Thursday 24 December 2015

Christmas and its supposed pagan links

Note. This discussion has now been superseded in many respects. See these follow-up pieces: on Yule (2018), on the nativity stories in the gospels (2020), more on Yule (2021), a four-part series on ‘the dates of Jesus’ (2021), on the construction of the Julian calendar (2022), and on the origins of Santa (2022).

The later pieces also correct a few errors made here. Notably: there’s no reason to reject the 25 December date found in Hippolytus as spurious; the date of the solstice in the Julian calendar isn’t quite as straightforward as I thought; and it turns out there is a 9th century source linking Pope Julius I to the 25 December date, though it’s almost certainly spurious.

Christmas ... blends elements including both the feast of the Saturnalia and the birthday of Mithra.
Encyclopaedia Britannica, ‘Roman religion’

Every year around Christmas, the world’s mythbusters love to remind everyone that Christmas is really a pagan festival, and that Christians plagiarised it by enforcing their own beliefs on a pre-existing set of customs. The choice of festival varies: sometimes it’s Saturnalia, sometimes the winter solstice, sometimes the birthday of Mithras, sometimes a Roman civic festival of Sol Invictus (‘the unconquered sun’). Often it’s a combo: for example, you may hear that Saturnalia was a solstice festival that the Christians corrupted.

Many Christians seem happy to accept this picture of things too, minus the hostile spin. After all there doesn’t need to be anything very sinister about using a well-known festival to hold a celebration of your own. It's happened to Christian festivals too: St Valentine's Day was a Christian feast day for a legendary martyr of the late 3rd century, now it's mainly a day for celebrating romantic love. No evil conspiracy, and hardly anyone actually minds. Why not adapt a pre-existing festival for new purposes?

Anyway, soon the mythbuster-busters come out to play too. They'll dutifully point out:

  • There's no evidence to link Christmas to Saturnalia, and in fact Saturnalia continued to be celebrated by Christians, alongside Christmas for at least a century and probably longer.
  • Sol Invictus (a) was a specific local cult associated with a specific temple in Rome, (b) there were numerous sun cults in Rome and Sol Invictus was just one of them, and (c) the festival of Sol Invictus on 25 December isn't attested any earlier than Christmas and is very likely the later of the two.
  • Not only did Mithras' birthday have no influence on Christian thinking: Mithras didn't even have a birthday. He emerged from a rock.
  • The solstice is not on 25 December, and any Greco-Roman armed with a gnomon would be able to tell that reasonably accurately.

In the early stages of researching this post I was firmly on the side of the mythbuster-busters. That's mostly still true: Christmas has absolutely nothing to do with Mithras or Saturnalia.

But not entirely. There is a bit of mythbuster-buster-busting to do here. The most important point, as it turns out, is that there almost certainly is a link between Christmas and the solstice. That, in turn, creates a fairly strong presumption that there is a link between the date of Christmas and the tradition of linking Jesus with sun imagery. But as we shall see, it does not follow that there was any kind of plagiarisation between Jesus and Sol Invictus, in either direction.

Let's do the mythbuster-busting first, then we’ll get onto the mythbuster-buster-busting. (This'll be a long post, in honour of the season: I'll change gear down after the new year.)

1. Saturnalia

Saturnalia was a Roman festival of Saturn on 17 December. Celebrations continued after Saturnalia for several days, finishing sometime between 19 and 23 December depending on which century we're talking about. It may originally have been a farming festival; the evidence is unclear. It was associated with an overturning of various regulations and social norms: free citizens often wore a freedman’s hat, the pilleus, and played gambling games that were normally illegal; some enslaved people were permitted to dine with the people who enslaved them. People would exchange gifts of candles and clay figurines.

There's no link to Christmas. The date? No: they're not on the same date. (Hey, what’s eight days between friends? Well, it's the difference between corroboration and no corroboration.) The fact that Saturnalia might have had some chance to have an influence on Christmas isn't evidence that it did.

Christmas trees? Yule logs? Holly and ivy? No, none of those come from Saturnalia. Individual customs may have pagan origins in some cases -- the Yule log may possibly be based on a late mediaeval Anglo-French or South Slavic custom -- but that has nothing to do with the claim that Christmas is based on Saturnalia.

Gift-giving? No: the magi may have given tribute to Jesus (traditionally at Epiphany, 6 January), but the modern custom of gift-giving at Christmas only goes back to the 16th century. That is when Luther introduced the Christkind in an attempt to discourage veneration of St Nicholas, who was associated with gift-giving on his feast day of 6 December. In late mediaeval Germany gift-giving had also been associated with the feast of the Holy Innocents, on 28 December. It's possible that Christmas charity from aristocrats to the poor goes back a bit further. But there's certainly no evidence to suggest continuity all the way back to when Saturnalia was still being celebrated.

And that brings us to the kicker: Saturnalia was still being celebrated, by Christians to boot, at least as late as the 5th century, alongside Christmas. By that time it was no longer a festival in honour of Saturn, in much the same way that Christmas has little to do with Jesus for modern atheists. But it'd be bizarre to conclude that Christmas, which was certainly being celebrated in the 4th century, was based on another festival that continued to co-exist with it for at least 100 years (and probably longer).

2. Mithras

Mithraism was a popular cult in the western Roman world in the first few centuries CE. Very little textual evidence about Mithraism survives: we have to rely heavily on the archaeology of mithraea, underground churches of Mithras. And interpretation of that evidence is very often uncertain and controversial. Popular accounts are even worse — more games of speculation than anything else.

Roger Pearse has written some good online catalogues -- here, and here -- of rebuttals to the claim that Mithraism and Christianity had anything to do with each other. To sum up:

  • No, Mithras didn’t have a virgin birth, and he wasn’t born on 25 December. Mithras wasn’t even born: he came out of a rock.
  • No, three wise men did not visit Mithras at his birth. (a) He didn't have a birth. (b) This idea is entirely derived from a single 1864 book that seems to have mistaken Mithras’ attendants Cautes and Cautopates for ‘wise men’. There isn't a shred of ancient evidence for it.
  • There is no good evidence of a concept of salvation through blood in Mithraism. This idea was based on a single inscription, but its reading isn't remotely clear-cut and it requires very heavy supplementation to get it to mean anything at all. (Here's what the inscription looked like in 1930; here’s the most recent professional sketch of it. Go on, you try deciphering it.)
  • No, Mithras didn’t die on a cross. That’s completely made up.
  • Mithras didn’t have twelve disciples, get buried and rise three days later, have a festival that coincided with Easter, and he didn't get called a ‘good shepherd’, ‘the way, the truth, and the light’, ‘logos’, ‘redeemer’, or ‘Messiah’. All of these things were made up by Dorothy Murdock, writing under the pseudonym ‘Acharya S’, in a series of books starting in 1999.

There’s no connection at all. Let’s just drop this one: it’s silly, and life is short.

3. How far back does Christmas = 25 December go?

The earliest explicit evidence for the 25 December date of Christmas is in a document known as the ‘Chronography of 354’, a compilation of histories and calendars compiled in the year 354. One calendar, a catalogue of martyrs' feast days, has the following as its first entry:

VIII kal. Ian. -- natus Christus in Betleem Iudeae.

Eight days before the kalends of January (i.e. 25 December): Christ born in Bethlehem in Judaea.

But 354 isn't when Christmas was invented, it represents the earliest explicit attestation of Christ's birth being celebrated on 25 December. The likelihood is that the choice of date was earlier; though it's arguable whether that means a couple of decades earlier, or a couple of centuries earlier.

Digression #1: false leads. A number of online sources claim that Pope Julius I instituted 25 December as the date of the nativity in the year 350. This is untrue. The source usually cited is 'Manual of Liturgical History, vol. 2 (1955)', a book which on further inspection turns out not to exist. Wikipedia instead cites the History Channel -- and we all know how reliable they are. Other sources cite Julius Africanus as evidence that the date was fixed by the early 3rd century; but the surviving fragments of Africanus contain no reference to this (see S. Hijmans, 'Sol Invictus, the winter solstice, and the origins of Christmas', Mouseion 3 (2003): 377-98, at 377 n. 3; cf. Wallraff's 2007 edition of the Africanus fragments).

There are a few earlier sources that can potentially be taken as pointing towards celebration of Christ's birth -- or the Incarnation, depending on the theological flavour of the source -- at an earlier date. They are:

  1. Clement of Alexandria, late 2nd/early 3rd cent., reports (Stromateis 1.21.145-6) that some people assigned Christ's birth to 'the 25th day of Pachon', and others to 'the 24th or 25th day of Pharmouthi'. These are dates in the Alexandrian calendar. When you convert them to the Julian calendar they're nowhere near December: they come out as 20 May and 19/20 April, respectively. However, the focus on the 25th (or 24th) day of the month is a tad conspicuous. Still, that could just be coincidence. Moreover, there are alternative interpretations of Clement's dates: see S. K. Roll, Towards the Origins of Christmas (1995), pp. 77-9.
  2. A reference to Christ's birth on 25 December appears in an early 3rd century writer, Hippolytus of Rome (Commentary on Daniel 4.23.3), but the reference is useless: there's no doubt that it is an interpolation of mediaeval date. (I give the text of the interpolation at the end of this post; see also Roll, pp. 79-81, esp. p. 80 with n. 106.)
  3. It was traditional among ancient Judaeo-Christian writers to treat prophets and saints as having the same date for their birthday and death-day. A modification to this appears starting in Clement, who reinterpreted the word 'birth' (genesis) as referring instead to conception (Strom. As a result, in this typological thinking, the death-day coincided with the day of conception and the birthday fell exactly nine months after the death-day. Now, by the 2nd century, Christians were celebrating Jesus' death and resurrection on Pascha, 14 Nisan in the Hebrew calendar, or alternatively on 16 Nisan, corresponding to Good Friday and Easter Sunday respectively; the late 2nd and early 3rd centuries saw a controversy over which date was more important, the Quartodeciman controversy. Pascha shifts around each year, since the Hebrew calendar is lunar. If it were believed that 14 Nisan fell on 25 March in the year of Jesus' death, typological thinking would consequently put his genesis (conception) on the same date, and his birth nine months later on 25 December. This is exactly what the spurious reference in Hippolytus, above, claims; again, see the end of this post for the text. More details in Roll, pp. 79-80.
  4. An anonymous text dating to 243, the pseudo-Cyprianic De Pascha computus or 'computations concerning Pascha', at sections 18-23 puts the creation of the cosmos on 25 March; the creation of the sun on 28 March (the fourth day of creation); and therefore also the genesis of Christ, the 'sun of righteousness' (a phrase from Malachi 4:2 which according to Christian tradition refers to Jesus), on 28 March. The author claims divine guidance for these dates. If by nativitas the author means 'conception' -- as indeed seems likely, with the parallel of Clement's use of genesis -- that would then translate to a birthday of 25 December or 28 December, depending on how much of the author's argument you reject.

The first two of these earlier references are uncertain and wrong, respectively, but the third and fourth are decidedly possible. The upshot is that 354 is the earliest uncontroversial date for an assignment of Jesus' birth to 25 December; but the date may well have been already decided at the time of the Quartodecimans in the mid-2nd century, 200 years earlier.

Correction, Dec. 2023. (1) In fact the Hippolytos fragment appears to be genuine: see note at end. The Hippolytos fragment puts the 25 december date for Christmas back to around 220 CE. (2) The Chronography of 354 dates to 354 CE in its present form, but its content shows that the material was compiled in 336 CE. (Hippolytos is still earlier.)

4. The winter solstice

The winter solstice does not fall on 25 December. The ancients were capable of identifying the solstices to within a day or so using gnomon measurements; and it seems to have been absolutely routine to do so.

However, there’s more to this one than meets the eye. The Julian calendar was not as well calibrated as the modern Gregorian calendar, so the date of the solstice drifted with respect to the calendar date. Around the time of Jesus' birth, the solstice was on 23 December; by the time of the Chronography of 354, it was 20 December. (In 1580, just before the Gregorian calendar was introduced, it had drifted all the way back to 11 December!)

And yet Roman writers regularly quote the date of the solstice as the 25th of December. Here’s Columella, a 1st century CE agricultural writer, on the subject (De re rustica 9.14.12):

ab occasu Vergiliarum ad brumam, quae fere conficitur circa VIII kalendas Ianuarii in octava parte Capricorni ...

From the setting of the Pleiades to midwinter, which occurs roughly around the 8th day before the kalends of January (i.e. 25 December), at 8° in Capricorn ...

We find similar wording in Pliny the Elder, also 1st cent. CE (Natural history 18.221):

... omnesque eae differentiae fiunt in octavis partibus signorum, bruma Capricorni a. d. VIII kal. Ian. fere.

... and all these changes occur at 8° in the (zodiacal) signs, the winter solstice in Capricorn on roughly the 8th day before the kalends of January (i.e. 25 December).

Note the parallels: the use of fere 'roughly', and the reference to 8° in Capricorn (most Babylonian-Greek astronomers reckoned the equinoxes and solstices as occurring when the sun was in the centre of each sign, i.e. at the 8° mark within that sign). Servius, in the 4th century, quotes the date by itself without the other parallels (commentary on Aeneid 7.720).

(Here, by the way, are links to published editions: Columella, and Pliny. The dating of the solstice to the 25th obviously worried the translators of these editions: they both mistranslate the date. This doesn’t reflect any ambiguity over how to interpret Roman dates: there’s absolutely no doubt that a. d. VIII kal. Ian. means 25 December. The translators here are either slipping up or being dishonest.)

Digression #2: why do Roman writers report the date of the solstice as 25 December? The textual parallels between Columella and Pliny, and the fact that the date was already wrong by their time, suggest they are both based on an older source. A few pages earlier Pliny discusses three treatises by Sosigenes, who designed the Julian calendar (Nat. hist. 18.212). Sosigenes can’t be the ultimate origin of the date either: in his time, in 46 BCE, the solstice had already drifted to 23 December. But he’s fairly likely to be Columella’s and Pliny’s immediate source. Sosigenes must surely have been aware that the 25 December date was already inaccurate -- hence the fere 'roughly' in both Columella and Pliny. (It's likely that Sosigenes wrote in Greek, but fere could easily be a translation of φαύλως. And it’s not actually impossible that he might have written in Latin, working for a Roman audience as he was. [Additional note, 19/1/16: the fact that the sources that give the solstice as 25 December are in Latin, and that there are none in Greek, also tends to suggest that Sosigenes wrote in Latin. Pliny is our only source for Sosigenes.])

R. Hannah, Greek and Roman calendars (2005) p. 151, suggests Hipparchus, in the 2nd century BCE, as the ultimate source. Pliny’s discussion of the periods between equinoxes and solstices in the surrounding passage appears to be taken from Hipparchos’ figures (94½ days from vernal equinox to summer solstice, etc.; see O. Neugebauer, History of ancient mathematical astronomy vol. 1 pp. 57-8 and p. 307, citing testimony from Ptolemy’s Almagest). However, Hipparchos still isn't early enough to get a solstice on 25 December. The last time the solstice actually fell on 25 December, using the retrojected Julian calendar, was in 230 214 BCE, half a century before Hipparchus was active. Moreover, Columella states explicitly that he is departing from Hipparchos’ practice: Hipparchos treated the equinoxes and solstices as occurring at the start of each zodiacal sign rather than at the mid-point; Columella/Sosigenes chooses instead to follow the more traditional practice of Eudoxus (early 4th cent. BCE) and Meton (5th cent. BCE), which was derived from Babylonian astronomy. And, at the time of Meton and Eudoxus, the solstice was indeed usually on 25 December (Julian calendar, retrojected).

So Eudoxus must be the ultimate source of the date. Here's how I suggest reconstructing the probable timeline:

  • 4th cent. BCE: Eudoxus quotes the date of the solstice as 25 December. (He didn’t use the Julian calendar, of course, but the date was later converted into the Julian calendar; we know the same conversion happened with Hipparchos’ observations. See Neugebauer, p. 276, for examples of Ptolemy converting dates quoted by Hipparchus.)
  • 2nd cent. BCE: Hipparchos, as Columella and other ancient sources tell us, treats the solstices and equinoxes as occurring at the beginning of each zodiacal sign, not at the 8° mark as in Babylonian astronomy.
  • ca. 46 BCE: Sosigenes quotes Eudoxos’ date. He realises that it’s no longer accurate, so he qualifies it as approximate (fere); he also mentions the sun being at the 8° mark in Capricorn, following traditional Babylonian-Metonic practice rather than Hipparchus.
  • 1st cent. CE: Columella and Pliny quote from Sosigenes’ account; Columella also mentions Hipparchos’ alternate practice.
  • 4th cent. CE: Servius mentions 25 Dec. as the date of the solstice. By his time it’s wrong by five days, but nonetheless a traditional piece of common wisdom.
Corrections, Dec. 2023. (1) The role of Sosigenes is very overblown. The calendar revisions were the doing of Caesar himself, who explained himself in his lost work De astris (‘on the stars’). (2) The measurement of the solstice/equinox dates probably actually originates with Kallippos in the 4th century BCE: the Kallippan cycle gave the solar year an average length of 365.25 days, and was the basis for the Julian/Alexandrian calendar revisions in the late 1st century BCE. For more info on both these points, see this 2022 piece.

Even if you don’t buy my argument in the digression above about the ultimate origin of the date, Columella and Pliny leave no doubt that 25 December was popularly regarded as the solstice.

Saturnalia, as we saw, is off by eight days: that's mere coincidence. But when Christmas falls exactly on the traditional date of the solstice, it’s a bit more of a stretch to say it’s coincidence.

5. Jesus and solstice festivals?

Sol Invictus. Many modern readers see a link between Christmas and the festival of Sol Invictus, ‘the unconquered sun’. This is often combined with a claim that (a) this equates to a celebration of Mithras and/or his birthday; or (b) Christmas is derived from the cult of the emperor, who in certain periods was often depicted with sun iconography.

The ultimate basis for the idea is a section of the Chronology of 354 known as the Philocalian calendar, which lists off civic festivals and other occasions in the city of Rome. In December it lists the following item:


8th (day before kalends of January, i.e. 25 December) -- festival of the Unconquered: thirty games ordered

Here N̅ stands for natalis (‘festival’) and C̅M̅ stands for circenses missi (‘games ordered’).

The confusion with Jesus is encouraged by the fact that in Latin natalis comes from a word meaning ‘birthday’: so you will often hear that the birth of Christ was chosen to coincide with the ‘birth’ of Sol Invictus. That is not the meaning of natalis in the Chronology of 354: there it refers to any kind of celebration. Compare for example the entries for 25 January, a natalis for the arrival of the annual papyrus shipment; 21 April, a natalis of the city. (See also M. Salzman, On Roman time (California, 1990) p. 119 n. 12, p. 126 n. 22).

There are two other equally important objections to the idea that Christmas was derived from the festival of Sol Invictus.

  1. Priority. The festival is first attested in the Chronology of 354, exactly the same document that gives us the first attestation of Christmas on 25 December. There's no basis for ascribing priority to one or the other. The Invictus celebration may be linked to an important temple of the Sun god founded by emperor Aurelian in 294 CE, but that's no more solid than the arguments I offered above for earlier allusions to Christmas.
  2. Lots of sun cults. Sol Invictus was just one of many aspects of the sun that received cult in Rome. In the 354 Chronology alone we find three other festivals of the sun: 6 June, the crowning of the Colossus; 28 August, the [natalis] Solis et Lunae; 19-22 October, the ludi Solis. Out of the four, the June festival is the one most likely to be linked to the imperial cult; either the August or October festivals stand just as much a chance as the December one of being linked to Aurelian's temple. S. E. Hijmans, Sol: the Sun in the Art and Religions of Rome (diss. Groningen, 2009) pp. 483-7 lists off three other temples to Sol within Rome; at p. 485 n. 17 he opts for 19 October as the festival of Aurelian's sun-cult.

And, in case it needs to be pointed out, the 25 December festival has nothing to do with Mithras. Mithras was depicted with sun iconography too, and was regularly called Sol Invictus Mithras or Deus Sol Mithras, but Mithraism was a mystery religion practised underground all over the empire; the 25 December festival was an official civic festival observed at a specific temple in Rome by the city of Rome.

Brumalia. Contrary to popular belief, solstice festivals were not a dime a dozen in antiquity: we have evidence of midsummer festivals from the Greek world, since that was the new year in Greek calendars; but not for the Romans. Brumalia is a rarity, as a clear case of a genuine winter solstice festival. In fact we're not even told explicitly that it was a solstice festival: we have to infer that, from the fact that bruma is the Latin for 'winter solstice', derived from an archaic word meaning 'shortest (day)'.

Christmas isn't based on Brumalia either. Brumalia isn't of any great antiquity: it's first attested in Tertullian (On idolatry 10.3), in the late 2nd century CE. It's fairly obscure, and we don't know very much about it: we do know it involved athletic games and gift-giving (but as we saw above, gift-giving wasn't introduced to Christmas until the modern era). Like Saturnalia, it continued to be celebrated long after Christmas was in place, and by Christians: in the 6th century, emperor Justinian organised a civic festival of Brumalia from which a celebratory oration by one Choricius of Gaza survives (Oration 13 ed. Foerster and Richtsteig; not in Boissonade's 1849 edition); by that time it had absorbed some elements of Saturnalia, both of them pagan festivals.

The solstice as a purely astronomical event. So it seems likely that Christmas is related to the solstice. But there's no particular reason to see it as linked to any pagan festival: we've firmly discounted Saturnalia, Mithras, and Brumalia, and there's only a potential case for Sol Invictus.

The most likely situation is that both Christmas and the Invictus celebration were assigned to 25 December because that was the traditional date of the solstice. That is, one wasn't borrowed from the other in any sense: they were sibling festivals, cognate rather than derivative. Note that we have evidence for the traditional date of the solstice 300 years before our earliest explicit evidence for the date of either festival. For Christians the motivation would be that early Christians already thought of Jesus as the 'sun of righteousness' (Malachi 4.2), as we saw above.

However, note well the discussion above of the relationship between Jesus' death-date and birthday: the death-date was primary, and the birthday calculated from that. That is, the important thing about 25 December wasn't that it was the traditional date of the solstice: it was exactly nine months after the traditional date of the vernal equinox, on 25 March. If that is indeed the basis for the date of Christmas, it's not because Jesus was understood as the sun returning light after a season of darkness: it's because his death and resurrection were believed to be represented by the centre-point of the sun's waxing, and therefore central in a cosmic sense too -- in the middle of life's journey, so to speak.

Further reading

  • Hijmans, S. 2003. ‘Sol Invictus, the winter solstice, and the origins of Christmas.’ Mouseion 3: 377–398. [DOI]
  • Hijmans, S. 2009. Sol: the sun in the art and religions of Rome. Diss. Groningen. See esp. chs. 5 and 9. Also published 2023 by Brill. [Rijksuniversiteit Groningen | Brill]
  • Mosshammer, A. A. 2008. The Easter computus and the origins of the Christian era. Oxford.
  • Roll, S. K. 1995. Towards the origins of Christmas. Kampen.

Endnote: pseudo-Hippolytus on the date of Christmas and Easter

Hippolytus, Commentary on Daniel 4.23.3 (M. Lefèvre, Hippolyte: Commentaire sur Daniel, Sources chrétiennes vol. 14, Paris: Éditions du Cerf, 1947):

ἡ γὰρ πρώτη παρουσία τοῦ κυρίου ἡμῶν ἡ ἔνσαρκος, ἐν ᾗ γεγέννηται ἐν Βηθλεέμ, ἐγένετο πρὸ ὀκτὼ καλανδῶν ἰανουαρίων, ἡμέρᾳ τετράδι, βασιλεύοντος Αὐγούστου τεσσαρακοστὸν καὶ δεύτερον ἔτος, ἀπὸ δὲ Ἀδὰμ πεντακισχιλιοστῷ καὶ πεντακοσιοστῷ ἔτει· ἔπαθεν δὲ τριακοστῷ τρίτῳ ἔτει πρὸ ὀκτὼ καλανδῶν ἀπριλίων, ἡμέρᾳ παρασκευῇ, ὀκτωκαιδεκάτῳ ἔτει Τιβερίου Καίσαρος, ὑπατεύοντος Ῥούφου καὶ Ῥουβελλίωνος.

For the first advent of the lord among us in the flesh, when he was born in Bethlehem, took place on the 8th day before the kalends of January (i.e. 25 December), a Wednesday (lit. 'the fourth day'), in the 42nd year of Augustus' reign, in the 5500th year from Adam; and he suffered in his 33rd year, on the 8th day before the kalends of April (i.e. 25 March), a Friday (lit. 'day of preparation'), in the 18th year of Tiberius Caesar's reign, in the consulship of Rufus and Rubellio.

Even if this were authentic, it would be either terribly corrupt or terribly incompetent. The year numbers make no sense. Augustus ruled only 40 years, so the birth date makes no sense unless the author thought Augustus' reign began in 44 BCE, immediately after Julius Caesar's death: in that case he would mean 1 BCE; that year 25 December fell on Saturday by modern reckoning, or within a day or two of that by Roman reckoning (Roman reckoning was not fully in synch with modern reckoning until 8 CE): certainly not a Wednesday. On the death date: the 18th year of Tiberius' reign began in September 31 CE, but the consulship of 'Rufus and Rubellio' (errors for C. Fufius Geminus and L. Rubellius Geminus) was in 29 CE. March 29 CE was in the 15th year of Tiberius' reign. Yet the consuls' names imply that the writer means the year 29 CE, and 25 March did fall on a Friday that year. A suggestion appears dotted around a few early sources that the sky darkening at Jesus' death (Mark 15:33) may be linked to a solar eclipse over Jersualem in 29 CE -- but the eclipse was in November of that year, not March/April. [Note, 19/1/16: just as a by-the-way, some modern enthusiasts instead link the report of darkness at Jesus' death to a solar eclipse in March 33 ... but that eclipse was over the southern Indian Ocean, and was certainly not visible in Jerusalem!]

Correction, Dec. 2023. In fact there’s no reason to reject the Hippolytos fragment, as I explain in this 2021 piece. Kellner rejected it as spurious in 1901, because (1) the quoted year disagrees with Hippolytos’ paschal table, and (2) the use of multiple calendar era systems is characteristic of 9th–10th century computistic research. Roll follows Kellner without going into the evidence in detail, and at the time I wrote this in 2015, I followed Roll. However, both of Kellner’s arguments are flat-out wrong. Ancient figures like Julius Africanus and Eusebius clearly illustrate the careful (and frequently erroneous) work done in antiquity on synchronising era and regnal year systems. Hippolytos’ flaky figures are entirely in keeping with 3rd–4th century Christian chronography. As a result Hippolytos, writing around 220 CE, stands as our earliest source for the 25 December date. See further this 2015 article by Thomas Schmidt.

Incidentally, we do not have adequate evidence to tell in what year 14 Nisan (Hebrew) might have been considered to correspond to 25 March (Julian). Modern reckoning is no use, as the Hebrew calendar at the time was observational; modern reckoning developed over the course of the 1st millennium CE.

[Note, 19/1/16: I've altered the wording and flow in a few passages to make my writing slightly less contorted. I've left annotations in the places where I've changed the content.]

[Note, 24/12/23: I’ve become aware that some people are still looking at this to get there information. Ongoing investigation reveals new information, though, and I now know that some of what I wrote in 2015 is inaccruate. I’ve added a note at the top to redirect readers to better information.]

Monday 14 December 2015

The library of Alexandria and the loss of knowledge

Note (Oct. 2023). This article is about the library’s weirdly overblown reputation. I recommend also taking a look at this piece from 2022, which talks about how it got that reputation.

Myth: the burning of the library of Alexandria was "the most destructive fire in the history of human culture".

Alexandria was the chief city of Hellenistic and Roman Egypt, and the most important cultural powerhouse of the ancient Mediterranean. The quotation above comes from this History Channel clip about its famous library, or rather libraries.

The narrator goes on (at the 1 min. 39 sec. mark):

In the battle that followed, Caesar ordered his soldiers to burn the Egyptian fleets lying in the harbour. The fire quickly spread from the waterfront to the great library. The flames consumed a large part of the library's collection, marking the single greatest loss of knowledge in history.
Some historians speculate that the fire set civilisation back by a thousand years. Who knows, if the great library of Alexandria hadn't burned, Columbus may not have sailed to the New World. He might have gone to the moon!
Recently a new library was built in Alexandria, but it can never replace the ancient collection burnt in the fire. It contained rare manuscripts, the comedies of Aristotle, and more than 200 plays by Aeschylus and Euripides — classic works forever lost.
Doctor sitting reading by an armarium holding books early 4th cent. CE; Met. Mus. of Art, New York)

This snippet ranges from absurd to outright false. (Let's do the easy bits right away: Aristotle didn't write comedies, and Aeschylus and Euripides wrote a combined total of about 170 plays.) The only bit that has any basis in reality is the first line, about Caesar burning the Ptolemaic fleet. Everything else is untrue, without any room for doubt on the point.

It's not like the History Channel is conveying an isolated opinion, by the way. It is really widely believed. Here's a full-length documentary that makes similar claims; the Wikipedia article on the subject refers to "the incalculable loss of ancient works"; Joel Levy's 2006 book Lost Histories calls it "the day that history lost its memory"; online forums frequently get questions about just how big a disaster it was.

Important point: I'm not talking today about the historical circumstances of the library's destruction. There certainly was a major fire in 47 BCE, and there may have been other important moments of destruction in later centuries. We're not here to pin down when it disappeared, or who's to blame: this is about the historical significance of the library's loss.

Several kinds of misconception feed into this myth.

  1. Misconceptions about the role of libraries in the ancient world.
  2. Misconceptions about what kinds of books the Alexandrian library actually held.
  3. Misconceptions about the actual causes for the loss of texts from antiquity.

1. The role of libraries

If the loss of the library was "the single greatest loss of knowledge" in history, that would mean the books destroyed were the only existing copies of those books.

Suppose — heaven forfend — that the British Library burned down tomorrow, or the Library of Congress. What kind of a loss would it be? In cultural terms, and purely in monetary terms, it would be catastrophic: millions of manuscripts, autographs, and rare and unique items would be lost, and the cost of replacing the printed collection would be vast.

But barely a scrap of actual knowledge would be lost. Ismail Kadare's novels would survive. The Thirty Years War would not be forgotten. Aeroplanes and computers would not become treasured relics, never to be recreated.

This is because there are lots and lots and lots of repositories of information in the world. And exactly the same was true in Greco-Roman antiquity. There were hundreds of libraries of Greek and Latin texts dotted around the Mediterranean. Alexandria was the biggest, but it was just one fish in a sea of libraries. There were also important centres at Pergamon, Athens, Rome, Constantinople, and many important private collections. Roman aristocrats founded many libraries in the early Principate; clubs and gymnasia in Greece were also centres of learning, with their own libraries, and we have inscriptions cataloguing regular deposits of books in their collections. Caesar's fire did not stop Athenaeus and Julius Africanus from being profoundly well-read more than two centuries later, and the likes of Pliny the Elder and Pausanias did their research privately or in Athens, not in Alexandria.

A fanciful depiction of the library in the Serapeion at Alexandria (Agora, 2009). (Who's in charge of this mess? The scrolls don't even have labels!)

The book trade thrived and had mass audiences. The literacy rate was higher than many modern people would naively expect: nowhere near modern First World levels, to be sure, but there was a big market for things like popular romances, basic reference books, and how-to manuals. Literacy was certainly not limited to a small elite class: almost anyone could scrawl graffiti on a wall without much education. Cicero refers to the publishing business on a scale that, for the time, we may as well consider industrial ( 3.6.6; Att. 12.6a). Books travelled from city to city easily: Pliny the Younger is delighted to hear that his own books were on sale at shops in Lyon (Letters 9.11.2). Book prices in 1st century CE Rome ranged from 6 sestertii for a cheap knockoff (Martial 1.66; one or two days' labourer's wage) to 5 denarii for a deluxe edition (Martial 1.117; = 30 sestertii). The amounts don't translate well into modern terms, but they're comparable to the prices of university textbooks: not chicken feed, but certainly not just for the elite either. To save costs further, publishers could recycle used papyrus (Catullus 22.5), or customers could commission copies made on the back of something else.

This last point is directly tied to one important function of ancient libraries. As well as being reading rooms, they were also scribal centres that bypassed the book trade. People could commission a scribe to go and make a copy of a book, and it seems this was a pretty economical thing to do. (Remember copyright is irrelevant in a society where reproduction is labour-intensive.) A beautiful example is the sole surviving copy of Aristotle's Constitution of the Athenians. An estate owner living near Hermopolis, Egypt, recycled four scrolls of his farm and business records by commissioning scribes to make a copy of some fairly high-powered intellectual works on the back, including Aristotle's book. (It's very unlikely that the copying was done at Alexandria, about 200 km away.) The economics of the situation are telling: the owner was willing to hire professional scribes, but not to pay for clean papyrus. In other words, scribes were cheap.

It is unlikely that more than a handful of texts of any consequence were lost in the fire of 47 BCE, for the simple reason that anything important certainly existed in many copies, in libraries and private collections, all over the Mediterranean.

2. The books in the library

In the popular imagination, the library held all manner of arcane knowledge lost in the mists of time — Babylonian mathematical treatises, dictionaries of Linear A, diplomatic correspondence between Egypt and Atlantis, the history of Göbekli Tepe, that kind of thing.

Illustrated edition of a poem about Herakles, probably for a popular audience: Herakles' fight with the Nemean lion (P.Oxy. 2331, 3rd century)

In reality it was not a repository of records left by the Pharaohs of the Old Kingdom. It was a Greek library, of Greek texts, for Greek people, founded around 300 BCE. One late source tells us that there were accessions of Egyptian, Chaldaean, and Roman books, but they were invariably translated into Greek (Syncellus, Chronographia 516,6-10). We don't know if the originals would have been preserved too; it doesn't seem likely that they were prized.

We have a very good idea of the kinds of things that were in the library. This is because surviving books routinely cite and discuss other books, including ones that have been lost. Many important pieces of modern research revolve around gathering together the fragments that we obtain this way: the most important such collection, the Fragmente der griechischen Historiker, lists over 1000 lost authors — and that's just in the genres of history and geography. In some cases we know a huge amount about these books; in other cases we know only titles. But it's more than enough to tell us that what we are missing is, essentially, pretty similar to what survived via the mediaeval manuscript tradition.

The thing that we're really missing out on is the colossal book-writing spree that Greek thinkers all round the Mediterranean went on in the late 4th to 1st centuries BCE: we have comparatively few intact books from that period — we have Aristotle, Euclid, and Dionysius of Halicarnassus, but we're missing out on the likes of Eratosthenes, Hipparchus, and Crates.

3. How ancient texts actually got lost

The destruction of a library is a terrible thing, but it's a drop in the ocean. The disappearance of Greco-Roman texts is a story about culture and economics, not a timeline of specific events. Left to themselves, books vanish over time without any need for someone stepping in to destroy them. Poor storage, poor longevity in the materials, environmental factors, and human agency all hasten that natural decay, but that decay will happen anyway. Over a thousand years, that's plenty to ensure the demise of nearly every book in existence.

Sure, it would be nice if the library of Alexandria had survived to the present day. But that means positing a miracle. No ancient library has survived to the present. Even if the Alexandrian library had survived the fires, eventually it would have gone the same way as the Palatine library in Rome — which suffered its own series of catastrophic fires (the History Channel never talks about those) — and the libraries of Pergamon, Tralles, Athens, and so on. Aristotle's Constitution of the Athenians, mentioned above, is a truly extraordinary case: only a handful of texts have survived by being preserved on an intact ancient papyrus.

Codex and scroll (Pompeii, before 79 CE): left, woman with note-taking codex (wax on wood); right, man with commercial scroll (with titulus)

Books survive if many different people ensure that they're copied. And the people of the past who did that copying weren't operating with any top-down, organised plan; they weren't members of a worldwide Book Preservation Society. They were independent institutions and individuals living in many different places and many different centuries, and their efforts just happen to have the fortunate combined effect that many texts have survived to the present.

Texts were disappearing long before Rome fell. The 2nd century CE is when we really start to notice extant sources treating old texts as things they haven't personally read — they only have second- or third-hand information. In other words, that's when texts start vanishing en masse. J. O. Ward, cited above, points out that many oratorical speeches from Cicero's time were already obscure in Tacitus' time. We have no evidence of any of the Epic Cycle surviving beyond the 2nd century. (Some of them did survive that long: so however they were lost, it had nothing to do with events in Alexandria.) Not a single ancient writer ever cites book 2 of Aristotle's Poetics, other than Aristotle himself: it was never as popular as the similar material in his On poets (also lost), which was intended for a wider audience, and about which we hear a great deal. Poetics book 2 may well have disappeared within a century of being written.

The 2nd-3rd centuries were also the time of a massive technical migration: from scroll to codex. ('Codex' is the word for a modern-style book, with pages sewn together at the spine.) The very biggest hurdle for the survival of books is nothing to do with libraries burning, or fictional stories about religious zealots destroying pagan books. It's about a format shift.

We first begin to hear about commercial use of codices by ancient booksellers in the 1st century CE poet Martial, who is impressed after seeing a codex edition of Ovid's Metamorphoses with the entire text in one volume (Epigrams 14.192):

haec tibi multiplici quae structa est massa tabella,
carmina Nasonis quinque decemque gerit.
Look at this bulk! It's built out of many­-layered leaves,
and holds fifteen books of Naso's poem.

Lionel Casson's Libraries in the Ancient World (2001), pp. 127-8, reports the following proportions in Egyptian papyrus finds:

Scroll Codex
1st-2nd centuries CE 98.5% 1.5%
ca. 300 CE 50% 50%
ca. 400 CE 20% 80%
ca. 500 CE 10% 90%
An armarium for codices: the real reason for the loss of Greco-Roman texts. (Codex Amiatinus, early 8th cent. CE)

A format shift doesn't only attach an extra cost to the survival of any text, it also attaches a time­-limit. If the storage units in your library are armaria for codices, scrolls that haven't been transferred by the deadline will simply not get stored in the library. In addition, ancient and mediaeval codices were normally stored flat on their backs — not on end, as in modern bookshelves — and they couldn't be piled high, if they could be piled at all. So even though a codex could hold a lot more text than a scroll, codices took up more space for the same amount of text!

Scrolls were effectively a self-destruct timer. A book published in scroll form might survive a century or three after 300 CE; but if it hadn't been copied into a codex by that date, the text was basically doomed.

Wars and fires don't help of course, but those are pretty minor things in comparison to a format shift that affected all books.

So don't lament for the library of Alexandria: celebrate it for what it was. It's an important chapter in the story of the development of knowledge. But in the story of the loss of knowledge, it barely warrants even a footnote.

Some other popular sources do a perfectly decent job with this topic: Carl Sagan's TV series Cosmos is a bit notorious for being unreliable on history, but it's on relatively steady ground here (1980; episode 1, "The shores of the cosmic ocean") —

Each of those million volumes which once existed in this library were handwritten on papyrus manuscript scrolls. What happened to all those books?
The classical civilisation that created them disintegrated. The library itself was destroyed. Only a small fraction of the works survived. And as for the rest, we're left only with pathetic scattered fragments.

This could be a lot worse. It's not flawless: elsewhere Sagan implies that figures like Aristarchus of Samos and Archimedes had something to do with Alexandria, when there's no evidence they ever even visited the city. But he's absolutely right to emphasise the demise of the civilisations that created libraries, or rather their governments — the Ptolemies in Alexandria, the Attalids in Pergamon — and not any single moment of destruction. If Caesar's Alexandrian War caused a loss of knowledge at all, it wasn't because of a fire: it was because he effectively ended the Ptolemaic dynasty, which had been supporting the library's operations for 250 years. If the Ptolemies had still reigned in 300 CE, it's likely that more work would have been put into preservation efforts.

Monday 30 November 2015

Eratosthenes and the well

Eratosthenes is one of the most famous individuals of the Greco-Roman world -- and justly so: he was a leading expert in cartography, philology, mythography, ethnography, geometry, and astronomy. In an age of nepotism, his raw talent and hard work got him headhunted by Ptolemy III while he was still living in Athens.

Nowadays, he is most famous for making a reasonably accurate calculation of the circumference of the earth, using 3rd century BCE data and methods. This was a celebrated feat in his own time too. The island of Elephantine, at Syene (modern Aswan), had a new hieroglyphic symbol for its name created, apparently in honour of his calculation, in the form of a plumb bob and try square.
for Elephantine
(one of many variants)

No myths so far: this story is all true. By calculating the relative angle of elevation of the midday sun in three cities on the same meridian and at the same season -- Alexandria, Syene (modern Aswan), and Meroë (the chief city of what the Greeks called Aithiopia; modern Bagrawiya, Sudan) -- with figures for the distances between these cities, and with the assumption that the earth's curvature was spherical -- he came up with a figure variously reported as either 250,000 or 252,000 stadia.

In terms of angular precision, the calculation was very exact. In terms of absolute distances, not so much. Eratosthenes' own writings on the subject do not survive. It's most likely that he calculated 250,000 stadia, but that the figure got "rounded" to 252,000 so as to give a tidy figure of 700 stadia per degree of the earth's circumference (360° × 700 = 252,000). More importantly, Ptolemaic methods for surveying long distances were very inexact -- not nearly as good as Roman measures, for example -- and, to boot, there were many variants of the stadion ranging from ca. 157 metres to ca. 262 metres. The problem of Eratosthenes' units is hair-pullingly complicated. (Maybe we'll revisit the subject one day. But then again, maybe not: it really is a messy topic.)

But how he calculated the earth's circumference -- that's where the myths come in. Here's an extract from an especially popular and influential account:
One day, while reading a papyrus book in the library, he came upon a curious account. Far to the south, he read, at the frontier outpost of Syene, something notable could be seen on the longest day of the year. On June 21st, the shadows of a temple column or a vertical stick would grow shorter as noon approached. And as the hours crept towards midday, the sun's rays would slither down the sides of a deep well, which on other days would remain in shadow. And then precisely at noon columns would cast no shadows, and the sun would shine directly down into the water of the well. At that moment the sun was exactly overhead. It was an observation that someone else might easily have ignored -- sticks, shadows, reflections in wells, the position of the sun: simple everyday matters. Of what possible importance might they be?
-- Carl Sagan, Cosmos (1980; episode 1, "The shores of the cosmic ocean")
NOT how Eratosthenes calculated the earth's circumference
The story of the well is repeated in a lesson at the Khan Academy, in an even more colourful (and fictional) account in Julia Diggins' 1965 book String, Straightedge, and Shadow, and in many more places.

And it is mostly false. There was a well like this at Syene: but it certainly had nothing to do with Eratosthenes, and nothing at all to do with his calculation.

Here's Pliny the Elder's account of the well (Natural History 2.183 [§75]):
Similarly they say that in the town of Syene, 5000 stadia south of Alexandria, no shadow is cast at noon on the solstice. A well was made to test this, and it was entirely illuminated. This showed that the sun was directly overhead at that time. Onesicritus states that the same thing happens at that season in India south of the river Hyphasis [i.e. the modern Beas].
(The source Pliny was using is vague: "south of the Hyphasis" sounds like it should indicate Punjab, but the tropic runs considerably south of Punjab. It does run close to Pataliputra, though, further to the south-east, which was the capital of the Maurya Empire until the early 2nd century BCE: that is probably what Pliny's Hellenistic source was talking about.) Strabo also describes the well (17.1.48), and his phrasing tends to suggest that it was moderately famous, though unlike Pliny he doesn't say that its unique feature was the very reason it was built.

No ancient source, at all, anywhere, connects this well to Eratosthenes. In the surrounding context of these passages, however, both Pliny and Strabo do mention the actual method that Ptolemaic surveyors used for measuring latitude: they used an instrument called the gnomon (Pliny NH 2.182; Strabo 17.1.48).

Gnomons were originally for determining the date of the solstice. This practice goes back many thousands of years, in many different civilisations. Meton used a gnomon in Athens in 432 BCE for this purpose; the Shang people in ancient China were using them to measure solstices in the 13th century BCE. In Egypt, one of the reliefs in the jubilee chapel of Senusret I depicts a 9-metre-high gnomon in connection with the festival of Min in the 20th century BCE.

In its simplest form, the gnomon was a vertical rod that cast a shadow. Measuring the ratio between the shadow and the length of the rod would constitute a gnomon reading. Old Egyptian gnomons typically had a bifurcated tip to make the shadow more defined (as in the Senusret relief). The Egyptians could use hand-held ones to mark the passage of time at night. Travellers in the Greco-Roman world had portable gnomons or sundials, in the form of a round vessel with a stylus embedded in the centre and markings on the sides: this set-up was called a skaphion (Greek) or umbilicus (Latin). The Egyptians were well aware that near the tropic it was difficult to measure the solstice with a vertical gnomon, because the shadows are so short at midsummer, and so they adopted the practice of tilting the gnomon to the north and supporting it with struts. (Further reading, for those with JSTOR access.) In later gnomons, plumb bobs were used to ensure it was exactly vertical: to judge from the hieroglyphic for Elephantine mentioned above, it looks like this was the case with the Ptolemaic gnomon. (And incidentally, remember that the symbol for Elephantine included a try square? It so happens that gnomon was also the Greek word for a try square.)

Ancient travellers regularly took gnomon readings as a way of recording their latitude. Pliny, just before the passage quoted above, tells us
Portable timepieces are not used the same way everywhere, because the sun's shadows change every 300 stadia, or at most 500 stadia [i.e. about 0.5° latitude]. So in Egypt at the equinox the shadow is only a little more than half the length of the umbilicus -- what they call a gnomon. In the city of Rome the shadow is 8/9 the length of the gnomon at the same season; in the town of Ancona it is 1/35 longer (i.e. 8/9 + 1/35, or 0.917); and in the region of Italy called Venetia the shadow is the same length.
Vitruvius gives another list of equinoctial gnomon readings in various cities. Ptolemy has an extended account of gnomons and latitude in book 2 of his Almagest. And Martianus Capella indicates that Eratosthenes' measurement was based on gnomon readings taken at the equinox (De nuptiis 6.597).

The practice of taking gnomon readings as a geographical measurement goes back at least to Pytheas of Massalia, a famed traveller of the early mid-4th century BCE. According to Martianus Capella (De nuptiis 6.595), Pytheas took gnomon readings all the way from southern France to "Thoule" (either Iceland, or one of the island groups in the North Sea, or perhaps Scandinavia). Also before Eratosthenes' time, Philon, a surveyor for Ptolemy II, reported gnomon readings at Meroë in his book the Aithiopika or Voyage to Aithiopia. The book itself does not survive, but this report does:
Philon discusses the latitude (κλῖμα) of Meroë in the Voyage to Aithiopia that he wrote. He says the sun is directly overhead 45 days before the summer solstice, and he reports his readings of the ratio between the gnomon and its shadow at the solstices and equinoxes. Eratosthenes agrees very closely (συμφωνεῖν ἔγγιστα) with Philon.
Philon, New Jacoby 670 F 2 (=Strabo 2.1.20)
So, to recapitulate:
  • Eratosthenes didn't use a well to measure anything: the instrument of choice was the gnomon.
  • Taking latitude readings from a gnomon was standard practice for Ptolemaic surveyors decades before Eratosthenes came along.
  • The summer solstice barely came into it; gnomon readings were taken year-round, but it looks like equinoctial readings were the basis of Eratosthenes' calculation.
  • Eratosthenes didn't take the readings himself: he probably used Philon's published work as the basis of his calculation.
The well at Syene was just a striking, large-scale visualisation of the Tropic of Cancer. Pliny's wording suggests it may not even been built until after Eratosthenes' calculation anyway. And native Egyptians had known for centuries that Syene was on the Tropic of Cancer. (In fact Syene was slightly north of the tropic: it's at 24.09° N, and the tropic was at 23.72° N in Eratosthenes' time. The plane of the ecliptic shifts slightly over the millennia: currently it's at 23.44°.)

Monday 16 November 2015

On the ‘losing’ of Troy

In Greek legend, the Trojan War ended with the Greeks using a colossal wooden horse to burn the city, sack it, and raze it to the ground. Men and boys were killed, women and girls were enslaved and transported. There were no survivors and no remains. Troy was utterly destroyed.

Many modern people are under the impression that the same thing happened to the historical city of Troy: that Troy ceased to exist at the end of the Bronze Age; that it was destroyed by the Greeks at the end of the Bronze Age, so that even the location of the city was lost; and that the ruins of the real Troy lay undiscovered until Heinrich Schliemann’s excavations in the 1870s-80s.

Everything in the above paragraph is unequivocally false.

We won’t focus on Schliemann today — his activities at Hisarlık (the modern name for the hill of Troy’s citadel) offer more than enough material for a lengthy debunking all by themselves. Today we’ll focus on the ‘loss’ of Troy. When was Troy ‘lost’?

Early Greek epic certainly gives us ample reason to think of Troy as a city that has been destroyed utterly. At one point in the Iliad, a defeated Trojan begs the Greek Menelaos for mercy. Menelaos is considering taking him captive instead of killing him, but his brother Agamemnon pops out of nowhere and says (Il. 6.55-60):
‘Menelaos, my dear, why do you care so much
about these men? Have you and your house been treated so finely
by the Trojans? Let none of them escape sheer destruction
at our hands, not even any boy that a mother carries
in her womb: let none escape, but let all the people
of Ilios be utterly destroyed, unmourned, wiped to oblivion!’
(Ilios/Ilion is an alternate name for Troy.) And here’s a fragment from the Little Iliad, a poem from the lost Epic Cycle, which uses one family as an emblem for the massacre of the children and enslavement of the women (fragment 21 ed. Bernabé = fr. 29 ed. West):
But Achilleus’ great-hearted shining son
led Hektor’s wife in captivity back to the hollow ships,
and he took her son from the embrace of his lovely-haired nurse,
grabbed him by the foot and threw him from a tower. As he fell,
a bloody death and hard fate snatched him up.
Sack of Troy: Neoptolemus kills king Priam,
bludgeoning him with the corpse of his grandson.
(Attic, ca. 520-10 BCE; Louvre)
Euripides’ play the Trojan Women (415 BCE) gives another angle on the sack of Troy. There the narrative focus is firmly on the survivors, the women of the city, who are about to be carted off into slavery while still mourning for their husbands and sons, in an act of destruction that was not caused by any of them. (Euripides’ picture of the destruction wrought upon Troy is especially thorough because he was using the legend as an allegory for current events: the previous summer, the Athenians had decided to commit genocide on the island of Melos, slaughtering the entire male population and enslaving all the women, rather than allow the Melians to remain neutral in the Peloponnesian War.)

That’s the legend. What about the reality?

Archaeological evidence is the most reliable way of corroborating or disproving the stories. And one piece of archaeological evidence is popularly linked to the legend. There are traces of a large fire on the citadel of Troy dating to the end of the level called ‘Troy VIIa’, that is, ca. 1190 BCE. The archaeological layers are numbered Troy I, II, III, etc. starting from the lowest and earliest level: the higher the number, the shallower and more recent the archaeological remains are. The fire of Troy VIIa is popularly equated with the legendary war especially thanks to Michael Wood's BBC TV documentary series and book In Search of the Trojan War (1985). For what was known at the time, it’s an extremely competent piece of work. The entire series can be watched on YouTube here.

It is perhaps worth pointing out that, among ancient historians who believe the Trojan War actually happened, they gravitate more towards Troy VIh as the best candidate for a historical war. That would put the ‘fall of Troy’ about a century earlier. Very few ancient historians nowadays would opt for Troy VIIa. But that’s neither here nor there. As another incidental by-the-way, some archaeologists involved in excavation at Troy would now refer to that layer as ‘Troy VIi’, not VIIa (for reasons that don’t matter just now).

The important thing, and it really is worth emphasising, is that Troy was not destroyed at that time. On the contrary: after the fire of Troy VIIa, the citadel was promptly rebuilt. It continued to be occupied without any pause for another 250 years or so. The population dwindled — not an exceptional thing: that also happened at many other sites in Greece and Anatolia in the early 12th century BCE — and the site was finally abandoned ca. 950 BCE.

Did I say abandoned? Well, yes... but the story doesn’t end there. Troy was not ‘lost’ in 950 BCE either. In fact, Greek colonists settled the site once again starting in the early 8th century BCE. It became a Greek city, and a part of the Greek world.

There were probably other ethnic groups already living in the region, who would account for references in Homer to Lelegians and other peoples living with and allied to the legendary Trojans. These peoples are not part of the history of Bronze Age Troy: there is no evidence to put these groups there in the 12th century, in spite of large quantities of Hittite textual evidence about the regional and ethnic divisions of Anatolia. In the Greek city of Troy, the main state cult was to Ilian Athena. And again, this Greek cult, dating to the time of Greek colonisation, accounts for the references to a cult of Athena in the legendary Troy: in Homer, the only cult inside the city walls that is mentioned is the shrine to Athena on the citadel (at Iliad 6.269-70 and 6.297-311), even though Athena is vehemently opposed to the legendary city.

Greek Troy continued to be inhabited for another two thousand years.

It went on to have a colourful history. Xerxes visited Troy on his way to invade Greece in 480 BCE, and made offerings to Ilian Athena as a propaganda gesture: it made it look as if he had come to avenge king Priam. When Alexander captured Troy from the Persians in 334 BCE, he too made offerings to Ilian Athena, gave Troy special legal privileges, and ordered the construction of a new temple to Athena. From 306 BCE Troy enjoyed still more status as the capital of a league of cities in the Troad.
Coin of Antiochus III, 197 BCE
The Seleucid king Antiochus III joined Xerxes and Alexander on the list of leaders who honoured Ilian Athena and Troy. So too did the Roman general Cornelius Scipio, when he overthrew Antiochus.

In the Roman era, Troy came to be more important still, as a emblem for Roman-Greek relations. There was already a long-standing legend that Romans had Trojans in their ancestry, so Troy took on great symbolic importance. There may have been one bad hiccup in 85 BCE: there’s a story (not corroborated) that a mutinying Roman commander, Fimbria, sacked the city and boasted that he had done in ten days what Agamemnon had taken ten years to do.

But afterwards Julius Caesar, as dictator of Rome, continued the tradition of honouring the city with tax breaks and other privileges. Caesar’s family claimed descent from the goddess Venus via the Trojan Aeneas, so Caesar tried to shift the emphasis of Trojan religious life away from Athena (Minerva) towards Aphrodite (Venus), and he issued coins showing Venus on one side and Aeneas’ flight from Troy on the other. To some extent this stuck: Aphrodite continued to appear on some later Trojan coins. Suetonius, a gossip-mongering biographer, claims that there was even a rumour floating around just before Caesar’s assassination that he had been planning to abscond with the city’s armies and treasury and set himself up as king of an eastern empire, with his capital in either Troy or Alexandria. That rumour is certainly untrue. But it may just be true that the rumour did exist.

Under the Principate, another new temple to Ilian Athena was built in the reign of Augustus. Many other public works followed, and Troy reached the pinnacle of its historical size and importance. In the 4th century CE, when the emperor Constantine was planning to establish a second capital city for the eastern half of the empire, he was seriously considering Troy as an alternative to Byzantium. It would never have made sense to actually choose Troy ahead of Byzantium — a tourist trap ahead of a major economic power with major strategic significance — but it shows that Troy still had huge symbolic importance.

Its importance only began to fade after around 500 CE, when it was badly damaged by a major earthquake. Increasing urbanisation around Constantinople must also have leeched people and money away from Troy. Even so, in the 10th century it became the seat of a minor Byzantine bishop. But it must have been badly hit by the Byzantine-Turkish wars in the 11th century; by the time the Ottomans finished conquering the region in 1308, it had probably been abandoned for some time.

At that point, and only at that point, does it begin to make any kind of sense to speak of Troy as ‘lost’. And even then, it was only ‘lost’ in the sense that people in the Latin west no longer had any direct knowledge of it because they didn’t travel in the region very much.
Edward Daniel Clarke, 1769-1822
Pretty much as soon as western visitors started writing memoirs of their tours in the area, the location of Troy became ‘known’ again. Five hundred years later, in 1801, the English traveller Edward Daniel Clarke became the first modern westerner to write about the site. In the 1850s, when British forces were stationed in the region during the Crimean War, an engineer named John Brunton carried out some brief excavations and uncovered a Roman mosaic, as can be read in his memoirs. As far as Brunton was concerned, there was no particular doubt or controversy about the identification of the site as Troy. Frank Calvert and Johann Georg von Hahn were the first people with archaeological expertise to visit the site, in 1863-65.

Schliemann was neither the discoverer of Troy nor the first person to identify the site as Troy (in fact he doubted Calvert's word on the matter at first). He was just the first excavator to get down to Bronze Age material, and he liked to pretend that there was an entrenched orthodoxy against him for rhetorical reasons. In reality, Troy didn’t need to be ‘discovered’: it was never lost in any meaningful sense.

Further reading. Trevor Bryce, The Trojans and their neighbours (Routledge, 2006), chapter 7 is an excellent brief summary of the history of Greco-Roman Troy (VIII, IX, and X). On the city’s cultural and political signifiance in the same age, see Andrew Erskine, Troy between Greece and Rome (Oxford, 2001).

Wednesday 4 November 2015

Were the Greeks scared of irrational numbers?

There is a widespread notion that the discovery of irrational numbers was a thing of horror to the ancient Greeks. This went especially for the school of Pythagoras. Pythagoras is best known today for a famous theorem about right-angled triangles -- and we shall look at that theorem another day -- but in antiquity, his significance lay in the fact that he was a semi-legendary guru who founded a philosophico-religious sect in southern Italy.

No writings by Pythagoras himself survive (and it is extremely unlikely he ever wrote any). But the things we hear about the sect make it sound bizarre at times: depending on who you read, the Pythagoreans conveyed their teachings only orally and only in a cave, they had weirdly specific beliefs about reincarnation, and they venerated unexpected plants like fava beans and mallow. The vast majority of this information is reported very late, and is almost certainly false; the bits that are true (whichever ones they are) are difficult to understand out of context.

The legendary Pythagorean veneration of orderly, rational numbers is well exemplified by a passage in William Meissner-Loeb’s graphic story Epicurus the sage, volume II (1991). Here the philosopher-hero Epicurus happens upon a group of Pythagoreans holding a ceremonious gathering to recite the powers of 2 (‘2 ... 4 ... 8 ...’), and Epicurus terrorises them by shouting out random numbers. They lose their concentration and flee, crying out, ‘Unclean numbers! Unclean! Unclean!’ and ‘Ahhhh! It’s happening again!’

In 1972 the mathematician Morris Kline wrote in his book Mathematical thought from ancient to modern times (vol. 1, p. 32):
Numbers to the Pythagoreans meant whole numbers only. ...Actual fractions... were employed in commerce, but such commercial uses of arithmetic were outside the pale of Greek mathematics proper. Hence the Pythagoreans were startled and disturbed by the discovery that some ratios -- for example, the ratio of the hypotenuse of an isosceles right triangle to an arm or the ratio of a diagonal to a side of a square -- cannot be expressed by whole numbers. …The discovery of incommensurable ratios is attributed to Hippasus of Metapontum (5th cent. B.C.). The Pythagoreans were supposed to have thrown Hippasus overboard for having produced an element in the universe which denied the Pythagorean doctrine that all phenomena in the universe can be reduced to whole numbers or their ratios.
Not to put too fine a point on it, but every claim in this paragraph -- apart from the bit about Greek commerce using fractions -- is untrue. In reality,
  1. Fractions were an integral (ha ha) part of Greek mathematics and held an important place in the Pythagorean theory of harmonics.
  2. There was no Pythagorean doctrine about reducing all phenomena to ratios.
  3. There is no evidence that anyone was ‘startled and disturbed’ by irrationals.
  4. The attribution of the discovery to Hippasus is speculative.
  5. No one threw Hippasus off a ship.
Kline is not alone. And worse, an apparently reputable source like Kline can mislead more popular writers. Simon Singh, in his bestseller Fermat’s last theorem (1997), goes seriously overboard -- even more so than Hippasus --
[T]he idea that rational numbers... could explain all natural phenomena... blinded Pythagoras to the existence of irrational numbers and may even have led to the execution of one of his pupils. One story claims that a young student by the name of Hippasus as idly toying with the number √2, attempting to find the equivalent fraction. Eventually he came to realise that no such fraction existed, i.e. that √2 is an irrational number. Hippasus must have been overjoyed by his discovery, but his master was not. Pythagoras had defined the universe in terms of rational numbers, and the existence of irrational numbers brought his ideal into question. ...Pythagoras was unwilling to accept that he was wrong, but at the same time he was unable to destory Hippasus’ argument by the power of logic. To his eternal shame he sentenced Hippasus to death by drowning.
The father of logic and the mathematical method had resorted to force rather than admit he was wrong. Pythagoras’ denial of irrational numbers is his most disgraceful act and perhaps the greatest tragedy of Greek mathematics.
(For the record: we know nothing of the circumstances of the discovery, there was no execution, and Hippasus lived in the late 5th century BCE, more than a century after Pythagoras’ death.)

Singh paints Hippasus’ discovery in vivid colours. Does that make up for the fact that it is not only imaginative, but also completely imaginary? Hm.

I do not exactly blame Singh. Half of the relevant primary sources have never been translated into any modern language. But it does go to show how a story that is already distorted can metamorphose into something completely fictional.

So, what does the actual evidence tell us? The surviving testimony is as follows, in chronological order.
  • Late 2nd century CE: Clement of Alexandria, Stromateis 5.9.57. Clement reports that a Pythagorean named "Hipparchus" revealed the teachings of Pythagoras in a book. As a symbol of his expulsion from the sect, the Pythagoreans erected a gravestone as if he were dead.
  • 3rd-4th century CE: Iamblichus, Life of Pythagoras tells us:
    • 88-9 (§18): Hippasus, a Pythagorean, revealed the discovery that the vertices of a regular dodecahedron coincide with the surface of a sphere, and because of his impiety he was lost at sea;
    • 246 (§34): a man who made public the nature of rational and irrational ratios was so hated by the Pythagoreans that they expelled him and erected a tomb as if he were dead;
    • 247 (§34): a man who revealed the construction of the dodecahedron drowned at sea, punished by a divinity; others say that this happened to the man who revealed the nature of rational and irrational ratios.
  • Early 4th century CE: Pappos’ commentary on Euclid’s Elements, book 10 (in the surviving Arabic version, 2.§2, p. 64 Thomson [warning: large PDF file]), and an anonymous ancient commentator on the Elements (scholion on book 10, proposition 1; lines 41-5 and 71-9 in the TLG text). According to these sources the Pythagoreans, to illustrate their reverence for ratios, spread a fable that the man who made public the existence of irrationals died by drowning. And the moral of this fable was that things that are irrational (alogon) prefer to be kept hidden and unspoken (alogon); and that someone who is too greedy for knowledge "gets sunk in the sea of reincarnation, and dashed by its chaotic currents" (εἰς τὸν τῆς γενέσεως ὑποφέρεται πόντον καὶ τοῖς ἀστάτοις ταύτης κλύζεται ῥεύμασιν).
  • Later than the 6th century CE: an interpolation in David of Armenia’s Exegesis of the Categories (Commentaria in Aristotelem Graeca vol. 18.1 [incorrectly attributed to Elias], p. 125). This interpolation, of unknown date, reports that a Pythagorean who wrote a book called On irrational proofs died in a shipwreck for disgracing secret teachings.
And the upshot of this testimony is:
  1. Hippasus did not discover irrationals: he made secret Pythagorean doctrines public.
  2. The nature of these doctrines is unclear. It may have been the nature of rational and irrational numbers; it may have been the existence of the dodecahedron, or the fact that its vertices coincide with a sphere.
  3. He was not executed or thrown off a ship: he died in a shipwreck, and some moralists attributed this to divine agency and made an allegorical fable out of it.
  4. Alternatively, his former comrades built a tomb for him, to represent that he was dead to them.
But the worst of it is that even this honest summary is probably completely untrue as well. The fullest account comes from Iamblichus, and Iamblichus is notoriously untrustworthy. Pappos makes it clear that as far as he was concerned, it was a morality fable, not a sequence of historical events. Most of the late biographical material about Pythagoras is based on one or both of two accounts written in the 1st century CE, six centuries after Pythagoras’ death: one by Nicomachus of Gerasa, the other by Apollonius of Tyana. To judge from Iamblichus, Nicomachus routinely attributed miracles to Pythagoras, and -- no joke -- regarded him as an avatar of the god Apollo. Apollonius came to be regarded as a miracle-worker himself, in a surviving ‘biography’ which dates to the 4th century. Their biographies, and the surviving one by Iamblichus, are more like gospels for a Pythagorean mystic cult than anything historical.

None of them can be trusted an inch.

Trustworthy testimony about Pythagoras and the Pythagoreans is in short supply. Generally speaking, the earlier, the better: and Iamblichus and the others are very late. We get hints about Pythagorean doctrines in Herodotus (5th cenutry BCE), Plato, and Aristotle (4th century BCE). But most of that material relates to the mystical side of Pythagoreanism: in particular, the early sources have nothing to say about Pythagorean teachings about irrational numbers. So we have essentially no corroboration for anything that Iamblichus and other late sources have to tell us. It is all suspect, and it is mostly false.

For what can be recovered about 5th-century-BCE Pythagorean teachings about mathematics, a good starting place would be Reviel Netz’ essay ‘The problem of Pythagorean mathematics’ (C. A. Huffman, ed., A history of Pythagoreanism, Cambridge, 2014, pp. 167-84): Netz argues that the Pythagorean mathematician par excellence of the time was not Hippasus, for whom no early evidence exists, but rather Archytas, about whom Aristotle tells us a good deal.

Did I say Plato has nothing to say about irrational numbers? Well, not in relation to Pythagoreanism, maybe. But one of Plato’s dialogues does have a section devoted to a discovery made by Theaetetus of Athens, that numbers other than exact squares (1, 4, 9, 16, 25...) have irrational square roots (Theaet. 147d-148b). Theaetetus was no slouch: much of book 10 of the Elements may well be his doing. Theaetetus divides the integers into two groups: exact squares, which he called ‘square and equilateral’ (τετράγωνόν τε καὶ ἰσόπλευρον), and numbers that are not squares but are ‘rectangular’ (ἑτερόμηκες). He calls their square roots, respectively, a ‘length’ (μῆκος) and a ‘power’ (δύναμις); and ‘lengths’ and ‘powers’ are incommensurable with one another. ‘And similarly for solids,’ he finishes on a tantalising note.

In the dialogue, what is Socrates’ reaction to the revelation of irrational numbers? Is he horrified? disoriented? ‘startled and disturbed’?

No. He is impressed at a nifty mathematical discovery.

As we all should be. Irrational numbers were not a skeleton in the Pythagoreans' closet: if the Pythagoreans had anything to do with their discovery -- and that’s a big if -- they should instead be regarded as one of the Pythagoreans’ greatest achievements. But in reality, it’s most likely that credit for the achievement belongs to Theaetetus: and he was not executed or ostracised, but was highly respected for his mathematical work.