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Thread: Ptolemy and Copernicus

  1. #121
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    But I think they just meant a Michelson interferometer. You split a beam and test the time to traverse two separate paths, in the laboratory. It won't help you resolve planets, but it will help you test for absolute motion-- if you don't know relativity.

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    Quote Originally Posted by Ken G View Post
    But I think they just meant a Michelson interferometer. You split a beam and test the time to traverse two separate paths, in the laboratory. It won't help you resolve planets, but it will help you test for absolute motion-- if you don't know relativity.
    Good point, but simply changing the light source to that of the planets would demonstrate Doppler patterns that would allow astronomers to note the Ptolemy's model fallacies. They wouldn't even have to know about Doppler if they would correlate known variations found for the Moon and compare these to the point-source planets' behaviors.
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    Quote Originally Posted by George View Post
    Good point, but simply changing the light source to that of the planets would demonstrate Doppler patterns that would allow astronomers to note the Ptolemy's model fallacies. They wouldn't even have to know about Doppler if they would correlate known variations found for the Moon and compare these to the point-source planets' behaviors.
    I'm still in the other camp!
    Quote Originally Posted by grapes View Post
    No, if you believe that one is true, you can find ways to work out the pesky details.

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    Quote Originally Posted by George View Post
    Good point, but simply changing the light source to that of the planets would demonstrate Doppler patterns that would allow astronomers to note the Ptolemy's model fallacies. They wouldn't even have to know about Doppler if they would correlate known variations found for the Moon and compare these to the point-source planets' behaviors.
    Which fallacies are you referring to, the geocentric nature or his method of dealing with the eccentricities? Or perhaps not having the orbits scaled properly?

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    Quote Originally Posted by Hornblower View Post
    Which fallacies are you referring to, the geocentric nature or his method of dealing with the eccentricities? Or perhaps not having the orbits scaled properly?

    “The third day is concerned with the astronomical arguments for and against Copernicus, and here Galileo is downright dishonest. That to ‘save’ the planets’ apparent stations and retrogressions, Ptolemy had to introduce ‘very great epicycles’ which Copernicus was able to dispense ‘with one single motion of the Earth.’ But he breathes not a word about the fact that Copernicus, too, needs a whole workshop full of epicycles; he keeps silent about the eccentricity of the orbits, the various oscillations and librations, the fact that the sun is neither in the center of the motions, nor lies in their plane; in a word, he deliberately evades the real problems of astronomy which had started Tycho and Kepler on their quest. Moreover, he keeps silent about the fact that the Tychonic system fits the phenomena equally well. He employs his usual tactics of refuting his opponent’s thesis without proving his own; in this case not by sarcasm, but by confusing the issue” (Arthur Koestler The Sleepwalkers, p483 re the 3rd day of arguments in The Dialogue on the Two Great World Systems).

  6. #126
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    Quote Originally Posted by wd40 View Post
    “The third day is concerned with the astronomical arguments for and against Copernicus, and here Galileo is downright dishonest. That to ‘save’ the planets’ apparent stations and retrogressions, Ptolemy had to introduce ‘very great epicycles’ which Copernicus was able to dispense ‘with one single motion of the Earth.’ But he breathes not a word about the fact that Copernicus, too, needs a whole workshop full of epicycles; he keeps silent about the eccentricity of the orbits, the various oscillations and librations, the fact that the sun is neither in the center of the motions, nor lies in their plane; in a word, he deliberately evades the real problems of astronomy which had started Tycho and Kepler on their quest. Moreover, he keeps silent about the fact that the Tychonic system fits the phenomena equally well. He employs his usual tactics of refuting his opponent’s thesis without proving his own; in this case not by sarcasm, but by confusing the issue” (Arthur Koestler The Sleepwalkers, p483 re the 3rd day of arguments in The Dialogue on the Two Great World Systems).
    wd40

    You seem to be making a habit of just posting quotes from others. Individually they are fine, but it can be a little frustrating to others. It would be nice, in the above example, if you just simply answered Hornblower's question in
    your own words, or explained in your own words how the quote expresses your ideas on the matter.
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  7. #127
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    It seems to me what all these quotes are doing is saying that Galileo was not giving the correct argument for preferring Copernicus' model. I think that's true, if all he said was that the Copernican model describes simpler orbits, rather than what we now know to be the correct reasons for preferring it (given in post 2 of this thread, which is that it is by far the more unifying model).

    It's actually mathematically obvious that simplicity-of-orbits does not favor Copernicus, that argument can be dispensed in a stroke by simply saying that if some Copernican-type model gives the orbit of the first six planets in the form of six vector functions rMer(t), rV(t), rE(t), rM(t), rJ(t), and rS(t), then a Ptolemaic-type model could give them with precisely the same six functions but now in the form rMer-rE(t), rV(t)-rE(t), 0, rM(t)-rE(t), rJ(t)-rE(t), and rS(t)-rE(t). So whatever complexity are in those six functions are there in both systems. One can object that in the Ptolemaic system, the same function appears 5 times, whereas only once in the Copernican, but if we count all the artificial satellites now orbiting Earth, it makes the Ptolemaic one the simpler model by that same argument! And indeed it is simpler to use geocentric coordinates when describing those artificial satellites, without reopening the Galilean debate because that was never really what the Galilean debate was about-- even if Galileo himself did not anticipate a potential future involving droves of artificial satellites. When all one is doing is comparing the simplicity of two coordinate systems, the winner depends on context-- it is not any kind of fundamental aspect of one model over the other. Thus, simplicity of coordinate system is the wrong reason to favor the Copernican model. The authors you are quoting could have just said that, but in the next breath, being sure to point out the right reasons for favoring Copernican-type models.

    As is very common in science, we require the improved perspective of hindsight to appreciate the actual stakes in Galileo's debate. So that's what these quotes should all be saying-- the actual stakes, which were spectacularly important and gave birth to modern astronomy, were not quite what the people of the day thought, including Galileo and Copernicus themselves. But it is clear that those two men could tell it was an important distinction, and sure enough, it was. The most important thing Galileo did was use actual observations to adjudicate between the systems, and had we lived in a universe where his observations favored the Ptolemaic perspective instead (notwithstanding Whitrow's point about the importance of which observations were available), one can hardly imagine more far-reaching implications for astronomy.
    Last edited by Ken G; 2018-Mar-12 at 01:57 PM.

  8. #128
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    Quote Originally Posted by Hornblower View Post
    Which fallacies are you referring to, the geocentric nature or his method of dealing with the eccentricities? Or perhaps not having the orbits scaled properly?
    Yes, it's the scaling that would prove erroneous as a result of his use of his equant. Ptolemy's model, as Fitzpatrick makes note, produced erroneous apparent sizes of the planets as they orbited the Earth, though, without a telescope, only small variations for the Moon and Sun would be the only two noted if studied. Had Ptolemy offset the Earth by one equant and the radius vector center by one equant opposite the center then he would have had a more accurate model (pg. 8 of the paper) and the apparent sizes would be much less erroneous. Thus, the motions to and from Earth for each object would be exaggerated by the model and an interferometer would demonstrate this error. The Tychonic model would be a far better match and further support this 17th century hypothetical MM result favoring geocentricity over Cop., which was the original, and correct, claim quoted earlier. This MM experiment would also discredit the rotation of the Earth, I suppose.
    Last edited by George; 2018-Mar-12 at 02:26 PM.
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    Quote Originally Posted by wd40 View Post
    “The third day is concerned with the astronomical arguments for and against Copernicus, and here Galileo is downright dishonest. That to ‘save’ the planets’ apparent stations and retrogressions, Ptolemy had to introduce ‘very great epicycles’ which Copernicus was able to dispense ‘with one single motion of the Earth.’ But he breathes not a word about the fact that Copernicus, too, needs a whole workshop full of epicycles; he keeps silent about the eccentricity of the orbits, the various oscillations and librations, the fact that the sun is neither in the center of the motions, nor lies in their plane; in a word, he deliberately evades the real problems of astronomy which had started Tycho and Kepler on their quest. Moreover, he keeps silent about the fact that the Tychonic system fits the phenomena equally well. He employs his usual tactics of refuting his opponent’s thesis without proving his own; in this case not by sarcasm, but by confusing the issue” (Arthur Koestler The Sleepwalkers, p483 re the 3rd day of arguments in The Dialogue on the Two Great World Systems).
    But this may be nit-pickin' since Galileo wrote this to argue for Copernicus, and his choice to use dialgoue form was to have this work reach everyone, not just physicists of his day. Phrases like "equally well" and, for our posts, "simpler" are too subjective. All three models have warts, but Cop seems to me to be less ugly. If we consider elegance (e.g. retrograde explanation and no equants) and unification as important distinctions, then Cop's model is much prettier. Kepler adding equants to the epicycles for Ptolemy indicates he gave Ptolemy's model great effort, yet he dropped it and went with Cop's. I'm still unclear just what both models would look like if we apply today's distances to each object and eccentricity, though I haven't read Fitzpatrick's work, which would help, no doubt.
    Last edited by George; 2018-Mar-12 at 03:26 PM. Reason: grammar
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    Quote Originally Posted by Ken G View Post
    The most important thing Galileo did was use actual observations to adjudicate between the systems, and had we lived in a universe where his observations favored the Ptolemaic perspective instead (notwithstanding Whitrow's point about the importance of which observations were available), one can hardly imagine more far-reaching implications for astronomy.
    Adjudicate is an appropriate word for what he was doing after he had falsified the theory. I wonder if Koestler made note that Galileo took a 1600 year theory and put it in a coffin with great efficacy --- one nail.

    Koestler is correct, from what I recall in the many books I've read on Galileo, that Galileo all but ignored the Tychonic model and likely for good reasons.

    Ok, I don't know the good reasons but here are some thoughts on his reluctance to address Tycho's model:

    1) It was ad hoc. [Was Galileo the father of eschewing ad hocness, too? Probably not, but the stakes seem very high in this case.]
    2) He knew Kepler dumped Tycho's model, and Kep worked for the guy!
    3) Tycho's model somewhat diminished one of Galileo's big discoveries -- objects orbit about other objects (i.e. moons of Jupiter). If the other planets orbit the big Sun, why not allow the Earth as well?
    4) The Occam approach would also support #3.
    5) Attacking Tycho's model, in bombastic style for The Dialogue, might further inflame the Jesuits who quickly adopted the Tychonic model. It would likely take time to win them over and he knew he had a number of enemies in that camp. It was likely worse than he had imagined, as it turned out.
    6) Cop was not just a Catholic, but a respected church canon. [His brother also was a canon and his sister a nun. Tycho was Lutheran, perhaps mainly by marriage.]
    7) Elegance and unification are greater for Cop's model.
    Last edited by George; 2018-Mar-12 at 04:03 PM.
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  11. #131
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    Quote Originally Posted by George
    Yes, it's the scaling that would prove erroneous as a result of his use of his equant. Ptolemy's model, as Fitzpatrick makes note, produced erroneous apparent sizes of the planets as they orbited the Earth, though, without a telescope, only small variations for the Moon and Sun would be the only two noted if studied. Had Ptolemy offset the Earth by one equant and the radius vector center by one equant opposite the center then he would have had a more accurate model (pg. 8 of the paper) and the apparent sizes would be much less erroneous. Thus, the motions to and from Earth for each object would be exaggerated by the model and an interferometer would demonstrate this error. The Tychonic model would be a far better match and further support this 17th century hypothetical MM result favoring geocentricity over Cop., which was the original, and correct, claim quoted earlier. This MM experiment would also discredit the rotation of the Earth, I suppose.
    Quote Originally Posted by George
    But this may be nit-pickin' since Galileo wrote this to argue for Copernicus, and his choice to use dialgoue form was to have this work reach everyone, not just physicists of his day. Phrases like "equally well" and, for our posts, "simpler" are too subjective. All three models have warts, but Cop seems to me to be less ugly. If we consider elegance (e.g. retrograde explanation and no equants) and unification as important distinctions, then Cop's model is much prettier. Kepler adding equants to the epicycles for Ptolemy indicates he gave Ptolemy's model great effort, yet he dropped it and went with Cop's. I'm still unclear just what both models would look like if we apply today's distances to each object and eccentricity, though I haven't read Fitzpatrick's work, which would help, no doubt.
    Well, which is it? Have you read the paper or not? Please explain.

    As a matter of fact it is my understanding from Fitzpatrick and other sources that Ptolemy did use the optimum construction for the deferents of the outer planets, with the equant and the Earth at distances ea from the center of the circle. (e is the eccentricity, a is the semimajor axis.) Only with the Sun did he use the inferior Hipparchus construction, with Earth at distance 2e from the center. He got away with it because there was no practical way to measure the Sun's angular diameter variations with any certainty. I don't know what he did with the Moon. Fitzpatrick did not go into details, and my attempt at reading Encyclopaedia Brittanica's English translation of the Almagest got nowhere, for reasons that are consistent with Fitzpatrick's remarks. Another source said that Ptolemy kludged the excessive angular diameter variation out of his model by piling on more terms in a manner that really outraged Copernicus.

  12. #132
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    Quote Originally Posted by Hornblower View Post
    Well, which is it? Have you read the paper or not? Please explain.
    I have only read the first part of his work but not all this work, and what I've read I don't fully understand. We could easily do a lengthy thread parsing his entire paper, and it might be interesting to do so. [I don't have a lot of free time to be very active if we do, unfortunately.]

    As a matter of fact it is my understanding from Fitzpatrick and other sources that Ptolemy did use the optimum construction for the deferents of the outer planets, with the equant and the Earth at distances ea from the center of the circle. (e is the eccentricity, a is the semimajor axis.) Only with the Sun did he use the inferior Hipparchus construction, with Earth at distance 2e from the center. He got away with it because there was no practical way to measure the Sun's angular diameter variations with any certainty.
    Thanks for correcting me that the model comparison (Fig. 1.1) is only for the Sun, I forgot about that fact.

    Here is Fitzpatrick's paper.

    Fitzpatrick notes six "errors" for Ptolemy's model (I don't fully understand what he's saying, admittedly):
    1) The use of the equant, which entails the center for the radial vectors... Fig. 1.1. [Applies only to the Sun.]
    2) He neglected the non-uniform "rotation" of the superior planets along their epicycles. [The epicycles represent the Earth's orbit for the outer planets, the deferent applies to the inner planets.]
    3) Should have neglected his non-uniform rotation of the epicycle centers.
    4) His lunar model, though ingenious for a complicated orbit, puts the Moon's distance off by almost a factor of 2, which would be a problem visually due to inaccuracy found in the apparent size for the Moon.
    5) Misalignment of certain orbital planes.
    6) "Scale invariance." He could determine the radii ratios of deferents to epicycles, but not the relative sizes of the deferents of different planets.

    Another source said that Ptolemy kludged the excessive angular diameter variation out of his model by piling on more terms in a manner that really outraged Copernicus.
    That's interesting and would be consistent with one reason why I think he [Cop] developed his model. I am fairly sure I read of at least two serious efforts to correct the tables, perhaps while he was in college. [I also think he was in and out of college for a period of about 12 years, but I could be wrong. I'm curious if this is true because it would be yet another fun fact. How many today make it in 8 semesters?]
    Last edited by George; 2018-Mar-13 at 02:46 PM.
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  13. #133
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    Quote Originally Posted by George View Post
    I have only read the first part of his work but not all this work, and what I've read I don't fully understand. We could easily do a lengthy thread parsing his entire paper, and it might be interesting to do so. [I don't have a lot of free time to be very active if we do, unfortunately.]

    Thanks for correcting me that the model comparison (Fig. 1.1) is only for the Sun, I forgot about that fact.

    Here is Fitzpatrick's paper.

    Fitzpatrick notes six "errors" for Ptolemy's model (I don't fully understand what he's saying, admittedly):
    I empathize with you. Even with Fitzpatrick's modernized and cleaned-up presentation it can be a bear to grasp.

    1) The use of the equant, which entails the center for the radial vectors... Fig. 1.1. [Applies only to the Sun.]
    In figure 1.1 the right construction, which Ptolemy actually used for the Sun,
    gives a good match for the angular velocity as the author showed geometrically around the middle of the paper, but gives too much variation in the distance from the Earth. At the low eccentricity here he got away with it because he probably had no means of measuring the Sun's angular diameter with the necessary precision. What's ironic, if I understood Fitzpatrick correctly, is that Copernicus did the same thing for the Sun, violating his own conviction that the same system for dealing with eccentricity should be used for everything. How and why he let that slip through the cracks is a mystery to me.

    2) He neglected the non-uniform "rotation" of the superior planets along their epicycles. [The epicycles represent the Earth's orbit for the outer planets, the deferent applies to the inner planets.]
    3) Should have neglected his non-uniform rotation of the epicycle centers.
    4) His lunar model, though ingenious for a complicated orbit, puts the Moon's distance off by almost a factor of 2, which would be a problem visually due to inaccuracy found in the apparent size for the Moon.
    Without seeing an intelligible sketch of what Ptolemy did here, I cannot judge him fairly one way or another. In hindsight I can see that if he had started with an equant-regulated eccentric circle with e about 0.05, he could have brought the residual irregularities down to an amplitude of a little over a degree. That could have been dealt with by means of some small epicycles which would not have caused much discrepancy in the Moon's distance. The Arab astronomer Ibn al-Shatir did just that during the Middle Ages and Copernicus did likewise not long afterward.*

    5) Misalignment of certain orbital planes.
    6) "Scale invariance." He could determine the radii ratios of deferents to epicycles, but not the relative sizes of the deferents of different planets.

    That's interesting and would be consistent with one reason why I think he [Cop] developed his model. I am fairly sure I read of at least two serious efforts to correct the tables, perhaps while he was in college. [I also think he was in and out of college for a period of about 12 years, but I could be wrong. I'm curious if this is true because it would be yet another fun fact. How many today make it in 8 semesters?]
    * https://en.wikipedia.org/wiki/Lunar_theory

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    Quote Originally Posted by Hornblower View Post
    Even with Fitzpatrick's modernized and cleaned-up presentation it can be a bear to grasp.In figure 1.1 the right construction, which Ptolemy actually used for the Sun, gives a good match for the angular velocity as the author showed geometrically around the middle of the paper, but gives too much variation in the distance from the Earth.
    What makes it a good match? I suppose there might not be much variance, but... using the uniform velocity along the deferent for the Ptolemy model (right in Fig 1.1), wouldn't this produce an excess in angular velocity at perihelion, too slow at aphelion?

    At the low eccentricity here he got away with it because he probably had no means of measuring the Sun's angular diameter with the necessary precision.
    If my math is correct, and if we use today's eccentricity of e = 0.167 [typo, should be 0.0167] for the equant, then the Ptolmey model would produce only about 1 arcminute (1.14') in diameter larger at perihelion than the Fitzpatrick model, which I assume is the accurate one. [I don't know what value would have been derived in the days of Copernicus in using Ptolemy's model.] This would have been difficult to notice unless Ptolemy's values were much greater.

    I will have time later to digest your interesting, subsequent comments. There is a slight chance I can come to grips with much of Fitzpatrick's views.
    Last edited by George; 2018-Mar-14 at 02:24 PM.
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    Stephen Hawking RIP's interesting take on Copernicus:

    "It was quite a shift in our view of the universe: If we are not at the center, is our existence of any importance? Why should God or the laws of nature care about what happens on the third rock from the sun, which is where Copernicus has left us? Modern scientists have out-Copernicused Copernicus by seeking an account of the universe in which man (in the old prepolitically correct sense) played no role.
    Although this approach has succeeded in finding objective impersonal laws that govern the universe, it has not (so far at least) explained why the universe is the way it is rather than being one of the many other possible universes that would also be consistent with the laws. Many people (myself included) feel that the appearance of such a complex and structured universe from simple laws requires the invocation of something called the anthropic principle, which restores us to the central position we have been too modest to claim since the time of Copernicus" (On the shoulders of giants pxi).

    Hawking wrote this in 2002. Has anything since then changed the current informed thinking in the astronomical world on Copernicus?
    Last edited by wd40; 2018-Mar-14 at 09:55 AM.

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    Quote Originally Posted by George View Post
    What makes it a good match? I suppose there might not be much variance, but... using the uniform velocity along the deferent for the Ptolemy model (right in Fig 1.1), wouldn't this produce an excess in angular velocity at perihelion, too slow at aphelion?

    If my math is correct, and if we use today's eccentricity of e = 0.167 for the equant, then the Ptolmey model would produce only about 1 arcminute (1.14') in diameter larger at perihelion than the Fitzpatrick model, which I assume is the accurate one. [I don't know what value would have been derived in the days of Copernicus in using Ptolemy's model.] This would have been difficult to notice unless Ptolemy's values were much greater.

    I will have time later to digest your interesting, subsequent comments. There is a slight chance I can come to grips with much of Fitzpatrick's views.
    It falls apart at the large eccentricity in figure 1.1. The Hipparchus construction, which Ptolemy erroneously used for the Sun, is not even close here. The equant construction does better, but is still way off. Only at low eccentricity as with most of the planets do we get agreement within an arcminute or so for the deferent longitude.

    Correction: The Earth's orbital eccentricity is about 0.0167, 1/10 of what you gave. At that low level, the fit was good with naked eye observations in ancient times.

    The place to go in Fitzpatrick's paper is pages 67-73. I took equations 4.29 and 4.33 for Ptolemy and Copernicus, and wrote them into Excel to make precise calculations at any eccentricity. I did not bother with Hipparchus because we have already concluded that it is inferior because of the distance discrepancy. In addition I found a calculator for Kepler here: http://www.jgiesen.de/kepler/kepler1.html
    You can use the truncated expansions for very small eccentricity or Newton for any value.

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    Quote Originally Posted by Hornblower View Post
    It falls apart at the large eccentricity in figure 1.1. The Hipparchus construction, which Ptolemy erroneously used for the Sun, is not even close here. The equant construction does better, but is still way off. Only at low eccentricity as with most of the planets do we get agreement within an arcminute or so for the deferent longitude.
    Although geometrically speaking the orbits are not perfect circles, they are not perfect ellipses either, but precess at different rates and contain various eccentricities. Is Sir Fred correct here re heliocentric longitude?

    "The planetary orbits are not strictly ellipses, as we have so far taken them to be, because one planet disturbs the order of another through the gravitational force that it exerts. In all cases the orbits are nearly circles. It is curious that although the actual orbits do not differ in shape much from circles the errors of a circular model can nevertheless be quite large. Indeed, errors as large as this were quite unacceptable to Greek astronomers of the stature of Hipparchus and Ptolemy. It was this, rather than prejudice, which caused them to reject the simply heliocentric theory of Aristarchus. The Hipparchus theory grapples with the facts whereas the circular picture of Aristarchus fails to do so. The theory of Ptolemy, a few minor imperfections apart, worked correctly to the first order in explaining the planetary eccentricities. Copernicus with his heliocentric theory had to do at least as well as this, which meant that he had to produce something much better than the simple heliocentric picture of Aristarchus. Kepler achieved improvements, but not complete success, and always at the expense of increasing complexity. Kepler and his successors might well have gone on in this style for generations without arriving at a satisfactory final solution, for a reason we now understand clearly. There is no simple mathematical expression for the way in which the direction of a planet – its heliocentric longitude – changes with time. Even today we must express the longitude as an infinite series of terms when we use time as the free variable. What Ptolemy, Copernicus, and Kepler, in his early long calculations, were trying to do was to discover by trial and error the terms of this series. Since the terms become more complicated as one goes to higher orders in the eccentricity, the task became successively harder and harder." (Nicolaus Copernicus: an essay on his life and work p11, 73)
    Last edited by wd40; 2018-Mar-14 at 01:06 PM.

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    Quote Originally Posted by wd40 View Post
    Hawking wrote this in 2002. Has anything since then changed the current informed thinking in the astronomical world on Copernicus?
    Not so much has changed in terms of our astronomical knowledge, but there remains in Hawkings' comments the problem of just what is the "anthropic principle" in the first place. There are many versions of this "principle," so we have to guess a bit (without more context) as to just which one Hawking is referring to. We need to supply an interpretation that fits with the rest of what Hawking is saying, while still allowing the statements to be correct.

    I can give this a go. It sounds like what Hawking did there was to imagine all the possible ways that the universe could have been, in terms of different laws instead of different initial conditions (so now treating laws as though they could be varied the way we imagine initial conditions can), and marveling at why the laws we find are the way they are. In effect, marveling at why the universe is the way it is. When one does this, one is often confronted with the problem of "fine tuning," in that small deviations in the laws and the parameters the laws use (things like h, c, G, and e) would seem to make lt impossible for any intelligent life to be in this universe. In the Copernican context, this problem is reminiscent of the problem of how special and rare the attributes of the Earth would appear to be (for example, that it has kept liquid oceans for billions of years despite myriad environmental challenges). How has such a perfect Earth been selected for us, and how has such a perfect universe?

    The anthropic principle that Hawking refers to says that we needn't wonder why the Earth and the universe are so special, because the universe is so large (and possibly, so many are all the "other universes" we cannot see) that we would have to find ourselves on just the special planet in the special universe that allows us to exist. Wondering "why" is a bit like, if a lottery was held and 100 people in the entire planet were randomly chosen to survive and all the rest were put to death, the 100 randomly chosen ones could wonder why them. To themselves, they are special, but it's kind of an illusion of their selection-- the process guaranteed there would be survivors, and that they would feel special, so there's really nothing to wonder about. So that's what the anthropic principle does, it removes the wondering by saying an illusion of specialness has been created by some kind of selection process that was guaranteed to generate that illusion.

    Now, to continue to interpret Hawking's comment, we must also understand what he means by Copernicus' legacy. He cannot simply mean the idea that the Earth is not in a special location in the universe, for even if one thinks anthropically, the "anthro" has to include any species of higher intelligence (defined as intelligent enough to be having some version of this very conversation), and there is no reason to doubt that such species can be sprinkled about all over the spatial locations and ages of our universe. So although the Earth is rare, it is not unique in the sense that a center of the universe would need to be. Scientifically, it means we can still understand the Earth better by putting it into a broader context of all those other earths.

    But this does not appear to be the way Hawking is interpreting the Copernican legacy when he concludes it is "too modest." He must be talking not about the place of the Earth in the context of the rest of the universe, but rather, the place of our universe in the context of all those other possible ones (whether or not you regard those other ones as "real," a concept that is difficult to clarify or defend in that context). He is saying that if our universe is special in the sense that it allows higher intelligence, while the vast majority of hypothetical or potential universes do not, then it is indeed our presence (and here I must interpret "us" to include all higher intelligence) that makes our universe special-- we are the reason the laws are the way they are, for we are the ones that have culled out this universe just by being in it.

    Assuming my interpretation of what he is saying is correct, where I differ from his perspective is that I don't actually count that as a break from the Copernican principle. I regard the Copernican principle as a principle for unification within this universe only, because I regard it as a scientific principle for our use in this universe-- not a metaphysical claim that is meant to unify all universes. I think the goal to unify our own universe is a key scientific goal, but I think the goal to unify all the universes is not. That's because the goal of unification is to unify all that is observed, and thereby separate or distinguish it from all that is not observed, so we have lost sight of our mission if we think the job of science is to unify all that is observed with all that is not observed, and even cannot be observed because it could not support enough intelligence to observe it. We are not trying to understand everything we can imagine observing, we are trying to understand what we do observe. Hence unification of what we actually observe is the tool for us, and nothing beyond that should be regarded as "Copernican" if we want to regard that as a scientific perspective.

    Ironically, I think the main value of anthropic thinking is how it helps us understand why we understand the universe in the way we do, rather than understanding "the universe itself" (in contrast, say, with "other universes themselves", a notion that is even more potentially self-contradicting than the idea of "our universe itself"). We understand it in terms of simple laws because that is all we are capable of understanding. Is it any coincidence that the most profound laws we have been so far able to glean are exactly difficult enough that only the sharpest minds our species has yet produced are able to fully understand the laws those very minds have discovered? Just look at the laws we have-- some are so simple that almost any child comes to understand them quickly (laws like gravity makes objects fall, or causes lead to effects), others are difficult enough that only students capable of doing calculus can really use them, and still others are so difficult that only a small collection of our best mathematical minds can see how to use them. How remarkable-- the laws of the universe span exactly the range of what our range of human minds can understand! Sounds like marveling at why the universe was chosen to be the way it was, doesn't it? We see, yet again, the illusion of specialness that is inevitable to the process-- it is simply the process of looking for laws that was always guaranteed to convey the illusion that the laws we find are remarkably well suited to our intelligence.

    So given my take on this, we would say that the Copernican principle is not too modest, it is smack on. The most general way to state this principle is that there exists selection processes that will inevitably convey the illusion of specialness upon what has been selected, much like the process of holding a lottery and choosing one person to win hundreds of millions of dollars, knowing both that there will be a winner, and that whoever is that winner is going to feel pretty darn special. But actually they are just like all the other lottery winners that will accumulate over the years, and when placed into the context of all the hypothetical ways those lotteries could have played out so far as the "laws of lotteries" is concerned, they are not special at all. What is important is not that we are special, it is that we have a perspective-- and it is always the nature of having a perspective that is guaranteed to convey the illusion of specialness. That's what I would call the Copernican legacy, even if most have still not quite got the lesson yet.
    Last edited by Ken G; 2018-Mar-14 at 02:22 PM.

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    Quote Originally Posted by wd40 View Post
    Stephen Hawking RIP's interesting take on Copernicus:

    "It was quite a shift in our view of the universe: If we are not at the center, is our existence of any importance? Why should God or the laws of nature care about what happens on the third rock from the sun, which is where Copernicus has left us? Modern scientists have out-Copernicused Copernicus by seeking an account of the universe in which man (in the old prepolitically correct sense) played no role.
    Although this approach has succeeded in finding objective impersonal laws that govern the universe, it has not (so far at least) explained why the universe is the way it is rather than being one of the many other possible universes that would also be consistent with the laws. Many people (myself included) feel that the appearance of such a complex and structured universe from simple laws requires the invocation of something called the anthropic principle, which restores us to the central position we have been too modest to claim since the time of Copernicus" (On the shoulders of giants pxi).

    Hawking wrote this in 2002. Has anything since then changed the current informed thinking in the astronomical world on Copernicus?
    It was sad to learn of his departure this morning. My wife told me that a number of years ago when asked if there was anything that had stumped him he replied, "Yes, women". [I did get to join him during a luncheon with about 20 folks. I didn't get to explain the Sun's color to him, much to everyone's relief. ]

    The idea of mankind not being at the center of the universe is hardly illogical, though some resisted such a notion, especially after Dante's work, I suppose. Why wouldn't God be at the center? The physical is not the spiritual, but how we see and handle the material serves metaphorically for the spiritual and there are countless examples. Discovering life on other planets will also not be a huge shock to the religious world, IMO, for the same reason. "Everything has its beauty, but not everyone sees it." (Confucius) It's not the structure of a house (Earth) that makes a loving home. [I'm sure someone has said this.]

    Copernicus, Kepler, Galileo were the key players in getting the ball rolling, so to speak. They were are all religious. Kepler was very strong in his Lutheran faith, which was opposed strongly by the Catholicism of which Copernicus and Galileo were members. "The bible teaches us how to go to heaven, not how the heavens go" (Galileo, who was quoting Cardinal Baronius).
    Last edited by George; 2018-Mar-14 at 03:14 PM.
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    Quote Originally Posted by Hornblower View Post
    Correction: The Earth's orbital eccentricity is about 0.0167, 1/10 of what you gave. At that low level, the fit was good with naked eye observations in ancient times.
    Oops, yes but it was typo so about 1 arcminute for the Sun should still be accurate, assuming they used something close to the equant value.
    Last edited by George; 2018-Mar-14 at 04:13 PM.
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    Quote Originally Posted by Ken G View Post
    Assuming my interpretation of what he is saying is correct, where I differ from his perspective is that I don't actually count that as a break from the Copernican principle. I regard the Copernican principle as a principle for unification within this universe only, because I regard it as a scientific principle for our use in this universe-- not a metaphysical claim that is meant to unify all universes.
    I think even Copernicus would like this view. I certainly do.

    We are not trying to understand everything we can imagine observing, we are trying to understand what we do observe. Hence unification of what we actually observe is the tool for us, and nothing beyond that should be regarded as "Copernican" if we want to regard that as a scientific perspective.
    Nice. Metaphysics can breed ideas and it can be fun, but it should never dilute true science, even if unintentionally.

    Ironically, I think the main value of anthropic thinking is how it helps us understand why we understand the universe in the way we do, rather than understanding "the universe itself" (in contrast, say, with "other universes themselves", a notion that is even more potentially self-contradicting than the idea of "our universe itself"). We understand it in terms of simple laws because that is all we are capable of understanding. Is it any coincidence that the most profound laws we have been so far able to glean are exactly difficult enough that only the sharpest minds our species has yet produced are able to fully understand the laws those very minds have discovered? Just look at the laws we have-- some are so simple that almost any child comes to understand them quickly (laws like gravity makes objects fall, or causes lead to effects), others are difficult enough that only students capable of doing calculus can really use them, and still others are so difficult that only a small collection of our best mathematical minds can see how to use them. How remarkable-- the laws of the universe span exactly the range of what our range of human minds can understand! Sounds like marveling at why the universe was chosen to be the way it was, doesn't it? We see, yet again, the illusion of specialness that is inevitable to the process-- it is simply the process of looking for laws that was always guaranteed to convey the illusion that the laws we find are remarkably well suited to our intelligence.
    Yep. Who doesn't pick the low-hanging fruit first especially when very few can climb higher? Nevertheless, when I consider the efficacy of what we do know and what we can do, it's as if we are at a sweet spot in intelligence. Perhaps exospecies that are far more intelligent may too often find themselves out of balance with wisdom, or perhaps silence really is golden and their silence comes from being too amused with us, especially given our, no doubt, superior sense of humor.

    So given my take on this, we would say that the Copernican principle is not too modest, it is smack on. The most general way to state this principle is that there exists selection processes that will inevitably convey the illusion of specialness upon what has been selected, much like the process of holding a lottery and choosing one person to win hundreds of millions of dollars, knowing both that there will be a winner, and that whoever is that winner is going to feel pretty darn special. But actually they are just like all the other lottery winners that will accumulate over the years, and when placed into the context of all the hypothetical ways those lotteries could have played out so far as the "laws of lotteries" is concerned, they are not special at all. What is important is not that we are special, it is that we have a perspective-- and it is always the nature of having a perspective that is guaranteed to convey the illusion of specialness. That's what I would call the Copernican legacy, even if most have still not quite got the lesson yet.
    Well said. The illusions have varied all over the place. The early ages saw the universe consisting of only a few useful objects and only mankind in it, along with spiritual beings. Then we imagined life, even sentient life, on all the planets, which goes back only a few decades (e.g. Lowell). That view has become as frozen as the outer planets, yet, perhaps surprisingly, with improved vision for sentient life elsewhere given our very new knowledge of the likely number of expolanets. We now seem hopeful in discovering who those lottery winners besides us are.
    Last edited by George; 2018-Mar-14 at 04:16 PM.
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    Quote Originally Posted by wd40 View Post
    Although geometrically speaking the orbits are not perfect circles, they are not perfect ellipses either, but precess at different rates and contain various eccentricities. Is Sir Fred correct here re heliocentric longitude?

    "The planetary orbits are not strictly ellipses, as we have so far taken them to be, because one planet disturbs the order of another through the gravitational force that it exerts. In all cases the orbits are nearly circles. It is curious that although the actual orbits do not differ in shape much from circles the errors of a circular model can nevertheless be quite large. Indeed, errors as large as this were quite unacceptable to Greek astronomers of the stature of Hipparchus and Ptolemy. It was this, rather than prejudice, which caused them to reject the simply heliocentric theory of Aristarchus. The Hipparchus theory grapples with the facts whereas the circular picture of Aristarchus fails to do so. The theory of Ptolemy, a few minor imperfections apart, worked correctly to the first order in explaining the planetary eccentricities. Copernicus with his heliocentric theory had to do at least as well as this, which meant that he had to produce something much better than the simple heliocentric picture of Aristarchus. Kepler achieved improvements, but not complete success, and always at the expense of increasing complexity. Kepler and his successors might well have gone on in this style for generations without arriving at a satisfactory final solution, for a reason we now understand clearly. There is no simple mathematical expression for the way in which the direction of a planet – its heliocentric longitude – changes with time. Even today we must express the longitude as an infinite series of terms when we use time as the free variable. What Ptolemy, Copernicus, and Kepler, in his early long calculations, were trying to do was to discover by trial and error the terms of this series. Since the terms become more complicated as one goes to higher orders in the eccentricity, the task became successively harder and harder." (Nicolaus Copernicus: an essay on his life and work p11, 73)
    I would say yes, Sir Fred (whoever) is correct in saying that the planets' heliocentric longitudes differ measurably from pure Kepler ellipses at modern levels of precision, but I think it is beyond the scope of comparing the merits of the Ptolemy, Copernicus and Kepler models as they stood before Newton's lifetime. For fitting the arcminute level of precision at the time Kepler is decisively the best. Only the Moon remained seriously out of line, and it is my understanding that Kepler labored mightily to develop an empirical model for it after finding the planets in good agreement with the pure ellipse. If I understand it correctly, a slowly precessing Keplerian reference ellipse is a good starting point for a modern empirical model that accounts for the perturbations.

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    Quote Originally Posted by Hornblower View Post
    I would say yes, Sir Fred (whoever) is correct in saying that the planets' heliocentric longitudes differ measurably from pure Kepler ellipses at modern levels of precision, but I think it is beyond the scope of comparing the merits of the Ptolemy, Copernicus and Kepler models as they stood before Newton's lifetime. For fitting the arcminute level of precision at the time Kepler is decisively the best. Only the Moon remained seriously out of line, and it is my understanding that Kepler labored mightily to develop an empirical model for it after finding the planets in good agreement with the pure ellipse. If I understand it correctly, a slowly precessing Keplerian reference ellipse is a good starting point for a modern empirical model that accounts for the perturbations.
    Addendum: According to an article in Sky and Telescope back in 1971, along with some Wiki references, Kepler derived a model for the Moon about 1620, at least 11 and possibly 16 or more years after finding the ellipse and equal-area laws for Mars. I am not surprised at that. What puzzles me is why it took him so long to find the third law, which gives the period-radius formula.

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    Quote Originally Posted by Hornblower View Post
    What puzzles me is why it took him so long to find the third law, which gives the period-radius formula.
    That's an interesting question. [I have a book on Kepler that I can revisit this weekend that may help.]

    Your question made me ask how many laws of physics were known to Kepler? In other words, was there understanding in his days that laws could be suddenly regarded as low-hanging fruit. Ignoring math and geometric laws, and looking only for laws of physics, a cursory Google search only presents Ibn Sahl of the 10th century who established what we call Snell's law of refraction. Oddly enough, this did not resurface until Thomas Harriot rediscovered it but never published his work. However, he did happen to correspond with at least one interesting fellow...Johannes Kepler. Did this serve to encourage law-making for Kepler? Perhaps not, but curious, ain't it? [Snellius (of Snel's or Snell's law) was soon afterward, 1621.]
    Last edited by George; 2018-Mar-16 at 02:38 PM.
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    Quote Originally Posted by George View Post
    That's an interesting question. [I have a book on Kepler that I can revisit this weekend that may help.]

    Your question made me ask how many laws of physics were known to Kepler? In other words, was there understanding in his days that laws could be suddenly regarded as low-hanging fruit. Ignoring math and geometric laws, and looking only for laws of physics, a cursory Google search only presents Ibn Sahl of the 10th century who established what we call Snell's law of refraction. Oddly enough, this did not resurface until Thomas Harriot rediscovered it but never published his work. However, he did happen to correspond with at least one interesting fellow...Johannes Kepler. Did this serve to encourage law-making for Kepler? Perhaps not, but curious, ain't it? [Snellius (of Snel's or Snell's law) was soon afterward, 1621.]
    What do you mean by "law of physics" that is not mathematical or geometric in nature? Snell's law certainly looks like a mathematical exercise to me.

    Back to orbital mechanics. The act of finding a mathematical relation between the period of a planet and the radius of its orbit certainly looks easy to us in hindsight, but perhaps Kepler had not yet learned to think in the ways we take for granted today. I am imagining that his mental vision could have been impaired by the fog of archaic ideas about mathematical truth inherited from the likes of Pythagoras and his merry band of number crunchers. In the early 17th century he was still not far removed from that idea that the nested Platonic solids might have anything more than coincidental to do with the number of planets and the pattern of their orbital radii.

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    Quote Originally Posted by Hornblower View Post
    What do you mean by "law of physics" that is not mathematical or geometric in nature? Snell's law certainly looks like a mathematical exercise to me.
    I mean the more literal view of physics directly as in a physical process, and not quite as indirectly applied. Pythagoras' right triangle equation for example is more mathematical that can be applied to physical objects, of course, but it is more a tool than a specific law for a process or phenomena. No physical observations are required for most mathematical rules and laws, I think. Snell's law, without observation, would never have come to us. It is a law that addresses a specific phenomena, just as Kepler's three laws are all due to the force of gravity, as Newton realized.

    Back to orbital mechanics. The act of finding a mathematical relation between the period of a planet and the radius of its orbit certainly looks easy to us in hindsight, but perhaps Kepler had not yet learned to think in the ways we take for granted today. I am imagining that his mental vision could have been impaired by the fog of archaic ideas about mathematical truth inherited from the likes of Pythagoras and his merry band of number crunchers. In the early 17th century he was still not far removed from that idea that the nested Platonic solids might have anything more than coincidental to do with the number of planets and the pattern of their orbital radii.
    That is likely true. I wonder how I would have done it given the same "fog"? I suppose I would chart the planet's position along the ellipse and look for any hint of a consistent pattern of motion, especially related to the radial vector, foccii, center, etc. The accurate data from Tycho may have given him the confidence he could accomplish something special no other had done before, with the double bonus of discovering that their orbits are ellipses. He likely had to research all the geometry and math for this, which would have delayed him partially. His personal life also became wild and wooly for a period, and I think this rough road was during this time frame.

    [Added: It is also curious that Galileo's inclined plane experiments giving the form of s = t2 were prior to Kepler's 3rd law.]
    Last edited by George; 2018-Mar-16 at 08:58 PM.
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    I did dig-up Kepler's Witch (Connor). Kepler practiced astrology, but it was more as a placebo/nocebo effect, as I understand his view of it, and not an actual direct physical influence upon mankind. Kepler even looked for a physical explanation of the orbits, perhaps after determining the perfect circle view of Cop and Ptolemy didn't work. I don't know much of Gilbert's influence upon him but it seems fair to assume he was aware of his work with magnetism. In fact, Kepler made the leap that planetary motions were a result of motion due to a physical force -- magnetism. He also held that this magnetic force was an inverse relationship with distance, which is impressive. Kepler, as Ken has noted, preferred Cop's model because it treated the planets as a whole and not a set of circumstances for each planet; unification, using Ken's word. With his view of a physical process (ie magnetism) he rejected Tycho's model since the Sun would be the dominant force driver, thus the Earth would necessarily be a mere planet as well. I suspect Kepler's public views against Tycho served Galileo in that Galileo could simply direct others to Kepler rather than step on more toes of the Jesuits and others who favored Tycho after Ptolemy was debunked.
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    Quote Originally Posted by George View Post
    This MM experiment would also discredit the rotation of the Earth, I suppose.
    It would be interesting to see what they would have made in that era of the null MM combined with the positive MG experiment.
    Last edited by wd40; 2018-Mar-19 at 11:50 AM.

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    Quote Originally Posted by wd40 View Post
    It would be interesting to see what they would have made in that era of the null MM combined with the positive MG experiment.
    What is MG?

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    Quote Originally Posted by Hornblower View Post
    What is MG?


    MM = Michelson-Morley experiment (no translational motion of Earth round Sun detected)

    MG = Michelson-Gale experiment (relative rotation between Earth and cosmos detected)

    Presumably in the Galilean era, such results would have been interpreted as proof positive of the Geocentric model.
    Last edited by wd40; 2018-Mar-19 at 11:05 PM.

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