The Golden Chain Argument

 

Rheticus

 

"With regard to the apparent motions of the Sun and Moon, it is perhaps possible to deny what is said about the motion of the Earth, although I do not see how the explanation of precession is to be transferred to the sphere of the stars. But if anyone desires to look either to the order and harmony of the system of the spheres, or to ease and elegance and a complete explanation of the causes of the phenomena, by no other hypotheses will he demonstrate more neatly and correctly the apparent motions of the remaining planets. For all these phenomena appear to be linked most nobly together, as by a golden chain; and each of the planets, by its position and order and very inequality of its motion, bears witness that the Earth moves. . . .

 

I sincerely cherish Ptolemy and his followers equally with my teacher, since I have ever in mind and memory that sacred precept of Aristotle: "We must esteem both parties but follow the more accurate." And yet somehow I feel more inclined to the hypotheses of my teacher. This is so perhaps partly because I am persuaded that now at last I have a more accurate understanding of the delightful maxim which on account of its weightiness and truth is attributed to Plato: "God ever geometrizes"; but partly because in my teacher's revival of astronomy I see, as the saying is, with both eyes and as though a fog had lifted and the sky were now clear, the force of that wise statement of Socrates in the Phaedrus: "If I think any other man is able to see things that can naturally be collected into one and divided into many, him I follow after and 'walk in his footsteps as if he were a god.'" 1540, Narratio Prima

 

Maestlin

 

"Certainly this is the great argument, viz. that all the phenomena as well as the order and magnitudes of the orbs are bound together in the motion of the Earth." [An annotation in Maestlin's own hand to his copy of Copernicus's De revolutionibus, probably made between 1570 and 1580.]

 

Kepler

 

". . . the ancient hypotheses clearly fail to account for certain important matters. For example, they do not comprehend the causes of the numbers, extents and durations of the retrogradations and of their agreeing so well with the position and mean motion of the sun. Copernicus alone gives an explanation to those things that provoke astonishment among other astronomers, thus destroying the source of astonishment, which lies in the ignorance of the causes." 1596, Mysterium Cosmographicum

 

Galileo

 

Salviati: "In the Ptolemaic hypotheses there are the diseases, and the Copernican their cure. . . . With Ptolemy it is necessary to assign to the celestial bodies contrary movements, and make everything move from east to west and at the same time from west to east, whereas with Copernicus all celestial revolutions are in one direction, from west to east. And what are we to say of the apparent movement of a planet, so uneven that it not only goes fast at one time and slow at another, but sometimes stops entirely and even goes backward a long way after doing so? To save these appearances, Ptolemy introduces vast epicycles, adapting them one by one to each planet, with certain rules about incongruous motions -- all of which can be done away with by one very simple motion of the Earth.

 

Sagredo: I should like to arrive at a better understanding of how these stoppings, retrograde motions, and advances, which have always seemed to me highly improbable, come about in the Copernican system.

 

Salviati: Sagredo, you will see them come about in such a way that the theory of this alone ought to be enough to gain assent for the rest of the doctrine from anyone who is neither stubborn nor unteachable. I tell you, then, that no change occurs in the movement of Saturn in thirty years, in that of Jupiter in twelve, that of Mars in two, Venus in nine months, or in that of Mercury in about eighty days. The annual movement of the Earth alone, between Mars and Venus, causes all the apparent irregularities of the five stars named. . . .

 

[Here Salviati explains Jupiter's motion, then follows with:]

 

Now what is said here of Jupiter is to be understood of Saturn and Mars also. In Saturn these retrogressions are somewhat more frequent than in Jupiter, because its motion is slower than Jupiter's, so that the Earth overtakes it in a shorter time. In Mars they are rarer, its motion being faster than that of Jupiter, so that the Earth spends more time in catching up with it. Next, as to Venus and Mercury, whose circles are included within that of the Earth, stoppings and retrograde motions appear in them also, due not to any motion that really exists in them, but to the annual motion of the Earth. This is acutely demonstrated by Copernicus . . .

 

You see, gentlemen, with what ease and simplicity the annual motion -- if made by the Earth -- lends itself to supplying reasons for the apparent anomalies which are observed in the movements of the five planets. . . . It removes them all and reduces these movements to equable and regular motions; and it was Nicholas Copernicus who first clarified for us the reasons for this marvelous effect." 1632, Dialogue Concerning the Two Chief World Systems

 

Gemma Frisius

 

"While at first glance the Ptolemaic hypotheses may seem more plausible than Copernicus', nevertheless the former are based on not a few absurdities, not only because the stars are understood to be moved nonuniformly in their circles, but also because they do not have explanations for the phenomena as clear as those of Copernicus. For example, Ptolemy assumes that the three superior planets in opposition -- diametrically opposite the sun -- are always in the perigee of their epicycles, that is, a "fact-in-itself." In contrast, the Copernican hypotheses necessarily infer the same thing, but they demonstrate a 'reasoned fact.'" 1560

 

Praetorius

 

"Now . . . everyone approves the calculations of Copernicus . . . . [and] this symmetry of all the orbs appears to fit together with the greatest of consonance . . . . [so] we follow Ptolemy, in part, and Copernicus, in part." 1592

 

Tycho Brahe

 

"[In examining the Ptolemaic hypotheses] . . . it gave me great concern that no necessary cause or natural combination explained why the superior planets are bound to the sun in such a way that at conjunction they always occupy the top of their epicycles, at opposition the lowest point of the same, and that the two planets that are called inferior always have the same mean position with the sun and are close to it at apogee and perigee of their epicycles." 1588 Letter to Casper Peucer

 

"The testimonies of the planets, in particular, agree precisely with the Earth's motion and thereupon the hypotheses assumed by Copernicus are strengthened." [A note in Tycho's hand in his copy of De revolutionibus -- approximately 1575 -- regarding the more "exquisite order" implied by the heliostatic arrangement.]

 

"I considered that the old Ptolemaic arrangement of the celestial orbs was not elegant enough, and that the assumption of so many epicycles by which the appearances of the planets towards the Sun and the retrogradations and stations of the same, with some part of the apparent inequality, are accounted for, is superfluous. . . . At the same time I considered that newly introduced innovation of the great Copernicus . . . by which he very elegantly obviates those things which occur superfluously and incongruously in the Ptolemaic system, and does not at all offend against mathematical principles. [Upon introducing his geoheliocentric alternative in his De Mundi Aetheri Recentioribus Phaenomenis (Uraniborg, 1588), explaining why, although he continued to believe "the Earth, large, sluggish and inapt for motion," he became convinced that "the simple motion of the Sun is necessarily involved in the motion of all five planets," that "the Sun regulates the whole Harmony of the Planetary Dance."]

 

 

Copernicus

 

"We find, then, in this arrangement the marvelous symmetry of the universe, and a sure linking together in harmony of the motion and size of the spheres, such as could be perceived in no other way. For here one may understand, by attentive observation, why Jupiter appears to have a larger progression and retrogression than Saturn, and smaller than Mars, and again why Venus has larger ones than Mercury; why such a doubling back appears more frequently in Saturn than in Jupiter, and still more rarely in Mars and Venus than in Mercury; and furthermore why Saturn, Jupiter and Mars are nearer to the Earth when in opposition than in the region of their occultations by the Sun and re-appearance . . . . All these phenomena proceed from the same cause, which lies in the motion of the Earth.

 

[In contrast with the Ptolemaic models] . . . although they have extracted from them the apparent motions, with numerical agreement, nevertheless . . . . They are just like someone including in a picture hands, feet, head, and other limbs from different places, well painted indeed, but not modeled from the same body, and not in the least matching each other, so that a monster would be produced from them rather than a man. Thus in the process of their demonstrations, which they call their system, they are found either to have missed out something essential, or to have brought in something inappropriate and wholly irrelevant, which would not have happened to them if they had followed proper principles. For if the hypotheses which they assumed had not been fallacies, everything which follows from them could be independently verified." De revolutionibus, 1543