(idea) by Two Sheds Sat Dec 04 2004 at 2:12:20

One of the most important claims made thus far in the field of history of science is that scientific theories are, as a product of human thought and labor, unavoidably influenced by the lives and ideas of the people who create them. The science of a period is a product of that period and, though it may well represent the physical world with great fidelity, it also betrays the fingerprints of its makers. In the somewhat esoteric words of historian of science James Moore, “science is underdetermined by facts.” These facts, which in fields like physics and astronomy change very little over human time spans, cannot be the only factor in the development of scientific theories; if they were than all scientists, perceiving the same facts, would agree on the same conclusions.

16th and 17th century astronomy provides a number of examples which support this claim. In particular Nicolas Copernicus and Johannes Kepler, two of the astronomers who most influenced the future of their science, were intensely influenced by metaphysical traditions with roots in ancient Greece, especially Pythagoreanism and Platonism. These philosophies led astronomers to theories that eventually helped bring down another, more empirically grounded tradition, that of Aristotelianism. Nevertheless, the three cosmologies of Copernicus, Kepler, and Claudius Ptolemy were not wholly the result of their respective major philosophical influences, Pythagoreanism, Platonism, and Aristotelianism. Instead the relationships between these major Greek philosophical traditions and the astronomical theories they influenced reveal more complexity, because each astronomical system was influenced by each metaphysical system. In addition, both Copernicus and Kepler were affected by the humanist ideal, omnipresent in their time, that there existed old, superior knowledge which was in need of renewal.

Nicolas Copernicus

Nicolas Copernicus was one of many 16th century astronomers who tried to topple Ptolemy’s dominant cosmology. He started from a different basis than most, though, for he was interested in a humanist revival of Pythagorean philosophy and noticed conflicts between Ptolemy’s theories and his Pythagorean ideals. Geometry played a major role in both, but in different ways. To the Pythagoreans, “all other things seemed in their whole nature to be modelled on numbers,” wrote Aristotle, and they “could show [these numbers] to agree with the attributes and parts and the whole arrangement of the heavens.” As a follower of Pythagoreanism, Copernicus’ astronomical goal was a clear one: to show that the heavens both agreed with and were based upon a mathematical model.

Most astronomers of his day would have argued that this was an unnecessary task, as Ptolemy had similar goals and had long before created a model good enough to dominate astronomy for centuries. In many ways Copernicus agreed, even basing the structure and much of the content of his 1543 book De Revolutionibus on those of Ptolemy’s Almagest, but he found Ptolemy’s system inelegant and not in keeping with Pythagorean metaphysics in a few major ways. The star of this conflict was the concept of circular motion, since many ancient Greek philosophers had declared the circle the perfect shape and the heavens—apparently perfect and unchanging—the domain of such ideals. Ptolemy himself wrote that “uniform circular motions… are proper to the nature of divine beings,” but Copernicus did not believe that his theory lived up to propriety.

Ptolemy’s geocentric version of what we now term the solar system required a construction called an equant in order to model observed reality (primarily due to the phenomenon of retrograde motion), and the motion of a planet on an equant is circular but non-uniform, at least in terms of velocity: the planet moves more quickly while near the earth than it does when far from it. The equant was not the only one of Ptolemy’s constructs to produce a questionably “uniform circular motion”—others included the deferent, the epicycle, and the eccentric—but it was considered by many to be the most egregious. The equant seemed to Copernicus to be variable enough to violate the aesthetic and philosophical reason for associating circles with the heavens. The results of Ptolemy’s model were relatively accurate, so it was useful, but it wasn’t the divine model on which the universe was based.

Copernicus’ response was to create another mathematical model with the same explanatory power as Ptolemy’s but without equants. In order to make such a model match apparent reality he placed the sun near the center of each planetary orbit and included the earth among the planets circling it. The resulting system included more epicycles than Ptolemy’s and was thus more complex, but it fulfilled Copernicus’ goal of removing the equant.

Copernicus aimed to discover the model on which the universe was actually based, and his humanist environment instilled in him the idea that this was an old model. He thus claimed that he was not creating an original system but reviving old Pythagorean ideas, and credited “Philolaus the Pythagorean,” a great mathematician, with the idea now termed Copernicanism, “that the Earth moved in a circle and wandered in some other movements and was one of the planets.” Copernicus was not without Platonic and Aristotelian influences, though. In placing the sun at the center of the universe, he mirrored its importance in Plato’s metaphysics, particularly in the allegory of the cave. Similarly, Copernicus used arguments drawn from Aristotelian physics in order to convince others of the truth of his theories. He argued, for instance, “that it was easier to imagine that the relatively small Earth moved, than that the great heavens hurled themselves around every twenty-four hours.”

Copernicus’ ideas also introduced a pair of philosophical problems for future astronomers to solve, though. The first was primarily religious in nature: a stationary sun seemed to contradict the Bible. The second was that Copernicanism seemed to predict the phenomenon of stellar parallax, in which stars appear to move with respect to each other, but it was not observed. Copernicus explained away the absence of this phenomenon by claiming that the universe was so large that observers couldn’t detect the parallax, but Tycho Brahe calculated the size of such a universe and declared it philosophically impossible, as there was no reason for a universe to be so large and waste so much space. Neither of these philosophical problems was ever solved within astronomy as a science, but the amount of evidence for both the sun-centered planetary system and the massive universe has increased a great deal, and it is now clear that opposing positions such as Tycho’s own Tychonic model do not fit modern observations.

Johannes Kepler

Tycho’s other work provided the data necessary for Johannes Kepler to develop his own cosmology, though, and Kepler’s ideas also show strong metaphysical influences. Kepler’s first major project was his 1596 Mysterium Cosmographicum, in which he both defended Copernicus’ theory and provided his own embellishments for it. His major new claim was that the sizes of the celestial spheres, on which he believed the planets travel, have the same proportions as nested regular polyhedra. Because there are only five such regular solids, as Kepler knew from reading Euclid, he placed them between the orbits of the six planets.

“The [orbit of the] Earth is the circle which is the measure of all. Construct a dodecahedron around it. The circle surrounding that will be Mars. Round Mars construct a tetrahedron. The circle surrounding that will be Jupiter. Round Jupiter construct a cube. The circle surrounding that will be Saturn. Now construct an icosahedron inside the Earth. The circle inscribed within that will be Venus. Inside Venus inscribe an octahedron. The circle inscribed within that will be Mercury.” There you have the explanation of the number of the planets.

These five shapes are also called the Platonic solids because of Plato’s use of them, and Kepler and Plato were clearly drawn to them for similar reasons. Plato had suggested that the four regular polyhedra formed from equilateral triangles—the tetrahedron, octahedron, icosahedron, and cube—were respectively the shapes of the corpuscles of fire, air, water, and earth, the four elements according to Empedocles. Furthermore, Plato claimed that the dodecahedron, the regular polyhedron most similar to a sphere, was the shape used by “the god… for the whole universe, embroidering figures on it.” The idea that the celestial spheres were connected to the regular polyhedra was thus not original to Kepler; in the imaginations of both Plato and Kepler these five solids literally explained the structure of the universe.

The work for which Kepler is remembered, though, is his 1619 Harmony of the World, which focused on the literal musical harmony of the planetary spheres and stated that planets orbit the sun on elliptical, not circular, orbits. Though Kepler tends to belittle the Pythagoreans as dreamers, as in his introduction to Book V of the Harmony, his main objective was one that they originated. The claim that “there is music in the spacing of the spheres” is attributed to Pythagoras, and Kepler set out to find that music. To this end he wrote the Harmony in five books, which he described on the title page: “The first is Geometrical…; the second is Architectonic, or comes from the Geometry of Figures…; the third is specifically Harmonic…; the fourth is Metaphysical, Psychological, and Astrological…; the fifth is Astronomical and Metaphysical, on the most perfect harmonies of the celestial motions, and the origin of the eccentricities in the harmonic proportions.” This explanation of orbital eccentricities is the reason why Kepler’s book is now considered to have contributed to science, but it was only part of a wide range of investigations into astronomy, music, and the mystical relationship between the two.

While participating in this originally Pythagorean quest, Kepler also tried to promote his neo-Platonic metaphysics and oppose Pythagoreanism in general. Kepler attached more metaphysical significance to the central placement of the sun than Copernicus; following his Platonic influences, he decided that a soul “resides in the center of the world, which for me is the Sun, and from there… is propogated over the length and breadth of it by the agency of the rays of light, which are equivalent to spirits in the animate body.” The idea that such a “soul of the whole universe” exists is contrary to Kepler’s conception of Pythagoreanism, and was “defended from the Pythagorean beliefs by Timaeus of Locri in Plato.” It’s an idea that Kepler sees as central to his metaphysical ideas, though, (and particularly to his astrological ones) and it is furthermore connected to Christianity, as “a Christian can easily understand by the Platonic mind, God the Creator, and by the soul, the nature of things.”

Metaphysical arguments such as these are not only present in but integral to the writings of both Copernicus and Kepler, and illustrate the influence which Plato and the Pythagoreans had on these astronomers. Facts alone were not sufficient to increase the accuracy of astronomical models—Tycho had the same data as Kepler and produced the geocentric Tychonic model—but other influences led to greater divergence from Aristotelian tradition. In particular, the metaphysical ideas that Copernicus and Kepler mixed with their astronomy had enough of an impact to transform the solar system as they portrayed it and explain the universe as it actually exists.

Works Cited

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