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?
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.
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.
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 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.
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):
You grasp [King Gelon, the recipient of Archimedes’s letter The Sand Reckoner] that the world is called by most astronomers the sphere whose center is the center of the earth and whose line from the center is equal to the straight-line between the center of the sun and the center of the earth, since you have heard these things in the proofs written by the astronomers. But Aristarchus of Samos produced writings of certain hypotheses in which it follows from the suppositions that the world is many times what is now claimed.
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:
[1] Some people believe, King Gelon, that the number of sand is infinite in multitude. I mean not only of the sand in Syracuse and the rest of Sicily, but also of the sand in the whole inhabited land as well as the uninhabited. There are some who do not suppose that it is infinite, and yet that there is no number that has been named which is so large as to exceed its multitude.
[2] It is clear that if those who hold this opinion should conceive of a volume composed of the sand as large as would be the volume of the earth when all the seas in it and hollows of the earth were filled up in height equal to the highest mountains, they would not know, many times over, any number that can be expressed exceeding the number of it.
[3] I will attempt to prove to you through geometrical demonstrations, which you will follow, that some of the numbers named by us and published in the writings addressed to Zeuxippus exceed not only the number of sand having a magnitude equal to the earth filled up, just as we said, but also the number of the sand having magnitude equal to the world.
...[7] In fact we say that even if a sphere of sand were to become as large in magnitude as Aristarchus supposes the sphere of the fixed stars to be, we will also prove that some of the initial numbers having an expression (or: “numbers named in the Principles,” cf. Heath, Archimedes, 222, and Dijksterhuis, Archimedes, 363) exceed in multitude the number of sand having a magnitude equal to the mentioned sphere, when the following are supposed.
[18] … Thus, it is obvious that the multitude of sand having a magnitude equal to the sphere of the fixed stars which Aristarchus supposes is smaller than 1000 myriads of the eighth numbers.
[19] King Gelon, to the many who have not also had a share of mathematics I suppose that these will not appear readily believable, but to those who have partaken of them and have thought deeply about the distances and sizes of the earth and sun and moon and the whole world this will be believable on the basis of demonstration. Hence, I thought that it is not inappropriate for you too to contemplate these things.
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.
If the Sandreckoner convinces you that Archimedes rejected heliocentrism, fine, whatever, but it sure doesn’t talk about parallax.
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.
Aristarchus using a large universe is evidence that he thought about parallax. It is not evidence that his opponents thought about parallax.
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.
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.
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?
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?
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?
The very question is whether the critics made good arguments. You are assuming the conclusion.
It’s assuming the conclusion to think critics agreed with Aristarchus’s criticism of a naive heliocentric theory?
Yes, Archimedes says that Aristarchus’s position is a minority. Not dubious. I do not see that in the quotes at all.
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?
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?
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.
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.
You have not explained why Aristarchus would make his universe so large if the criticisms were as bogus as some of Copernicus’s critics. Shits and giggles?
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.
If he rejects heliocentrism, as he clearly does, it does not matter for your original argument why exactly.
You still have not addressed the quotes from Sand Reckoner I gave which clearly show Archimedes rejects heliocentrism and describes it as a minority rejected position and he only draws on Aristarchus as a worst-case a fortiori argument. Far from being a weak argument from silence (weak because while we lack a lot of material, I don’t think we lack so much material that they could have seriously maintained heliocentrism without us knowing; absence of evidence is evidence of absence), your chosen Sand Reckoner example shows the opposite.
If this is the best you can do, I see no reason to revise the usual historical scenario that heliocentrism was rejected because any version consistent with observations had absurd consequences.
Aristarchus made the universe big because he himself thought about parallax. Maybe some critic first made this objection to him, but such details are lost to time, and uninteresting to compared to the question of the response to the complete theory.
As to the rest, I abandon all hope of convincing you. I ask only that any third parties read the whole exchange and not trust Gwern’s account of my claims.
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.
The sun revolves around the earth.
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?
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?
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.
You have not explained why Aristarchus would make his universe so large if the criticisms were as bogus as some of Copernicus’s critics. Shits and giggles?
If he rejects heliocentrism, as he clearly does, it does not matter for your original argument why exactly.
You still have not addressed the quotes from Sand Reckoner I gave which clearly show Archimedes rejects heliocentrism and describes it as a minority rejected position and he only draws on Aristarchus as a worst-case a fortiori argument. Far from being a weak argument from silence (weak because while we lack a lot of material, I don’t think we lack so much material that they could have seriously maintained heliocentrism without us knowing; absence of evidence is evidence of absence), your chosen Sand Reckoner example shows the opposite.
If this is the best you can do, I see no reason to revise the usual historical scenario that heliocentrism was rejected because any version consistent with observations had absurd consequences.
Aristarchus made the universe big because he himself thought about parallax. Maybe some critic first made this objection to him, but such details are lost to time, and uninteresting to compared to the question of the response to the complete theory.
As to the rest, I abandon all hope of convincing you.
I ask only that any third parties read the whole exchange and not trust Gwern’s account of my claims.
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.