The progress of Science is generally regarded as a kind of clean, rational advance along a straight ascending line; in fact it has followed a zigzag course, at times almost more bewildering than the evolution of political thought. The history of cosmic theories, in particular, may without exaggeration be called a history of collective obsessions and controlled schizophrenias; and the manner in which some of the most fundamental discoveries were arrived at reminds one more of a sleepwalker’s performance than an electronic brain’s.
Arthur Koestler

The Sleepwalkers is an enlightening history of astronomy from the Ancient Greeks to Newton. It particularly focuses on three characters who shifted scientific consensus from the Ptolemaic geocentric model of the solar system to a heliocentric one: Copernicus, Kepler, and Galileo. And characters is the right word, because Koestler digs into their personal quirks and foibles with gusto. If he is to be believed, these three key scientists were all temperamental to the point of self-destructiveness.

Copernicus and Kepler

Copernicus, according to Koestler, was “a man of the Middle Ages: haunted by its anxieties, ridden with its complexes, a timid, conservative cleric, who started the revolution against his will.” The origin of his heliocentric system was in fact his attempt to fix an aesthetic flaw which made Ptolemy’s system “neither sufficiently absolute nor sufficiently pleasing": that it modelled planets as moving at variable speeds. In doing so, he was inspired by Ancient Greek writings, and in particular references to the heliocentric system that Heraclides of Pontos and Aristarchus of Samos proposed in the 3rd century BC. Copernicus was terrified by the prospect of criticism, so that it took decades for him to publish his conclusions (On the revolutions of the celestial spheres only came out just before his death in 1543). But in fact, the publication itself was fairly irrelevant: it was tedious and actually more complicated than existing geocentric systems. As previous astronomers had done, Copernicus explained complex-looking orbits using models in which planets rotated on circles which themselves rotated in circles (known as epicycles). Epicycles were a very powerful modelling tool (in fact, equivalent to Fourier series!) but made theories much uglier and more complex - and Copernicus needed more of them than previous geocentric models. But the important thing was that heliocentrism, an idea which been floating around without much fanfare since the Greeks, was brought to greater prominence - inspiring others, particularly Kepler and Galileo.

Kepler was prone to bursts of passion, alternating between fury and self-deprecation. He was also driven primarily by a philosophical taste verging on mysticism: his first system of astronomy matched the six known planets with the five perfect Platonic solids for aesthetic reasons, and was complete bunk. So too was his theory that the positions of the planets were determined by the ratios of musical harmonies. Yet these instincts kept him pushing, mostly by accident, in the right direction. His breakthrough came when given access to the meticulous observations of Tycho Brahe (also quite a character: after his nose was chopped off in a duel, he wore a silver replacement). The two had a stormy relationship, but after Tycho’s death Kepler slogged through years of calculations to try and pin down the shape of planetary orbits. Through determination and luck (he made several errors which fortunately cancelled out), he eventually formulated his three laws: that planets move in ellipses, with the sun at one focal point; that they travel at variable speeds such that the line between them and the sun sweeps out the same area per unit time; and that the squares of the periods of the planets’ revolutions are proportional to the cubes of their mean distances from the sun.

Why the delay?

It's worth highlighting two contributing factors to this very impressive achievement. Firstly, Tycho was very well-funded, and took data collection unprecedentedly seriously (note that this was all done before telescopes!). Secondly, Kepler deserves great credit for his persistence in testing his theories against that data, and throwing them out when they failed to meet it. But there’s a much broader question of why it took almost 2000 years from the first heliocentric system to the discovery of these laws, and even longer until acceptance of heliocentrism became widespread - why, in Whitehead’s words, “in the year 1500 Europe knew less than Archimedes who died in the year 212 BC.”

In short, the answer seems to be Plato and Aristotle: as Koestler portrays them, “two frightened men standing in [Plato’s] Cave, facing the wall, chained to their places in a catastrophic age, turning their back on the flame of Greece’s heroic era, and throwing grotesque shadows which are to haunt mankind for a thousand years and more.” This is unduly harsh - and yet how damaging the blind adherence to their ideas which lasted, with few exceptions, until the 16th century! Two of Plato’s most influential tenets: that true knowledge cannot be obtained by the study of nature, but must be gained by consideration of the perfect world of Forms and Ideas; and that, for metaphysical reasons, all celestial motion must be in perfect circles at uniform speed. Aristotle then introduced the distinction between the imperfect and changeable earth, and the eternal and unchanging cosmos; also, that each movement was due to an object’s telos, or purpose. Lastly, God was placed on the outermost sphere, furthest away from the Earth. Their combined influence had astronomers thinking in circles for almost 2000 years! And even the scientists whose work led to the end of these dogmas were still somewhat trapped by them: Kepler spent years trying to make Tycho’s data consistent with circular orbits. Only when he felt that he’d conclusively ruled those out did he move on to ovals and ellipses.

More specifically, Koestler identifies five main obstacles to scientific progress between the Greeks and the scientific revolution. "The first was the splitting up of the world into two spheres, and the mental split which resulted from it. The second was the geocentric dogma, the blind eye turned on the promising line of thought which had started with the Pythagoreans and stopped abruptly with Aristarchus of Samos. The third was the dogma of uniform motion in perfect circles. The fourth was the divorcement of science from mathematics. The fifth was the inability to realise that while a body at rest tended to remain at rest, a body in motion tended to remain in motion. The main achievement of the first part of the scientific revolution was the removal of these five cardinal obstacles."

Galileo and Newton

An early step forward was Tycho Brahe’s observation of a supernova in 1572, and his demonstration that it wasn’t just a comet, but a new (and changing!) phenomenon beyond the orbit of the moon. Then, soon after Kepler published his first two laws in 1609, another blow against the Aristotelean conception of the universe was struck by Galileo’s observations of several moons of Jupiter, as well as terrain on the moon and phases of Venus. These were all evidence that the Earth was less special than had been thought. While Galileo hadn’t invented the telescope, or been the first to notice the new moons using one, he was the first to bring them to prominence in his book Sidereal message. The book faced heavy criticism from other scientists, but eventually became accepted after Kepler threw his support behind it.

This makes Galileo’s biggest blunder even more confusing: he simply refused to accept Kepler’s system of elliptical orbits, and instead propounded a version of Copernicus’ theory which neither was elegant nor matched the data very well. He also dismissed Kepler’s correct theory of moon-caused tides in favour of the clearly flawed hypothesis that they were driven by the Earth’s motion. This would have been unimportant, if not for his insistence that the Church start reinterpreting scripture based on the evident truth of Copernican heliocentrism, as shown by the existence of tides.* Koestler attributes Galileo’s persecution by the Church not to an inevitable clash between science and religion, but rather to Galileo’s own bullheadedness in attempting to force a theological surrender without having much evidence, and his tendency to insult and alienate important people. (A particularly damaging example: in his Dialogue concerning the two chief world systems, the views of Pope Urban are put into the mouth of a dimwit called Simplicio.) Koestler argues that the Church had a lot of respect for scientists, and in general was willing to reinterpret doctrine based on compelling scientific arguments, but that Galileo’s actions made opposition to heliocentrism last much longer than it otherwise would have.**

Nevertheless, we have Galileo to thank for informal precursors to Newton’s laws of motion: that objects remain at the same velocity unless acted upon by a force; and that (ignoring air resistance) objects fall with the same constant acceleration regardless of their weight. At this point, science was in a pivotal position. Kepler’s laws applied to celestial objects; Galileo’s applied to terrestrial objects. There was a growing acceptance that the two were fundamentally the same, but no agreement on what force drove celestial motion, or what planets would do without the influence of the sun, or even what weight meant in a celestial context. People believed Kepler's laws, but didn’t understand them: why ellipses? Why an equal area? Ideas were also floating around to do with reciprocal attraction between objects in a way that varied by distance, but nothing concrete - and the introduction of magnetism made people even more confused about which force might be doing what.

Then, of course, came Newton’s grand synthesis of gravity in 1687. Consider his thought experiment of firing a cannonball horizontally from a mountain. If fired slowly, it will fall to the earth quite soon. If fired faster, it will curve around the earth a little before falling. But if fired fast enough, it will continually “fall” towards the earth but never hit it: it will be in orbit. Newton was then able to use calculus to derive the fundamental reasons why Kepler’s laws must be true (for an intuitive demonstration of why elliptical orbits make sense, try throwing a marble into a cone). Key to this was Newton’s acceptance of gravity as “action at a distance”, which had always been very controversial. Apart from this, there were almost no cases of two objects affecting each other except by some medium physically between them. The one known exception, as mentioned, was magnetism - a helpful precedent for building acceptance of Newtonian gravity. Koestler on Newton’s importance: “If one had to sum up the history of scientific ideas about the universe in a single sentence, one could only say that up to the seventeenth century our vision was Aristotelian, after that Newtonian. Copernicus and Tycho, Kepler and Galileo, Gilbert and Descartes lived in the no-man’s-land between the two.”

Science as sleepwalking

As mentioned in the opening quotation, the book is called The Sleepwalkers because that whole transition was so confused and messy. Out of Copernicus, Kepler, and Galileo, the first and last never let go of the Platonic ideal of circular orbits. And while Kepler’s laws were correct, his actual arguments were riddled with mistakes and contradictions. In addition to the mysticism mentioned above, one anecdote is particularly telling. Kepler believed that elliptical orbits had to result from the combination of two different forces: one linking a planet to the sun, and the other simply acting on the planet itself. This is basically correct: the first is gravity, which pulls planets towards the sun; the second is centrifugal force or inertia, which prevents them from falling inwards. However, in Kepler’s theory of physics these are exactly the other way around! He envisaged the sun as providing a force which swept the planets around their rotations, and a planet’s intrinsic magnetism as what pulled it towards or away from the sun. His “proof” of his 2nd law was another case of coming to the right conclusion for the wrong reasons. Even Newton, in the midst of his great triumph, had to appeal to God to explain why gravity didn’t cause the whole universe to collapse inwards.

Overall I think reading this book is helpful in understanding what it looks like to be very smart and also very confused. It’s also notable just how much the leading scientists involved were held back from publishing by concerns about their reputation amongst other scientists - and if the ones who we remember now were so worried about that, there were probably many more who succumbed to those worries and who we’ve therefore never heard of. Lastly, as Koestler highlights several times, the empirical arguments in favour of geocentrism - like “why don’t we feel the Earth moving?”, “why don’t we observe Venus getting closer and further away?", and “why don’t we see the stars shifting as we orbit?” - were actually fairly sophisticated and reasonable.*** And given the messiness of Copernicus’ system, there simply wasn’t enough evidence to conclusively decide in favour of heliocentrism at least until Kepler’s ellipses - which were only discovered because Kepler had already devoted his life to the hypothesis. This supports the Kuhnian view of scientific revolutions as driven to a significant extent by personal taste in paradigms. The Sleepwalkers was actually published just three years before The Structure of Scientific Revolutions, and in the epilogue Koestler discusses some very similar ideas:

“The philosophy of nature evolved by occasional leaps and bounds alternating with delusional pursuits, culs-de-sac, regressions, periods of blindness, and amnesia. The great discoveries which determined its course were sometimes the unexpected by-products of a chase after quite different hares. … There occur in biological evolution periods of crisis and transition when there is a rapid, almost explosive branching out in all directions, often resulting in a radical change in the dominant trend of development. The same kind of thing seems to have happened in the evolution of thought at critical periods like the 6th century BC or the 17th AD. ... ‘Intellectual progress’ has, as it were, linear associations - a continuous curve, a steadily rising water level; whereas ‘evolution’ is known to be a wasteful, fumbling process characterised by sudden mutations of unknown cause, by the slow grinding of selection, and by the dead-ends of over-specialisation and rigid inadaptability."

And finally, a prescient passage on the increasing power of science:

"Thus within the foreseeable future, man will either destroy himself or take off from the stars. It is doubtful whether reasoned argument will play any significant part in the ultimate decision, but if it does, a clearer insight into the evolution of ideas which led to the present predicament may be of some value. The muddle of inspiration and delusion, of visionary insight and dogmatic blindness, of millennial obsessions and disciplined double-think, which this narrative has tried to retrace, may serve as a cautionary tale against the hubris of science - or rather of the philosophical outlook based on it. The dials on our laboratory panels are turning into another version of the shadows in the cave."

* One important concept here is the difference between a model which matches observed data (thereby “saving the phenomenon”) and a hypothesis which is claimed to be literally true. My impression is that geocentric models with epicycles were generally considered part of the former category, because while they matched the data pretty well, there was no good explanation of why planets would move as if they were on wheels attached to wheels, when the existence of such wheels in the sky would be absurd. The Church also had no problem with heliocentrism when presented as the former (which Galileo refused to do). Note that the question of when we should treat theories as descriptive models or literal truth is still a key question in philosophy of science (now under the headings of scientific anti-realism versus scientific realism).

** Note that while Koestler’s scholarship generally seems meticulous, with copious quotes from original sources, I’m still slightly skeptical about this argument - particularly after reading the epilogue, which displays a pro-religion bias and credulity towards ESP and time travel. See also this argument that even easily-avoidable censorship is dangerous.

*** For another excellent perspective on this, see Jacob Lagerros' essay here.

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This essay argues against the idea of "saving the phenomenon", and suggests that the early astronomers mostly did believe that their models were literally true. Which rings true to me; the idea of "it doesn't matter if it's real or not" comes across as suspiciously modern.

Hmm, interesting. It doesn't discuss the Galileo affair, which seems like the most important case where the distinction is relevant. Nevertheless, in light of this, "geocentric models with epicycles had always been in the former category" is too strong and I'll amend it accordingly.

Oh, I totally buy that it was relevant in the Galileo affair; indeed, the post does discuss Copernicus. But that was after the controversy had become politicized and so people had incentives to come up with weird forms of anti-epistemology. Absent that, I would not expect such a distinction to come up.

I'm not sure I parsed this comment thread, wondering if you could explain in a bit more detail what you think happened?

Irresponsible and probably wrong narrative: Ptolemy and Simplicius and other pre-modern scientists generally believed in something like naive realism, i.e., that the models (as we now call them) that they were building were supposed to be the way things really worked, because this is the normal way for humans to think about things when they aren't suffering from hypoxia from going up too many meta-levels, so to speak. Then Copernicus came along, kickstarting the Scientific Revolution and with it the beginnings of science-vs.-religion conflict, spurring many politically-motivated clever arguments about Deep Philosophical Issues. Somewhere during that process somebody came up with scientific anti-realism, and it gained traction because it was politically workable as a compromise position, being sufficiently nonthreatening to both sides that they were content to let it be. Except for Galileo, who thought it was bullshit and refused to play along, which (in conjunction with his general penchant for pissing people off, plus the political environment having changed since Copernicus due to the Counter-Reformation) got him locked up.

Thanks, that at least sounds like a plausible narrative and I understand what you meant better.

I've just returned from a science fiction convention, and in a panel about mechanical computing, someone put out the speculation (I have no idea if this can be supported from historical evidence) that as the Greeks knew all about conic sections, they might have known that the planets moved in elliptical orbits. The epicycles (it was suggested) come about because if you're making machinery to forecast the heavens, such as the Antikythera mechanism, it's easier to make circular wheels than elliptical ones. So you model the elliptical orbits as circles, then correct them with smaller circles moving on the circles. Thus, not bad science, but good engineering.

That's reasonable, but most likely the Greeks didn’t know the orbits were ellipses, but just knew them as solutions to Newton’s laws and used calculus to approximate them as deviations from circles.

The Greeks didn't have Newton's laws, or calculus except for the method of exhaustion for calculating certain areas.

Obviously I disagree. How can you boldly state that they didn't have things? Maybe there's no written record, but someone writing about the Antikythera Mechanism should know the limits of that! Indeed, the Method of Mechanical Theorems was discovered after even the Mechanism. But there is a written record. There's a lot more calculus in Archimedes than the method of exhaustion. That's barely calculus and it's interesting more because it's rigorous than because it's a forerunner to calculus. But the Method is a pretty big chunk of integral calculus.

The missing part is differential calculus; Newton's laws do not appear in the written record. But Vitruvius appears to discuss how the planetary orbits are the result of inertia and centripetal force, so it is really not a big stretch to posit further elaboration.

I think using ellipses only really gets you good mileage once you have the planets moving around the sun. If, like Aristotle, you have the planets moving around the earth, then epicycles are just being a very general way of representing periodic motion phenomenologically.

Apollonius introduced epicycles and proved a theorem of the commutativity of addition: a small epicycle about a large orbit appears the same as a large epicycle about a small orbit. This makes it seems like he was using them to represent heliocentrism, not just fitting data.

The Ptolemaic model has an epicycle and an equant for each planet. One of them corresponds to heliocentrism and the other to the non-circularity of an orbit. (That's very vague because the correspondence is different for the inner planets vs the outer planets. The role of epicycle vs deferant gets switched and (thus) which orbit, the planet or the earth's has its non-circularity approximated differs.)

Heliocentrism was around then as well, e.g. Aristarchus of Samos.

I'm currently stewing in a weird of mixture of this post, with it's reflections on what it's like to be smart but confused during periods where people barely understand complex motions (with all the mysticism and aesthetic preferences and perfect circles thrown in)...

...and Scott Alexander's latest post boggling at the fact that so much human collection action seems to reduce to simple functions that can be mapped onto straight lines.

Figuring out what's up with that seems like a major puzzle of our time. I'm chuckling at future hypothetical historians who might read old Scott Alexander posts and be like "hmm, this guy was grappling with the thing we now mostly understand, but was weirdly fixated on the Gods of the Straight Lines and maybe confused about it in ways that are now clear to us. Also, what the hell is up with that Unsong book that he wrote?"

Figuring out what's up with that seems like a major puzzle of our time.

Would be curious to hear more about your confusion and why it seems like such a puzzle. Does "when you aggregate over large numbers of things, complex lumpiness smooths out into boring sameness" not feel compelling to you?

If not, why not? Maybe you can confuse me too ;-)

So this runs the risk of being tangential, but I generally view straight lines in graphs with acute suspicion. This is not the usual expectation: people expect things to keep changing the same way they have been, so they predict a straight line; we have lots of straight lines which come out of diligent aggregation of data like this.

My thinking shifted when I did an electromagnetic theory course for antennas, which contra the rest of engineering school was mostly about Maxwell's Equations and how to derive them. We relied a lot on the linearity property for those equations, and I was ceaselessly impressed by the stupendous power this gave us.

An unreasonable amount of power. So much power did linearity yield that I look at this first as an explanation for things that we don't do well. Linearity gives us electricity and computers, precision and control. The impression I got was that anything in a graph that looks like a line isn't really a line, but is actually just an approximate sum of different curves.

So this is now my prior. Granted, this basically punts the question of straight lines on graphs to 'why do different curves seem to sum to approximately straight lines so often' so it doesn't get me much. My working guess is something like 'because we expect straight lines, any more growth than that probably gets left on the table.'

If the curves are constructed randomly and independently then in some cases a linear relationship would be implied by the central limit theorem.

Not sure if this is helpful or not - CLT assumptions may or may not be valid in the instances you're thinking of. I think my brain just went "Sum of many different variables leading to a surprising regular pattern? That reminds me of CLT".

“in the year 1500 Europe knew less than Archimedes who died in the year 212 BC.”
In short, the an­swer seems to be Plato and Aris­to­tle (OP)

But Plato and Aristotle came before Archimedes! How is this an answer? Bad ideas can retard progress, but they didn’t hurt Archimedes.

By the end of the third century BC, the heroic period of Greek science was over. From Plato and Aristotle onward, natural science begins to fall into disrepute and decay (Koestler)

This is complete garbage. The Hellenistic period after Aristotle was much better than the “heroic” period before him. Aristotle appears to have created science. While there were some scientific Presocratics (Thales, Democritus), Koestler’s Pythagoras is a fantasy. Aside from inflating the achievements of the Pythagoreans, relying too much on Simplicius a thousand years later, he also gerrymanders the real achievements of real people, arbitrarily crediting the Pythagoreans. Maybe Herakleides was a Pythagorean, but he was also a student of Plato, as Koestler mentions in passing, but fails to credit. Classifying Aristarchus as Pythagorean rather than Hellenistic is crazy.

Hellenistic science didn't decay, but abruptly collapsed, with civil war in Alexandria in 144BC and, more mysteriously, with the peaceful Roman annexation of Pergamon in 133BC.

Koestler says a bunch of contradictory things about Plato. He recognizes that there are a bunch of different time periods to explain, so he seems to recognize that his explanations don't fit together.

One place he says that it's not Plato's fault, but the fault of the Neoplatonists. Maybe that could explain the decline after Ptolemy and the lack of interest of the Byzantines in science, but in the quote above he's talking about decline before Ptolemy, so Plato proper. He specifically notes a gap between Hipparchus and Ptolemy, so he is talking about a fast fall, not decay past Ptolemy.

He recognizes that the Western Dark Age didn't have Plato or Aristotle. He specifically mentions that the West got Aristotle before Plato. In between it got Archimedes and science exploded. Aristotle is generally seen as promoting medieval science (Roger Bacon was a fan), but at the very least he didn't interfere with reading Archimedes. There was a decline of science and civilization generally when Petrarch translated Plato, but I think that's a coincidence, really the fault of the Black Death.


When I saw this post I initially thought it was going to be about The Sleepwalkers: How Europe Went to War in 1914. I read that a few years ago and it caused me to update a lot on what happened then, from my previous view based largely on The Guns of August, and the implications for how such dynamics tend to operate in general. Certainly good enough to be worth recommending.


I've been thinking a lot lately about how intellectual progress happens and how LessWrong can do a good job facilitating it.

I found this post useful, both for some concrete examples of what happened during various revolutions of astronomy, and for helping frame my understanding of they fit together.

I do think this post could have benefited from a bit more structure (especially for re-reading – I remembered liking the post a month ago when it was first posted, but as I reviewed it today I found it somewhat hard to remember what the major points where. It would have been helpful to refactor the post somewhat into multiple sections with clearer headings.

Thanks for the kind words. I agree that refactoring would be useful, but don't have the time now. I have added some headings though.

Funny how in this case I would side with the Church against Galileo: scientific anti-realism avoids a lot of silly arguments about what exists and what is real. Galileo committed a cardinal sin of post-rationality, claiming that his map is the territory, and amply deserved the punishment.

Overconfidence in sentences like "the moon has craters" may be a sin. (Though I'd disagree that this sin category warrants banning someone from talking about the moon's craters and trapping them within a building with threats of force for nine years. YMMV.)

Thinking that the sentence "the moon has craters" refers to the moon, and asserts of the moon that there are craters on it, doesn't seem like a sin at all to me, regardless of whether some scientific models (e.g., in QM) are sometimes useful for reasons we don't understand.

Re Galileo's punishment, my comment was a bit tongue in cheek :). As for the rest, you and I have always disagreed about the ontological content of "reality", you being realist and me tending toward the anti-realism/pragmatism/instrumentalism side of the debate. Sadly, I never got to meet any of you rationality big wigs in person, maybe it would have been more useful than online encounters.

Maybe someday! :)