Wednesday, 28 November 2018

Cosmos #2. The Ionians (and others)

The second of three annotated transcripts of segments on ancient Greek science from Carl Sagan’s Cosmos (1980). See my introduction in part 1 on the impact Cosmos has had, its extraordinary influence in propagating some myths, and in creating others.

In this segment, Sagan focuses on natural philosophy from the early Ionians up to Plato, with Aristarchus wedged in rather awkwardly as well. It’s the longest of the three segments: it occupies 23 minutes of the television episode.

Remains of temple of Hera, Samos

Like the Eratosthenes segment, we have a number of misrepresentations. This time, though, it’s much clearer that they aren’t innocent imprecisions for the sake of telling a good story, or imperfect research. Many of the untruths are directly motivated by Sagan’s choice to caricature science and religion as antithetical to one another.

The inventions attributed to Theodorus, or the idea that Pythagoras was a round-earther: those are just harmless fiction. Sagan puts too much trust in unreliable sources: OK, fine, professionals do that too. At worst it’s a little sloppy, but it isn’t dishonest.

But when Sagan decides to cast Democritus and Anaxagoras as atheists, and Plato as a mystic; when he claims that science after Plato entered a ‘long, mystical sleep’, and that Platonists suppressed ‘disquieting facts’ -- that’s a totally different matter. Those are outright fabrications, designed to serve a predetermined narrative.

Claims like that leave a bad taste, especially when Sagan has previously been canonising Kepler, who in 1597 wrote to Galileo of Pythagoras and Plato as ‘our genuine masters’. It’s fine to point out errors made by historical figures. Blaming them for errors that weren’t discovered until thousands of years later, though, is unreasonable. Plato did get many, many things wrong -- but not as many as Empedocles and Democritus. And you’ll notice Sagan doesn’t mention any of the Ionians’ errors. It’s wrong to praise Empedocles as a rationalist and demonise Plato as a mystic, when in reality, Empedocles was a cult leader and Plato founded a university.


Episode 7. ‘The backbone of night’

YouTube link. First broadcast 9 November 1980.

Carl Sagan:
Our ancestors groped in darkness to make sense of their surroundings. Powerless before nature, they invented rituals and myths, some desperate and cruel, others imaginative and benign. The ancient Greeks explained that diffuse band of brightness in the night sky as the milk of the goddess Hera, squirted from her breast across the heavens. We still call it the Milky Way.

In gratitude for the many gifts of the gods, our ancestors created works of surpassing beauty. This is all that remains of the ancient temple of Hera, queen of heaven: a single marble column standing in a vast field of ruins, on the Greek island of Samos. It was one of the wonders of the world, built by people with an extraordinary eye for clarity and symmetry. Those who thronged to that temple were also the architects of a bridge from their world to ours. We were moving once again in our voyage of self-discovery, on our journey to the stars.

The temple of Hera on Samos didn’t appear in any ancient canon of ‘seven wonders’. Sagan had probably read Herodotus 3.60 and his reference to three of the ‘largest works of all the Greeks’, including the temple of Hera and the tunnel built by Eupalinus.

Here, 25 centuries ago on the island of Samos, and in the other Greek colonies which had grown up in the busy Aegean Sea, there was a glorious awakening. Suddenly people believed that everything was made of atoms, that human beings and other animals had evolved from simpler forms, that diseases were not caused by demons or the gods, that the earth was only a planet going around a sun, which was very far away.

This revolution made cosmos out of chaos. Here, in the sixth century BC, a new idea developed, one of the great ideas of the human species. It was argued that the universe was knowable. Why? Because it was ordered, because there are regularities in nature, which permitted secrets to be uncovered. Nature was not entirely unpredictable. There were rules which even she had to obey.

This ordered and admirable character of the universe was called cosmos. And it was set in stark contradiction to the idea of chaos. This was the first conflict of which we know between science and mysticism, between nature and the gods.

But why here, why in these remote islands and inlets of the eastern Mediterranean? Why not in the great cities of India, or Egypt, Babylon, China, Mesoamerica? Because they were all at the center of old empires. They were set in their ways, hostile to new ideas. But here, in Ionia, were a multitude of newly colonized islands and city-states. Isolation, even if incomplete, promotes diversity. No single concentration of power could enforce conformity. Free inquiry became possible. They were beyond the frontiers of the empires. The merchants and tourists and sailors of Africa, Asia, and Europe met in the harbors of Ionia to exchange goods and stories and ideas. There was a vigorous and heady interaction of many traditions, prejudices, languages, and gods.

These people were ready to experiment. Once you are open to questioning rituals and time-honored practices, you find that one question leads to another.

What do you do when you’re faced with several different gods, each claiming the same territory? The Babylonian Marduk and the Greek Zeus were each considered king of the gods, master of the sky. You might decide, since they otherwise had different attributes, that one of them was merely invented by the priests. But if one, why not both?

And so it was here that the great idea arose, the realization that there might be a way to know the world without the god hypothesis; that there might be principles, forces, laws of nature, through which the world might be understood without attributing the fall of every sparrow to the direct intervention of Zeus. This is the place where science was born. That’s why we’re here.

This great revolution happened between 600 and 400 BC. It was accomplished by the same practical and productive people who made the society function. Political power was in the hands of the merchants, who promoted the technology on which their prosperity depended. The earliest pioneers of science were merchants and artisans and their children.

The first Ionian scientist was named Thales. He was born over there in the city of Miletus, across this narrow strait. He had traveled in Egypt and was conversant with the knowledge of Babylon. Like the Babylonians, he believed that the world had once all been water. To explain the dry land, the Babylonians added that their god Marduk had placed a mat on the face of the waters, and piled dirt on top of it. Thales had a similar view, but he left Marduk out. Yes, the world had once been mostly water, but it was a natural process which explained the dry land. Thales thought it was similar to the silting up he had observed at the delta of the river Nile. Whether Thales’ conclusions were right or wrong is not nearly as important as his approach. The world was not made by the gods, but instead was the result of material forces, interacting in nature. Thales brought back from Babylon and Egypt the seeds of new sciences, astronomy and geometry: sciences which would sprout and grow in the fertile soil of Ionia.

Anaximander of Miletus, over there, was a friend and colleague of Thales, one of the first people that we know of to have actually done an experiment. By examining the moving shadow cast by a vertical stick, he determined accurately the lengths of the year and seasons. For ages, men had used sticks to club and spear each other. Anaximander used a stick to measure time.

Ancient sources do attribute the invention of the gnomon to Anaximander, but they are definitely wrong. The use of gnomons to pinpoint dates goes back at least as far as early 2nd millennium BCE Egypt. One important function, it seems, was to pinpoint dates for religious festivals. (Similar interests seem to have existed in the mid-3rd millennium BCE: the alignment of the pyramid of Khufu with the compass points must necessarily have required similar techniques.)

In other words, Sagan’s ‘merchants and artisans’ on the ‘frontiers’ were drawing on techniques that had been pioneered by religious researchers in ‘old empires’.

In 540 BC, or thereabouts, on this island of Samos, there came to power a tyrant named Polycrates. He seems to have started as a caterer, and then went on to international piracy. His loot was unloaded on this very breakwater. But he oppressed his own people. He made war on his neighbors. He quite rightly feared invasion. So Polycrates surrounded his capital city with an impressive wall, whose remains stand to this day.

To carry water from a distant spring through the fortifications, he ordered this great tunnel built. A kilometer long, it pierces a mountain. Two cuttings were dug from either side, which met almost perfectly in the middle. The project took some 15 years to complete. It is a token of the civil engineering of its day, and an indication of the extraordinary practical capability of the Ionians. The enduring legacy of the Ionians is the tools and techniques they developed, which remain the basis of modern technology.

This was the time of Theodorus, the master engineer of the age, a man who is credited with the invention of the key, the ruler, the carpenter’s square, the level, the lathe, bronze casting. Why are there no monuments to this man? Those who dreamt and speculated and deduced about the laws of nature talked to the engineers and the technologists. They were often the same people. The practical and the theoretical were one.

For Samos generally, Sagan is mainly following Herodotus book 3, who discusses Polycrates at length; at 3.60 he mentions Eupalinus’ tunnel and the second temple of Hera (though the temple had collapsed over a century before Herodotus’ time, and been replaced by a third temple, the one shown at the start of this segment). Just bear in mind that plenty of places had engineering feats to their name -- places that were in ‘old empires’ and not on the ‘frontiers’. Think of the pyramids of Egypt, or the ‘hanging gardens’ of Babylon and/or Nineveh (reportedly irrigated by Archimedean screws several stories high, nearly 500 years before Archimedes).

For Theodorus and his supposed inventions, Sagan is following Pliny Natural history 7.198. But in the same passage, Pliny also attributes inventions to mythological figures like the Cyclopes, Prometheus, and Palamedes. He also attributes the inventions of pottery, carpentry, archery, and other prehistoric technologies to specific named individuals. In other words, Pliny’s testimony is totally untrustworthy. Sagan missed an opportunity here: there’s no need to focus on dodgy anecdotes when Theodorus had real accomplishments, especially the temple of Hera on Samos -- why not mention that Theodorus was its architect?

The idea that Polycrates ‘started as a caterer’ seems to be either a misunderstanding or a fiction.

This new hybrid of abstract thought and everyday experience blossomed into science. When these practical men turned their attention to the natural world, they began to uncover hidden wonders and breathtaking possibilities. Anaximander studied the profusion of living things, and saw their interrelationships. He concluded that life had originated in water and mud, and then colonized the dry land. ‘Human beings,’ he said, ‘must have evolved from simpler forms.’ This insight had to wait 24 centuries until its truth was demonstrated by Charles Darwin.

Here’s what Anaximander actually thought: ‘there arose from heated water and earth either fish or fish-like creatures, inside which human beings grew and were retained as fetuses up until puberty; then at last the creatures broke open, and men and women emerged who were already capable of feeding themselves’ (fr. A 30 Diels-Kranz, tr. Waterfield).

Nothing was excluded from the investigations of these first scientists. Even the air became the subject of close examination by a Greek from Sicily named Empedocles. He made an astonishing discovery with a household implement that people had used for centuries. This is the so-called ‘water thief’. It’s a brazen sphere with a neck and a hole at the top, and a set of little holes at the bottom. It was used as a kitchen ladle. You fill it by immersing it in water. If, after it’s been in there a little bit, you pull it out with the neck uncovered, then the water trickles out the little holes, making a small shower. Instead, if you pull it out with the neck covered, the water is retained. Now try to fill it, with the neck covered with my thumb. Nothing happens. Why not? There’s something in the way. Some material is blocking the access of the water into the sphere. I can’t see any such material. What could it be? Empedocles identified it as air. What else could it be? A thing you can’t see can exert pressure, can frustrate my wish to fill this vessel with water if I were dumb enough to leave my thumb on the neck. Empedocles had discovered the invisible. Air, he thought, must be matter in a form so finely divided that it couldn’t be seen.

Empedocles seems to have been much more an esoteric mystic than a scientist. His association with the ‘water thief’ or klepsydra is real -- see Empedocles fr. B 100 Diels-Kranz -- but neither it, nor treating air as a substance, was a novelty. As early as the mid-500s BCE Anaximenes of Miletus explained the earth’s motionlessness in space by claiming that it was suspended by air pressure, and used a klepsydra as an analogy (Anaximenes fr. A 20 Diels-Kranz).

But much of the surviving fragments of Empedocles and testimony about him is very different. He frequently refers to himself as divine. One fragment promises that his initiates will gain the ability to control the weather (fr. B 111 D-K). He shared several mystic teachings with Pythagoras, including reincarnation, and treating broad beans as sacred. Ancient sources regularly conflate Empedoclean, Pythagorean, and Orphic religious doctrines. He claimed, supposedly, that he could walk on air. He died, again supposedly, by falling into a volcano crater. (Maybe while attempting to demonstrate his skills at hovering? That isn’t how Diogenes Laertius tells the story, but it’s a beautiful match for Iamblichus’ stories of Empedocles ‘the air-walker’.)

This hint, this whiff of the existence of atoms, was carried much further by a contemporary named Democritus. Of all the ancient scientists, it is he who speaks most clearly to us across the centuries. The few surviving fragments of his scientific writings reveal a mind of the highest logical and intuitive powers. He believed that a large number of other worlds wander through space; that worlds are born and die; that some are rich and living creatures, and others are dry and barren. He was the first to understand that the Milky Way is an aggregate of the light of innumerable faint stars. Beyond campfires in the sky, beyond the milk of Hera, beyond the backbone of night, the mind of Democritus soared. He saw deep connections between the heavens and the earth. ‘Man,’ he said, ‘is a microcosm’ -- a little cosmos.

Democritus came from the Ionian town of Abdera, on the northern Aegean shore. In those days, Abdera was the butt of jokes. If, around the year 400 BC, in the equivalent of a restaurant like this, you told a story about someone from Abdera, you were guaranteed a laugh. It was, in a way, the Brooklyn of its time. For Democritus, all of life was to be enjoyed and understood. For him, understanding and enjoyment were pretty much the same thing. He said, ‘A life without festivity is a long road without an inn.’ Democritus may have come from Abdera, but he was no dummy.

Democritus understood that the complex forms, changes, and motions of the material world, all derived from the interaction of very simple moving parts. He called these parts atoms. All material objects are collections of atoms, intricately assembled, even we. When I cut this apple, the knife must be passing through empty spaces between the atoms, Democritus argued. If there were no such empty spaces, no void, then the knife would encounter some impenetrable atom, and the apple wouldn’t be cut. Let’s compare the cross sections of the two pieces. Are the exposed areas exactly equal? No, said Democritus, the curvature of the apple forces this slice to be slightly shorter than the rest of the apple. If they were equally tall, then we’d have a cylinder, and not an apple. No matter how sharp the knife, these two pieces have unequal cross sections. But why? Because on the scale of the very small, matter exhibits some irreducible roughness. And this fine scale of roughness Democritus of Abdera identified with the world of the atoms. His arguments are not those we use today. But they’re elegant and subtle and derived from everyday experience. And his conclusions were fundamentally right.

Democritus believed that nothing happens at random, that everything has a material cause. He said, ‘I would rather understand one cause than be king of Persia.’ He believed that poverty in a democracy was far better than wealth in a tyranny. He believed that the prevailing religions of his time were evil, and that neither souls nor immortal gods existed. There is no evidence that Democritus was persecuted for his beliefs. But then again, he came from Abdera.

Democritus definitely believed in both souls and immortal gods. He even regarded the soul as more important than the body (fr. B 187 Diels-Kranz). He considered immaterial things to be made of atoms too, like dreams, colours, and tastes. According to one report, he specified that a living body consists of alternating soul-atoms and body-atoms linked together (fr. A 108 D-K).

There is nothing to suggest that he thought contemporary religions were evil. At most, he divorced natural phenomena like lightning and eclipses from purely supernatural causes. He may not have had a very well-thought-out theology: his ideas about the gods were shifting and inconsistent, Cicero tells us (fr. A 74 D-K).

Sagan’s statement that Democritus believed in many ‘worlds wander[ing] through space’ is misleading. Sagan wants us to think of planets, but it’s really about universes. Sources on Democritus consistently use the word kosmos in this context.

Sagan’s story of the apple slice accurately reflects a story of Democritus posing a paradox to Chrysippus, though the original is in more abstract terms. If a cone is cut by a plane parallel to the base, are the two surfaces equal or not? If equal, the cone must have no slope and so must actually be a cylinder; if unequal, it must have uneven step-like notches or the two slices wouldn’t fit together (fr. B 155 D-K). (A generation earlier, some thinkers had already begun to make mathematical use of infinitesimals: Antiphon of Athens had used exhaustion to set a bound on the area of a circle.)

For what it’s worth, and this is admittedly nit-picking, extant jokes about Abderites date to the 1st centuries BCE and CE, not 400 BCE. The earliest is in Cicero.

However, in his time, the brief tradition of tolerance for unconventional views was beginning to erode. For instance, the prevailing belief was that the moon and the sun were gods. Another contemporary of Democritus, named Anaxagoras, taught that the moon was a place made of ordinary matter, and that the sun was a red-hot stone far away in the sky. For this, Anaxagoras was condemned, convicted, and imprisoned for impiety, a religious crime. People began to be persecuted for their ideas. A portrait of Democritus is now on the Greek 100-drachma note. But his ideas were suppressed, and his influence on history made minor. The mystics were beginning to win.

It is true that Anaxagoras was charged with impiety (asebeia). He wasn’t ‘condemned, convicted, [or] imprisoned’, though. He chose to leave Athens rather than fight the charges.

Democritus’ ideas were not suppressed. That’s made up. Aristotle, Plato, Aëtius, and many others discussed him, cited him, and drew on his ideas.

The idea of treating asebeia as a crime was an oddity in ancient Greece. We know of a handful of prosecutions, but only in Athens, and only between 432 and 399 BCE. This coincided with the Peloponnesian War, a period of intense religious tension in Athens -- not between religious fanatics and atheists, but between old-fashioned and new-fangled types of cult. Diagoras and Socrates weren’t charged with rejecting the god hypothesis, they were charged with introducing new gods. (Though in Socrates’ case it’s clear that it was only a convenient pretext for prosecuting his links to the Thirty Tyrants.) Not that that’s a good thing, mind! But it isn’t a story of mysticism vs. materialism.

You see, Ionia was also the home of another quite different intellectual tradition. Its founder was Pythagoras, who lived here on Samos in the 6th century BC.

According to local legend, this cave was once his abode. Maybe that was once his living room. Many centuries later, this small Greek Orthodox shrine was erected on his front porch. There’s a continuity of tradition from Pythagoras to Christianity. Pythagoras seems to have been the first person in the history of the world to decide that the earth was a sphere. Perhaps he argued by analogy with the moon or the sun; maybe he noticed the curved shadow of the Earth on the moon during a lunar eclipse; or maybe he recognized that when ships leave Samos, their masts disappear last.

Pythagoras believed that a mathematical harmony underlies all of nature. The modern tradition of mathematical argument, essential in all of science, owes much to him. And the notion that the heavenly bodies move to a kind of music of the spheres was also derived from Pythagoras. It was he who first used the word cosmos to mean a well-ordered and harmonious universe, a world amenable to human understanding.

For this great idea, we are indebted to Pythagoras. But there were deep ironies and contradictions in his thoughts. Many of the Ionians believed that the underlying harmony and unity of the universe was accessible -- through observation and experiment, the method which dominates science today. However, Pythagoras had a very different method. He believed that the laws of nature can be deduced by pure thought. He and his followers were not basically experimentalists: they were mathematicians, and they were thoroughgoing mystics.

It’s true Pythagoras was more mystic than mathematician. So far as anyone knows, we don’t owe any mathematics to Pythagoras himself, or even to his immediate followers. The famous right-angled triangle theorem is over 1000 years older, and the Pythagoreans drew on it mainly for mystic symbolism. So in the 3-4-5 right-angled triangle: 3 = male = Osiris, 4 = female = Isis, 5 = child = Horus. Even there, the use of Egyptian gods tends to suggest Hellenistic-era mysticism, centuries later than Pythagoras.

There were some Pythagoreans who were also significant mathematicians, especially Archytas and Philolaus in the 300s BCE. But we’ve got no reason to suspect that the Pythagoreans worshipped numbers or anything like that.

Pythagoras definitely did not know or believe that the earth is spherical. Diogenes Laertius does claim that (8.48), but it is untrue.
  1. Diogenes also attributes round-earthism to Hesiod and Anaximander, and those are both definitely false. (In a similar way Crates of Mallos attributes round-earthism to Homer, also wrongly.)
  2. Other sources show very clearly that the earth’s sphericity was discovered around 400 BCE, a century after Pythagoras’ lifetime. We know of many discussions of the earth’s shape in the 500s and 400s BCE, and without exception they depict it as flat (Anaximenes, Anaxagoras, Archelaus, Empedocles, Leucippus, Diogenes of Apollonia, Democritus). After 400, it is routinely known to be spherical, and some sources give well-reasoned arguments (Plato, Aristotle, Archimedes, etc.).
  3. Other sources on the Pythagoreans’ picture of the cosmos show that they actually regarded the earth, moon, sun, and planets as objects attached to the sides of transparent celestial spheres which all orbited around the ‘central fire’ (whatever that may be). Pythagoras was no round-earther -- but maybe it’s even more remarkable that he wasn’t a geocentrist.
The earth’s curved shadow on the moon during a lunar eclipse is one of the pieces of evidence Aristotle cites for the spherical earth (On the sky 297b). So far as I know, no ancient source mentions ships’ masts staying visible over the horizon: that seems to be a modern myth.

They were fascinated by these five regular solids, bodies whose faces are all polygons: triangles or squares or pentagons. There can be an infinite number of polygons, but only five regular solids.

The five so-called ‘Platonic solids’: tetrahedron (4 faces), cube (6), octohedron (8), dodecahedron (12), and icosahedron (20). (These shapes will be especially familiar to players of Dungeons & Dragons.)

Four of the solids were associated with earth, fire, air and water. The cube, for example, represented earth. These four elements, they thought, make up terrestrial matter. So the fifth solid they mystically associated with the cosmos. Perhaps it was the substance of the heavens. This fifth solid was called the dodecahedron. Its faces are pentagons, 12 of them. Knowledge of the dodecahedron was considered too dangerous for the public.

Ordinary people were to be kept ignorant of the dodecahedron. In love with whole numbers, the Pythagoreans believed that all things could be derived from them -- certainly all other numbers. So a crisis in doctrine occurred when they discovered that the square root of two was irrational. That is, the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were. ‘Irrational’ originally meant only that: that you can’t express a number as a ratio. But for the Pythagoreans, it came to mean something else, something threatening, a hint that their world-view might not make sense -- the other meaning of ‘irrational’. Instead of wanting everyone to share and know of their discoveries, the Pythagoreans suppressed the square root of two and the dodecahedron. The outside world was not to know.

Most of the historical claims in these two paragraphs are false. The association of the regular solids with the elements comes from Plato, not Pythagoras -- hence the title ‘Platonic solids’ (Timaeus 53c-56c). Our earliest evidence of the study of irrational numbers also comes from Plato, who treats them as a discovery made by Theaetetus of Athens (Theaetetus 147d-148b).

The context of the association between the solids and the elements is that the atomists (Leucippus and Democritus) were interested in discovering the shape of individual atoms. Democritus thought fire atoms must be spherical; Plato, or rather Timaeus as depicted by Plato, offers an alternate theory.

The story that the Pythagoreans concealed dodecahedrons or irrational numbers from the public is a late fiction. It starts to appear in the 300s CE, nearly seven centuries after Plato, in Iamblichus and then Pappos (and most of Iamblichus’ stories about Pythagoras are pure fiction). See this post from 2015 for details. In Plato, by contrast, characters react to irrationals with admiration for Theaetetus’ mathematical feat, with no fear and no trace of mysticism.

The Pythagoreans had discovered, in the mathematical underpinnings of nature, one of the two most powerful scientific tools. The other, of course, is experiment. But instead of using their insight to advance the collective voyage of human discovery, they made of it little more than the hocus-pocus of a mystery cult. Science and mathematics were to be removed from the hands of merchants and artisans. This tendency found its most effective advocate in a follower of Pythagoras named Plato. He preferred the perfection of these mathematical abstractions to the imperfections of everyday life. He believed that ideas were far more real than the natural world. He advised the astronomers not to waste their time observing stars and planets. It was better, he believed, just to think about them. Plato expressed hostility to observation and experiment. He taught contempt for the real world, and disdain for the practical application of scientific knowledge. Plato’s followers succeeded in extinguishing the light of science and experiment that had been kindled by Democritus and the other Ionians.

Plato’s unease with the world as revealed by our senses was to dominate and stifle Western philosophy. Even as late as 1600, Johannes Kepler was still struggling to interpret the structure of the cosmos in terms of Pythagorean solids and Platonic perfection. Ironically, it was Kepler who helped re-establish the old Ionian method of testing ideas against observations.

This is Sagan at his worst. The judgement he gives on Plato here, coming after his praise for Empedocles and Democritus, is the rawest hypocrisy. Look at the double standard:
  • Democritus and Plato both think about the shape of atoms: Democritus good, Plato bad.
  • Empedocles and Democritus declare the earth to be a disc, Plato knows it’s a sphere because of empirical evidence {edit: presumably, at least! We don’t get explicit discussion of the evidence until Aristotle.}: Empedocles/Democritus good, Plato bad.
  • Empedocles proclaims himself divine and sets himself up as a cult leader, Plato founds Europe’s first university: Empedocles good, Plato bad.
  • Modern physicists use mathematics as an abstract language for formalising the behaviour of the physical world, Plato uses a theory based on noetic categories and language as a (deeply wrong) attempt at the same goal: modern physics good, Plato bad.
Plato often thought in terms of analogies, but that’s not the same thing as being opposed to empiricism. Sagan’s double standard betrays his ulterior motives. The real reason he doesn’t like Plato isn’t because he was opposed to empiricism, it’s because Plato was influential on Christian thought. Is it reasonable for Sagan to despise Plato because he was influential on the wrong people? Maybe -- though I think most people, myself included, would say no -- but either way, you don’t have to be dishonest about it.

But why had science lost its way in the first place? What appeal could these teachings of Pythagoras and of Plato have had for their contemporaries? They provided, I believe, an intellectually respectable justification for a corrupt social order.

The mercantile tradition which had led to Ionian science also led to a slave economy. You could get richer if you owned a lot of slaves. Athens, in the time of Plato and Aristotle, had a vast slave population. All of that brave Athenian talk about democracy applied only to a privileged few. Plato and Aristotle were comfortable in a slave society. They offered justifications for oppression.

They served tyrants. They taught the alienation of the body from the mind -- a natural enough idea, I suppose, in a slave society. They separated thought from matter. They divorced the Earth from the heavens -- divisions which were to dominate Western thinking for more than 20 centuries. The Pythagoreans had won.

The theory that a slave economy affects the way people think is coherent -- enough to make a decent essay topic at least. But Sagan would need a lot more than this to back it up. The horror of slavery is much easier to see in economic, moral, and personal terms, than in the history of the scientific method.

Incidentally, Plato and Aristotle didn’t live under a tyranny, but in Athens under a democratic constitution.

In the recognition by Pythagoras and Plato that the cosmos is knowable, that there is a mathematical underpinning to nature, they greatly advanced the cause of science. But in the suppression of disquieting facts, the sense that science should be kept for a small élite, the distaste for experiment, the embrace of mysticism, the easy acceptance of slave societies, their influence has significantly set back the human endeavor.

The books of the Ionian scientists are entirely lost. Their views were suppressed, ridiculed, and forgotten by the Platonists, and by the Christians who adopted much of the philosophy of Plato.

No one suppressed the Ionians. There isn’t a shred of evidence to suggest such a thing. Books disappearing is just what happens if you wait a few centuries. Even in antiquity people complained of no longer being able to find books that were less than 200 years old. Plato’s works got lucky, and were very influential, and so survived. That isn’t the same thing as suppression.

Suppression has happened at various times throughout history, of course. But to attribute it to the Platonists is pure fiction. For example, suppression did occur under the Christian emperor Theodosius, in the 380s and 390s CE, for religious reasons -- but somehow I don’t think that’s the kind of thing Sagan had in mind. The Platonists, and the school that Plato founded, were among Theodosius’ main victims. Correction, following day: as Tim O'Neill points out in the comments below, I blundered here: I was thinking of Justinian’s suppression of Neo-Platonism and closure of the second Academy, over a century later.

Sagan’s sentiments here are based on the idea that the loss of knowledge is a crime, and therefore there must be someone who is responsible for it. That isn’t the case. (Though it is, incidentally, a very Platonic way of thinking.) We’ll come back to that in part 3.

Finally, after a long, mystical sleep, in which the tools of scientific inquiry lay moldering, the Ionian approach was rediscovered. The Western world reawakened. Experiment and open inquiry slowly became respectable once again. Forgotten books and fragments were read once more. Leonardo, and Copernicus, and Columbus were inspired by the Ionian tradition.

During this ‘long, mystical sleep’ lived many of the ancient scientists and empiricists that Sagan elsewhere praises: Eratosthenes (see part 1), Aristarchus (see below), Archimedes, Hipparchus, Ptolemy -- and many, many more, in antiquity and all the way through the mediaeval period too. But let’s not think about them.

Copernicus revered Pythagoras above all the ancients. Columbus didn’t respect anyone, and cherry-picked all the wrong ideas about the size of the earth to suit his colonial agenda. As for Leonardo, I’m afraid I don’t know what he thought of ancient philosophers.

The Pythagoreans and their successors held the peculiar notion that the earth was tainted, somehow nasty, while the heavens were pristine and divine. So the fundamental idea that the Earth is a planet, that we’re citizens of the universe, was rejected and forgotten.

This idea was first argued by Aristarchus, born here on Samos, three centuries after Pythagoras. He held that the Earth moves around the sun. He correctly located our place in the solar system. For his trouble, he was accused of heresy. From the size of the Earth’s shadow on the moon during a lunar eclipse, he deduced that the sun had to be much much larger than the Earth, and also very far away. From this he may have argued that it was absurd for so large an object as the sun to be going around so small an object as the Earth. So he put the sun rather than the earth at the center of the solar system. And he had the earth and the other planets going around the sun. He also had the earth rotating on its axis once a day. These are ideas that we ordinarily associate with the name Copernicus. But Copernicus seems to have gotten some hint of these ideas by reading about Aristarchus -- in fact, in the manuscript of Copernicus’ book, he referred to Aristarchus, but in the final version he suppressed the citation.

Resistance to Aristarchus, a kind of geocentrism in everyday life, is with us still. We still talk about a sun rising and the sun setting. It’s 2,200 years since Aristarchus, and the language still pretends that the earth does not turn, that the sun is not at the center of the solar system. Aristarchus understood the basic scheme of the solar system -- but not its scale. He knew that the planets move in concentric orbits about the sun, and he probably knew their order out to Saturn.

But he was much too modest in his estimates of how far apart the planets are. In order to calculate the true scale of the solar system, you need a telescope. It wasn’t until the 17th century that astronomers were able to get even a rough estimate of the distance to the sun. And once you knew the distance to the sun, what about the stars? How far away are they?

Sagan gives Aristarchus at once too much and too little credit. On the one hand, we can be pretty sure Aristarchus’ heliocentrism wasn’t motivated by empirical evidence, but by assumptions about how the universe ought to be arranged. That’s certainly the case with the only other ancient heliocentrist we know of, Seleucus (see my annotation in Part 1).

On the other hand, Aristarchus didn’t ‘estimate’ the size of the solar system. He calculated it.

His result was off, because the observations he based it on were inexact. But the method was sound in principle. He measured the angle between the sun, earth, and moon, when both sun and moon were in the sky, at half-moon. Half-moon is special, because at that time the line between the moon and an observer on earth is perpendicular to the line between the moon and the sun. In other words, the sun-moon-earth triangle is a right-angled triangle.

That means you can do trigonometry on it. And Aristarchus was a pioneer in trigonometry. (See Aristarchus’ inequality, a theorem that he used in this very calculation.)

An accurate observation would make the sun-earth-moon angle 89.85° at half-moon. Aristarchus measured it as about 87°. Unfortunately, when you’re dealing with angles close to 90°, a small error in the observation means a large error in the result. So Aristarchus reckoned the sun as being only 18-20 times further away than the moon, when in reality it’s about 390 times further away.

Aristarchus’ measurement of the size of the solar system. At half-moon, Aristarchus reasoned, the angle where the moon is is a right angle. He could measure the angle where earth is, θ, albeit not very precisely. The relative distance of the sun and moon is given by 1/cos θ. For θ = 87°, that comes out close to 19. Aristarchus essentially invented the cosine function for this calculation.

Tuesday, 20 November 2018

Cosmos #1. Eratosthenes

Carl Sagan’s TV series Cosmos has had an enduring effect on people’s perceptions of antiquity. Most of those perceptions are only half-true.


There is some genuine factual material in Cosmos, but it’s pretty evenly blended with fiction. Sometimes that’s for the sake of making a good story. But often it comes from relying on sources who were lazy, who knew little about their subject, or who were heavily biased.

For those who like to challenge popular misconceptions, it can be a little laborious to work out exactly which misconceptions come from Cosmos. So, here and in the next two posts, I’ll give a transcript of the segments that deal with ancient Greek science, with a few selected annotations.

I’ve found that many people don’t appreciate just how much of an impact Cosmos has had in the 38 years since it was first broadcast. Let me illustrate.

In 2009 the film Agora, directed and written by Alejandro Amenábar, perpetuated the myth that Hypatia’s death was linked to the catastrophic destruction of the famous libraries of Alexandria. There’s no reason to imagine any link between these two events (and little reason to believe that the second actually happened). Guess who invented the link?

In 2016 a prominent website published a video on Eratosthenes’ measurement of the earth’s circumference. Guess who the video cited as its sole historical source? This video got 24 million views when it was posted on Facebook. Half of it was false. And every one of the falsehoods was repeated from Cosmos.

Business Insider video on Eratosthenes’ measurement of the earth, July 2016: final shot (left) and the entire credits sequence (right).

In 2017 an article in The Guardian pulled the same trick. Once again, it’s only half true. Once again, the author got all his history directly from Cosmos.

Cosmos is getting a bit long in the tooth, but the entire series is on YouTube; it had a revival in 2014; another series is scheduled for 2019. Its influence lives on. So, for those who want to know what stories Sagan spread, but who don’t want to have to spend thirteen hours watching the whole thing, here are the relevant bits, in three parts. Today: Eratosthenes.


Episode 1. ‘The shores of the cosmic ocean’

YouTube link. First broadcast 28 September 1980.

Carl Sagan:
There was once a time when our little planet seemed immense, when it was the only world we could explore. Its true size was first worked out in a simple and ingenious way by a man who lived here in Egypt, in the third century BC.

This tower may have been a communications tower, part of a network running along the North African coast, by which signal bonfires were used to communicate messages of state. It also may have been used as a lighthouse, a navigational beacon for sailing ships out there in the Mediterranean Sea. It is about 50 kilometers west of what was once one of the great cities of the world, Alexandria.

In Alexandria, at that time there lived a man named Eratosthenes. One of his envious contemporaries called him ‘Beta’, the second letter of the Greek alphabet because, he said, Eratosthenes was second best in the world in everything. But it seems clear that in many fields, Eratosthenes was Alpha. He was an astronomer, historian, geographer, philosopher, poet, theater critic, and mathematician. He was also the chief librarian of the great library of Alexandria. And 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? But Eratosthenes was a scientist and his contemplation of these homely matters changed the world -- in a way, made the world. Because Eratosthenes had the presence of mind to experiment, to actually ask whether, back here, near Alexandria, a stick cast a shadow near noon on June the 21st. And it turns out, sticks do.

Notes: see this older post and this one on Eratosthenes’ measurement of the earth.
  1. Eratosthenes was not discovering secrets in obscure texts, but making use of long-standing public knowledge. The shape of the earth was well-known; measuring latitude with a gnomon was standard practice.
  2. The calculation was based on readings taken at Syene and Meroë, not Alexandria and Syene. Correction, two days later: thanks to Seb, in the comments, for pointing out my error here. According to Martianus Capella, Eratosthenes used readings taken at Syene and Meroë (not Alexandria); according to Cleomedes, at Alexandria and Syene (not Meroë). Cleomedes tends to have greater clout, but there’s absolutely no doubt that Eratosthenes did use readings from Meroë too. He regarded all three sites as being on the same meridian, and equidistant. He may have used one set of readings to corroborate the other.
  3. A well at Syene played no role in the calculation.
  4. Observations were taken at the equinoxes, not the solstice. Correction, two days later: thanks to Seb again. According to Cleomedes, Eratosthenes used observations taken at the solstice; according to Vitruvius, at the equinox. The equinox appears to have been the standard time of year for gnomon readings designed to measure latitude (see e.g. Pliny NH 2.182). Strabo 2.1.20 points out that Philon took gnomon readings at Meroë at both the solstices and equinoxes, and that ‘Eratosthenes agrees very closely with Philon’: it seems simplest to infer that Eratosthenes actually used both. (Equinoctial observations make it trivial to calculate latitude, because at the equinox, and only at the equinox, the sun’s rays are parallel to the plane of the earth’s equator.)
  5. The gnomon readings Eratosthenes used were taken decades before his time, and the overland distance estimates over a millennium earlier.
  6. The distance units definitely did not correspond to 800 km or 40,000 km. They were in the region of 900-960 km and 45,000-48,400 km. Still impressive, but more than ‘a few percent’ off. Eratosthenes improved on estimates reported by Aristotle (ca. 74,000 km) and Archimedes (ca. 55,000 km), but it was not a radical novelty.

An overly skeptical person might have said that the report from Syene was an error. But it’s an absolutely straightforward observation. Why would anyone lie on such a trivial matter? Eratosthenes asked himself how it could be that, at the same moment, a stick in Syene would cast no shadow, and a stick in Alexandria, 800 kilometers to the north, would cast a very definite shadow.

Here is a map of ancient Egypt. I’ve inserted two sticks, or obelisks: one up here in Alexandria, and one down here in Syene. Now, if at a certain moment each stick casts no shadow, no shadow at all, that’s perfectly easy to understand -- provided the earth is flat. If the shadow at Syene is a certain length and the shadow at Alexandria is the same length, that also makes sense on a flat earth. But how could it be, Eratosthenes asked, that at the same instant there was no shadow at Syene, and a very substantial shadow at Alexandria?

The only answer was that the surface of the earth is curved. Not only that, but the greater the curvature, the bigger the difference in the lengths of the shadows. The sun is so far away that its rays are parallel when they reach the earth. Sticks at different angles to the sun’s rays will cast shadows at different lengths. For the observed difference in the shadow lengths, the distance between Alexandria and Syene had to be about 7 degrees along the surface of the earth. By that I mean, if you would imagine these sticks extending all the way down to the center of the earth, they would there intersect at an angle of about 7 degrees. Well, 7 degrees is something like a 50th of the full circumference of the earth, 360 degrees. Eratosthenes knew the distance between Alexandria and Syene. He knew it was 800 kilometers. Why? Because he hired a man to pace out the entire distance so that he could perform the calculation I’m talking about. Now, 800 kilometers times 50 is 40,000 kilometers. So that must be the circumference of the earth, that’s how far it is to go once around the earth.

That’s the right answer. Eratosthenes’ only tools were sticks, eyes, feet, and brains -- plus a zest for experiment. With those tools he correctly deduced the circumference of the earth to high precision, with an error of only a few percent. That’s pretty good figuring for 2,200 years ago.

Then, as now, the Mediterranean was teeming with ships: merchantmen, fishing vessels, naval flotillas. But there were also courageous voyages into the unknown. 400 years before Eratosthenes, Africa was circumnavigated by a Phoenician fleet in the employ of the Egyptian pharaoh Necho. They set sail, probably in boats as frail and open as these, out from the Red Sea, down the east coast of Africa up into the Atlantic and then back through the Mediterranean. That epic journey took three years, about as long as it takes Voyager to journey from earth to Saturn. After Eratosthenes, some may have attempted to circumnavigate the earth. But until the time of Magellan, no one succeeded. What tales of adventure and daring must earlier have been told as sailors and navigators, practical men of the world, gambled their lives on the mathematics of a scientist from ancient Alexandria.

The story of the Phoenician circumnavigation of Africa in ca. 600 BCE is based on a single source, Herodotus 4.42, written ca. 425 BCE. It is not strictly impossible, but it is doubtful. Herodotus did not have direct access to written reports of the expedition, but relied on oral interlocutors. The most thorough geographic account of Africa that we have from the Mediterranean world, that of Ptolemy, has no known southern boundary to Africa. The one point that supports the story, that the sailors reportedly saw the sun in the northern half of the sky, is not necessarily proof: this would be observed in summer anywhere south of the Tropic of Cancer (still within the latitude of Egypt).

Today, Alexandria shows few traces of its ancient glory, of the days when Eratosthenes walked its broad avenues. Over the centuries, waves of conquerors converted its palaces and temples into castles and churches, then into minarets and mosques. The city was chosen to be the capital of his empire by Alexander the Great on a winter’s afternoon in 331 BC. A century later, it had become the greatest city of the world. Each successive civilization has left its mark.

But what now remains of the marvel city of Alexander’s dream? Alexandria is still a thriving marketplace, still a crossroads for the peoples of the Near East. But once, it was radiant with self-confidence, certain of its power.

Can you recapture a vanished epoch from a few broken statues and scraps of ancient manuscripts? In Alexandria there was an immense library and an associated research institute, and in them worked the finest minds in the ancient world. Of that legendary library all that survives is this dank and forgotten cellar. It’s in the library annex, the Serapeum, which was once a temple but was later reconsecrated to knowledge. These few, moldering shelves probably once in a basement storage room are its only physical remains. But this place was once the brain and glory of the greatest city on the planet earth.

If I could travel back into time, this is the place I would visit. The library of Alexandria at its height, 2,000 years ago. Here, in an important sense, began the intellectual adventure which has led us into space. All the knowledge in the ancient world was once within these marble walls. In the great hall, there may have been a mural of Alexander with the crook and flail and ceremonial headdress of the pharaohs of ancient Egypt. This library was a citadel of human consciousness, a beacon on our journey to the stars.

It was the first true research institute in the history of the world. And what did they study? They studied everything, the entire cosmos. ‘Cosmos’ is a Greek word for the order of the universe. In a way it’s the opposite of chaos. It implies a deep interconnectedness of all things, the intricate and subtle way that the universe is put together.

Genius flourished here. In addition to Eratosthenes, there was the astronomer Hipparchus, who mapped the constellations and established the brightness of the stars. And there was Euclid, who brilliantly systematized geometry, who told his king, who was struggling with some difficult problem in mathematics, that there was no royal road to geometry. There was Dionysius of Thrace, the man who defined the parts of speech -- nouns, verbs, and so on -- who did for language in a way what Euclid did for geometry. There was Herophilus, a physiologist who identified the brain rather than the heart as the seat of intelligence. There was Archimedes, the greatest mechanical genius until the time of Leonardo da Vinci. And there was the astronomer Ptolemy, who compiled much of what today is the pseudoscience of astrology. His earth-centered universe held sway for 1,500 years, showing that intellectual brilliance is no guarantee against being dead wrong. And among these great men, there was also a great woman. Her name was Hypatia. She was a mathematician and an astronomer, the last light of the library, whose martyrdom is bound up with the destruction of this place seven centuries after it was founded.

  • Hipparchus did a lot more than Sagan says. He discovered many difficult points about the dynamics of the sun-earth-moon system, the periodicity of eclipses, the relationship between the solar and sidereal years, and much more. He should probably be regarded as the greatest astronomer of antiquity, perhaps alongside Eudoxus.
  • Ptolemy was much more than a superstitious astrologer. His astronomical model was a more effective predictive tool than Copernicus’, and his works on cartography, music theory, and other matters are easily the most influential historical works ever written on those subjects.
  • Archimedes lived in Sicily, not Alexandria.
  • Hypatia was a major mathematician, but her astronomical work was confined to editing the text of Ptolemy’s Almagest. There is little to suggest a connection between her death and the destruction of the Mouseion: Sagan is directly responsible for the myth that a connection exists.

Look at this place. The Greek kings of Egypt who succeeded Alexander regarded advances in science, literature, and medicine as among the treasures of the empire. For centuries they generously supported research and scholarship -- an enlightenment shared by few heads of state, then or now. Off this great hall were ten large research laboratories; there were fountains and colonnades; botanical gardens; and even a zoo with animals from India and sub-Saharan Africa. There were dissecting rooms and an astronomical observatory.

But the treasure of the library consecrated to the god Serapis, built in the city of Alexander, was its collection of books. The organizers of the library combed all the cultures and languages of the world for books. They sent agents abroad to buy up libraries. Commercial ships docking in Alexandria harbor were searched by the police, not for contraband, but for books. The scrolls were borrowed, copied and returned to their owners. Until studied, these scrolls were collected in great stacks called ‘books from the ships’. Accurate numbers are difficult to come by, but it seems that the library contained at its peak nearly one million scrolls.

The papyrus reed grows in Egypt. It’s the origin of our word for ‘paper’. Each of those million volumes which once existed in this library were handwritten on papyrus manuscript scrolls. What happened to all those books? Well, the classical civilization 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.

But how tantalizing those remaining bits and pieces are! For example, we know that there once existed here a book by the astronomer Aristarchus of Samos, who apparently argued that the earth was one of the planets, that like the other planets, it orbits the sun, and that the stars are enormously far away. All absolutely correct! But we had to wait nearly 2,000 years for these facts to be rediscovered.

The astronomy stacks of the Alexandria library. Hipparchus, Ptolemaeus ... here we are: Aristarchus. This is the book. How I’d love to be able to read this book, to know how Aristarchus figured it out. But it’s gone, utterly and forever. If we multiply our sense of loss for this work of Aristarchus by 100,000, we begin to appreciate the grandeur of the achievement of classical civilization and the tragedy of its destruction.

Aristarchus was a gifted mathematician, but his heliocentric model was apparently speculative, not based on any observational evidence. That’s certainly how it is with the only other heliocentrist that we know of, Seleucus, who relied solely on a priore assumptions for some of his arguments (see Neugebauer, History of ancient astronomy pp. 697-8). Archimedes reports that Aristarchus actually made the stars infinitely distant. Heliocentrism was not taboo: Archimedes for one took it seriously. But only Seleucus is known to have been persuaded by it.

Copernicus wasn’t delighted to ‘rediscover’ Aristarchus, he was annoyed that someone else got to the heliocentric model first. He erased Aristarchus from the published version of his book, deleting references Correction: one reference that he had written in his manuscript. Correction, a few days later: Viktor Blåsjö has pointed out on Twitter that Copernicus was only barely aware of Aristarchus’ heliocentrism. Our main source (Archimedes’ Sand-reckoner) was published the year after Copernicus’ death. He certainly didn’t plagiarise Aristarchus or anything like that: he simply removed a passage discussing ancient proponents of the idea that the earth moves.

We have far surpassed the science known to the ancient world, but there are irreparable gaps in our historical knowledge. Imagine what mysteries of the past could be solved with a borrower’s card to this library. For example, we know of a three-volume history of the world now lost, written by a Babylonian priest named Berossus. Volume 1 dealt with the interval from the creation of the world to the great flood, a period that he took to be 432,000 years, or about 100 times longer than the Old Testament chronology. What wonders were in the books of Berossus?

But why have I brought you across 2,000 years to the library of Alexandria? Because this was when and where we humans first collected, seriously and systematically, the knowledge of the world. This is the earth as Eratosthenes knew it: a tiny, spherical world, afloat in an immensity of space and time. We were at long last beginning to find our true bearings in the cosmos.

The scientists of antiquity took the first and most important steps in that direction before their civilization fell apart. But after the Dark Ages, it was by and large the rediscovery of the works of these scholars, done here, that made the Renaissance possible and thereby powerfully influenced our own culture. When in the 15th century Europe was at last ready to awaken from its long sleep, it picked up some of the tools, the books, and the concepts laid down here more than a thousand years before.

By 1600, the long-forgotten ideas of Aristarchus had been rediscovered. Johannes Kepler constructed elaborate models to understand the motion and arrangement of the planets the clockwork of the heavens. And at night, he dreamt of traveling to the moon.

Next time: episode 7, ‘The backbone of night’

Tuesday, 6 November 2018

Tiamat ... and other dragons

Tiamat is the most famous dragon of ancient Near Eastern mythology. Just a small hitch: no ancient Babylonian text actually describes her as a dragon.

But it isn’t actually a problem after all. This story has a twist: we probably should think of Tiamat as a great serpent, even though there’s no direct testimony. It’s just that the reasons for thinking that are indirect.

Marduk fighting Tiamat? Or Marduk charging into battle alongside the mušḫuššu, his personal symbol and ally? Or some other god with a serpent-like monster? (Assyrian cylinder seal, ca. 800-750 BCE)

The following summaries, at least, are straight-up wrong --
Some sources identify [Tiamat] with images of a sea serpent or dragon. ... In the Enûma Elish, the Babylonian epic of creation, she ... wars upon her husband's murderers, taking on the form of a massive sea dragon ... Tiamat is usually described as a sea serpent or dragon ...
-- Wikipedia, ‘Tiamat’ (retrieved 14 Oct. 2018)

The dragon’s form varied from the earliest times. The Chaldean dragon Tiamat had four legs, a scaly body, and wings ...
-- Encyclopaedia Britannica, ‘Dragon’ (retrieved 14 Oct. 2018)
The Wikipedia article does give a citation for the claim that some sources identify her with images of a serpent. But the source it cites -- Jacobsen (1968), a very competent and clear article -- says nothing of the kind. And where Wikipedia claims that Tiamat is ‘usually described as a sea serpent’, there’s a conspicuous absence of citations. The reason for that absence is that no such descriptions exist.

As for the Britannica article, its description is pretty clearly based on the illustration below, from Nimrud in what is now northern Iraq. We definitely don’t have any textual source giving Tiamat four legs, scales, or wings. Yet you’ll often see this same illustration cited as if it’s a typical ancient depiction of Tiamat.

Just one thing: Tiamat is a primordial female divinity, right? So ... notice a tiny problem?

Definitely NOT Tiamat: this monster has a penis. (Drawing of a Neo-Assyrian relief from the temple of Ninurta at Nimrud, 800s BCE. Source: Layard, The monuments of Nineveh vol. 2 (1853), plate 5)

(You’ll probably need to click on the image and zoom in. Yes, it is tiny, yes that’s very funny, ha ha.) Anthony Green (1997a: 142, 1997b: 258) points out that the relief comes from a temple of Ninurta, and suggests that the monster might be Asakku or Asag, slain by Ninurta in the poem Lugal-e.

Moreover, the Britannica claims to be talking about a Chaldaean Tiamat; the illustration is Assyrian. And just in case you weren’t sure already that the Britannica article is garbage: a couple of lines later it claims, as a matter of historical fact, that it was Uther Pendragon himself who established dragons’ role in English heraldry. Yes, seriously.

How is Tiamat really depicted?

In the Enuma elish, the Babylonian creation epic, Apsu and Tiamat are primordial divinities of the cosmic waters, husband and wife, and the ancestors of the gods. Misbehaviour among the gods leads to battles between Ea and Apsu (tablet 1), and then between Marduk and Tiamat (tablets 2-5). Marduk’s conquest of Tiamat, who is the stormy salt sea, is a key step in bringing about cosmic order.

However, the poem is short on physical descriptions. Marduk gets a bit of a description in tablet 1; Tiamat, not so much. We’re told that she creates or gives birth to eleven monsters in preparation for the battle:
She created the Hydra, the Dragon, the Hairy Hero,
the Great Demon, the Savage Dog, and the Scorpion-man,
(three?) fierce demons, the Fish-man, and the Mighty Bull ...
-- Enuma elish 1.141-143 = 2.27-29, 3.31-33, 3.89-91 (trans. Lambert)
Some of her physical features get mentioned. She has a throat (4.31), blood (4.32), entrails (4.41), a mouth (4.65), legs (4.91), lips and a belly (4.98-99), a head (4.130), and eyes, nostrils, and breasts (5.55-56).

There’s just one clearly non-human detail: Tiamat has a tail (5.59), which Marduk uses to make the Durmahu or ‘great bond’ that holds the earth in place. So whatever she is, she isn’t totally humanoid. Still, it’s not exactly specific.

Another couple of possible candidates for depicting Marduk fighting Tiamat. Left: cylinder seal, yellow frit, glazed, 17 mm high; Assyrian, Nineveh, ca. 900-700 BCE (Berlin VA 7951). Right: cylinder seal, serpentine, 17 mm high; Assyrian, Nineveh, ca. 800-600 BCE (Pierpont Morgan Library, NY).

Do the pictorial arts help? Well, potentially. But they don’t exactly simplify things.
  1. Text ≠ image. There’s no reason to expect that textual sources and pictorial arts should resemble each other, or even try to resemble each other. Verbal narratives and visual myths are very different things, with different storytelling techniques, different symbols, and maybe even completely separate stories. For example, in the Ninurta relief above, it may be surprising to see Ninurta carrying lightning bolts; but one variant makes Adad, the storm god, the hero of the Asakku story instead. From the point of view of someone that relies on texts, this looks like distinct stories leaking into each other, contaminating each other. For someone who begins with the pictorial arts, it’ll seem artificial to unravel the textual sources into distinct variants.
  2. No name tags. Mesopotamian pictorial arts don’t give many clues as to who’s who. There are several options for identifying a giant serpent. It might be Tiamat. But it might also be another sea divinity, Irhan, whose name is written with a symbol for ‘snake’. It might be the mušḫuššu serpent that serves as Marduk’s symbol and ally. It might be another monster which is Nabu’s symbol. It might be one of Tiamat’s eleven monstrous offspring. Or it might be an entity that doesn’t even get mentioned in any textual source.

... and other dragons

That brings us to the subject of other dragons. What do we know about them? Do we have stories about battles with them? The Greek god Zeus has links to storm gods in other mythologies, like Jupiter and Thor: does Tiamat have links to actual dragons?

The story-type of a god battling a Chaos Monster in order to establish the order of the cosmos is a widespread one, and the Chaos Monster is quite often a serpent. In Babylonian-Assyrian myth Marduk defeats Tiamat and Nergal defeats a giant serpent called a bašmu. In Greece Zeus defeats Typhoeus, and Apollo defeats Python, both giant serpents. In Ugarit Baal defeats Yamm and Litan, and in Israel Yahweh defeats Leviathan, all of them serpents.

There are poetic and linguistic links between many dragon-slaying stories, too, as argued by Calvert Watkins in his classic study How to kill a dragon (1995).

Tiamat as a five-headed dragon in the game Dungeons and Dragons. Left: Monster manual, 1st edition (1977); right: The rise of Tiamat (2014).

Don’t think of explaining this as some cultures copying their myths from another. That isn’t how myth works. Think instead of people drawing on a common pool of myths, story-types, and imagery, a bundle of mythical elements that they have all inherited.

A good example is the parallels between Job, in the Hebrew Bible, and the Ugaritic Baal Cycle. Job has Yahweh defeating several monsters, and the Baal Cycle talks about Baal’s and Anat’s conquests. Take this passage where Anat boasts of her victory over Yamm:
I (Anat) fought Yamm, the Beloved of El,
surely I finished off River (Nahar), the Great God [or: god of the great waters],
surely I bound Tunnanu and destroyed (?) him.
I struck down the Twisty Serpent,
the Powerful One with Seven Heads.
-- Baal Cycle 3.iii.38-42 Smith (= CAT 1.3)
and compare it with this passage from the Hebrew book of Job --
By his power he stilled the sea (yam);
by his understanding he struck down Rahab.
By his wind the heavens were made fair;
his hand pierced the fleeing serpent.
In the Baal Cycle Yamm is a sea divinity/monster, in Job the same name may simply mean ‘the sea’, lower-case -- though I think it’s worth considering it a possible personification there too. The Baal Cycle passage isn’t a list of different enemies, but a list of titles for Yamm (Smith and Pitard 2009: 248-249); the same may be true of the Job passage. Tunnanu is cognate with Hebrew tannin, ‘serpent’ or ‘dragon’.

Later on Job devotes an entire chapter to Yahweh’s victory over Leviathan (Job 41). There Leviathan is a sea monster that spits fire and breathes smoke, and has glowing eyes. Other passages in the Hebrew Bible make it clearer that Leviathan is a serpent. In Psalm 74.13-14 Leviathan is a water serpent with multiple heads. And then there’s this passage:
On that day the Lord with his cruel and great and strong sword will punish Leviathan the fleeing serpent, Leviathan the twisting serpent, and he will kill the dragon (tannin) that is in the sea (yam).
Compare this to the Baal Cycle passage above, and to the following passage about Litan:
Litan, the Fleeing Serpent,
... the Twisty Serpent,
the Powerful One with Seven Heads
-- Baal cycle 5.i.1-3 Smith (= KTU 1.5)
We get the same formulas referring to both Yamm and Litan in Ugaritic, and to Leviathan in Hebrew: ‘fleeing serpent’, ‘twisty serpent’, ‘Tunnanu/tannin’, multiple heads.

Leakage between dragon stories. I think it’d be a mistake to draw a firm distinction between Yamm and Litan, because the sources seem to make a point of blurring sea serpents together.

Should Yamm/Litan/Leviathan be equated with Tiamat as well? Well, given how much blurring we’ve already got ... maybe. Hebrew does have a cognate for Tiamat as well -- tehom, the ‘sea’, and also the word for the primordial waters before creation in Genesis 1.1. We don’t have any multi-headed dragons in Mesopotamian textual sources, but there are a couple of pictorial depictions.

{Correction, three days later: we do in fact have a seven-headed serpent in a Sumerian myth: it is one of the ‘Slain Heroes’ killed by Ningirsu or Ninurta in the poem Lugal-e. Green 1997a: 141, 1997b: 259 identifies it with one or both of the serpents shown below.}

Left: engraved shell plaque of unknown provenance; 39 mm high, ca. 2600-2300 BCE (Bible Lands Museum, Jerusalem). Right: stone cylinder seal from Tell Asmar, Iraq; 32 mm high, ca. 2271-2154 BCE (Iraq Museum, Baghdad). Source: Green 1997a, plates 13 and 14 (= ANEP 671 and 691).

The dragon dies one head at a time. In the left figure a god (Ningirsu/Ninurta?) has already killed one head; in the right, two figures are fighting the dragon and four of its heads are drooping dead. In both pictures, flames seem to be shooting from the monster’s back.

Some later sources, ranging from the Greek world to Mesopotamia, also feature multi-headed dragons, with varying degrees of similarity:
  • Zeus vs. Typhoeus (Hesiodic Theogony 810-868, Greek, ca. 700 BCE): Typhoeus is a serpent with a hundred heads (825, cf. 855-856), and flames shoot from his body when he is struck (859-867).
  • Heracles vs. Hydra (ps.-Apollodoros Library 2.5.2, Greek, ca. 100-1 BCE): the Hydra has nine heads, and its blood is a deadly poison; Heracles’ ally Iolaus burns the root of each head as Heracles defeats it, one by one. The final head is immortal and ends up being buried under a rock. After the battle, Heracles ‘cuts up’ (anaschis-) the Hydra’s body.
  • The Christian New Testament, Revelation (Anatolian/Syrian?, ca. 80-100 CE): ‘a great red dragon, with seven heads and ten horns’ (Rev. 12.3-4). A ‘beast’ with the same number of heads and horns (13.1-14) has had one head mortally wounded, but the wound heals. (One or both of these also symbolises Rome, with its seven hills.)
  • Rav Acha vs. the demon: the Babylonian Talmud, Kiddushin 29b (ca. 500 CE) tells how Rav Acha bar Ya’akov defeated a demon in the shape of a serpent with seven heads, and how one head died each time that he bowed and prayed.
It’s not hard to draw parallels between the pairing-up of two figures in the Tell Asmar seal, and Heracles and Iolaus; or between the flames shooting from the dragon’s body in the Mesopotamian images and the Typhoeus story; the one immortal head in the Heracles story and in Revelation 13; or the one-head-at-a-time procedure that we see in most of these variants.

Does Tiamat herself belong to the same family? That’s another question. On the one hand, there aren’t many echoes between the Tiamat story and the multi-headed dragons.

But there are some. When Heracles ‘cuts up’ the Hydra, explicitly a water dragon (hydr- = ‘water’), that’s reminiscent of Marduk cutting up Tiamat. The stormy sea winds that come from Typhoeus (Theogony 869-880) are reminiscent of the storm winds that Marduk appoints ‘to harass Tiamat’s entrails’, that is, to create storms at sea (Enuma elish 4.42-48). And the narrative of a divine battle to destroy chaos and establish order in the cosmos is a common theme.

That probably isn’t enough to justify identifying Tiamat with the seven-headed dragon, specifically. However, there’s a lot of leakage between dragon stories. It probably is justified to imagine Tiamat as some kind of dragon. And it doesn’t seem like it would have been impossible for an ancient Assyrian to have interpreted a seven-headed dragon as a picture of Tiamat.

References and further reading

  • Blust, R. 2000. ‘The origin of dragons’ (subscription required). Anthropos 95.2: 519-536.
  • Green, A. 1997a. ‘Myths in Mesopotamian art.’ In: Finkel, I. L.; Geller, M. J. (eds.) Sumerian gods and their representations. Cuneiform Monographs 7. Styx. 135-158.
  • Green, A. 1997b. ‘Mischwesen. B. Archäologie.’ In: Meissner, B., et al. Reallexikon der Assyriologie. Berlin: De Gruyter. Vol. 8, 246-264.
  • Jacobsen, T. 1968. ‘The battle between Marduk and Tiamat’ (subscription required). Journal of the American Oriental Society 88.1: 104-108.
  • Lambert, W. G. 2013. Babylonian creation myths. Winona Lake: Eisenbrauns.
  • Miller, R. D. 2014. ‘Tracking the dragon across the ancient Near East.’ Archiv Orientální 82.2: 225-245.
  • Smith, M. S. 1997. ‘The Baal cycle.’ In: Parker, S. B. (ed.) Ugaritic narrative poetry. Society of Biblical Literature. 81-180.
  • Smith, M. S.; Pitard, W. T. 2009. The Ugaritic Baal Cycle, vol. 2. Leiden: Brill.

Tuesday, 30 October 2018

Modern coins in a Roman market

If you had a time machine, would you be able to exchange modern coinage in an ancient market? If you could, how much value would it have?

I saw this question posed in an online forum once and it has come back to my mind every now and then. It’s a silly question in the sense that we don’t have time machines. But I can also see how someone writing a time travel story might find it interesting.


On the one hand, the main factor that determines a coin’s value is its fiduciary value -- that is, how much exchange value it is acknowledged to possess. The same goes for ancient coins. On one level it is the component metals that give it value. But the stamp of a Ptolemaic king or a Roman aristocrat on a coin is what guarantees that value and allows it to be used in legitimate transactions.

Modern stamping would offer no fiduciary value at all in an ancient market. So the main factor in their value would be the bullion value: the value of the metals composing the coin.

Pretty much all modern coins are alloys. And they’re alloys that were not standardly used in antiquity. In many modern currencies, low-denomination coins are even more base, made of copper- or nickel-plated steel.

This means that the practical value would be the value of the component metals, minus the cost of extracting those component metals. This would very likely result in a net negative value. You would literally need to pay people to take the coins from you.

If you could magic the metals out of the coin and convert them to bullion, then you’d get some positive value. How much value?

In modern coins, the only value worth looking at is the value of the copper (and modern coins tend to contain about 4 to 8 g copper). This was the basest metal used in ancient coins; but even in antiquity, the value of copper/brass/bronze coins was primarily fiduciary, not intrinsic. Good coinage that could be used in international trade was silver. Gold was for ultra-high-value exchanges and storage. For domestic use, copper and bronze coins were dominant, as they still are today.

The upshot is: in an ancient market you might be able to fob off modern coins to someone as a souvenir, but then the coins’ value is going to be a function of your haggling skills rather than any intrinsic value.

Below I give some sample coins. To work out the intrinsic values, or ‘bullion’ value, is easy if we wanted to sell the materials in the modern era: we simply look at the current price of copper. For that column, I’ve gone for a price per kg of EUR€5.41, USD$6.06, GBP£4.81, and NZD$9.43.


How to reckon the ancient price of copper, though? Well, in the early Principate, during the reigns of Augustus and Tiberius, the material that the sestertius was made of, brass or orichalcum, was reckoned as double the value of copper. Sestertii of that time range between about 22.5 to 26.5 grams. So, for want of anything better, I’m going to set the exchange rate at 1 sestertius = 24 grams of orichalcum = 48 grams of copper. However, this has to come with the caveat that in actual practice, the value could be anything up to an order of magnitude on either side of that.

Euro coins

Coin Copper content Modern value (EUR€) 1st cent. Roman value (sestertii)
€2, €1 can’t calculate
50 c 6.94 g 3.76 c 0.145 HS
20 c 5.11 g 2.77 c 0.106 HS
10 c 3.65 g 1.98 c 0.0760 HS
5c/2c/1c negligible (steel)

US coins (post-2009)

Coin Copper content Modern value (USD$) 1st cent. Roman value (sestertii)
$1 6.24 g 3.78 c 0.130 HS
Susan B. Anthony dollar 7.43 g 4.50 c 0.155 HS
25 c 5.20 g 3.15 c 0.108 HS
10 c 2.08 g 1.26 c 0.0433 HS
5c 3.75 g 2.27 c 0.0781 HS
1c negligible (97.5% zinc)

UK coins (1997-2016)

Coin Copper content Modern value (GBP£) 1st cent. Roman value (sestertii)
£2 can’t calculate
£1 6.65 g 3.15 p 0.139 HS
50 p 6.00 g 2.84 p 0.125 HS
20 p 3.75 g 1.77 p 0.0781 HS
10 p 4.88 g 2.31 p 0.102 HS
5p/2p/1p negligible (steel)

New Zealand coins (post-2006)

Coin Copper content Modern value (NZD$) 1st cent. Roman value (sestertii)
$2 9.20 g 8.55 c 0.192 HS
$1 7.36 g 6.83 c 0.153 HS
50c/20c/10c negligible (steel)

I’m ignoring the value of the steel in the coins, because the modern price of steel is on the order of 1/10 that of copper. Also, I can't evaluate the 1€/2€ coins or the £2 coin, because they’re made of an outer ring and an inner ring, each made of a separate alloy, and I haven’t managed to track down figures on overall composition.

In term of practical value: it is impossible to make direct equations between ancient and modern currency because the goods traded are different, and where they are the same, they are generally used very differently. Donkeys and slaves were commonly traded in ancient Roman markets; not so much in a modern first world urban setting. Wine was cheap, wheat was expensive. Many goods that are standard commodities in modern markets simply didn’t exist (heating oil, coffee, cocoa ...). The Big Mac index has no meaning for antiquity.

What we can say is that a Roman infantryman was paid 900 sestertii per annum in that period, and on that scale, the sestertii prices that we see above for modern coins are ... not inconsiderable, actually. A tenth of a sestertius comes out to about 1/24 of a soldier’s daily wage.

On balance, it might well be fair to say that modern coins would after all have some value in an ancient market -- assuming the people you were selling them to (a) recognised the metal content of your coins, and (b) had access to a means for extracting the raw materials.