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parallaxicality
2018-Feb-11, 12:26 AM
As far as I can determine, at least from his Little Commentary (http://dbanach.com/copernicus-commentarilous.htm), Copernicus's big beef with Ptolemy seems to have been his use of the equant. Now, I have read the Almagest, many years ago, but I'm pretty sure that Ptolemy's system only required 12 circles, not the up to 240 claimed by some science writers. (http://www.geocentricity.com/conference/Frank/epicycle_conference_bible_1_final.pdf). Copernicus, at the end of his essay, says that his system requires 34 circles. So, my question is, does a Ptolemaic system without an equant require more circles than Copernicus's? If not, I can't really understand what Copernicus was trying to do.

Ken G
2018-Feb-11, 01:14 AM
If not, I can't really understand what Copernicus was trying to do.I can't speak to the accuracy of either system, other than to say that neither system was at all accurate by today's standards. Neither was the key issue some attempt to get working approximations with the least degree of complexity-- you get what you pay for, so if you want more accuracy, you will need more complexity. Copernicus may have achieved some improved efficiency by having the orbits centered on the correct object, but he gave back a lot of that accuracy by requiring that the orbits be circles, which of course is way off for several planets. I don't think the story of Copernicus vs. Ptolemy should be framed as an attempt to achieve greater accuracy, nor even an attempt to achieve greater simplicity. Instead, this is what I would say it was really all about, even if part of this is in a hindsight that Copernicus did not have access to:

1) By placing the Sun at the center, Copernicus made the first step toward explaining why orbits behave as they do-- in particular, the role of the mass of the object ruling those orbits. In his day, no one knew which had more mass, the Earth or the Sun, but the Sun certainly had a very significant role in the solar system, so it made some degree of sense to allow it to rule the orbits. Of course, later on, it was quite a breakthrough to look for what aspect of the Sun gave it that power.

2) By putting the Earth in motion, Copernicus allowed the Earth to be unified with the other planets. This allowed us to start looking for laws that were obeyed on Earth as a way to understand other planets as well, and even the entire cosmos. This was such a huge breakthrough its importance should never be overlooked.

3) Having the Earth in motion, yet not showing stellar parallax, required that the distant stars be so far away that they themselves were like Suns of their own. This was another vastly important unification of the cosmos, it allowed us to understand other stars by using the Sun as a basic example. It also allowed us to speculate on the possibility of, and then search for, planets around distant stars.

So that's what Copernicus was really doing, I just don't know how much of that he himself actually realized at the time. Certainly the issue of whether a proper coordinate system placed the Earth at the center, or the Sun, was a question that went completely out the window with general relativity. Unfortunately, that last issue tends to be the one many people focus on, though it is utterly irrelevant in comparison to the above three.

wd40
2018-Feb-11, 02:09 AM
The problem for Ptolemy wasn’t epicycles, but was that he didn’t know the distances to the planets. But in place of that ignorance he provided six variables for correction for those who might find the correct distances. Copernicus’ system was more complex since he used 48 epicycles whereas Ptolemy used 40. Do we still use “epicycles” today, but they are called by different names, such as Fourier analysis? It is next to impossible to determine the exact revolutions of the planets due to their constant perturbations. We can estimate them, but they are never exact, since we have no math beyond a three-body problem to calculate them.

Hornblower
2018-Feb-11, 12:30 PM
I don't think Ptolemy's lack of proper distance ratios would have been an issue for the outer planets in his geocentric model, but the light curves of Mercury and Venus would have been seriously at odds with his construction which kept them inside the Sun's sphere. It would appear that he did not pay attention to their brightness variations. For all we know he may not have even recognized that they shine by reflected sunlight.

George
2018-Feb-12, 01:48 AM
Here (http://farside.ph.utexas.edu/Books/Syntaxis/Almagest.pdf) is a nice paper on this topic. Only 6 epicycles and 6 deferents are needed, apparently, given today's knowledge.

Iphone

Hornblower
2018-Feb-13, 03:46 AM
Here (http://farside.ph.utexas.edu/Books/Syntaxis/Almagest.pdf) is a nice paper on this topic. Only 6 epicycles and 6 deferents are needed, apparently, given today's knowledge.

Iphone

Good find, George. Clearly the equant-regulated eccentric circle was an excellent approximation of the Kepler ellipse at the relatively low eccentricities of the planets' orbits. While Copernicus, with his insistence on returning to the ideal of uniform circular motions or combinations thereof, made more sense mechanically in the paradigm which predated a gravitational dynamic theory, it appears that Ptolemy would have been significantly more accurate had he not messed up in some of his constructions.

To demonstrate the idea of making sense mechanically, we could make a mechanical model of the Copernican system with small potter's wheels spinning on bearings that are carried on the rims of larger wheels. The planets would be bright spots on the small wheels. In a thought exercise with no friction, it would run forever once set in motion. Ptolemy would require a rod rotating around the equant, with the planet sliding in and out radially on the rod while riding on a deferent track of some sort. Mechanically it would be a nightmare compared with the Copernican wheels.

parallaxicality
2018-Feb-13, 08:27 AM
Thanks George; that helped a lot :-)

George
2018-Feb-13, 07:00 PM
Good find, George. Clearly the equant-regulated eccentric circle was an excellent approximation of the Kepler ellipse at the relatively low eccentricities of the planets' orbits.Yes, that's interesting since we, or me at least, thought the big break-through was in Kepler's discovery of the elliptical orbits. This improved the accuracy, which was intended to match Tycho's accurate data of about 1 arcminute, though a few objects were about 1/2 arcminute in accuracy. The key is the eccentricity (an offset from Earth for the center of the radial vector).


While Copernicus, with his insistence on returning to the ideal of uniform circular motions or combinations thereof, made more sense mechanically in the paradigm which predated a gravitational dynamic theory, it appears that Ptolemy would have been significantly more accurate had he not messed up in some of his constructions. Since Copernicus did use eccentric orbits by offsetting the center of the orbits from the center of the Sun, I would expect he may have been just as accurate. It seems also, though I haven't read all that I need of the paper, that, like Fitzpatrick's model, the apparent size of the Sun and other objects are a better fit with Cop's model.

wd40
2018-Feb-14, 12:37 PM
Since Copernicus did use eccentric orbits by offsetting the center of the orbits from the center of the Sun, I would expect he may have been just as accurate.

Copernicus' main reason for opposing Ptolemy’s model was not because Ptolemy put the Earth in the center, but because he departed from the Greek practice of using perfect circles to depict the revolutions of the planets:

"In both De revolutionibus and the Commentariolus Copernicus attacks the Ptolemaic astronomy not because in it the sun moves rather than the earth, but because Ptolemy has not strictly adhered to the precept that all celestial motions must be explained only by uniform circular motions or combinations of such circular motions. Ptolemy had recognized that an accurate representation of planetary motion necessitated the abandoning of uniform circular motion, and he boldly introduced what was later called an “equant,” from which non-uniform motion along an arc would appear uniform. From the point of view of accuracy, this was a great step forward, indeed, the best representation of planetary motion before Kepler. But Copernicus considered the use of an equant to be a violation of fundamental principles and devoted his original astronomical research to devising a system of sun, planets, moon, and stars in which the planets and the moon glide with uniform motion along a circle or with some combination of such motions." (I. Bernard Cohen, Revolution in Science, 1994, p.112)

George
2018-Feb-14, 02:48 PM
Copernicus' main reason for opposing Ptolemy’s model was not because Ptolemy put the Earth in the center, but because he departed from the Greek practice of using perfect circles to depict the revolutions of the planets:

"In both De revolutionibus and the Commentariolus Copernicus attacks the Ptolemaic astronomy not because in it the sun moves rather than the earth, but because Ptolemy has not strictly adhered to the precept that all celestial motions must be explained only by uniform circular motions or combinations of such circular motions. Ptolemy had recognized that an accurate representation of planetary motion necessitated the abandoning of uniform circular motion, and he boldly introduced what was later called an “equant,” from which non-uniform motion along an arc would appear uniform. From the point of view of accuracy, this was a great step forward, indeed, the best representation of planetary motion before Kepler. But Copernicus considered the use of an equant to be a violation of fundamental principles and devoted his original astronomical research to devising a system of sun, planets, moon, and stars in which the planets and the moon glide with uniform motion along a circle or with some combination of such motions." (I. Bernard Cohen, Revolution in Science, 1994, p.112) [my bold] But they both used perfect circles, Ptolemy used constant angular motion for the radial vector but offsetting the Earth (equant) from the center of the orbit, which produced the non-uniform motion along the orbit, relative to the Earth. Cop favored uniform motion along the orbit and I assume he thought the equant was ad hoc and without physical reasoning. I am fairly sure each planet had to have its own equant, multiplying ad hocness.

It's interesting to me that Ptolmey's model required, IIRC, two major overhauls to produce usable tables during Cops younger years. These constant updates may have prompted interest in seeking an alternative model. The elegant and simple explanation for retrogrades had to be another big plus when he put his model to work. Having support from others, including one or more cardinals, probably helped as well, at least in moral support.

antoniseb
2018-Feb-14, 03:47 PM
Just as a side note: I don't think that Ptolemy, or Hipparcos thought that celestial objects moved in perfect circles, but rather that perfect circles were easy (or at least possible) to compute, hence the epicycles on circles approach as a good approximation. Kepler's big advance wasn't that he guessed it was ellipses, it was his hard work developing the arithmetic enabling the calculation of positions along the ellipses.

Hornblower
2018-Feb-14, 04:49 PM
Yes, that's interesting since we, or me at least, thought the big break-through was in Kepler's discovery of the elliptical orbits. This improved the accuracy, which was intended to match Tycho's accurate data of about 1 arcminute, though a few objects were about 1/2 arcminute in accuracy. The key is the eccentricity (an offset from Earth for the center of the radial vector).

Since Copernicus did use eccentric orbits by offsetting the center of the orbits from the center of the Sun, I would expect he may have been just as accurate. It seems also, though I haven't read all that I need of the paper, that, like Fitzpatrick's model, the apparent size of the Sun and other objects are a better fit with Cop's model.

The presentation on pp. 71-73 in the paper makes it clear to me that Ptolemy and Copernicus differ from Kepler by the same amount in the position angle calculation, but that Copernicus is off by twice as much in the distance from the Sun. At or near quadrature Copernicus's resultant is about as far outside Ptolemy's circle as that circle is outside the Kepler ellipse. I could see it clearly when drawing the Copernican model with a compass at e = 0.2. That difference between the two models would be immaterial for naked eye or low power telescopic views of the planets from the Sun's position, but when looking at Mars at quadrature with Earth near the Martian line of apsides there would be a significant difference in the angular position of Mars.

The Copernican resultant is approximately an ellipse with its major axis aligned with Kepler's minor axis, and its minor axis coinciding with Kepler's major axis.

Clear as mud? If necessary I can scan and upload some sketches. Sometimes a picture is worth many words.

George
2018-Feb-14, 06:27 PM
Just as a side note: I don't think that Ptolemy, or Hipparcos thought that celestial objects moved in perfect circles, but rather that perfect circles were easy (or at least possible) to compute, hence the epicycles on circles approach as a good approximation. Kepler's big advance wasn't that he guessed it was ellipses, it was his hard work developing the arithmetic enabling the calculation of positions along the ellipses. I'm unsure why perfect circles wouldn't be favored, if not required? Shootin' from the hip...perfection was of above; the simplest path around is a circle; crystaline spheres are spherical (you like that one?); ellipses were exotic geometric shapes occurring only if you cut a cone improperly (georgecentricity running amuck). Why would uniform motion be important if ellipses were tolerated; a crooked path should allow for variable speeds, perhaps?

[Added: Is it just me that hears "eccentric" and an ellipse comes to mind? I had to become clear what they meant by that term since it was used by the Greeks and yet Kepler took several years to install his ellipses.]

George
2018-Feb-14, 06:34 PM
The presentation on pp. 71-73 in the paper makes it clear to me that Ptolemy and Copernicus differ from Kepler by the same amount in the position angle calculation, but that Copernicus is off by twice as much in the distance from the Sun. At or near quadrature Copernicus's resultant is about as far outside Ptolemy's circle as that circle is outside the Kepler ellipse. I could see it clearly when drawing the Copernican model with a compass at e = 0.2. That difference between the two models would be immaterial for naked eye or low power telescopic views of the planets from the Sun's position, but when looking at Mars at quadrature with Earth near the Martian line of apsides there would be a significant difference in the angular position of Mars. A drawing would be helpful and if I had some free time I would like to try it on my own, but time is a problem for me these days.

I think I may be confused on this issue, or perhaps the Sun's size is a separate story. Perhaps I misunderstood the following found near the bottom of page 8 (after the diagram):

"Nevertheless, the Hippachian model is incorrect, since it predicts too large (by a factor
of 2) a variation in the radial distance of the sun from the earth (and, hence, the angular size of the
sun) during the course of a year (see Cha. 4). Ptolemy probabaly adopted the Hipparchian model
because his Aristotelian leanings prejudiced him in favor of uniform circular motion whenever this
was consistent with observations. (It should be noted that Ptolemy was not interested in explaining
the relatively small variations in the angular size of the sun during the year—presumably, because
this effect was difficult for him to accurately measure.)"

antoniseb
2018-Feb-14, 06:35 PM
I'm unsure why perfect circles wouldn't be favored, if not required? Shootin' from the hip...perfection was of above; the simplest path around is a circle; crystaline spheres are spherical (you like that one?); ellipses were exotic geometric shapes occurring only if you cut a cone improperly (georgecentricity running amuck). Why would uniform motion be important if ellipses were tolerated; a crooked path should allow for variable speeds, perhaps?
I'm not sure when perfect crystalline spheres became the meme. but Ptolemy never mentioned it. He was merely trying to explain how to predict where things would be, and was pretty aware that the formulas weren't quite right, especially for Mars and Mercury.

George
2018-Feb-14, 06:51 PM
I'm not sure when perfect crystalline spheres became the meme. but Ptolemy never mentioned it. He was merely trying to explain how to predict where things would be, and was pretty aware that the formulas weren't quite right, especially for Mars and Mercury. Yes. [I just added to my post as you were making this post.] You may be right, but even his epicycles were circles. His equant will produce a tight fit for any ellipse, but the non-uniform motion hurts that modeling except for near-circular orbits, which the Sun and Earth have with one another. If a geometric model without initial physical restraints was used, why not have tried ellipses? That may be asking too much of Ptolmey but he was likely a genius.

ngc3314
2018-Feb-15, 01:27 AM
Good thing Ptolemy et al. liked circular epicycles. A retrograde elliptical epicycle with 2:1 axial ratio does a stunning job of approximation Keplerian motion for even pretty substantial eccentricity (and relaxing the axial ratio and ratio of periods gives a pattern that works well for stellar orbits within galaxies).

Hornblower
2018-Feb-15, 04:36 AM
22959

Here is my sketch. The solid arc is a Kepler ellipse of eccentricity e = 0.2, about that of Mercury. The short-dashed arc is what Ptolemy's circle should have been, here transformed to a heliocentric model and sharing geometric center CPK with the ellipse. The long-dashed arc is Copernicus's circular deferent with an epicycle riding on it and with its geometric center at CC. The radius vectors from the Sun's position to the ellipse are shown for 1/8 and 1/4 of the orbital period from perihelion. The corresponding radius vectors for Ptolemy and Copernicus are plotted with dashed lines.The three dots for each time show where the planet is in the respective model, with Copernicus being the resultant of the deferent and epicycle vectors. As mentioned in the paper, the epicycle revolves in the same direction at twice the rate. To reduce visual clutter, I did not bother to plot the Copernicus resultant arc, but the two points I did plot are clearly about twice as far from the ellipse as are the corresponding Ptolemy points. The Kepler angles were calculated from the author's equation in the paper.

ETA: Use the thumbnail at the top. I don't know how the bottom one got there, and I cannot find a way to delete it.

wd40
2018-Feb-15, 06:17 AM
Clearly the equant-regulated eccentric circle was an excellent approximation of the Kepler ellipse at the relatively low eccentricities of the planets' orbits.

“The equant got Ptolemy into a lot of trouble as far as many of his successors were concerned. It wasn’t that his model didn’t predict the
angular positions satisfactorily. Rather, the equant forced the epicycle to move non-uniformly around the deferent circle, and that was somehow seen as a deviation from the pure principle of uniform circular motion. Ptolemy himself was apologetic about it, but he used it because it generated the motion that was observed in the heavens. Altogether his system was admirably simple considering the apparent
complexity and variety of the retrograde loops” ('The Book that Nobody Read', O.Gingerich p. 53).

George
2018-Feb-15, 04:58 PM
22959

Here is my sketch. The solid arc is a Kepler ellipse of eccentricity e = 0.2, about that of Mercury. The short-dashed arc is what Ptolemy's circle should have been, here transformed to a heliocentric model and sharing geometric center CPK with the ellipse. The long-dashed arc is Copernicus's circular deferent with an epicycle riding on it and with its geometric center at CC. The radius vectors from the Sun's position to the ellipse are shown for 1/8 and 1/4 of the orbital period from perihelion. The corresponding radius vectors for Ptolemy and Copernicus are plotted with dashed lines.The three dots for each time show where the planet is in the respective model, with Copernicus being the resultant of the deferent and epicycle vectors. As mentioned in the paper, the epicycle revolves in the same direction at twice the rate. To reduce visual clutter, I did not bother to plot the Copernicus resultant arc, but the two points I did plot are clearly about twice as far from the ellipse as are the corresponding Ptolemy points. The Kepler angles were calculated from the author's equation in the paper.

ETA: Use the thumbnail at the top. I don't know how the bottom one got there, and I cannot find a way to delete it.
Thanks Hornblower for the graph. I want to study your points closer but thought I would try a few things graphically since it is fairly easy to do and I am pressed for time today.

Your drawing does indeed match the eccentricity you state. The blue dashed line is an ellipse with e = 0.2.

22960

If I try a retrograde epicycle at twice the rotation rate of the deferent, I get...
22961
Perhaps I'm missing something, ngc3314?

But if I use a 1 to 1 rate, I get....
22962

ngc3314
2018-Feb-15, 05:34 PM
Perhaps I'm missing something, ngc3314?


To be clear - same period as the main orbit (guiding center), axial ratio of epicyclic ellipse 2:1 (compressed radially).

Hornblower
2018-Feb-15, 09:23 PM
To be clear - same period as the main orbit (guiding center), axial ratio of epicyclic ellipse 2:1 (compressed radially).

It is not at all clear to me.

1. How is the long axis of the ellipse oriented?

2. Does the radius vector rotate around a point on the deferent at a constant rate?

3. Is that point on the deferent at
a. the center of the ellipse?
b. a focus of the ellipse?
c. neither?

A sketch would help.

Hornblower
2018-Feb-15, 09:47 PM
My sketches cause me to question the author of the paper where he says that Ptolemy and Copernicus are in agreement on the true anomaly when calculated to 2nd order in equations 4.31 and 4.35 respectively. He did not say how small the eccentricity had to be for the approximation to be "good enough", and he did not show how he did the expansions. I am guessing a Taylor series, but it has been 50 years since I studied the technique. If I am not mistaken, that 2nd order expression is truncated from an infinite series. I found an online calculator for Kepler. http://www.jgiesen.de/kepler/kepler1.html It shows the expansion to 5th order along with a Newtonian calculation to 8 decimal places. Taking it to 5th order reduced my true anomaly at 1/4 of the orbital period by about half a degree, with a vanishingly small difference from Newton. Since I don't know how to do the expansion I am unable to test it for Ptolemy and Copernicus, but I could see differences between them in my graphical plots. Those appear to be exact constructions, and the two pairs of points appear to be exactly parallel with the respective deferent radius vectors and thus not aligned with the Sun. Of course I cannot draw to that level of precision but I could see what was happening geometrically.

Hornblower
2018-Feb-16, 01:11 AM
In making some more sketches, I find myself between a rock and a hard place trying to improve the fit between Copernicus and Kepler. In the sketch I posted, the two constructions have the same eccentricity. Copernicus is too slow in angular velocity around the Sun around perihelion, and the resultant orbital radius is too large around the 1/4 point. If I try to speed up the perihelic angular velocity by increasing the eccentricity a bit compared to Kepler, the excess quadrature radius just gets worse. As I understand it, Kepler knew he could kludge these discrepancies out by piling on a series of higher-order small epicycles, but he concluded it was much better as an exercise in physics to find an analytically simple figure that would do the job, thus breaking once and for all with the ideal of uniform circular motion. After some hard mathematical slogging he found that the ellipse regulated by the equal area rule made a good fit with Tycho's positional data.

wd40
2018-Feb-16, 07:45 AM
As I understand it, Kepler knew he could kludge these discrepancies out by piling on a series of higher-order small epicycles, but he concluded it was much better as an exercise in physics to find an analytically simple figure that would do the job, thus breaking once and for all with the ideal of uniform circular motion

"From the time of Newton, it has been known that Kepler’s laws are mere approximations, computer’s fictions, handy mathematical
devices for finding the approximate place of a planet in the heavens. They apply with greater accuracy to some planets than to
others. Jupiter and Saturn show the greatest deviations from strictly elliptical motion. The latter body is often nearly a degree
away from the place it would have been had its motion about the sun been strictly in accord with Kepler’s laws. This is such a
large discrepancy that it can be detected by the unaided eye. The moon is approximately half a degree in diameter, so that the
discrepancy in the motion of Saturn is about twice the apparent diameter of the moon. In a single year, during the course of one
revolution about the sun, the Earth may depart from the theoretical ellipse by an amount sufficient to appreciably change
the apparent place of the sun in the heavens." (Charles Lane Poor, 'Gravitation versus Relativity' p129)

Hornblower
2018-Feb-16, 02:00 PM
"From the time of Newton, it has been known that Kepler’s laws are mere approximations, computer’s fictions, handy mathematical
devices for finding the approximate place of a planet in the heavens. They apply with greater accuracy to some planets than to
others. Jupiter and Saturn show the greatest deviations from strictly elliptical motion. The latter body is often nearly a degree
away from the place it would have been had its motion about the sun been strictly in accord with Kepler’s laws. This is such a
large discrepancy that it can be detected by the unaided eye. The moon is approximately half a degree in diameter, so that the
discrepancy in the motion of Saturn is about twice the apparent diameter of the moon. In a single year, during the course of one
revolution about the sun, the Earth may depart from the theoretical ellipse by an amount sufficient to appreciably change
the apparent place of the sun in the heavens." (Charles Lane Poor, 'Gravitation versus Relativity' p129)

Did Mr. Poor say how much time was required for Saturn to depart by a degree from a best-fit Kepler ellipse? Tycho's data set covered roughly one orbit period of Saturn. Is Mr. Poor saying that Jupiter perturbed Saturn that severely during that time? If so, I think we would have seen mention of it in writings about Kepler.

Jeff Root
2018-Feb-16, 04:30 PM
The way I read that quote, I get the impression that the discrepancy
occurs about once each orbit, and is way, way too big to be just a
perturbation by the other planets. I have no clue what's going on.

-- Jeff, in Minneapolis

Hornblower
2018-Feb-16, 05:09 PM
The way I read that quote, I get the impression that the discrepancy
occurs about once each orbit, and is way, way too big to be just a
perturbation by the other planets. I have no clue what's going on.

-- Jeff, in Minneapolis

My hunch is an unreliable source. As I understand it, Kepler could get a good fit with Tycho's data with a cleaned up Ptolemaic or Copernican construction for Venus, Jupiter and Saturn. I don't know about Mercury, but Tycho would have had a hard time getting good data for most of its orbit. Mars was the rogue because of a double whammy of large eccentricity and close approaches to Earth. His equal area rule ellipse gave him good agreement with Tycho's data for Mars. It did not work for the Moon without adding on some large empirically determined periodic fudge terms, and we now know that severe perturbation by the Sun is the cause. Analogous fudge terms were not needed for the planets at arcminute precision because their mutual perturbations are proportionately vastly smaller.

Hornblower
2018-Feb-18, 03:14 AM
Check out this animation.
http://science.larouchepac.com/kepler/newastronomy/part1/copernicus.html
Some of the 34 circles he announced initially were superfluous by our construction standards. To construct his eccentric deferent he started with a radius vector revolving about the Sun at constant rate. The tip of this vector carried an epicycle vector that rotated retrograde with respect to the deferent vector, thus creating the eccentric circle with a stationary center in a non-rotating frame of reference. This epicycle carried a second smaller epicycle which rotated at twice the rate direct with respect to the other epicycle. Nowadays we reduce the clutter by simply constructing the eccentric circle in the stationary frame of reference.

wd40
2018-Feb-22, 03:04 AM
So, my question is, does a Ptolemaic system without an equant require more circles than Copernicus's? If not, I can't really understand what Copernicus was trying to do.

"It is very important to acknowledge that the Copernican theory offers a very exact calculation of the apparent movements of the planets, even though it must be conceded that, from the modern standpoint practically identical results could be obtained by means of a somewhat revised Ptolemaic system. It makes no sense, accordingly, to speak of a difference in truth between Copernicus and Ptolemy: both conceptions are equally permissible descriptions. What has been considered as the greatest discovery of occidental wisdom, as opposed to that of antiquity, is questioned as to its truth value." ("From Copernicus to Einstein", Hans Reichenbach)

Ken G
2018-Feb-22, 06:18 AM
"It makes no sense, accordingly, to speak of a difference in truth between Copernicus and Ptolemy: both conceptions are equally permissible descriptions. What has been considered as the greatest discovery of occidental wisdom, as opposed to that of antiquity, is questioned as to its truth value." ("From Copernicus to Einstein", Hans Reichenbach)Yet this is what I meant above, when I said that so many people miss the real issue in the geocentric vs. heliocentric models when they focus on accuracy of prediction. The three points I listed in post #2 do indeed represent the "greatest discovery of occidental wisdom", and very much relate to the "truth value" of the Earth's relationship to the rest of the cosmos, with nothing at all to do with accuracy of prediction.

George
2018-Feb-22, 07:02 PM
I wonder, given GR, if it will always be the case that a modified geocentric model can be made to match, perhaps exactly, that of a modified heliocentric model, both including elliptical orbits without restrictions of circles and uniform radial vectors, eccentricity (e.g. equants) allowed? A modified Tychonic model likely is the one to use for the geocentric case.

Ken G
2018-Feb-22, 07:54 PM
I wonder, given GR, if it will always be the case that a modified geocentric model can be made to match, perhaps exactly, that of a modified heliocentric model, both including elliptical orbits without restrictions of circles and uniform radial vectors, eccentricity (e.g. equants) allowed? A modified Tychonic model likely is the one to use for the geocentric case.
That is more or less the defining principle of relativity.

George
2018-Feb-22, 10:49 PM
That is more or less the defining principle of relativity.That's what I thought and it makes it seem logical that the models of Ptolemy and Copernicus would be very close to each other with enough tweaking even for circle-only geometry.

Hornblower
2018-Feb-23, 02:39 PM
That's what I thought and it makes it seem logical that the models of Ptolemy and Copernicus would be very close to each other with enough tweaking even for circle-only geometry.

I'm sorry, but I do not see your logic here. For a two body thought exercise problem a Kepler ellipse is an exact consequence of Newtonian gravity, and a slowly precessing Kepler ellipse is an exceedingly close approach to orbital motion that is a consequence of GR. As I see it, the Ptolemaic and Copernican resultants have no basis in the dynamics of bodies in free fall in either Newton or GR, so the similarities and differences between them and between either one and Kepler are geometric facts that are independent of the dynamic basis for Kepler.

Am I missing something?

Ken G
2018-Feb-23, 03:45 PM
It didn't sound like George was claiming that Ptolemy and Copernicus were both consistent with Keplerian ellipses, it sounded like he was saying that since neither is based on the "correct" dynamics, they can be regarded as equivalent to each other in their ability to approximate the true motion. This comes from the idea that the main difference between Ptolemy and Copernicus is "which object is really stationary," which in relativity is a moot issue anyway. But what I've been saying is, "which object is really stationary" was never the key issue in the confrontation of those models, even though it is often described as the key issue. What is actually the key issue is, which object rules the orbits when we look for a dynamical explanation of those objects, and whether or not the Earth is like other planets, versus something completely different from the other planets. Those issues have nothing to do with coordinate systems or relativity, or even ellipses versus circles, but they are the reason we care if "eppur si muove."

George
2018-Feb-23, 06:53 PM
I'm sorry, but I do not see your logic here. For a two body thought exercise problem a Kepler ellipse is an exact consequence of Newtonian gravity, and a slowly precessing Kepler ellipse is an exceedingly close approach to orbital motion that is a consequence of GR. As I see it, the Ptolemaic and Copernican resultants have no basis in the dynamics of bodies in free fall in either Newton or GR, so the similarities and differences between them and between either one and Kepler are geometric facts that are independent of the dynamic basis for Kepler.

Am I missing something?My point was simply geometric, not kinematic and would need to include a variable radial vector speed, though kinematics would be the next modification required. An epicycle can nearly produce an ellipse, otherwise it would be immediately problematic within GR.

I'm just toying with these models by working backwards starting with GR, which allows any point to be central, then noting that Copernicus, Tycho, and even Ptolemy can use eccentrics and circles to geometrically produce accurate models. Non-constant radial vectors (kinematics) may be less of a problem, however, than all those fictitious forces that would be needed for any cause and effect claims, though Cop would be sitting pretty nice.

George
2018-Feb-23, 07:17 PM
It didn't sound like George was claiming that Ptolemy and Copernicus were both consistent with Keplerian ellipses, it sounded like he was saying that since neither is based on the "correct" dynamics, they can be regarded as equivalent to each other in their ability to approximate the true motion. Well, with an eccentric (equant for Ptolmey and offset(?) for Cop) and epicycles, it is surprising how tight a fit can be made to match an ellipse. I would not bet much on it, but an exact fit might be possible. The calculus to make the kinematics work properly would be too much for my rusty math, however. It is interesting how we can take all three models make them useable, if modified, given the strength of GR.


This comes from the idea that the main difference between Ptolemy and Copernicus is "which object is really stationary," which in relativity is a moot issue anyway. Right, GR is an important aspect to all of this, at least for me, in realizing that neither model necessarily must be considered "wrong" in an unusable way. Galileo forced Ptolemy out but only the Tycho touch was needed to restore it. GR makes this all the more obvious.


But what I've been saying is, "which object is really stationary" was never the key issue in the confrontation of those models, even though it is often described as the key issue. What is actually the key issue is, which object rules the orbits when we look for a dynamical explanation of those objects, and whether or not the Earth is like other planets, versus something completely different from the other planets. Those issues have nothing to do with coordinate systems or relativity, or even ellipses versus circles, but they are the reason we care if "eppur si muove." I think your ideas are correct. I suspect that Ptolemy gave little attention as to what objects might have greater control over others. He worked with what he had and he may have assumed mass was meaningless for those etherial objects above. The Sun was known to be much larger, but how heavy is fire?

Cop, however, numerous times mentions gravity, though not quite the way its used today. IIRC, he argued that size matters and the Sun was the big guy. Given that teleological thinking was very influential, it is that much more impressive he moved forward with his model.

Hornblower
2018-Feb-23, 07:40 PM
Neither Copernicus nor Ptolemy can be made an exact match to Kepler's ellipse. As has been pointed out, for any given eccentricity, Ptolemy's resultant with just the equant is invariably a circle, tangent at the apsides and outside the ellipse as it goes by the minor axis. Copernicus, with just an epicycle, gives an orbit that is elongated even farther from the ellipse at that crossways position. They could be kludged arbitrarily close to matching by piling on more epicycles.

George
2018-Feb-23, 08:37 PM
Neither Copernicus nor Ptolemy can be made an exact match to Kepler's ellipse. As has been pointed out, for any given eccentricity, Ptolemy's resultant with just the equant is invariably a circle, tangent at the apsides and outside the ellipse as it goes by the minor axis. Copernicus, with just an epicycle, gives an orbit that is elongated even farther from the ellipse at that crossways position. They could be kludged arbitrarily close to matching by piling on more epicycles. Geometrically only, the original expansion on your work that I gave is not off, after I tweaked it just now -- I can attach it if you wish -- by more than the tiny width of the blue dashed line. This is also the worst case scenario since e = 0.2 and most planetary eccentricities are more circular. I'm not sure this is in disagreement to what you are saying, however, since getting both the deferent and epicycle radial vectors to behave per Newton's laws might be tricky. Yet wouldn't they be doable, if someone were really stuck on such things?

Copernicus used a center offset from the center of the Sun, so it could be matched with a given, but not too variable, barycenter. The equant, I assume, serves Ptolemy equally well, perhaps. Both methods give eccentric circles and require epicycles to produce an ellipse. Is much more needed?

wd40
2018-Feb-25, 12:55 AM
"The claim for a great simplicity of the Copernican system, as opposed to a great complexity of the Ptolemaic system, must therefore – insofar as the number of circles is concerned – be taken cum grano salis, in fact, with the whole saltcellar. It takes only the most cursory leafing through the pages of De revolutionibus to be struck by Copernicus’ use of epicycles page after page. Even a neophyte will recognize in the diagrams of De revolutionibus and the Almagest a kinship of geometrical methods and constructions that belies any simple claim that Copernicus’s book is in any obvious sense a more modern or a simpler work than Ptolemy’s." (I. Bernard Cohen, Revolution in Science, p119)

Ken G
2018-Feb-25, 01:54 AM
Yes, but simplicity of the orbital shape is not the issue, it's not the simplicity that matters there. See post #2, none of it has to do with simplicity of the orbit itself, it all has to do with the simplicity of the incredibly vast degree of unification that comes with the Copernican approach. Ptolemy does not unify Earth with the planets, it does not unify the Sun with the stars, and it does not unify the laws of physics on Earth with the laws of the evolution of the entire rest of the universe. The Copernican approach goes a very long way to doing all of that. Thus, there was never a more incredibly important simplifying theory in the entire history of astronomy than the Copernican view of the solar system! So why don't these "experts" just pipe down, it's like they have missed the entire point of the Copernican system, which makes me worry they may have also missed the entire point of scientific thinking.

parallaxicality
2018-Feb-25, 08:48 AM
To be fair though Ken, Copernicus didn't do that either; Newton did.

Ken G
2018-Feb-25, 02:34 PM
It's not that Copernicus did it, it's that his model laid the key groundwork (it could actually have happened thousands of years earlier if people had been convinced by Aristarchus). It's not about giving credit to individuals (we could say Galileo did it, but who doubts someone else would have within a century or less), that's of little importance-- what matters is understanding the significance. It's the actual importance of "eppur si muove," which Cohen's quote above appears to completely miss! That's another thing that gets my goat, when historians seem to act like the importance of science is a process of giving credit. This isn't Olympic skating where we need to score the participants, what we need to do is understand the process of discovery and its key watersheds. Few were of so huge a far-reaching (no pun intended) significance as Copernicus' model of the solar system.

wd40
2018-Feb-25, 05:58 PM
That is more or less the defining principle of relativity.

Einstein himself stated:

"The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS [coordinate system] could be used with equal justification. The two sentences: “the sun is at rest and the Earth moves,” or “the sun moves and the Earth is at rest,” would simply mean two different conventions concerning two different CS." (The Evolution of Physics: From Early Concepts to Relativity and Quanta p212, 1966)

Ken G
2018-Feb-25, 06:51 PM
We would need to know the larger context of Einstein's statements, but what I interpret him as saying here is that the aspect of the argument that so many people think was significant, i.e., whether it is the Sun or the Earth that is the one that is "really moving," is not actually significant at all when one understands relativity. But once relativity pulls the rug out from under that idea that it matters which one is in motion in some absolute sense, it opens the space to see what was actually the significance all along. That's what's in post #2, and it has nothing to do with coordinates or accuracy or simplicity of describing the shape of an orbit, it's all about unifying our current view of the cosmos. It's easy to forget that when we look up into the sky, we see something completely different from what just about everyone saw for thousands of years before Copernicus. We see stars like the Sun and imagine planets like the Earth orbiting them-- ponder for a moment how spectacularly different that is from what the ancients saw! A spectacular difference is not at all two different conventions concerning two different coordinate systems.

parallaxicality
2018-Feb-25, 09:11 PM
It's not that Copernicus did it, it's that his model laid the key groundwork (it could actually have happened thousands of years earlier if people had been convinced by Aristarchus). It's not about giving credit to individuals (we could say Galileo did it, but who doubts someone else would have within a century or less), that's of little importance-- what matters is understanding the significance. It's the actual importance of "eppur si muove," which Cohen's quote above appears to completely miss! That's another thing that gets my goat, when historians seem to act like the importance of science is a process of giving credit. This isn't Olympic skating where we need to score the participants, what we need to do is understand the process of discovery and its key watersheds. Few were of so huge a far-reaching (no pun intended) significance as Copernicus' model of the solar system.

My problem with this reasoning Ken, is that Copernicus had no evidence for his idea. Yes, he originated the model in the modern age but one has to wonder if Galileo even needed him. If he hadn't originated the model, would Galileo not likely have come to the same conclusions based on his discoveries (mainly the rotation of the Sun and the phases of Venus)? Ultimately Copernicus was just a name to attach to an idea.

Hornblower
2018-Feb-26, 02:34 AM
We can only guess at how far Galileo would have gone in his celestial thinking without Copernicus to inspire him. He certainly would be my choice to come up with a heliocentric model on his own in such a case. The phases of Mercury and Venus as seen in his telescope would have been a powerful impetus.

I think it is important that Copernicus was thinking like a physicist in seeking a unified model that used the same system for all of the planets rather than Ptolemy's ad hoc methods. While he had no viable dynamic theory (neither did Kepler) he laid the ground work for Newton.

Robert Tulip
2018-Feb-26, 03:19 AM
Copernicus had no evidence for his idea.

The postulated observation that planets are moving objects is itself evidence for heliocentricity. The geocentric system involves the appalling addition of regular loops around the exact points of earth's superior conjunction for the outer planets and inferior conjunction for the inner planets, for objects that give no basis for the conjecture of a cause for such looping, other than saving the phenomena. The inelegance of epicycles is itself evidence for heliocentricity.

Several decades before Copernicus, Leonardo Da Vinci wrote "the sun does not move". (Note 886 (https://www.gutenberg.org/files/5000/5000-8.txt))

Ken G
2018-Feb-26, 07:00 AM
My problem with this reasoning Ken, is that Copernicus had no evidence for his idea.Neither did Aristarchus, which is why it took so long. The reason it happened after Copernicus is that the evidence came. So that's it, Copernicus had a model, and the evidence came. And the result was a spectacular change in how we look at the universe. It's not Copernicus that matters, its the watershed moment. And yes, it wasn't a moment, so much as the start of a process. But that was the start of that process.

Ultimately Copernicus was just a name to attach to an idea.Yes, exactly, but it's the idea that matters, not the name. By now, "Copernicus" is the name of an idea, more than a name of a person. Who knows anything about the person? It's not relevant to science, so we know more about the idea than the individual. That's the double-edged sword of scientific fame.

antoniseb
2018-Feb-26, 11:18 AM
... By now, "Copernicus" is the name of an idea, more than a name of a person. ...
We might not know much about Copernicus at all if Kepler's model with the ellipses hadn't been presented in a paper Kepler named "The New Copernican Astronomy".

grapes
2018-Feb-26, 11:57 AM
The postulated observation that planets are moving objects is itself evidence for heliocentricity. The geocentric system involves the appalling addition of regular loops around the exact points of earth's superior conjunction for the outer planets and inferior conjunction for the inner planets, for objects that give no basis for the conjecture of a cause for such looping, other than saving the phenomena. The inelegance of epicycles is itself evidence for heliocentricity.

Several decades before Copernicus, Leonardo Da Vinci wrote "the sun does not move". (Note 886 (https://www.gutenberg.org/files/5000/5000-8.txt))
Interesting! But there doesn't seem to be any context for the note. From that link:


886.

The sun does not move. [Footnote: This sentence occurs incidentally among mathematical notes, and is written in unusually large letters.]

887.

PROOF THAT THE NEARER YOU ARE TO THE SOURCE OF THE SOLAR RAYS, THE LARGER WILL THE REFLECTION OF THE SUN FROM THE SEA APPEAR TO YOU.

[Footnote: Lines 4 and fol. Compare Vol. I, Nos. 130, 131.] If it is from the centre that the sun employs its radiance to intensify the power of its whole mass, it is evident that the farther its rays extend, the more widely they will be divided; and this being so, you, whose eye is near the water that mirrors the sun, see but a small portion of the rays of the sun strike the surface of the water, and reflecting the form of the sun. But if you were near to the sun—as would be the case when the sun is on the meridian and the sea to the westward—you would see the sun, mirrored in the sea, of a very great size; because, as you are nearer to the sun, your eye taking in the rays nearer to the point of radiation takes more of them in, and a great splendour is the result. And in this way it can be proved that the moon must have seas which reflect the sun, and that the parts which do not shine are land.

Looks like he had a lot of work to do! :)

grapes
2018-Feb-26, 12:01 PM
Einstein himself stated:

"The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS [coordinate system] could be used with equal justification. The two sentences: “the sun is at rest and the Earth moves,” or “the sun moves and the Earth is at rest,” would simply mean two different conventions concerning two different CS." (The Evolution of Physics: From Early Concepts to Relativity and Quanta p212, 1966)
I've quoted this on this board many times, but it's from a book by Einstein and Infeld. As near as I can tell, Infeld wrote it, Einstein approved it, encouraged it, maybe contributed to it--even using it to advance his realism agenda. :)

Ken G
2018-Feb-26, 01:17 PM
We might not know much about Copernicus at all if Kepler's model with the ellipses hadn't been presented in a paper Kepler named "The New Copernican Astronomy".

Good point, sometimes it is the generosity of one person that creates the fame for someone else.

George
2018-Feb-26, 05:17 PM
Einstein himself stated:

"The struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus would then be quite meaningless. Either CS [coordinate system] could be used with equal justification. The two sentences: “the sun is at rest and the Earth moves,” or “the sun moves and the Earth is at rest,” would simply mean two different conventions concerning two different CS." (The Evolution of Physics: From Early Concepts to Relativity and Quanta p212, 1966)I've quoted this on this board many times, but it's from a book by Einstein and Infeld. As near as I can tell, Infeld wrote it, Einstein approved it, encouraged it, maybe contributed to it--even using it to advance his realism agenda. :)
Perhaps one of the best quotes to use to note a key difference between physics and engineering. I doubt many engineers would see any real "equal justification" in spite of the fact of the equality of conventions as established in GR. Cop appears "more equally justified", IMO (engineering-minded only).

wd40
2018-Feb-26, 10:01 PM
The geocentric system involves the appalling addition of regular loops around the exact points of earth's superior conjunction for the outer planets and inferior conjunction for the inner planets, for objects that give no basis for the conjecture of a cause for such looping, other than saving the phenomena. The inelegance of epicycles is itself evidence for heliocentricity.

"But this apparent economy of the Copernican system, though it is a propaganda victory that the proponents of the new astronomy rarely failed to emphasize, is largely an illusion. The seven-circle system presented in the First Book of the De revolutionibus, and in
many modern elementary accounts of the Copernican system, is a wonderfully economical system, but it does not work. It will not predict the position of planets with an accuracy comparable to that supplied by Ptolemy’s system. (Thomas S. Kuhn, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, p169).

This brief sketch of the complex system of Copernicus indicates the third great incongruity of the De revolutionibus and the immense irony of Copernicus’ lifework. The preface to the De revolutionibus opens with a forceful indictment of Ptolemaic astronomy for its
inaccuracy, complexity, and inconsistency, yet before Copernicus’ text closes, it has convicted itself of exactly the same shortcomings. Copernicus’ system is neither simpler nor more accurate than Ptolemy’s. And the methods that Copernicus employed in constructing it
seem just as little likely as the methods of Ptolemy to produce a single consistent solution of the problem of the planets. The De revolutionibus itself is not consistent with the single surviving early version of the system, described by Copernicus in the early manuscript Commentariolus. Even Copernicus could not derive from his hypothesis a single and unique combination of interlocking circles, and his successors did not do so. Judged on purely practical grounds, Copernicus’ new planetary system was a failure; it was neither more accurate nor significantly simpler than its Ptolemaic predecessors" (p171).

George
2018-Feb-26, 10:19 PM
This seems overstated, wd40. Kuhn wrote that in 1957 long before Fitzgerald's work showing that both models can be made fairly accurate if we use modern data.

grapes
2018-Feb-27, 01:59 AM
This seems overstated, wd40. Kuhn wrote that in 1957 long before Fitzgerald's work showing that both models can be made fairly accurate if we use modern data.
I think the focus is on the "Copernicus’ system is neither simpler nor more accurate than Ptolemy’s."

Ken G
2018-Feb-27, 07:02 AM
Yes, that's why it's such a shame that people continue to stress the heliocentric model on grounds that it was simpler, even if they admit it wasn't more accurate. The situation was not at all resolved until Galileo's observations, and it would have been had the heliocentric model really been so much simpler. The final nail in the coffin of geocentrism was the modern detection of stellar parallax, so it is always observations that must adjudicate models.

But let us correct the record here, the actual reason that Copernicus' system was so vastly superior to Ptolemy's, and probably should have been accepted even in the days of the ancients Greeks (had they understood better what we now view as the goals of science), is the way it unifies the planets with Earth and the stars with the Sun. That's very much a 20-20 hindsight kind of statement, but it still speaks to the significance of the heliocentric model. So I beg to differ with Kuhn when he says "Judged on purely practical grounds, Copernicus’ new planetary system was a failure; it was neither more accurate nor significantly simpler than its Ptolemaic predecessors." It seems he has overlooked the fact that there is nothing more practical than being able to use the same laws of physics for other planets that we use on Earth, and the stars as well. Perhaps his remark is intended to be restricted to the nuts and bolts of the model itself, and hopefully he recognizes the larger significance that so dwarfs the importance of those details. But what I'm saying is, as soon as we had a model that allowed the unification of which I speak, we should have grabbed it with both hands, until observations rejected it. It should never have been an issue of how many parameters the model needs, that level of simplification is of trivial importance compared with all the rest!

wd40
2018-Feb-27, 09:00 AM
The final nail in the coffin of geocentrism was the modern detection of stellar parallax, so it is always observations that must adjudicate models.


The geocentrists maintain that both the modified and unmodified Tychonian model can account for parallax.

"People need to be aware that there is a range of models that could explain the observations. For instance, I can construct for you a spherically symmetrical universe with Earth at its center, and you cannot disprove it based on observations. You can only exclude it on philosophical grounds. In my view there is absolutely nothing wrong in that. What I want to bring into the open is the fact that we are
using philosophical criteria in choosing our models. A lot of cosmology tries to hide that." (Profile: George F. R. Ellis, Scientific American, October 1995) ie it is Relativity that has put the nail in both Geocentrism and Heliocentrism (with capitals), but not geocentrism and heliocentrism.

parallaxicality
2018-Feb-27, 11:17 AM
It seems he has overlooked the fact that there is nothing more practical than being able to use the same laws of physics for other planets that we use on Earth, and the stars as well.

Practical how? Without telescopes there is no way to know if such a statement is true. Ultimately until you get observations, such reasoning is philosophical, not scientific.

Ken G
2018-Feb-27, 02:29 PM
Practical how? Without telescopes there is no way to know if such a statement is true. It was practical because it helped motivate the use of telescopes, by motivating similar approaches to discovery that we use on Earth. That's a form of practical-- looking to the future. This is what determines a model that should be embraced-- one that stimulates new discovery. People who held to the Copernican view were so motivated, those who held to the Ptolemaic view were often hesitant to look too closely into the heavens, expressly because they were not thinking scientifically about them. It's practical to motivate looking without fear, consider medicine for example.


Ultimately until you get observations, such reasoning is philosophical, not scientific.Science is philosophy too, it's just philosophy that tries hard to motivate observations and uses those observations as the final arbiter. But just as the better theory is always the simpler one among those that fit the observations, the better theory is also the one that offers the best potential to understand. The cosmological principle is the one that allows us to tell a story that fits the data about the history of the universe, and make new predictions that can be checked. The Copernican principle is like that too, it was more or less the local forerunner to its cosmological grandchild. And that's very practical indeed, which is what I believe these historians are missing. If by "practical", they only mean "of help to a mariner needing to navigate at sea," then yes, the Copernican principle is of little value. But I daresay they are missing the point entirely there.

George
2018-Feb-27, 05:24 PM
I think the focus is on the "Copernicus’ system is neither simpler nor more accurate than Ptolemy’s." But it depends on what we mean by "simpler". I don't really like fictitious forces required in Ptolemy's or Tycho's models.

Ptolemy, apparently, only determined the size ratio of epicycle to deferent but not the size of the deferent (or epicycle) itself.

"Likewise, the ratio of the epicycle radius to that of the deferent for an inferior planet, which is again easily determined observationally, also corresponds to the ratio of the planet’s orbital radius to that of the earth.
Using this type of reasoning, Copernicus was able to construct the first accurate scale model of the solar system, and to firmly establish the order in which the planets orbit the sun. In some sense, this was his main achievement." Fitzgerald

I recall reading that there was some debate with Ptolemy as to whether or not Venus' orbit was beyond the Sun or within the Sun's orbit. Ptolemy argued that God wouldn't choose to waste the space by having Venus outside the orbit. [I'm going on weak memory, but I think this account is correct.]

However, as you we know, it wasn't a better model if accuracy was the only determining factor. Ken's point about unification gives it the edge. Kepler learned the Ptolemaic model very well and yet he favored Cop's model. I assume ellipses will modify either model effectively so why did he go with Cop?

I'm surprised we haven't made a list of all the advantages to Cop's model, including that the Sun was the "giant planet" favoring it as a central controlling beast, the explanation for retrogrades appear more sensible, the goofy equant is all but eliminated, the deferent can be determined (apparently). Kepler, btw, using Ptolemy's model before Cop's, added an equant to the epicycles as he struggled for accuracy to match Tycho's data. [Perhaps this answers my question.]

Ken G
2018-Feb-27, 06:36 PM
Good point George, from the perspective of the basic ability of either model to be made consistent with new data, we have a clear case study in how Kepler actually did it. Tycho had a model where the other planets go around the Sun but the Earth (which of course Tycho would not have considered to be a planet, which is the whole point I'm making) is stationary and the Sun goes around it. Kepler could have expressed his laws that way, they would have said the Sun goes in a circle around Earth and the other planets go in ellipses with the Sun at one focus. But he clearly saw no advantage to pinning the Earth in place, which is virtually tantamount to making it a planet like all the others. That is a simply huge change in thought, and Kepler must have seen the economy of exposition in doing so. He couldn't have known we'd someday be landing probes on those other planets, but it was the idea that led to all the rest. Anyone prior to Copernicus would likely have thought it blasphemous, probably punishable by death, to propose sending probes to the planets!

wd40
2018-Feb-27, 07:33 PM
Anyone prior to Copernicus would likely have thought it blasphemous, probably punishable by death, to propose sending probes to the planets!

"Celestial Matters" (https://en.wikipedia.org/wiki/Celestial_Matters) is an 'alternative science' novel about a geocentric Ptolemaic universe and what happens when they try to reach the planets by traversing the crystalline spheres!

George
2018-Feb-27, 07:33 PM
Good point George, from the perspective of the basic ability of either model to be made consistent with new data, we have a clear case study in how Kepler actually did it. Tycho had a model where the other planets go around the Sun but the Earth (which of course Tycho would not have considered to be a planet, which is the whole point I'm making) is stationary and the Sun goes around it. Kepler could have expressed his laws that way, they would have said the Sun goes in a circle around Earth and the other planets go in ellipses with the Sun at one focus. But he clearly saw no advantage to pinning the Earth in place, which is virtually tantamount to making it a planet like all the others. That is a simply huge change in thought, and Kepler must have seen the economy of exposition in doing so. He couldn't have known we'd someday be landing probes on those other planets, but it was the idea that led to all the rest. Earth seen as of the same essence of other planets may well be the biggest thing to come out of it all. This was the death to ether, no doubt, which had them in a stupor. [I think there's a pun in there.] I wonder who first espoused this claim explicitly?


Anyone prior to Copernicus would likely have thought it blasphemous, probably punishable by death, to propose sending probes to the planets!I haven't seen much evidence for this. The Bruno story, for instance, gets distorted for anti-theological reasons. There are, however, always a few bad apples that would make your argument true but not for any majority for any religion that I am familiar with. Heliocentricity was only slightly more reviled then than this century's heliochromology. ;)

parallaxicality
2018-Feb-27, 11:10 PM
Bruno didn't need the exoplanets thing to get toasted. His saying that Jesus wasn't divine and Mary wasn't a virgin were enough for that. And Galileo probably wouldn't have ended up under house arrest if he was less of a belligerent blowhard.

George
2018-Feb-28, 02:25 PM
Bruno didn't need the exoplanets thing to get toasted. His saying that Jesus wasn't divine and Mary wasn't a virgin were enough for that. And Galileo probably wouldn't have ended up under house arrest if he was less of a belligerent blowhard.Yes, Bruno attacked at least 5 major tenets of the Church. Astronomy was never a tenet, though perhaps cosmogony would have been. Copernicus, on the other hand, seemed apprehensive about dethroning Earth but was encouraged by some prominent clergy to publish. It's interesting to me that his publication went unbothered by church censorship for decades. Galileo appeared to be using it, however, to mock the views of the Pope who was encouraged to take it personally and at a time other countries (e.g. Spain) questioned the Pope's fervor. Galileo's belligerence was part of the problem, but such styles may have been more common back then for many leaders, from what I gather. Luther was known to make ugly remarks as hyperbole including his dinner remark against the view of Copernicus.

Hornblower
2018-Feb-28, 06:02 PM
It has been my understanding that the Church was generally supportive of scientific inquiry during Copernicus's lifetime and for a while afterward. His book was not even placed on the Index until several decades later, about the time Galileo was getting started on Jupiter's moons. The way my dad described it, Galileo was making waves at a time when the Pope was in political trouble of the sort that had not been a problem earlier, and as such was a convenient scapegoat.

George
2018-Feb-28, 06:29 PM
It has been my understanding that the Church was generally supportive of scientific inquiry during Copernicus's lifetime and for a while afterward.Yes, and the universities were formed from Church roots throughout Europe, I think. The Jesuits were some of the scholars and were quick to recognize Galileo's debunking of the Ptolemy model once they used a telescope (perhaps one Galileo made) to confirm the phases of Venus. I suppose it helped that they had the geocentric Tycho model in hand during that time, which they adopted. It is worth noting they highly respected Galileo, but some became enemies later.


His book was not even placed on the Index until several decades later, about the time Galileo was getting started on Jupiter's moons. Starry Messenger was published in 1609. But it was 1616 when Galileo got his formal rebuke and de Revolutionibus of Copernicus got censored, so about 73 orbits for Earth till that time.


The way my dad described it, Galileo was making waves at a time when the Pope was in political trouble of the sort that had not been a problem earlier, and as such was a convenient scapegoat.Yes, it seems like the greatest strife came as a result of the fiercer Spanish Inquisition and their demands for greater zeal from the Pope. Galileo also had managed to acquire a few fierce enemies that were within the Pope's circle that also made it easier to make Galileo a scapegoat. Apparently, a document restricting Galileo from teaching heliocentricity was presented in some way to the Pope, but this document was never signed. [The Cardinal that held the meeting with that document has passed away before things got heated.] There is one book in particular that addresses this inside story better than others like Drake, though Drake is overall about the best I've read.

wd40
2018-Mar-01, 11:40 PM
"Galileo found Copernicus’ proposal convincing not because it better fit the observations of planetary positions but because of its simplicity and elegance, in contrast to the complicated epicycles of the Ptolemaic model. In Dialogues Concerning Two Sciences, Galileo’s characters, Salviati and Sagredo, put forward persuasive arguments in support of Copernicus. Yet, it was still possible for his third character, Simplicio, to defend Aistotle and Ptolemy and to maintain that in reality the Earth was at rest and the sun went round the Earth." (Stephen Hawking, On the Shoulders of Giants p.ix).

[Is not Hawking wrong here in thinking that only Ptolemy had "complicated epicycles", and not Copernicus?]

Ken G
2018-Mar-02, 05:02 AM
Yes, I think that "elegance" and "simplicity" is not really the issue if one is focused strictly on the shapes of the orbits, because any model of orbital shapes can be made simpler if accuracy will be sacrificed. Ironically, the character named "Simplicio" is the one that is essentially simple-minded, so in Galileo's view, too much simplicity is the last refuge of the scoundrel! It's not so much that Simplicio preferred the simpler model, it's more that it is always in some sense simpler to stick with what you have been told, and not delve into unfamiliar territory. When you think for yourself, you may ultimately find simplicity, as Newton eventually did, but usually you have to first navigate significant new complexities. The ultimate simplicity and elegance of Copernicus' picture really had little to do with the shapes of the orbits, it had to do with the unification of the suns and the planets. You can't get more elegant than "the universe is all one place with only one set of rules."

George
2018-Mar-02, 06:51 PM
"Galileo found Copernicus’ proposal convincing not because it better fit the observations of planetary positions but because of its simplicity and elegance, in contrast to the complicated epicycles of the Ptolemaic model." Well, the elegance claim is a logical reason, but this story is rarely so simple. I don't know, however, what he is thinking when comparing epicycles for the two models since they are very similar. Cop eliminating the equant is the more typical argument favoring Cop.

Galileo taught the Ptolemaic model prior to his telescope creation, though, IIRC, he was already leaning to Cop prior to his 1609 telescope date. His telescope first revealed an imperfect Moon, which was not supposed to be. Then came the moons of Jupiter which gave us objects orbiting another, which were supposed to only be orbiting the geocentric Earth. Cop's argument for the Earth orbiting looked far more favorable with both of these discoveries. It took Galileo a little longer to discover that Venus (and Mercury) exhibit gibbous and crescent phases, thus debunking Ptolemy since both phases are impossible for the Ptolemy model.


In Dialogues Concerning Two Sciences, Galileo’s characters, Salviati and Sagredo, put forward persuasive arguments in support of Copernicus. Yet, it was still possible for his third character, Simplicio, to defend Aristotle and Ptolemy and to maintain that in reality the Earth was at rest and the sun went round the Earth." (Stephen Hawking, On the Shoulders of Giants p.ix). This somewhat common dialogue-style book presentations of that time were useful to convince others of the way to see things, namely the way the author favors things. Simplicio was taken as the impleton and his arguments were less persuasive against Salviati and Sasgredo. Simplicio's role was to help others see that the Ptolemy model was wrong. Galileo, using Simplicio, made the mistake of using the same arguments, then beating them down, that his friend the Pope had used, which is what set off the fireworks. Using the Simplicio name was seen as further insult, though Galileo had a friend of this name, so perhaps he didn't quite mean it that way.

George
2018-Mar-02, 06:57 PM
You can't get more elegant than "the universe is all one place with only one set of rules." Yep, and I'm all for only four forces. :)

wd40
2018-Mar-03, 09:36 PM
Well, the elegance claim is a logical reason, but this story is rarely so simple. I don't know, however, what he is thinking when comparing epicycles for the two models since they are very similar. Cop eliminating the equant is the more typical argument favoring Cop.

Galileo taught the Ptolemaic model prior to his telescope creation, though, IIRC, he was already leaning to Cop prior to his 1609 telescope date.



Did Galileo recant on Copernicus?

On March 29 1641 Galileo wrote to Rinuccini:

"The falsity of the Copernican system should not in any way be called into question, above all, not by Catholics, since we have the unshakeable authority of the Sacred Scripture, interpreted by the most erudite theologians, whose consensus gives us certainty regarding the stability of the Earth, situated in the center, and the motion of the sun around the Earth. The conjectures employed by Copernicus and
his followers in maintaining the contrary thesis are all sufficiently rebutted by that most solid argument deriving from the omnipotence of God. He is able to bring about in different ways, indeed, in an infinite number of ways, things that, according to our opinion and observation, appear to happen in one particular way. We should not seek to shorten the hand of God and boldly insist on something
beyond the limits of our competence. D’Arcetri, March 29, 1641. I am writing the enclosed letter to Rev. Fr. Fulgenzio, from whom I have heard no news lately. I entrust it to Your Excellency to kindly make sure he receives it.” (Le Opere Di Galileo Galilei, 1968, vol. 18, p. 316, & S.Drake, Galileo At Work: His Scientific Biography, 1978, p. 417).

Hornblower
2018-Mar-03, 09:45 PM
I would say yes, for the record he recanted or at least went through the motions. Legend has it that he still believed Copernicus was on the right track.

Ken G
2018-Mar-04, 12:04 AM
"Eppur si muove." I suspect Galileo understood the difference between what he had to say to avoid persecution, versus what the scientific world would quickly come to understand. The church had a lot more power over Galileo's life than they had on the future of scientific progress, and Galileo likely knew that. (In fact, if you read between the lines in Galileo's words above, you might detect more than a hint of sarcasm. He is basically saying that Catholics have their own truth, held to by their own authorities, and so no unifying truth that applies to others should apply to them. He never said they had any evidence or logic to support them! That's quite a sarcastic thing for any scientist to say.)

George
2018-Mar-04, 12:47 AM
Did Galileo recant on Copernicus?
Yes, he underestimated the subterfuge from his enemies that were close to the Pope, IMO. His trial would be a big part of any major picture about Galileo. His recant became his instrument for escape. It's hard to say what all he was thinking. Both he and his former friend the Pope, who he had offended, were in a difficult spot. Perhaps he felt a retreat was in order. I think I read that the official documents are still locked-up.

George
2018-Mar-04, 12:55 AM
"Eppur si muove." As moving as that is, it's been argued pretty convincingly by folks like Drake that he likely never said it. I can see why, however, it would have been a popular quote, even if never uttered, since it honors his convictions and make him even more a hero, and the church a loser. It was accepted that he had dethroned Ptolemy, and he rarely if ever gave credence to Tycho, which left him with Cop so he never really recanted in his heart, no doubt.


I suspect Galileo understood the difference between what he had to say to avoid persecution, versus what the scientific world would quickly come to understand. The church had a lot more power over Galileo's life than they had on the future of scientific progress, and Galileo likely knew that. (In fact, if you read between the lines in Galileo's words above, you might detect more than a hint of sarcasm. He is basically saying that Catholics have their own truth, held to by their own authorities, and so no unifying truth that applies to others should apply to them. He never said they had any evidence or logic to support them! That's quite a sarcastic thing for any scientist to say.)Agreed, it's very well crafted and that's how I read it as well. The falseness of the Copernican system should indeed not be called into question. Brilliant duality.

wd40
2018-Mar-05, 09:59 AM
The falseness of the Copernican system should indeed not be called into question. Brilliant duality.

"Today we cannot say that the Copernican theory is “right” and the Ptolemaic theory is “wrong” in any meaningful physical sense. The two theories are physically equivalent to one another." (Fred Hoyle, Nicholaus Copernicus p.88) "If the Galileo Affair had taken place after Einstein had framed his General Theory, it would have resulted in an even draw out of physical and mathematical necessity".

Hornblower
2018-Mar-05, 12:48 PM
"Today we cannot say that the Copernican theory is “right” and the Ptolemaic theory is “wrong” in any meaningful physical sense. The two theories are physically equivalent to one another." (Fred Hoyle, Nicholaus Copernicus p.88) "If the Galileo Affair had taken place after Einstein had framed his General Theory, it would have resulted in an even draw out of physical and mathematical necessity".

That's a good point, but there is still a sound reason to choose the heliocentric model, or better yet a barycentric model, for practical purposes. In such a model GR closely approaches Newton's formula. In a geocentric model my hunch is that the gravitational model would be hideously messy and not scientifically useful in a practical sense.

George
2018-Mar-05, 04:26 PM
"Today we cannot say that the Copernican theory is “right” and the Ptolemaic theory is “wrong” in any meaningful physical sense. The two theories are physically equivalent to one another." (Fred Hoyle, Nicholaus Copernicus p.88) "If the Galileo Affair had taken place after Einstein had framed his General Theory, it would have resulted in an even draw out of physical and mathematical necessity". This, however, is a little sloppy on his part. Specific modified models for the heliocentric model or the geocentric model (e.g. modified Tychonic) are valid within GR, thus with this restriction, he's right. But the Ptolemy model was indeed falsified and GR doesn't claim to fix falsified models. You cannot have Venus orbit between the Earth and the Sun and produce both a gibbous and crescent phase. GR won't fix that.

wd40
2018-Mar-05, 06:23 PM
But the Ptolemy model was indeed falsified and GR doesn't claim to fix falsified models.

“Einstein’s theories reveal they may actually slightly favor an Earth-centered model,” and that the only advantage of Copernican theory is it “is more easily falsifiable than Ptolemy’s” (Kitty Ferguson, Measuring the Universe p106).




You cannot have Venus orbit between the Earth and the Sun and produce both a gibbous and crescent phase. GR won't fix that.

"Even astronomers and historians who should know better claim that Galileo’s discovery that Venus exhibits moon-like phases
disproved the Ptolemaic model. All that Galileo’s observations actually meant insofar as the Ptolemaic model was concerned, was that the radii of the epicycles were much larger than had previously been suspected; and all that Kepler’s elliptical orbits meant to the Ptolemaic model was that two of the epicycles could be combined into one ellipse" (G.Bouw, Geocentricity p309).

George
2018-Mar-05, 06:45 PM
“Einstein’s theories reveal they may actually slightly favor an Earth-centered model,” and that the only advantage of Copernican theory is it “is more easily falsifiable than Ptolemy’s” (Kitty Ferguson, Measuring the Universe p106). That's an interesting claim and one that would require some evidence to support. Was any given?


"Even astronomers and historians who should know better claim that Galileo’s discovery that Venus exhibits moon-like phases
disproved the Ptolemaic model. All that Galileo’s observations actually meant insofar as the Ptolemaic model was concerned, was that the radii of the epicycles were much larger than had previously been suspected; and all that Kepler’s elliptical orbits meant to the Ptolemaic model was that two of the epicycles could be combined into one ellipse" (G.Bouw, Geocentricity p309). Odd claim. To have the epicycle so large to swing the planet on either side of the Sun in such a fashion I think would be in direct contrast to the actual model given in his Almagest. I suspect such a large epicycle would greatly compromise the accuracy. If it could have been tweaked, why didn't they? I doubt they really wanted the Tychonic model as their substitute.

On 2nd thought, such a large epicycle would work but it would be obvious that Venus would have to orbit the Sun as would be confirmed by the phase observations. This is in direct conflict with Ptolemy, but not Tycho.

Ken G
2018-Mar-06, 03:17 AM
"Today we cannot say that the Copernican theory is “right” and the Ptolemaic theory is “wrong” in any meaningful physical sense. The two theories are physically equivalent to one another." (Fred Hoyle, Nicholaus Copernicus p.88) "If the Galileo Affair had taken place after Einstein had framed his General Theory, it would have resulted in an even draw out of physical and mathematical necessity".
Again, Hoyle is talking strictly about the representation of the orbits themselves. He is missing what is much much much more important-- that Copernicus' model makes the Earth a planet. say that to yourself as many times as it takes, it's the whole point of the Copernican model, and GR doesn't change that one bit. Hoyle is dead wrong-- the Copernican model is about as "right" as you can get, in that the Earth is very definitely now regarded as a planet, and it never was prior to Copernicus (except by heretics like Bruno).

wd40
2018-Mar-06, 05:51 AM
Hoyle is dead wrong


If Hoyle is 'dead wrong', is then Bertrand Russell even more dead wrong when he stated:

"Whether the Earth rotates once a day from west to east, as Copernicus taught, or the heavens revolve once a day from east to
west, as his predecessors believed, the observable phenomena will be exactly the same. This shows a defect in Newtonian
dynamics, since an empirical science ought not to contain a metaphysical assumption, which can never be proved or disproved by observation." (Dennis W. Sciama, The Unity of the Universe, p102)

?

Geo Kaplan
2018-Mar-06, 06:45 AM
If Hoyle is 'dead wrong', is then Bertrand Russell even more dead wrong when he stated:

"Whether the Earth rotates once a day from west to east, as Copernicus taught, or the heavens revolve once a day from east to
west, as his predecessors believed, the observable phenomena will be exactly the same. This shows a defect in Newtonian
dynamics, since an empirical science ought not to contain a metaphysical assumption, which can never be proved or disproved by observation." (Dennis W. Sciama, The Unity of the Universe, p102)

?

You aren't paying attention to the point that KenG is making (and has had to repeat several times, because careless readers aren't listening to what he's saying).

To place the earth at the center is to make a metaphysical assumption. Bertrand Russell's quote addresses the issue of computational equivalency. That's rather irrelevant to Ken's point, and if the quote is correct, it shows that Russell failed to appreciate the philosophical import of the heliocentric model. The revolutionary shift was to remove the earth from its special place, to make it "just" another planet.

profloater
2018-Mar-06, 10:09 AM
Indeed the intellectual achievement is all the greater because the evidence is hard to obtain. The casual everyday observation that everything appears to rotate about us is very powerful.

wd40
2018-Mar-06, 12:28 PM
it shows that Russell failed to appreciate the philosophical import of the heliocentric model.

How much discussion of the philosophical, and hence religious import of heliocentrism is allowed in this section?

I think you underestimate the English thinkers that once were, like Hoyle and Russell:

"Before Copernicus, people thought that the Earth stood still and that the heavens revolved about it once a day. Copernicus taught that ‘really’ the Earth revolves once a day, and the daily rotation of sun and stars is only ‘apparent.’ Galileo and Newton endorsed this view, and many things were thought to prove it – for example, the flattening of the Earth at the poles, and the fact that bodies are heavier there than at the equator. But in the modern theory the question between Copernicus and his predecessors is merely one of convenience; all motion is relative, and there is no difference between the two statements: ‘the earth rotates once a day’ and ‘the heavens revolve about the Earth once a day.’ The two mean exactly the same thing, just as it means the same thing if I say that a certain length is six feet or two yards. Astronomy is easier if we take the sun as fixed than if we take the Earth, just as accounts are easier in decimal coinage. But to say more for Copernicus is to assume absolute motion, which is a fiction. All motion is relative,
and it is a mere convention to take one body as at rest. All such conventions are equally legitimate, though not all are equally convenient" (Bertrand Russell, The ABC of Relativity p13).

Ken G
2018-Mar-06, 02:54 PM
If Hoyle is 'dead wrong', is then Bertrand Russell even more dead wrong when he stated:

"Whether the Earth rotates once a day from west to east, as Copernicus taught, or the heavens revolve once a day from east to
west, as his predecessors believed, the observable phenomena will be exactly the same. This shows a defect in Newtonian
dynamics, since an empirical science ought not to contain a metaphysical assumption, which can never be proved or disproved by observation." (Dennis W. Sciama, The Unity of the Universe, p102)

?
Are you not hearing me? Hoyle, and Russell, and Einstein are all talking about the same thing: the motion itself. They are all talking about relativity, which states that motion is relative. But asserting which object, the Earth or the Sun, is the one "actually in motion" was never the important thing about the Copernican model. So if they are saying "the Copernican model was not important," they are all dead wrong. But from their quotes, and especially that last one, it's not at all clear they are saying the Copernican model was not important, they are saying that since motion is relative, identifying "which object is moving" is not what matters about the Copernican model. So what does matter about the Copernican model?

To see that, ask yourself this simple question, a question I would put to Einstein, Hoyle, and Russell if I could (and I'm sure they'd all see the point). If you have a model where the Earth is stationary and everything else goes around it, thereby obeying completely different rules from the Earth, versus another model where the Earth follows orbits and rules quite similar to the other planets, in which of those models does the Earth seem like a planet? That issue is not at all metaphysical, it is quite easily testable-- you either apply the laws that work on Earth to other planets, and look for models of the formation of the Earth that are similar to the formation of other planets, and speculate on the potential for life on other planets, and look for conditions on other planets that could be similar to conditions on Earth-- or you don't. And it's all testable! Do you see the importance of the Copernican model now? The verification of the Copernican model was a revolution in astronomy, the likes of which is not even rivaled by the Big Bang model, so to say the model "didn't matter" because it wasn't more accurate, or wasn't more parsimonious, or made claims inconsistent with relativity, misses the significance of that model. To wit:

The Copernican model made modern astronomy possible. Had it's key elements been falsified rather than simply modified, then even by now we'd know essentially nothing about the universe, as Galileo didn't, as Kepler didn't.

Ken G
2018-Mar-06, 03:15 PM
To place the earth at the center is to make a metaphysical assumption. Bertrand Russell's quote addresses the issue of computational equivalency. That's rather irrelevant to Ken's point, and if the quote is correct, it shows that Russell failed to appreciate the philosophical import of the heliocentric model. The revolutionary shift was to remove the earth from its special place, to make it "just" another planet.Exactly, and it makes us wonder just exactly what Russell was trying to say there. I suspect his point was simply that the way people tend to frame the importance of the Copernican model misses the point of its true importance, which is they tend to stress the way it set up the particular element of Newtonian dynamics that was the concept of absolute motion. He is certainly right that the Copernican model had no significance insofar as it embraced the concept of absolute motion, and argued about whether it is the Earth or the Sun that exhibits said absolute motion, as all that is rendered irrelevant by relativity. And it's true that Copernicus placed the Sun at the unmoving center of the universe, though it's still unclear to me if Copernicus understood the profound ramifications of his model that forces us to explain the absence of stellar parallax by placing the stars at such vast distances that they are unified with our Sun. But it's not unusual for the full significance of a model to be appreciated well after the model is suggested, and this is certainly true of the Copernican model. The true significance is what you and I are talking about.

Indeed, I wonder if Russell would have appreciated the irony in his choice of Newtonian mechanics as the target of his criticism about building metaphysical claims into a predictive theory. The great breakthrough of Newton was the way he unified our understanding of motion everywhere from a laboratory table to the motions of the galaxies, for his laws were found to work on all scales (that were not quantum-mechanically small or relativistically fast, though of course the jury is still a bit out on dark matter vs. MOND). In particular, he unified the gravity that makes apples falls out of trees with the gravity that rules Kepler's laws of planetary motion! Such a unification was made possible by the Copernican model, because while astronomers still embraced Ptolemy, it would never even occur to them to try to unify Earthbound laws with the motions of the planets (which Kepler, growing up as he did in the Ptolemaic way of thinking about cosmic scales, thought was some kind of celestial concert). So although I wholeheartedly agree with Russell that physics laws are machines for making testable predictions and not metaphysical belief systems, the ultimate goal of all physics is to achieve unification of our understanding of disparate phenomena. That's not metaphysics, it's just plain good physics.

So the problem is, the Copernican model should never be presented as an effort to address the question "is it beneficial to us to imagine that the Sun is the absolutely stationary object rather than the Earth," it should always be presented as an effort to address "do we have to treat the Earth as something special and different, as the Ptolemaic system does, or are all observations consistent with the Earth having a motion and status quite similar to all the other planets, and the Sun to all the other stars?" Framed like that, it becomes clear that the Copernican system should always have been regarded as a default system of doing good science, a system to be accepted until proven otherwise, rather than a system on which falls the burden of proof. We have now learned our lesson, and in cosmology we regard the cosmological principle in that same light-- the default system in need of being disproven, rather than some metaphysical claim that cannot be known to be true.

Hornblower
2018-Mar-06, 04:24 PM
Ken's posts here sum up the reasoning that by the 19th century had nailed up the coffins of Ptolemy and Tycho with nails the size of railroad spikes, while Bessel's belated success in observing stellar parallax with a powerful telescope finished the job with a carpet tack.

George
2018-Mar-06, 04:36 PM
It might also be worth noting that GR refutes the Ptolemaic model. GR incorporates gravity (mass). Ptolemy knew the Sun was large but may have held that the ethereal objects were light. If the Sun is fire, how heavy is fire? It probably didn't matter to him to speculate on mass as he had no way to measure such things, even if he understood its importance, I assume. Tycho, however, at least had all but the Earth orbiting the Sun. A modified version of his model, therefore, is not falsifiable by GR since relativity works in this case, even for a fixed Earth, or any fixed point.

Copernicus, interestingly, comes very close to getting the importance of the Newtonian view of gravity that Cop considered as an impulse when he wrote (de Revolutionibus; chpt. 9):

"For my part I believe that gravity is nothing but a certain natural desire, which the divine providence of the Creator of all things has implanted in parts, to gather as a unity and a whole by combining in the form of a globe. This impulse is present, we may suppose, also in the sun, the moon, and the other brilliant planets, so that through its operation they remain in that spherical shape which they display. Nevertheless, they swing round their circuits in divers ways. If, then, the earth too moves in other ways, for example, about a center, its additional motions must likewise be reflected in many bodies outside it. Among these motions we find the yearly revolution."

George
2018-Mar-06, 06:21 PM
I think you underestimate the English thinkers that once were, like Hoyle and Russell:

"Before Copernicus, people thought that the Earth stood still and that the heavens revolved about it once a day. Copernicus taught that ‘really’ the Earth revolves once a day, and the daily rotation of sun and stars is only ‘apparent.’ Galileo and Newton endorsed this view, and many things were thought to prove it – for example, the flattening of the Earth at the poles, and the fact that bodies are heavier there than at the equator. But in the modern theory the question between Copernicus and his predecessors is merely one of convenience; all motion is relative, and there is no difference between the two statements: ‘the earth rotates once a day’ and ‘the heavens revolve about the Earth once a day.’ The two mean exactly the same thing, just as it means the same thing if I say that a certain length is six feet or two yards..."
But the details make one quite absurd over the other. The Earth's rotation period is different each day due to air mass movements, primarily. This time difference for a fixed earth requires that it's the entire universe that must accelerate and decelerate accordingly. Fictitious forces are bad enough, but consider their magnitude and apply it to any equivalence claims. The "math is fine but your physics is abominable." [Einstein to LeMaitre, though I'm having some fun flipping things. :)]

Hornblower
2018-Mar-06, 06:58 PM
It might also be worth noting that GR refutes the Ptolemaic model. GR incorporates gravity (mass). Ptolemy knew the Sun was large but may have held that the ethereal objects were light. If the Sun is fire, how heavy is fire? It probably didn't matter to him to speculate on mass as he had no way to measure such things, even if he understood its importance, I assume. Tycho, however, at least had all but the Earth orbiting the Sun. A modified version of his model, therefore, is not falsifiable by GR since relativity works in this case, even for a fixed Earth, or any fixed point.

Copernicus, interestingly, comes very close to getting the importance of the Newtonian view of gravity that Cop considered as an impulse when he wrote (de Revolutionibus; chpt. 9):

"For my part I believe that gravity is nothing but a certain natural desire, which the divine providence of the Creator of all things has implanted in parts, to gather as a unity and a whole by combining in the form of a globe. This impulse is present, we may suppose, also in the sun, the moon, and the other brilliant planets, so that through its operation they remain in that spherical shape which they display. Nevertheless, they swing round their circuits in divers ways. If, then, the earth too moves in other ways, for example, about a center, its additional motions must likewise be reflected in many bodies outside it. Among these motions we find the yearly revolution."

If I am not mistaken, Ptolemy not only did not have any theory involving masses of the various bodies and forces acting on them, but he did not care. At least that is the case if the British authors Stephen Toulmin and June Goodfield* had their facts straight about how the Greek philosophy had evolved by his time. In the five centuries since Aristotle they appeared to have lost their zeal to develop a comprehensive theory of celestial physics and to have looked upon such points of physics as being in the realm of the gods, not to be speculated upon by mortal human beings. Ptolemy limited himself to developing a geometric model that enabled the calculation of a good ephemeris of the planets, with no concern for a physical explanation for why it worked as well as it did by the standards of the time.

Tycho's model is just an adaptation of Ptolemy in which he allows orbits to cross and gives the planets a common center of orbital motion that coincides with the Sun. It still does not allow a unification of the gravity that governs the planets' motion around the Sun with that which governs the Moon's motion around the Earth, at least not with simple formulas. Perhaps a valid dynamic theory is possible in principle under GR, but as I have said many times I think it would be horrendously messy and not good practical physics.

*Toulmin and Goodfield, The Fabric of the Heavens, Harper and Brothers, 1961

George
2018-Mar-06, 07:59 PM
If I am not mistaken, Ptolemy not only did not have any theory involving masses of the various bodies and forces acting on them, but he did not care. At least that is the case if the British authors Stephen Toulmin and June Goodfield* had their facts straight about how the Greek philosophy had evolved by his time. In the five centuries since Aristotle they appeared to have lost their zeal to develop a comprehensive theory of celestial physics and to have looked upon such points of physics as being in the realm of the gods, not to be speculated upon by mortal human beings. Ptolemy limited himself to developing a geometric model that enabled the calculation of a good ephemeris of the planets, with no concern for a physical explanation for why it worked as well as it did by the standards of the time.That's well-stated, and I was implying nothing different. He likely knew that the Sun is huge in size but that wouldn't make any difference given the science of his day. Working with apparent motions to produce a predictive model for planetary positions makes perfect sense, though it may have surprised him just how tricky that became. Kepler having to add an equant to the epicycles of Ptolemy was something I only recently learned, but adds to the story of its difficulty.


Tycho's model is just an adaptation of Ptolemy in which he allows orbits to cross and gives the planets a common center of orbital motion that coincides with the Sun. Well, they are both geocentric but Tycho's model favors the heliocentric model far more. Tycho's is a hybrid model, and not the first. He introduced it 40 years after Cop. But Tycho was the world's expert on astrometry and he held that stars are not point-sources since each seem to have a size to them, one arcminute I would guess. He reasoned that if Copernicus were right about their distance then they would have to be unimaginably large in order to not exhibit parallax and still appear to have size. [He didn't understand, of course, the eye's resolution limits.] There is also a teleological argument that I don't recall reading about regarding the purpose of such vast distances. This may also have been a factor.

[Added: It just dawned on me that perhaps Galileo all but ignored the Tychonic model since his telescope would easily argue that since stars apparent sizes are not enlarged one iota, unlike planets, then parallax was far more likely. Have you ever heard of this idea?]


It still does not allow a unification of the gravity that governs the planets' motion around the Sun with that which governs the Moon's motion around the Earth, at least not with simple formulas. Perhaps a valid dynamic theory is possible in principle under GR, but as I have said many times I think it would be horrendously messy and not good practical physics.Agreed, fictitious with a fictitious exponent. ¯\_(ツ)_/¯ That's why I tossed-in Einstein's quote agreeing with the math but not the physics, though his was regarding the "primeval atom" (BBT).

Ken G
2018-Mar-06, 09:55 PM
There is also a teleological argument that I don't recall reading about regarding the purpose of such vast distances. This may also have been a factor.Yes, holding that stars are suns requires an unbelievable amount of wasted space in the design of the universe. I am certain that argument from incredulity played a key part in Ptolemy's thinking.


[Added: It just dawned on me that perhaps Galileo all but ignored the Tychonic model since his telescope would easily argue that since stars apparent sizes are not enlarged one iota, unlike planets, then parallax was far more likely. Have you ever heard of this idea?]Yes, one of the things Galileo did is point his telescope at the "Milky Way", and he noted that part of that swath of light resolves into points of light when you do that. He reasoned by extension that all of it would if the telescope were powerful enough, and in that way was able to demonstrate that stars are indeed fantastically far away.

That's why I tossed-in Einstein's quote agreeing with the math but not the physics, though his was regarding the "primeval atom" (BBT).And we must always remember, Einstein wasn't always right!

George
2018-Mar-06, 10:14 PM
Yes, holding that stars are suns requires an unbelievable amount of wasted space in the design of the universe. I am certain that argument from incredulity played a key part in Ptolemy's thinking. Yes, those that argued that the orbit of Venus was outside the Sun were diminished by his argument that God wouldn't waste the space between us to do so. :)


Yes, one of the things Galileo did is point his telescope at the "Milky Way", and he noted that part of that swath of light resolves into points of light when you do that. He reasoned by extension that all of it would if the telescope were powerful enough, and in that way was able to demonstrate that stars are indeed fantastically far away. Yep, but I'm curious if there is anything explicit as to why he all but ignored Tycho's model. The Jesuits didn't seem to have much trouble dumping Ptolemy with this ready-to-go off-the-shelf model, so there may be an interesting story or perhaps he was reluctant to get too entangled even in these earlier years. The politics between Rome and Tuscany added to the drama.


And we must always remember, Einstein wasn't always right! Einstein did, reportedly, quickly stand and applaud a subsequent Lemaitre presentation, once he realized he had missed the elephant in the large GR room he built.

Hornblower
2018-Mar-07, 03:35 AM
This discussion shows how our ancestors needed centuries, even millennia, to learn how to think in terms that are very elementary exercises in physics to us. Among other things, they could not understand that the Sun, if moved far enough away to become invisible if non-luminous, would still be plenty bright to be visible at night.

wd40
2018-Mar-07, 03:46 AM
This discussion shows how our ancestors needed centuries, even millennia, to learn how to think in terms that are very elementary exercises in physics to us. Among other things, they could not understand that the Sun, if moved far enough away to become invisible if non-luminous, would still be plenty bright to be visible at night.

Ptolemy had estimated the distance from the Earth to the Sun to be to be 610 Earth diameters, while Copernicus estimated it to be 571 Earth diameters. The actual distance is 11,500 Earth diameters.

Ken G
2018-Mar-07, 03:52 AM
This discussion shows how our ancestors needed centuries, even millennia, to learn how to think in terms that are very elementary exercises in physics to us. Among other things, they could not understand that the Sun, if moved far enough away to become invisible if non-luminous, would still be plenty bright to be visible at night.This is the real legacy of genius. It's not so much that the genius has a thought that is impossible for future generations to emulate, it is that they have a thought, unimagined in their time, that future generations accept so automatically it comes almost without thinking at all.

Hornblower
2018-Mar-07, 03:52 AM
Ptolemy had estimated the distance from the Earth to the Sun to be to be 610 Earth diameters, while Copernicus estimated it to be 571 Earth diameters. The actual distance is 11,500 Earth diameters.

Both of them were attempting something that is next to impossible. They were trying to determine when the terminator on the Moon was perfectly straight, and do triangulation from the difference between 90 degrees and the actual elongation of the Moon from the Sun. This was with naked eye observations, and there were ample sources of error.

Ken G
2018-Mar-07, 03:55 AM
Ptolemy had estimated the distance from the Earth to the Sun to be to be 610 Earth diameters, while Copernicus estimated it to be 571 Earth diameters. The actual distance is 11,500 Earth diameters.
Yes, it took a long time for the size of the Sun to be correctly appreciated. The Greeks had the size of the Earth right (to Columbus' shame), but they had no easy way to tell how far and how large the Sun was, and neither did Copernicus. This is always the problem in astronomy-- even 100 years ago we did not know the size and distance of the Andromeda galaxy, for example. It's not what Copernicus understood in his head that made his model so very important, it is what it made possible to understand by future generations.

Interestingly, what is easy for anyone with geometry skills to know is that the ratio of the Sun's diameter to its distance is 1/100. So if they thought the distance was some 600 Earth diameters, then they thought the Sun was 6 times larger than the Earth. That could have been reason enough to suspect it ruled the orbits of the solar system, and not the Earth, had the Greeks thought in terms that did not elevate the role of the Earth automatically. In hindsight, they made the simple error of mistaking an illusion of perspective for a physical principle. This is the common error of the geocentrist, the anthropocentrist, and the egocentrist.

wd40
2018-Mar-07, 06:05 AM
Ken's posts here sum up the reasoning that by the 19th century had nailed up the coffins of Ptolemy and Tycho with nails the size of railroad spikes


"Why, then, does Ptolemy come off so badly in this contest? Paradoxically, the enormous success of Ptolemaic astronomy is not an
apparent movement in the heavens. It could also account for a great deal that never happens. It allows for too much.
Copernican astronomy, as it has evolved, allows for far less. It’s easier to think of something that Copernican theory could not explain. The more scientific way of putting this is that Copernican theory is more easily “falsifiable” than Ptolemy’s, easier to disprove. Falsifiability is considered a strength if new discoveries don’t undermine it but fall neatly into place." (Kitty Ferguson, Measuring the Universe p107)

Hornblower
2018-Mar-07, 03:03 PM
"Why, then, does Ptolemy come off so badly in this contest? Paradoxically, the enormous success of Ptolemaic astronomy is not an
apparent movement in the heavens. It could also account for a great deal that never happens. It allows for too much.
Copernican astronomy, as it has evolved, allows for far less. It’s easier to think of something that Copernican theory could not explain. The more scientific way of putting this is that Copernican theory is more easily “falsifiable” than Ptolemy’s, easier to disprove. Falsifiability is considered a strength if new discoveries don’t undermine it but fall neatly into place." (Kitty Ferguson, Measuring the Universe p107)

Can you give us some details? What, in principle, makes Copernicus more easily falsifiable, according to her line of thought?

slang
2018-Mar-07, 03:52 PM
Moved from Q&A as the topic has moved beyond a simple question/answer thread.

Ken G
2018-Mar-08, 05:01 AM
"Why, then, does Ptolemy come off so badly in this contest? Paradoxically, the enormous success of Ptolemaic astronomy is not an
apparent movement in the heavens. It could also account for a great deal that never happens. It allows for too much.
Copernican astronomy, as it has evolved, allows for far less. It’s easier to think of something that Copernican theory could not explain. The more scientific way of putting this is that Copernican theory is more easily “falsifiable” than Ptolemy’s, easier to disprove. Falsifiability is considered a strength if new discoveries don’t undermine it but fall neatly into place." (Kitty Ferguson, Measuring the Universe p107)

There's some truth to what she is saying, because highly unifying theories are always easier to falsify, because they make claims about similarities of behaviors that make it easy to look for dissimilarities. But I still don't think this is the right way to frame the situation. Can you imagine telling some elementary school child that it's better to think of the Earth as orbiting the Sun than the Sun as orbiting the Earth because the former is "easier to falsify"? The poor child would miss everything that matters about the Earth orbiting the Sun. Just tell them the Earth is a planet too, and you're done.

wd40
2018-Mar-08, 06:15 AM
There's some truth to what she is saying, because highly unifying theories are always easier to falsify, because they make claims about similarities of behaviors that make it easy to look for dissimilarities.

If those pesky interferometers had been available sooner:

"It is both amusing and instructive to speculate on what might have happened if such an (MM) experiment could have been performed in the sixteenth or seventeenth centuries when men were debating the rival merits of the Copernican and Ptolemaic systems. The result would
surely have been interpreted as conclusive evidence for the immobility of the Earth, and therefore as a triumphant vindication
of the Ptolemaic system and irrefutable falsification of the Copernican hypothesis. The moral of this historical fantasy is that it is often dangerous to believe in the absolute verification or falsification of a scientific hypothesis. All judgments of this type are necessarily made in some historical context which may be drastically modified by the changing perspective of human knowledge." (G. J. Whitrow, The Structure and Evolution of the Universe p79)

George
2018-Mar-08, 11:00 PM
If those pesky interferometers had been available sooner:

"It is both amusing and instructive to speculate on what might have happened if such an (MM) experiment could have been performed in the sixteenth or seventeenth centuries when men were debating the rival merits of the Copernican and Ptolemaic systems. The result would surely have been interpreted as conclusive evidence for the immobility of the Earth, and therefore as a triumphant vindication of the Ptolemaic system and irrefutable falsification of the Copernican hypothesis. "

Huh? Newton's gravitational laws of the 17th century would favor Ptolemy how? It is kinda amusing to hear such a claim. ;) Is this a claim based on one specific experiment or something?

Jeff Root
2018-Mar-09, 12:19 AM
George,

Isn't what is being referenced Michaelson and Morely's proof that
the Earth is motionless? If Earth moved, they certainly would have
detected it with their interferometer. So we now know that the Sun
and Moon and planets and stars all revolve about the Earth.

And North Korea wants to stop nuclear weapons development.

-- Jeff, in Minneapolis

Ken G
2018-Mar-09, 01:32 AM
If those pesky interferometers had been available sooner:

"It is both amusing and instructive to speculate on what might have happened if such an (MM) experiment could have been performed in the sixteenth or seventeenth centuries when men were debating the rival merits of the Copernican and Ptolemaic systems. The result would
surely have been interpreted as conclusive evidence for the immobility of the Earth, and therefore as a triumphant vindication
of the Ptolemaic system and irrefutable falsification of the Copernican hypothesis. The moral of this historical fantasy is that it is often dangerous to believe in the absolute verification or falsification of a scientific hypothesis. All judgments of this type are necessarily made in some historical context which may be drastically modified by the changing perspective of human knowledge." (G. J. Whitrow, The Structure and Evolution of the Universe p79)
Whitrow has a point, often we are asked to choose which is the more plausible among two competing potential solutions to a problem, and our track record for getting the right choice may not be all that great. Sometimes we are even wrong that we have to choose at all-- as with light as particle vs. wave (rather than a particle that obeys wave mechanics), or Earth vs. Sun as the one that is "actually moving" (rather than the Earth simply being more noninertial in the Newtonian sense).

George
2018-Mar-09, 03:30 PM
George,

Isn't what is being referenced Michaelson and Morely's proof that
the Earth is motionless? If Earth moved, they certainly would have
detected it with their interferometer. So we now know that the Sun
and Moon and planets and stars all revolve about the Earth.
Yes, of course. I seem to read and text poorly when using my iPhone and missed the MM reference.

George
2018-Mar-09, 03:39 PM
Whitrow has a point, often we are asked to choose which is the more plausible among two competing potential solutions to a problem, and our track record for getting the right choice may not be all that great. Sometimes we are even wrong that we have to choose at all-- as with light as particle vs. wave (rather than a particle that obeys wave mechanics), or Earth vs. Sun as the one that is "actually moving" (rather than the Earth simply being more noninertial in the Newtonian sense).I suspect, nevertheless, that such use of interferometery to argue geocentricty could be used to favor only one model --- Tycho's. The interference variations found for the light from the planets would not vary in accord with the Ptolemy model.

Ken G
2018-Mar-10, 01:27 PM
Actually a MM interferometer requires a laser. But yes, technologies exist in concert with various other advances too, so it would require a rather strange lens to look at the universe and see a stationary Earth. You are also right that it would really be Tycho's model that would be favored, but even though Tycho's model differs from Ptolemy's in many ways, and from Copernicus' in only one way, that one way is really the only one that matters.

grapes
2018-Mar-10, 02:40 PM
But the details make one quite absurd over the other. The Earth's rotation period is different each day due to air mass movements, primarily. This time difference for a fixed earth requires that it's the entire universe that must accelerate and decelerate accordingly. Fictitious forces are bad enough, but consider their magnitude and apply it to any equivalence claims. The "math is fine but your physics is abominable." [Einstein to LeMaitre, though I'm having some fun flipping things. :)]
No, if you believe that one is true, you can find ways to work out the pesky details. :)


Actually a MM interferometer requires a laser.
MM had a laser?

Hornblower
2018-Mar-10, 04:30 PM
Actually a MM interferometer requires a laser. But yes, technologies exist in concert with various other advances too, so it would require a rather strange lens to look at the universe and see a stationary Earth. You are also right that it would really be Tycho's model that would be favored, but even though Tycho's model differs from Ptolemy's in many ways, and from Copernicus' in only one way, that one way is really the only one that matters.

My bold. Then how did Michelson and Morley do the experiment several decades before lasers were invented?

wd40
2018-Mar-10, 05:37 PM
Fictitious forces are bad enough, but consider their magnitude and apply it to any equivalence claims. The "math is fine but your physics is abominable." [Einstein to LeMaitre, though I'm having some fun flipping things]

“For the mechanics of the planetary system the view of Copernicus is certainly the more convenient. But it is meaningless to call the gravitational fields that occur when a different system of reference is chosen ‘fictitious’ in contrast with the ‘real’ fields produced by near masses: it is just as meaningless as the question of the ‘real’ length of a rod in the special theory of relativity. A gravitational field is neither ‘real’ nor ‘fictitious’ in itself. It has no meaning at all independent of the choice of co-ordinates just as in the case of the length of a rod. Nor are the fields distinguished by the fact that some are directly produced by masses while others are not; in the one case it particularly is the near masses that produce an effect; in the other it is the distant masses of the cosmos.” (Max Born, Einstein’s Theory of Relativity p344)

Ken G
2018-Mar-11, 03:35 AM
MM had a laser?
Oops! We always do it that way in lab class, but you're right, you only need a half-silvered mirror to split a beam from an emission line, it doesn't have to be a laser.

Ken G
2018-Mar-11, 02:22 PM
“For the mechanics of the planetary system the view of Copernicus is certainly the more convenient. But it is meaningless to call the gravitational fields that occur when a different system of reference is chosen ‘fictitious’ in contrast with the ‘real’ fields produced by near masses: it is just as meaningless as the question of the ‘real’ length of a rod in the special theory of relativity. A gravitational field is neither ‘real’ nor ‘fictitious’ in itself. It has no meaning at all independent of the choice of co-ordinates just as in the case of the length of a rod. Nor are the fields distinguished by the fact that some are directly produced by masses while others are not; in the one case it particularly is the near masses that produce an effect; in the other it is the distant masses of the cosmos.” (Max Born, Einstein’s Theory of Relativity p344)That's an interesting perspective, although it doesn't gibe with what I've heard elsewhere. It is not unusual for people to distinguish 'real' gravity from the 'fictitious' gravity of a frame accelerating relative to the distant cosmos, on grounds that only the former exhibits tidal variations. Those people say that gravity is actually a tidal effect, which is somewhat ironic given that Einstein's key principle of GR is the equivalence principle (which breaks down when one considers tidal stress). But I rather prefer Born's point of view, that if the sources of gravity are distant enough and spread out enough, they produce a kind of background field that conditions the spacetime in so isotropic a way that there is not tidal stresses, yet it's still gravity.

George
2018-Mar-11, 05:21 PM
Fitzgerald's note that Ptolemy's model produces gross apparent size variations from what would be observed given a telescope for planetary observations or Tycho-quality visual for the Moon and Sun demonstrates why an interferometer would falsify the model.

Ken G
2018-Mar-11, 06:21 PM
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.

George
2018-Mar-11, 07:30 PM
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.

grapes
2018-Mar-11, 08:14 PM
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!

No, if you believe that one is true, you can find ways to work out the pesky details. :)

Hornblower
2018-Mar-11, 08:53 PM
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?

wd40
2018-Mar-12, 11:56 AM
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).

Swift
2018-Mar-12, 12:51 PM
“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.

Ken G
2018-Mar-12, 01:33 PM
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.

George
2018-Mar-12, 02:16 PM
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.

George
2018-Mar-12, 02:43 PM
“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.

George
2018-Mar-12, 04:00 PM
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.

Hornblower
2018-Mar-12, 10:05 PM
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.


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.

George
2018-Mar-13, 02:33 PM
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 (http://farside.ph.utexas.edu/Books/Syntaxis/Almagest.pdf) 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?]

Hornblower
2018-Mar-13, 05:17 PM
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 (http://farside.ph.utexas.edu/Books/Syntaxis/Almagest.pdf) 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

George
2018-Mar-13, 06:05 PM
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. :)

wd40
2018-Mar-14, 09:19 AM
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?

Hornblower
2018-Mar-14, 10:48 AM
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.

wd40
2018-Mar-14, 01:03 PM
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)

Ken G
2018-Mar-14, 02:05 PM
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.

George
2018-Mar-14, 03:10 PM
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).

George
2018-Mar-14, 03:20 PM
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.

George
2018-Mar-14, 04:12 PM
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.

Hornblower
2018-Mar-14, 06:44 PM
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.

Hornblower
2018-Mar-14, 11:48 PM
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.

George
2018-Mar-16, 02:34 PM
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.]

Hornblower
2018-Mar-16, 08:02 PM
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.

George
2018-Mar-16, 08:41 PM
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.]

George
2018-Mar-17, 03:30 PM
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.

wd40
2018-Mar-19, 11:45 AM
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.

Hornblower
2018-Mar-19, 12:15 PM
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?

wd40
2018-Mar-19, 08:54 PM
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.

George
2018-Mar-20, 11:56 AM
MG = Michelson-Gale experiment (relative rotation between Earth and cosmos detected)But relative rotation is seen all day long, so, in light of the MM exp., doesn't it mainly confirm the accuracy of interferometry more than argue that the Earth is the one rotating? If greater accuracy could be achieved, however, then it would show that the rate of rotation varies slightly. This inconstancy would favor little Earth's erratic behavior over all that stuff above.


Presumably in the Galilean era, such results would have been interpreted as proof positive of the Geocentric model.I'm unsure how the MG experiment would be taken if it only shows relative rotation, or am I missing something?

Ken G
2018-Mar-21, 09:50 AM
Presumably in the Galilean era, such results would have been interpreted as proof positive of the Geocentric model.One experiment deals with orbit and the other with spin. The most straightforward interpretation in history would have been to say the MM experiment says the Earth is not orbiting but the MG experiment says it is rotating. That would have favored neither heliocentric nor geocentric, but been a rather ugly mix of the two! People would have been put into a downright tizzy, I should think.

wd40
2018-Mar-21, 10:26 AM
I'm unsure how the MG experiment would be taken if it only shows relative rotation, or am I missing something?

In that distantly pre-Relativity era, the conclusion drawn from a positive MG combined with a zero-velocity MM, would be to indicate a non-rotating non-revolving Earth. with the cosmos doing the moving round it. Airy's Failure, Fresnel drag, Bradley's aberration, Sagnac Effect and belief in an ether, all together, would have been taken in the Galilean era as proof of the Tychonic/tweaked Ptolemaic model.

George
2018-Mar-21, 02:08 PM
In that distantly pre-Relativity era, the conclusion drawn from a positive MG combined with a zero-velocity MM, would be to indicate a non-rotating non-revolving Earth. with the cosmos doing the moving round it. Airy's Failure, Fresnel drag, Bradley's aberration, Sagnac Effect and belief in an ether, all together, would have been taken in the Galilean era as proof of the Tychonic/tweaked Ptolemaic model.I think it's still hard to say just how many would favor rotation even with the positive MG result. The MG result could be interpreted in other ways such and if they leaped to the idea that the spinning universe caused such a result, and, if so, they would have guessed correctly if my limited understanding of GR is correct. More importantly, there were still the "obvious" arguments countering rotation including why our atmosphere wasn't spinning at extreme speeds, etc. Then there were the more dogmatic religious or teleological arguments that would favor the Tychonic model.

Ken G
2018-Mar-21, 07:50 PM
In that distantly pre-Relativity era, the conclusion drawn from a positive MG combined with a zero-velocity MM, would be to indicate a non-rotating non-revolving Earth. with the cosmos doing the moving round it. Airy's Failure, Fresnel drag, Bradley's aberration, Sagnac Effect and belief in an ether, all together, would have been taken in the Galilean era as proof of the Tychonic/tweaked Ptolemaic model.I don't see why you conclude a positive MG effect supports a non-revolving Earth with the cosmos doing the movement around it. I would say the MG result is moot on the issue, because it can equally be explained by a rotating ether and a rotating Earth within a stationary ether. All it does is rule out an ether that is dragged around by the Earth, so it makes the null MM result say either the Earth is not orbiting through the ether, or there is no ether. It doesn't say what is happening with spin, even for those committed to the existence of an ether. Indeed, one could ask, why would the ether follow around the distant stars, rather than the closer objects like the Sun? In other words, pinning the ether to the stars makes more sense when both are being regarded as stationary, and therefore in a special frame.

loglo
2018-Mar-25, 01:44 PM
Returning to the OP and the origin of Copernicus' claim that Ptolemy needed 34 circles. I have been reading Barbour's "The Discovery of Dynamics" where he describes how Ptolemy used an algorithm to produce successively more accurate approximations to the orbits of the planets.

p 170 "Thus, the solution of Ptolemy's problem involves solution of a succession of generalised Hipparchan problems, each one leading to a better approximate solution until the observations are reproduced to realistic accuracy. Ptolemy in fact found that it was necessary to make only one or two corrections."

From looking at the method it looks like each correction requires 2 or 3 circles to be determined along with the epicycle, so determining the orbits of all the planets to sufficient accuracy will approach the 34 that Copernicus complains of, especially given the greater accuracy of observations in Copernicus' era.

The end of the section on Hellenistic astronomy has some interesting commentary. On Copernicus vs Aristarchus heloicentric hypotheses and the role of Ptolemy:-

p 189 "I suspect the difference between the two men was precisely that Copernicus grasped fully the immense significance of the proposal (which was, after all, not originally his own), stated it clearly, and provided solid arguments in its support. And the reason why Copernicus could do this but Aristarchus could not is clearly at hand: all the detailed observations and analysis on which Copernicus could base his case were not available to Aristarchus; for they were made by his successors. They were the true creators of the heliocentric system; Copernicus only added the final touch.

For the real evidence for heliocentricity was in the demonstration by Ptolemy that in all cases the the second [Kepler] inequality can be unravelled from the first and then when this is done it leaves behind in each case a first inequality characterized by essentially the same functional dependence and structure (circular motion with eccentric centre and equant). Without the solid basis that these factual data provided, the Copernican revolution would have been impossible.

The transition from the old cosmology of Plato and Aristotle to the new astronomy of Kepler required four major steps: liberation of astronomy from the diurnal motion of the earth, liberation from the annual motion, liberation from uniformity of motion, and liberation from circularity of the motion. The first and second of these were presented almost 'on a plate' to Copernicus by the combined efforts of the ancient astronomers. The third was entirely Ptolemy's achievement. And the fourth, in some ways the least important in the historical perspective, could never have been achieved without the previous three."

p190 "What then was left for Copernicus to do? First, he realized how the scale invariance of the Ptolemaic algorithmic procedure could be exploited to convert the geometrical similarity of the epicyclic motion into identity, that is, he postulated that all the epicyclic radii of the superior planets should be set equal to the earth-sun distance and that the same should be done for the deferents of the inferior planets. Next, he inverted the deferent and epicycle of the two inner planets. then he stretched out his hand, plucked the luminous planets from the tips of the epicyclic spokes and calmly placed them in the ghostly deferent points. Finally, he reversed the earth-sun vector. Thus he made the transition from the geoastral to the helioastral frame. The move was deft, almost cheeky; but at a fundamental level he did precious little else.

Ptolemy built the carousel. Long after the fair-keeper has retired to bed, Copernicus came in the night, moved the linchpin, and switched on the lights. The effect was magical. Science, already stirring, woke from its millennial torpor. Copernicus's proposal is a never-ending source of fascination, bizarre in the manner he made it, incredible in the extent of its far-reaching consequences, and the parallel in science of Richard II's soliloquy on the fate of kings: the merest pinprick that finds the point on which all hinges."

wd40
2018-Mar-25, 05:23 PM
The effect was magical.

Judging by Goethe, Copernicus actually ended the era of Harry Potter-type 'magic':

"But among all the discoveries and new convictions nothing may have produced greater effect on the human spirit than the doctrine of Copernicus. The world had scarcely been recognized as round and complete in itself when it was expected to relinquish the enormous privilege of being the center of the universe. A greater demand may never have been addressed to mankind. For think of all the things that went up in smoke as a result of accepting this: a second Paradise, a world of innocence, poetry and piety, the testimony of the senses, the conviction of a poetic-religious faith: it is no wonder that people did not want to give up all of this, and that they opposed such a doctrine in every way--a doctrine that justified those who accepted it in, and summoned them to a previously unknown, indeed unimagined freedom of thought and largeness of views" (H.Blumenberg, The genesis of the Copernican world p700).



Science, already stirring, woke from its millennial torpor.

One wonders how the Industrial/Scientific Revolution would have played out, if at all, if the Tychonic/tweaked Ptolemaic model had persisted as the consensus view past 1740.

parallaxicality
2018-Mar-26, 07:33 AM
The world had scarcely been recognized as round and complete in itself when it was expected to relinquish the enormous privilege of being the center of the universe.

*bashes head against keyboard repeatedly*

grapes
2018-Mar-26, 09:49 AM
*bashes head against keyboard repeatedly*
Ha! Blumenberg did come up with metaphorology, after all.

Ken G
2018-Mar-26, 08:13 PM
The world had scarcely been recognized as round and complete in itself when it was expected to relinquish the enormous privilege of being the center of the universe.I don't agree with essentially anything that Blumenberg claimed in that quote, but this one is the most blatantly inaccurate. It tries to promote the myth that the ancient Greeks placed the Earth at the center of the universe out of some kind of self-congratulation, or "enormous privilege." To understand why that is so wrong, one must understand the Greek view of the four elements. The loftiest element was fire, which travels up toward the exalted heavens and is found in the "heavenly fires" we see in the night sky. The next most lofty was air, which also travels upward but not as far as fire. Then comes water, which is below the air but is pure enough to be used to wash, and sits atop that lowest of the low elements: earth. Earth was the crud, the muck, that sinks to the center. Get it? Some privilege.

In fact, it is a matter of pure personal preference, and not Copernican doctrine, to decide if you think the Copernican model lowers the rest of the heavens to the status of cruddy Earth, or if it elevates the Earth into a heavenly chariot on a par with those ridden by the gods themselves.

parallaxicality
2018-Mar-26, 09:47 PM
Well yeah that's bad too but I was thinking more about the idea that the Greeks thought the Earth was flat.

wd40
2018-Mar-26, 10:14 PM
I don't agree with essentially anything that Blumenberg claimed in that quote

The quote is actually by the famous Wolfgang Johann Goethe in 1810, and brought in Blumenberg's book.

Ken G
2018-Mar-27, 08:04 AM
The quote is actually by the famous Wolfgang Johann Goethe in 1810, and brought in Blumenberg's book.
Famous for lots of things-- but not astronomy, no. I'll give Goethe the benefit of the doubt though, I suspect he was not talking about what the Greeks thought, but rather, how that all got packaged for the common folk of the Renaissance era. Those uneducated people might have thought the Earth was flat (the Greeks did not), and those folks might have thought it was a "privilege" to be at the center (the Greeks did not). And perhaps if we saw the rest of his writings, we might conclude Goethe did not actually think that a "world of innocence" was somehow shattered by removing the Earth from the center of the universe. I mean, did he not know that the main enemy to the Copernican model was the "innocent" inquisition? Perhaps he felt the common folk felt innocent based on what they were being told by the far-from-innocent authorities of their day, innocent by virtue of not being given the facts. The main point Goethe seems to be making is in agreement with what many have argued on this thread: the Copernican picture of the solar system ushered in a revolutionary new era of openmindedness about our place in the cosmos.

George
2018-Mar-27, 03:07 PM
For the 16th and 17th centuries, I doubt we would find anything but a continuous spectrum of thought between the ranges of a flat Earth and round one, an open Church (Catholic or Protestant) and an oppressive one regarding heliocentricity, pro-Kepler and anti-Kepler views, pro-Galileans and anti-Galileans, etc. Believing what we tend to want to believe can cause cherry-picking that can lead to false conclusions. Bruno held modern views of astronomy, thus some stumble by arguing that he was killed for these views, ignoring his years of heresy against the key tenets of the faith.

I can't imagine that many people then would have a problem with a flat Earth. What difference would it really make for them? I also can't imagine that many people then were not convinced of a spherical Earth especially after Aristotle was hammered into Church doctrine thanks mainly to Aquinas (13th century).