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.


  1. The dodecahedron was regarded as the fifth Platonic solid? Was the icosahedron number four?

    Didn't the idea that our universe follows predictable laws come from the notion that our existence is an artifact of an intelligence?

    I've heard of Christian historians giving Christianity credit for this. There also some who want to credit Islam. But I guess the Christians and Muslims got it from Plato.

    But whether from Christians, Muslims or Plato, it does seem the scientific method was developed, at least in part, by people who believed in The Architect. A fact that cracks the foundations of Sagan's model of history.

    1. Thanks for the comment David. Plato only mentions the dodecahedron in passing (Tim. 55c), and is vague about its role. The five solids do share a set of geometrical properties -- all their faces are identical equilateral polygons, all internal angles are similar, etc. -- which are unique to them and cannot appear in any other 3-dimensional polyhedron, so they are regularly grouped as a set of five. The late stories about Hippasus may possibly suggest that the dodecahedron was discovered later than the others, but the sources on that are very unreliable.

      I strongly resist the suggestion that the idea of predictable physical laws developed in any one time or place. Long before Christianity and long before the Ionians, the Babylonians knew the sun, moon, and planets stick close to the ecliptic; they knew that things like areas, and diagonals of physical shapes, could be predicted mathematically; they knew that lunar eclipses come in regular cycles. All of these are geometrical (and therefore mathematical) predictions of real phenomena.

      The classical-era Greeks developed on this in many ways - so Oenopides (it seems) discovered that the ecliptic is a great circle at an angle to the equator, Theaetetus discovered that real-world shapes can generate irrational numbers, and Hipparchus used lunar eclipse cycles to predict solar eclipses as well - but so did lots of other people.

      Over the centuries we see discoveries like these popping up in all sorts of environments, in a variety of intellectual contexts. If someone wants to argue that any one group or any one ideology bears the greatest credit for formalising the idea of the predictability of the cosmos, I'd want to see a very strong and thorough supporting argument for that.

  2. "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."

    I found these statements rather puzzling. The dominant Neo-Platonism of the fourth and fifth centuries was generally very compatible with Christianity and was substantially accepted and even adopted theologically by early Christian thinkers. This is why Augustine's theology is so heavily Platonic and why even non-Christian Platonists like Hypatia had many Christian students. The only form of Neo-Platonism that was in any way "suppressed" by Theodosius was the aggressively pagan and anti-Christian mystical theurgical school of Iamblichus, whose members did things like murder and torture Christians and openly boast about it. And Theodosius didn't exactly crush them anyway. So what "suppression" are you talking about?

    The reference to "the school that Plato founded" being suppressed by THeodosius is especially odd. Plato's Academy had ceased to exist centuries before Theodosius was born and the later Athenian "Academy" that espoused the mystical/theurgical teachings of Plotinus and Proclus was not established until the fifth century, long after Theodosius' death. So what "school founded by Plato" did Theodosius suppress?

    I'm loving this series, as I've long recognised Sagan as a peddler of pseudo history, but those comments about Theodosius don't seem to fit the evidence.

    1. Tim, thanks for your comment. I blundered. A post like this needs to be extra-careful about checking its facts, and in this case I messed up. Twice. I've added a correction above.

      I was thinking of Justinian's closure of the (second?) Academy and expulsion of the Neo-Platonists, over a century after Theodosius, and got the two mixed up in my head. Which is a pretty bad mistake.

      I also hadn't appreciated that there is good reason to think the Academy ceased to exist after Sulla. I knew Horace said he had studied "in the woods of the Academy", so had taken it for granted that it carried on. I see now that there's good reason to believe it ceased to function altogether.

      If you'll allow, I'll regard the first as a blunder and the second as an inaccuracy! Two mistakes for the price of one, anyway. My apologies.

    2. Yes, I thought you may have been thinking of Plotinus and Proclus' Iamblichan Academy. The idea that it was closed by Justinian is another myth that won't die - and another one that we can blame largely on Gibbon. Justinian certainly passed a law banning pagan teachers from being paid from the public purse (much as Julian had passed a similar law against Christian teachers), but this was not aimed specifically against the Athenian Neo-Platonists.

      Edward J. Watts makes a pretty powerful case that Justinian's more general edict was taken and used by the local authorities in Athens to target Damascius' anti-Christian school. See Watts, “Justinian, Malalas and the End of Athenian Philosophical Teaching in A.D. 529”, The Journal of Roman Studies, 94, 2004, pp. 168-182. It was more of a local power play than an overt and specific act by Justinian. And after the philosphers of Damascius' school found the philosophical grass wasn't greener in the Persian Empire, Justinian accepted them back into the Roman Empire where they taught unmolested (just not on public salaries). Of course, all this has been turned into part of the "Christians killed Classical culture" topos projected by Gibbon and perpetuated more recently by that silly book by Catherine Nixey.