Physics

The Middle Ages inherited a wealth of knowledge from antiquity, including the systematic philosophy of Aristotle (384–322 B.C.E.) and the synthesis of ancient astronomy in the work of the Hellenistic astronomer Ptolemy (fl. second century C.E.). In agreement with those before him, Aristotle maintained that the terrestrial and celestial realms, separated by the orbit of the Moon, featured entirely different physical behaviors. His terrestrial physics was founded on the existence of four elements (earth, water, air, and fire) and the idea that every motion requires the specification of a cause for that motion. Aristotle considered two broad classes of motion: natural motion, as an object returned to its natural place (as dictated by its elemental composition), and violent motion, as an object was removed forcibly from its natural place. Because the natural place of the element earth was at the center of the cosmos, Aristotle's physics necessitated a geocentric, or Earth-centered, model of the heavens.

Whereas the terrestrial realm featured constant change, the heavenly bodies moved in uniform circular orbits and were perfect and unchanging. Starting from an exhaustive tabulation of astronomical data, Ptolemy modeled the orbits of each heavenly body using a complex system of circular motions, including a fundamental deferent and one or more epicycles. Often, Ptolemy was forced to make additions, including the eccentric model (in which the center of rotation of the orbiting body was offset from Earth) and the equant model (in which a fictitious point, also not located at Earth, defined uniform motion).

Despite the great value of this work, the West lost a good portion of it with the erosion of the Roman Empire. Luckily, a number of Islamic scholars took an interest in the knowledge of the ancients. In addition to translating Aristotle and Ptolemy (among others) into Arabic, they commented on these works extensively and made a number of innovations in astronomy, optics, matter theory, and mathematics (including the use of "Arabic numerals," with the zero as a placeholder). For example, al-Battani (c. 858–929) made improvements to Ptolemy's orbits of the Sun and Moon, compiled a revised catalog of stars, and worked on the construction of astronomical instruments. Avempace (Ibn Badja, c. 1095–1138 or 1139) developed a position first staked out by the Neoplatonist philosopher John Philoponus (fl. sixth century C.E.), arguing that Aristotle was wrong to claim that the time for the fall of a body was proportional to its weight. After the reconquest of Spain during the twelfth century, ancient knowledge became available once again in the Latin West. Arab commentators such as Averroes (Ibn Rushd, 1126–1198) became influential interpreters of an Aristotle that was closer to the original texts and quite different from the glosses and explanatory aids that the West had grown accustomed to.

During the late Middle Ages, there was a general revival of learning and science in the West. The mathematician Jordanus de Nemore (fl. thirteenth century C.E.) pioneered a series of influential studies of static bodies. In addition to studying levers, Jordanus analyzed the (lower) apparent weight of a mass resting on an inclined plane. Despite the church's condemnation of certain radical interpretations of Aristotelianism during the late thirteenth century, there followed a flowering of activity during the fourteenth century, particularly concerning the problem of motion. Two important centers of activity were Merton College (at Oxford), where a group of mathematicians and logicians included Thomas Bradwardine (c. 1290–1349) and Richard Swineshead (d. 1355), and the University of Paris, which included John Buridan (c. 1295–1358) and Nicole Oresme (c. 1325–1382).

The scholars at Merton College adopted a distinction between dynamics (in which the causes of motion are specified) and kinematics (in which motion is only described). The dynamical problems implied by Aristotelian physics, especially the problem of projectile motion, occupied many medieval scholars (see sidebar, "Causes of Motion: Medieval Understandings"). In kinematics, the release from the search for causation encouraged a number of new developments. The Mertonians developed the concept of velocity in analogy with the medieval idea of the intensity of a quality (such as the redness of an apple), and distinguished between uniform (constant velocity) and nonuniform (accelerated) motion. They also gave the first statement of the mean velocity theorem, which offered a way of comparing constant-acceleration motion to uniform motion.

While the Mertonians presented their analyses of motion through the cumbersome medium of words, other scholars developed graphical techniques. The most influential presentation of the mean speed theorem was offered by Oresme, who recorded the duration of the motion along a horizontal line (or "subject line") and indicated the intensity of the velocity as a sequence of vertical line segments of varying height. Figure 1 shows that an object undergoing constant acceleration travels the same distance as if it were traveling for the same period of time at its average velocity (the average of its initial and final velocity). Although this work remained entirely abstract and was not based on experiment, it helped later work in kinematics, most notably Galileo's.

Following Aristotle's physics, medieval scholars pictured the celestial realm as being of unchanging perfection. Each heavenly body (the Sun, the Moon, the planets, and the sphere of the fixed stars) rotated around Earth on its own celestial sphere. Ptolemy's addition of epicycles on top of Aristotle's concentric spheres led medieval astronomers to speak of "partial orbs" within the "total orb" of each heavenly body. The Figure 1. Mechanics: Oresme's proof for average velocity orbs communicated rotational movement to one another without any resistive force and were made of a quintessence or ether, which was an ageless, transparent substance. Beyond the outermost sphere of the fixed stars was the "final cause" of the Unmoved Mover, which was usually equated with the Christian God. Buridan suggested that God impressed an impetus on each orb at the moment of creation and, in the absence of resistance, they had been rotating ever since. Both Buridan and Oresme considered the possibility of a rotating Earth as a way of explaining the diurnal motion of the fixed stars, and found their arguments to be promising but not sufficiently convincing.