Talk:Deferent and epicycle

message: Is it correct to speak of planetary "orbits" in Ptolemaic astronomy?  As I understand it (someone correct me if I'm wrong), before astronomers began to seriously attack that idea of the heavens being eternal (e.g., Tycho Brahe's calculations that comets move through different planetary spheres and are not sub-lunar, widespread observation of novae, etc.), the basic cosmology involved planets embedded within rotating spheres and not actually orbiting anything.--ragesoss 18:52, 19 May 2006 (UTC)
replies: text: I agree, but because there are so many presentist histories and translations that say "orbit," you might find some opposition unless you dig up a source that does terminology. Maestlin 20:29, 19 May 2006 (UTC)
replies: text: One of the meanings of orbit is sphere.  -- Another Stickler (talk) 22:44, 4 December 2008 (UTC)
thread_title: Ptolemy and "orbits"

message: I find this sentence: "The popular total of about 80 circles for the Ptolemaic system seems to have appeared in 1898" rather strange. Could it be a mistake or a typo? Or maybe it suggests that this large number was added in posterior sources (modern encyclopedias)? Hugo Dufort 02:04, 16 November 2006 (UTC)
replies: text: Yes, it's suggesting that there wasn't ever a system actually in use with 80.--ragesoss 03:10, 16 November 2006 (UTC)
thread_title: 1898? 

message: The last paragraph starts "The difficulty with this account" and corrects some errors in the previous several paragraphs. As it is, the "Epicycles on epicycles" section is confusing and contradictory. I hope someone fixes this. Roger 06:00, 28 December 2006 (UTC)
thread_title: Fix errors

message: I propose that Equant be merged into this article and the article be renamed as to have a more general name (such as Elements of Ptolemaean astronomy or something) as if deferents and epicycles are covered in one article, so should equants be, presumably. I am basing the assumption that all the aforementioned items are elements of Ptolemaean astronomy on pp. 30-31 of . It Is Me Here (talk) 18:41, 7 July 2008 (UTC)
replies: text: I disagree. The equant is peculiar to Ptolemy's models. Copernicus was able to eliminate it from his models. Ptolemy was not the only one to use the deferent/epicycle method for modeling planetary orbits. Virgil H. Soule (talk) 05:09, 6 November 2008 (UTC)
replies: text: I disagree too.  Since the merge template has been on this page for over a year and a half, I will remove it.  --SteveMcCluskey (talk) 14:27, 3 May 2010 (UTC)
thread_title:  [[Equant]] merger 

message: Characterizing use of epicycles as "Bad Science" is nonsense. Observers of the time of Ptolemy were trying to find ways to derive mathematical descriptions of the planetary motion they saw against the (apparently) invariant star field. They didn't know orbits. They didn't know geocentric. They didn't know science. They may not have been aware that the Earth rotated about its own axis. They saw the star field moving cyclically on a daily basis so naturally they assumed that the Earth was fixed at the center of the universe. This fit in with religious dogma (particularly Christian) that asserted that the universe was miraculously created and the Earth was the center of that creation.
They used epicycles to trace out planetary motions because that's what worked. The problem was made more complicated by the retrograde motion that the planets displayed from time to time. The solution was to superimpose more epicycles and bring in the equant idea to make the math work. The cost was inordinate complexity in the model. They did the best they could with what they had at the time.
Copernicus' great contribution was in discovering that moving the center of the universe to the Sun greatly simplified Ptolemy's model. The motion of the planets as seen from the Sun is much simpler than that seen from the Earth. He also introduced the notion that the Earth rotated on its axis and presented the trigonometric transformations needed to resolve observations made on Earth to Heliocentric coordinates. Again, he used epicycles because that's what worked. They worked because the orbits of the then-known planets are nearly circular. Copernicus probably didn't know orbits, however. The idea of the Earth moving about the Sun was not well received particularly by the Catholic Church but also by many astronomers of the time.
The notion of orbital motion came with Galileo's discovery of the moons of Jupiter. Kepler refined the idea with his discovery that planetary orbits were elliptical rather than circular.
Characterizing use of epicycles as bad science implies that people like Ptolemy were cranks or quacks who didn't know what they were doing. They were honest people trying to make sense of the universe they saw around them. Virgil H. Soule (talk) 19:31, 19 October 2008 (UTC)
replies: text: Yes it is nonsense, but what do you suggest? Roger (talk) 20:15, 19 October 2008 (UTC)

text: Bad science confuses theories of motion with descriptions of motion. The Earth based observations are what is known and these support a description whether it be epicycles or osculating Keplerian orbits. Egotism and predujice also taint interpretations as does the propaganda battle between the "old" world and the "new." --Jbergquist (talk) 18:57, 4 July 2011 (UTC)
thread_title:  Bad Science? 

message: I just read the article and viewed the Java applet it links to, and it really doesn't adequately describe the subject. From the article I get the impression that if you approximate all the orbits in this system, then you'd get a model that is heavily centered on the angle between the earth and the sun. And that in turn should have triggered the question of what made the sun so special much sooner, especially for the inner planets.
Then furthermore I can't square the Java applets with the text. The Ptolemy version clearly shows deferents and epicycles, but no hint of equants. Also for the outer planets the epicycles are somewhat unexpected, although I can kind of see the behaviour it tries to model, I can't say it's really understandable. What is the Ptolemaic location versus the real location of the planets in these cases? Then there's Brahe's version, which is what you'd expect to find, but with no equant again.
I can't make sense of these mismatches and the article is not sufficiently referenced or illustrated to really tell what's going on... what was the motivation for example for the equant, and the motion of the epicycles with respect to these? Why this and not something else? What did it really look like? The illustration in the article doesn't show this at all, and the applets appear inconsistent with the article. What was the modelled location and the now known real location of the planets in various situation in the various models?
Also, part of the article needs to be rewritten for accessibility to laypeople. 82.139.86.37 (talk) 01:48, 21 March 2009 (UTC)
thread_title:  Inadequate article 

message: The ancients worked from a geocentric perspective because the Earth was the platform on which they stood. Some Greek astronomers (e.g., Aristarchus of Samos) had speculated that the planets (Earth included) orbited the Sun but the mathematics needed to transform geocentric observations to a heliocentric perspective didn’t exist in Ptolemy’s time.
The latter claim is highly dubious. Indeed, considering this property of the Ptolemaic system:
Despite the fact that the Ptolemaic system is considered geocentric, the planets' motion was not thought to be actually centered on the Earth. Instead, the deferent was centered around a point halfway between the Earth and another point called the equant. The epicycle, meanwhile, rotated and revolved along the deferent with uniform motion. The rate at which the planet moved on the epicycle was fixed such that the angle between the center of the epicycle and the planet was the same as the angle between the earth and the sun.
the claim can be seen to be nonsense, since a heliocentric system requires less complication in the math than a deferent-centric system of the kind described. It would be a mistake to assume that anything as general as a modern understanding of coordinate transformations would have been required.
Also, according to Bartel Leendert van der Waerden's "The Heliocentric System in Greek, Persian and Hindu Astronomy", there is evidence that the math needed was available to and used by Seleucus of Seleucia, well before Ptolemy's time.
There is some discussion of more plausible reasons why heliocentric theories might not have been accepted earlier in the Heliocentrism article.
--David-Sarah Hopwood ⚥ (talk) 00:14, 6 January 2010 (UTC)
thread_title:  Dubious 

message: Both Deferent and epicycle and Phlogiston theory were theories that fit the data but were abandoned due to other reasons. 96.26.97.207 (talk) 00:54, 27 February 2012 (UTC)
replies: text: In the case of Ptolemy's theory, the problem was that with a fixed number of epicycles per body you can only approximate the elliptical orbits that we now know are correct (ignoring perturbations), so eventually the data outed the theory. So, no, Ptolemy's theory doesn't match the data. The whole idea in experimental science is to design an experiment (produce data) which will differentiate between competing theories. SkoreKeep (talk) 17:22, 3 August 2014 (UTC)
thread_title:  Theories that fit the data yet become abandoned due to other reasons 

message: I'm no expert on complex valued Fourier series, but comparing the  Mathematical Formalism subsection of this article with the  Exponential Fourier Series subsection of the  Fourier Series article suggests the k_j terms are under specified (they are in fact left undefined). Comparing the mathematics in the Mathematical Formalism subsection with Hanson's paper, for the Fourier expansion in the latter there are two epicycles for each value of j, one for a_j e^{i k_j t} and one for a_{-j} e^{-i k_j t}. Hanson sums from -N to N, whereas the series in the subsection sums from 0 to N. Furthermore, I think the k_j must be defined using integer multiples of the fundamental frequency, e.g., k_j=\frac{2j\pi}{T}.
Perhaps it is possible to fix things up so the sum goes from 0 to N, but I think there are advantages to summing from -N to N. Specifically, for j = 0, there would be only one term, which can be used to center the deferent on a point other than the origin of the coordinate system. This seems to fall out naturally, since a_0 e^{i (0) t} = a_0, which is a constant.
One other point. It probably is prudent to indicate in this section that the Mathematical Formalism provided is an extension of the Deferent and Epicycle system used in the Ptolemaic model. I believe the latter only used one epicycle per deferent. Dnessett (talk) 16:50, 17 April 2013 (UTC)
replies: text: I have investigated further and now believe that the formulation given in the article is correct. The expansion z_N=\sum_{j=0}^N a_j e^{i k_j t} is a type of Fourier Series known as a Besicovitch almost periodic function. I have added a reference to the Wikipedia article that describes such functions. Dnessett (talk) 15:36, 7 May 2013 (UTC)
replies: text: Actually it's a Bohr almost periodic function, the sum being finite.  The Besicovitch almost periodic functions are one of several generalizations listed in the article you cite to infinite sums; in Besicovitch's case the sequence of coefficients aj is required to come from an ℓ2 space, i.e. the sequence must be square-summable, which holds vacuously for finite sums.  Vaughan Pratt (talk) 17:47, 18 September 2014 (UTC)
thread_title:  Is the mathematics in the "Mathematical Formalism" correct? 

message: It seems to me that there is a lot more information in this article than there needs to be.  It's about "deferents and epicycles", but it gets into eccentrics, equants, Ptolemy, Copernicus and Brahe, stuff related to but way beyond the named subjects, all of which should be moved to articles on geocentrism and the planetary theories of the afore-mentioned worthies. Compare, for example, to the article on the equant. I have myself lately been guilty of gilding the lily on this article, before I pulled back somewhat for a larger picture.
I propose to rewrite it to that standard, and while I'm waiting for comment, I'll wander on over to geocentrism and see what needs to happen there.SkoreKeep (talk) 20:01, 5 August 2014 (UTC)
replies: text: I agree it does wander  too much into the history of geocentrism (e.g. The 6 paragraphs starting 'Owen Gingerich')  but I don't agree with excluding  eccentrics and equants.  The title may not be terribly appropriate but it's the only article covering this whole Ptolemaic system and I think it's useful for that. Where else would one look? Chris55 (talk) 21:57, 5 August 2014 (UTC)
thread_title: Too much

message: I'm not much of a mathematician, but I don't believe this statement is true. Certainly many complex paths can. But a straight line cannot, and does not have a Fourier transform valid for all time. Neither does a non-periodic trivial predator-prey model. If there is no analytical expression possible, then while an infinite set of points could be said to represent such curves, one cannot represent such points exactly without the original "open-form" expressions which are not based on epicycles nor a fourier basis.
Dpleibovitz (talk) 16:46, 9 February 2016 (UTC)
replies: text: The key here is an "infinite" number of epicycles.  They resolve down, I believe, to sinusoids and an infinite number of them will reproduce any given function (even a constant).  That it does not do so near the end points is not a problem for them, because the end points physically are embedded in the chaotic beginning of the solar system and the far future. For a time interval of a couple of thousand years on either side of 1 AD is not a problem. To say you need to have an analytical solution is to negate the usefulness of Fourier, LaPlace and Taylor series in general. And there, you've also heard the sum of my math knowledge on the matter.  SkoreKeep (talk) 20:59, 11 February 2016 (UTC)
thread_title:  Any path—periodic or not, closed or open—can be represented with an infinite number of epicycles. 

message: I question whether Hanson is in this section a reliable source in general, and for the quote in particular.
Having read the reference I cannot help but feel that Hanson is out of his depth on this matter. The relevant section is outside of his regular area and he clearly lacks the required historical knowledge to accurately present what he discusses.
Further, the quote in this article is pulled out of context. As it is quoted, it is subtly wrong. It would be correct if it said ‘infinite’ instead of ‘finite’, but that would go against what the reference is trying to say, namely that a wide variety of curves can be approximated by stacking a few epicycles on top of each other. But due to the quote being pulled out of context it appears to say that any curve in use can be exactly reproduced and that isn't true.
Considering that the quote is wrong, needs a lot of context to become right, isn't necessary nor particularly relevant to this article, doesn't really add anything to this article and comes from a relatively shaky source, I propose to remove it altogether.  — Preceding unsigned comment added by 80.114.146.117 (talk) 22:31, 9 May 2016 (UTC)
thread_title:  About the quote in the section Mathematical formalism 

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thread_title:  External links modified 

message: Dear Wikipedians, I've just created an animated javscript program that draws any given close curve with a number of epicycles (gianmarco-todesco.github.io/epicycles). 
The animation is similar to other animations currently linked in the article but it has its own specificity and value. The program is open-source and released with an MIT license. The content is - IMHO - good visual support to the article. 
I want to contribute to Wikipedia (that I use daily) and so I added the external link. The link has been removed and I've received a warning.
I understand that I can not use Wikipedia to publish my own websites. On the other side, Wikipedia uses very many images that have been created and donated by contributors. I created the JavaScript program with the same spirit: I want to contribute to Wikipedia with a specific medium. 
Is there a specific procedure that I can follow to submit an animation that I've created? 
best regards, gmt  Gianmarco-todesco (talk) 10:08, 21 January 2020 (UTC)
thread_title:  How to submit an external link? 

message: In the first line of the article, Galileo is not mentioned, although he seems to have used epicycles. Galileo never accepted Kepler's ellipses, which were brought to his notice in 1609 and 1612.  — Preceding unsigned comment added by 213.48.238.18 (talk) 16:27, 10 October 2021 (UTC)
replies: text: It is not mentioned anywhere in the article that Galileo retained the epicycles of Copernicus and rejected Kepler's ellipses.  — Preceding unsigned comment added by 213.48.238.18 (talk) 17:40, 18 May 2022 (UTC)
thread_title:  Should be mentioned 

message: On the latter sections, more than the first ones, there is an increase in the number of quotations, which partially goes against the wiki's guidelines on article writing, and I will paraphrase them to fit the guidelines better if any believe that this is incorrect, please feel free to undo my changes or reach out to me.
Besmeraldo (talk) 03:14, 9 November 2021 (UTC)
thread_title:  Quotations