Talk:Celestial spheres/Archive 1

Proposed merger with Sphere (geocentric)
Comparing these two articles I think a merger is in order. Sphere (geocentric) has a somewhat better overall presentation on the background in Greek philosophy, the Ptolemaic system, and on the literary impact.

The section on Kepler in Celestial spheres is extraneous; it would be better to discuss the continued use of the spheres by Copernicus and their ultimate rejection by Tycho and Kepler.

There is a definite need for a consideration of the philosophical and theological implications, on which Grant spends 670 pages, plus a hundred more of notes.

As for title of the merged article, I'd recommend Celestial spheres or Celestial orbs; but then I'm a medievalist and would look there. --SteveMcCluskey 20:55, 23 January 2007 (UTC)


 * For the moment, I have begun to edit and expand the two articles into a more coherent and fully documented one here. --SteveMcCluskey 01:53, 24 January 2007 (UTC) (Edited 14:47, 24 January 2007 (UTC))

Merger implemented
OK, I've rewritten the article; saved it as Celestial spheres; and made Sphere (geocentric) a redirect. There are still some gaps but I think it's an improvement. --SteveMcCluskey 15:37, 25 January 2007 (UTC)

Unmoved mover
Deor: Recently we've been involved in an edit skirmish -- it certainly hasn't escalated to the level of a war -- involving changes back and forth between the Prime Mover to the Primum Mobile. The changes have improved the precision of the discussion, but I think it would help if we clarified the intent of the paragraph being revised.

The paragraph involved concerns the movers of the spheres, not the spheres themselves. In that context the discussion of the first moving sphere should concentrate on its mover, the Prime Mover (who is, as Aristotle says, unmoved), not on the first moving sphere, the Primum Mobile, itself.

I'm going to revise again to take this approach; I hope it meets your concerns. let me know what you think. SteveMcCluskey 14:58, 17 February 2007 (UTC)


 * I'm not going to push it any farther. Before I began editing the article, it contained the sentence "The outermost mover, whose movement affected all others, was referred to as the Prime Mover and identified with God," which was clearly muddled, since the whole point of the Prime Mover is that it has no "movement" itself. In an effort to fix that, I seem to have stepped on your toes. I'm still not exactly sure what objection you have to linking the mention of "the first moving sphere" to the Primum Mobile article, but it's not worth arguing about. Deor 15:11, 17 February 2007 (UTC)


 * Ah; now I see. It was the link to the Primum Mobile that you wanted.  I think we've already resolved the muddle you saw and since I've no problem with the link, I've added it now.  (It's always hard to understand what's in an other editor's mind.)  SteveMcCluskey 18:22, 17 February 2007 (UTC)

Harmonia Mundi
Why has the reference to Kepler's work Harmonia Mundi been removed?

"Johannes Kepler dealt with the concept of the spheres in his work Harmonia Mundi. Kepler drew together theories from the world of music, architecture, planetary motion and astronomy and linked them together to form an idea of a harmony and cohesion underlying all world phenomena and ruled by a divine force. This work remained untranslated into English for over 400 years, until astronomer and mathematician Dr J. Field translated the Latin into English for publication by the American Philosophical Society in Philadelphia in 1997." Above removed 25 January 2007 by SteveMcCluskey   Lumos3 19:57, 18 February 2007 (UTC)


 * Two reasons:
 * First, the removal was part of a total rewrite of the article. In that rewrite I made it clear that Kepler largely abandoned the idea of the spheres, which he had used in several of his earlier works, not just the Harmonia Mundi.  I didn't feel like mentioning all the specific works where he used the spheres.  My replacement read:
 * Although in his early works Johannes Kepler made use of the notion of celestial spheres, by the Epitome of Copernican Astronomy (1621) Kepler was questioning the existence of solid spheres and consequently the need for intelligences to guide the motions of the heavens. An immobile sphere of the fixed stars, however, was a lasting remnant of the celestial spheres in Kepler's thought.
 * I thought the paragraph about Field's translation cluttered the body of the article.
 * Hope this explains my changes. SteveMcCluskey 22:41, 18 February 2007 (UTC)

Spheres not geocentrist
The current opening paragraph is:

"The celestial spheres, or celestial orbs, were the fundamental element of Earth-centered (geocentric) astronomies and cosmologies developed by Plato, Aristotle, Ptolemy, and others. In these geocentric models the stars and planets are carried around the Earth on spheres or circles."

But it is profoundly misleading in respect of ahistorically tying spherism to geocentrism, historically refuted by the case of Copernicus's heliocentric spherism and geoheliocentric celestial models such as those Wittich and Ursus etc. Also Plato did not propose spheres, but rather mere bands for each planet in his Timaeus. Rather it seems it was Aristotle who first introduced spheres, and instead of mere bands for some reason as yet unexplained. And to say the planets are carried around on circles is obviously both physically absurd and geometrically false re planetary orbital paths. I therefore propose this first paragraph be replaced by the following historically less misleading paragraph:

'The celestial spheres, or celestial orbs, were the fundamental celestial entities of the cosmological celestial mechanics founded by Aristotle and developed by Ptolemy, Copernicus and others. [ref] Before Aristotle, in his Timaeus Plato had previously proposed the planets were transported on rotating bands.[ref] In this celestial model the stars and planets are carried around by being embedded in rotating spheres made of an aetherial transparent fifth element (quintessence), like jewels set in orbs. In Aristotle's original model the spheres have souls and they rotate because they are endlessly searching for love, which is the scientific historical origin of the popular saying 'Love makes the world go round'. Arguably nobody has ever proposed a more beautifully romantic cosmology, or at least until the great Yorkshireman Fred Hoyle proposed we are all made of stardust.'

One potential important function of the last two sentences here is to promote educational interest in the article and the fundamental historical importance and cultural influence of cosmology, and thus interest in physics. In his 2005 Lakatos Award lecture, Patrick Suppes emphasised how the theory of the celestial spheres was the most brilliantly successful longstanding cosmology of all time, but ironically so little understood by historians and philosophers of science, especially including the reasons for its termination.

The current untenable geocentrist bias of the remainder of the article should also be corrected. --Logicus (talk) 19:15, 20 February 2008 (UTC)

Anti-Deor: Deor reverted this edit implemented on 20 Feb, with the mistaken justifying comment "rv edit introducing unsourced info and POV - you should wait for feedback on the Talk page)". But in fact (i) the revised text was no more unsourced than the original and (ii) nor did it introduce a POV, but rather corrected the existing untenable geocentrist biassed POV of the original. And whilst Logicus is happy to await feedback before reverting, and indeed in most instances normally both posts proposed edits for discussion first, unlike most other editors, and also awaits feedback except perhaps where text is apparently unquestionably mistaken, he would be grateful if in future Deor would devote his efforts to reverting all other breaches of the rule he proposes before reverting Logicus's, whose edit Deor reverted just 9 minutes after its implementation. --Logicus (talk) 19:58, 22 February 2008 (UTC)
 * "Arguably nobody has ever proposed a more beautifully romantic cosmology, or at least until the great Yorkshireman Fred Hoyle proposed we are all made of stardust" was unacceptable POV in more than one respect. And the sentence preceding that one was factually incorrect. Deor would be grateful if Logicus eschewed personal comments. Deor (talk) 21:23, 22 February 2008 (UTC)


 * Logicus to Deor:I would be grateful to know what you claim is factually incorrect in "the sentence preceding", and why. It is

"In Aristotle's original model the spheres have souls and they rotate because they are endlessly searching for love, which is the scientific historical origin of the popular saying 'Love makes the world go round' "

Re personal comments, Logicus has not made any personal comments about you, but you issued the following very personal dictatorial instruction to Logicus: "YOU should wait for feedback on the Talk page."

I propose to implement at least the uncontested part of the proposed edit pro-tem whilst you explain the alleged error in the following sentence, supplemented with a diagram of a heliocentric model of celestial orbs to correct the historically untenable geocentrist bias.--Logicus (talk) 19:59, 23 February 2008 (UTC)
 * I would be grateful to know what you claim is factually incorrect in "the sentence preceding." No problem: "Endlessly searching for love" is a misrepresentation of what Aristotle wrote ("endlessly moved by their love for the Unmoved Mover" would be more accurate), and the extremely unlikely "is the scientific historical origin of the popular saying 'Love makes the world go round'" is unacceptable without some source other than your say-so. Deor (talk) 15:57, 24 February 2008 (UTC)

Was Dante's God simultaneously in two different places?
The article currently claims:

"Near the beginning of the fourteenth century Dante, in the Paradiso of his Divine Comedy, described God as a light at the center of the cosmos.[15]. Here the poet ascends beyond physical existence to the Empyrean Heaven, where he comes face to face with God himself and is granted understanding of both divine and human nature."

Is this contradictory ? i.e. was God both at the centre and also in the Empyrean Heaven at the same time ? Or is his light at the centre and his face in Heaven ?

This is not a frivolous issue. If both human beings (e.g. Scipio) and/or also God can ascend through the spheres or interpenetrate them, then why not comets also ? --Logicus (talk) 15:22, 24 February 2008 (UTC)
 * As you probably know, God isn't in any "place"; note "beyond physical existence" in the sentences you've quoted from the article. As C. S. Lewis wrote: "All this time we are describing the universe spread out in space; dignity, power and speed progressively diminishing as we descend from its circumference to its centre, the Earth. But I have already hinted that the intelligible universe reverses it all; there the Earth is the rim, the outside edge where being fades away on the border of nonentity. … [refers to the passage in Dante referred to in the article] The universe is thus, when our minds are sufficiently freed from the senses, turned inside out."
 * What this has to do with the penetrability or nonpenetrability of the physical spheres (which Dante himself has already passed through to reach the Empyrean) is, to say the least, unclear. Deor (talk) 16:09, 24 February 2008 (UTC)

Proposed section on inertia and the celestial spheres
Logicus proposes the following text be added to the end of the current 'Middle Ages' section. Another user has deleted a previous posting of it with the clearly mistaken justification that it is irrelevant.
 * I agree that it's irrelevant in this article. You may want to add some of it (with better sourcing) to the appropriate sections of Inertia. Deor (talk) 15:47, 14 June 2008 (UTC)


 * I have now made the footnoted sourcing refs visible. You are both wildly wrong about relevance. The physics of the celestial spheres is absolutely central.--Logicus (talk) 14:46, 15 June 2008 (UTC)

The crucial notion of inertia as an inherent resistance to motion in bodies that was to become the central concept of Kepler's and then Newton's dynamics in the 17th century first emerged in the 12th century in Averroes' Aristotelian celestial dynamics of the spheres to explain why they do not move with infinite speed and thus avoid the refutation of Aristotle's law of motion v @ F/R by celestial motion (where v = average speed of a motion, F = motive force and R = resistance to motion). For in Aristotle's celestial mechanics the spheres have movers but no external resistance to motion such as a resistant medium nor any internal resistance such as the gravity or levity of sublunar bodies that resist 'violent' motion, [ref>Aristotle's quintessence has neither gravity nor levity such as resist violent motion, including rotation, in Aristotle's sublunar physics. 0, and so speed must be infinite. But yet the fastest sphere of all, the stellar sphere, observably takes 24 hours to rotate. In the 6th century Philoponus had sought to resolve this devastating celestial empirical refutation of mathematical dynamics by rejecting Aristotle's core law of motion and replacing it with the alternative law v @ F - R, whereby a finite force does not produce an infinite speed when R = 0.[ref>Some regard this rejection of the core law of Aristotle's dynamics as the overthrow of Aristotelian dynamics tout court. See Sorabji's 1987 Philoponus and the Rejection of Aristotelian Science.</ref]

But some six centuries later Averroes rejected Philoponus's 'anti-Aristotelian' solution to this celestial counterexample, and instead restored Aristotle's law of motion by adopting the 'hidden variable' approach to resolving apparent refutations of parametric laws that posits a previously unaccounted variable and its value for some parameter. For he posited a non-gravitational previously unaccounted inherent resistance to motion hidden in the spheres, a non-gravitational inherent resistance to motion of superlunary quintessential matter. Thus Averroes most significantly transformed Aristotle's law of motion v @ F/R into v @ F/M for the special case of celestial motion with his auxiliary theory of what may be called celestial inertia M. However, Averroes denied sublunar bodies have any inherent resistance to motion other than their gravitational (or levitational) inherent resistance to violent motion.

But Averroes’ 13th century disciple Thomas Aquinas rejected this denial and extended this development in the celestial physics of the spheres to sublunar bodies.[ref>For Aquinas's innovation in extending Averroes' purely celestial inertia to the sublunar region and thus universalising inertia, see Bk4.L12.534-6 of Aquinas's Commentary on Aristotle's Physics Routledge 1963. See Duhem's analysis of this - St Thomas Aquinas and the Concept of Mass - on p378-9 of Roger Ariew's 1985 Medieval Cosmology, an extract also to be found at . But Duhem notably fails to accord Averroes his originating innovatory due compared with Avempace and Aquinas, as more clearly accorded by Sorabji's 1988 Matter, Space and Motion p284.</ref]He thereby claimed this non-gravitational inherent resistance to motion of all bodies would also prevent infinite speed of gravitational motion of sublunar bodies in a vacuum, as otherwise predicted by the law of pre-inertial Aristotelian dynamics in one of Aristotle's famous examples of the impossibility of motion in a vacuum (i.e. a void with natural places and therefore with gravity, as opposed to a pure void without any natural places, and thus without gravity, 'the great inane'.) in which the variant of the law for the special case of natural motion v @ W/R thus became v @ W/0. [ref> See Aristotle's Physics 215a24f  See e.g. the section on Kepler's physics in Koyre's Galilean Studies Thus Newton annotated his Definition 3 of the inherent force of inertia in his copy of the 1713 second edition of the Principia as follows: "I do not mean Kepler's force of inertia, by which bodies tend toward rest, but a force of remaining in the same state either of resting or of moving." See p404 Cohen & Whitman 1999 Principia </ref] Hence the crucial notion of classical mechanics of the resistant force of inertia inherent in all bodies was born in the heavens of medieval astrophysics, in the Aristotelian physics of the celestial spheres, rather than in terrestrial physics or in experiments. This Aristotelian auxiliary theory of inertia, originally devised to account for the otherwise anomalous finite speed rotations of the celestial spheres for Aristotle's law of motion, was the most important development in Aristotelian dynamics in its second millenium of progress in its core law of motion towards the quantitative law of motion of classical mechanics a @ (F - R)/m by providing its denominator, whereby acceleration is not infinite when there is no other resistance to by virtue of the inherent resistant force of inertia m that prevents this.[ref>Its first millenium had seen Philoponus's 6th century innovation of net force in which those forces of resistance by which the motive force was to be divided in Aristotle's dynamics (i.e. media resistance and gravity) were rather to be subtracted, and also Avicenna's most important 10th century terrestrial impetus dynamics innovation, which maintained that gravitational free-fall under a constant gravitational force would be dynamically endlessly accelerated, rather than only initially accelerated as in the analysis of gravitational fall in the Hipparchan impetus variant.</ref]

--Logicus (talk) 14:52, 14 June 2008 (UTC) --80.6.94.131 (talk) 15:51, 16 June 2008 (UTC)

I now provisionally propose something like the following on inertia and the celestial spheres, to be improved, footnotes to be revealed:

Inertia in the celestial spheres

However, the motions of the spheres came to be seen as presenting a major anomaly for Aristotle's celestial dynamics and even refuting his general law of motion v α F/R, according to which all motion is the product of a motive force (F) and some resistance to motion (R), and whose ratio determines its average speed (v). And the ancestor of the crucial classical mechanics concept of inertia as an inherent resistance to motion in bodies was born out of attempts to resolve it. To understand this major problem first we must understand Aristotle's sublunar dynamics, in which all motion is either 'natural' or 'violent'. Natural motion is motion driven solely by the body's own internal 'nature' or gravity (or levity), that is, a centripetal tendency to move straight downward towards their natural place at the centre of the Earth and universe and to be at rest there. And its contrary, violent motion, is simply motion in any other direction whatever, including motion along the horizontal, and it is resisted by the body's own nature or gravity, thus being essentially anti-gravitational motion. Thus gravity is the driver of natural motion but a brake on violent motion.

The only two resistances to sublunar motion Aristotle identified were this gravitational internal resistance to violent motion, measured by the body's weight, and also the external resistance of the medium of motion to being cleaved by the mobile in the sublunar region he held to be a media plenum with no voids. Finally, in sublunar natural motion the law v α F/R becomes v α W/R (because Weight is the measure of the motive force of gravity), with the body's motion driven by its weight and resisted by the medium. But in the case of violent motion the general law then becomes v α F/W because the body's weight now acts as a resistance that resists the violent mover F, whatever that might be, such as a hand pulling a weight up from the floor or a gang of ship-hauliers hauling a ship along the shore or a canal..

However, in Aristotle's celestial physics, whilst the spheres have movers, whereby F > 0, there is no resistance to their motion whatever since Aristotle's quintessence has neither gravity nor levity, whereby they have no internalresistance to their motion, and there is no external resistance such as any resistant medium to be cut through, whereby altogether R = 0. Yet in such terrestrial dynamical conditions as in the case of gravitational fall in a vacuum, driven by gravity but with no resistant medium, Aristotle's law of motion predicts it would be infinitely fast or instantaneous, since then v α W/R = W/0 = infinite. But in spite of these same dynamical conditions of (celestial) bodies with movers without any resistance to them, in the heavens even the fastest sphere of all, the stellar sphere, apparently takes 24 hours to rotate. Thus when interpreted as a cosmologically universal law, Aristotle's basic law of motion was cosmologically refuted by his own dynamical analysis of celestial natural motion as a driven motion without resistance.

In the 6th century Philoponus argued that the rotation of the celestial spheres empirically refuted Aristotle's thesis that natural motion is instantaneous in a vacuum where there is no medium the mobile has to cut through as follows:


 * "For if in general the reason why motion takes time were the physical [medium] that is cut through in the course of this motion, and for this reason things that moved through a vacuum would have to move without taking time because of there being nothing for them to cut through, this ought to happen all the more in the case of the fastest of all motions, I mean the [celestial] rotation. For what rotates does not cut through any physical [medium] either. But in fact this [timeless motion] does not happen. All rotation takes time, even without there being anything to cut through in the motion."

Philoponus sought to resolve this devastating celestial empirical refutation of Aristotelian mathematical celestial dynamics by Aristotle's own rotating celestial spheres by rejecting Aristotle's core law of motion and replacing it with the alternative law v α F - R, whereby a finite force does not produce an infinite speed when R = 0.

But some six centuries later, in the 12th century Averroes rejected Philoponus's 'anti-Aristotelian' solution to this refutation of Aristotelian celestial dynamics, and instead restored Aristotle's law of motion by adopting the 'hidden variable' approach to resolving apparent refutations of parametric laws that posits a previously unaccounted variable and its value(s) for some parameter. For he posited a non-gravitational previously unaccounted inherent resistance to motion hidden in the celestial spheres, a non-gravitational inherent resistance to motion of superlunary quintessential matter, whereby R > 0 even when there is neither any gravitational nor media resistance to motion. Thus Averroes most significantly revised Aristotle's law of motion v α F/R into v α F/M for the case of celestial motion with his auxiliary theory of what may be called celestial inertia M, whereby R = M > 0. But Averroes restricted inertia to celestial bodies and denied sublunar bodies have any inherent resistance to motion other than their gravitational (or levitational) inherent resistance to violent motion, just as in Aristotle's original sublunar physics.

However, Averroes’ 13th century disciple Thomas Aquinas rejected this denial of sublunar inertia and extended his development in the celestial physics of the spheres to all sublunar bodies, whereby he posited all bodies universally have a non-gravitational inherent resistance to motion. He thereby predicted this non-gravitational inherent resistance to motion of all bodies would also prevent an infinite speed of gravitational free-fall as otherwise predicted by the law of pre-inertial Aristotelian dynamics in one of Aristotle's famous examples of the impossibility of motion in a vacuum. Thus by eliminating the prediction of its infinite speed, Aquinas made gravitational fall in a vacuum possible in an alternative way than Philoponus had.

But some four centuries later it was Kepler who first dubbed this non-gravitational inherent resistance to motion in all bodies universally as 'inertia', and then Newton who revised it to exclude resistance to uniform straight motion, a purely ideal form of motion. Hence the crucial notion of 17th century early classical mechanics of a resistant force of inertia inherent in all bodies was born in the heavens of medieval astrophysics, in the Aristotelian physics of the celestial spheres, rather than in terrestrial physics or in experiments.

This Aristotelian auxiliary theory of inertia, originally devised to account for the otherwise anomalous finite speed rotations of the celestial spheres for Aristotle's law of motion, was the most important conceptual development in physics and in Aristotelian dynamics in its second millenium of progress in the transformation of its core law of motion towards the quantitative law of motion of classical mechanics a α (F - R)/m. For it provided what was eventually to become its denominator, whereby acceleration is not infinite when there is no other resistance to motion by virtue of the inherent resistant force of inertia m.

--Logicus (talk) 18:17, 18 June 2008 (UTC) Updated 19 June --Logicus (talk) 18:16, 19 June 2008 (UTC)


 * It seems that Logicus is proposing to use the discussion of the celestial spheres as a coatrack on which he wishes to hang a discussion of his idiosyncratic pov on the history of inertia. Strangely, his discussion ignores the elemental distinction between the terrestrial and celestial realm and the nature of the motion (circular and unchanging) that was natural to the substance (Aether or quintessence) which makes up the celestial region.  As mentioned above, this is increasingly irrelevant to the topic of this article.
 * Secondly, the anachronistic use of ratios to discuss Aristotle's (and Philoponus's) concepts of celestial motion moves this article away from a proper discussion of the physics of the celestial region. A good start would be the studies by G. E. R. Lloyd and Edward Grant on these matters.  --SteveMcCluskey (talk) 14:33, 19 June 2008 (UTC)


 * Logicus commentary on McCluskey (emboldened in square brackets):


 * It seems that Logicus is proposing to use the discussion of the celestial spheres as a coatrack on which he wishes to hang a discussion of his idiosyncratic pov on the history of inertia. [Not at all. Rather the history of the concept of inertia is of central relevance to the physics of the celestial spheres, just as was also the concept of impetus.] Strangely, his discussion ignores the elemental distinction between the terrestrial and celestial realm and the nature of the motion (circular and unchanging) that was natural to the substance (Aether or quintessence) which makes up the celestial region. [Strangely, McClusky ignores the fact that Logicus's discussion does not in any way ignore this distinction in this context, albeit the very medieval question at issue here was precisely whether there was such a distinction.] As mentioned above, this is increasingly irrelevant to the topic of this article. [Aux contraire, as revealed by the quotation from McCluskey's mentor Grant provided by Logicus below on 20 June, it is increasingly relevant.]


 * Secondly, the anachronistic use of ratios to discuss Aristotle's (and Philoponus's) concepts of celestial motion moves this article away from a proper discussion of the physics of the celestial region. [But as the evidence from Philoponus, Averroes and Aquinas clearly shows, the use of ratios, ultimately stemming from Eudoxus, was to the contrary central to their discussions of the physics of the celestial region, in such considerations of the importance of the ratio of the power of the mover to the resistance of the mobile asserted by Aquinas in the reference to his Commentary given, which it seems McCluskey cannot have read.] A good start would be the studies by G. E. R. Lloyd and Edward Grant on these matters.[Perhaps McCluskey would be good enough to show why the studies of Lloyd and Grant, with which Logicus is well familar, would be a good start, rather than possibly a bad start, for example. But at least Grant apparently agrees with Logicus on the central relevance of the physics of the spheres, contra McCluskey] --SteveMcCluskey (talk) 14:33, 19 June 2008 (UTC)

--Logicus (talk) 16:25, 20 June 2008 (UTC)

Proposed restoration of the section on the history of inertia of the spheres

There has been no response in 3 months to Logicus's proposed invitation to objections and corrections to his proposed text on the history of inertia in the spheres. The history of the introduction of the notion of inertia as an inherent force of resistance to motion within the context of the Aristotelian dynamics of celestial motion and the spheres is clearly of central importance and relevance both to the history of physics and of the celestial spheres, as revealed by Pierre Duhem's important pioneering work in deconstructing the Enlightenment-positivist historical model of a 17th century revolution in physics by demonstrating the origins of the concepts of 17th century dynamics of such as Galileo and Newton in scholastic physics. Logicus therefore proposes the restoration of this section with the following hopefully improved text:

The dynamics of the celestial spheres

Inertia in the celestial spheres

However, the motions of the celestial spheres came to be seen as presenting a major anomaly for Aristotelian dynamics, and as even refuting its general law of motion v α F/R, according to which all motion is the product of a motive force (F) and some resistance to motion (R), and whose ratio determines its average speed (v). And the ancestor of the central concept of Newtonian mechanics, the concept of the force of inertia as an inherent resistance to motion in all bodies, was born out of attempts to resolve it. This problem of celestial motion for Aristotelian dynamics arose as follows.

In Aristotle's sublunar dynamics all motion is either 'natural' or 'violent'. Natural motion is motion driven solely by the body's own internal 'nature' or gravity (or levity), that is, a centripetal tendency to move straight downward towards their natural place at the centre of the Earth (and universe) and to be at rest there. And its contrary, violent motion, is simply motion in any other direction whatever, including motion along the horizontal, and such motion is resisted by the body's own 'nature' or gravity, thus being essentially anti-gravitational motion. Hence gravity is the driver of natural motion, but a brake on violent motion, or as Aristotle put it, a principle of both motion and rest. And gravitational resistance to motion is virtually omni-directional, whereby in effect bodies have horizontal 'weight' as well as vertically downward weight. The former consists of a tendency to be at rest and resist motion along the horizontal wherever they may be on it, as distinct from their tendency to centripetal motion as downwards weight that resists upward motion.

The only two resistances to sublunar motion Aristotle identified were this gravitational internal resistance to violent motion, measured by the body's weight, and also the external resistance of the medium of motion to being cleaved by the mobile in the sublunar plenum, measured by its density. Finally, in sublunar natural motion the general law v α F/R becomes v α W/R (because Weight is the measure of the motive force of gravity), with the body's motion driven by its weight and resisted by the medium. But in the case of violent motion the general law v α F/R then becomes v α F/W because the body's weight now acts as a resistance that resists the violent mover F, whatever that might be, such as a hand pulling a weight up from the floor or a gang of ship-hauliers hauling a ship along the shore or a canal.

However, in Aristotle's celestial physics, whilst the spheres have movers, each being 'pushed' by its own soul towards its own god as it were, whereby F > 0, there is no resistance to their motion whatever, since Aristotle's quintessence has neither gravity nor levity, whereby they have no internal resistance to their motion. And nor is there any external resistance such as any resistant medium to be cut through, whereby altogether R = 0. Yet in such terrestrial dynamical conditions as in the case of gravitational fall in a vacuum, driven by gravity but which has no resistant medium, Aristotle's law of motion predicts it would be infinitely fast or instantaneous, since then v α W/R = W/0 = infinite. But in spite of these same dynamical conditions of (celestial) bodies having movers but no resistance to them, in the heavens even the fastest sphere of all, the stellar sphere, apparently took 24 hours to rotate. Thus when interpreted as a cosmologically universal law, Aristotle's basic law of motion was cosmologically refuted by his own dynamical model of celestial natural motion as a driven motion without any resistance to it.

In the 6th century Philoponus argued that the rotation of the celestial spheres empirically refuted Aristotle's thesis that natural motion would be instantaneous in a vacuum where there is no medium the mobile has to cut through, as follows:


 * "For if in general the reason why motion takes time were the physical [medium] that is cut through in the course of this motion, and for this reason things that moved through a vacuum would have to move without taking time because of there being nothing for them to cut through, this ought to happen all the more in the case of the fastest of all motions, I mean the [celestial] rotation. For what rotates does not cut through any physical [medium] either. But in fact this [timeless motion] does not happen. All rotation takes time, even without there being anything to cut through in the motion."

Consequently Philoponus sought to resolve this devastating celestial empirical refutation of Aristotelian mathematical dynamics by Aristotle's own rotating celestial spheres by rejecting Aristotle's core law of motion and replacing it with the alternative law v α F - R, whereby a finite force does not produce an infinite speed when R = 0. The essential logic of this refutation of Aristotle's law of motion can be reconstructed as follows. The prediction of the speed of the spheres' rotations in Aristotelian celestial dynamics is given by the following logical argument [ (i) v α F/R &  (ii) F > 0  &  (iii) R = 0 ]  entail  v is infinite. These premises comprise the conjunction of Aristotle's law of motion in premise (i) with his dynamical model of celestial motion expressed in premises (ii) & (iii). But the contrary observation v is not infinite entails at least one premise of this conjunction must be false. But which one ? Philoponus decided to direct the falsifying arrow of modus tollens at the very first of the three theoretical premises of this prediction, namely Aristotle's law of motion, and replace it with his alternative law v α F - R. But logically premises (ii) or (iii) could have been rejected and replaced instead.

But some six centuries later, in the 12th century Averroes rejected Philoponus's 'anti-Aristotelian' solution to this refutation of Aristotelian celestial dynamics, and instead restored Aristotle's law of motion by adopting the 'hidden variable' approach to resolving apparent refutations of parametric laws that posits a previously unaccounted variable and its value(s) for some parameter, thereby modifying the predicted value of the subject variable. For he posited a non-gravitational previously unaccounted inherent resistance to motion hidden within the celestial spheres. This was a non-gravitational inherent resistance to motion of superlunary quintessential matter, whereby R > 0 even when there is neither any gravitational nor any media resistance to motion.

Hence the alternative logic of Averroes' solution to the refutation of the prediction of Aristotelian celestial dynamics [ (i) v α F/R &  (ii) F > 0  &  (iii) R = 0 ] entails  v is infinite was to reject its third premise R = 0 instead of rejecting its first premise as Philoponus had. Thus Averroes most significantly revised Aristotle's law of motion v α F/R into v α F/M for the case of celestial motion with his auxiliary theory of what may be called celestial inertia M, whereby R = M > 0. But Averroes restricted inertia to celestial bodies and denied sublunar bodies have any inherent resistance to motion other than their gravitational (or levitational) inherent resistance to violent motion, just as in Aristotle's original sublunar physics.

However, Averroes’ 13th century follower Thomas Aquinas rejected this denial of sublunar inertia and extended Averroes' innovation in the celestial physics of the spheres to all sublunar bodies. He posited all bodies universally have a non-gravitational inherent resistance to motion constituted by their magnitude or mass. In his Systeme du Monde the pioneering historian of medieval science Pierre Duhem said of Aquinas's innovation:


 * "For the first time we have seen human reason distinguish two elements in a heavy body: the motive force, that is, in modern terms, the weight; and the moved thing, the corpus quantum, or as we say today, the mass. For the first time we have seen the notion of mass being introduced in mechanics, and being introduced as equivalent to what remains in a body when one has suppressed all forms in order to leave only the prime matter quantified by its determined dimensions. Saint Thomas Aquinas's analysis, completing Ibn Bajja's, came to distinguish three notions in a falling body: the weight, the mass, and the resistance of the medium, about which physics will reason during the modern era....This mass, this quantified body, resists the motor attempting to transport it from one place to another, stated Thomas Aquinas."

He thereby predicted this non-gravitational inherent resistance to motion of all bodies would also prevent an infinite speed of gravitational free-fall as otherwise predicted by the law of motion applied to pre-inertial Aristotelian dynamics in Aristotle's famous Physics 4.8.215a25f  argument for the impossibility of natural motion in a vacuum i.e. of gravitational free-fall. Thus by eliminating the prediction of its infinite speed, Aquinas made gravitational fall in a vacuum dynamically possible in an alternative way to that in which Philoponus had.

Another logical consequence of Aquinas's theory of inertia was that all bodies would fall with the same speed in a vacuum because the ratio between their weight, i.e. the motive force, and their mass which resists it, is always the same, or in other words in the Aristotelian law of average speed v α W/m,  W/m = 1 and so v = k, a constant. But it seems the first known published recognition of this consequence of the Thomist theory of inertia was in the early 15th century by Paul of Venice in his critical exposition on Aristotle's Physics, as follows:


 * "It is not absurd that two unequal weights move with equal speed in the void; there is, in fact, no resistance other than the intrinsic resistance due to the application of the motor to the mobile, in order that its natural movement be accomplished. And the proportion of the motor to the mobile, with respect to the heavier body and the lighter body, is the same. They would then move with the same speed in the void. In the plenum, on the other hand, they would move with unequal speed because the medium would prevent the mobile from taking its natural movement."

As Duhem commented, this "glimpses what we, from the time of Newton, have expressed as follows: Unequal weights fall with the same speed in the void because the proportion between their weight and their mass has the same value." But the first mention of a way of testing this novel prediction of Aristotelian dynamics seems to be that of comparing pendulum motions in air as detailed in the First Day of Galileo's 1638 Discorsi.

But some five centuries after Averroes' innovation, it was Kepler who first dubbed this non-gravitational inherent resistance to motion in all bodies universally 'inertia'. Hence the crucial notion of 17th century early classical mechanics of a resistant force of inertia inherent in all bodies was born in the heavens of medieval astrophysics, in the Aristotelian physics of the celestial spheres, rather than in terrestrial physics or in experiments.

This auxiliary theory of Aristotelian dynamics, originally devised to account for the otherwise anomalous finite speed rotations of the celestial spheres for Aristotle's law of motion, was a most important conceptual development in physics and Aristotelian dynamics in its second millenium of progress in the dialectical evolutionary transformation of its core law of motion into the basic law of motion of classical mechanics a α (F - R)/m. For it provided what was eventually to become its denominator, whereby when there is no other resistance to motion, the acceleration produced by a motive force is still not infinite by virtue of the inherent resistant force of inertia m. Its first millenium had seen Philoponus's 6th century innovation of net force in which those forces of resistance by which the motive force was to be divided in Aristotle's dynamics (e.g. media resistance and gravity) were rather to be subtracted instead to give the net motive force, thus providing what was eventually to become the numerator of net force F - R in the classical mechanics law of motion.

The first millenium had also seen the Hipparchan innovation in Aristotelian dynamics of its auxiliary theory of a self-dissipating impressed force or impetus to explain the sublunar phenomenon of detached violent motion such as projectile motion against gravity, which Philoponus had also applied to celestial motion. The second millenium then saw a radically different impetus theory of an essentially self-conserving impetus developed by Avicenna and Buridan which was also applied to celestial motion.

--Logicus (talk) 18:25, 15 September 2008 (UTC)

Did Ptolemy have spheres or discs ?
The article currently claims:

"In Ptolemy's model, each planet is moved by two or more spheres (or strictly speaking, by thick equatorial slices of spheres): one sphere is the deferent, with a center offset somewhat from the Earth; the other sphere is an epicycle embedded in the deferent, with the planet embedded in the spherical epicycle." [My italics]

But what does the italicised text mean ? A thick equatorial slice of a sphere is surely just a thick disc. So did Ptolemy have spheres or discs ? Or maybe even anular discs ?

If discs, surely following proposed edit would be better ?:

'In Ptolemy's model, each planet is moved by two or more discs: one disc is the deferent, with a centre offset somewhat from the Earth; the other disc is an epicycle embedded in the deferent, with the planet embedded in the epicyclical disc.'

--Logicus (talk) 14:35, 20 June 2008 (UTC)


 * Good point. The reason for this ambiguity is that later interpreters of Ptolemy (e.g., Alhacen and the authors of the various theorica planetarum texts) interpreted the Ptolemaic model as referring to solid spheres and that became the dominant interpretation.  Perhaps it could best be clarified by transforming the text to:
 * "In the Ptolemaic model, each planet is moved by two or more spheres (Ptolemy himself considered sometimes spoke of them as thick equatorial slices of spheres while later interpreters generally considered them to be complete spheres): one sphere is the deferent, with a center offset somewhat from the Earth; the other sphere is an epicycle embedded in the deferent, with the planet embedded in the spherical epicycle."
 * --SteveMcCluskey (talk) 19:44, 21 June 2008 (UTC)


 * Rechecking the reference cited in the article (Murschel, JHA, 1995), I find that Ptolemy was inconsistent, speaking in Book I of spheres and in Book II of thick equatorial slices. Murschel considers this as a concession to the needs of instrument makers while Neugebauer, HAMA, p. 923 considers them "a return to the plane figures of the Almagest".  Incidentally, since the citation was provided at the end of the paragraph, the citation needed template was unnecessary.  --SteveMcCluskey (talk) 20:14, 21 June 2008 (UTC)


 * Logicus comments:Thanks a lot for this interesting clarification. But re the citation I was seeking was rather to what Ptolemy himself actually said with a reference to where he said it (in some English translation). Is “thick equatorial slice” a literal translation of something he actually wrote, or if not what phrase did he use and where ? You must appreciate I am by long experience sceptical of claims made by historians of science that do not provide the original reference for them, as so often false re claims made e.g. about Aristotle’s physics that give no reference in his texts. Ultimately I am just trying to make any possible mechanical sense of the celestial physics of spheres/bands about which historians of science are terribly equivocal. I drafted the following before seeing your response here.


 * ‘However, if 'sphere' is interpreted as a 'hollow sphere' or spherical shell rather than a solid sphere, then a thick equatorial slice of it is simply a thick ring or short cylindrical band with a convex rather than flat outer surface, or in other words, a band as in Plato's Timaeus cosmology rather than a sphere as in that of Eudoxus and Aristotle. But how can an epiyclical ring possibly be physically "embedded in" the deferential ring without physically impossible intersection if these two rings are solids? The only possibility would seem to be if the epicyclical band were somehow axially mounted on the circumference of the deferential band, somewhat like a catherine wheel pinned through its centre onto a point on the perimeter of another catherine wheel. But then the epicylical ring must in fact be a disc or like a cartwheel with spokes for there to be a physical centre. Can anybody make any physical sense of this model ?


 * But whatever, since Ptolemy's model is not spherist, but rather bandist, it has no place in an article on the celestial spheres on Deor and McCluskey type reasoning.(-:’


 * The philosophical problem that looms in the background is that of the possibility or not of interpenetrating substances, of which there was much discussion as Sorabji 1988 most interestingly reveals. And that relates to crucial questions e.g. like whether comets can pass through spheres, of whether Christ could achieve Ascension, problem of the Eucharist, or whether the Martian and solar orbits can interpenetrate.


 * It should also be clarified whether the spheres are indeed solid spheres or not, or rather nested spherical shells, because if they are solid all through, then we have interpenetrating spheres, as some people did. I reckon they were spherical shells.


 * I provisionally propose the following edit of your re-edit:


 * ‘In the Ptolemaic model, each planet is moved by two or more spheres, but in Book 2 of his Planetary Hypotheses Ptolemy depicted circular bands as in Plato’s model rather than spheres as in its Book 1.[ref to where he says this.] Later interpreters [of Ptolemy ?] generally considered them to be spheres. One sphere/band is the deferent, with a centre offset somewhat from the Earth; the other sphere/band is an epicycle embedded in the deferent, with the planet embedded in the epicyclical sphere/band.’


 * But the problem with this still remains that of what on earth physical sense can be made of the bands model, as opposed to the spheres model which allows for physical embedding ? I suspect all celestial mechanics was ultimately based on terrestrial mechanics somehow. --Logicus (talk) 17:06, 22 June 2008 (UTC)
 * I think you're overlooking the possibility that for Ptolemy and for some others, including many Muslim and early Renaissance astronomers, the spheres (however interpreted) were primarily computational models, and that Ptolemy, for one, didn't devote much thought to the problems and consequences associated with positing the physical existence of spheres, epicyles, etc. Deor (talk) 18:17, 22 June 2008 (UTC)
 * Logicus on Deor:No, Logicus has not overlooked that possibility. Rather he has never seen it established with reliable evidence that for Ptolemy and many other astronomers the spheres were primarily or only idealistic computational models rather than real, albeit some historians of science have claimed such, but without evidence. The latter have been unduly influenced by the philosophical 'realism versus instrumentalism' debate, or rather 'realism versus idealism' debate, stemming from the philosophies of science of such as Duhem and Mach. History of science is typically (rotten) philosophy fabricating examples. It is, for example, patently false as Deor claims that Ptolemy "didn't devote much thought to the problems and consequences associated with positing the physical existence of spheres, epicyles, ", as his Planetary Hypotheses amply reveals to the contrary of this standard mantra of historians of science parroted by Deor. But the ultimately idiotic nature of the claim that "the spheres (however interpreted) were primarily computational models," is that only geometrical circles were mathematically required as computing devices, not spheres, so why bother positing or mentioning spheres at all rather than circles, since they were not practically used as such in computation ? And even more idiotically, what does 'spheres (however interpreted)' mean ? Interpreted as cubes or as cones or as cylinders, for example ? The point is the geometrical computational model was only the circle and no other geometrical figure, not spheres however interpreted, but only if interpreted as a circle. Logicus would appreciate it if Deor would desist from his frequent apparently ignorant and silly comments on Logicus's contributions.
 * --Logicus (talk) 17:59, 3 July 2008 (UTC)

Logicus on McCluskey's Ptolemy inconsistency claim:

McCluskey wrote above "Rechecking the reference cited in the article (Murschel, JHA, 1995), I find that Ptolemy was inconsistent, speaking in Book I of spheres and in Book II of thick equatorial slices. Murschel considers this as a concession to the needs of instrument makers while Neugebauer, HAMA, p. 923 considers them "a return to the plane figures of the Almagest".

But in apparent contrast with McCluskey's above claim that Ptolemy is inconsistent about the shapes of the celestial bodies between Bk 1 and Bk 2 of his Planetary Hypotheses, according to Langermann 1990 rather he simply set out two alternative possible models that could not be decided by mathematical investigation. And also to confirm Logicus's realist speculation above that astronomers were concerned with developing real physical models based on terrestrial mechanical models rather than purely idealistic computational models, just like Aristotle, Ptolemy was certainly concerned with fashioning his celestial mechanics on terrestrial mechanical models, such as the tambourine, for example. For Langermann wrote [p19]:

"In Book II [of Planetary Hypotheses] Ptolemy undertakes to establish the shapes of the bodies that carry out the heavenly motions....He states

'For each of these motions, which are different in quantity or kind, there is a body that moves freely on poles and in space and which has a special place...'

Ptolemy then postulates two possible paths of approach to the physical explanation of the workings of the cosmos.

'The first of them is to assign a whole sphere to each motion, either hollow like the spheres that surround each other or the earth, or solid and not hollow like those which do not contain anything other than the thing [itself], namely those that set the stars in motion and are called epicyclic orbs. The other way is that we set aside for each one of the motions not a whole sphere but only a section (qitcah) of a sphere. This section lies on the two sides of the largest circle which is in that sphere, namely that from which the motion is longitude [is taken]. That which this section closes from the two sides is [equal to] the amount of latitude. Thus the shape (shakl) of this section, when taken from an epicyclic orb, is similar to a tambourine (duff). When taken from the hollow sphere, it is similar to a belt (nitaq), an armband (siwar) or a whorl (fulkah), as Plato said. Mathematical investigation shows that there is no difference between these two ways that we have described.' [Nix 113:16-33  Goldstein 37:9-17]

However, it may be that McCluskey is right that Ptolemy was also inconsistent and asserted both of these two alternative mutually exclusive models in two different places in his Planetary Hypotheses. But in the light of Langermann's above analysis, and especially given the notorious traditional difficulties historians of science have in identifying logical inconsistencies or not in scientific works, then McCluskey surely needs to produce and source Ptolemy's statements in this work that are claimed to be inconsistent, showing that he asserted both of two mutually incompatible physical models, before any such logical claim is accepted.

--Logicus (talk) 18:17, 30 June 2008 (UTC)

The unjustified disruptive deletions of Deor?
Logicus writes: User Deor has adopted McCluskey's practice of unjustifiably deleting highly relevant and informative material on the celestial spheres added to the article, in compliance with Wikipedia's request for expansion in general, and in particular in line with the views of Edward Grant, whose views were advocated by McCluskey above on 19 June, that discussion of the physical nature of the celestial spheres was a central topic of medieval science.

Logicus added at the beginning of the section 'Middle Ages': "Since it was unanimously agreed [in the middle ages] that the planets and stars were carried round on physical spheres, numerous questions were posed about the nature and motion of those spheres. How many are there ? Does God move the primum mobile or first moveable sphere, directly and actively as an efficient cause, or only as a final or ultimate cause ? Are all the heavens moved by one mover or several; and if by several, what kinds are they ? Are the celestial movers conjoined to their orbs or distinct from them ? Are the spheres moved by intelligences, angels, forms or souls, or by some principle inherent in their very matter ? Do celestial movers experience exhaustion or fatigue ? Does the celestial region form a continuous whole, or are the spheres contiguous and distinct ? Are the orbs all of the same specific nature or of different natures ? Are the orbs concentric with the Earth as common centre, or is it necessary to assume eccentric and epicyclic orbs ? The nature of celestial matter was widely discussed. Was it like terrestrial matter in possessing an inherent substantial form and inherent qualities such as hot, cold, moist and dry ? Does it undergo change involving generation and corruption, increase and diminution ?"[ref>Quotation from Edward Grant's Cosmology, Chapter 8 of Science in the Middle Ages Lindberg(Ed)1978 Chicago p268. To this list should surely be added the following two most crucially important questions: Do the spheres obey the laws of terrestrial motion ? Do the spheres have any inherent resistance to motion or not ?

Arguably this list also provides a most useful guide to issues that need discussing in the article.

But Deor deleted this addition with an untenable justification, namely "noninformative long quotation". Why ? It is surely highly informative about the issues discussed on the nature of the spheres in the middle ages.

Deor also deleted the highly informative centrally relevant section added by Logicus on the Parisian impetus dynamics of the spheres. This issue is traditionally regarded as of great relevance in the history of physics and astronomy because of allegedly being the very first elimination of animistic explanations of celestial motion that explained the sphere's rotations in terms of their supposed souls instead of its explanation in terms of terrestrial physics, namely impetus dynamics.

Logicus had added the following text to the end of the 'Middle Ages' section

Parisian impetus dynamics and the celestial spheres In the 14th century the logician and natural philosopher Jean Buridan, Rector of Paris University, subscribed to the Avicennan variant of Aristotelian impetus dynamics according to which impetus is conserved forever in the absence of any resistance to motion, rather than being evanescent and self-decaying as in the Hipparchan variant. In order to dispense with the need for positing continually moving intelligences or souls in the celestial spheres, which he pointed out are not posited by the Bible, he applied impetus theory to their endless rotation by extension of a terrestrial example of its application to rotary motion in the form of a rotating millwheel that continues rotating for a long time after the originally propelling hand is withdrawn, driven by the impetus impressed within it.[ref>According to Buridan's theory impetus acts in the same direction or manner in which it was created, and thus a circularly or rotationally created impetus acts circularly thereafter. He wrote on the celestial impetus of the spheres as follows: "God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more...And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus."[ref>Questions on the Eight Books of the Physics of Aristotle: Book VIII Question 12  English translation in Clagett's 1959 Science of Mechanics in the Middle Ages  p536

However, having discounted the possibility of any resistance due to a contrary inclination to move in any opposite direction and due to any external resistance, Buridan obviously also discounted any inherent resistance to motion in the form of an inclination to rest within the spheres themselves, such as the inertia posited by Averroes and Aquinas. And in fact contrary to that inertial variant of Aristotelian dynamics, according to Buridan "prime matter does not resist motion". But this then raises the question within Aristotelian dynamics of why the motive force of impetus does not therefore move them with infinite speed. The impetus dynamics answer seemed to be that it was a secondary kind of motive force that produced uniform motion rather than infinite speed, just as it seemed Aristotle had supposed the planets' moving souls do, or rather than uniformly accelerated motion like the primary force of gravity did by producing increasing amounts of impetus.

Logicus proposes Deor attempts to justify his arguably vandalous deletions in this forum or else desists from such deletion. —Preceding unsigned comment added by Logicus (talk • contribs) 15:48, 20 June 2008 (UTC)
 * The article should deal with exactly what its title implies—the spheres, their natures, and their history in human thought—not the theories of impetus or inertia or the details of planetary motions. If those are the topics that you are interested in, I suggest that the relevant sections of Inertia or Theory of impetus or Celestial mechanics may be appropriate places for various portions of the information you want to add, inappropriately, to Celestial spheres. We have different articles on different topics for a reason; one doesn't need to attempt to regurgitate everything one knows (or thinks one knows) in any one of them. In addition, the unintroduced quotation you added at the beginning of the "Middle Ages" section consisted entirely of a series of questions and provided the general reader with no relevant information.
 * I'll assume that "arguably vandalous" was just a poor attempt at humor on Logicus's part. You've brought various lengthy suggestions to this Talk page and have found no editors who agree with you about them. I'd say that insisting on inserting the information in the article anyway is what borders on disruption. Deor (talk) 16:30, 20 June 2008 (UTC)


 * Logicus on Deor's invalid justifications: Thanks for making the gross invalidity of your justification for excluding material on the physics of the celestial spheres from this article so transparent on these pages, as I had anticipated. See my inserted critical comments emboldened in square brackets:


 * The article should deal with exactly what its title implies—the spheres, their natures, and their history in human thought—not the theories of impetus or inertia or the details of planetary motions. [WRONG. Both the theories of impetus and of inertia are exactly of central relevance to the issue of the natures of the spheres, namely to whether they have inertia in their natures as an essential inherent resistance to motion, and to whether they have essentially divine natures with souls that move them around or only accidental internal impetus which assimilates them to the nature of inanimate terrestrial physics such as projectile motion. And the details of planetary motions are crucial to whether the spheres intersect or not, and thus what their physical nature must be e.g. solid or fluid and whether interpenetrable.]


 * If those are the topics that you are interested in, I suggest that the relevant sections of Inertia or Theory of impetus or Celestial mechanics may be appropriate places for various portions of the information you want to add, inappropriately, to Celestial spheres. [WRONG, my information is highly appropriate.] We have different articles on different topics for a reason; one doesn't need to attempt to regurgitate everything one knows (or thinks one knows) in any one of them. [So do you want an entirely separate article on the Physics of the Celestial Spheres then, in order to bring all the relevant information on it together in one place ?] In addition, the unintroduced quotation you added at the beginning of the "Middle Ages" section consisted entirely of a series of questions and provided the general reader with no relevant information.[WRONG AGAIN! Here you make an elementary  literacy error. These are not questions to the reader, but are rather informing the reader of the kinds of questions that were asked about the physical nature of the spheres in the middle ages, and they also provide a list of topics on the physics of the spheres that should be discussed in the article. The quotation is thus highly informative, and has the added virtue that its author is revered by McCluskey. We are dealing here with an article on the most long lasting and successful cosmology in the history of physics, and one that surely deserves detailed treatment of its physics at least for what it reveals about the scientific enterprise, rather than being stifled by Deleting Deor.]
 * I'll assume that "arguably vandalous" was just a poor attempt at humour on Logicus's part. [No, serious !] You've brought various lengthy suggestions to this Talk page and have found no editors who agree with you about them. [Have you made you made up some spurious rule that one must find other editors to agree with it before implementing an edit ? All has happened here is that only a mere two editors have objected, and both with utterly invalid reasons.]
 * I'd say that insisting on inserting the information in the article anyway is what borders on disruption. [I’d say that if I had done that, it would be educational good sense against the apparently short-minded attitudes of yourself and McCluskey. The article should obviously go into all the physics of the spheres, just as its current discussion of whether they were solid or fluid does, which I note you have inconsistently not deleted.]

Deor (talk) 16:30, 20 June 2008 (UTC)


 * I suggest you critically review your perspicuously untenable position on this issue. Do you also think an article on the atom, for example, should not go into the physics of the atom and its laws of motion ? --Logicus (talk) 18:48, 22 June 2008 (UTC)

--Logicus (talk) 18:48, 22 June 2008 (UTC)

How many movers does each planetary sphere have ?
The article currently claims that in the 'Middle Ages'

"Each of the lower spheres was moved by a subordinate spiritual mover (a replacement for Aristotle's multiple divine movers), called an intelligence."

But this is ambiguous between the following two meanings

1. Each lower sphere had its own single spiritual mover whereas Aristotle had many divine movers in each sphere.

OR

2. Just a single spiritual mover moved every inner sphere, whereby altogether there were only two spiritual movers for the whole system of spheres, namely God who moved the outermost sphere and the other single spiritual mover who moved all the other spheres, rather than the 48 or 56 spiritual movers in Aristotle's system, comprising the 47 or 55 who moved each of the 47 or 55 inner spheres plus the mover of the primum mobile.

Now 1 is definitely false because in his Metaphysics 12.8 Aristotle only assigned one god as mover to each one of the inner spheres rather than many to each sphere.

As for 2, it is definitely false at least inasmuch as there were those who retained Aristotle's model of each inner sphere having its own single spiritual mover, typically an angel in the Christian cosmology. But further, did anybody at all propose just a dual mover model for the whole system ?

Immediately I shall flag citation needed for these claims, but suggest this sentence should be replaced by

'Each lower sphere was moved by just one subordinate divine mover per sphere.'

Called an intelligence ?

"...called an intelligence. " is false in general inasmuch as there was also an ontology according to which the actual mover was the soul of the sphere, and its intelligence was only the navigator or driver regulating the movement, not its mover nor motor. Thus, for example, in denying this medieval ontology for the case of the Sun, in his 1630 Epitome (p516) Kepler argued the although the Sun had a soul that moved it, the constancy of its rotation was not regulated by any intelligence, but rather just by the law of inertial dynamics that governed it:


 * "I think a soul must be postulated [for the Sun] rather than an inanimate form...[But] there is absolutely no need of mind or intelligence for the functions of [its rotating] movement. [For] the constancy of the revolution and of the periodic time [of the solar body]...depends upon the ratio of the constant power of the mover to the obstinacy [i.e. inertia] of the matter [ i.e. v @ F/m ]."

This, by the way, is why it is ludicrous to claim as Wikipedia does that Kepler invented celestial physics, at least in the sense of a non-animistic physics. It seems that important innovation in the middle ages must be attributed to Buridan who in the 14th century replaced the spiritual movers of the spheres by incorporeal but inanimate impetus, which is permanently conserved in the absence of any resistance. But impetus as a celestial mover was not an option in Kepler's Thomist inertial dynamics, in which all bodies have an inherent resistance to motion he called 'inertia', unlike Buridan's dynamics in which prime matter does not resist motion, whereby such impetus would be destroyed by this inertia. But important information about Buridan's crucial innovation in the physics of the spheres added by Logicus has unjustifiably been deleted from this article by Deor. --Logicus (talk) 17:33, 23 June 2008 (UTC)

Planetary attachments?
In its Antiquity section the article currently claims

"The planets are attached to anywhere from 47 to 55 concentric spheres that rotate around the Earth."

But this claim is arguably false because the 7 planets are only directly attached to 7 spheres, namely to one each. The great majority of spheres - 39 or 47 in all ? - have nothing whatever attached to them. Maybe the author meant 'attached to' in the sense of 'somehow interconnected to' ?

For greater clarity I propose this sentence be edited to become something like

'The planets are moved by anywhere from X to Y uniformly rotating geo-concentric nested spheres. Each planet is attached to the innermost of its own particular set of spheres.'

The numbers of spheres X and Y here are to be determined according to the outcome of a forthcoming Logicus discussion about just how many celestial spheres there are in Aristotle’s model, a matter of interpretation about which historians of science disagree, as per usual. --Logicus (talk) 17:48, 23 June 2008 (UTC)

Are the astronomers the experts on the exact numbers of spheres and of gods for Aristotle?
In its 'Antiquity' section the article currently claims

"Aristotle says [in his Metaphysics] that to determine the exact number of spheres and the number of divine movers, one should consult the astronomers." with the two footnotes "^ G. E. R. Lloyd, Aristotle: The Growth and Structure of his Thought, pp. 133-153, Cambridge: Cambridge Univ. Pr., 1968. ISBN 0-521-09456-9. ^ G. E. R. Lloyd, "Heavenly aberrations: Aristotle the amateur astronomer," pp.160-183 in his Aristotelian Explorations, Cambridge: Cambridge Univ. Pr., 1996. ISBN 0-521-55619-8."

It is G.E.R. Lloyd whose studies McCluskey recommends, along with those of Grant, as a good starting point for "a proper discussion of the physics of the celestial region." compared with Logicus's discussion McCluskey condemns as improper.

But this claim is significantly false and misleading in various respects, two of which are as follows:

1) Its most misleading aspect is its apparent meaning that Aristotle said that to know the exact number of spheres and divine movers one should simply ask the astronomers what they are and simply take their word for it i.e. ask the experts. But Aristotle did not do so. For he reported the astronomer Eudoxus as having 27 spheres and Callippus as having 34 spheres (on one reckoning), whereas he argued 56 spheres or at least 48 are required to explain the observed planetary motions.. The reason for the difference seems to have been that Aristotle wanted the otherwise separate spheres for each planet to be interconnected such that the daily rotation of the outermost stellar sphere was automatically transmitted inwards to each planet.'s own spheres without the additional specific motions of any intervening planet also being transmitted to the next inner planet, thus requiring sets of counteracting 'rollers' to nullify the differences in their motion from that of the daily stellar rotation in the motion transmitted to the next planet inwards. So rather than saying one should consult the astronomers to know the exact number of spheres, Aristotle said (in Ross's translation):

"But in the number of the movements [i.e. of uniformly rotating spheres] we reach a problem which must be treated from the standpoint of that one of the mathematical sciences which is most akin to philosophy - viz. of astronomy; for this science speculates about substance which is perceptible but eternal, but the other mathematical sciences, i.e. arithmetic and geometry, treat of no substance." Metaphysics 1073b

So what he said was that the question of the number of spheres must be dealt with from the standpoint of astronomy, which speculates about the observable eternal planets. Not that we should get the exact number of spheres and movers from astronomers.

But he then quotes what some astronomers say about the number of spheres, but only in order to start the ball rolling from some definite figures from which to determine the exact number for himself. For he says:

"But as to the actual number of these movements, we now - to give some notion of the subject - quote what some of the mathematicians say, that our thought may have some definite number to grasp; but for the rest, we must partly investigate for ourselves, partly learn from other investigators, and if those who study this subject form an opinion contrary to what we have now stated, we must esteem both parties indeed, but follow the more accurate." Metaphysics 1073b

So it seems Aristotle learnt from Eudoxus and Callippus to some extent, largely followed the more accurate Callippus re their differences, and then added another 22 spheres himself. Aristotle's real disagreement with them seems to lay in the nature of the celestial mechanics involved, and whether the spheres were one totally interconnected system, rather than 7 unconnected independent sub-systems of spheres for each planet, plus the stellar sphere itself.

In conclusion, one does not get the EXACT number of spheres from the astronomers, but rather one must do astronomy oneself to get it.

2) "...and the number of divine movers...

Whilst one may get the exact number of spheres from doing astronomy, Aristotle does not also say, as claimed above, one also gets the number of divine movers - eternal imperceptible substances - from astronomy. Rather that is the subject of metaphysics. such as whether the rule is indeed one divine unmoved mover per sphere or not. And as Aristotle concludes:

"Let this [number, 47 or 55], then, be taken as the number of the [planetary] spheres, so that the unmoveable substances and principles may also probably be taken as just so many; the assertion of necessity must be left to more powerful thinkers." Metaphysics 1074a15

Aristotle is apparently not too certain about the one-one relationship of gods to spheres.

So in conclusion the article's claim here attributed to Lloyd - that Aristotle's says one should get the exact number of spheres from astronomers - is significantly false and misleading, whether or not Lloyd has in effect been misreported.

I propose the following replacement.

'Aristotle says the exact number of spheres is to be determined by astronomical investigation. The exact number of divine unmoved movers is to be determined by metaphysics, and Aristotle assigned one unmoved mover per sphere. '

But the historically important point this overlooks is that Aristotle apparently made a major historical innovation in the celestial mechanics of astronomy in respect of interconnecting all the different planets' spheres together into just one mechanical transmission model rather than a collection of separate models for each planet. His specific innovation was the introduction of 'unrolling' spheres to achieve this, but which the astronomers had not accounted. This information should be added once it has been clarified by further discussion.

So much for Lloyd being a good start on Aristotle's celestial physics ! Useful reading here in addition to Aristotle's Metaphysics is Dreyer's History of Astronomy on Eudoxus, Callippus and Aristotle, and Grant's 1996 Foundations of Modern Science in the Middle Ages p65-7, although both may be numerically mistaken in their analyses of Aristotle's spheres, as may well have been Aristotle himself. See the following discussion to come on these problems. --Logicus (talk) 17:37, 24 June 2008 (UTC)

How many spheres are there in Aristotle's model ?
The article currently gives the impression Aristotle's celestial model had " ...anywhere from 47 to 55 concentric spheres..."

But this is the number of spheres stated by many historians of science* who fail to read the logical context of Aristotle's presentation when he announces 47 or 55 planetary spheres, namely that he is discussing the number of extra spheres and unmoved movers required by the planets in addition to the stellar sphere and prime unmoved mover he has already discussed. So the stellar sphere must be added to the 47 or 55 planetary spheres to get the total number of 48 or 56 celestial spheres altogether. {*e.g. Edward Grant says "Aristotle's [cosmological] system consisted of 55 concentric celestial spheres..." on p71 of his 1977 Physical Science in the Middle Ages]

So I provisionally edit the numbers in the article.

But there are also various other problems with gleaning the number of spheres posited variously by Eudoxus, Callippus and Aristotle from Aristotle’s Metaphysics analysis. It may be that he made a counting error and the maximum number should have been 49.

Immediately here I just post a simple table, for other editors to ponder and criticise, that currently seems to me to be the most plausible account of Aristotle’s analysis, whereby the max number of spheres should have been 49 rather than his 56. But I may well have blundered somehow.

Column 1 gives the number of spheres it seems Aristotle may attribute to Eudoxus, and Column 2 for Callippus. Column 3 gives the number for Callippus when the daily stellar sphere counterpart he and Eudoxus gave to each planet's set of spheres is knocked out when the single stellar sphere does that job when Aristotle connects up all the spheres to get total transmission of the stellar rotation to reach planet's spheres. Column 4 enumerates Aristotle’s unroller spheres required when he connects up, with his final grand totals of 'actives' plus 'unrollers' in Column 5.

1	 2		3	    4		5

Eudoxus   Kalippus      Kalippus     Aristotle's  Aristotle minus dailies 'unrollers'	Totals

Moon		3	  5		4	     0		4

Venus		4	  5		4	     4		8

Mercury	       4	   5		4	     4		8

Sun		3	  5		4	     4		8

Mars		4	  5		4	     4		8

Jupiter		4	  4		3	     3		6

Saturn		4	  4		3	     3		6

Stellar Sph    1	   1		1	     0		1

27	  34		27   +	     22    =	49

NB To see this Table formatted properly use Edit mode

To be discussed further…

--Logicus (talk) 18:13, 24 June 2008 (UTC)

Estimating the number of spheres Aristotle required:

There are disagreements between different historians of science on their estimates of how many spheres Aristotle posited or really needed. But on the most logically coherent interpretation, to save the planetary phenomena his model only required 49 or else 41 spheres rather than his 56 or 48. In fact it seems that rather than, as some historians of science seem to suggest, his estimate of the numbers of spheres just included practically redundant spheres whilst yet saving the phenomena, instead on Aristotle's numbers the Moon must orbit the Earth 8 times per day rather than just once and Saturn twice a day, Jupiter thrice, and so forth. For it seems Aristotle forgot to eliminate Callippus's 7 separate spheres for the daily rotation of the fixed stars in each planet's independent set of spheres that are no longer required when their function is taken by the single outermost stellar sphere once it is mechanically connected to and transmits its daily rotation to all the other spheres. Thus a daily rotating sphere axially fixed within an already daily rotating sphere would produce a 12-hourly compounded revolution, and yet another daily rotating sphere an 8-hourly compounded revolution, and so forth. So it seems Aristotle's model with 56 spheres rather than 49, and hence with a daily rotating outermost stellar sphere connected to 7 further daily rotating spheres, one for each planet, would have massively contradicted the phenomena. The logical reasoning for this interpretation based on the text of Aristotle's Metaphysics and its commentaries by Dreyer 1906, Grant 1996 and Heath 1913 is as follows.

[To be continued]--Logicus (talk) 18:05, 3 July 2008 (UTC)

Is the common geocentric planetary order right ?
The article currently claims:

"In geocentric models the spheres were most commonly arranged outwards from the center in this order: the sphere of the Moon, the sphere of Mercury, the sphere of Venus, the sphere of the Sun, the sphere of Mars, the sphere of Jupiter, the sphere of Saturn, the starry firmament, and sometimes one or two additional spheres."

But is this right, rather than rather Moon, Venus, Mercury, Sun...? Although the Apian diagram shows Moon Mercury Venus, the geoheliocentric diagrams show Moon Mercury Venus Sun as it were, and I had also somehow got the impression this was the most common arrangement for the pure geocentric model. I suggest this claim at least needs a citation, so will flag it. --Logicus (talk) 17:48, 25 June 2008 (UTC)

Almagest a purely geometrical model ?
The article currently claims:

"The astronomer Ptolemy (fl. ca. 150 AD) defined a geometrical model of the universe in his Almagest and extended it to a physical model of the cosmos in his Planetary hypotheses"

But what is the evidence that the Almagest is a non physical purely geometrical model ? It clearly talks of the spheres as though real, such as in Book 9 for example.

A citation to the Almagest itself in English translation denying the physical reality of the spheres is surely needed here, so I shall flag it.

It then claims next

"In doing so, he achieved greater mathematical detail and predictive accuracy than had been lacking in earlier spherical models of the cosmos."

But in doing what ? By extending a geometrical model to a physical model ? This needs clarifying, disambiguating.

--Logicus (talk) 18:01, 26 June 2008 (UTC)

What did Ptolemy explain or improve upon ?
The article currently claims:

"Through the use of the epicycle, eccentric, and equant, this model of compound circular motions could account for all the irregularities of a planet's apparent movements in the sky.[7][8]"

But if this means Ptolemy explained all the observed phenomena in exact detail, as it appears to mean, then it is patently false, since otherwise this would have been the end of planetary astronomy in completely perfect predictions without room for improvement.

But if "irregularities" means deviations from some rule, it is meaningless unless the rule(s) and irregularities are identified.

So what does it mean ? Is it trying to say Ptolemy explained more types of phenomena than previously had been ? But what ?

One thing the Ptolemaic model explained to some extent was variable brightness for planets such as Venus and Mars, but this is hardly an irregularity rather than a variation, and anyway such had already been explained by the epicyclical models of Heraclides, Apollonius and Hipparchus.

What is actually required here is a statement of what preceding model/astronomy Ptolemy's model improved upon and how, if indeed it did. Presumably it was the astronomy of Hipparchus he was trying to improve on, including in such important respects as increasing the Hipparchan star catalogue by hundreds(?) of stars.

However, mention of Robert Newton's 1977 thesis that Ptolemy was a massive fraudster who concocted his claimed observations from those of Hipparchus to fit his model also needs to be included. (Gingerich's 1980 apologetics 'Was Ptolemy a fraud ?' is of interest).

In the interim of a reliable statement of Ptolemy's achievement being provided, I propose the deletion of this false or meaningless claim, unless it can be acceptably clarified.

It should perhaps be noted that Gingerich's assessment of Ptolemy's astronomical achievement seems patently false:

"...for the first time in history (so far as we know) an astronomer has shown how to convert specific numerical data into the parameters of planetary models, and from the models has constructed a homogeneous set of tables...from which solar, lunar and planetary positions and eclipses can be calculated as a function of any given time." (p55 The Eye of Heaven)

But obviously the conversion of "specific numerical data into the parameters of planetary models" was already long entrenched, for example in such trivialities as the observed data of a 24 hour rotation of the fixed stars converted into the parameter of the period of revolution of a uniformly rotating sphere, or Aristarchus's conversion of data into parameters of the sizes of spheres. And publishing the predictions of a model is a publishing achievement rather than an astronomical achievement.

--Logicus (talk) 15:30, 27 June 2008 (UTC)


 * User Deor has restored this false or meaningless claim deleted by Logicus without justification. The fact that somebody makes this bizarre claim does not mean it should therefore be repeated in Wikipedia. But in the first instance I propose Deor should provide the actual quotation from the source supplied that actually makes this bizarre claim, to see whether it does justify it.. One often finds with Wikipedia history of science sources for claims made that they do not justify the claim made because the author has misinterpreted what they actually said. I shall delete the claim again until it is reliably justified, but which of course it cannot be essentially because it is blatantly false. --Logicus (talk) 17:35, 28 June 2008 (UTC)


 * User Deor uncivilly transgresses Wikipedia courtesy requirements


 * User Deor has yet again restored the following untenable claim first deleted by Logicus on 27 June after demonstrating it was either false or meaningless:


 * "Through the use of the epicycle, eccentric, and equant, this model of compound circular motions could account for all the irregularities of a planet's apparent movements in the sky.[7][8]"


 * without providing any justifying quotation for this claim from the justifying sources given, as courteously requested by Logicus here on 28 June in Talk as follows:


 * "User Deor has restored this false or meaningless claim deleted by Logicus without justification. The fact that somebody makes this bizarre claim does not mean it should therefore be repeated in Wikipedia. But in the first instance I propose Deor should provide the actual quotation from the source supplied that actually makes this bizarre claim, to see whether it does justify it.. One often finds with Wikipedia history of science sources for claims made that they do not justify the claim made because the author has misinterpreted what they actually said. I shall delete the claim again until it is reliably justified, but which of course it cannot be essentially because it is blatantly false. --Logicus (talk) 17:35, 28 June 2008 (UTC)"


 * Thus Deor is apparently in breach of the courtesy requirement stipulated in the second and third paragraphs of the following Wikipedia rules for Verifiability in reliable sources


 * " # ^ When content in Wikipedia requires direct substantiation, the established convention is to provide an inline citation to the supporting references. The rationale is that this provides the most direct means to verify whether the content is consistent with the references. Alternative conventions exist, and are acceptable when they provide clear and precise attribution for the article's assertions, but inline citations are considered "best practice" under this rationale. For more details, please consult Wikipedia:Citing_sources#How_to_cite_sources.


 * ^ When there is dispute about whether the article text is fully supported by the given source, direct quotes from the source and any other details requested should be provided as a courtesy to substantiate the reference.


 * The burden of evidence lies with the editor who adds or restores material. All quotations and any material challenged or likely to be challenged should be attributed to a reliable, published source using an inline citation.[1] "


 * Logicus would be grateful for Deor's compliance with these courtesy requirements, especially noting that Logicus has repeatedly shown Deor's friend McCluskey's cited sources do not justify the claims he makes, whereby McCluskey stands exposed as committing Original Research and breaching NPOV in such cases. In one recent major blunder in this respect, in the Scientific Revolution article's Talk page on 18 April McCluskey tried his usual stunt of insinuating or accusing Logicus's corrections of his untenable POV handiwork breach NPOV because Logicus had pointed out Aristotle did not maintain all motion requires an external force but only violent motion, contrary to McCluskey's claim that Aristotle did according to Stillman Drake, whereupon Logicus had to quote the Stanford Encyclopedia of Philosophy on Aristotle at McCluskey before he would accept Logicus was right and he and Drake as reported were wrong. The triumvirate of Deor, McCluskey and Ragesoss would do well to study this episode as a powerful illustration of how it is they, not Logicus, who impose POVs and Original Research in Wikipedia history of science articles, whilst making insulting unjustified accusations of such against Logicus who challenges them.


 * Will the outcome be similar in this case ? Will Deor manage to find some textual quotation that shows some historians of science do indeed hold this manifestly mistaken view ?
 * --Logicus (talk) 01:01, 7 July 2008 (UTC)