Secretum secretorum - De Mirabilibus Mundi - Cosmos
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The Heavens

Before entering the Cosmos, let us pause just outside it: what if, anything, exists there? All agreed that no material substance is found outside the cosmos; if the cosmos is held to contain all the material substance that God created, this conclusion is unavoidable. Yet what about space devoid of corporeal substance? Aristotle had explicitly denied the possibility of place, space or vacuum outside the world, and this conclusion was generally accepted until a reevaluation of the issue was provoked by the condemnation of 1277.

As we enter the cosmos, we immediately encounter celestial spheres. How many of these exist, what is their nature, and what are their functions? There are seven planets - moon, Mercury, Venus, sun, mars, Jupiter and Saturn, generally held to be arranged in that order. In the simplified version of the cosmos preferred by medieval writers on cosmology, which ignored most of the astronomical details, each plate required a single sphere to account for its motion. In addition, according to Aristotle, outside the planetary spheres, defining the outer limit of the cosmos, is the sphere of the fixed stars or primum mobile. Several problems arose as medieval scholars thought about this outermost sphere.

One of them was to define its place. The place of a thing, according to Aristotle, is determined by the body or bodies that contain it. However, if the sphere of fixed stars is itself the outermost body, there is nothing outside it to serve as container. The natural conclusion of this line of argument - that the primum mobile is not a place - was too paradoxical to be accepted by all but a few of the toughest minds. Various solutions were therefore proposed, including an attempt to redefine place to allow it to be determined by the contained, rather than the containing, body.

Another problem for Aristotle's outermost sphere grew out of the account of creation in the book of Genesis, where a distinction was made between the "heaven [caelum]" created on the first and the "firmament [firmamentum]" created on the second - obviously two different things, since created on two different days. Moreover, the biblical texts states that the firmament separates waters beneath it from waters above it; the waters beneath the firmament could be equated with the sphere of water in the terrestrial region, but the waters above the firmament apparently constituted yet another celestial sphere. Discussion of this problem led some Christian commentators to postulate three spheres beyond the seven planetary spheres: the outermost of these, the invisible and motionless empyrean, served as the abode of the angels; next came the aqueous or crystalline heaven, perfectly transparent, consisting of water (possibly in a hard or crystallized form but more likely fluid, and possibly water only in a figurative sense); and then the firmament, bearing the fixed stars. The total number of heavenly spheres, for those who accepted this line of argument, came to ten. In time, all three outer spheres were assigned cosmological and astronomical functions; some scholars, wishing to account for an additional stellar motion, postulated an eleventh sphere as well. It is important to note the mutual interaction between cosmology and theology in these discussions: Aristotelian cosmology was adjusted to meet the demands of biblical interpretation; at the same time, the biblical account absorbed the fundamentals of Aristotelian cosmology, with its medieval modifications, and took substantial portions of its meaning from contemporary cosmological theory.

Medieval cosmologists were, of course, interested in the substance or material cause of the celestial region. Many writers of the early middle Ages drawing on the Stoic tradition, supposed the heavens to consist of a fiery substance. After the recovery of Arsitotle's works, some version of Aristotle's opinion that the heavens were formed out of the quintessance or aether (a perfect, transparent substance not subject to change) was generally accepted. There were debates about the nature of this aether - for example, whether it was a composite of form and matter. Among those who admitted the existence of form and matter in the heavens, some argued that the matter of the heavens was similar in kind to terrestrial matter, while others maintained that the two matters must be totally different. Whatever the nature of the aether might be, everybody agreed that it was divided into distinct spheres, in perfect contact (for otherwise there would be void space), all rotating frictionlessly in their proper directions and with their characteristic speeds. Individual spheres were assumed to be continuous - that is, without interstices or gaps. Seldom did a writer inquire whether they were fluid or hard; both alternatives found support among the few who addressed this issue. The planets were judged to be small spherical regions of greater density or lucidity in the transparent, lucid aether.

A much more hotly debated question was the nature of the celestial movers. Aristotle had identified a set of unmoved Movers as the causes of celestial motion - the objects of desire of the planetary spheres, which do their best to imitate the changeless perfection of the Unmoved Movers by rotating with eternal, uniform circular motion. The Unmoved Movers are thus final, rather than efficient, causes. Now the Unmoved Mover of the uppermost movable sphere (the "Prime Mover") was customarily identified with the Christian God; but the identity of the additional unmoved Movers was a more troublesome problem. It would have been easy to identify them with the planetary deities described in Plato's Timaeus; but to acknowledge any deity besides the Creator would have been a clear case of heresy within the Christian tradition, and it was therefore important for Christian scholars to distance themselves from such notions by assigning the Unmoved Movers a status well short of divinity. A common solution was to conceive of them as angels or some other kind of separated intelligences (minds without bodies). There were alternative solutions, however, which dispensed entirely with angels and intelligences. Robert Kilwardby (ca. 1215-79) assigned the celestial spheres an active nature or innate tendency to move spherically. John Buridan (ca. 1295- ca. 1358) argued that there is no need to postulate the existence of celestial intelligences, since they have no scriptural basis; it is possible, therefore, that the cause of celestial motion is an impetus or motive force, analogous to the impressed force that moves a projectile (I will discuss motion later), which God imposed on each of the celestial spheres at the moment of creation.

The analysis thus far has assumed that the heavens consist of a simple set of tightly nested, concentric spheres. This seems to have ben Aristotle's view; it was articulated and vigorously defended by Ibn Rushd (Averroes) in Muslim Spain; and it had a number of important Western adherents. Yet, some medieval cosmological writers modified their cosmology to take into account the eccentric deferents and epicycles or Ptolemaic astronomy - an attempt to harmonize cosmology and planetary astronomy. This will need to be dealt with in more depth in another place, it is sufficient to note that the solution was to endow each of Aristotle's planetary spheres with thickness sufficient to contain the Ptolemaic deferent and epicycle for that planet within it. The radius of the inside of a given planetary sphere would then equal the minimum distance between the earth and that planet on the Ptolemaic model; the radius of the outside of that planetary sphere would equal the planet's maximum distance from the earth.

The packing principle followed in this system - thick planetary spheres, packed contiguously, without wasted space - made it possible to calculate the size of the various planetary orbits and ultimately the dimensions of the cosmos. To get the calculation started, an estimate of the size of the innermost sphere, that of the moon, was needed. Several Muslim astronomers, including al-Farghn and Thbit ibn Qurra in the ninth century and al-Battn in the ninth or tenth, performed the calculation, borrowing the required date from Ptolemy's Almagest, with modifications. In the West, Campanus of Novara (d. 1296), gave his version of the calculation, assigning a figure of 107.936 miles to the radius of the inner surface of the moon's sphere (the moon's closest approach to the earth) and 209,198 miles to the radius of the outer surface of the moon's sphere. Similar calculations for Mercury and Venus produced a "theoretical" distance for the sun that accorded roughly with the parallax calculated for the sun by astronomers in antiquity. Continuation of the computation for the superior planets yielded a radius of 73,387,747 miles for the outside of Saturn's sphere and the inside of the stellar sphere. These figures, or figures close to them, prevailed until revised by Copernicus in the sixteenth century. (Companus defined a mile as the equivalent of 4,000 cubits and gives the circumference of the earth as 20,400 miles.)

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Last modified: Sun Dec 27, 1998 / Jeremiah Genest