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How Eratosthenes measured the earth: the angle of the sun
Part 4 of 4 on Eratosthenes' measurement. The final hole in his methodology: the angle of the sun.
The angle of the sun is the last hurdle Eratosthenes had to overcome with his data collection methods.
Here we review the popularly believed story -- measuring shadows of sticks -- before looking at a likelier and methodologically simpler alternative.
Concludes with a bibliography.
(Reading time: 15 minutes)
How Eratosthenes measured the earth. Part 2b: Distance
The ongoing story of how Eratosthenes measured the earth, based on ancient evidence. Part 2b: distance.
Part 2b: the problem of measuring distances in antiquity, and the question of Eratosthenes' units.
How did Eratosthenes find out the distance from Syene to Meroƫ? What units did he use, and what do they mean in modern units? What's the difference between the 'metrological stadion' and the 'itinerary stadion'? (And how do they compare to the kilometre and the 'itinerary kilometre'?)
(Reading time: 18 minutes)
How Eratosthenes measured the earth. Part 2a
The story of how Eratosthenes measured the earth. Part 2a: basic principles; the problem of simultaneous measurements.
The ongoing story of how Eratosthenes measured the earth, informed by actual ancient evidence.
Part 2a introduces the basic principle of the measurement; the technological hurdles involved; and how he solved the problem of simultaneous measurements.
(This was not a problem to be solved with two sticks!)
Reading time: 16 minutes
An ancient device for measuring the angle of the sun
Left: an ancient device for determining the azimuth of the sun at midday transit, described by Ptolemy in his Almagest.
Right: a 2nd century BCE graffito from Meroƫ, Sudan, apparently depicting an astronomer using this instrument.
The device and a gnomon are aligned with the meridian (i.e. north-south). Use the gnomon to determine midday. Then at midday you move the inner ring of the device until the shadow of ridge A falls on ridge B. Then you read the angle of the sun on the outer ring.
Precision is to closer than 1 degree, according to Ptolemy.
Eratosthenes' wobbly Alexandria meridian
In the mid-200s BCE Eratosthenes invented the device of lines of longitude and latitude. The Alexandria meridian held a central place in his Geography, an account of the geography of the known world.
Key locations on the meridian: Olbia (Ukraine), Lysimacheia (TĆ¼rkiye), Rhodes (Greece), Alexandria (Egypt), Syene (Egypt), MeroĆ« (Sudan).
Ancient geographers were aware that their meridians weren't perfectly straight. But measuring longitude was a difficult problem, and it wasn't properly solved until the 1700s.
Eratosthenes went on to use published reports of gnomon readings from three of these locations, and a traditional measure of the length of Egypt, to determine the earth's polar circumference. His result was 250,000 stadia -- ca. 46,220 km, plus or minus 2000 km (the stadion isn't a very precise measure). The true figure is 40,008 km.
How Eratosthenes measured the earth
Part 1: the discovery of the earth's shape.
An accurate version of the story of how Eratosthenes measured the earth. Part 1: the discovery of the earth's shape.
Prior to around 400 BCE, everyone was a flat-earther. After 400 BCE, it seems pretty much everyone in the ancient Mediterranean was a round-earther. We look at Archaic Greek thought on the shape of the cosmos and the earth's location, astronomical observations of the celestial pole and the angle of the ecliptic, leading up to the earliest estimate of the size of the spherical earth in Aristotle.
(Reading time: 18 minutes)
Chrest or Christ
'Chrest' and 'Christ' appear side-by-side in two Roman authors of the 110s CE, Tacitus and Suetonius. Why?
2nd century Roman sources refer to 'Chrest' and 'Christ'. What's the difference and which is correct?
The answer lies in a mix of Greek pronunciation, Latin transliteration conventions, phonetic spelling, and Christian palaeographic conventions.
Reading time: 10 minutes
Tacitus mentioning Christians: the manuscript of Annals 15.44, Cod. Laurentianus Plut.68,2 fol. 38r.
In the first highlighted line the scribe wrote 'Chrestianos'. Later part of the e was scraped away to leave an i -- correcting a spelling error, as the corrector believed, but actually introducing an error.
This manuscript is carefully made. Note the glosses above the lines to explain Tacitus' wording. In the margin, a scribe has marked Christian martyrs' deaths with a cross.
Lies, damned lies, and ChatGPT
ChatGPT is a chat bot that is really, REALLY good at relevance, coherence, and sounding plausible. But it's incredibly bad at factual accuracy.
If you're a teacher, why not use it as a teaching tool rather than banning it? Students are going to use it anyway: best they learn about it's limitations.
An exploration of some of ChatGPT's strengths and weaknesses from a classicist's point of view.
(14 minutes reading time)
ChatGPT is a great relevance engine. But it's really, REALLY bad at specifics.
Homer's metre: Hermann's Bridge
Hermann's Bridge is by far the most fundamental feature of Homeric prosody.
You'll find a short syllable at the start of the line more often than you'll find a violation of Hermann's Bridge.
Reading time: 11 minutes
Hermann's Bridge is far and away the most fundamental prosodic feature of Homeric language.
Dactylic hexameter - rhythms and phrases
The building block of Homeric poetry is the prosodic phrase.
This is part 1 of a look at Homeric verse, without using the artifical concept of feet. (Feet are to Homeric poetry what roads are to geology. Handy for getting around, but nothing to do with the actual thing.)
Part 2 will look at what is by far the strictest prosodic feature of Homeric verse: Hermann's Bridge.
Reading time: 13 minutes
The epic hexameter is built out of phrases, prosodic units, not feet.
Translating gender
On translating characters' pronouns in ancient texts: some test cases.
What are Athena's pronouns in Odyssey 1? How about Teiresias? Attis?
A look at some questions involved in gendered language in ancient texts, and what modern translators do with it. Reading time: 14 minutes.
Doctor Who, 'The Myth Makers' (1965)
In 1965 Doctor Who witnessed the fall of Troy. The Doctor ends up designing the wooden horse, Steven takes the guise of Diomedes, and Vicki becomes Cressida and stays behind with Troilus.
Here we take a look at the sources that the serial uses and abuses: Homer, Shakespeare, and of course the 1956 film Helen of Troy.
(Reading time: 15 minutes)
In 1965 Doctor Who witnessed the fall of Troy. This is a look at the sources that the serial uses and abuses.
Literary terms #2. Gradatio
Gradatio. A construction where each phrase repeats the end of the previous phrase.
For your brother and my sister no sooner met but they looked, no sooner looked but they loved, no sooner loved but they sighed, no sooner sighed but they asked one another the reason, no sooner knew the reason but they sought the remedy. ā Shakespeare
Fear leads to anger, anger leads to hate, hate leads to suffering. ā Yoda
Literary terms #1. Zeugma
Zeugma. The device of attaching multiple words or phrases to a single verb, whether or not they are strictly parallel.
'He hastened to put out the cat, the wine, his cigar, and the lamps.' ā Flanders and Swann
'She made no reply, up her mind, and a dash for the door.' ā Flanders and Swann
The Twelve Myths of Christmas
The first myth of Christmas my true love told to meā¦
The 'Christmas is pagan' meme was invented twice. Once by Naturalistic approaches to ancient religions in the 1800s (Invictus, sun cults); once by the Puritans in 1600s England (Saturnalia, Yule).
Mainstream scholars haven't taken Naturalism seriously since the 1920s. And no one should ever take Puritan propaganda at face value.
The second myth of Christmas my true love told to meā¦
Christmas was assigned to a traditional date for the solstice, for several spurious reasons, but pagan festivals weren't one of them.
The only reason to assume 'solstice' means 'pagan' is because Naturalism told you so. (Or the Puritans.)
The third myth of Christmas my true love told to meā¦
Christmas trees originated in Lutheran Germany in the 1500s. Their origins are firmly Christian. No one's ever traced a sensible historical link from any pagan sacred tree to 16th century Christmas trees.
The fourth myth of Christmas my true love told to meā¦
St Boniface didn't invent Christmas trees in 723. Willibald's story is simply that Boniface chopped down an oak sacred to Jupiter -- to destroy it.
There's no way to draw a link between that and Lutheran decorated trees 800 years later.
The fifth myth of Christmas my true love told to meā¦
Santa isn't Odin.
This idea was invented by a 1902 book about Dutch customs, then popularised by a Wikipedia editor in 2010.
Odin's horse didn't fly, and Santa didn't have reindeer until the 1820s. The reindeer were invented in New York.
The sixth myth of Christmas my true love told to meā¦
Christmas isn't based on Yule.
Yule was a mediaeval Germanic name for the winter months. We see it in north Germanic sources from the 700s onwards; its earliest appearance is in a Christian calendar dating to the 500s.
Christmas had been a Mediterranean-wide festival for 300 years by that point.
The seventh myth of Christmas my true love told to meā¦
The 'Yule log' isn't pagan. It isn't even a Yule custom. One scholar, Ronald Hutton, puts its origins in 1800s England, but it's a bit older: Robert Herrick mentions it in the 1600s.
Herrick calls it a 'Christmas log'. Guess who renamed it a 'Yule log'? Answer: the Puritans.
The eighth myth of Christmas my true love told to meā¦
Christmas isn't based on a 25 December Sol Invictus festival.
The 25 December date is first reported by Hippolytus of Rome in the early 200s, and was celebrated all over the Roman empire. The Invictus festival (not 'Sol' Invictus) appears in only one document ever, dating to 354, and was specific to Rome.
The ninth myth of Christmas my true love told to meā¦
Christmas isn't based on Mithras, Horus, or the Ptolemaic Kikellia. Mithras and Horus didn't have birthdays. Kikellia was confined to a single location: Alexandria, Egypt (like Invictus in Rome). Christmas was pan-Mediterranean by the 200s.
The tenth myth of Christmas my true love told to meā¦
While we're at it, 'Xmas' isn't an attempt at secularisation. It's a Christian abbreviation.
The X stands for Ī§ĻĪ¹ĻĻĻĻ ('Christ'). It comes from an abbreviation convention in ancient Christian manuscripts, called a nomen sacrum ('sacred name'), perhaps with some influence from the chi-rho monogram shown below (Ī§Ļ = Ī§ĻĪ¹ĻĻĻĻ).
The eleventh myth of Christmas my true love told to meā¦
Christmas trees, wreaths, presents, cards, and flying reindeer are all modern developments. In England they caught on in the early 1800s. Most of them are Lutheran in origin ā¦ that is to say, Protestant. The reindeer are an American innovation.
The ancient bits of Christmas are the bits in the nativity story. The ox and ass, the cave, the ā¦ midwife? (None of these are in the Bible. But they are ancient!)
The twelfth myth of Christmas my true love told to meā¦
There isn't a nativity story in the Bible. There are two. And they're completely different. They have some motifs in common -- angels, dreams, Bethlehem -- but they incorporate them in different ways.
The idea of synthesising them into a single story is ancient, though. It was first done in a 2nd century text, the Protevangelium of James, which also introduced the cave and the midwife. (The ox and ass came later.)
ADDITIONAL SOURCES
History of the 'Christmas is pagan' meme in 19th-20th century scholarship: Roll 2000; Nothaft 2012
Assigning Christmas to 25 December: Nothaft 2011, Dating the Passion: the life of Jesus and the emergence of scientific chronography; Nothaft 2013; Gainsford 2021
The Christmas tree and St Boniface: McDaniel 2018
Santa and Odin: McDaniel 2019; Gainsford 2022
Yule: Tille 1899: 90-96; Koivulehto 2000; Landau 2006; Gainsford 2018; Gainsford 2021
Invictus and Sol: Hijmans 2003; Hijmans 2009
The nativity stories: Brown 1977, The birth of the Messiah; Gainsford 2020
Miscellaneous other ancient festivals and non-Christian divinities: Epiphanius, Panarion 51.22.3-13; McDaniel 2019; O'Neill 2020
Cave, virgin birth (as opposed to virgin conception), and midwife: Protevangelium of James
The ox and ass: Origen, 13th homily on Luke
Santaās reindeer, Odinās horse, and Siberian shamanism
Is Santa based on Odin? Or is he a Siberian shaman?
These theories are being repeated on social media more every year, but they're based on partial information, misinterpretation, and an overdependence on Mircea Eliade. Both theories revolve around Santa's reindeer.
The key facts are:
Santa's reindeer were invented in New York in the 1820s.
Other Anglo-American traditions about Santa Claus are derived from 17th century Dutch customs.
Sleipnir isn't a flying horse.
Eight-legged horses aren't a typical thing in Siberian shamanism.
Each of these facts is a fairly involved matter. And each has some interest in its own right. Here they get explored in some detail, plunging into the evidence with much more thoroughness than is usual with these theories. This piece has a full set of documentation and citations.
The upshot -- unsurprisingly -- is that these facts don't support the 'Odin' and 'shaman' arguments.
(Reading time: 15-20 minutes)
Many popular beliefs about ancient Greece and Rome are misconceptions. This blog digs into the evidence and looks for the reality behind the