The guiding themata or paradigm of Greek planetary astronomy is attributed to Plato by the philosopher Simplicius of Athens in his commentary on Aristotle's book On the Heavens. Around a.d. 500 Simplicius wrote that Plato had set as a task for astronomers to explain the apparently irregular motions of the planets, the Sun, and the Moon as a combination of circular motions with constant speeds of rotation.
To "save the appearances" with a system of uniform circular motions is, in the context of modern science, an arbitrary and absurd task. Granted, the motions of the planets and the Sun and the Moon could be reproduced using, in clever combination, circles of various sizes with unchanging rotational speeds. But it would be a cumbersome contraption. Modern science has achieved a more elegant and informative solution to a more productively formulated problem, at least in the opinion of modern scientists.
The fact remains, however, that a task was set for astronomers; the task was generally accepted; and the task was pursued for nearly two thousand years, from the Greeks in the fourth century b.c. to Copernicus and the European Renaissance in the sixteenth and seventeenth centuries a.d. Historical importance is not necessarily negated by lack of plausibility, especially when plausibility is judged in hindsight by different people in a different age with different standards.
Simplicius lived nearly a thousand years after Plato and Aristotle and the beginning of Greek astronomy, and he lacked direct access to Plato's original writings. Nor is any explicit statement about saving the appearances with a system of uniform circular motions now found in Plato's surviving writings. Hence some historians of science question the central role in the development of planetary theory often assigned to Plato. But whether it began with Plato or slightly afterward, the task for Greek astronomers working in what came to be regarded, rightly or wrongly, as the Platonic tradition, was to save the appearances: to explain apparently irregular motions detected by the senses as a combination of uniform circular motions.
Plato's ideas were taught to pupils at the Academy, possibly the world's first university, which he founded in Athens in about 380 b.c. Plato believed that mathematics provided the finest training for the mind, and over the door of the Academy was written "Let no one unversed in geometry enter here." The Academy survived until banished from Athens by the emperor Justinian in a.d. 529.
Eudoxus, the greatest genius in mathematics and astronomy of his time, may have attended Plato's lectures at the Academy, and certainly he was familiar with Plato's ideas. Upon Eudoxus's report of what Plato said a string of statements followed. Eudoxus's report is lost. However, it was summarized by Eudemus in his own History of Astronomy. This work, too, is lost. But it was commented on by Sosigenes in the second century a.d. Sosigenes' work is also lost. It was used, however, by Simplicius, with whom the string of lost-but-summarized works finally ends, in the sixth century a.d. Simplicius wrote:
Plato lays down the principle that the heavenly bodies' motion is circular, uniform, and constantly regular. Thereupon he sets the mathematicians the following problem: what circular motions, uniform and perfectly regular, are to be admitted as hypotheses so that it might be possible to save the appearances presented by the planets? (Duhem, To Save the Phenomena, 5)
Continuing, Simplicius explained:
The curious problem of astronomers is the following: First, they provide themselves with certain hypotheses: . . . Starting from such hypotheses, astronomers then try to show that all the heavenly bodies have a circular and uniform motion, that the irregularities which become manifest when we observe these bodies—their now faster, now slower motion; their moving now forward, now backward; their latitude now southern, now northern; their various stops in one region of the sky; their at one time seemingly greater, and at another time seemingly smaller diameter—that all these things and all things analogous are but appearances and not realities. (Duhem, To Save the Phenomena, 23)
A combination of uniform circular motions now seems absurd. Within Plato's philosophy, however, the concept is plausible. And his philosophy is plausible when viewed within the context of his life. Plato's philosophy can be understood as a reaction to the temporary moral values of his age, which left him highly dissatisfied and sent him searching for a new philosophy.
In 479 b.c. , a year after the Persians under Xeres I captured and burned Athens, 31 Greek city-states defeated the Persians in decisive land and sea battles. The victory capped 20 years of struggle to stop the westward expansion of the Persian Empire. Now began Greece's Golden Age. Increasingly, Athens dominated. Tribute poured in from other city-states, giving support to
Athenian writers and artists. Led by Sparta, several Greek city-states revolted against Athenian rule, setting off the Peloponnesian Wars of 431—404 b.c. Initially Athens prevailed, but the fortunes of battle shifted after an unsuccessful attack by Athens on Syracuse, a city in Sicily, in 413 b.c. Athens surrendered to Sparta in 404 b.c.
In the turmoil enveloping Greece, searches for a new and more useful philosophy occurred. Socrates, who lived from 469 to 399 b.c. , led the reaction against the old philosophy. He was trained as a stonecutter in his father's shop in Athens but preferred to spend his time arguing in the marketplace. There he encouraged the youths of Athens to question every moral precept handed down to them. Elder citizens believed, with justification, that Socrates was demoralizing their children.
Socrates' critical questioning also extended to the government and its actions. In addition to corrupting the youths of Athens, Socrates now was accused of impiety. The charge may have been intended to frighten him into fleeing Athens, but Socrates stayed and forced the issue. He welcomed his trial as a forum for his ideas.
A trial then consisted of two parts. First, guilt or innocence was established. If guilt was established, punishment was determined in a second part. After the jury found Socrates guilty, the prosecution recommended death. Socrates suggested board and lodging at public expense because his actions had been for the public benefit. The jury chose, and Socrates drank the fatal and famous cup of hemlock.
Socrates' death and related political conditions in Athens influenced Plato, who had been Socrates' pupil and a close friend. Born in 427 b.c., Plato was of an age to enter public life at about the time of the defeat of Athens in 404 b.c. Furthermore, both his mother's brother and cousin were members of the oligarchy of the Thirty Tyrants designated by Sparta to rule Athens. In a letter purportedly Plato's and accepted by many, but not all, scholars as genuine, Plato wrote:
When I was a young man I had the same ambition as many others: I thought of entering public life as soon as I came of age. And certain happenings in public affairs favored me, as follows. The constitution we then had . . . was overthrown; and a new government was set up consisting of . . . thirty other officers with absolute powers. . . . Some of these men happened to be relatives and acquaintances of mine, and they invited me to join them at once. (Epistles, VII: 324b—c)
But the actions of the tyrants disgusted Plato. They quelled criticism by intimidation, and opposition by assassination. They met treasury deficits by the arbitrary execution of wealthy individuals for treason, followed by confiscation of the alleged traitors' properties. Also, they attempted to involve Socrates in their illegal actions. Plato chose not to join the government:
I thought that they were going to lead the city out of the unjust life she had been living and establish her in the path of justice . . . But as I watched they showed in a short time that the preceding constitution had been a precious thing . . . . I was appalled and drew back from that reign of injustice. (Epistles, 325b—c)
A year later a democratic faction drove out the tyrants, and Plato again considered entering politics:
Not long afterwards the rule of the Thirty was overthrown and with it the entire constitution; and once more I felt the desire, though this time less strongly, to take part in public and political affairs. (Epistles, 325a—b)
But then the new democracy persecuted Socrates. Plato now determined to set aside political ambition and search for unchanging standards to hold against the shifting judgments of men:
Certain powerful persons brought into court this same friend Socrates, preferring against him a most shameless accusation . . . and the jury condemned and put to death the very man. The more I reflected upon what was happening . . . the more I realized . . . the corruption of our written laws and our customs was proceeding at such amazing speed that whereas at first I had been full of zeal for public life, when I noted these changes and saw how unstable everything was, I became in the end quite dizzy . . . At last I came to the conclusion that all existing states are badly governed and the condition of their laws practically incurable . . . and that the ills of the human race would never end until either those who are sincerely and truly lovers of wisdom come into political power, or the rulers of our cities, by the grace of God, learn true philosophy. (Epistles, 325b-326b)
Subsequent experiences confirmed Plato in this opinion. According to legend, in about 388 b.c. the dictator of Syracuse, Dionysius I, asked Plato if he didn't think that he, Dionysius, was a happy man. Plato answered that he thought no one who was not mad would become a tyrant. Enraged, Dionysius supposedly ordered Plato sold into slavery, from which he was rescued by a friend arriving just in time with ransom money. Or maybe on Plato's return voyage to Athens his ship was captured and he was put up for sale in a slave market, where he was ransomed by a friend.
Plato imparted his love of virtue above pleasure and luxury to Dion, the tyrant's brother-in-law. When Dionysius I died, Dion asked Plato to return to Syracuse to help arouse in his nephew, the new tyrant Dionysius II, desire for a life of nobility and virtue. Plato went, though not without trepidation. His worst apprehensions were surpassed:
When I arrived—to make the story short—I found the court of Dionysius full of faction and of malicious reports to the tyrant about Dion. I defended him as well as I could, but was able to do very little; and about the fourth month Dionysius, charging Dion with plotting against the tyranny, had him put aboard a small vessel and exiled in disgrace. Thereupon we friends of Dion were all afraid that one of us might be accused and punished as an accomplice in Dion's conspiracy. About me there even went abroad in Syracuse a report that I had been put to death by Dionysius as the cause of all that had happened. . . . Dionysius . . . devised a means for preventing my departure by bringing me inside the citadel and lodging me there, whence no ship's captain would have dared to take me away . . . Nor would any merchant or guard along the roads leading out of the country have let me pass alone, but would have taken me in charge at once and brought me back to Dionysius . . . I made every effort to persuade Dionysius to let me depart, and we came to an agreement that when peace was restored [Syracuse was then at war with Sicily] and when Dionysius had made his empire more secure, he would recall both Dion and me. . . . On these conditions I promised that I would return. (Epistles, 329b—e; 338a)
Peace was restored, and Plato returned to Syracuse. There he found Dionysius II not on fire with philosophy. Indeed, Dionysius II acted as if what Plato said was of no value. Again, Plato sought to leave Syracuse and was held against his will. He became even more deeply entangled in the quarrel between Dionysius II and Dion, which ended in disaster.
Plato's philosophy and its implications for the study of astronomy are particularly understandable as a response to the time of troubles in which he found himself. Reacting to the temporary moral values of his time, Plato searched for unchanging standards. The changing, visible world was without permanent values. So Plato turned to the world of ideas. Here he hoped to find the real and unchanging standards so sadly absent in his world of experience.
In his Allegory of the Cave in his book the Republic, Plato explained that the prison of the cave corresponds to the part of the world revealed by the sense of sight. Escape from the cave corresponds to the use of intelligence to reach the real world of knowledge.
In the Republic, as in most of his books, Plato created a dialog. He distrusted the fixed, dead words of textbooks and believed that learning could be achieved only through discussion and shared inquiry:
I magine the condition of men living in a sort of cavernous chamber underground, with an entrance open to the light and a long passage all down the cave. Here they have been from childhood, chained by the leg and also by the neck, so that they cannot move and can see only what is in front of them, because the chains will not let them turn their heads. At some distance higher up is the light of a fire burning behind them; and between the prisoners and the fire is a track with a parapet built along it, like the screen at a puppet-show, which hides the performers while they show their puppets over the top.
Now behind this parapet imagine persons carrying along various artificial objects, including figures of men and animals in wood or stone or other materials, which project above the parapet. Naturally, some of these persons will be talking, others silent.
It is a strange picture, he said, and a strange set of prisoners.
Like ourselves, I replied; for in the first place prisoners so confined would have seen nothing of themselves or of one another, except the shadows thrown by the fire-light on the wall of the cave facing them, would they?
Not if all their lives they had been prevented from moving their heads.
And they would have seen as little of the objects carried past.
Now, if they could talk to one another, would they not suppose that their words referred only to those passing shadows which they saw?
And suppose their prison had an echo from the wall facing them? When one of the people crossing behind them spoke, they could only suppose that the sound came from the shadow passing before their eyes.
In every way, then, such prisoners would recognize as reality nothing but the shadows of those artificial objects.
Now . . . suppose one of them set free and forced suddenly to stand up, turn his head, and walk with eyes lifted to the light; all these movements would be painful, and he would be too dazzled to make out the objects whose shadows he had been used to see. What do you think he would say, if someone told him that what he had formerly seen was meaningless illusion, but now, being somewhat nearer to reality and turned towards more real objects, he was getting a truer view? Suppose further that he were shown the various objects being carried by and were made to say, in reply to questions, what each of them was. Would he not be perplexed and believe the objects now shown him to be not so real as what he formerly saw?
And suppose someone were to drag him away forcibly up the steep and ragged ascent and not let him go until he had hauled him out into the sunlight, would he not suffer pain and vexation at such treatment, and, when he had come out into the light, find his eyes so full of its radiance that he could not see a single one of the things he was now told were real?
Now imagine what would happen if he went down again to take his former seat in the Cave. Coming suddenly out of the sunlight, his eyes would be filled with darkness. He might be required once more to deliver his opinion on those shadows, in competition with the prisoners who had never been released, while his eyesight was still dim and unsteady; and it might take some time to become used to the darkness. They would laugh at him and say that he had gone up only to come back with his sight ruined; it was worth no one's while even to attempt the ascent. If they could lay hands on the man who was trying to set them free and lead them up, they would kill him.
They did kill Socrates. And students whom Plato tried to free from the shackles of ignorance so they might live enlightened lives in the sunlight of understanding were unappreciative of his effort to teach them.
Plato's concept of reality is plausibly illustrated with a simple example. Think of a circle and draw a circle. Which is real? The circle drawn on paper is not a real circle, no matter how skilled the draftsman. The drawn circle is an imperfect representation in the visible world of experience of a perfect circle. The perfect circle exists only in the mind, only in the world of thought. Plato wrote:
There is something called a circle. . . . The figure whose extremities are everywhere equally distant from its center is the definition of precisely that to which the names "round," "circumference," and "circle" apply . . . what we draw or rub out, what is turned or destroyed; but the circle itself to which they all refer remains unaffected, because it is different from them. (Epistles, VII: 342a-344a)
Taking up the discussion of astronomy in the Republic, Plato alluded to its utilitarian benefits: in agriculture, in navigation, and in war. Not for these purposes, however, was astronomy to be esteemed. The true utility of the regimen of study prescribed in the Republic was saving souls.
An obvious way of doing astronomy is to observe the motions of the objects in the heavens. But only a discipline dealing with unseen reality will lead the mind upward. The true motions are not to be seen with the eye. It is not by looking at the heavens that one can become truly acquainted with astronomy. Again, Plato put his ideas in a dialog:
Plato's Pervasive Persuasive Philosophy
Plato's philosophy has affected many human intellectual endeavors over many centuries. His emphasis on an ideal reality in place of observed shadows and reflections guided ancient astronomers.
More recently, the twentieth-century Romanian sculptor Constantin Brancusi tried to make his art a working philosophy of Plato. Brancusi wrote that what is real is not the external form, but the essence of things. Starting from this truth it is impossible for anyone to express anything essentially real by imitating its exterior surface. Brancusi looked beneath the surface of human experience for a deeper and truer reality. He abandoned details—forms that express little—keeping only essential anatomical elements. His sculptural kissing couple represent an ideal. They are not just a particular pair of people in love, but all the pairs that lived and loved, here, on Earth. Plato's philosophy paid off big-time: the world auction record (as of 2002) for any sculpture is $18,159,500—for a Brancusi.
The movie The Matrix is another modern variation on Plato's cave. We may not be living in the world we perceive. Rather, our brains may be floating in a vat of amniotic fluid and connected to electrodes feeding us sensations, or hallucinations. In The Matrix, people lie comatose in cocoons, stacked in incubators, clear pods piled high in high towers. Their brains are penetrated by cables delivering an interactive virtual-reality program, the Matrix, its simulation mistaken for reality.
[Astronomy] is important for military purposes, no less than for agriculture and navigation, to be able to tell accurately the times of the month or year. I am amused by your evident fear that the public will think you are recommending useless knowledge. . . .
And now, Socrates, I will praise astronomy on your own principles, instead of commending its usefulness in the vulgar spirit for which you upbraided me. Anyone can see that this subject forces the mind to look upwards, away from this world of ours to higher things.
Anyone except me, perhaps, I replied. I do not agree.
As it is now handled by those who are trying to lead us upward to philosophy, I think it simply turns the mind's eye downwards.
What do you mean?
You put a too generous construction on the study of "higher things." Apparently you would think a man who threw his head back to contemplate the decorations on a ceiling was using his reason, not his eyes, to gain knowledge. Perhaps you are right and my notion is foolish; but I cannot think of any study as making the mind look upwards, except one which has to do with unseen reality. No one, I should say, can ever gain knowledge of any sensible object by gaping upwards any more than by shutting his eyes and searching for it on the ground, because there can be no knowledge of sensible things. His mind will be looking downwards, though he may pursue his studies lying on his back or floating on the sea.
I deserve to be rebuked. But how did you mean the study of astronomy to be reformed, so as to serve our purposes?
In this way. These intricate traceries in the sky are, no doubt, the loveliest and most perfect of material things, but still part of the visible world, and therefore they fall far short of the true realities—the real relative velocities, in the world of pure number and all perfect geometrical figures, of the movements which carry round the bodies involved in them. These, you will agree, can be conceived by reason and thought, not seen by the eye.
Accordingly, we must use the embroidered heaven as a model to illustrate our study of those realities, just as one might use diagrams exquisitely drawn by some consummate artist like Daedalus. An expert in geometry, meeting with such designs, would admire their finished workmanship, but he would think it absurd to study them in all earnest with the expectation of finding in their proportions the exact ratio of any one number to another.
The genuine astronomer, then, will look at the motions of the stars with the same feelings. He will admit that the sky with all that it contains has been framed by its artificer with the highest perfection of which such works are capable. But when it comes to the proportions of day to night, of day and night to month, of month to year, and of the periods of other stars to Sun and Moon and to one another, he will think it absurd to believe that these visible material things go on forever without change or the slightest deviation, and to spend all his pains on trying to find exact truth in them.
Now you say so, I agree.
If we mean, then, to turn the soul's native intelligence to its proper use by a genuine study of astronomy, we shall proceed as we do in geometry, by means of problems, and leave the starry heavens alone. (Republic, VII: 527d—530c)
Plato's instruction immediately above, to "leave the starry heavens alone," has dismayed supporters and delighted detractors. The admonishment is anti-empirical, and it could easily lead to a purely speculative study of bodies in motion with no connection to the celestial objects we see. This is especially so if the translation produces in place of "let alone" or "leave" the stronger sense of "dismiss" or "abandon." An injunction to astronomers to dismiss celestial phenomena from the subject matter of their science and to ban sense-perception would result not in a reform of astronomy but in its liquidation.
A few lines earlier, however, Plato instructed that "we must use the embroidered heaven as a model to illustrate our study of those realities." Plato's supporters construe this phrase as scientific, calling for a science of astronomy to ascertain the real motions of the heavenly bodies.
Plato's science, however, cannot be equated with modern science. He wasn't urging astronomers to develop just any theory that would account for observed facts. He was urging astronomers to fit their observations into a predetermined geometrical pattern based on certain a priori assumptions about the behavior of bodies in the sky: that heavenly bodies move in uniform circular orbits.
Plato's science of astronomy had as its subject reality. He wrote that he could not "think of any study as making the mind look upwards, except one which has to do with unseen reality." Plato's reality, however, is not reality as it is now commonly understood. This is evident from the conclusion of the sentence immediately following: "there can be no knowledge of sensible things."
The type of reality discussed in the Allegory of the Cave is what is real for Plato. What is real is the idea or ideal of a perfect geometrical figure, not its imperfect realization in the world of the senses. Plato insisted that the "intricate traceries in the sky are, no doubt, the loveliest and most perfect of material things, but still part of the visible world, and therefore they fall far short of the true realities."
It mattered not to Plato whether a person stared at the ground or at the heavens. As long as he was trying to study any sensible object, he could not be said to have learned anything, because no objects of sense admitted of scientific treatment. In this belief, Plato is antiempirical, and he is antiobservational, but he is not antireality.
Uniform circular orbits have been characterized as "pi in the sky" or in the sky," a word play on the fact that the circumference of a circle is equal to tc times the diameter. A serious case, however, can be made for the reality of Platonic entities. Plato thought that "forms" are more real than what is observed because logical reasoning is more certain than fallible observations, susceptible as they are to being proved false by subsequent refinements in observational capability. Logical inference and analysis, Plato believed, produce more certain knowledge than does observation.
The aim of ancient Greek geometrical astronomy became to save the appearances with a system of uniform circular motions. The philosophical background for this paradigm is found in Plato's writings. Under the spell of the paradigm, Plato's student Eudoxus would attempt to develop a system of uniform circular motions reproducing the observed motions of the planets.
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