History Weblecture for Unit 10
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The Greeks struggled to explain how things move in general terms. They realized hat objects in motion have both speed and direction, and that speed can increase or decrease, while direction can change. Direct observation of movement was hampered by one critical problem: they had no way to measure time accurately.
Philolaus was a contemporary of Socrates. He popularized the Pythagorean idea that the earth orbited a central fire (not the sun), and was not motionless in the center of the cosmos. Since we have only a few fragments, we can't really tell whether Philolaus' theories were meant to be taken literally or were metaphors for his religious ideas. He is important as a transmitter of Pythagorean views for which Aristotle had no other source. Philolaus' system could explain the sidereal motion of the planets from west to east against the background stars, but it did not address the problems of changes in brightness of the planets, or their occasional retrograde motion from east to west.
It was Eudoxus who first provided a theory that addressed the phenomenon of retrograde motion, which he explained with a mechanical model of interlocking spheres. An Ionian by birth, Eudoxus studied under philosophers who had been influenced by Pythagoras, and under Plato at the Academy in Athens. Eudoxus also studied in Egypt, where he is reported to have astronomical observations, then returned to Asia Minor and founded his own school and astronomical observatory at Cnidus. Much of his work centered on mathematics, but unfortunately we now only have the reports of his accomplishments in the Geometry of Euclid, the Metaphysics of Aristotle, and other ancient authorities who quoted him or gave him credit for a number of important methods in determining ratios. One of Eudoxus great mathematical achievements was the method of approximation: repeating a particular kind of calculation and varying one factor in it until the errors produced become small enough not to matter. Archimedes later used this method to estimate the value of π, the number that relates the diameter of a circle to its circumference. One estimation method is to draw the sides of a polygon, like a triangle. We can use the geometry of an equilateral triangle to estimate the distance from the midpoint of the side of the triangle to its center. If we do this with a square, then a pentagon, then a hexagon, we get progressively closer to a circle, if we think of the circle as a polygon with infinitely many sides. At some point, we decide not to bother with any more calculations. 22/7 is close enough to π for some work. [Many mathematical values that require this kind of iterative (over and over again) approach have been more accurately calculated since the invention of the computer.]
Eudoxus' work in astronomy was equally important. He took as a fundamental axiom Plato's requirement that the planets move uniformly in perfect circles centered on the earth. Eudoxus proposed a set of increasingly smaller spheres nested inside one another, with the earth at the center. Planets needed four spheres each, and rode on the innermost sphere of the set. The outermost sphere (not shown in the diagram) turned at the speed of the planet's revolution around the sun, and carried the planet on its annual motion eastward. The next sphere turned daily, to account for the motion eastward at a rate of one revolution each day. The inner two spheres rotated about axes that were offset from one another, and turned in opposite directions to account for the slight north-south movement and the planet's annual retrograde motion. As described by Aristotle in his Metaphysics, Eudoxus' system had 26 concentric spheres. It was able to account for not only daily and sidereal annual motion, but also retrograde motion. Callipus modified Eudoxus system by adding more spheres to account for variations in the retrograde motion of Venus and Mercury and the variable speeds of the sun and moon. It was Callipus who took Eudoxus theory, along with his own corrections, to Aristotle at the Lyceum in Athens.
We've seen how Aristotle's match of natural motion with one of the four types of matter led to a theory of motion for all terrestrial materials. Fire and air moved up, water and earth moved down. Things on earth could change, and even be destroyed.
But celestial objects like the sun, moon, planets, and stars moved in unending circles, and appeared to be eternal and unchanging. They could not be made of the same matter as earth, so Aristotle posited a fifth kind of matter, the quintessence. Things made of quintessence had not been created and could not be destroyed. They moved at a constant speed and did not speed up or slow down.
Remember Plato's ideal chair? Plato believe the idea or concept of chair was the reality, and that this idea was manifested in multiple actual chairs, each of which exhibited "chairness", although none could do it perfectly.
In contrast to his teacher, Aristotle was much more of a materialist or realist. He thought only actual chairs were real, and that insofar as the individual chairs shared common characteristics, they could indicate what "chairness" was about.
To help him analyze what chairness was, Aristotle looked at the causes underlying the existence of a specific object. He recognized that we use the idea of causality in at least four "senses":
The material cause of one particular chair was the wood from which it was made; another chair might have material cause of plastic or metal. The formal cause was the shape that made it a chair (this is where Plato's Idea of chair comes in): it has a seat, a back and four legs, which differentiates it from a stool with no backrest and only three legs. The efficient cause was the carpenter who made the chair. The final cause was so that the exhausted philosopher could sit down. While the first three causes could differ quite a lot, final cause (something you can sit on and rest your back against) at least usually dictated the purpose and the essential characteristic of the chair -- the characteristic that made it a chair and not something else.
This framework gave Aristotle a basis for claiming that the outermost sphere moved according to its own nature, and, as the efficient cause, provided the impetus for all subsequent motion.
The planet-bearing spheres, made of quintessence (their material cause) and in the most perfect shape (their formal cause), transmitted this motion to the matter of terrestrial objects and provided the efficient cause of the movement of everything on earth. In this way, Aristotle accounted for phenomena like the rising of the Nile River that followed the heliacal rising of the star Sirius. The motions of the heaven had a physical connection to objects on earth.
To adjust this mechanical and material model so that it would better mimic the observed motions of the planets, Aristotle had to add more spheres between each set of planetary spheres to undo the influence of the outer spheres on the inner ones. In all, Aristotle's system needed fifty-five interlocking spheres.
Following Aristotle and Plato were a number of other Greek philosophers who speculated on the motion of the planets, sun, moon, stars...and even the possible motion of the Earth itself. Heracleides of Pontus, who was born in Ionia and moved to Athens to study at the Academy of Plato, proposed that the daily motion of the sun and stars was due to the rotation of the Earth on its axis. Later scholars like Simplicius of Cilicia (writing nearly eight centuries later) also believed Heracleides had proposed that the irregular movements of the planets, in particular, retrograde motion, could be explained if the Earth orbited a stationary sun, but no remaining works by Heracleides or contemporary references to him support Simplicius' claim. In proposing that the Earth rotated, Heracleides could not overcome the arguments Aristotle had used against earlier Pythagoreans who also proposed the rotation of the Earth to explain daily motion:
Aristotle, de Caelo Book II, section 14
Aristotle's objection that the motion of the Earth should produce parallax, a periodic shift in the positions of the stars as the Earth moves around the sun, was used to counter Heracleides claims as well. Similar arguments would be used against Copernicus, Kepler, and Galileo until stellar parallax was at last observed in 1838 ce.
The webpages listed in this section usually are optional: I try to find sites related to the weeks topic, and you can read them if you have time. I would encourage you this week, though, to check out at least one of the sites listed below. They were written by authors who have very different opinions on the accomplishments of the ancient Greeks and the early medieval thinkers. Some websites present Aristotle's synthesis of observations and Ptolemy's system of planetary motion as among the supreme intellectual achievements of western civilization. Others have considerably different opinions. For example, Barbara Ryden forcefully presents the Greek assumptions of a stable earth and circular planetary motion as "wrong"; and she doesn't seem to think much of their accomplishments.
NB: Rediscovery of Ptolemy's work on spherical projection provided the Renaissance with a concept of perspective, leading to revolutions in art, science, and technology by changing the way information could be presented graphically. Ptolemy's name is used today for a CAD (computer aided design program).
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