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gwern comments on Open thread, August 4 - 10, 2014 - Less Wrong
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Eh? I was under the impression that most of the Greeks accepted geocentrism, eg Aristotle. Double-checking https://en.wikipedia.org/wiki/Heliocentrism#Greek_and_Hellenistic_world and https://en.wikipedia.org/wiki/Ancient_Greek_astronomy I don't see any support for your claim that heliocentrism was a respectable position and geocentrism wasn't overwhelmingly dominant.
Cite? I don't recall anything like that in the fragments of the Pre-socratics, whereas Eleatic arguments about Being are prominent.
Lucretius talks about the motion of dust in light, but he doesn't claim that it is the origin of the theory. When I google "Leucippus dust light" I get lots of people making my claim and more respectable sources making weaker claims, like "According to traditional accounts the philosophical idea of simulacra is linked to Leucippus’ contemplation of a ray of light that made visible airborne dust," but I don't see any citations to where this tradition is recorded.
The Greeks cover hundreds of years. They made progress! You linked to a post about the supposed rejection of Aristarchus's heliocentric theory. It's true that no one before Aristarchus was heliocentric. That includes Aristotle who died when Aristarchus was 12. Everyone agrees that the Hellenistic Greeks who followed Aristotle were much better at astronomy than the Classical Greeks. The question is whether the Hellenistic Greeks accepted Aristarchus's theory, particularly Archimedes, Apollonius, and Hipparchus. But while lots of writings of Aristotle remain, practically nothing of the later astronomers remain.
It's true that secondary sources agree that Archimedes, Apollonius, and Hipparchus were geocentric. However, they give no evidence for this. Try the scholarly article cited in the post you linked. It's called "The Greek Heliocentric Theory and Its Abandonment" but it didn't convince me that there was an abandonment. That's where I got the claim about Hipparchus refusing to choose.
I didn't claim that there was any evidence that it was respectable, let alone dominant, only that there was no evidence that it was rejected. The only solid evidence one way or the other is the only surviving Hellenistic astronomy paper, Archimedes's Sandreckoner, which uses Aristarchus's model. I don't claim that Archimedes was heliocentric, but that sure sounds to me like he respected heliocentrism.
Maybe heliocentrism survived a century and was finally rejected by Hipparchus. That's a world of difference from saying that Seleucus was his only follower. Or maybe it was just the two of them, but we live in a state of profound ignorance.
As for the ultimate trajectory of Greek science, that is a difficult problem. Lucio Russo suggests that Roman science is all mangled Greek science and proposes to extract the original. For example, Seneca claims that the retrograde motion of the planets is an illusion, which sounds like he's quoting someone who thinks the Earth moves, even if he doesn't. More colorful are Pliny and Vitruvius who claim that the retrograde motion of the planets is due to the sun shooting triangles at them. This is clearly a heliocausal theory, even if the authors claim to be geocentric. Less clear is Ruso's interpretation, that this is a description of a textbook diagram that they don't understand.
So, you just have an argument from silence that heliocentrism was not clearly rejected?
I just read through the bits of Sand Reckoner referring to Aristarchus (Mendell's translation), and throughout Archimedes seems to be at pains to distance himself from Aristarchus's model, treating it as a minority view (emphasis added):
Not language which suggests he takes it particularly seriously, much less endorses it.
In fact, it seems that the only reason Archimedes brings up Aristarchus at all is as a form of 'worst-case analysis': some fools doubt the power of mathematics and numbers, but Archimedes will show that even under the most ludicrously inflated estimate of the size of the universe (one implied by Aristarchus's heliocentric model), he can still calculate & count the number of grains of sands it would take to fill it up; hence, he can certainly calculate & count the number for something smaller like the Earth. From the same chapter:
And he triumphantly concludes in ch4:
All I have ever said is that you should stop telling fairy tales about why the Greeks rejected heliocenrism. If the Sandreckoner convinces you that Archimedes rejected heliocentrism, fine, whatever, but it sure doesn't talk about parallax.
I listed several pieces of positive evidence, but I'm not interested in the argument.
The Sand Reckoner implies the parallax objection when it uses an extremely large heliocentric universe! Lack of parallax is the only reason for such extravagance. Or was there some other reason Aristarchus's model had to imply a universe lightyears in extent...?
Aristarchus using a large universe is evidence that he thought about parallax. It is not evidence that his opponents thought about parallax.
You are making a circular argument: you say that the Greeks rejected heliocentrism for a good reason because they invoked parallax, but you say that they invoked parallax because you assume that they had a good reason.
There is a contemporary recorded reason for rejecting Aristarchus: heresy. There is also a (good) reason recorded by Ptolemy 400 years later, namely wind speed.
Uh... why would the creator of the system consider parallax an issue, and the critics not consider parallax an issue?
And you still haven't addressed my quotes from The Sand Reckoner indicating Archimedes considered heliocentrism dubious and a minority view, which should override your arguments from silence.
No. I said parallax is why they rejected it in part because to save the model one has to make the universe large, then you said 'look! Archimedes uses a large universe!', and I pointed out this is 100% predicted by the parallax-rejection theory. So what? Where is your alternate explanation of why the large-universe - did Archimedes just make shit up?
And how do these lead to a large universe...?
The very question is whether the critics made good arguments. You are assuming the conclusion.
People make stupid arguments all the time. Anaxagoras was prosecuted for heresy and Aristarchus may have been. How many critics of Copernicus knew that he was talking about what happens over the course of a year, not what happens over the course of a day?
Yes, Archimedes says that Aristarchus's position is a minority. Not dubious. I do not see that in the quotes at all. Yes, Archimedes probably uses Aristarchus's position for the purposes of worst-case analysis to get numbers as large as possible; indeed, they are larger than the numbers Ptolemy attributes to Aristarchus. As I said at the beginning, I do not claim that he endorsed heliocentrism, only that he considered it a live hypothesis.
One mystery is what is the purpose of the Sandreckoner. Is it just about large numbers? Or is it also about astronomy? Is Archimedes using exotic astronomy to justify his interest in exotic mathematics? Or is he using his public venue to promote diversity in astronomy?
It's assuming the conclusion to think critics agreed with Aristarchus's criticism of a naive heliocentric theory?
I disagree strongly. I don't see how you could possibly read the parts I quoted, and italicized, and conclude otherwise. Like, how do you do that? How do you read those bits and read it as anything else? What exactly is going through your head when you read those bits from Sand Reckoner, how do you parse it?
Gee, if only I had quoted the opening and ending bits of the Sand Reckoner where Archimedes explained his goal...
Many people object to Copernicus on the grounds that Joshua made the Sun stand still, or on grounds of wind, without seeming to realize that they object to the daily rotation of the Earth, not to his special suggestion of the yearly revolution of the Earth about the Sun.
If Copernicus had such lousy critics, why assume Aristarchus had good critics who were aware of his arguments? Maybe they objected to heresy, like (maybe) Cleanthes.
Archimedes was a smart guy who understood what Aristarchus was saying. He seems to accept Aristarchus's argument that heliocentrism implies a large universe. If (if!) he rejects the premise, that does not tell us why. Maybe because he rejects the conclusion. Or maybe he rejects the premise for completely different consequences, like wind. Or maybe he is not convinced by Aristarchus's main argument (whatever that was) and doesn't even bother to move on to the consequences.
Ptolemy does give a reason: he says wind. He has the drawback of being hundreds of years late, so maybe he is not representative, but at least he gives a reason. If you extract any reason, that is the one to pick.
The principal purpose of the Sandreckoner is to investigate infinity, to eliminate the realm of un-nameable numbers, thus to eliminate the confusion between un-nameably large and infinite. But there are many other choices that go into the contents, and they may be motivated by secondary purposes. Physical examples are good. Probably sand is a cliche. But why talk about astronomy at all? Why not stop at all the sand in the world? Or fill the sphere of the sun with sand, stopping at Aristarchus's non-controversial calculation of that distance? Such choices are rarely explained. I offered two possibilities and the text does not distinguish them.