Episode 10: The Ionian School

October 19, 2021

Miletus became a wealthy Greek city during the Archaic Period and developed a thriving intellectual culture which included many of the most important pre-Socratic astronomers. We looked at Thales in the last episode and now we try to understand the astronomy of other members of the Ionian School --- Anaximander, Anaximenes, and Heraclitus. What did their astronomy have in common with each other and what are the connections between their ideas and the ideas of modern physics?


Good evening, and welcome to the Song of Urania, a podcast about the history of astronomy from antiquity to the present with new episodes every full moon. My name is Joe Antognini.

In the last episode we explored the ideas and discoveries attributed to the first named Greek astronomer, Thales of Miletus. Our picture of Thales was somewhat vague for two reasons: firstly, he never wrote anything down, and secondly, even if he had written anything down, nearly all texts from his time and the subsequent few centuries were lost. So we have to go on later authors describing what earlier thinkers like Thales believed, and sometimes these later surviving sources were several times removed from the original philosophers, quoting texts which quoted texts, which quoted the original work. So we unfortunately have to be somewhat imprecise about what Thales thought, and unfortunately this lack of precision will continue to be with us for the other early Greek natural philosophers.

Now as his name, will tell you, Thales of Miletus was from a town called Miletus. The town of Miletus is essentially just a set of ruins today, but during the latter part of the Archaic period of ancient Greece, around the sixth century BC, Miletus was one of the richest cities in Greece or indeed the ancient Mediterranean. Miletus was on the western coast of Asia Minor and was ideally situated between Greece to the west, Babylonia to the east, and Egypt to the south. As a lynchpin of international trade in its day, grew wealthy and became capable of supporting a rich intellectual life, both because of the material wealth that the city saw, but also as a nexus for Greek, Mesopotamian, and Egyptian ideas to mix. Many of the earliest known Greek philosophers either hailed from Miletus or its environs, or came to Miletus to make their name. This early intellectual revolution was termed the Ionian Enlightenment by the late American physicist John Freely, Ionia being the region of Greece in western Anatolia where Miletus was situated. In due time the intellectual center of gravity in ancient Greece shifted from Miletus to the better known city of Athens, but during the Archaic period, Miletus was where it was all happening. Miletus continued to be an important city for many centuries to come — it’s even mentioned in the Acts of the Apostles as one of the cities to which St. Paul travels — but over time environmental degradation led to the decay of the city. The harbor accumulated silt, nearby pastures were overgrazed, the land was deforested, and by the 15th century AD the city was abandoned.

Well we heard extensively about the best known Milesian in the last episodes, Thales. But Thales was not the only astronomer to come from Miletus. In this episode, we will cover three others: Anaximander, Anaximenes, and Heraclitus. These three, together with Thales, make up what we today call the Ionian school of philosophy, or sometimes the Milesian school. So let’s start with the first of these, Anaximander.

It seems that Anaximander was slightly younger than Thales. Whereas Thales lived from around 623 to 545 BC, Anaximander lived from around 610 to 546 BC. So Anaximander was perhaps 10 to 15 years younger than Thales. For this reason, it is generally thought that Anaximander was a pupil of Thales, though it is entirely possible that Anaximander came to philosophy independently of Thales and the two were peers. As I mentioned in the previous episode, unlike Thales, Anaximander actually wrote his ideas down in a work we today call On Nature, although we don’t actually know what he himself titled it because, like almost all works of the time, it was lost to history. According to Diogenes Laërtius, Anaximander wrote this text very late in life, at the age of 64, which if you do the math, is only four years or so before he died. Though, as you may recall, Diogenes Laërtius is a rather dodgy source.

Well, you may remember from the last episode that one of the few things we know for certain about the natural philosophy of Thales was that he believed that water was the source of all things. Anaximander was also interested in this question of metaphysics. Unlike Thales, though, Anaximander did not believe that the source of the material world was any particular form of matter. Instead he posited that material things came from what he called the “apeiron” which could be translated as the “Infinite.” Anaximander argued that the material world in all its variety, and in particular its sets of opposing pairs: hot and cold, wet and dry, could not have come from any single material substance since any single substance would have particular qualities and would be unable to generate its own opposite. Thales said that all matter comes ultimately from water: the Earth and atmosphere separated out from the water, but the Earth was dry. Anaximander asked how this could be possible. You would need some substance which was already or inherently dry that could dry out the water and precipitate earth. But if all was water in the beginning no such substance existed. So there had to be something else, something which contained in itself all pairs of opposites.

Well, I am riffing a little bit on these ideas, again, we only have fragments of Anaximander’s original texts so we have to guess a little bit about why he thought the way that he did by trying to piece together a coherent thread of argumentation from the various mentions of his philosophy here and there by other authors. But an idea that was central to Anaximander was that this apeiron, this Infinite, contained opposites and that these opposites were dynamically, continually created from the Infinite and continually returning to the Infinite. In Anaximander’s world, everything was in motion and motion was eternal. Because of this Anaximander believed that there were a multitude of worlds — an infinite number, in fact. The text is a bit ambiguous as to what exactly he meant here. It is possible that he meant that there were a multitude of worlds continually springing into being and a multitude of worlds continually being destroyed, so that at any given time there were an infinite number of worlds in various stages of existence. Or it is possible that he believed that at any given time only a single world existed, but after it died away a new one would be born in its place. One of the few lines we seem to have direct from Anaximander can be found in Simplicius’s work Physics. Simplicius writes:

Anaximander of Miletus, son of Praxiades, who was the successor and pupil of Thales, said that the first principle (or material cause) and element of existing things is the Infinite, and he was the first to introduce this name for the first principle. He maintains that it is neither water nor any other of the so-called elements, but another sort of substance, which is infinite, and from which all the heavens and the worlds in them are produced; and into that from which existent things arise they pass away once more, “as is ordained; for they must pay the penalty and make reparation to one another for the injustice they have committed, according to the sequence of time” as he says in these somewhat poetical terms.

And this eternal cycle of generation and destruction was not limited to entire worlds, but Anaximander argued that we saw it in smaller form through the course of seasons and days and in the weather as the Earth and heavens continually exchanged heat and cold, light and dark, wet and dry.

This dynamic, cyclical picture of the universe in which pairs of opposites are continually generated, exchanged, and destroyed back into the apeiron in fact has some parallels to the modern picture of quantum field theory which developed in the middle part of the 20th century AD. In this picture the vacuum of space is not so much a void, but has something of the infinite to it and sees an eternal dynamically changing landscape of pairs of virtual particles and anti-particles springing from the vacuum, lasting a short while, and then collapsing back in on themselves, annihilating each other in the process. Indeed, in the latter part of Werner Heisenberg’s life in the 1950s and 1960s, he, like many other physicists of that era, was searching for a unified field theory, a theory of physics that would encompass all known physical forces. And he came to believe that ultimately, the various elementary particles that we observe are not distinct, but must be particular stable solutions to an underlying, indeterminate form of matter, in a similar way to how the six Platonic solids, the cube, pyramid, icosahedron, and so on, are various manifestations of the underlying concept of a three dimensional solid with equal faces. The physicist Max Born saw the similarity of this underlying substance to the apeiron of Anaximander and began to call it such. Well, ultimately Heisenberg was not able to work out a complete and consistent unified field theory before his death, but it is apparently a very tricky problem. Physicists have now been attempting to find a unified field theory, or more generally a grand unified theory, for half a century now without success.

Well, although Anaximander’s metaphysical idea of apeiron, the Infinite primordial substance, may be somewhat back in fashion today, we cannot say the same of some of his other ideas. According to Pseudo-Plutarch, you’ll remember him as the unknown author who tried to pass of his writings as those of the more famous author Plutarch, he wrote about Anaximander’s cosmogony,

…that which is capable of begetting the hot and the cold out of the eternal was separated off during the coming into being of our world, and from this there was produced a sort of sphere of flame which grew round the air about the earth as the bark round a tree; then this sphere was torn off and became enclosed in certain circles or rings, and thus were formed the sun, the moon, and the stars.

Like Thales, Anaximander also had a cosmology — a model of the structure of the universe. Anaximander agreed with Thales that the Earth was a short cylinder. However, Anaximander went further than Thales and actually specified the proportions of the cylinder — he claimed that the diameter of the cylinder was three times as large as its height. Unfortunately only this claim survives, we don’t actually know how he arrived at this assertion. Pseudo-Plutarch simply writes that

The earth [Anaximander] says, is cylinder-shaped, and its depth is such as to have a ratio of one-third to its breadth.

And that is all there is to that. So it would appear from his cosmology that we do not see any especially sophisticated ideas. But there is an interesting detail in his cosmology that is actually remarkably sophisticated and would have important implications through the history of physics right down to today. And this is that unlike Thales, who posited that the cylinder of the Earth was floating in a vast ocean, Anaximander posited that the cylinder of the Earth was actually suspended in air.

Well how is this possible? How could the Earth maintain itself suspended in air when gravity, it would seem, should pull it down? When Aristotle was explaining the ideas of Anaximander in his work on physics Aristotle presented the argument that this was possible because the Earth was equidistant from all the other heavenly bodies. Specifically, Aristotle says,

for that which is located in the center and is similarly situated with reference to the extremities can no more suitably move up than down or laterally, and it is impossible that it should move in opposite directions at the same time, so that it must necessarily remain at rest.

In essence, because the Earth is in the center of all things, it cannot arbitrarily pick out some direction to go and move toward it. So it stays in one place, at rest. Aristotle rightly describes this argument as ingenious. Centuries later Isaac Newton invoked a similar argument. As we’ll discuss in depth in a much later episode, one of Newton’s crowning achievements was the discovery of the force of gravity, the attraction of all masses in the universe for each other. This discovery beautifully explained the observed motions of the planets, but it presented some serious cosmological issues as Newton started to think about it more deeply. Some time earlier, the chemist Robert Boyle, after his death, had left some money in an endowment to fund an annual series of lectures to combat atheism, a dangerous idea that God did not exist and which was starting to spread alarmingly in the intellectually raucous London coffeehouses of the late 17th century. In 1692 a theologian named Richard Bentley was selected to give the first of these lectures, and he decided to use the modern scientific ideas of Newton to demonstrate the error of the atheists’ notions by demonstrating that the known laws of physics necessitated divine intervention. Newton, being a strong, though unorthodox, theist, readily approved of Bentley’s idea. Bentley wanted to make sure he had the science correct and the two sent a number of letters back and forth with Bentley asking points of clarification and Newton responding.

In particular, what Bentley wanted to know was what would happen if the universe were finite, and what would happen if it were infinite? Because it would seem that if the universe were finite in extent, then the mutual attractive force of gravitation would pull all the matter together and it would all collapse in on itself. Newton agreed that all matter would “fall down to the middle” and “compose one great spherical mass.” But if the universe were infinite, Newton assured Bentley that the universe could not collapse in on itself because the force of gravity would pull equally in all directions and the matter would not know which way to fall. Since we observe that the universe was not one great spherical mass, this meant that the universe was necessarily infinite in extent, which was invoked in the lecture as evidence of God’s infinite power and majesty.

This sort of argument from symmetry, that the Universe could not simply arbitrarily choose between two equal things, grew in importance in physics over the following centuries and became a centerpiece of 20th and 21st century physics. By the 20th century, physicists were frequently invoking various kinds of symmetries to place constraints on the various possible form of physical laws. Of course the details of these kinds of arguments were frequently very technical, but we can get a taste for what this kind of argument looks like by considering how we might go about deriving Newton’s law of gravitation. You may remember Newton’s law, it just says that the gravitational force between two objects is the gravitational constant times the mass of the first object times the mass of the second object, divided by the distance between the two masses squared. \(G m_1 m_2 / r^2\).

So why does this equation have the form that it does? Well the first part, G, the gravitational constant can just be stuck in automatically. From a physical standpoint, this factor isn’t really doing anything except converting between units. We have masses and distances on the right hand side and we need a force on the right hand side, and the gravitational constant is basically just a way to convert the units on the right to be units of force on the left. Of course, the specific value of the gravitational constant has to be measured experimentally, but from the perspective of just figuring out what the equation looks like, the specific value isn’t super important. Its numerical value simply tells us how strong the force of gravity is in whatever units system we’ve chosen. So that’s where the G comes from. But even this first step we’ve already made use of symmetry. Because we are implicitly assuming that gravity has the same strength everywhere in the universe. This is a plausible thing to believe. If we assume that no location or direction in the universe is special in any way, that there is complete symmetry of translation in the technical jargon, then that would imply that the force of gravity is the same strength everywhere, and that would imply that G is a constant, independent of position.

What about the $m_1$ and $m_2$? Well we can figure out that the gravitational force must be proportional to $m_1$ and $m_2$ by imagining the gravitational force between two blobs of matter. Take the second blob, and now draw an invisible line through it, dividing it into a left half and a right half. Instead of calculating the gravitational force between the first blob and the entire second blob, you could instead calculate the force between the first blob and the left half of the second, and also calculate the force between the first blob and the right half of the second. From the perspective of the universe, there is no difference how you do it. So if you add the forces from the two halves, you’d better get the same force as if you’d calculated it from the entire blob all at once. Well maybe you’re washing dishes or driving right now as you’re listening to this and can’t work out the math, but the only way for this to be true no matter how you divide the second blob with imaginary lines is if the force is proportional to the mass of the blob. And, by symmetry, what goes for the second blob also has to go for the first blob, because we chose one to be first and the other second arbitrarily. So we know that the gravitational force has to be proportional to $G m_1 m_2$.

What next? The only other thing we can say is that the gravitational force must also depend only on the distance between the two objects. If we assume that the universe treats all directions equally, the force cannot depend on the x-coordinate acting on its own or the y-coordinate or the z-coordinate, because the universe doesn’t have any x- y- or z-coordinates built into it. We simply impose these coordinate systems on the universe and we can choose them to be whatever we want. So the laws of physics need to be independent of them. The only thing that makes one direction different from any other is the direction between the two objects. So all we can say is that the force is proportional to some function of the distance between these two objects along this direction. This is about as far as we can go in deriving the gravitational force from arguments of symmetry. In principle, it could be $G m_1 m_2 / r$ or $G m_1 m_2 / r^2.0001$, or $G m_1 m_2 / r^{4000}$. But it is in practice either $1 / r^2$ or something very, very, very close to $1 / r^2$.

These sorts of arguments from symmetry are used all the time in contemporary physics. It is hard to overstate the importance of symmetry to physics today. But some two and a half millennia ago, Anaximander was the first to invoke this principle. And even Aristotle, who generally didn’t like other people’s ideas, thought that this idea was pretty clever.

Now you may remember that, like a lot of other highly opinionated ancient thinkers, Aristotle generally explained the ideas of others so that he could then explain why they were wrong and his own ideas were right. So after explaining Anaximander’s argument from symmetry, Aristotle then went right on to say that, clever as it was, it was obviously absurd.

Aristotle made a few arguments against Anaximander’s idea that the Earth could remain suspended in air by virtue of there being no direction for it to preferentially go. The most colorful of these was to imagine a man who is very hungry and thirsty but stands equidistant between some water at his left and food at his right. Are we to assume that he will simply die of hunger or thirst because he cannot choose which direction to go? According to Anaximander it would seem that the man would perish. This argument became more famously known as Buridan’s Ass after it was revived in the 1300s by the French philosopher Jean Buridan. Buridan was an extremely important natural philosopher of the late Middle Ages who developed the impetus theory of motion, which broke with Aristotelian physics and laid the groundwork for the theory of inertia which developed a few centuries later, and we will have much more to say about him in a later episode. But here Buridan took Aristotle’s argument and turned it from physics to the philosophy of the mind. He claimed that if a person had to choose between two options each of which were equally good, or each of which were equally evil, their will would be unable to decide until circumstances changed. Buridan’s critics viewed this position as ridiculous and invoked the example of a donkey being set equidistant between two equal piles of hay and starving to death because it can’t decide which one to eat, the donkey becoming known as Buridan’s Ass.

Now, Buridan was no dummy and it turns out that the philosophical argument at play in Buridan’s writings that led to this claim of his was a little more subtle than it might first appear from the donkey starving to death. One of the major intellectual debates of his day concerned the relationship between the intellect and the will. Aristotle and St. Thomas Aquinas had staked out a position in which they claimed that the will was completely subordinate to the intellect, a position known as intellectualism or naturalism. By contrast there was another school of thought that had developed in Franciscan circles from the philosophy of St. Augustine that claimed that the will could sometimes act independently of the intellect, a position known as voluntarism. Buridan here was attempting to find a compromise position between the intellectualist and voluntarist philosophies. In this framework, the intellect was responsible for judging the moral ramifications of a particular action whereas the will was responsible for selecting which action to carry out. Jean Buridan emphasized the role of uncertainty in the intellect’s judgment of the moral consequences of an action. Since in this life we cannot know the full consequences of our actions, it is often the case that the intellect simply cannot make a judgment as to whether one action is morally superior to another, and in these circumstances the will is forced to a position of inaction until the situation changes and the intellect can make a definitive judgment. Now, modern philosophers seem to be of the opinion that this was not really a very good compromise between the intellectualist and voluntarist positions. It looks a great deal like the intellectualist position dressed up in the language of the voluntarists. But the intellectualist position had been targeted in the Condemnation of 1277 and so there was a need for those ideas to be stated in somewhat different language. I won’t go into much more detail on these philosophical issues because it would take us further astray than we already are, but be assured that I will probably devote an entire episode to the Condemnation of 1277 once we get to the astronomy of the Middle Ages because the condemnation and the debates that led to it were a highly consequential event in which the western intellectual tradition seriously grappled with the question of life on other worlds.

Well back to Anaximander. We have seen now that he believed all matter to have its roots in the apeiron, or Infinite, and that the world was a cylinder floating in air. But Anaximander had more to say about the structure of the planets and Sun which we might call his “wheel theory.” Now we’re once again butting up against the limitations of learning about his ideas from sources several times removed from the original because the versions of this wheel theory that survive are somewhat ambiguous. But the most common interpretation is that Anaximander believed the Sun to be a giant wheel that lay along the ecliptic with the Earth at the center of the wheel. So imagine a bicycle wheel whose center is at the Earth, and we standing on the Earth are looking out along the spokes at the inner part of the rim across the sky. Anaximander claimed that this wheel was not visible to us except that it had a circular hole in it, sort of like the nozzle of the bike wheel. The wheel contains compressed air and fire which are emitted by the circular vent which produces the disk of the Sun which we see on the sky. Likewise there is another wheel for the Moon, and possibly wheels for each of the stars as well. In Anaximander’s cosmology, the Moon was closer to the Earth than the Sun and the stars were even closer than the Moon.

Now we don’t know exactly what Anaximander thought these wheels were made of. Evidently the material is unusual because it clearly is sort of invisible since the Moon’s wheel does not block out the light from the Sun at the places where they overlap. But it also cannot be completely invisible since it doesn’t show the fire inside the wheel — the light from the Sun is only visible through the circular vent.

Nevertheless, Anaximander used this idea of vents in a wheel to explain solar and lunar eclipses, along with the phases of the moon. These were simply instances when the vents partially or completely closed.

Anaximander went into even more detail about the structure of his wheel theory. He specified that the size of the Sun was 27 or 28 times as large as the Earth. Now this is a bit of an odd assertion because these two numbers both come to us from the same source, Aëtius. In one part Aëtius says that Anaximander claimed that the Sun was 28 times as large as the Earth, and in another part he claims that it was 27 times as large, and to make matters even worse, in the same sentence he also says that the Sun is the same size as the Earth. Specifically, in one line he says:

The sun is a circle twenty-eight times the size of the earth; it is like a chariot-wheel, the rim of which is hollow and full of fire, and lets the fire shine out at a certain point in it through an opening like the nozzle in a pair of bellows; such is the sun.

In the other line, Aëtius says

The sun is equal to the earth, and the circle from which the sun gets its vent and by which it is borne round is twenty-seven times the size of the earth.

The way this should probably be interpreted is that the overall size of the wheel is 27 or 28 times the size of the Earth, but the size of the vent in the wheel is equal to the size of the Earth. In more modern terms, we would say that the distance from the Earth to the Sun is 27 or 28 times the radius of the Earth. Now why the ambiguity in 27 or 28? We have to read between the lines a little bit, but what is probably meant here is that the inner radius of the wheel is 27 times the size of the Earth, whereas the outer rim of the wheel is 28 times the size of the Earth. This would make the thickness of the wheel the same size of the Earth, which then explains why Anaximander claims the disk of the Sun itself to be the same size as the Earth.

As with Anaximander’s claim that the height of the Earth’s cylinder was one-third its diameter, we don’t know exactly how Anaximander came up with these numbers for the size of his proposed wheel. What we do know, however, is that they aren’t plausible. If the vent out of which we viewed the Sun were the size of the Earth and 27 times farther away than the size of the Earth, this would imply that the angular diameter of the Sun was 4 degrees, whereas its actual value is very close to half a degree. Now, the ancient Greeks did not have sophisticated measuring equipment, but you don’t need to have any sophisticated measuring equipment to know that the angular diameter of the Sun is way less than four degrees. In fact, the thickness of your pinky finger held at arm’s length is about one degree. So the disk of the Sun is about half as wide as your pinky finger. If the Sun were four degrees in size, it would be nearly as wide as your index, middle, and ring fingers put together.

We can get a possible hint as to what might be going on here by looking at Anaximander’s picture of the Moon. In Anaximander’s cosmology, the size of the Moon’s wheel is 19 times larger than the size of the Earth. A theory by Thomas Heath is that this described the outer rim of the Moon’s wheel and that the inner rim of the wheel was 18 times as large as the Earth. So we would then have the inner rim of the Sun’s wheel being 27 Earth sizes and the inner rim of the Moon’s wheel being 18 Earth sizes, both factors of nine. Since Anaximander postulated that the stars were closer to the Earth than the Moon it is natural to imagine that he may have placed them at 9 Earth sizes. It is entirely possible that the number nine may have had some special meaning in his cosmology and the entire distance scheme was more numerological in nature than physical. This would also fit with the diameter of the cylinder of the Earth being three times larger than its height.

Now, to be clear, this is a somewhat speculative idea. There is nothing surviving in which Anaximander specifies the inner radius of the Moon’s wheel or the size of the Moon, nor do we know what he said about the distance to the stars. But it is also not an entirely implausible idea. Numerology was very popular in ancient Greece due in particular to their numeral system. Unlike the ancient Babylonians, but like the ancient Israelites, the ancient Greeks did not have separate characters for their numerals. Instead they used the first letter of their alphabet, alpha, to denote the number one, the second letter beta for two, the third, gamma, for three and so on. Then when they reached iota they would be at 10 and the next letter, kappa, represented 20, lambda 30, and so on, up until they got to rho, which was the number 100. Then numbers increase by one hundred until they got to the end of the alphabet at omega and were at the number 800. Now, 800 is a somewhat awkward spot to stop, so a character called sampi from an older eastern dialect stuck around for a few more centuries to represent the number 900.

Any listeners who know some Hebrew will be finding this numbering system familiar, because Hebrew does something similar. And a consequence of this is that if you take a word in Hebrew, you can interpret the characters as numbers and add them up. This then establishes a numerological connection between the number and the word which is a practice called gematria. Well ancient Greek did much the same thing, but called it isopsephy. Because of this intimate connection between words and numbers, the Greeks tended to be somewhat numerologically minded. So it is not entirely unreasonable to suppose that Anaximander may have developed the distances in his cosmology on numerological grounds.

But setting aside how exactly Anaximander determined what these distances were, another significant aspect of this cosmology was that he had something to say about distances at all. Anaximander is the first of the Greek natural philosophers to concern himself with the scale of the universe. In the Greek tradition prior to this, all we see about distances is some lines in Homer about how Hephaestus took nine days to fall to Earth when he was cast out of Olympus by Zeus.

And while we might view his model of the Earth as a squat cylinder floating in air as fairly primitive it was also a critical conceptual step forward. Because in Anaximander’s cosmology, the Sun and stars didn’t dip into the river Okeanus when they set and then journey along the river to the east so they would be ready to rise the next day. Instead in Anaximander’s cosmology the Sun is always present event when it’s night, it’s just on the other side of the Earth and not visible to us. This is a sophisticated idea with big consequences, and as far as we know, Anaximander made that conceptual leap first.

So while Thales earned the honor of being elevated to one of the famous seven sages of Greece, at least based on the surviving fragments of his thought, it does seem as though Anaximander was the more sophisticated thinker of the two, though we don’t know exactly how many of Anaximander’s ideas came ultimately from Thales since Thales didn’t write anything down.

Anaximander made a few other contributions to the natural philosophy of his day. One of these was the introduction of the gnomon to Greek astronomy. Gnomon is a fancy word, but it’s basically just a stick in the ground. By looking at the length of the shadow cast by the stick you can measure the elevation of the Sun and then measure how it changes over the course of a year. You may recall that we discussed something similar in Babylonian astronomy way back in Episode six. The Babylonians had been using the gnomon prior to Anaximander’s time, and it is probable that Anaximander did not develop this independently but learned about it from the Babylonians and was the first to introduce the gnomon to Greek astronomy.

Anaximander was also the first Greek to draw a map of the known world. But since none of Anaximander’s texts have survived you won’t be surprised to hear that the map doesn’t survive either.

And Anaximander had ideas about meteorology. In Anaximander’s conception lightning and thunder are produced by collisions of clouds. Sometimes, however, the collisions are weak which produces thunder but no lightning.

The final thing I’ll say about Anaximander is that he also proposed a theory of evolution. The surviving fragments about Anaximander’s ideas on the origin of species are a little confused, but it seems like in Anaximander’s theory humans ultimately came from fish. According to Aëtius,

Anaximander said that the first living creatures came into existence in the moist element, and had prickly coverings, but as they advanced in age, they moved to the drier part; and, when the covering peeled off, they survived in their changed state for a short time.

Anaximander’s evidence for this theory was that humans have such a long infancy compared to other animals. Because of this we humans could not have been primordial species because we could not have survived in the early world with this long an infancy. This seems to imply that in Anaximander’s view the conditions for survival in the early world were harsher than they are today, but we don’t see any surviving texts that corroborate that.

Well, there we have Anaximander of Miletus. In many ways he is the high point of the astronomy of the Ionian school, but we still have two more astronomers to talk about: Anaximenes and Heraclitus.

Just as Anaximander was probably a student of Thales, Anaximenes was probably a student of Anaximander. And just as Anaximander rejected Thales’s theory that all matter had its origin in water, Anaximenes rejected Anaximander’s theory that all matter had its origin in the Infinite, his so-called apeiron. Anaximenes was also interested determining the origin of all matter, but for him the origin of matter was in air rather than some unknown substance. One of the few fragments we have from Anaximenes’s writings says

Just as our soul, being air, holds us together, so does breath and air encompass the whole world.

In other respects Anaximenes’s cosmology was pretty similar to Anaximander’s. He also held that the Earth was a cylinder, although he seems to have believed that the Earth was much flatter than Anaximander’s cylinder, which had a height of one-third its diameter. But just as with Anaximander, Anaximenes believed the flat Earth to be floating in air. Anaximenes didn’t invoke an argument from symmetry as to what keeps the Earth aloft, though. Instead he argued that because the Earth was flat, the pressure from the air kept the Earth from falling.

And Anaximenes didn’t limit himself to flattening only the Earth. He got rid of Anaximander’s wheels and held that the Sun and Moon were also flat discs, comparing them to leaves. This structure made them susceptible to the vagaries of the winds. This was why the Sun and Moon pursued such an unusual course in the sky relative to the static stars — they were simply being blown about by the winds. The stars, by contrast, Anaximenes said were embedded in a sphere like nails in a hollow shell.

Anaximenes broke from Anaximander in one other important way, concerning these stars embedded in a shell, which was that he argued that the stars were further from us than the Sun because unlike the Sun we do not feel their heat.

We don’t have nearly as many references to the thought of Anaximenes compared to Anaximander, so this is essentially all we know about him. By far the most enduring of his ideas was this last one about the stars being like nails embedded in a shell. This idea has two important features. The first is that implies that all the stars essentially move together in lockstep, as a single unit. And importantly, it also implies that they do not disappear when they set. They are simply on the other side of the Earth. Today we call this concept the celestial sphere and it’s still a very convenient way for describing the motions of the heavens. This idea was to become a key feature of Greek astronomy and then Western astronomy more generally through the Middle Ages until we arrive at Copernicus.

So we have just one more astronomer to discuss in the Ionian School — Heraclitus. Of the three astronomers I’ve talked about in this episode, Heraclitus is certainly the most famous, but it is probably something of a mischaracterization to call him an astronomer. He was primarily a philosopher, and like any self-respecting Greek philosopher of the ancient world, he had opinions on just about everything, astronomy just happened to be one of the things he opined about.

You have probably heard of some of Heraclitus’s maxims. His best known adage is that no man steps in the same river twice. And this gets to the heart of his philosophy which was that all things are in flux. This is similar to Anaximander’s idea of eternal motion and worlds continually being born and dying. But for Heraclitus, the key was that this motion consisted in exchanges between opposites — an exchange between the Earth and heaven of hot and cold, between night and day. The transmission from Earth to Heaven was called the upward path, and the transmission from Heaven to Earth was the downward path. These exchanges are described as exhalations and some of them are pure and bright, others dark. Bright exhalations induced fire, dark exhalations induced moisture. Unfortunately it’s very hard to understand what exactly is meant by all this because our only source for it is essentially from Diogenes Laërtius, who you’ll remember oftentimes has no idea what he is talking about, and in this particular case is very upfront about the fact that he does not understand the subject matter, although he blames Heraclitus, saying “he explains nothing clearly.” Though, to be fair to Diogenes Laërtius, Heraclitus got the nickname Heraclitus the Obscure for his cryptic maxims, so apparently Diogenes Laërtius wasn’t the only person to find him confusing.

Well just as Thales, Anaximander, and Anaximenes were interested in the so-called “arche” the source of all matter, Heraclitus had to say something on the matter as well. But by this point, Thales had taken water, Anaximenes had taken air, and Anaximander had made up some infinite substance called apeiron. So Heraclitus had to choose something else and concluded that the source of all things was fire. In his view, when fire was compressed it became moist, and eventually condensed into water, which in turn had precipitated Earth out of it.

As to the structure of the celestial bodies, you’ll recall that Anaximander thought that the Sun and Moon were essentially tubes and Anaximenes thought that they were flat disks. Heraclitus thought that they were bowls with the concave side facing us. The concave part of the bowls collected and concentrated the bright exhalations from the Earth which produced fire. Because the Moon was closer to the Earth, the air around it was less pure which gave it a dimmer light. Heraclitus also had a convenient explanation for eclipses and the phases of the moon. These occurred whenever the bowls happened to turn around, either partially or fully, depending on the phase or kind of eclipse. Since the convex side could not collect the bright exhalations, they were dark. Now, how you can have a bowl turn in such a way as to produce a crescent shape I couldn’t tell you. But it is probable that Heraclitus did not think about his astronomy all that hard and was interested in more fundamental matters of philosophy and metaphysics. This kind of bizarrely inadequate theory from an otherwise intelligent philosopher also shows up in his statement that the Sun was only a foot across. Aristotle, who is usually pretty harsh on other philosophers, calls this idea “childish,” and it’s hard to say he’s wrong there.

Heraclitus also had some interesting opinions on the motions of the heavens, although they were largely a regression on the ideas of Anaximenes. In his view, since the Sun was a bowl collecting bright exhalations from the Earth, when it set in the evening, it dipped into the river Okeanus that surrounded the world and became extinguished. Then it travelled around the world to the East where it rose again the next morning. It began to collect new exhalations from the Earth and became reignited once again. Heraclitus is quite clear on this point that the Sun is renewed every day. Likewise he claims that the stars do not in fact set under the Earth. Instead he likens the motion of the stars over the course of the night to a cap turning on a man’s head. He imagined that the Earth was perhaps somewhat bowl-shaped, and so the horizon we observed was not the edge of the world, but simply a place where the mountains or sea rose high enough to block out our view from anything beyond it. When the stars seemed to set, they were still above the Earth, just over another part of it and being blocked from our sightline.

If this explanation doesn’t seem to make much sense to you, don’t worry you are not wrong. Trying to explain this line of thought in a convincing way is really pretty much impossible since we just don’t have any of his original works, and end up relying so much on secondary and tertiary sources who themselves were frequently confused. Some scholars have supposed that Heraclitus may have actually believed that the stars went under the Earth when they set and that the cap he was talking about is more like a kippah that is sort of set slightly back on the head instead of like a bowler hat that is perched right on top. But this doesn’t seem to work well with the idea that the Sun gets extinguished when it sets into the river Okeanus every night. On the whole, the astronomy of Heraclitus seems to be a regression back towards the primitive astronomy of Homer and Hesiod.

But as I mentioned, Heraclitus was far better known for his other philosophy. He just gets short shrift here because this is an astronomy podcast and his astronomy was less compelling. He was also quite well known for his misanthropy and his general lack of faith in the in the moral capability of humanity, believing that most men were semi-conscious at best and evil at worst, and only rare exceptions were truly good. For this attitude he later acquired the nickname “the weeping philosopher,” in contrast to Democritus who became known as “the laughing philosopher” for his jovial attitude when he pondered upon the folly of man.

Okay, so there you have Anaximander, Anaximenes, and Heraclitus, who, together with Thales from the previous episode, constituted the Ionian School. I’ll end by making just a few notes about the Ionian School in general, because these thinkers had a few things in common besides all coming from the region of Ionia.

Certainly the most salient commonality among them was that they had a deep interest in metaphysics, and in particular, in understanding what the fundamental composition of matter was. And more than just pondering on this question, the philosophers of the Ionian School all came to the same general position, namely monism, which is the idea that at its root, all matter is of the same substance, we merely view it in different states. They all disagreed with each other as to what exactly that fundamentally substance was, Thales said water, Anaximenes said air, Heraclitus fire, and Anaximander the apeiron. But they were in agreement that one such substance existed. This position of monism is still with us today. We heard a little bit about it in the efforts of Werner Heisenberg at the end of his life, and other physicists today carry on the tradition in string theory and other speculative theories of fundamental physics that posit that the vast diversity of apparently elementary particles we observe are in fact different states of a single kind of matter, whether it be a small loop or string or D-brane, or something else entirely.

But monism wasn’t the only available position, and over the course of the centuries of natural philosophy in the West, it was certainly not the dominant view. Generally the pluralistic view, that there are multiple fundamental substances has reigned supreme in Western thought, whether those substances were the four classical Aristotelian elements of earth, air, fire, and water, or the elements of the periodic table in the 19th century, or the particles of the standard model of the 20th. A third option, which could be considered a special case of pluralism, is dualism, which holds that there are only two fundamental substances, and usually these are opposites in some way. Dualism has been the fundamental Western approach to the philosophy of mind since the time of Descartes and is still popularly accepted. But this is not a material dualism — instead Descartes had argued that the material world and the mental experience of consciousness, were composed of two fundamentally different substances. In other words you have a mind and you have a body, but they are fundamentally separate things. You cannot make a mind purely out of matter and you cannot make matter purely out of a mind. This idea was dominant in Western philosophy for centuries and today most people accept that they have both a body and a soul and that these are two separate things. But material dualism hasn’t held the same sway in the West as mind-body dualism. Material dualism was far more prominent in Eastern philosophies and we will discuss them when we arrive at the astronomy of the various Asian civilizations, most notably China and India.

Another noteworthy development of the Ionian School, was the attempt to explain the observed natural phenomena by means of a naturalistic explanations. The explanations as to why eclipses occurred or how the universe was created, were entirely naturalistic. None of them invoked the supernatural to explain the world they saw. So even if the particular explanations they developed seem naive to us, the mode of explanation they used was a radical break from the past and was the first step towards modern science.

And the final development of the Ionian School was that there was a school at all. This was the first instance in Greek civilization of people deciding to devote their lives to thinking about questions of philosophy and astronomy, and then communicating their ideas to pupils who studied from them. The institution of the philosophical school became more formalized in Athens during the Classical period, but the major feature of this institution, a philosopher who developed his own unique ideas and taught a group of students, originated here in Miletus in the Ionian school.

So there you have it, the Ionian school, the first of many in the Greek tradition. Well, I have perhaps made a small lie by omission. I talked about Thales, Anaximander, Anaximenes, and Heraclitus. But the philosopher Pythagoras was also from Ionia and so could technically be included in the Ionian School. But the ideas of Pythagoras and the Pythagoreans were so distinct that they are usually placed in their own category, which is exactly what we are going to do on this podcast when we talk about the astronomical ideas of Pythagoras and the Pythagoreans in the next episode. I hope you’ll join me then. Until the next full moon, good night and clear skies.

Additional References

  • Dreyer, A History of Astronomy from Thales to Kepler
  • Harrison, Newton and the infinite universe, Physics Today
  • Heath, Aristarchus of Samos
  • Heath, Greek Astronomy
  • Simonyi, A Cultural History of Physics