might be a celebration of his imprisonment in Tartaros. It might be apotropaic (‘let’s honour Kronos so he doesn’t come back’). I’d prefer not to assume in advance that it’s just a peaceful, innocent harvest festival -- not unless there’s some evidence I’m just unaware of.
Kronos as depicted in the execrable film of Percy Jackson and the Sea of Monsters (2013). But read the books instead -- please, for the love of Zeus, read the books instead. (I hate that Surtr in Thor: Ragnarok reminds me of this godsawful film.)

Two families of divinities?

When you see a pantheon with two ‘orders’ of gods, one popular interpretation is that two pantheons, from different cultures, have been combined. For example: we might say that at some point there was a Minoan pantheon consisting of just the Titans, and when the Mycenaeans conquered the Minoan civilisation, they imposed their own gods -- the Olympians -- as a kind of superior caste. This is wrong, by the way.

But this binary interpretation, that Olympians and Titans originated as a superimposition and a substrate, had a lot of currency among theorists of the early 20th century. Here’s how Walter Burkert puts it.
Historians have long sought to understand Greece and Greek religion as a synthesis of an indigenous substratum and Indo-European superimposition. How far this idea holds good and can be verified in detail is another question. Global dualisms which exaggerate the distinctino between Indo-European and non-Indo-European assert themselves all too easily: male and female, patriarchy and matriarchy, heaven and earth, Olympian and chthonic, and intellect and instinct. The interaction of the two poles is then supposedly reflected in Greek religion as the new gods overthrow the Titans, or as the Indo-European Sky Father takes the mediterranean Mistress as his bride.
-- Burkert 1985: 18 = 2011: 37.
In the work of Georges Dumézil, this division takes on classist tones too: the newer gods are worshipped by the upper class, the older gods by the proles. That seems to be coming more from the Romans than from anything Greek: the Romans with their division of patrician and plebeian, and the worship of Jupiter and Ceres.

younger gods elder gods
Olympians Titans
Mycenaean Minoan
Indo-European non-Indo-European
patriarchy matriarchy
celestial earthly
intellect instinct
culture nature
upper class lower class

Important note: everything about the above table is wrong. (We’ve got no reason to think of the Minoans as matriarchal. That idea still has some currency, thanks to Friedrich Engels, but it’s an extremely tendentious interpretation of very indirect, and very thin, evidence. It comes from Johann Jakob Bachofen’s 1861 book Das Mutterrecht: Bachofen’s theory of an even earlier ‘hetairistic’ phase, where everyone was sexually promiscuous, kind of suggests that the whole idea has its roots in his sexual fantasies. No archaeologists or anthropologists have taken it seriously for many decades.)

But this theory boils down to a thinly-veiled nationalism. ‘Indo-European’ versus ‘non-Indo-European’? Just say what you mean: Aryan versus Untermensch.

(Incidentally, Burkert goes on to point out that when it comes to ritual practice, it’s earthly libations that are related to Indo-European religion, while the rising smoke of Olympian sacrifices is more closely linked to Semitic practices.)

The idea that two castes of divinities reflect two ethnic groups has been suggested for other bodies of myth. In Norse myth, figures like Gro Steinsland have suggested that the two orders of divinities -- the Æsir, with Odin, Thor, Tyr, etc., and the Vanir with Njord, Freyr, and Freyja -- are a result of two distinct mythological traditions coming into contact with each other. So the war of the Æsir and the Vanir supposedly reflects a historical war.

As with the Olympians and the Titans, it may sound like a reasonable working hypothesis. Let’s just emphasise the word hypothesis, though. There’s never any direct evidence to support this kind of thing. And there’s good reason to doubt it.

The parallel between the Greek and Norse pantheons sounds suspiciously like something systematic: it’s integral to the design, baked into each pantheon from the start. That impression gets even stronger if you draw comparisons to other pantheons: Indian myth has the devás warring against the ásuras, Irish myth has the Tuatha Dé Danann as successors to the monstrous Fomorians.

pantheon younger gods elder gods
Greek Olympians Titans
Norse Æsir Vanir
Hurro-Hittite Kumarbi karuilies siunes
Indian Devas Asuras
Irish Tuathe Dé Danann Fomorians
Mesopotamian gods ilani kamûti

For more on this, see West 2007: 162-164.

We certainly don’t have enough evidence to draw genetic links between any of these cases. If the idea of two orders of gods is one that the Greeks inherited, it’s best to assume it came via the Hittites. The Hittite former gods, or karuilies siunes, are incarcerated in the underworld, and there are usually twelve of them, just like the Titans.

But that isn’t to say we know how the myth developed. The Greek and Hittite pantheons have the closest link of any pair in this table, but no one’s going to suggest that Hesiod had a copy of the Kumarbi cycle in front of him. The date and means by which Anatolian and Near Eastern mythical patterns made their way to Greece are obscure.
There’s a similar sentiment in Clay and Gilan 2014: 5-6. Van Dongen 2010 suggests a relatively late date for mythical narratives spreading from Anatolia to the Greek world, with contact between Greeks and Phrygians and Lydians around the 8th century: personally I’d be very happy with a much earlier date, even in the Bronze Age. We have Greek gods in the Bronze Age, but alas, no direct evidence of Titans. See also Bachvarova 2016 for a more luxurious discussion.
I find the parallels compelling enough to accept that a two-generation structure is generally going to be something baked into the pantheon, not a result of two cultures having a war.

But not compelling enough to conclude there are genetic links. M. L. West, too, thinks the parallels are ‘suggestive’, but not so close ‘as to make the hypothesis [of a common heritage] ... irresistible.’ OK, for the Olympians vs. Titans, we’ve got Kumarbi and the Hittite ‘former gods’ to point to as a possible influence. But we don’t have anything like that for Indian, Irish, or Norse myth. There, the ‘two orders of gods’ structure seems more likely to have been created from scratch, rather than inherited from older traditions.
Another view of the Disney Titans -- this time, from the game Kingdom Hearts III (2019). Here Hercules isn’t teaming up with the Olympians, but with (left to right) Goofy, Sora, and Donald Duck. I wonder what Hesiod would think.
That doesn’t mean we have to revert to the ‘Mycenaeans absorb the Minoan pantheon’ model, or the ‘Æsir absorb the Vanir’ model -- let’s call it the ‘two cultures’ model. That model isn’t impossible. But it is euhemerism, and euhemerism has never been a useful guide to any myth’s development over time.

Another good reason to be skeptical of the ‘two cultures’ model is that when people are interested in the elder gods, and don’t know much about the historical background, they regularly go for the exact same interpretation. It’s a repeating pattern -- just like the ‘two orders of gods’ is a repeating pattern. Myths are really good at falling into similar patterns, whether or not they have a genetic relationship to each other.


  • Bachvarova, M. 2016. From Hittite to Homer. The Anatolian background of ancient Greek epic. Cambridge University Press
  • Burkert, W. 1985. Greek religion. (Translated by John Raffan.) Blackwell.
  • ---- 2011 [1977]. Griechische Religion der archaischen und klassischen Epoche, 2nd edition. Verlag W. Kohlhammer.
  • Clay, J. S.; Gilan, A. 2014. ‘The Hittite “Song of emergence” and the Theogony.’ Philologus 2014: 1-9.
  • van Dongen, E. W. M. 2010. Studying external stimuli to the development of the ancient Aegean. The ‘Kingship in Heaven’ theme from Kumarbi to Kronos via Anatolia. PhD dissertation, UCL.
  • West, M. L. 2007. Indo-European poetry and myth. Oxford University Press.

Thursday, 13 June 2019

Bad Latin in the movies: Constantine (2005)

Keanu Reeves. Yup, he’s hot stuff right now. And his films do seem to have a fair bit of Latin. His latest, John Wick Chapter 3: Parabellum (2019), has a Latin subtitle, a short form of ‘if you want peace, prepare war’ -- a motto favoured by the alt-right, and also Parabellum was the official brandname of the Luger pistol.

Looking back further: in the first John Wick (2014), the gold coins used by professional assassins have Latin inscriptions -- on one side ens causa sui, ‘existing for its own sake’ -- I’m not sure that’s the intended meaning, but it’s what it does mean -- and on the other ex unitae vires, an error for ex unitate vires ‘strength from unity’. In The Matrix (1999), the Oracle has a Latin motto over her kitchen door, temet nosce ‘know yourself’. And Bill & Ted (1989) -- well, there’s no Latin, but we do have Socrates speaking ancient Greek. In a British accent.
John Constantine consults the archangel Gabriel. Left: Hellblazer 43 (1991); right: Tilda Swinton and Keanu Reeves in Constantine (2005).
And then there’s Constantine (2005), loosely based on a storyline in the comic book Hellblazer. Yes, there’s the good old tradition inherited from The Exorcist of repeating ‘in the name of the father, the son, and the holy spirit’ in Latin as an incantation for dispelling demons.

But there’s a more substantial chunk too. At one point we get to see a passage from a demonic bible, with an extra chapter at the end of 1 Corinthians. The original text, Paul’s letter to the church at Corinth, was in Greek ... but, well, I guess demons do love them some Latin.

Here’s the text shown on screen.
The surrounding text has nothing to do with 1 Corinthians, by the way. The verse above the chapter heading is actually Isaiah 1.23.
Ad Corinthios XVII

Amor enim patris modo Satanae possessionis, atque potestatis et voluptatis eius excessus fuit. Atque in lumbis et ex lumbis eius conceptus est filius. Filio de quo fierit damnatio mundi. Hoc modo solo homines orbis terrae verum fatum suorum, certam vocationem, verum dolorem sub calce veri Domini explere poterunt per potestatem veri fili poterunt. Animas enim suas homines in fornace semper ardente sub pedibus verorum angelorum invenient.

Filius, in lucis ardore Patris conceptus, in umbra eius qui cecidit naturus est, nec umquam luce creatoris contaminatus erit. Et lux ignis veri sui patris flammae ardentes in cordibus hominum erint.

Peccata patris modo peccatis fili excessa erint.

Mammon erit nomen eius qui caput patris percutuit. Vires suae desuper patrem descendunt et potentia sua tanta erit ut lucem soli extingueret. Et tenebrae super Terram et super homines descendent.
The interpretation given out loud in the film is related to the Latin text, but isn’t a direct translation.

This isn’t exactly good Latin. OK, I’ve seen worse in students’ homework. This is good enough to work out the intended meaning -- mostly -- and it’s certainly way better than anything you’d get from Google Translate. (That’s setting a very low bar: Google Translate is notoriously bad at Latin. I guarantee you are much, much better at Latin than Google is, even if you’ve never studied any Latin at all.)
Never, ever, ever use Google Translate for Latin. Here’s its attempt at the first bit of Latin I ever read. This is day one material: you’ll be able to follow it even if you’ve never considered learning Latin.
But it’s very obviously translated from English, and translated by someone with a very shaky idea of verb tenses and noun cases. Here’s my best effort at working out the intended meaning:
For the love of the father was exceeded only by Satan’s lust for possession and power. And in his loins and from his loins a son is conceived. From that son will come about the damnation of the world. In this way alone will humans be able to fulfil the true destiny of their world, its assured calling, its true agony, beneath the heel of their true Lord: through the power of his true son they will be able (to do this). For humans will find their souls in a furnace, ever burning, beneath the feet of the true angels.

The son, conceived in the heat of his Father’s light, is to be born in the shadow of him who fell, never tainted by the light of the creator. And the light of the true fire of his father will be flames burning in people’s hearts.

The sins of the father will be exceeded only by the sins of the son.

Mammon will be his name, the one who beheaded his father. His strength descends upon his father, and his power will be great enough to extinguish the light of the sun. And shadows will descend upon the Earth and upon humans.
There’s an awful lot of mistakes in the Latin. Not historically plausible mistakes, mind: we’re talking classic mistakes made by English-speakers who just don’t get how noun cases work.

The first sentence, for example, is mangled enough that I’m not confident it was meant to say what I wrote in my translation. Here’s a literal version of what the Latin actually says:
For the love of the father had been had exceeded only of Satan or of possession and of power and of his desire.
Yeah. And verb tenses are all over the place. The phrase excessus fuit would be a kind of more-pluperfect-than-pluperfect, if that were a thing. My impression is that the translator forgot that Latin doesn’t really do tenses with auxiliary verbs, and shoved in English expressions in their place. In the second paragraph, contaminatus erit is literally ‘he will have been tainted’, not ‘he will be tainted’, which is what I think the writers were going for. Naturus est is clearly a translation of a faux-biblical English phrase ‘he is to be born’: authentic Latin would just use the future nascetur.

There are other problems. They’re all typical of an English speaker with dodgy Latin.

Reflexive possessives are used where ordinary possessives ought to be used. The phrase ‘of the son’ (paragraphs 1 and 3) is misspelled, so that the text actually means ‘oh my son!’. When humans ‘find’ their souls in a furnace (paragraph 1), the choice of words implies that they hit upon a research finding, not that they awake to a realisation. In paragraph 2, the ‘light of the true fire’ is singular, but the verb is plural -- another classic student’s mistake, agreeing with the complement instead of the subject. In paragraph 4 the Latin for ‘sun’, soli, is given a second-declension form when it should be third-declension.

Just for the sake of it, here’s a re-written version of the passage with some better Latin.
Amor enim patris solo Satanae possessionis atque potestatis voluptate exceditur. Atque in lumbis et ex lumbis eius concipitur. Quo de filio fiet damnatio mundi. Hoc modo solo homines verum fatum mundi sui, certam vocationem, verum dolorem sub calce veri Domini explere poterunt, per potestatem veri filii. Homines enim animas suas in fornace semper ardenti reperient sub pedibus verorum angelorum.

Filius, in lucis ardore Patris conceptus, in umbra illius qui cecidit nascetur; nec umquam luce creatoris contaminabitur. Et lux ignis veri sui patris erit, flammae ardentes in cordibus hominum.

Peccata patris modo peccatis filii excedentur.

Mammon erit nomen eius qui caput patris percutiet. Vires eius desuper patrem descendent et tanta erit potentia eius ut lucem ipsius solis extinguat. Et tenebrae super terram et super homines descendent.
You just can’t have demon stuff going on without some bad Latin. (Rich Burlew, The Order of the Stick 635 [2009])

Monday, 13 May 2019

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


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.
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)


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.

Wednesday, 20 March 2019

Newly discovered essay by an Analyst scholar

Tucked inside the back cover of a book recently acquired by the Victoria University of Wellington library was a short paper on the authenticity of certain parts of the Homeric Odyssey. I reproduce below a copy of this idiosyncratic essay, clearly composed within the Analyst school of thought. Regrettably I have not yet succeeded in identifying the author.

A word to the wise: no, this isn’t real, it’s a parody. I have to make that clear, because it’s esoteric enough that I bet many people wouldn’t spot how ridiculous it is. This essay tries to capture how it genuinely feels, to me, when I read stuff written by Analysts. I wrote it about a decade ago, and found it while sorting through some old files.

Helen tells Telemachus the story of Odysseus as a beggar (A. Boizot and A. Clément, ‘Telemachus at the court of Menelaus’, 18th cent.)
It was known already to Zoilos that repeated passages in the Homeric epics are indicative of the hand of a lesser poet intruding his desires and designs upon the poems in a singularly unimaginative and banal way. From Aristarchos onwards, who produced the first serious edition of the epics, this simple observation has risen to become a fundamental principle of the scientific study of Homer.

In more recent years it has become progressively and continually more obvious that not only individual lines, but whole scenes, physical settings, and even the very characters of the poems, become suspect under this light, the most obvious instance being perhaps the farm of Laertes in ω, which is a naïf repetition of that of Eumaios in ξ, modified only to the extent of making it a farm for fruit rather than animals. But also in the Odyssey we find the oxherd Philoitios, who is nothing more than a reflection of the swineherd Eumaios, the two not even being clearly separated in the scene where Odysseus reveals himself to them in φ; similarly the nursemaid Eurynome is a poorly motivated duplicate of Eurykleia, and Kalypso a copy of Kirke. (This last duplication was so self-evident even to the ancients that the negligible Diktys actually made them sisters ruling over neighbouring islands.) In all such cases we see the signs of late interpolations, which postdate the original Odyssey, that is to say, the elder compilation of three lays by a relatively talented Ionian poet in whose hands the epic attained its peak of quality, such that we all now rightly regard this phase of the poem’s development, the work of the so-called redactor, as the genuine Odyssey, as has been shown in many places.

One duplication, however, poses problems. It has always been difficult to determine what exactly has happened in the case of Helen and Penelope. The two show very strong parallels: Helen’s marriage to Menelaos was preceded by being courted by an army of suitors; so Penelope too has to be courted by an enormous group of suitors. Uniquely for a woman, Helen possesses κλέος and ἀρετή; therefore so too must Penelope, so that these two women alone in Homer possess those qualities. Helen is stolen away by an intruder and has to be won back by her proper husband; only a modest change has been made in the case of Penelope, namely that Odysseus’ return anticipates the stealing away. But Penelope was such a prominent character in one of the lays that predate the Ionian phase of the Odyssey that it has so far been difficult to imagine what the return of Odysseus looked like before her character was added.

Some passages demonstrate such strong similarities that no reservations can rationally be sustained. The most astounding such passage is δ 244-59, where Helen recalls the incident of Odysseus stealing into Troy, how she recognised him immediately but chose not to betray him. In this passage we find explicitly stated that Odysseus entered the city disguised as a beggar; that Helen alone saw through his disguise; that he cleverly evaded her questions; that she made arrangements for a bath for her disguised guest; that she swore not to reveal him to his enemies; and that afterwards there was lamentation among the other women at what had happened. When we consider that these events are all too clearly identical to those in τ, the late-night conversation between Penelope and Odysseus -- remembering that in the pre-Ionian phase of the Odyssey, Penelope likewise was the first to recognise Odysseus, as evidence internal to τ shows, and that a later hand disguised this fact, ineptly, to make way for a second recognition in ψ -- no doubt can remain that one of these two is an inferior copy of the other.

The passage spoken by Helen cannot be an interpolation. Aristarchos could find no fault with it, and indeed corrected Zenodotos’ incompetence in misinterpretating δέκτῃ as a name in 248. The only clear interpolation in the passage is 249, shown by the neologism ἀβάκησαν. But the passage as a whole is most ancient: the most important proof of this is the variants in 252. There we find λόεον corrected to Ionic ἐλόευν, and ἔχρισ’ ἐλαίῳ (which must originally have been ἔχρισε ϝ’ ἐλαίῳ) corrected to Ionic χρῖον ἐλαίῳ. Only the Ionian redactor could be responsible for these adaptations into the Ionic dialect. Therefore, the line predates the Ionian compilation.

Thus it is not a matter of deciding whether this passage is copied from the lay of the reunion of Odysseus and Penelope. Rather, the antiquity of this passage means that it is a matter of whether the entire character of Helen is copied from Penelope, or vice versa.

Faced with such a choice, no doubt can be entertained: Helen is the original, and Penelope the copy. Without Helen, the entire basis for the Trojan War -- and the reason for Odysseus being absent in the first place -- would be gone. The figure of Penelope, then, postdates Helen: she is nothing more than a meaningless redundancy, with no true role in the story of Odysseus’ return.

What, then, prompted the poet who created the lay of the reunion of Odysseus and Penelope (which, in the hands of the redactor, became ρστ) to copy and adapt the figure of Helen in this way, and at such an early date? It can only be that Penelope was a figure already established in myth in a different context. The missing datum is that Penelope is borrowed from Arcadian cult. For this our earliest source is Apollodoros. She was worshipped in Mantineia as the mother of the god Pan; in later times, after the rise in importance of Homeric epic, Arcadian legend was rewritten to accommodate the Odyssey. In the wake of Homer, the devout worshippers refashioned their own Penelope, as though she had originally been Odysseus’ wife and became the object of worship only later, after Odysseus found that she had committed adultery and expelled her from his house, after which she came to Arcadia and there gave birth to Pan.

This conclusion has an impact beyond just ρστ. The story of Odysseus’ return originally featured no Penelope, as we have seen; but from other considerations, as is well known, Telemachos is also a late addition (the Telemachy was added after the redactor’s compilation), and Laertes even later (ω is of course the latest part of the Odyssey). The only remaining member of Odysseus’ household is the slave Eumaios; but even he should be rejected, as his status indicates an ethos of slavery that obviously belongs to the period of Greek colonisation.

In short Odysseus’ household, as originally conceived, contained no one for Odysseus to return to. The original story, therefore, was not about Odysseus’ return but rather about an invasion -- about a foreigner arriving and attacking the local inhabitants, killing them, and claiming the throne. This explains certain problems in the conflict between the Odysseus and the ‘suitors’. In the Odyssey as we have it, the suitors are guests under the protection of Zeus, and Odysseus’ slaughter of them should be viewed as a monstrous crime; but in the Ur-form of the tale they enjoyed no such protection, and so Odysseus could attack and kill them without any impropriety, and no violation of Greek morals.

Given the strong ties that Odysseus has with northwestern Greece -- Lykophron records that there were oracles of Odysseus among the Eurytanians and Trampyans, Bouneima near Trampya was founded by Odysseus, and the epithet ‘Alkomenean Odysseus’ surely refers to the Alkomenai in Illyria rather than the Ithacan town --, the Ur-form of the ‘return’ story must have been about an invasion from the northwest. This can be none other than the Dorian invasion, whose historicity is undoubted.

The Ur-Odyssey thus stands as our earliest source of information for a violent Dorian incursion. It seems that an echo of this may survive in some of the later interpolated parts of the epic. Notably, we are now in a position to explain Telemachos’ journey to Sparta as being, in its origin, an account of a contingent sent to invade the southern Peloponnesos. This contingent had aid from Pylos, so that we now see Pylos was evidently the first city in the Peloponnesos to accept and support their new Dorian masters. Historians of the Dark Age will want to take note of this discovery, as will students of the role and status of Pylos in early Greece, and adjust the historical record accordingly.
WARNING: this map is very garbled. It comes from some poor sap’s presentation to a class, but it’s basically the Bronze Age equivalent of 1066 and All That.
‘Hey, let’s imagine the Dorian invasion really happened, and not only that, but that it was an integral part of the Bronze Age Collapse and the Sea Peoples, and all these things were actually the same event!’
‘Sure, everyone knows that if three things happened within two centuries of each other and within 1000 km of each other, they must be directly linked. The first one is based on legendary sources from 500-1000 years later, the second one is grounded in archaeological evidence from Greece, Anatolia, and Syria, and the third in contemporary textual evidence from Egypt. Yes, these are all clearly the same thing.’
‘Um, do we need to put the Dorian homeland in its correct place?’
‘No, why would that matter?’
‘So we’ve got an existing Greek civilisation being invaded by more Greeks from Serbia, that’s OK?’
‘That makes complete sense to me.’
‘How about the fact that Mersin, Tarsus, Carchemish, and Hamath weren’t destroyed, but were either damaged but remained standing, like Troy and Knossos, or even became more important after the Hittite collapse -- do we care about that?’
‘Bah, just trivial details.’
‘What about colonists heading ...’
‘Shut up and draw the map.’


I won’t labour all the in-jokes in this essay, but it may be worth mentioning that some of its claims are perfectly true.
  • ‘[T]he elder compilation of three lays by a relatively talented Ionian poet’: this is essentially how Wilamowitz argued the Odyssey was put together.
  • The parallels between Helen and Penelope are all real.
  • ‘Penelope … the first to recognise Odysseus’: the idea that Penelope supposedly secretly recognises Odysseus in Odyssey book 19 has a long tradition behind it, and it has had a long-lasting impact even on people who don’t believe it. Many modern interpretations -- even those adamantly opposed to the Analyst school -- still contain echoes of the idea.
  • The variation δέκτῃ/Δέκτῃ in Od. 4.248, and the manuscript variants of λόεον and χρῖον ἐλαίῳ in Od. 4.252, are real. That episode has often been of keen interest to Analysts because of a supposed relation to Cyclic epic material.
  • Penelope genuinely was honoured in Mantineia as the mother of Pan. A form of the story existed at least as early as Herodotus 2.145; cf. ps.-Apollodoros epit. 7.38, Pausanias 8.12.6.
  • The Telemachy and Odyssey book 24 are indeed normally regarded by Analysts as later than the rest of the epic (though the idea is very doubtful, and there’s zero support from properly sampled statistical analysis of the language in those episodes).
  • The name ‘Odysseus’ is not Illyrian in origin. However, the northwestern cult-sites at Trampya (Thesprotia) and Bouneima (Thesprotia/Aitolia) seem to have been real. The Alkomenai in Illyria is real, as is the town on Ithaca, and the epithet ‘Alkomenean Odysseus’. It isn’t impossible that the name ‘Alkomenai’ has Odyssean connections, but it’s more likely that it alludes to Athena, who had a cult-site at Alalkomenai in Boiotia.
  • The Dorian invasion is still sometimes treated by ancient historians as though it were real. There is no direct archaeological evidence for it, and the indirect evidence is very contestable. Perhaps the worst thing about the Dorian migration hypothesis is that there’s no falsehood condition: no kind of evidence could ever disprove it.

Wednesday, 27 February 2019

The golden ratio

‘Ancient architecture and art are chocker with full of examples of the golden ratio’ is a myth that we should blame on Walt Disney. He didn’t invent it, but he sure did popularise it.

[Edited: I hadn’t realised the kiwiism ‘chocker’ doesn’t cross oceanic boundaries well.]

In 1959 Disney released a half-hour educational cartoon starring Donald Duck, Donald in Mathmagic Land. For decades the cartoon was shown to maths classes in thousands of schools. I saw it at my school in New Zealand in the 1980s. For a good while, I believed its claims -- even though I only half-remembered them.
Donald in Mathmagic Land (Disney, 1959)
Here’s a sample:
To the Greeks, the golden rectangle represented a mathematical law of beauty. We find it in their classical architecture. The Parthenon, perhaps one of the most famous of early Greek buildings, contains many golden rectangles.
-- Donald in Mathmagic Land (Disney, 1959)
The cartoon also states that the golden ratio can be found in pentagrams, and that it can be found in naturally-occurring pentagonal and spiral shapes. The thing about pentagrams is absolutely true, and there’s some truth to the claims about pentagons -- but natural spirals are much more diverse than Donald Duck led us to think. And as for the golden ratio in architecture ...

Mathematical explanation

The ‘golden ratio’, also known as φ, is equal to (√5 + 1)/2, or 1.61803...
A golden rectangle with dimensions 1 × φ. The gold-coloured region has the same proportions as the larger rectangle. If you continue to cut off squares, the remaining rectangles will still all have the same proportions as the original.
The golden ratio is defined as follows. If you have a rectangle with sides 1 × φ, you can chop off a 1 × 1 square and the remaining smaller rectangle will have exactly the same proportions as the original one. This will only work if the original proportion is exactly φ. Such a rectangle is commonly known as a ‘golden rectangle’.

You can use golden rectangles to construct other ‘golden’ shapes: a ‘golden angle’, at the angle of a golden rectangle’s diagonal, and a ‘golden spiral’ like the one shown below superimposed on a nautilus shell.
Nautilus shells famously follow a golden spiral ... except, um, they obviously don’t.
The myth is that golden rectangles pop up all over the history of art and architecture, and golden spirals pop up all over nature. There are elements of truth to this. But they aren’t remotely as common as you might imagine from watching Donald Duck, or from reading Wikipedia’s ‘list of works designed with the golden ratio’.

φ also has some interesting numerical properties:
  • φ – 1 = 1/φ, and φ + 1 = φ2.
  • The first of these equations is simply a restatement of the definition of the golden ratio (see diagram above). From it, we can extract the quadratic equation φ2 – φ – 1 = 0. Solving this gives the value φ = (√5 + 1)/2.
  • In the Fibonacci sequence, each number is the sum of the previous two numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. The longer the sequence goes on, the closer the ratio between each number and its predecessor gets to φ: the ratios go 1, 2, 1.5, 1.667, 1.6, 1.625, 1.615, 1.619, and so on.
  • Powers of φ are closely related to the Fibonacci numbers. If we define Fn = the nth number in the Fibonacci sequence, then
    • φ2 = F1 + φF2
    • φ3 = F2 + φF3
    • φ4 = F3 + φF4, etc.
These mathematical claims, at least, are absolutely true, and there’s a lot more we could add. It’s when we get to the physical world that the problems begin.

The problem

The golden ratio isn’t nearly as omnipresent as its fans would have you believe. You will find φ in some natural phenomena that involve pentagonal shapes, or a repeating growth process. That’s because these things are directly related to the mathematics of φ. The Fibonacci sequence is a recursive growth process, so Fibonacci numbers do pop up in nature, and as we saw above, the Fibonacci sequence generates the golden ratio.

But it definitely doesn’t happen everywhere. In particular, nature does not favour golden spirals. There are other logarithmic spirals in nature -- nautilus shells are the best known example -- but only a spiral at a specific angle is a golden spiral. Even in situations where Fibonacci numbers arise, like clustered leaf arrangements on a plant stem, the spirals aren’t golden spirals.
NGC 232: no golden spirals in sight. If you get the spiral arms to match the curve at the top and right, then they are obviously inaccurate at the left and bottom, and in the centre.
And then there’s art and architecture. Here, you have to look really hard to find the golden ratio. In ancient Greek art and architecture you won’t find it at all. Unless you fudge it.
Fudged golden rectangles. From top left: caryatids on the Erectheium, Athens; Leonardo’s ‘Mona Lisa’; a live human woman (all from Donald in Mathmagic Land, 1959); the Parthenon (from this webpage). What are the drawn rectangles even supposed to demonstrate? That you can draw rectangles on pictures? None of the Disney ones match anything in the images. In the Parthenon picture the top edge matches the building, but the left and right edges are only approximate, and others just show the theory’s falsehood: the bottom edge of the largest rectangle, and the right edge of the largest square, don’t match anything on the building.
Sure, you’ll find websites all over the place claiming to find golden rectangles in all sorts of places, especially the Parthenon. They’re heavily flavoured with conspiracy-theory-style thinking. Some people can get very, very angry if you express doubts. The talk page on the Wikipedia ‘list of works designed with the golden ratio’ is interesting reading. In 2008 there was a minor war over the subject: there’s one person patiently and doggedly requesting substantiation, details, and documentation, while others -- one person in particular -- get increasingly frustrated. The reason they’re frustrated is because they can’t find any decent substantiation. And the reason they can’t find it is because it doesn’t exist.

It can sometimes be a good joke to satirise some of the claims. Here’s a page from the webcomic xkcd that superimposes golden spirals over anything and everything. You can draw rectangles and spirals anywhere you want ... it doesn’t mean that they’ll fit anything.

Let’s move on to some specifics.

Myth 1: The Parthenon is designed around φ

This is probably the most popular golden ratio myth. The Parthenon is the famous temple of Athena in Athens. Across the internet -- and in Donald in Mathmagic Land -- you’ll see many images of the Parthenon with golden rectangles superimposed on various bits of its facade.
Donald in Mathmagic Land (1959) uses a hand-drawn Parthenon. Not too surprising, then, that the fit is so tidy.
If you do this with an accurate elevation plan, though, you’ll quickly find that golden rectangles don’t actually fit any edges on the building. If the architects of the Parthenon had wanted to embed the golden ratio in the building, they certainly could have done so: ancient Greek temples do display various other ratios, to fairly high precision, as documented by Lehman and Weinman (2018: 61-104). But they’re ratios like 2:1, 9:4, 7:3, and in some parts of the Parthenon, 81:30. The golden ratio doesn’t enter into it.

Here’s one diagram that depicts the Parthenon with measurements full of various multiples of φ, π, and e. A few problems:
  1. The measurements are all wrong. For accurate figures, see Orlandos (1976-1978). Selected measurements are also quoted by Lehman and Weinman (2018: 167-168).
  2. If you’re giving examples of the golden ratio and you have to resort to proportions like φ3√5 and 10π/3, you’re doing it wrong.
  3. The ancient Greeks didn’t know the values of φ and π to any great accuracy. There’s no evidence anyone even knew of φ until Euclid. As for π, Archimedes calculated its value precise to two decimal places two centuries after the Parthenon was built; in the earlier period, the best approximation of π would have been that of Antiphon, who calculated only a lower bound for its value, and was doubtless less accurate. And the ancient Greeks had no clue what e is, because they hadn’t invented logarithms or compound interest: e wasn’t defined until the 1600s.
[Addendum, a couple of days later: I spoke rashly in point 3. φ probably was known to mathematicians of the late 5th century BCE. Important points about the icosahedron and dodecahedron appear in book 13 of the Elements, which owes a lot to, and may even be largely copied from, Theaetetus of Athens, a key early figure in the study of irrational numbers.]

Here’s another site that looks at a whole bunch of supposed golden rectangles in the Parthenon facade. Its conclusions are negative, but in my opinion not nearly negative enough.
A photo used on Claim 1(a), below, relates to the yellow rectangle, and claim 1(b) to the red rectangle.
Myth 1(a): In the Parthenon frieze, each square metope + rectangular triglyph together form a golden rectangle. The triglyph is another golden rectangle.

Reality: To avoid problems with foreshortening, let’s get some accurate measurements. I’m taking my figures from Lehman and Weinman 2018: 167.

On the west facade, the average metope width is 1275 mm, and the average triglyph width is 844.6 mm, making a total rectangle of 1275 × 2119.6 mm. A golden rectangle of the same height ought to be 1275 × 2063 mm, or if the same width, 1310 × 2119.6 mm. On the east facade, the figures are almost the same: average metope width 1274 mm, average triglyph width 844.5 mm, total rectangle 1274 × 2118.5 mm. The triglyphs are more than 7% too fat to be golden rectangles.

The actual ratio intended between metope and triglyph is 3:2. On the west facade it’s 3.019:2, on the east facade 3.017:2. Combined, each metope + triglyph would then produce a 5 × 3 rectangle, not φ × 1. They miss φ by 2.7%, but they miss 5 × 3 by only 0.23% to 0.25%.
Actual proportions of Parthenon metope + triglyph (west facade dimensions), with superimposed golden rectangles in red (the correct height) and blue (the correct width).
Myth 1(b): A rectangle the width of a metope + triglyph, and the height of the entablature, is a golden rectangle.

Reality: The height of the entablature is 3.295 m, so based on the figures above, the rectangle is 2.1196 × 3.295 m (west facade) or 2.1185 × 3.295 m (east). A golden rectangle of the same height ought to be 2.036 m wide, or if the same width, 3.430 m high (west) or 3.428 m high (east). The entablature is 4% too short, or alternatively, the metopes + triglyphs are 4% too wide.

Myth 1(c): Each pair of columns and the space between them form a golden rectangle.

Reality: The columns are 10.433 m tall. The diameter at the bottom is 1.905 m, and the average intercolumniation is 4.296 m (not counting the corner columns, which are more narrowly spaced). This gives a rectangle of 6.201 m × 10.433 m. A golden rectangle with that width ought to be 6.201 × 10.033 m (so the real columns are 4% too short), or with that height, 6.448 m × 10.433 m (so the real columns are 4% too close together).
Photo of the Parthenon from this webpage: the green rectangles are original, the red rectangle added by me. The green rectangles supposedly show golden ratios all over the place. The red rectangle is a real golden rectangle. It doesn’t fit.
You might reply that these are near enough: that the intent was to produce golden rectangles, and the inaccuracies are just the result of imperfect building techniques.

You could argue that. But only if you ignore the fact that the Parthenon is actually rather well engineered. The precision is way better than one part in a hundred. Remember how the metope:triglyph ratio is within 0.25% of the intended proportion, 3:2 (myth 1(a), above).
The Parthenon, reconstructed, with superimposed golden rectangles and golden angles all over the place. None of them come even close to fitting anything. This elevation was drawn up by the architects James Stuart and Nicholas Revett in the 1750s: I use it here, rather than a photograph, to avoid foreshortening. (Source: Stuart 1787, chap. 1 plate 3)

Myth 2: The sculptor Pheidias used φ

This myth is closely allied to myth 1, because Pheidias was credited for the colossal statue of Athena Parthenos in the Parthenon. Taken in conjunction, they’ve often ended up making Pheidias the architect of the building (he wasn’t) as well as a sculptor.

[Addendum, a couple of days later: I should have qualified this. Pheidias was the supervisor of the Parthenon project. But the architect was a different man, Ictinus, who also designed the extraordinary temple of Apollo at Bassae, and had a hand in the Telesterion in Eleusis and the Periclean Odeon in Athens. He was a very skilled architect.]

The myth about the sculptures was made up in the 1910s. It happened hand-in-hand with choosing the letter φ to represent the ratio. According to Theodore Cook, the letter φ was suggested by the engineer Mark Barr
partly because it has a familiar sound to those who wrestle constantly with π (the ratio of the circumference of a circle to its diameter), and partly because it is the first letter of the name of Pheidias, in whose sculpture this proportion is seen to prevail when the distances between salient points are measured. So much is this the case that the φ proportion may be fitly called the ‘Ratio of Pheidias.’
-- Cook 1914: 420
The idea of φ as a counterpart to π is reasonable. The stuff about Pheidias is pure fiction. We don’t know the proportions of Pheidias’ free-standing sculptures, for the simple reason that none of them survive. We have many of the decorative sculptures on the Parthenon, but they don’t exhibit the golden ratio so as you’d notice. We do have descriptions of some of Pheidias’ statues, but the descriptions don’t discuss any ratios, let alone the golden ratio.

It’s not clear whether the myth was invented by Barr or by William Schooling, the person that passed Barr’s suggestion to Cook. Apparently in 1929 Barr stated that he didn’t ‘believe’ Pheidias actually used the golden ratio, but I haven’t managed to get hold of the later article to read what he actually says there.

Myth 3: Plato’s divided line, something something

Plato’s analogy of the divided line (Republic vi.509d-511e) chops up the world into the physical and non-physical realms, which are then each divided up into two sub-sections in the same proportion.
It has nothing at all to do with the golden ratio. I bring it up here because Plato talks about the visible and intelligible realms being subdivided in the same ratio as the overall division, and apparently some of Plato’s readers are unable to imagine this happening with any ratio other than φ.

Myth 4: Vergil’s Aeneid uses φ

This one actually originates with a classicist, George E. Duckworth. He argued it in a series of articles and a 1962 book. Hardly anyone took it seriously at the time -- see the reviews by Dalzell and Clarke -- and no classicist takes it seriously nowadays.

Duckworth assumes that Vergil knew the numerical value of φ, knew the Fibonacci sequence, and understood the relationship between them. He then identifies examples of the golden ratio in passages with relative lengths anywhere between 1.5 and 1.75, and in passages whose length in lines is a Fibonacci number.

Fibonacci numbers, unfortunately, weren’t known in Europe until Fibonacci wrote about them in the 1200s. Their connection to φ wasn’t known, or at least not widely known, until Simon Jacob noticed it in the 1500s. So imagining Vergil using these ideas is ... difficult.

The reviews linked above also point out copious examples of how Duckworth cherry-picks his data, massages it, and conceals imprecisions. Clarke takes the additional step of illustrating that arbitrary ratios can be found in any poet if you look hard enough, by analysing a poem by John Betjeman in the same way. (He picks Betjeman, ‘a poet certainly oblivious of the Golden Section’, because his style is antithetical to the abstract; perhaps also because of Betjeman’s documented incompetence at maths and laziness as a student.)

Myth 5: ‘European paper sizes’ -- A4, A3, etc. -- are golden rectangles

Yes, I really have seen people claim this. This one is a twofer:
  1. Those paper sizes aren’t European, they’re the ISO international standard.
  2. The actual ratio of A4/A3/etc. paper size is √2 (1.414...), not φ.
(Actually the paper size closest to a golden rectangle is US legal: 215.9 × 355.6 mm, a ratio of 1.647. And legal looks weird. So much for golden rectangles being the ideal proportions.)

Myth 6: If you ask people to pick a random number between 1 and 100, they’ll prefer 61 and 37 because of φ

The idea here is that the human brain is naturally attracted to the golden ratio. There aren’t any well tested scientific studies showing that, though. I’ve seen someone seriously claim that these choices are hardwired into the human brain because 61 = 100/φ and 37 = 100/φ2. (Why on earth would our brains care about 1/φ2?)

It certainly seems to be true that people choose odd numbers, prime numbers, and numbers ending in 7 or 3 extraordinarily frequently when asked to pick a number randomly. I haven’t managed to find any scientific studies on this either. Some informal surveys that I’ve found (1, 2, 3) don’t bear out the 61 claim at all, and the 37 claim only inconsistently.

But it does seem to be the case that when people choose a number from 1 to 10, by far the most frequent choice is 7; when they choose a number from 1 to 20, they’ll pick 17 as much as 20% of the time. For some reason, though, golden ratio fans don’t mention these two phenomena so much. I guess it’s too obvious that they have nothing at all to do with the golden ratio.

In any case the calculations are wrong. 100/φ is 61.803..., that is, closer to 62, and 100/φ2 is 38.197..., not 37.

Myth 7: Leonardo da Vinci’s drawing ‘Vitruvian man’ uses φ

It doesn’t. This article by Takashi Ida does a detailed investigation of some claims and possible uses of φ in the drawing, and none of them are true. In particular, Ida shows that the ratio of Leonardo’s circle to his square is about 0.606 to 0.609, rather than 1/φ = 0.6180..., a difference of 1.51%; and he argues from the marks Leonardo placed on the diagram that the ratio he intended to use was precisely 137/225, or 0.6089, which corresponds well to the measured ratio of the circle.

In closing ...

I’d better stop: I’ve gone a long way off-topic from Greek architecture anyway.

There are some genuinely interesting things about the ‘golden ratio’. It does have some pretty interesting numerical properties. Several proofs in Euclid’s Elements book 6 do deal with φ in one way or another. He calls it ‘the extreme and mean’: the phrase ‘golden ratio’ wasn’t invented until the 1800s.

And it’s true that φ can be found embedded in the diagonals and other ratios of several geometrical shapes. In a regular pentagram, each vertex and intersection has two adjacent line segments with lengths in the ratio φ. Or, put another way, the diagonals of a regular pentagon intersect to create line segments with the ratio φ. As a result, any geometrical structure with pentagonal features is going to feature φ in some way -- including two of the ‘Platonic solids’, the dodecahedron and icosahedron, as well as the areas of the tiles in Penrose tiling.

And some artists and architects have definitely used φ in their work. The Swiss-French architect Le Corbusier based a design system on φ and the Fibonacci numbers in the 1940s. (Whether this has anything at all to do with the supposed golden rectangles on the UN headquarters building in New York is another matter.) Salvador Dali’s Last supper definitely takes inspiration from the mathematics of φ: the canvas is within 1% of being a perfect golden rectangle; the figures are in groups of 2, 5, and 13 (all Fibonacci numbers); and the painting is dominated by a dodecahedron (remember pentagons feature φ heavily) whose design is modelled on one of Leonardo da Vinci’s illustrations for Pacioli’s Divina proportione (1509), the book that kickstarted the modern interest in φ.
Salvador Dali, The sacrament of the last supper (1955)
But other than really blatant cases like these, I recommend treating claims of the golden ratio in art and architecture with great suspicion. Golden ratio fans are wont to interpret any old proportion as a golden rectangle, to gloss over imprecisions, and to make completely fictional claims about the history of the ratio. Don’t ignore the fact that there are other ratios in the neighbourhood of 1.6. Always be alert for cherry-picking.