Episode 15: On Plato's Broad Shoulders

March 22, 2022

Before leaving the world of the Pre-Socratics, we look briefly at the astronomy of Oenopides, which had a more observational character than many of his contemporaries. Then we turn to Plato, the first of the great astronomers in the Socratic tradition, whose astronomy synthesized the best ideas of his predecessors.


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.

Well, over the last eight episodes, I have tried to lead you, dear listener, through the development of Greek astronomical thought, starting with the mythological and poetic cosmologies expressed by Homer and Hesiod, along with the variety of Greek myths, and then moving through the philosophers of the first philosophical school in ancient Greece, the Ionian School. As Miletus came to occupy a more important position in Greek culture, the ideas of the Ionian philosophers came to spread to other Greek colonies and we traced the development of other schools of philosophy, the Pythagoreans, the Eleatics, and, in the last episode, the atomists. These are all philosophers which have been scandalously lumped together as the “pre-Socratics”, but, despite the title of this episode, there is one last pre-Socratic astronomer whom I would be remiss to omit before we make that irreversible leap out of the realm of the pre-Socratics. So, my apologies for the bait and switch, but before we get to the main subject of this episode, Plato, I want to talk briefly about an astronomer by the name of Oenopides of Chios. Oenopides doesn’t neatly fit into any of the schools that we’ve followed in the past eight episodes, so at least in this telling, he is something of an appendix to the broader narrative. But, he made several important discoveries and was influential among ancient Greek astronomers so it is worth spending a few minutes to recount his greatest hits.

We don’t know very much about Oenopides’s life, basically just that he was active in the middle of the fifth century BC, probably living from around 490 to 420 BC, so roughly contemporaneous with Anaxagoras and Leucippus and living right during the time that Athens was becoming a political and cultural powerhouse in ancient Greece. Oenopides was born on the island of Chios, but not much is known for certain about his subsequent whereabouts. There is a tale which by know I’m sure you’re familiar with that he traveled to Egypt and there learned the secrets of astronomy and mathematics from the Egyptian priests. And he probably spent some time in Athens as well. But apart from that there is really nothing more to say about his life.

So all that does survive are his astronomical and mathematical discoveries. Of his astronomical discoveries there are two of note that have come down to us. The first of these is the “discovery” of what is called the obliquity of the ecliptic. Now, one of the disadvantages of conveying this information in podcast form is that you cannot see the air quotes around the word “discovery.” Because the obliquity of the ecliptic was at this time well known to the Babylonians, as well as the Indians and Chinese, and, in fact, later on the Egyptian priests, apparently anxious to maintain their priority in this discovery, claimed that Oenopides had learned of the obliquity of the ecliptic from them. But he was the first of the Greeks to notice this. The phrase “obliquity of the ecliptic” will come up again and again over the course of this podcast series so we had better get to know it, but it’s just an overly fancy way of saying that the ecliptic, the path that the Sun takes across the background stars over the course of a year, is tilted with respect to the direction that the stars rotate every night. In our modern model of the solar system this is at root due to the fact that the Earth’s axis of rotation is tilted with respect to its orbit around the Sun by an angle of about 23 and a half degrees. This tilt gives us the seasons since the Sun is higher in the sky in the northern latitudes during the summer and lower in the sky during the winter.

Now, on the one hand if you are tracking the positions of the Sun and planets with any sort of attention, this is not an especially difficult observation to make. Measuring the exact angle of the ecliptic with respect to the motion of the background stars is a little more difficult, but just noticing that there is an angle doesn’t take too much work. But that said, at this point in the podcast, nine episodes into Greek astronomy, you will probably have noticed that Greek astronomers up to now were not all that interested in anything more than a cursory observation of the heavens. They got their kicks debating with each other about the fundamental nature of matter and how the universe was created. I specifically tried to highlight occasions where they pointed to physical evidence, like Xenophanes noticing that there were seashells up on mountains, because these were the exception rather than the rule. But, unlike many of his contemporaries, Oenopides bothered to look up at the heavens and note carefully what he saw. We could plausibly make the case that he was the first observational astronomer of ancient Greece.

Now, it seems that Oenopides did not really go any further with this discovery than noticing that the ecliptic was inclined with respect to the celestial equator. There isn’t any evidence that he went so far as to actually measure what that angle was. But, later authors, who are the only ones who preserved Oenopides’s work for posterity, stated that other astronomers, unnamed of course, had later gone and measured this angle and found it to be 24 degrees. Actually, these authors did not put things in a way that is quite so clear to us moderners. What they really said was that this angle was given by the angle subtended by the side of a regular pentadecagon inscribed in a circle, and this angle happens to be 24 degrees. In fact, if you read Euclid’s Elements, Book 4 goes through methods to construct various regular polygons. Euclid demonstrates a method to construct a square, a four sided polygon; a pentagon, a five-sided polygon; and a hexagon, a six-sided polygon. Then he jumps all the way up to the pentadecagon, a 15-sided polygon and that’s the last polygon he shows you how to construct. It’s speculated here that Euclid highlights the construction of the pentadecagon in particular due to its importance for astronomy since its internal angle of 24 degrees approximated the observed obliquity of the ecliptic.

Oenopides was also noted for one other result which is his measurement of the Great Year. Now, a great Year has various meanings in astronomy and so is pretty context dependent, but the underlying idea is that the motions of the Sun, Moon, planets, and stars all repeat with different periods, and over long enough times these cycles all eventually repeat themselves. So, you could make the case that the Saros Cycle that the Babylonians discovered is a sort of Great Year. You might recall that this is a period of about 18 years after which eclipses roughly recur.

Well Oenopides’s Great Year was 59 regular years. Unfortunately the later authors who recorded Oenopides’s work didn’t actually explain why he arrived at 59 years, so modern historians of astronomy have had to do some reverse engineering to work out what this number was supposed to represent. The basic idea is that if you assume a year to be 365 days and a lunar month to be 29 1/2 days, both of which are decent approximations, then you will find that 59 years is exactly 720 lunar months. So this is the smallest amount of time it takes to get an integer number of lunar months to fit in an integer number of years. After a Great Year you’ll find that the same lunar phases happen at the same time of the year.

Now, it seems that Oenopides went a little further than this, too, and tried to use his Great Year to measure the length of the regular year more accurately. To get at his initial guess of the Great Year he started with the assumption that the year is exactly 365 days. But of course we know that it’s closer to 365 and a quarter which is why we add leap days once every four years, or almost every four years anyway. So Oenopides very likely looked at calendrical data to see how many months had actually occurred in 59 years since new months happened at the new moons. From this he found that in this 59 year period, there had been 21,557 days instead of the 21,535 days which you would have gotten if the year were exactly 365 days long. Then he just divided that number of days by 59 and concluded that the year was 365 days and 22/59 of a day, or about 365.37 days long. This is a bit of an overestimate, but is closer to the true value of about 365.24 days than 365 was exactly.

Now I’ll qualify this once more by saying that this is all reverse engineered. We know that he said that the Great Year is 59 years and that the length of the year is 365 days and 22/59ths. But the methodology is essentially reverse engineered to figure out how he could have arrived at those numbers.

Well, Oenopides’s work wasn’t limited to astronomy. He was apparently a very talented geometer as well. It’s believed that two proofs in Euclid’s Elements were first discovered by him. One of these is Proposition 12 which asks how to draw a line that is perpendicular to a given line and passes through a given point. And, probably even more influential than that was his rule that the only instruments allowed in geometry were the straightedge and compass. So you could draw a line between two points and draw a circle around a point, but you could not do anything else like break out a ruler or a protractor when trying to square a circle or trisect an angle. This rule became codified in the axioms of Euclid’s Elements, and from thereon, for millennia, geometry became synonymous with straightedge and compass constructions.

Well, those are, in sum, the highlights of Oenopides’s professional work. And we can see that his work is really quite different in its overall character from the other Greek philosophers I’ve discussed to date. Rather than being the last of the pre-Socratics, as I’ve presented him here, he really fits in more as a herald of the astronomy to come about a century later. Rather than speculating on the nature of matter and telling tales about how the universe was formed, Oenopides’s astronomy feels rather more hard-headed and a bit closer to what we call science today. He was observing things and making calculations. Now, I don’t want to get too carried away here and claim that Oenopides was the first true scientist or something like that. He retained some of the mythological character of the astronomy of his day. He posed an explanation of the Milky Way that the Sun originally moved through the Milky Way. But, then there happens an event that involves yet another figure, in this case Atreus, killing someone’s sons, and then serving them during a feast to the unsuspecting father, in this case Thyestes. After seeing this, the Sun became so appalled that it changed its path in the sky, leaving the Milky Way as a remnant of where it had once gone. So in this history of Greek astronomy we now have come across cannibal feasts on three separate occasions. I will leave it to a Freudian psychologist to attempt to comment on what it says about the Greek psyche that this kind of story shows up with this frequency in Greek history and mythology.

Anyhow, all this is to say that while the flavor of Oenopides’s astronomy is overall more rigorous than the astronomy that came before it, we should not imagine him to have been a 21st century astronomer plucked from modernity and transplanted into ancient Greece. Like those that came before him he had thoughts about the nature of the arche for example, he thought that it was fire and air, but he at the same time was more interested in measuring periodicities in the heavens and in observing what was going on in the heavens than his predecessors generally were. So he is very much a transitional figure in that regard.

Well, at long last we have done it. We have exhausted the pre-Socratics. But hopefully we are not exhausted as well. Because now it’s time to move beyond to the Socratics. But before we do, one thing I do want to make clear is that the term pre-Socratic isn’t exactly a chronological classification. Of course the vast majority of the pre-Socratics were active before the time of Socrates which is why they get their name, but as a term it really also has much do with the kind of philosophy that they were interested in rather than a strict chronology. So there are later pre-Socratics who were active after the time of Socrates, some of whom we’ve already talked about, like Philolaus the Pythagorean. But a major feature of pre-Socratic philosophy is the subjects we’ve been talking about up to now. Their interest in natural philosophy, cosmology, cosmogony and so on. Of course this wasn’t all they were interested in, many of them had things to say about ethics and epistemology and how to live the good life and we saw some of that in our exploration of them.

But, now that we have said as much as I want to say about the pre-Socratics it’s naturally time to move on to the broad grouping of the Socratic philosophers. And the first of these that we’ll look at is none other than Plato.

Now, it admittedly feels a little odd for me to make this leap from the pre-Socratic into the Socratic philosophers and in so doing just casually hop right over the man of the hour, the great Socrates himself. But there are two problems with Socrates from our perspective, if I can be so bold. The first is that we don’t know of anything he said about astronomy, so his realm of inquiry was somewhat tangential to ours. And, as by now I’m sure you’re aware, I like to keep this podcast laser focused on the history of astronomy. The second problem is somewhat related to the first. The reason we don’t know of anything that Socrates had to say about astronomy is that it’s actually very difficult to divine what he said about anything at all. Socrates wrote nothing down and his personality is only conveyed to us through the writings of contemporaries, particularly Xenophon, Aristophanes, and, above all, Plato. But Socrates was apparently such a signal figure that these authors mixed in their own philosophy into the words they put in his mouth so separating out what is Plato, what is Xenophon, and what is Socrates is very difficult. Now you may be objecting that plenty of the earlier philosophers I talked about also wrote nothing down and yet that didn’t stop me from squinting through copies of quotations of bits and bobs that students of theirs had written down centuries later in an effort to understand what, say, Thales thought about the arche or whether or not he had really predicted that eclipse. But those earlier philosophers had much to say on the subject of astronomy so the juice was worth the squeeze. But while it’s worth sussing out Socrates’s thoughts about ethics and virtue, nothing that we can say for sure about Socrates’s astronomy, or even whether he for sure had said anything on the topic has survived. So with apologies to the great philosopher, we will just have to pass over him lightly.

But we cannot do the same for his greatest student, Plato. Quite unlike his teacher, Plato wrote extensively, some 35 dialogs and 13 letters. And in a first in our journey through Greek astronomy, these writings have in large part survived. In fact with Plato we have the opposite problem than we did before — there are too many works attributed to him and some of them were probably written by other authors. And to make matters even better for a podcast about the history of astronomy, he had plenty to say on the subject of astronomy.

But before we really dig in, it would be no good unless I started with some of Plato’s biographical details. Now, maybe a bit surprisingly for a figure of such tremendous stature in the history of philosophy and from whom so many works survive, we really don’t know a lot about Plato’s life, certainly not as much as we would like. And given how much he wrote I won’t spend too much time dwelling on his biography, but he was born in the mid to late 420s BC around the beginning of the First Peloponnesian War and came of age as a young man around the end of the Second Peloponnesian War. The end of the Second Peloponnesian War traditionally marks the end of the Golden Age of Athens after Athens lost the war to Sparta and came under Spartan rule. After Athens’s defeat, Sparta installed a government consisting of a pliant committee of thirty individuals who became known as the Thirty Tyrants, and although they were in power for less than a year, they led a purge which ended up killing around 5% of the Athenian population and exiled many others. So Plato entered public life really right at the tail end of the good times in Athens. The leader of the Thirty Tyrants, Critias, was actually an Athenian himself, so he was a kind of Quisling figure, a traitor of his own people. And because Critias was an acquaintance of Socrates and apparently several others of the Thirty Tyrants were students of Socrates, Socrates did not exactly become a popular figure in Athens after the Athenians rebelled against the rule of the Thirty Tyrants. So this was the political background that Plato came of age in.

Now the name Plato was not actually his given name, but was a nickname which literally translates to “broad.” What exactly this refers to is not known for sure. According to the dodgy Diogenes Laërtius, Plato was apparently quite a good wrestler and this nickname was given to him by his wrestling coach on account of his broad shoulders. But some have speculated that it could have referred to his forehead being broad or maybe the broad scope of his learning.

Where exactly Plato was born is also something of a mystery. It could have been Athens or it could have been on the island of Aegina. Regardless, his family had ties to Athens, so at some point in his education he moved there.

Well, like every other philosopher of the day, Plato was aristocratic and had a good education. Of course, formal schools as we think of them did not exist in his day, so he had a variety of tutors, eventually becoming a devotee of Socrates. Plato then would have been in his mid thirties or so during the trial of Socrates, which affected him deeply. In this trial, in 399 BC, Socrates was accused and convicted on two charges: impiety and corruption of the youth, with the punishment of execution by drinking hemlock. From a modern perspective, these charges may strike us as rather vague, maybe like a modern charge of obstruction of justice, so just looking at the trial in isolation it’s a little hard to understand what problem the Athenians had with Socrates. It’s easy to spin this as a case of a freethinking teacher suffering the backlash of a close-minded society, but the broader political context in which the trial took place helps to provide a little more motivation as to the real reasons for the trial. This trial took place just seven years after the defeat of the Athenians, and then the bloody rule of the Thirty Tyrants. Athens was still struggling to reassert its independence from Sparta and restore its earlier democratic style of government. In just a few years Athens would go so far as to seek the support of Persia to rebel against Sparta in an effort to regain full independence in the Corinthian War. Socrates, however, was not really in favor of any of this. He wasn’t really very keen on the idea of democratic government at all. Although we don’t know exactly what his political philosophy was because he never wrote his ideas down, it’s clear that his sympathies were more for an oligarchy or even better rule by technocrats. He seemed to believe that Athens’s enemy Sparta had a better system of government than Athens did. His students had been members of the Thirty Tyrants. And here he was openly singing the praises of Spartan rule to young students and warning them of the dangers of democracy. So in this context it’s perhaps no surprise even if maybe not justified that he was put on trial and 280 jurors found him guilty. What is maybe more of a surprise is that 220 of them voted that he was innocent. Nevertheless, a simple majority was all that was needed and, despite his students’ offers to spirit him away to friendlier jurisdictions, Socrates agreed to submit to the rule of his government and drank the poisoned elixir.

Perhaps motivated by the execution of his teacher Socrates, sometime after this Plato began traveling, probably around his late thirties. He apparently traveled to Italy and found himself disgusted by the hedonism of the natives there. But his travels in Italy had the benefit that they almost certainly exposed him to Pythagoreanism, which had a major influence on his overall philosophy and his astronomy specifically. Ultimately he ended up back in Athens, perhaps once the political turmoil had settled down a little bit and there founded his philosophical school, one of the first formal, organized schools in the West. This school was located on some land just outside of Athens called the Grove of Hekademos. How it acquired this name is unclear and sources vary. Some say that it was named after the figure Hekademos who was a hero in a Greek myth involving Theseus. Or it may have just been named after a previous owner of the land and maybe that person happened to be named Hekademos. At any rate, the fame of the location as center of learning and debate led to it being memorialized down the ages. The Romans later Latinized the name Hekademos to Academus, and the term The Academy as a synonym for institutional higher learning has been with us ever since.

Towards the end of his life Plato evidently achieved his lifelong dream of entering political life and had the opportunity to try out some of his political theories in the real world. This was not in Athens, however, but in the town of Syracuse in Sicily. But this experiment did not go very well for Plato, because the tyrant of Syracuse, Dionysius the Elder, did not take to Plato’s suggestions and had the philosopher imprisoned. The details are a little sketchy, but at least according to the story as it comes to us through Diogenes Laërtius, Plato was condemned to death, but the tyrant ultimately relented and decided to sell the philosopher into slavery instead. Fortunately for Plato, a friend of his, the philosopher Anniceris purchased his freedom for the low price of 20 minas. You might recall from Episode 5 that a mina was an intermediate unit of currency between the shekel and the talent. The average laborer could expect to earn a few minas in a year, so 20 minas was a relatively large sum of money for most people, about a few years wages, maybe roughly two or three hundred thousand dollars in today’s money. But for an aristocratic philosopher this really was very reasonable. Certainly nothing compared to the fine of five talents that Anaxagoras was forced to pay!

Now, believe it or not, this was not Plato’s last interaction with the tyrants of Syracuse. Some time later Dionysius the Elder died and was succeeded by none other than Dionysius the Younger. Dionysius the Younger was evidently something of a playboy and had had no real experience with public affairs until he was thrust upon the throne. But his uncle, a man by the name of Dion, had been a fan of Plato all those years ago when Plato was on the island, at least until he lost the favor of Dionysius the Elder. So Dion had the idea of bringing Plato back to the island to tutor Dionysius the Younger in the ways of statecraft and guide him to become the ideal philosopher-king. Well, evidently Dionysius the Younger was actually quite taken by Plato’s ideas but seems to have put a somewhat Machiavellian spin of his own on them, and ultimately came to see his uncle as a dangerous rival to the throne, so he had his uncle expelled from the island. And then decided to prevent Plato from leaving the island so that he could continue to learn from the great philosopher at his own leisure. Well, somehow Plato managed to escape, but nothing else of note happened in his life after that and he died sometime in his eighties.

Well, as I mentioned a bit ago, Plato is quite different relative to the earlier philosophers because he wrote extensively — 35 dialogs and 13 letters — and as far as we know these works all survived, so we have a much more direct and complete understanding of his thought relative to the philosophers we’ve discussed thus far. Now, none of these works are dated, so no order or chronology is definitively known. But traditionally, classicists have divided his works into three periods, an early, middle, and late, based on an evolution in style. The dialogs are really where it’s at when it comes to Plato’s philosophy, Plato’s letters are more useful to glean biographical information about his life, though his seventh letter is the notable exception. But the dialogs prominently feature Socrates as the main character and by and large just present a conversation between Socrates and one or more individuals. It’s generally believed that the dialogs of the early period hew closer to Socrates’s own thought. Here Plato was attempting to act as a conduit to simply record Socrates’s philosophy. But later on Plato’s works start to reflect his own personal philosophy although he continues with the device of recording Socrates engaging in a conversation, though now he is stuffing his own ideas in Socrates’s mouth.

35 dialogs is quite a lot to parse and there are certainly a lot of beefy philosophical ideas in there. But for our purposes there are only five works that touch on astronomy: Phaedrus, Phaedo, and the Republic, all from the middle period, and then the Laws and the Timaeus which are from the late period.

Now before going too deep into what exactly his astronomical ideas were, we should first try to understand how Plato conceived of astronomy as a system of thought. What was its place among the different kinds of human knowledge? His thoughts on the subject were detailed in The Republic. These days Plato’s Republic is his best known work, and it basically sets out Plato’s conception of the ideal state. I won’t go into the political philosophy he presents, but core to his beliefs is the idea that the state ought to be governed by a philosopher-king, a single man, who, through philosophical study, had attained the wisdom necessary to govern justly. This then raised the question — how do you create a philosopher-king? It’s certainly not the natural state of affairs. So in Book 7 Plato sets out about explaining what the proper course of study is for an aspiring philosopher-king. Central to this course of study is the goal that the child’s study should elevate the soul to ponder only the highest of things. Now, for the sake of time I’m going to gloss over some of the central tenets of Plato’s philosophy, because really it takes a whole lecture series to do justice to Plato’s philosophy, but Plato was very much of the opinion that the real world was at a sort of lower plane of being than what he called the eidos or ideas, what is usually translated as the Forms. To Plato, the truly real world was the world of Forms. The Forms were ideal and unchanging and what we think of as the real world around us is but a pale image of the forms. Geometry gives the best illustration of the idea. To Plato, there exists the Form of a square, which is, in a sense, the idea of a perfect square. All four sides are exactly the same length, the lines are infinitely thin, the angles are all exactly 90 degrees, and naturally, this perfect square never changes. But we, in this world around us, never see the Form. All we can do is create poor approximations of the Form. We can draw things that look like squares, but the lines are never exactly the same length, the angles are never exactly 90 degrees, if I draw a square in the sand on a beach, the ocean can destroy it. This is a natural enough idea when it comes to geometry, but Plato believed that it extended to everything else as well. There is a Form corresponding to the chair that you sit in. There is even a Form corresponding to you and me. The first step towards wisdom is recognizing that what we perceive as the real world isn’t the realest of worlds. There exists a hyperreal world, the world of Forms. The philosopher-king therefore cannot be distracted by the mess of the real world but, to attain clarity of thought, must turn his attention exclusively to the world of forms. Now, it’s impossible to do this perfectly, but the subjects of study should bring him as close as possible to this ideal.

Consequently the subjects of his study should not touch upon things farthest from the forms, objects of sensation and perishable goods. Plato, speaking through the character Socrates then considers various subjects to ask whether or not they are suitable for the philosopher-king to study. First he considers gymnastics and music, but he immediately rejects both of these. Gymnastics, after all, deals with the body, which is inherently corruptible. The word for music in ancient Greek is actually somewhat broader than we use it today and it also encompassed poetry and drama as well, since these were customarily set to music. But music is inherently transient and so is no good for the young philosopher-king. Naturally none of the useful arts like carpentry are considered worthy of the philosopher king.

But then Plato comes to mathematics and here Plato starts to find this interesting. Now we’re starting to deal with something in the world of the Forms. Now, when Plato uses the word mathematics, he is actually referring to two distinct subjects: arithmetic, which to him is basically number theory; and logic, which is confusingly, more like what we call arithmetic today, though of course Plato discouraged the philosopher-king from performing any calculations that might be of use for anything. But geometry was not included under this umbrella. Plato considered geometry to be a separate subject from mathematics. Nevertheless, Plato believed geometry, too, to be an excellent subject of study for the philosopher-king, and then said that the next step would be the study of solids of rotation and then solid geometry. There’s actually a bit of an interesting digression in the Republic at this point where Plato then takes some time lamenting the poor state of knowledge of solid geometry in his day and calls on the state to provide more funding for the field so the knowledge can be advanced. It really sounds like an ancient Greek version of an NSF grant proposal.

Well, there’s an interesting progression here in these subjects where you can kind of think of arithmetic and logic as being the mathematics of one dimensional objects, geometry as being the mathematics of two dimensional objects, and solid geometry being the mathematics of three dimensional objects, with the geometry of solids of rotation being sort of in between. So we see a progression from one to three dimensions and the subjects become more noble and bring the philosopher-king closer to the realm of the Forms.

Plato then goes one step further to say that next highest stage of study is astronomy. Because to him, astronomy is the study of solids in motion. So we have now gone beyond simple static three dimensional objects, but three dimensional objects moving in time. Now at this point Plato falls over himself to be quite clear about what he considers to be good astronomy versus bad astronomy. You might think that astronomy is a valuable subject for the philosopher-king to study because it naturally elevates the mind towards higher things, namely the heavens. What can be higher than the heavens, they’re right above us. Plato says, sure you can think that, as long as you’re an idiot. To him, the physical location of the heavens has nothing to do with it, because that’s just how things happen to be in the real world, and that does not represent the world of Forms. He gives a little thought experiment to try to disprove this mistaken attitude. Suppose that you lived in a room with a high ceiling that was carved with intricate artwork. Would staring at this ceiling be the highest subject of study simply because it’s above your head? Certainly not! So similarly we shouldn’t assume that astronomy is the highest subject of study just because it is literally over our heads. It takes pride of place because it is the study of solids in motion, a sort of four-dimensional geometry.

Now a consequence of this is that to Plato, the astronomy that the philosopher-king should study must never be what we might call contingent astronomy. The philosopher-king should never be so vulgar as to bother himself with doing something like predicting the motions of the planets on the sky. How they appear on the sky tonight or tomorrow is just how they happen to be in this world, not how they actually are in the world of Forms. So instead the focus of study should be on what he called “problems.” By this he seems to have meant a sort of generalization of geometrical problems, how to bisect an angle, for example, to astronomical problems. But what exactly would constitute an astronomical problem in Plato’s meaning is a little unclear. The discovery of Neptune by Adams and Le Verrier through their mathematical analysis of Uranus’s orbit is probably a little too messy to count for Plato. But Newton’s discovery of his three laws of motion maybe gets a little closer at the spirit of Plato’s ideal astronomy.

Well, all this is to say that astronomy, at least the right kind of astronomy, held an exalted place for Plato in his hierarchy of knowledge, but only a very specific kind of astronomy. We can very much see the contrast between the character of Plato’s astronomy and the astronomy of Oenopides that I was telling you about earlier.

Now, as always I don’t want to get too carried away with this. Plato seems to have softened his stance later in life on the value of astronomy as it regards the actual heavens above us. We have testimony from the author Sosigenes that according to Plato, the biggest open problem in astronomy of the day was discovering the pattern of the motions of the planets and Plato challenged his students to go out and find this pattern.

Well, okay, we’ve now gotten to know a little bit about Plato’s attitude towards astronomy, but what were his actual theories of astronomy? Here, Plato’s astronomy was something of a synthesis. He didn’t propose any revolutionary new ideas, but seemed to pick and choose from the available theories of the day to compose something that made the most sense to him. By and large the overall cosmology is very similar to that of the early Pythagoreans with a geocentric model and the planets moving in circles around the Earth, but we’ll do a whirlwind tour of the five dialogs in which Plato talks about astronomy.

The first of these is Phaedrus. Much of this dialog is a discussion about the nature of the soul, and here Plato introduces his famous Chariot Allegory. You may have heard this idea before, the soul is like a charioteer driving a chariot attached to two horses in the sky. One horse as always trying to bring the chariot higher, and the other horse is trying to bring the chariot lower. Thus the soul needs to mediate between the nobler side of our nature and the side that is driven towards base desires. But the rest of the surrounding context of the Chariot Allegory is usually lost and has something to do with Plato’s astronomy. After all, the chariot allegory makes sense, but it is a little bit odd that the chariot is flying through the sky. In the surrounding context of the Phaedrus, Plato describes a sky that is evidently filled with flying chariots. Some of these chariots are driven by the gods and their motion is regular, and others are driven by human souls, and the motion of these is irregular. The chariots of the gods form an orderly procession, flying higher and higher in the sky until they reach the summit of heaven, where they can look and see what is beyond. The goal of the human soul is to follow this procession by driving one’s chariot higher and higher. But because of the horse that tends downward, this motion is always somewhat erratic. Nevertheless, capable individuals can sometimes control their chariot well enough to reach the summit of heaven and see beyond into what is evidently the realm of Forms. Apparently though even if you get to this point, perceiving what you are looking at is very difficult for a mortal. Although the gods can see the realm of the Forms in perfect clarity, a mortal, if they are lucky, may only be able to perceive one or two things. Then the procession continues downward back to Earth. Mortals who managed to see something in the realm of Forms are given the privilege of getting another go on this cosmic Ferris wheel, but otherwise are reincarnated, with their position in the subsequent life being dictated by how high they managed to drive their chariots. Naturally the highest position one can be reincarnated into is a philosopher. But Plato is very clear that this does not include the sophists. Those are souls that in their cosmic journey flew even lower than manual laborers, but at least higher than tyrants.

Well this doesn’t sound super astronomical, but Plato goes into some detail about the chariots of the gods. The greatest of them all is Zeus as Zeus is the captain of heaven. But there are eleven divisions of gods under him, making twelve divisions in all. Zeus, of course, is at the highest level and at the lowest is Hestia, who represents the fixed Earth. Then in between there are the five planets, along with the Sun and the Moon. This all makes up 9 of the chariots, so there are three that remain. What these three are is more speculative, but they may represent air, water, and aether in shells surrounding the Earth. So first is the air of the atmosphere, then there must be a layer of water where the rain comes from, and beyond that is the aether through which the planets in the superlunary realm move.

Well that’s about all the astronomy there is in Phaedrus, but from the little that is there we can at least intuit a sense of Plato’s cosmology. The next dialog, Phaedo, is similar in that it’s largely about the nature of the soul and the afterlife. The setting of the work is that it is a discussion with Socrates on the day of his death. But instead of mentioning his cosmology in this work, Plato spends a bit of time discussing his ideas about the shape of the Earth. To Plato, the shape of the Earth is not a randomly chosen thing, but has been shaped by Anaxagoras’s Mind, the Nous. Indeed all things in the universe have deeper reasons for their current configuration. Well the first part of Plato’s model of the Earth is quite sensible. He states that the Earth is spherical and sits at the center of the universe by symmetry. In this way he seems to have combined the best from Anaximander, who believed that the Earth floated in the center of the universe by symmetry, with the Pythagorean model of a spherical Earth. So far everyone is probably nodding their heads in agreement. But then Plato goes a bit farther and says that, well, the Earth isn’t exactly spherical, it’s actually dimpled, like a golf ball. Everything we know to be the Earth is actually just in one of these dimples. This implies that the Earth is much, much larger than we perceive it to be. Aristotle actually talks about this theory of Plato’s and is skeptical of it and for more than just his usual knee-jerk rejection of other people’s ideas. Aristotle points out that the Earth cannot be all that large because there are stars in the southern part of the sky that can be seen in Egypt that cannot be seen in Greece, and similarly there are stars which in Greece are always above the horizon and which in Egypt rise and set. If Egypt and Greece were in the same dimple of a vastly larger sphere the skies would look identical in those two locations — you’d have to move from one dimple to another to start to see changes in the sky.

Well, there’s one more line related to astronomy in Phaedo, and this is that Plato notes in passing that some people have blinded themselves by looking at the Sun during an eclipse and that if you want to do it safely you should look at it reflected in water or something similar. So when you hear astronomers warn you not to look at the Sun during an eclipse, this is not a new thing, astronomers have been warning you against doing anything of sort for at least 2500 years.

Okay, well the last of the works from Plato’s middle period that are of interest to us is the Republic. I’ve already talked a fair amount about the Republic with regard to Plato’s thoughts on the status of astronomy as a field. But he also presents his cosmology in a little more detail. Now, as we saw with Phaedrus, Plato’s astronomical theories are wrapped up in philosophical and mythological imagery, which can make it a little hard to understand what exactly these ideas are or even that he’s talking about astronomy at all if you’re reading the text on a superficial level. This is also the case in the Republic where his astronomy is wrapped up into the Myth of Er. The Myth of Er is a story about a man named Er who dies in battle. Twelve days later his body is about to be burned when he suddenly revives and gives an account of his experience in the afterlife.

Er had found himself in a vast meadow. There were two doors, one leading up to the sky, and one leading into the ground. People would come before a set of judges who would direct them either to one of the doors leading up into the sky or into the one leading into the ground. There was another pair of doors, one in the sky and one in the ground, out of which people would return from their journey in the afterlife. The returning souls were permitted to mingle in the meadow for seven days before traveling onward another four days and then selecting their station in the next life. Then they would drink from the River Lethe which would cause them to forget their experience in the afterlife and their souls would be transported down to Earth to begin their new life.

On this fourth day after journeying from the meadow, the souls had come to a location in which they appear to see the structure of the universe. Plato says that they see what he calls the “Spindle of Necessity”. His description of it is that it is:

A straight light extending from above through the whole heaven and earth, like a pillar, most like to the rainbow, but brighter and purer. There at the middle of the light they saw, extended from heaven, the extremities of the chains thereof, for this light it is which binds the heaven together, holding together the whole revolving firmament as the undergirths hold together triremes; and from the extremities they saw extended the Spindle of Necessity by which all the revolutions are kept up.

Now, thanks to this poetic description, what exactly the Spindle of Necessity is is a bit of a mystery. One interpretation is that it refers to the Milky Way. Of course, from here on Earth the Milky Way appears curved above us on the sky, but the thought is that the souls are seeing the heavens from beyond the sphere of the fixed stars, so they may be looking at the Milky Way from outside at an angle where it appears to be a straight pillar. The other thought is that this pillar represents the axis of rotation of the universe, but that this light is only visible in the afterworld since we clearly don’t see any pillar of light shooting up to the north star in this life.

Well, regardless, Plato then goes on to describe how around the Spindle of Necessity there are rotations of eight whorls, and describes the size and color of each of these whorls. The largest of these whorls is multi-colored and represents the fixed stars, then, getting closer to Earth we have Saturn, Jupiter, Mars, Venus, Mercury, the Sun, and finally the Moon, although he doesn’t actually specify their names. But naturally for example the whorl which is described as pale red is also the fourth to most outermost whorl just where you would expect Mars to be. The whorl second closest to us is the brightest and corresponds to the Sun. The whorl closest to us borrows its light from the second and so is the Moon, which reflects the light from the Sun.

The whorls themselves are described to have rims around the edges. Now this seems to imply that the whorls cannot be spheres. The planets are then carried around on the rim of each of their respective whorls, though of course this doesn’t seem to make too much sense for the fixed stars since they clearly form a sphere. One way around this is to imagine the whorls to be hemispheres that sit one inside the other. The outermost hemisphere is speckled with stars and then the other seven carry their respective planets at their edge. But it may not be possible to get a very literal understanding of the structure here. After all, it’s not even clear whether or not the souls described in the Myth of Er are actually looking at the whorls of the actual universe, or are simply looking at a model of the universe, in which case the shapes of the whorls in the model may have been opened up so to speak so that you could look inside and see what was going on, see the internal workings of the universe.

Well, in addition to this, Plato also describes the dynamics of these whorls. The whorls have a collective motion which is their 24 hour rotation, but then they also have their own slower individual motions as well. The Moon’s individual motion is the most rapid, the Sun, Mercury and Venus all have similar motions, then Mars and Jupiter with Saturn slowest of all. Now, this is actually quite an insightful observation to make. Because in absolute terms, Saturn appears to move the fastest and the Moon appears to move the slowest. But this is simply an illusion because most of that motion is the east to west daily rotation of the sky. If we subtract that motion off, then the planets have a slow drift from west to east with Saturn drifting most slowly and the Moon drifting the fastest.

Finally, Plato also says that sirens sit atop the rims of each of the eight whorls and sing as they spin around, producing a harmony of the spheres, a concept he almost surely borrowed from the Pythagoreans when he visited them in Italy.

Okay, so that’s the astronomy of Plato’s Republic. But in the grand scheme of history, Plato’s Republic is really quite a piddling work, hardly worth discussing. Now we turn to Plato’s most influential work: the Timaeus. And I am not being facetious here. Of course everyone today has heard of Plato’s Republic and I would venture a guess that unless you studied classics or ancient Greek philosophy, you probably would not have heard of the Timaeus. But historically the Timaeus is by far Plato’s most significant work. By a fluke of history, a Roman author by the name of Cicero, who also was known for his political activities, happened to translate the Timaeus into Latin. Cicero’s translation was not complete, but it was enough to maintain interest in the work in the later Roman Empire, and spurred a later author, Calcidius, to do a more complete translation. Consequently, in the Middle Ages the Timaeus remained largely available throughout the western world, whereas virtually all of Plato’s other works were not. In fact, up until the 1300s or so, when the rest of Plato’s work starts to get introduced into Europe, to say that you were reading Plato was to say that you were reading the Timaeus. There was nothing else of Plato’s to read at the time. This started to change in the 1100s as a consequence of the Crusades in the East, which brought Byzantine scholars into closer contact with the Latins, and also, importantly, the Reconquista in Spain, as various Spanish kings attempted with varying degrees of success to push the Muslims out of the Iberian peninsula. This also brought Latin scholars into contact with the intellectual culture of Islam, and Muslim scholars had long ago translated many Greek texts into Arabic and added their own commentaries on them with Plato included. We will go into much more depth in a later episode about this cultural exchange because it was critical for the development of medieval science in Europe. But all this is to say that for Plato at least, until about the 1300s there wasn’t anything but the Timaeus in Europe. Even after other texts came to be available, the Timaeus retained its immense stature in Plato’s oeuvre by sheer inertia. It wasn’t really until the 19th century that the Republic came to be regarded as one of Plato’s more important works and came to displace the Timaeus. By the 20th century, however, the Timaeus had become almost totally eclipsed by Plato’s other works because it is, well, rather strange to moderners. Whereas many of Plato’s other works deal with Plato’s political philosophy or ethical philosophy or epistemology, all subjects excellent for philosophical discussions, and maybe tangentially incorporate his ideas about astronomy here and there, the Timaeus really does feature Plato’s cosmology front and center as the central topic of discussion. So a 20th century philosophy class can get a lot from reading the Republic and having those eternal debates about what constitutes an ideal state, and just sort of skim over all the strange tales of 8 whorls spinning around a Spindle of Necessity. But it’s not so easy to do that with the Timaeus because the cosmology really is what it’s all about. So the Timaeus has now rather fallen from its pride of place in Plato’s oeuvre. The classicist Benjamin Jowett wrote that “Of all the writings of Plato, the Timaeus is the most obscure and repulsive to the modern reader.” So let’s dive right in.

The first thing I’ll say about the content of the Timaeus is that you have actually heard of one piece of it. The myth of Atlantis actually originates in the Timaeus. The story is actually only told in passing, which I think makes it all the more surprising that it has ended up having the cultural impact that it has. It perhaps speaks to the dearth of information from the ancient world that even minor details in surviving works were poured over by centuries of scholars in the middle ages and became indelibly ingrained in the larger culture. In Plato’s telling, there had at one time been a great nation called Atlantis which existed on an island somewhere out in the Atlantic Ocean. Atlantis had attacked Athens a long time in the past. However, the government of Athens in those days was organized according to Plato’s conception of the ideal state and so was able to fend off this great power — indeed, it was apparently the only state capable of beating back Atlantis. Atlantis’s attack against this ancient Athens then displeased the gods who caused great earthquakes and floods so that the entire island sank into the ocean. The whole description is only a paragraph, but it has had an outsized impact since generations of scholars and explorers have wondered if Plato knew something they didn’t and perhaps there really was such an island that sank into the sea. But as far as we can tell, this story is entirely a product of Plato’s prodigious imagination.

Well, most of the Timaeus is dedicated to Plato’s cosmogony. As the description of the universe gets going, we learn that the universe takes the form of a perfect sphere, as the sphere is the most perfect of all the shapes. Moreover, there are no other universes and the universe is eternal and alive, imbued with a soul similar to the Nous, or mind, of Anaxagoras. The Creator of the universe set the universe about in rotation, this being the 24 hour rotation of the stars above us. Now, this soul of the universe consists of three parts. The first here is Unity. The Creator then separated out a second component which was Difference. Then the Creator combined these two components to create a third, called Essence. This division of the essential nature of being into three parts from one might sound familiar from our episode on the Pythagoreans. After setting the universe rotating, the Creator then imbued the universe with this mixture of unity, difference, and essence, different parts of the universe receiving different proportions of this mixture.

Now the way that this was done was that the Creator made a strip and imbued this strip with the soul, but with different parts of the strip having different proportions of the three components of unity, difference, and essence. The different parts of the strip had proportions in order to produce a musical scale and infuse it with harmony. Then the Creator split the strip in two and formed an X with the now two strips. He then bent the strips around two form two circles at an angle to each other. The way that the strip was originally split in two, the outer circle ended up being composed of Unity, and the inner circle composed of Difference. The Creator then split the inner circle into seven individual circles, and now we see where things are going. The outer circle represents the fixed stars, and because their shapes are unchanging, they are composed of Unity. The seven circles from the other strip form the five planets along with the Sun and Moon. Since their positions change over time, they must contain some of the element of Difference, but in different proportions since they move at different speeds. These seven circles then get their own unique rotations in an opposite direction on top of the overall 24 hour rotation that the Creator instigated at the beginning of the universe.

Now one detail in all this that is a little bit unclear is that when Plato describes the 24 hour rotation of the stars, he describes it as being “to the right.” But in ancient Greek culture, this would have referred to motion to the east. Diviners would predict the future by looking toward the north and studying the paths of birds on the skies, so motion to the east would be described as motion to the right, and in another text, the Laws, Plato also uses the phrase “to the right” and is clearly referring to motion from the west to the east. But of course the stars rotate from the east to the west. So what is going on here? Did Plato just mix up his left and right? One theory is that in this text Plato is describing the universe from the outside looking in, in which case the left and right could be reversed. But it’s a little hard to say what’s going on here for sure.

Well, Plato also tells us the dimensions of these seven circles, and these are 1, 2, 3, 4, 8, 9, and 27. Now, once again, it’s somewhat unclear what exactly these dimensions refer to. Is it the diameter of the circles? Or is it the distance of one circle to the next. But it is clear from this sequence that these are not physical measurements, but have been arrived at through Pythagorean numerology. These are numbers associated with the Pythagorean Tetraktys, the sacred symbol of ten points arranged in a triangle. You’ll recall from the episode on the Pythagoreans that the Pythagoreans considered 10 to be the most perfect of numbers because it was the combination of the first four numbers and so contained all things. The physical representation of the number 10 was this Tetraktys a triangular arrangement with four dots at the base, three above it, then two, and then one at the top. Then down the left leg of this triangle they put the sequence of squares, 1, 2, 4, 8, and so on and on the right hand side the sequence of cubes, 1, 3, 9, 27. Plato then associated these sequences with the relative sizes of the planetary circles. So, this is all in keeping with Plato’s belief that astronomy was best done without reference to observations, but as a pure product of philosophy.

Plato then relates the motions of the planets to the metaphysics of time. In Plato’s philosophy the forms are eternal, but the created world is not. The created world is instead an image of the forms. But the heavens come closest to a true image of the forms, after all they are geometry in motion. So they move in a periodic pattern, which comes as close to the eternity of the forms as we can see in this world. In a sense, to Plato the motions of the planets actually create time. The periodic motion of the stars produces the day, the periodic motion of the Moon produces the month, and the periodic motion of the Sun creates the year. Plato then asserts that the periodic motions of the other planets produce more subtle units of time, which are only known to a wise few. Then there is a perfect unit of time, which is when all eight revolutions, from the fixed stars up through Saturn are commensurate and end up in the same place that they started. This period is known as Plato’s Great Year and although Plato never explicitly gave its length, later authors estimated it to be about 36,000 years.

Plato then describes how the planets closer to the Earth move more quickly than the ones farther away. But when he gets to the motions of Mercury and Venus he gives a rather vague and confusing statement that seems to relate to their retrograde motion, the fact that sometimes these planets, along with all the rest, to be clear, halt in their usual west-to-east progression relative to the background stars, and then turn around and go the other way for a while. Plato says:

The Morning Star, and that which is held sacred to Hermes he placed in those orbits which move in a circle having equal speed with the Sun, but a contrary tendency to it; hence it is that the Sun and the star of Hermes, and the Morning Star overtake, and are in like manner overtaken by, one another.

Now, scholars have spilled vast oceans of ink trying to decipher exactly what Plato meant by “contrary tendency”. The most natural interpretation of this is that Plato is saying that Mercury and Venus both move in the opposite direction from the Sun. But this is very plainly not supported by the actual motions of Venus and Mercury since neither of them get very far from the Sun. Some ancient authors suggested that Plato may have been referring to epicycles here and that the motion of these planets on their epicycles was in the opposite direction of the motion of the Sun. But the problem here is that this seems to be somewhat anachronistic. There are no mentions of epicycles anywhere in Plato’s works. We could also imagine a model in which Mercury and Venus have variable motion along their orbits and are attached by a sort of spring to the Sun. So as one gets too far away from the Sun, the spring brings the planet back towards the Sun and overshoots in the other direction. This is closer to what we see observationally, but there is no indication in Plato’s writings that the planets move in anything but a constant speed along their circles. Indeed just one sentence before, Plato says that “they move in a circle having the same speed as the Sun.” No one has really provided a satisfactory explanation of what Plato meant by this. Sir Thomas Heath writes, “it is not surprising that commentators have exhausted their ingenuity to find an interpretation less compromising to Plato’s reputation as an astronomer.”

Well, the last thing I’ll say about the Timaeus is that a little later in the text Plato also says a little bit about the stars, namely that they are made of fire and that the Creator distributed souls to the various stars and set about their rotation. Given that the Timaeus has had such a huge influence on scientific thought in the West, every word has been poured over by centuries of scholars and there have been long debates about what exactly Plato meant here and there. Some scholars have argued that one part of the Timaeus seems to indicate that Plato believed that the Earth rotated, although the evidence for this claim is pretty thin and this is not a consensus view. But in the interests of time, we’ll have to move on to the last work of Plato’s that touches upon astronomy, the Laws.

This work was one of Plato’s last and was actually left unfinished by him. His student Philippus completed it, so some of the ideas may have been Philippus’s. The work is also a little unusual for Plato in that it’s one of very few which do not feature Socrates, at least explicitly. Instead there are two older men, Megillos and Cleinias going on a religious pilgrimage joined by a third, unnamed individual who is simply called a stranger from Athens. Nevertheless, the speech of this stranger from Athens is rather Socratic so even if Plato has not told us who this fellow is, we can all maybe guess who he had in mind.

As the title suggests, most of the work is about the nature of laws. But Plato touches on a variety of other subjects and in Book 7 has mind to expound on the kind of education that is appropriate to children. Plato, speaking through the Athenian stranger, is naturally in favor of arithmetic and geometry as subjects of study and then goes on to say that astronomy is quite appropriate as well. Here he makes an interesting point about how the study of astronomy can bring the student closer to the gods. He says that the word “planet” is blasphemous. The Athenian stranger explains that, well, the word “planet” literally means wanderer. But this seems to say that the gods wander about to and fro in the sky with no aim or purpose and this is a blasphemous assertion. A child must study astronomy to understand that the movements of the planets are not aimless wanderings, but follow a regular path — this is one way to become closer to the gods. Furthermore, the study of astronomy is salutary to the student because it teaches that things are not always what they appear to be. In the case of the motions of planets, the planet that appears to move fastest, Saturn, is in fact the slowest, and the Moon, which appears to move the slowest, actually moves the fastest. Because in Plato’s system, all planets have the diurnal east to west motion of the stars, and then on top of that have their own unique motions west to east. So if we just look at the overall motions, Saturn appears to move the fastest, but if we subtract off its daily rotation, it now moves the slowest.

The Athenian stranger makes the point that if we were watching runners or horses on a racetrack, we would want to know which one is the fastest and which one is the slowest. If we had gotten it backwards, we would be completely embarrassed. But if that’s true for athletes, how much more true it is of the gods in the heavens. So Plato, speaking through the Athenian stranger, is very much in favor of astronomy in a child’s course of study.

Well, with that we more or less wrap up the astronomy that is mentioned in these five works of Plato. Plato’s astronomy was not influential because he made a radical departure from the astronomy of earlier philosophers, but because he collected their best ideas and synthesized them into a simple, fairly robust model. In fact, some of you may be thinking at this point, what astronomy of Plato? All he did was say that the planets go around the Earth and sprinkled on top a little mystic mumbo-jumbo about Unity and Difference and Essence. But there had been debate about things like the shape of the Earth and the order of the planets and Plato’s model became the standard model of the age, except for his ginormous Earth. He also included Oenopides’s observation of the obliquity of the ecliptic when the Creator took the two strips of souls and formed an X in the Timaeus. And really crucial to later models of the Solar System was recognizing that all the planets had a daily east to west motion and that the really interesting motion was what happened when you subtracted this daily rotation off.

Now his attitude that observation wasn’t worth bothering with was certainly not a productive direction for the astronomy of his day. But he did spur the field forward by identifying what he thought was the most important astronomical question of the time: the motions of the planets. After all, in Plato’s philosophy the heavens were the most perfect icons of the forms. They were images of time itself. They represented the deliberate movement of the gods. Although they appeared to wander, Plato’s philosophical and religious intuitions told him that they could not wander randomly.

But Plato was not able to achieve this vision of deciphering the planetary movements himself. So he posed this problem to his students as a challenge. And, one of his most brilliant students took him up on it. I am talking, of course, about Eudoxus. Next month we’ll learn about the first serious attempt by a Greek astronomer to describe the motions of the planets. I hope you’ll join me then. Until the next full moon, good night, and clear skies.