Episode 13: Ex Uno, Plura

January 19, 2022

As we transition from the Archaic Period of Greece to the Classical Period, two philosophers, Empedocles and Anaxagoras, rebel against the prevailing dogma of monism and present a new idea — that matter consists of mixtures of multiple fundamental elements.

Thanks to William Little of Ohio State for help with the Latin to get the opposite of E Pluribus Unum for the title.

If you would like to register for the Stellar Spectacles symposium that I mentioned at the beginning of the episode, go to www.asxsociety.com.


Transcript

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.

Before we begin, a listener from the University of Toronto, Adam Lam, asked me to plug an astronomy symposium he is helping to organize. From what I’ve seen of it, it looks quite interesting, so if you happen to be in the Toronto area from February 10–12, I encourage you to check it out. The title is Stellar Spectacles and there will be a number of astronomers speaking about advances in detector technology, including LIGO and JWST. You can learn more and register at asxsociety.com.

Well, I’m afraid I have to start this episode by telling you that I have done a bit of a bait and switch. I ended the last episode with a tantalizing segue into the atomic theory of Democritus. But before we get there, we’ll need to develop another critical intellectual development that preceded atomic theory. This was the pluralism of Empedocles and Anaxagoras.

To recap where we’ve been, in the last four episodes, we’ve been wending our way through a number of the pre-Socratic philosophers, at least those who had a particular interest in natural philosophy. We started with Thales of Miletus, who is the first Greek natural philosopher we know of and who was active in the early 500s BC. We then looked at the later members of the philosophical tradition that Thales founded, which is usually called the Milesian or Ionian school. These were Anaximander, Anaximenes, and Heraclitus. Then we followed Pythagoras from Ionia to Magna Graecia, where he founded his own unique secretive, one might say cult-like, philosophical tradition. And in the last episode, we looked at anther tradition that was heavily influenced by both the Ionian school and the Pythagoreans — the Eleatic School of Parmenides and Zeno.

Now, in all the philosophies of the various thinkers I talked about, there is a common thread through them all. One of the questions that particularly interested these philosophers was the ultimate origin of all things. Karl Popper argued that the question of cosmogony, how the universe came to be, is really the origin of all philosophy. And given the attention that the earliest of the philosophers gave to it, Popper may have been on to something here.

Well, starting from Thales all the way to the last philosopher I mentioned in the previous episode, Zeno, these philosophers all approached this question in the same way. They all held to some form of monism — some more loosely than others. But for all of them a foundational component of their philosophy was that the ultimate nature of the world was a single substance. What exactly this substance was varied among the philosophers, but the idea that there was one thing that undergirded all matter was common to all of them.

To briefly retrace how these ideas developed, we started with Thales, who held that all things had their origin in water. Now, this has a certain plausibility to it. Although Thales himself didn’t point to it, there was some evidence from fossils of fish in mountains that water had once covered the Earth. But his student Anaximander, in a prelude of things to come, found it too hard to understand how one kind of matter could produce the variety of matter we see around us. So he instead proposed that this fundamental substance was not any kind of ordinary matter, but was a new kind of substance which he called the “apeiron”, or the Infinite. Now, this in a way sidestepped the crucial question of how different kinds of matter could come from a single kind of matter — the fundamental substance was infinite, after all, so why not. But at the same time it does seem to be a bit too convenient. No one had ever seen the apeiron, no one had felt it — how could we know that it really existed? Anaximander’s student, Anaximenes rejected the idea of this mysterious substance and claimed that it was the air instead. Now, to some of us, this may seem like something of a regression, but Anaximenes’s idea had a certain logic to it. After all, unlike the other basic kinds of matter, air was compressible. Anaximenes reasoned that perhaps under sufficient compression, the air could condense out other forms of matter like water and Earth. And finally, Heraclitus had proposed that the source of all matter was fire. Heraclitus’s system also had a certain logic to it, because Heraclitus emphasized the constantly changing nature of the universe. All things, from a leaf burning in a fire to even the seemingly most permanent rock are always changing, perhaps quickly perhaps slowly, but always changing nonetheless. Moreover, these changes manifested themselves by continual exchanges from what he called the upward path and the downward path. And fire was the purest manifestation of this transfer between the upward path like the smoke rising up and the downward path with the ash falling to the ground.

Now these philosophers, who formed the core of the Ionian School, brought the idea of monism to prominence — the idea that matter is, fundamentally, all the same. But even among the Ionians, monism was already showing itself to be a philosophy with some rickety foundations. Anaximander could only reconcile himself to the position with this mysterious unobserved apeiron. And Heraclitus’s stress on the upward and downward path seemed to point more towards dualism with the fire acting as more of a mediator between two fundamentally different kinds of matter.

The Pythagoreans then took monism in a more mystical direction by claiming that the fundamental source of all things was not any physical matter, but was, instead number. Now, the Pythagoreans probably had a more concrete conception of what number was than the more abstract idea that we do today, so this for them was not just the source of matter in some vague sense like “the laws of physics obey mathematical laws”, but that there was a thing, and groupings of those things in different numbers, produced different kinds of matter.

But finally, the Eleatics took the ideas of monism to their logical extreme. Parmenides couldn’t explain how a single substance could produce the observed variety of the world so he was forced to argue that the world as we see it just didn’t exist — it’s all an illusion. The universe is a solid, uniform block, completely static and ever-unchanging. This was the conclusion of centuries of development of monist ideas

Now, to give monism its due, monism was only popular for as long as it was because it does have certain things to recommend it as an approach to natural philosophy. Monist systems can be very attractive because the mind is naturally looking for patterns across the things of the universe, commonalities across what we see so that we can explain the whole of nature. In monist systems, we can explain the whole variety of nature with a single, unified concept.

But as always seems to be the case in philosophy, one philosopher’s feature is another philosopher’s bug. The idea that you can explain everything with a single substance that makes monism so attractive also presents some tough philosophical problems. In particular, the question naturally arises: Well, okay, sure, suppose everything really is a single substance, say water or air or number or apeiron. The fact of the matter is is that I actually do in practice see different things. Thales claims that all things have their origin in water, but I see things that are not water. So what is going on there? We can argue that perhaps some things do not appear to be water because its true watery nature is somehow “hidden” from us. But at the same time we do see things in the world that do appear to us to be water. So why does some water look like water to us and other water does not look like water to us? If the things that don’t look like water are a sort of “hidden” water, what exactly is hiding the water? Can it really just be more water?

This problem can be put more pithily with the following argument. The monists claim that all things are really one substance. But we observe that there are, in fact, many substances. Now, if two things are different from each other, they must be different in quantity or quality. Now, if two things in this world are different only in terms of quantity, then monism cannot explain the variety of substances we see in the world. Because if we just add more water to water, we don’t get earth or air or fire. We just get more water. Likewise adding fire to fire just produces more fire, not water. But if the things are different in terms of quality, then by definition monism is necessarily incorrect.

At root, the main problem with monism is this: if everything is one thing, how do you get anything else out of that? Parmenides and the Eleatics took this argument to its logical conclusion and stated that, in fact, everything is one, and that the variety we observe is nothing more than an illusion.

Well, by the middle of the 5th century BC, an alternative system began to appear, and this was due to two philosophers who were roughly contemporaneous: Empedocles and Anaxagoras. Now, Empedocles is really the first of the philosophers we’ve looked at who really doesn’t seem to have any predecessors in his vicinity. All the others were either from Ionia, taught by philosophers who themselves had traveled from Ionia, or had been taught by someone who had been taught by someone who had traveled from Ionia. But Empedocles came from way out in the boonies of Magna Graecia in Sicily and didn’t really have any connections to the mainstream of Greek intellectual life until he traveled, probably to Italy where he likely met some Pythagoreans and then later in his life to Athens. Like pretty much all the philosophers of the time he was both wealthy and noble.

Empedocles has the distinction of being the last natural philosopher to write in verse. After this, philosophers wrote their treatises exclusively in prose. Unfortunately the work itself doesn’t survive in its entirety, but we do have fragments which total several hundred lines, which by comparison to many other philosophers of the time, is pretty good.

Well, perhaps his most enduring innovation was his claim that all matter consisted of four elements: these were earth, water, air, and fire. The variety of matter we see in the universe is, ultimately, these four fundamental elements mixed together in different proportions. This idea, what came to be known as the four classical elements, was later enthusiastically taken up by Aristotle and from there became the foundation of natural philosophy in the West for some two thousand years, not just in physics and astronomy, but in alchemy and medicine as well. In later episodes we will see how this idea of the four classical elements formed the cornerstone of a sort of grand unified theory of medieval science.

But for our story for now, the main innovation of Empedocles’s system of four elements was that it was the first decisive break in natural philosophy from the clutches of monism. What exactly led Empedocles to a pluralistic system is not entirely, clear. Perhaps it’s a consequence of him being a relative outsider to the other natural philosophers of his day, but one thought experiment does survive. Empedocles had noted that if you take a cup and you submerge it upside down in a pail of water, the water does not fill the cup. There will be a little pocket of air that gets trapped in the cup. You can stick a dry leaf to bottom of the cup and it will never get wet. Now, it was well understood at the time that air was compressible. But Empedocles reasoned that if Thales was correct that all things were water, if you compressed air, it should turn back into water. So the air in the cup should turn into water and wet the leaf. But this does not happen. So Empedocles concluded that air was fundamentally of a different nature than water.

Now Empedocles’s system also had a number of features that did not survive for two thousand years. In his system, there were two other forces in the world, which he called Love and Strife. The force of Love is what drew matter together and the force of Strife is what broke it apart. So by combining the four elements with these two forces, Empedocles hoped to explain not just the nature of matter in a static universe, but in a dynamic universe as well — how things in the universe seem to change. To Empedocles, the complex behavior of life required a balance between love and strife. If matter is dominated by strife, the result is chaos, and life cannot persist. But equally well if matter is dominated by love, the result is perfect harmony, absolute order. This can produce the orderly behavior of the heavens or a crystal, but also cannot sustain life. Life must inhabit a regime balanced between the two, on the edge between love and strife, order and chaos. This idea of eternal competition between the forces of love and strife did not take on quite as well as the four classical elements. But the general framework has some parallels with chaos theory, which developed in the second half of the twentieth century AD. Around this time, electrical computers were developing to the point where it was becoming feasible for mathematicians and physicists to study non-linear dynamical systems. These kinds of systems are generally very difficult to study analytically, with pen and paper, so in many cases the only way to make much progress is numerically, do just do brute force calculations over and over and over again to obtain approximate solutions. But some of the early researchers in the field like Benoît Mandelbrot and Mitchell Feigenbaum were surprised to find that systems with apparently simple non-linear equations produced exceedingly intricate dynamics. For example, a pendulum is a system with extremely predictable dynamics. The pendulum simply swings back and forth at an exactly predictable interval. But if you take a pendulum and add a hinge in the middle, this produces what is called a double pendulum. If you start this pendulum swinging by just a small amount, once again the pendulum has very simple, predictable dynamics. But if you start it out by raising it through a critical angle of about 70 degrees, suddenly the dynamics become chaotic. The pendulum starts swinging every which way and it becomes in practice impossible to predict its behavior over long time periods.

Now, this feature, of a critical point between simple, very predictable behavior, and chaotic, almost unpredictable behavior, is actually quite general to many non-linear systems of interest to us. On one side of this point, the system behaves very predictably. If you take two identical double pendulums, and set them going at a small angle, but one is just a fraction of a degree different than the other, they will continue to oscillate in a similar way forever into the future. They will oscillate perhaps at slightly different frequencies, so they will gradually desynchronize from each other, but even the rate of desynchronization is perfectly predictable. By contrast if you take two identical double pendulums and set them going above this critical angle of about 70 degrees, but with one of double pendulums at a fraction of an angle different than the other, they will have roughly the same trajectory for maybe a few swings, but after that, all of a sudden, they will start to do wildly different things. One of them might spin around or flip over the top while the other is swinging through the bottom and vice versa. In practice what this means is that it’s impossible to exactly simulate the dynamics of this system because our computers can only handle finite numbers and time steps. At each time step, this means that there will be small errors in the simulation. But in the chaotic regime, these small errors compound exponentially and very quickly produce qualitative changes in the dynamics of the system. It’s for this same reason that the weather cannot be predicted with any accuracy after about 10 days or so. The weather is a chaotic system and these unavoidable microscopic uncertainties build up to produce large changes at the macroscopic scale.

But, even though we cannot say what the weather will be like on August 31st 2052, nevertheless large scale patterns can still exist in this background of chaos. We know that summer will be on average hotter than winter. We can say what months hurricanes are more likely to impact the Caribbean. And, in particular, physicists and mathematicians studying non-linear dynamical systems, observed that the most interesting behavior seems to occur around the critical point between simple non-chaotic dynamics and chaotic dynamics. Around these critical points, the behavior of the system is not especially simple, but is not entirely chaotic either. These kinds of systems very frequently develop some sort of self-similarity across different scales, which is a hallmark of a fractal pattern. These kind of fractal patterns appear in a huge variety of systems that are of interest to us. Spectrographs of music can have some fractal behavior. EEG recordings of the brain also exhibit this kind of balance between chaos and order. Patients with dementia or delirium have highly disordered EEGs. But a highly ordered EEG is indicative of a seizure. A healthy brain has behavior that is not completely random, but not too highly ordered either.

Well, this has been something of a digression, but the idea of Empedocles that life exists as a balance between order and chaos is one which, while it didn’t survive in his formulation as a competition between Love and Strife, is a general framework that has received more attention in the last several decades.

Now, Empedocles also had thoughts on astronomy as well. In particular he believed that the heavens were a crystal sphere made of air that had been condensed by fire. This air contains some fire and the fire gets squeezed out at particular points, which we see as these stars. These stars are therefore fixed to the sphere. There are others, however, which are not fixed and these are the planets.

Probably Empedocles’s strangest astronomical theory though had to do with the nature of the Sun. To Empedocles, the Sun that we observe is really just an illusion. Instead the celestial sphere is not actually uniform. Firstly, it is not spherical really — the top is closer to us than the bottom is. This makes sense intuitively — clouds directly overhead appear closer to us than clouds on the horizon. But the celestial sphere itself — well, sphere again is not really the right word to use, maybe the celestial ellipsoid — has two halves. One hemisphere is the night sky, and the other hemisphere is the daytime sky. The night sky is as I have already described it. It is mostly compressed air with some pockets of fire that form the stars. But the daytime sky is composed of a much higher proportion of fire. Thus the entire daytime sky is, in fact, the Sun. The bright spot we see on the sky is only the apparent Sun and this is a reflection from the true Sun, which consists of the entire hemisphere. Now, how exactly reflections produce this bright spot on the sky is a little hard to say in detail because the fragments here are a bit confusing. But one plausible reading is that the light from the daytime sky reflects off of the Earth and gets focused back on one part of the sky to form the apparent Sun.

Empedocles’s picture of the heavens as being half dominated by air, and hence dark, and half dominated by fire, and hence bright, was also a dynamic one, not static. The forces of love and strife worked equally well in the heavens as on the Earth. Over the course of spring as summer approached, the fires of the bright hemisphere expanded and came to dominate a larger and larger portion of the sphere, so that the firey portion wasn’t just one hemisphere, but somewhat more than a hemisphere and produced longer days and shorter nights. But as the fire continued to encroach on the territory of the airy hemisphere, the air was compressed until it could resist the fire and ultimately reverse its progression. Then as winter approached the night hemisphere began to overtake the day hemisphere and the nights got longer and then the days shorter as it gradually quenched the fire. But eventually the air became too rarefied and no longer held the same power that it used to and the fire could retake the air once again.

Apart from his strange theory of the nature of the Sun, Empedocles did not have too much else to say about astronomy. He argued that the Moon consisted of frozen air and was sort of like a giant hailstone and was surrounded by some fire. But he claimed that the Moon got its light from the Sun and that eclipses were due to the shadows of the Earth. Although he was correct on these points, he was not the first to make these claims.

The final thing I’ll say about the astronomy of Empedocles was another idea he had that ultimately was vindicated centuries later. And this was the finite speed of light. As far as we know, Empedocles was the first natural philosopher to argue that the speed of light was finite. Our knowledge of this theory comes to us from Aristotle, who presented the following argument:

When something moves, it goes from one place to another. So the light from the Sun must pass through intermediate space. But every period of time is divisible. So there must have been “a time when the ray was not yet seen, but was being transmitted through the medium.”

Now, I will confess that I do not find this to be a very compelling argument. It essentially to me seems to presuppose the conclusion. The light takes some finite amount of time to travel from one place to another because there must be a time during which it is moving. It seems to me to be a bit circular. Now, to be fair to Empedocles, it’s not clear at all whether this was Empedocles’s own argument. This may have been Aristotle’s argument and Aristotle was not always known for putting the strongest arguments in his opponents’ mouths. So it is perhaps no surprise that Aristotle rejects this argument and says that light is in fact instantaneous. Aristotle regards light no so much as a discrete thing that moves from place to place, but rather a quality of the medium itself. When the appearance of something changes, this is due to a change in the medium that happens everywhere all at once. Aristotle makes the comparison to how water freezes all at once, not in a linear direction.

Well, Empedocles was not the only philosopher of his day to rebel against the prevailing dogma of monism. Anaxagoras was born at around the same time as Empedocles, just after the start of the fifth century BC. Now, at this point I will briefly say that you may be forgiven for getting your Anaximander mixed up with your Anaximenes mixed up with your Anaxagoras. This prefix Anax- keeps coming up because it means “lord”. In the case of Anaxagoras, we have Anax- for lord, and -agora, which means assembly-place or marketplace, and is the same root from which we get agoraphobia, or a fear relating to unfamiliar environments and frequently associated with panic in large, crowded spaces. So, at any rate, in the case of Anaxagoras the name literally translates to “the lord of the assembly-place.”

Well, unlike Empedocles, Anaxagoras happened to be born in a more promising intellectual environment. Whereas Empedocles was born out in the hinterlands of Sicily, Anaxagoras was born in the city of Clazomenae, which was part of Ionia, close to Miletus, which had, by this point, a tremendous intellectual heritage. Now, Ionia during the early fifth century was a tumultuous time, politically. We talked a bit in the last episode about how the Persian invasion of 545 BC led to an exodus of Greeks to various colonies, including, probably, the philosopher Xenophanes, who ended up in Elea in Italy, and probably influenced the founding of the Eleatic School. But not everyone in Ionia fled. In fact, the popular picture of the united Greeks fighting tooth and nail against the advances of the Persians, most vividly exemplified by the Battle of Thermopylae, where in 480 BC a group of 300 Spartans fought to their death in a narrow pass against some 100,000 Persians, was more the result of later propaganda by Greek historians. Which is not to say that no Greek states did fight tooth and nail against the invading Persians, King Leonidas and his 300 Spartans certainly did. But not all did. In fact, the vast majority didn’t. Remember that Greek city-states were independent political entities. Sometimes they entered into alliances with others to form things like the Ionian League, and these alliances could be looser or stronger, and were pretty much essential if the Greeks were to repel the vast armies of the Persians. But other city-states found it more advantageous to voluntarily submit to Persian rule, paying a tribute to Xerxes or whoever the ruler of the Persians happened to be, and get on with their lives rather than fight the enormous armies of the Persians and invite complete annihilation. During the Greco-Persian wars, it’s estimated that around 90% of Greek city-states either attempted to remain neutral or took the side of the Persians. And this was not just at the city-state level, but at the individual level as well. Many individual Greek men, particularly poorer men, found that they had better prospects becoming mercenaries for the relatively wealthy Persians.

All this is to say that in the early 400s BC, Ionia, right on the border between the Greek world and the advancing Persians, was a politically tumultuous place to be. A Greek man’s political allegiances were by no means guaranteed. It’s right around this time, as Greece is struggling against the advances of Persian Empire, that we transition from the Archaic Period of Ancient Greece, to the so-called Classical Period. Around this time we start to see the intellectual center of gravity shift from Ionia in western Anatolia, to Athens, and Anaxagoras played an important role in this shift.

So Anaxagoras was born right at the time of the Ionian Revolt, when the city-states of Ionia, centered around Miletus, which had been under Persian rule for the past half century, started to rebel against their Persian overlords. The Persians put these revolts down in a year or two, but the Persian king at the time, Darius, realized that the western border of his empire was going to be a perpetual problem. He had conquered Ionia and put down revolts there, sure, but it was adjacent to the rest of Greece which was free, and it would be impossible to sever the close cultural ties Ionia had with the rest of Greece.

Darius thought that Ionia was always likely to pose a threat to him since the rest of Greece would invariably channel resources to Ionia to periodically revolt and otherwise harass the Persian occupiers. Darius concluded that the only way to eliminate this strategic weakness was to conquer the rest of Greece. So, seven years after the Ionian revolt, in 492 BC, King Darius invaded Thrace and Macedon, setting off the first part of the Greco-Persian Wars.

To briefly recapitulate the Greek history here during Anaxagoras’s childhood, Persia was able to take Thrace and much of Macedonia, but an alliance of Greek city-states led by Athens was able to prevent King Darius from taking Athens itself. The decisive battle here was the famous Battle of Marathon, where, according to legend, a Greek messenger named Philippides noticed that after the Greeks had defeated the Persians, the Persian ships started sailing for Athens anyway in an attempt to trick the Athenians into believing that the Persians had won so that they could capture the city by deceit. So Philippides ran the 26.2 miles from Marathon to Athens without stopping and announced that the Greeks had won before his heart gave out and he collapsed and died. Well, the legend of poor Philippides is almost certainly just a legend, but after the Battle of Marathon, the Persian army was spent, so an uneasy peace reigned for a time as King Darius attempted to raise a fresh army. But shortly afterwards Egypt also revolted so Darius was forced to turn his attention there and secure the southwestern border of his empire. As he was preparing to march to Egypt he died and his son Xerxes I took the Persian throne.

Xerxes was able to put down the revolt in Egypt fairly easily and then pick up where his father had left off in Greece. He raised one of the largest armies that the world had seen up to that point and invaded Greece in 480 BC, around the time that Anaxagoras was coming of age. Xerxes had a strong start. Despite the famous Spartan resistance during the Battle of Thermopylae, the Spartan’s courage didn’t really have much of an impact on the war and Xerxes was able to march to Athens and burn it. But, to skip over a lot of details, the following year, the momentum shifted to the Greeks, who not only defeated the Persians, but were able to push them back out of Ionia. It’s around this time that Anaxagoras migrates from Clazomenae to Athens, but what exactly his role was around this time is unclear. At least according to some accounts Anaxagoras fought on the side of the Persians in which case he probably defected to Athens after the Persians began losing the war. Or this may have been propaganda spread by his political enemies later in life.

What we do know is that Anaxagoras came from a wealthy family, unsurprising for a philosopher. But he was suspicious of material possessions. According to one account he gave away all his belongings so that he could focus exclusively on philosophy. In another story during a Persian attack he had fled his home, and upon returning found that all his possessions had burned to the ground. He said that this was in fact a good thing, for if “these had not perished, my soul would have.”

Now I should also mention that there is an alternative, somewhat unorthodox timeline for Anaxagoras. Rather than being born around 500 BC and moving to Athens during the second Persian invasion, this timeline has him born some 30 years earlier, around 533 BC and then moving to Athens after a revolt in Miletus was put down in 494 BC, around the time of the Ionian revolt. So even in this period as we transition from Archaic to Classical Greece, there are still important figures whose birth has an uncertainty of some 30 years.

Regardless, the historical record becomes somewhat more definite when Anaxagoras moved to Athens. Here he became friends with the statesman Pericles, who was roughly the same age as him if the orthodox timeline is to be believed. It is really thanks to Pericles that the city of Athens has become so closely associated with Ancient Greece. After the defeat of the Persians in 479 BC, Pericles’s project was to transform Athens into the pre-eminent power of Greece, economically, militarily, and culturally. Many of the most well known Greek figures were active in Athens at the same time as Pericles: Socrates, Plato, Aristotle, Sophocles, Euripides, Aeschylus.

Pericles was a strong proponent of democracy in Athens and as a result was frequently in conflict with the aristocracy of the city. And while he was generally successful, the careers of any of the great political figures of history all have ups and downs, and Pericles was no different. And as Anaxagoras was a close friend of Pericles, Anaxagoras ended up as collateral damage in Pericles’s political dramas. During the year 450 BC, Anaxagoras was put on trial by Cleon, one of Pericles’s political opponents, both a general and a general defender of the interests of the aristocracy. It seems that Anaxagoras was convicted on two charges. The first was impiety, because he taught that the Sun was a red-hot stone, and in so doing, denied the divinity of the Sun-god Apollo. The second was having Persian leanings. Now, on the first charge it’s a little unclear the extent to which these charges were manufactured to damage a political rival, or whether or not there was genuine religious outrage about Anaxagoras’s heretical teachings. And similarly on the second, it is unclear whether there was any truth to the idea that he had in the past been on the side of the Persians. At the very least it is not implausible.

At any rate, Anaxagoras was convicted, and at least in some accounts was sentenced to death. However, Pericles did manage to get his friend’s sentence commuted to the lighter sentence of exile and a fine of five talents. Now, if you recall from Episode 4, a talent was a considerable sum of money, roughly the wages of a laborer for 10 to 20 years. So in modern terms, this fine would have been on the order of a few million dollars, so not a trivial amount of money. But, better than execution. After his conviction, Anaxagoras was exiled from Athens and settled in the city of Lampascus which was just north of Ionia, basically on the border with the region of Thrace. Incidentally, this area was known for harboring pro-Persian sentiments, so this may have been one of the reasons that Anaxagoras ended up here. Here in Lampascus Anaxagoras lived out the last 20 or so years of his life in relative quiet, teaching students, but far from the political fray in Athens.

Well, as with so many other pre-Socratics of the time, Anaxagoras did write a treatise, but it was lost, though we do have some fragments. So we are not as completely in the dark as we are with the earlier philosophers, but we still do have to rely on more guesswork and reading between the lines than we would like to get at his philosophy.

Now, along with Empedocles, Anaxagoras was the other major figure to break away from monism and propose a different system of matter. One source we have here is Aristotle, but even by Aristotle’s standards, his account doesn’t really seem to do Anaxagoras justice. Aristotle says that to Anaxagoras, the ultimate constituents of the universe were “homoiomereses”, and he says that these are things like “flesh, bone, and other parts of organisms.”

It seems that what Aristotle may have been getting at here was a thought experiment that Anaxagoras may have proposed. Anaxagoras considered what it was that happened when you ate bread. After all people eat bread every day, and this his how they sustain themselves. If they don’t eat much, they waste away and become skinny, and if they don’t eat enough for too long, they die. So somehow bread must turn into flesh, blood, and bone. But, and here is the key, if you take some bread and you crumble it up, you just get little tiny pieces of bread. Where is the flesh, blood, and bone? This is a hard thing to explain in the monist picture. Half of this makes perfect sense. The observation that if you crumble up bread you just get little bread crumbs fits in very well with monism. You haven’t changed the nature of the substance, you have just changed its size. But the body seems to transform it into something entirely different, and no amount of grinding away at it will produce flesh, blood, and bone. How can this happen in a monist system? Anaxagoras concluded that any explanation of this would have to abandon monism.

Anaxagoras instead developed a system founded on the unity of opposites. He held that there was a vast number of fundamental elements, possibly an infinite number, or possibly just a very large number. So, while Empedocles had broken from monism in a rather modest way — he bumped up the number of fundamental elements from one to four — a big conceptual change, of course, but not a tremendous increase, Anaxagoras really went gangbusters.

Furthermore, all these elements came in pairs of opposites. So for example there would be an element of light and an element of dark, an element of warm and an element of cold, an element of fast and an element of slow. It doesn’t seem like Anaxagoras ever attempted to enumerate all the possible elements, or even thought that it could be possible to enumerate them in this way, but he thought of the elements as any quality of matter that was in a sense independent of all others. So the warmth of an object is independent of how fast or heavy it is.

In Anaxagoras’s system all matter contains all the elements, including all the opposites. But the proportions of these different opposing elements varies from one kind of matter to the next. So snow has a high proportion of the light element, but some dark is still present, and likewise it has a high proportion of the cold element, but still some warm.

Now, one of the key features of Anaxagoras’s system was that one of the elements was size itself. So there was an element of greatness and an element of smallness, and these both were present in all things. Because of this, Anaxagoras argued that nothing can be infinitely large or infinitely small, since every small thing must have the element of greatness in it, at least in some amount which prevents it from being infinitely small, and similarly every large thing must have at least some amount of smallness in it, which prevents it from being infinitely large. An important corollary of this idea was that you cannot destroy anything by dividing it. Since all matter had some of the element of greatness, you could not destroy it by dividing it infinitely. It is not hard to see how this idea in particular had a strong influence on the later philosopher Democritus, who developed the theory of atoms and who was probably a student of Anaxagoras.

Well, there is one last critical feature of Anaxagoras’s system of elements. There is one special element which I have not mentioned yet, and this is the element of “nous”, spelled n-o-u-s, which can be variously translated as mind or intellect or perhaps consciousness. Of all the elements, nous is the only one which has no opposite. In a sense all other elements are its opposite because only it has volitional power. Nous reigns over all the other elements of the universe and stands apart from them. Unlike the other elements which are inextricably mixed together in all things, nous does not mix with the other elements. Instead nous is responsible for motion by pushing against them. If nous could mix, Anaxagoras said that then it would be unable to move the elements, since when it pressed up against them, it would just be absorbed.

This element nous seems to have been more than just an element for Anaxagoras, Anaxagoras viewed it as a God, the sort of divine will of the universe. As such, it is the source of motion not just now, but at the beginning of the universe starting everything in motion. Anaxagoras held that in the beginning all the elements were strewn about the universe and the nous then set this matter into motion into a giant vortex. The vortex started from the center and expanded outwards until it encompassed everything. Under the centrifugal force of the motion, the matter begins to separate out. A hot, rarefied kind of matter, which Anaxagoras called Aether rose to the outskirts and the colder, denser matter, which he called air condensed in the center. Now, calling this matter “air” is maybe something of a misnomer since it eventually becomes all the matter we’re familiar with. As the vortex continues, the matter continues to separate out such that matter with higher densities sink to the center, and lighter matter rises outward. So water precipitates out of the air and then the Earth precipitates out of water.

Now, this process was not entirely peaceful. When the vortex was particularly energetic, rocks were thrown out from the center towards the outer heavens and in the process ignited and became stars.

All in all, of all the ancient cosmogonic theories, this vortex theory of Anaxagoras holds up really remarkably well. From a pure physical standpoint, his idea of heavier matter condensing out under the influence of the vortex and of rocks being flung out in the process implies some understanding of centrifugal forces and is really the first time that this phenomenon was incorporated into any physical theory. And the overall picture of an initially homogeneous blob of matter spinning faster and faster and differentiating into different layers is, in fact, in broad strokes more or less an accurate picture of how planets and stars do in fact form. The main ingredient which was missing was the idea that the matter would not simply spontaneously start rotating under the influence of nous, but that it would attract itself and contract, rotating more rapidly as it collapsed. But this crucial piece would have to wait some two thousand years for Newton to formulate his theory of gravity, and then another few decades for Emanuel Swedenborg, Immanuel Kant, and Pierre-Simon Laplace to apply this new theory of gravity to the formation of the universe.

As for Anaxagoras’s cosmology, once the universe had formed and the vortex had settled down, his overall picture looked similar to that of Anaximenes. The Earth was flat and suspended in air. Some of the rocks that had been flung out during the time of the vortex were still circulating around the Earth and this motion created heat and light. All the stars and planets were due to these burning rocks. The stars, however, were very far away, which was why we do not feel any heat from them. But one large rock, in particular, was close by and created a great deal of heat, and this was of course the Sun, this idea being the one that got him in so much trouble with certain factions of the Athenian political classes. But in Anaxagoras’s conception the rock that formed the Sun was still considerably smaller than the Earth.

Now, interestingly, it seems as though Anaxagoras thought that the Moon was fundamentally different from the Sun and the stars. He held that it did not produce its own light, so maybe it was made of some other material, or wasn’t moving fast enough to generate the same heat as the Sun did as it moved through the sky.

When it came to eclipses, however, Anaxagoras had the right explanation that it was due to the Earth or the Moon blocking out light from the Sun, although he wasn’t the first to say this. But he did say, however, that lunar eclipses could sometimes be caused by other bodies in the universe which we do not see. Now, Anaxagoras was not the only ancient astronomer to have this hypothesis, you may recall that Philolaus, the Pythagorean, said much the same thing. In that case the main motivation was probably numerological and secondarily to explain why lunar eclipses were observed more frequently than solar eclipses. But a more sophisticated argument that some other body must be causing lunar eclipses, at least occasionally, came about later on. Now, it’s a little unclear whether or not Anaxagoras himself noted this, but later an astronomer by the name of Cleomedes, whose date is fairly uncertain, but may have been writing around the 4th century AD, had written that the ancient astronomers had noticed certain rare lunar eclipses which happened right at sunset or sunrise. During this time, a person would see, simultaneously, the Sun on one horizon, and the eclipsed moon on the other horizon. In this case the Earth clearly was not between the Sun and the Moon and could not be causing the eclipse. Some mathematicians had proposed that the shadows of the Earth somehow produced a kind of conical shape, but the far simpler explanation here was that there was just some other body somewhere between the Sun and the Moon which, maybe due to an inconvenient location in the twilight, we were unable to see.

As far as experimental evidence for an otherwise unseen body goes, this is pretty compelling. The phenomenon was readily observed, a lunar eclipse at sunrise or sunset is rare, but not all that rare, it certainly happens at least every decade or so, and the explanation was very simple. To say that this was wrong would be to say that the Earth somehow was casting a shadow not in a straight line and this was a kind of wacky thing to claim.

But, one of the nice things about ancient astronomy was that the natural philosophers of the day were not averse to making wacky claims, and some of them did, in fact, propose what we today take to be the correct explanation of this phenomenon, namely that during a lunar eclipse the Moon and Sun can be simultaneously visible because the Earth’s atmosphere refracts the light. Although it appears that the Sun and Moon are above the horizon, they are both, in fact, below the horizon, and refraction from the Earth’s atmosphere makes them appear slightly higher than they really are. In support of this bizarre theory that the air bends the path of light Cleomedes had pointed to the fact that if you put an object at the bottom of a jug, it will be out of sight. But if you pour water into the jug, the object comes into sight again. Since the water can clearly deflect the path of the light, it is not unreasonable to suppose that the air could do so as well. Cleomedes also pointed to the Black Sea as being an area where refractive phenomena was especially pronounced and the sizes of objects near the horizon appeared much different from what they truly were due to the damp, cold air.

Well, although Anaxagoras had gotten the sensible, but wrong conclusion on the subject of these unusual eclipses, he was no stranger to wacky ideas of his own, and his theory of the Milky Way is one where he redeems himself. His idea here was that the Milky Way is made of a great number of faint stars. But what is going on here is that during the night, the Sun is under the Earth and the Earth casts a shadow upwards. Now you’ll recall that in Anaxagoras’s system, the shape of the Earth is flat, so the Earth’s shadow produces a narrow band across the sky. On the parts of the sky where the Earth’s shadow doesn’t fall, the rays from the Sun interfere with the stars there and essentially wash them out. But in the Earth’s shadow, the stars are no longer competing with the light from the Sun and can shine more freely. This then produces a swath of faint stars across the sky.

It’s a creative idea, but it didn’t take long for other philosophers of the day to find issues with it. Aristotle, in particular, whom we can always trust to poop in the punch bowl, noted that if this were true, we would expect the Milky Way to fall along the ecliptic, whereas it is fairly perpendicular to the ecliptic, only crossing it most prominently in Sagittarius and again to a lesser degree in Gemini. More seriously, any time the Moon passed through the Milky Way, it should be eclipsed and this is not observed. And finally, the geometry just didn’t make sense. If the stars were as far away as Anaxagoras said they were, they would be outside of the Earth’s shadow.

Well, the last thing I’ll say about Anaxagoras is that like some of the other philosophers before him, Anaximander in particular, he believed that there were other worlds and that these other worlds contained life. And as with Anaximander it’s a little unclear whether he meant that this was the case today, in other parts of the universe, or whether he thought that the universe as a whole went through cycles of death and rebirth. At least one fragment seems to suggest that Anaxagoras held that there was life in our universe in other parts, and that during the great vortex that created the world, large rocks had been flung out into other parts of the universe and those rocks developed their own Sun, Moon, and Earth, and life as well. Part of this fragment reads:

Men were formed and the other animals which have life; the men too have inhabited cities and cultivated fields as with us; they have also a sun and moon and the rest as with us, and their earth produces for them many things of various kinds, the best of which they gather together into their dwellings and live upon. Thus much have I said about separating off, to show that it will not be only with us that things are separated off, but elsewhere as well.

Well, I ended the last episode with an implicit promise that I would talk about the atomic theory of Leucippus and Democritus and I have instead tricked you into listening to the pluralism of Empedocles and Anaxagoras. But on the next episode, I will make good on my promise, we will see how one of Anaxagoras’s students, Democritus, and another of his teachers, a rather shadowy figure named Leucippus, were inspired by the pluralism of Empedocles and Anaxagoras to develop a new theory of matter that attempted to synthesize the benefits of monism and pluralism into a single theory — the theory of atoms.

I hope you’ll join me then. Until the next full moon, good night, and clear skies.

Additional references

  • Cleve, Felix: The Philosophy of Anaxagoras, 1949