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gwern comments on Open thread, August 4 - 10, 2014 - Less Wrong Discussion
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The earth revolving around the sun was also armchair reasoning, and refuted by empirical data like the lack of observable parallax of stars. Geocentrism is a pretty interesting historical example because of this: the Greeks reached the wrong conclusion with right arguments. Another example in the opposite direction: the Atomists were right about matter basically being divided up into very tiny discrete units moving in a void, but could you really say any of their armchair arguments about that were right?
Atoms can actually be divided into parts, so it's not clear that the atomists where right. If you would tell some atomist about quantum states, I would doubt that they would find that to be a valid example of what they mean with "atom".
The atomists were more right than the alternatives: the world is not made of continuously divisible bone substances, which are bone no matter how finely you divide them, nor is it continuous mixtures of fire or water or apeiron.
You could say the same of Dalton.
It is not clear that the Greeks rejected heliocentrism at all, let alone any reason other than heresy. On the contrary, Hipparchus refused to choose, on the grounds of Galilean relativity.
The atomists got the atomic theory from the Brownian motion of dust in a beam of light. the same way that Einstein convinced the final holdouts thousands of years later.
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?