I have not read Kuhn’s work, but I have read some Ptolemy, and if I recall correctly he is pretty careful not to claim that the circles in his astronomy are present in some mechanical sense. (Copernicus, on the other hand, literally claims that the planets are moved by giant transparent spheres centered around the sun!)
In his discussion of his hypothesis that the planets’ motions are simple, Ptolemy emphasizes that what seems simple to us may be complex to the gods, and vice versa. (This seems to me to be very similar to the distinction between concepts that are verbally simple and concepts that are mathematically simple, which EY and others have referenced repeatedly here and at OB.) And while the device of the Equant* is fairly simple mathematically, it would raise so many mechanical complications that Copernicus rejected it, not because it’s inaccurate, but because he considered it too mechanically complicated.
Ptolemy also tended to demonstrate equivalence between two ways of accounting for observations, which again suggests that he was not trying to describe the mechanics of the planets’ motion, but rather only the mathematics of their motion.
I am not familiar with later Geocentric astronomy, and it may for all I know be the case that later thinkers thought that the epicycles had their own existence and moved the planets mechanically, but the history of astronomy is a little more complex than the popular account of the Copernican revolution would suggest.
If anything, Copernicus’s insight was to permit the mathematics to inform his physical judgment rather than the other way around. Ptolemy rejected the heliocentric hypotheses intentionally and explicitly on common-sense grounds. Copernicus permitted the famous Ptolemaic coincidences (e.g. the fact that all the planets’ epicycles tend to follow the mean motion of the sun) to suggest the sun as a more simple and natural center.
*The Equant is a device for describing planets whose uneven motion relative to the earth cannot be adequately accounted for by eccentricity and epicycles. In essence, Ptolemy assigns three centers to the planet’s motion. One is the earth (the point of observation), another is the center of the circle the planet describes in space (the eccenter), and the third is the point with respect to which the angular motion of the planet is constant (i.e. the planet would appear to be revolving at a uniform rate if observed from this third point).
From what I’ve heard and read, Ptolemy was a believer in the “shut up and calculate” interpretation of astronomical mechanics. If the equations make accurate predictions, the rest doesn’t matter, right?
Bohr took a similar attitude toward quantum mechanics when Einstein complained about it not making any sense: the “meaning” or “underlying reality” simply isn’t important—the only thing that matters is whether or not the equations work.
Considering that, in the end, the Earth does go around the Sun, there are some fascinating lessons to be derived from all this.
In particular—yes, the Gods may have a different notion of simplicity, as ’twere, but unless you can exhibit that alternative notion of simplicity, it seems we should still penalize hypotheses that sure look complicated.
Would it have been better for Ptolemy to forego the epicycles and suggest that the planets describe simple circles around the earth? Not only would that have been less accurate, but it would have obscured the coincidences that enabled later astronomers like Copernicus to take a god’s eye view and notice that a heliocentric framework was a much simpler interpretation of the data.
My point is that complexity was not the problem. If Ptolemy had tried on purpose to make his model less complex, it would likely have come at the expense of accuracy. The problem was that Ptolemy had too much common sense, and was not willing to let the math dictate his physics rather than the other way around.
Considering that, in the end, the Earth does go around the Sun,
I offer this linknot as any sort of pedantic correction, but simply as a resource for those interested in learning exactly what modern physics has to say about this question. (Not difficult; highly recommended.)
(An ulterior motive for posting this is that I always have a terrible time tracking down that particular post.)
Of course, most of the observation that led to people thinking that the Sun goes around the Earth in the first place was based on the Earth’s rotation on its axis, so that’s a whole different issue.
I have not read Kuhn’s work, but I have read some Ptolemy, and if I recall correctly he is pretty careful not to claim that the circles in his astronomy are present in some mechanical sense. (Copernicus, on the other hand, literally claims that the planets are moved by giant transparent spheres centered around the sun!)
In his discussion of his hypothesis that the planets’ motions are simple, Ptolemy emphasizes that what seems simple to us may be complex to the gods, and vice versa. (This seems to me to be very similar to the distinction between concepts that are verbally simple and concepts that are mathematically simple, which EY and others have referenced repeatedly here and at OB.) And while the device of the Equant* is fairly simple mathematically, it would raise so many mechanical complications that Copernicus rejected it, not because it’s inaccurate, but because he considered it too mechanically complicated.
Ptolemy also tended to demonstrate equivalence between two ways of accounting for observations, which again suggests that he was not trying to describe the mechanics of the planets’ motion, but rather only the mathematics of their motion.
I am not familiar with later Geocentric astronomy, and it may for all I know be the case that later thinkers thought that the epicycles had their own existence and moved the planets mechanically, but the history of astronomy is a little more complex than the popular account of the Copernican revolution would suggest.
If anything, Copernicus’s insight was to permit the mathematics to inform his physical judgment rather than the other way around. Ptolemy rejected the heliocentric hypotheses intentionally and explicitly on common-sense grounds. Copernicus permitted the famous Ptolemaic coincidences (e.g. the fact that all the planets’ epicycles tend to follow the mean motion of the sun) to suggest the sun as a more simple and natural center.
*The Equant is a device for describing planets whose uneven motion relative to the earth cannot be adequately accounted for by eccentricity and epicycles. In essence, Ptolemy assigns three centers to the planet’s motion. One is the earth (the point of observation), another is the center of the circle the planet describes in space (the eccenter), and the third is the point with respect to which the angular motion of the planet is constant (i.e. the planet would appear to be revolving at a uniform rate if observed from this third point).
From what I’ve heard and read, Ptolemy was a believer in the “shut up and calculate” interpretation of astronomical mechanics. If the equations make accurate predictions, the rest doesn’t matter, right?
Bohr took a similar attitude toward quantum mechanics when Einstein complained about it not making any sense: the “meaning” or “underlying reality” simply isn’t important—the only thing that matters is whether or not the equations work.
Considering that, in the end, the Earth does go around the Sun, there are some fascinating lessons to be derived from all this.
In particular—yes, the Gods may have a different notion of simplicity, as ’twere, but unless you can exhibit that alternative notion of simplicity, it seems we should still penalize hypotheses that sure look complicated.
Would it have been better for Ptolemy to forego the epicycles and suggest that the planets describe simple circles around the earth? Not only would that have been less accurate, but it would have obscured the coincidences that enabled later astronomers like Copernicus to take a god’s eye view and notice that a heliocentric framework was a much simpler interpretation of the data.
My point is that complexity was not the problem. If Ptolemy had tried on purpose to make his model less complex, it would likely have come at the expense of accuracy. The problem was that Ptolemy had too much common sense, and was not willing to let the math dictate his physics rather than the other way around.
I offer this link not as any sort of pedantic correction, but simply as a resource for those interested in learning exactly what modern physics has to say about this question. (Not difficult; highly recommended.)
(An ulterior motive for posting this is that I always have a terrible time tracking down that particular post.)
And the Sun does go around the Earth.
Of course, most of the observation that led to people thinking that the Sun goes around the Earth in the first place was based on the Earth’s rotation on its axis, so that’s a whole different issue.