These theories only differ in their prediction of whether we should be able to observe stellar parallaxes.
This surprised me, but I think I figured out what it means. Basically, we know that we can predict the movement of things inside the solar system equally well whether we put the Earth or the Sun at the center of our calculations page. But if the stars are rotating in a circle around the center of our calculations page, then we’d see parallax from the Earth if the Sun were at the center and we’d see parallax from the Sun if the Earth were are the center. But neither theory predicts that we’d see parallax from both the Sun and the Earth!
That is, maybe I’m too much in the Newtonian-Einsteinian paradigm, but it seems to me like heliocentrism vs. geocentrism is fundamentally confused / asking the wrong question; it assumes there’s a privileged “origin point” to the map of the world when that’s actually a model parameter not related to any predictions. (The computationally simplest option for predicting the dynamics of the solar system, putting it at the center of mass of the solar system, isn’t really “orbiting around the sun” because the sun also has an orbit around the center of mass.) The deep conceptual breakthrough here isn’t that the sun is in the middle, it’s that the underlying laws are position-invariant, and thus you can abstract away the position.
That is, I think I don’t agree with your central claim that they were right to be heliocentric, because heliocentrism is only slightly less mistaken than geocentrism on the next level of clarity, and doesn’t appear to be meaningfully so. The actual advances were in mathematical modeling, and I’m not convinced that it was more than a coincidence that Kepler was a heliocentric. He was converted to that theory for theological reasons as a teenager, well over a decade before he had Brahe’s superior data. Note that Kepler didn’t try the elliptical orbit for years because he thought it was so simple that someone else must have tried it before—if Brahe had tried it, it would have been seen as a significant success for the Tychonic system, as Mars’s orbit around the Sun would be well-explained, and the Sun’s orbit around the Earth could be explained similarly.
It’s a very interesting and controversial claim that heliocentrists were not really any more justified, epistemically, than the geocentrists. I will have to think more about that.
I feel like it might benefit from some additional clarification, because of the trap Asimov points at here:
John, when people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.
It seems to me like there are about six important advances relevant to astronomical phenomena:
Periodic, predictable motion
Circular motion
Elliptical motion
Inverse square law
No privileged reference frame
The metric tensor / general relativity
Most of those are approximations to later principles--2 is an approximation to 3, which is an exact solution to 4, but 4 is only an approximation to 6. (This also isn’t the end of knowledge; I haven’t included things here that a working cosmologist would, let alone a future physicist.)
My view is that the geocentrists and heliocentrists (as factions) are both stuck in having just 1+2, and openly contradicting 5. That says the interesting questions are: how did Kepler come up with 3, how did Newton come up with 4, and how did Einstein come up with 5 and 6?
Even there the answer might sometimes be luck, as opposed to good thinking skill. One could imagine a version of Kepler who thought ellipses were theologically significant, and tried to apply them to everything, and discovered that they happened to work for astronomy. This doesn’t seem like a strategy worth stealing, whereas the strategy of “get good data, and try lots of functions on the data” does seem like a good strategy worth stealing. (And we can see Kepler’s mistake of not doing the Occamian thing and recognize that it was a mistake.)
This view looks like it has two weaknesses. First, the list of six things that I picked. The scale of the universe didn’t make the list, but might seem comparably important to 5. The position of the center of mass of the solar system also didn’t make the list, because ‘center of mass’ isn’t an interesting concept until you have conservation of momentum. (Since Aristarchus people have known the sun was bigger than the Earth, but until you understood gravitation, why would that be inconsistent with the sun moving around the Earth?) But I don’t think there’s a thing that could be added to the list such that the heliocentrists have clearly made an advance that the others haven’t.
Second, the claim that heliocentrists and geocentrists both openly contradict 5. In retrospect, many present heliocentrism as giving up on Earth’s privileged position, which is one of the inferential steps towards thinking that there’s no privileged position. But it’s not clear to me that this is the right way to view things; in particular, it seems important to distinguish the statements “the Earth isn’t special” from “the Sun is more special than the Earth.” My second-hand understanding is that Copernicus wouldn’t endorse the Copernican Principle. (One could point to Bruno or Galileo or so on as pointing towards this advance, but they don’t get credit for empirically discriminating between possibilities, much like Democritus doesn’t get credit for proving that matter is made of atoms.)
It’s worth noting that Kepler had the intuition that the motions of the planets ought to be produced by distinct lines of force adding up to regular curves—much as Galileo points out that constant acceleration is enough to cause mundane objects to fall in parabolic curves. But he didn’t quite have enough math to formalize this persuasively—that had to wait until Newton.
Likewise, ellipses are more difficult to work with than circles, until something like Cartesian analytic geometry lets you formalize them simply without any direct reference to conic sections.
This surprised me, but I think I figured out what it means. Basically, we know that we can predict the movement of things inside the solar system equally well whether we put the Earth or the Sun at the center of our calculations page. But if the stars are rotating in a circle around the center of our calculations page, then we’d see parallax from the Earth if the Sun were at the center and we’d see parallax from the Sun if the Earth were are the center. But neither theory predicts that we’d see parallax from both the Sun and the Earth!
That is, maybe I’m too much in the Newtonian-Einsteinian paradigm, but it seems to me like heliocentrism vs. geocentrism is fundamentally confused / asking the wrong question; it assumes there’s a privileged “origin point” to the map of the world when that’s actually a model parameter not related to any predictions. (The computationally simplest option for predicting the dynamics of the solar system, putting it at the center of mass of the solar system, isn’t really “orbiting around the sun” because the sun also has an orbit around the center of mass.) The deep conceptual breakthrough here isn’t that the sun is in the middle, it’s that the underlying laws are position-invariant, and thus you can abstract away the position.
That is, I think I don’t agree with your central claim that they were right to be heliocentric, because heliocentrism is only slightly less mistaken than geocentrism on the next level of clarity, and doesn’t appear to be meaningfully so. The actual advances were in mathematical modeling, and I’m not convinced that it was more than a coincidence that Kepler was a heliocentric. He was converted to that theory for theological reasons as a teenager, well over a decade before he had Brahe’s superior data. Note that Kepler didn’t try the elliptical orbit for years because he thought it was so simple that someone else must have tried it before—if Brahe had tried it, it would have been seen as a significant success for the Tychonic system, as Mars’s orbit around the Sun would be well-explained, and the Sun’s orbit around the Earth could be explained similarly.
It’s a very interesting and controversial claim that heliocentrists were not really any more justified, epistemically, than the geocentrists. I will have to think more about that.
I feel like it might benefit from some additional clarification, because of the trap Asimov points at here:
It seems to me like there are about six important advances relevant to astronomical phenomena:
Periodic, predictable motion
Circular motion
Elliptical motion
Inverse square law
No privileged reference frame
The metric tensor / general relativity
Most of those are approximations to later principles--2 is an approximation to 3, which is an exact solution to 4, but 4 is only an approximation to 6. (This also isn’t the end of knowledge; I haven’t included things here that a working cosmologist would, let alone a future physicist.)
My view is that the geocentrists and heliocentrists (as factions) are both stuck in having just 1+2, and openly contradicting 5. That says the interesting questions are: how did Kepler come up with 3, how did Newton come up with 4, and how did Einstein come up with 5 and 6?
Even there the answer might sometimes be luck, as opposed to good thinking skill. One could imagine a version of Kepler who thought ellipses were theologically significant, and tried to apply them to everything, and discovered that they happened to work for astronomy. This doesn’t seem like a strategy worth stealing, whereas the strategy of “get good data, and try lots of functions on the data” does seem like a good strategy worth stealing. (And we can see Kepler’s mistake of not doing the Occamian thing and recognize that it was a mistake.)
This view looks like it has two weaknesses. First, the list of six things that I picked. The scale of the universe didn’t make the list, but might seem comparably important to 5. The position of the center of mass of the solar system also didn’t make the list, because ‘center of mass’ isn’t an interesting concept until you have conservation of momentum. (Since Aristarchus people have known the sun was bigger than the Earth, but until you understood gravitation, why would that be inconsistent with the sun moving around the Earth?) But I don’t think there’s a thing that could be added to the list such that the heliocentrists have clearly made an advance that the others haven’t.
Second, the claim that heliocentrists and geocentrists both openly contradict 5. In retrospect, many present heliocentrism as giving up on Earth’s privileged position, which is one of the inferential steps towards thinking that there’s no privileged position. But it’s not clear to me that this is the right way to view things; in particular, it seems important to distinguish the statements “the Earth isn’t special” from “the Sun is more special than the Earth.” My second-hand understanding is that Copernicus wouldn’t endorse the Copernican Principle. (One could point to Bruno or Galileo or so on as pointing towards this advance, but they don’t get credit for empirically discriminating between possibilities, much like Democritus doesn’t get credit for proving that matter is made of atoms.)
It’s worth noting that Kepler had the intuition that the motions of the planets ought to be produced by distinct lines of force adding up to regular curves—much as Galileo points out that constant acceleration is enough to cause mundane objects to fall in parabolic curves. But he didn’t quite have enough math to formalize this persuasively—that had to wait until Newton.
Likewise, ellipses are more difficult to work with than circles, until something like Cartesian analytic geometry lets you formalize them simply without any direct reference to conic sections.
Newton has 5 for everything except the weird speed of light anomaly that Einstein exploited.
What do you mean by “Newtonian-Einsteinian paradigm”? Galileo invented relativity and Newton rejected it.