The Danish Peace Academy

SCIENCE AND SOCIETY

John Avery
H.C. Ørsted Institute, University of Copenhagen

Chapter 2 ANCIENT GREECE

The Minoans

Histories of the development of western civilization usually begin with the Greeks, but it is important to remember that the Greek culture was based on the much earlier civilizations of Mesopotamia and Egypt. The cultural achievements of these very early civilizations were transmitted to the Greeks in part through direct contact, and in part through the Minoan and Mycenaean civilizations.

The Minoan civilization on Crete is the civilization which is familiar to us through the legends of Thesius, the Minotaur and the Labyrinth, and the legend of Daedalus and Icarus. Apart from the Greek legends, whose truth was doubted, nothing was known about the Minoan civilization until 1900. In that year, the English archaeologist, Sir Arthur Evans, began to dig in a large mound at Knossos on Crete. What he uncovered was a palace of great beauty which, to his astonishment, seemed once to have boasted such conveniences as hot and cold running water and doors with metal locks and keys. Sir Arthur Evans considered this to represent the palace of the legendary King Minos.

The Minoan civilization seems to have been based not on agriculture, but on manufacture and on control of the Mediterranian sea trade. It flourished between 2,600 B.C. and 1,400 B.C.. In that year, the palace at Knossos was destroyed, and there is evidence of scattered looting. Other evidence shows that in about 1,400 B.C., a nearby island called Theria exploded in a volcanic eruption of tremendous violence; and probably this explosion, combined with an invasion of Mycenaeans, caused the end of the Minoan civilization. The palace at Knossos was inhabited later than 1,400 B.C., but the later people spoke Greek.

The Minoan civilization, as shown in the graceful works of art found at Knossos, seems to have been light-hearted and happy. The palace at Knossos was not fortified and was apparently protected by sea power. Women’s dresses on ancient Crete looked a bit like the dresses which were popular in Europe during the 1900’s, except that they left the breasts bare. Some of the wall paintings at Knossos show dances and bull-fights. In the bull-fights, the bull was not killed. The bull-fighter was an acrobat, often a girl, who seized the lowered horns of the charging bull and was tossed in a summersault over its back.

The Mycenaean civilization

The Mycenaean civilization developed at Troy, Mycenae (the home of the legendary Agamemnon), and other sites around the Aegean Sea. It is the civilization familiar to us through the stories of Ulysses, Priam, Ajax, Agamemnon, Paris and Helen. Like the Minoan civilization, the Mycenaean culture was thought to be purely legendary until quite recent times. We now know that the Homeric epics have a basis in fact, and this surprising revelation is mainly due to the work of a brilliant businessman-turned-archaeologist named Heinrich Schliemann.

As a young (and poor) boy, Schliemann was inspired by reading Homer’s Iliad, and he decided that when he grew up he would find the site of ancient Troy, which most people considered to be a figment of Homer’s imagination. To do this, he first had to become very rich, a task which he accomplished during the first 45 years of his life. At last he had accumulated a huge fortune, and he could follow the dream of his boyhood. Arriving in Greece, Schliemann put an advertisement into a newspaper describing himself and saying that he needed a wife. This was answered by a beautiful and intelligent Greek girl, whom he promptly married.

Aided by armies of excavators, his beautiful wife, his brilliant intellect and a copy of Homer, Schliemann actually succeeded in unearthing ancient Troy at a site in Asia Minor! At this site, he uncovered not one, but nine ancient cities, each built on the ruins of the last. He also found beneath the walls of Troy a treasure containing 8,750 pieces of gold jewelry, which he considered to be King Priam’s treasure. He went on to uncover many other remains of the Mycenaean civilization at sites around the Aegean.

Schliemann’s discoveries show the Mycenaeans to have been both technically and artistically accomplished. They spoke an Indo-European language (a form of Greek), and they were thus linguistically related to the tribes which conquered Persia, India and Europe.

The Mycenaean civilization lasted until about 1,075 B.C.. Between that date and 850 B.C., the Greek-speaking peoples of the Aegean entered a dark age. Probably the civilized Mycenaeans were conquered by fresh waves of semi-primitive Greek-speaking tribes from the north. It is known that the Greeks arrived in the Aegean region in three waves. The first to come were the Ionians. Next came the Achaeans, and finally the Dorians. Warfare between the Achaeans and the Ionians weakened both groups, and finally they both were conquered by the Dorians. This conquest by the semi-primitive Dorians was probably the event which brought the Mycenaean civilization to an end. At any rate, during the dark ages between 1,075 B.C. and 850 B.C., the art of writing was lost to the Greeks, and the level of artistic and cultural achievement deteriorated.

Thales of Miletus

Beginning in about 850 B.C., there was a rebirth of Greek culture. This cultural renaissance began in Ionia on the west coast of presentday Turkey, where the Greeks were in close contact with the Babylonian civilization. Probably the Homeric epics were written in Miletus, a city on the coast of Asia Minor, in about 700 B.C.. The first three philosophers of the Greek world, Thales, Anaximander and Anaximenes, were also natives of Miletus.

Thales was born in 624 B.C. and died in 546 B.C.. The later Greeks considered him to have been the founder of almost every branch of knowledge. Whenever the wise men of ancient times were listed, Thales was invariably mentioned first. However, most of the achievements for which the Greeks admired Thales were probably not invented by him. He is supposed to have been born of a Phoenecian mother, and to have travelled extensively in Egypt and Babylonia, and he probably picked up most of his knowledge of science from these ancient civilizations. One of the achievements which made Thales famous was his prediction of a solar eclipse which (according to modern astronomers) occurred on May 28, 585 B.C.. On the day of the eclipse, the Medes and the Lydians were about to begin a battle, but the eclipse convinced them that they ought instead to make peace and return home. Thales predicted, not the exact day, but only the year in which the eclipse would occur, but nevertheless the Greeks were impressed. The astronomical knowledge which allowed him to make this prediction was undoubtedly learned from the Babylonians, who had developed a system for the accurate prediction of lunar eclipses two centuries earlier. Thales brought Egyptian geometry to Greece, and he also made some original contributions to this field. He changed geometry from a set of ad hoc rules into an abstract and deductive science. He was the first to think of geometry as dealing not with real lines of finite thickness and imperfect straightness, but with lines of infinitessimal thickness and perfect straightness. (Echoes of this point of view are found in Plato’s philosophy).

Thales speculated on the composition of matter, and decided that the fundamental element is water. He thought this because animals can live by eating plants, and plants (Thales mistakenly believed) can live on water without any other nourishment.

Many stories are told about Thales. For example, Aristotle says that someone asked Thales, “If you’re so wise, why aren’t you rich?” Thales was offended by this question, and in order to prove a point, he quietly bought up all the olive presses of the city during the winter of a year when his knowledge of weather told him that the olive harvest would be exceptionally large. When summer came, the harvest was enormous, and he was able to rent the presses at any price he liked to charge. He made himself rich in one season, and then went back to philosophy, having shown that philosophers could easily be rich if they liked, but they have higher ambitions than wealth. Another story is told about Thales by Plato. According to Plato, Thales was so interested in some astronomical observations which he was making that he failed to look where he was going and fell into a well. He was helped out by a pretty and clever serving maid from Thrace who laughed at him because he was so interested in the stars that he could not see things that were right under his feet!

Thales had a student named Anaximander (610 B.C. - 546 B.C.) who also helped to bring Egyptian and Babylonian science to Greece. He imported the sundial from Egypt, and he was the first to try to draw a map of the entire world. He pictured the sky as a sphere, with the earth floating in space at its center. The sphere of the sky rotated once each day about an axis passing through the polar star. Anaximander knew that the surface of the earth is curved. He deduced this from the fact that as one travels northward, some stars disappear below the southern horizon, while others appear in the north. However, Anaximander thought that a north-south curvature was sufficient. He imagined the earth to be cylindrical rather than spherical in shape.

The idea of a spherical earth had to wait for Pythagoras.

The third philosopher in the school of Militus was Anaximenes (570 B.C. - 500 B.C.), a pupil of Anaximander. He was the first of the Greeks to distinguish clearly between the planets and the stars. Like Thales, he speculated about the composition of matter, and he concluded that the fundamental element was air. This (he thought) could be compressed to form water, and still further compressed to form earth. Thus Anaximenes conceived in principle the modern idea of the three states of matter: gas, liquid and solid, which change into one another as the pressure and temperature are changed.

Pythagoras

Pythagoras founded a brotherhood that lasted about a hundred years and greatly influenced the development of mathematics and science. The pythagorian theorem, which he discovered, is considered to be the most important single theorem in mathematics.

Pythagoras, who lived from 582 B.C. to 497 B.C., is one of the most important and interesting figures in the history of European culture. It is hard to decide whether he was a religious leader or a scientist. Certainly, in order to describe him, one has to say a little about the religion of ancient Greece.

Besides the official religion, the worship of the Olympian gods, there were also other cults which existed simultaneously, and among these the worship of Bacchus or Dionysos was the most important. Bacchus, Dionysos and Bromios were all names of a many-named Thracian god who represented the forces of nature. The worshippers of Dionysos tried to return to nature, gaining release from the tensions generated by civilization by casting off all civilized constraints and returning temporarily to an animal-like state, reviving long-suppressed instincts. Often the worshippers were women, young girls and slaves, who gathered on the mountain slopes on certain evenings and began to dance. The dancing and drinking of wine continued throughout the whole night, becoming progressively wilder and more primitive.

Intoxicated by wine (the blood of Bacchus) and by the wild rhythm of the drums and pipes, the Bacchae would gradually reach a state of primitive frenzy in which they would tear living animals to bits and eat their raw flesh. By these acts, the Bacchae were re-enacting the legend of Dionysos. According to legend, Dionysos, the beautiful son of Zeus and Persephone, was torn to pieces by the Titans and eaten, all except for his heart, which was returned to Zeus. Dionysos was then reborn, and the Titans were killed by the thunderbolts of Zeus. From the ashes of the Titans mankind was created, and thus the human race contains not only the evil of the Titans, but also the divinity of Dionysos The legend of Orpheus contains a parallel to the legend of Dionysos. In grief over his lost wife, Orpheus decides to give up sex forever, and this angers the women of Thrace. As Orpheus sings a last beautiful melody, the women of Thrace tear him to pieces, and his head, still singing, floats down the river Hebrus.

In Orphism, which was a reformed version of the cult of Dionysos, the idea of the simultaneously divine and evil nature of the human race is stressed. Followers of the Orphic religion believed that because of the element of evil and original sin in the human soul, it was doomed to a cycle of death and rebirth. However, the soul could be released from the cycle of reincarnation, and it could regain its divinity and immortality. The methods which the Orphists used to purge the soul included both Bacchic catharsis and asceticism. Also, Orphism included primitive tabus. For example, the followers of the cult were forbidden to eat beans, to touch a white cock, too stir the fire with an iron, to eat from a whole loaf, etc..

Pythagoras, who was a student of Anaximander, became a leader and reformer of the Orphic religion. He was born on the island of Samos, near the Asian mainland, and like other early Ionian philosophers, he is said to have travelled extensively in Egypt and Babylonia. In 529 B.C., he left Samos for Croton, a large Greek colony in southern Italy. When he arrived in Croton, his reputation had preceded him, and a great crowd of people came out of the city to meet him. After Pythagoras had spoken to this crowd, six hundred of them left their homes to join the Pythagorean brotherhood without even saying goodbye to their families.

For a period of about twenty years, the Pythagoreans gained political power in Croton, and they also had political influence in the other Greek colonies of the western Mediterranian. However, when Pythagoras was an old man, the brotherhood which he founded fell from power, their temples at Croton were burned, and Pythagoras himself moved to Metapontion, another Greek city in southern Italy.

Although it was never again politically influential, the Pythagorean brotherhood survived for more than a hundred years, and the ideas of the Pythagoreans became one of the foundations on which western civilization ultimately was built. Together with Thales, Pythagoras was the founder of western philosophy; and the ideas of Pythagoras have an astonishing breadth and originality which is not found in Thales.

The Pythagorean brotherhood admitted women on equal terms, and all its members held their property in common. Even the scientific discoveries of the brotherhood were considered to have been made in common by all its members.

Pythagorean harmony

The Pythagoreans practiced medicine, and also a form of psychotherapy. According to Aristoxenius, a philosopher who studied under the Pythagoreans, “They used medicine to purge the body, and music to purge the soul”. Music was of great importance to the Pythagoreans, as it was also to the original followers of Dionysos and Orpheus.

Both in music and in medicine, the concept of harmony was very important. Here Pythagoras made a remarkable discovery which united music and mathematics. He discovered that the harmonics which are pleasing to the human ear can be produced by dividing a lyre string into lengths which are expressible as simple ratios of whole numbers. For example, if we divide the string in half by clamping it at the center, (keeping the tension constant), the pitch of its note rises by an octave. If the length is reduced to 2/3 of the basic length, then the note is raised from the fundamental tone by the musical interval which we call a major fifth, and so on.

Having discovered that musical harmonics are governed by mathematics, Pythagoras fitted this discovery into the framework of Orphism. According to the Orphic religion, the soul may be reincarnated in a succession of bodies. In a similar way (according to Pythagoras), the “soul” of the music is the mathematical structure of its harmony, and the “body” through which it is expressed is the gross physical instrument. Just as the soul can be reincarnated in many bodies, the mathematical idea of the music can be expressed through many particular instruments; and just as the soul is immortal, the idea of the music exists eternally, although the instruments through which it is expressed may decay.

In distinguishing very clearly between mathematical ideas and their physical expression, Pythagoras was building on the earlier work of Thales, who thought of geometry as dealing with dimensionless points and lines of perfect straightness, rather than with real physical objects. The teachings of Pythagoras and his followers served in turn as an inspiration for Plato’s idealistic philosophy.

Pythagoras also extended the idea of harmony to astronomy. He was the first person we know of who recognized that the earth is spherical in shape. He was also the first person to point out that the plane of the orbit of the moon is inclined with respect to the plane of the earth’s equator, and the first Greek to recognize that the morning star (Phosphorus) and the evening star (Hesperus) are the same planet. After his time it was called Aphrodite by the Greeks, and later Venus by the Romans.

Pythagoras pointed out that the sun and the planets do not have the same apparent motion as the sphere of the stars. Each has its own motion. This led him to introduce into his cosmology an independently revolving sphere for each of the planets and for the sun. Pythagoras imagined these spheres to be concentric and transparent, and to revolve about the spherical earth.

The idea of spheres carrying the planets was developed further by later Greek astronomers, the greatest of whom was Hipparchus (190 B.C. - 120 B.C.), and it was incorporated into a famous book by Ptolemy (75 B.C. - 10 B.C.). After the fall of Rome, Ptolemy’s book, the Almagest, survived in the highly civilized Arab world. It was translated into Latin in 1175 A.D., and it dominated astronomical thinking until the Renaissance. Thus the celestial spheres of Anaximander, Pythagoras, Hipparchus and Ptolemy had a long period of influence, and even some calculational usefulness, before they were replaced by the very much better sun-centered cosmology of Copernicus, Tycho Brahe, Kepler, Galileo and Newton.

Pythagoras searched for mathematical harmony in the motions of the planets. He thought that, just as the notes of the musical scale are connected by simple mathematical relationships, so the motions of the planets should obey a simple mathematical law. The Pythagoreans even imagined that as the celestial spheres turned, they produced a kind of cosmic music which only the most highly initiated could hear. The Pythagorean vision of mathematical harmony in the motion of the planets was laughed at by Aristotle, but in the end, after two thousand years, the dream was fulfilled in the laws Newton.

Having found mathematical harmony in the world of sound, and having searched for it in astronomy, Pythagoras tried to find mathematical relationships in the visual world. Among other things, he discovered the five possible regular polyhedra. However, his greatest contribution to geometry is the famous Pythagorean theorem, which is considered to be the most important single theorem in the whole of mathematics.

The Babylonians and the Egyptians knew that for many special right triangles, the sum of the squares formed on the two shorter sides is equal to the square formed on the long side. For example, Egyptian surveyors used a triangle with sides of lengths 3, 4 and 5 units. They knew that between the two shorter sides, a right angle is formed, and that for this particular right triangle, the sum of the squares of the two shorter sides is equal to the square of the longer side. Pythagoras proved that this relationship holds for every right triangle. In exploring the consequences of his great theorem, Pythagoras and his followers discovered that the square root of 2 is an irrational number. (In other words, it cannot be expressed as the ratio of two integers.) The discovery of irrationals upset them so much that they abandoned algebra. They concentrated entirely on geometry, and for the next two thousand years geometrical ideas dominated science and philosophy.

The Pythagorean ideal

According to the Pythagoreans, the mind can be out of tune, just as a musical instrument can be out of tune. In medicine and psychiatry, they aimed at achieving harmony in the bodily organs and in the mind. When we speak of “muscle tone” or a “tonic” or “temperence”, we are using words which have a Pythagorean origin. The word “philosophy”, (“love of wisdom”), was also coined by the Pythagoreans.

In psychiatry, the Pythagoreans used various methods to free the mind from the tyrannical passions and tensions of the body. These methods were graded according to the degree of initiation of the patient. At the lowest level was the catharsis of a Bacchic orgy, followed by a long tranquilizing sleep and then an ascetic regimen to develop selfcontrol. At the highest level of liberation, the mind was drawn away from preoccupation with self by the study of the eternal truths of nature as revealed by mathematics. According to Plutarch, “The function of geometry in Pythagorism is to draw us away from the world of the senses to the world of the intellect and the eternal”.

The Orphic religion in some ways resembles the Buddhist and Hindu religions. It is not inconceivable that they have a common origin, since the Greeks were linguistically related to the Indo-European-speaking peoples who conquered India in the first millenium B.C.. In Buddhism, as in Orphism, one aims at release from the wheel of death and rebirth by mastery over self. However, the Pythagorean modification of Orphism introduces an element which is not found in Buddhism. In Pythagorism, the highest level of release and purification is achieved by contemplation of the structure of the universe; and the key to this structure is mathematics.

Pythagoras was the first person to maintain that mathematics is the key to the understanding of nature. In this belief he was completely correct. In the Pythagorean view of nature, mathematical harmony governs the fundamental laws of the universe. In the Pythagorean ethic, the highest vocation is that of the philosopher, and the aim of philosophy is to understand nature through the discovery of the mathematical relationships which govern the universe.

Much of what Pythagoras hoped to achieve in mathematics has been achieved today. For example, quantum theory has shown that the inner structure of an atom is governed by mathematical relationships closely analogous to those governing the harmonics of a lyre string. We have indeed found mathematical harmony in the fundamental laws of nature; but one can ask whether philosophy has brought harmony to human relations, as Pythagoras would have hoped!

We mentioned that the word “philosophy” was invented by the Pythagoreans. The word “theory” in its modern sense is also due to them. The word is derived from the Greek word “thea”, meaning “spectacle”, (as in the English word “theater”). In Greek, there is a related word, “theorio”, meaning “to behold” or “to contemplate”. In the Pythagorean ethic, contemplation held the highest place. The Pythagoreans believed that “The greatest purification of all is disinterested science; and it is the man who devotes himself to that, the true philosopher, who has most effectively released himself from the wheel of birth.”

One of the Pythagorean mottos was: “A diagram and a step, not a diagram and a penny”. Euclid, who belonged to the Pythagorean tradition, once rebuked a student who asked what profit could be gained from a knowledge of geometry. Euclid called a slave and said (pointing at the student): “He wants to profit from geometry. Give him a penny.” The student was then dismissed from Euclid’s school.

The Greeks of the classical age could afford to ignore practical matters, since their ordinary work was performed for them by slaves. It is unfortunate that the craftsmen and metallurgists of ancient Greece were slaves, while the philosophers were gentlemen who refused to get their hands dirty. An unbridgable social gap separated the philosophers from the craftsmen; and the empirical knowledge of chemistry and physics, which the craftsmen had gained over the centuries, was never incorporated into Greek philosophy.

The idealism of Pythagoras was further developed and exaggerated by Plato, the most famous student of the Pythagorean school. Plato considered the real world, as revealed by the senses, to be an imperfect expression of the world of ideas; and he thought that philosophers should not concern themselves with the real world. The factors mentioned above prevented the classical Greeks from making use of observation and induction; and for this reason they were far better in mathematics than in other branches of science. In mathematics, one proceeds by pure deduction from a set of axioms. This insistence on pure deduction gives mathematics its great power and certainty; but in other branches of science, deduction alone is sterile. To be fruitful, deduction must be combined with observation and induction.

The Pythagorean preoccupation with harmony and with ideal proportion was reflected in Greek art. The classical Greeks felt that, just as harmony in music is governed by ideal ratios, so also harmony in architecture and in sculpture is governed by ideal proportions. All Greek temples of the classical period exhibited certain ratios which were considered to be ideal; and Greek sculpture showed, not real individuals, involved in emotions of the moment, but calm ideal figures. Greek drama did not represent the peculiarities of particular individuals, but rather searched for universal truths concerning human nature. In classical Greek drama, one can even see a reflection of the deductive method which characterized Greek philosophy: In the beginning of a play, the characters are faced with a set of circumstances from which the action inevitably follows, just as the theorems of Euclid inevitably follow from his axioms.

The golden age of Athens

Between 478 B.C. and 431 B.C. Athens enjoyed a golden age. Their victory in the Persian war gave great prestige to Athens and Sparta, and these two cities became the leaders of the other Greek city states. Athens was the leader of the Delian league, while Sparta was the leader of the Peloponesian League. The Greek world was divided into two blocks, and although Athens and Sparta had been allies during the Persian war, they soon became political and commercial rivals. Aided by her large navy, Athens pursued a very aggressive com- mercial policy aimed at monopolistic control of the Mediterranian sea trade. This brought great prosperity to Athens, but it also brought the Delian League into conflict with the Peloponesian League, a conflict which ultimately led to the downfall of Athens. However, during the period between 478 B.C. and 431 B.C., Athens enjoyed enormous prosperity. Refugees from the Ionian cities on the Asian mainland flocked to Athens, bringing with them their sophisticated culture. These refugees greatly enriched the cultural life of Athens, and their arrival marked the beginning of Athenian intellectual leadership.

The Athenians decided to use the surplus from the treasury of the Delian League to rebuild the Acropolis, which had been destroyed by the Persians. Pericles, the leader of Athens, put his friend, the sculptor Pheidias, in charge of the project. The new Acropolis was dominated by the Parthenon, which was built between 447 B.C. and 432 B.C.. Most of the sculptures of the Parthenon were brought to England in the nineteenth century by Lord Elgin, and they are now in the British Museum. The famous “Elgin marbles”, together with the ruins of the Parthenon in Athens, symbolize the genius of the age of Pericles. Wealthy, full of self-confidence, proud of their victory in the Persian war, and proud of their democratic constitution, the Athenians expressed the spirit of their age in sculpture, architecture, drama, poetry and philosophy which shine like beacons across the centuries. Anaxagoras

One of the close friends of Pericles was the philosopher Anaxagoras (500 B.C. - 428 B.C.), who came to Athens from Ionia when he was 38 years old. This move by Anaxagoras was important, because it brought to Athens the philosophic tradition of the Ionian cities of Asia Minor. (In a similar way, a century earlier, Pythagoras had carried Ionian philosophy to the Greek colonies of the western Mediterranian.) Anaxagoras was a rationalist and probably also an atheist (unlike the Pythagoreans). He believed that the stars and planets had been brought into existence by the same forces which formed the earth, and that the laws of nature are the same for celestial bodies as they are for objects on the earth. He thought that the sun and stars were molten rocks, and that the sun was about the same size as the Greek peninsula. (A large meteor which fell on Greece during the lifetime of Anaxagoras may have caused him to form this opinion).

Anaxagoras knew that the moon shines by reflected light, and that there are mountains on the moon. In fact, he believed that the moon is very much like the earth, and he thought that it might possibly be inhabited. He explained correctly the cause of both solar and lunar eclipses, and the phases of the moon.

Even the cultured Athenians found these views a bit too advanced. Anaxagoras was thrown into prison, accused (probably correctly) of atheism. The fact that he was a close friend of Pericles did not help him. The political enemies of Pericles, not daring to attack the great leader directly, chose to embarrass him by attacking his friends. Pericles used his eloquence to defend Anaxagoras, and he succeeded in having his friend released from prison. However, Anaxagoras felt that it was not safe to remain in Athens. In 434 B.C. he retired to the little town of Lampsacus on the Hellespont, where he spent the remainder of his life.

The atomists

In the 5th century B.C. there was a great deal of discussion among the Greek philosophers about whether there is anything permanent in the universe. Heraclitus (540 B.C. - 475 B.C.) maintained that everything is in a state of flux. Parmenides (540 B.C. - c. 470 B.C.) maintained that on the contrary nothing changes - that all change is illusory. Leucippus (490 B.C. - c. 420 B.C.) and his student Democritus (470 B.C. - c. 380 B.C.), by a lucky chance, hit on what a modern scientist would regard as very nearly the correct answer.

According to Democritus, if we cut an apple in half, and then cut the half into parts, and keep on in this way for long enough, we will eventually come down to pieces which cannot be further subdivided. Democritus called these ultimate building blocks of matter “atoms”, which means “indivisible”. He visualized the spaces between the atoms as being empty, and he thought that when a knife cuts an apple, the sharp edge of the blade fits into the empty spaces between the atoms and forces them apart.

Democritus believed that each atom is unchanged in the processes which we observe with our senses, where matter seems to change its form. However, he believed that the atoms are in a state of constant motion, and that they can combine with each other in various ways, thus producing the physical and chemical changes which we observe in nature. In other words, each atom is in itself eternal, but the way in which the atoms combine with each other is in a state of constant flux because of the motion of the atoms.

This is very nearly the same answer which we would give today to the question of which things in the universe are permanent and which change. Of course, the objects which we call “atoms” can be further subdivided, but if Democritus were living today he would say that we have merely made the mistake of calling the wrong things “atoms”. We should really apply the word to fundamental particles such as quarks, which cannot be further subdivided.

In discussing which things in the universe are permanent and which change, we would also add, from our modern point of view, that the fundamental laws of the universe are permanent. In following these unchanging laws, matter and energy constantly alter their configuration, but the basic laws of nature remain invariant. For example, the configuration of the planets changes constantly, but these constant changes are governed by Newton’s laws of motion, which are eternal.

Of the various ancient philosophers, Democritus is the one who comes closest to our modern viewpoint. However, the ideas of Democritus, like those of Anaxagoras, were too advanced for his contemporaries. Although Democritus was not actually thrown into prison for his beliefs, they aroused considerable hostility. According to Diogenes Laertius, Plato dislike the ideas of Democritus so much that he wished that all of his books could be burned. (Plato had his wish! None of the seventy-two books of Democritus has survived.) Aristotle also argued against atomism, and because of the enormous authority which was attached to Aristotle’s opinions, atomism almost disappeared from western thought until the time of John Dalton (1766 - 1844).

That the ideas of Democritus did not disappear entirely was due to the influence of Epicurus (341 B.C. - 270 B.C.), who made mechanism and atomism the cornerstones of his philosophy. The Roman poet Lu- cretius (95 B.C. - 55 B.C.) expounded the philosophy of Epicurus in a long poem called De Natura Rerum (On the Nature of Things). During the middle ages, this poem disappeared completely, but in 1417, a single surviving manuscript was discovered. The poem was then published, using Gutenberg’s newly-invented printing press, and it became extremely popular. Thus, the idea of atoms was not entirely lost, and after being revived by John Dalton, it became one of the cornerstones of modern science.

Hippocrates

The physician Hippocrates was born in about 460 B.C. on the island of Kos. According to tradition, he visited Egypt during the early part of his life. There he studied medicine, especially the medical works of Imhotep. He is also said to have studied under Democritus. Returning to the island of Kos, he founded the most rational school of medicine of the ancient world. He had many students, among whom were his sons and his sons-in law. During the later part of his life, he also taught and practiced in Thrace and Athens.

The medical school founded by Hippocrates was famous for its rationality and for its high ethical standard. The medical ethics of Hippocrates live on today in the oath taken by physicians. The rationality of Hippocrates is evident in all the writings of his school. For example, a book on epilepsy, called The Sacred Disease, contains the following passage:

“As for this disease called divine, surely it has its nature and causes, as have other diseases. It arises, like them, from things which enter and leave the body... Such things are divine or not - as you will, for the distinction matters not, and there is no need to make such a division anywhere in nature; for all alike are divine, or all are natural. All have their antecedent causes, which can be found by those who seek them.” More than fifty books of Hippocrates’ school were collected in Alexandria in the 3rd century B.C.. All of them were attributed by the Alexandrians to Hippocrates himself, but undoubtedly many of the books were written by his students. The physicians of the school of Hippocrates believed that cleanliness and rest are important for a sick or wounded patient, and that the physician should interfere as little as possible with the natural healing processes of the body. The books of the school contain much careful observation of disease. Hippocrates and his school resisted the temptation to theorize without a basis of carefully observed facts, just as they also resisted the temptation to introduce supernatural causes into medicine.

Hippocrates is said to have died in his hundredth year. According to tradition, he was humane, observant, learned, orderly and calm, with a grave and thoughtful attitude, a complete mastery of his own passions and a profound sympathy for the sufferings of his patients. We feel his influence today, both as one of the great founders of rational medicine, and as a pioneer of observation and inductive reasoning in science.

The Sophists and Socrates

Since Athens was a democracy, the citizens often found themselves speaking at public meetings.Eloquence could be turned into influence, and the wealthy Athenians imported teachers to help them master the art of rhetoric. These teachers, called “Sophists” (literally “wisdomists”), besides teaching rhetoric, also taught a form of philosophy which denied the existence of absolute truth, absolute beauty and absolute justice. According to the Sophists, “man is the measure of all things”, all truths are relative, “beauty is in the eye of the beholder”, and justice is not divine or absolute but is a human institution.

Opposed to the Sophists was the philosopher Socrates, who believed passionately in the existence of the absolutes which the Sophists denied. According to Socrates, a beautiful object would be beautiful whether or not there were any humans to observe it. Socrates adopted from the Sophists a method of conducting arguments by asking questions which made people see for themselves the things which Socrates wanted them to see.

The Sophists talked about moral and political questions, rather than about the nature of the universe. Socrates was an opponent of the Sophists, but like them he also neglected the study of nature and concentrated on the moral and political problems of man, “the measure of all things”.The Sophists, together with Socrates and his pupil Plato, exerted a great influence in causing a split between moral philosophy and natural philosophy.

The beginning of the end of classical Greek civilization came in 431 B.C., when Athens, pushing her aggressive commercial policy to an extreme, began to expel Corinthian merchants from markets around the Aegean. Corinth reacted by persuading the Peloponesian League to declare war on Athens. This was the beginning of a long war which ruined Greece.

Realizing that they could not resist the Spartan land forces, the Athenians abandoned the farmland outside their city, and took refuge inside the walls. The Athenians continued their prosperous foreign trade, and they fed their population with grain imported from the east. Ships bringing grain also brought the plague. A large part of the population of Athens died of the plague, including the city’s great leader, Pericles. No leader of equal stature was found to replace him, and the democratic Athenian government degenerated into mob rule. In 404 B.C., when the fleet of Athens was destroyed in a disastrous battle, the city surrendered to the Spartans. However, the Spartans remembered that without Athens, they would be unable to resist the Persian Empire. Therefore they did not destroy Athens totally, but were content to destroy the walls of Athens, reducing the city to the status of a satellite of Sparta.

Looking for scapegoats on whom to blame this disaster, the Athenian mobs seized Socrates (one of the few intellectuals who remained alive after the Peloponesian War), and they condemned him to death for failing to believe in the gods of the city.

For a short period, Sparta dominated the Greek world; but soon war broke out again, and the political scene degenerated into a chaos of wars between the city states.

Plato

Darkness was falling on the classical Greek world, but the light of civilization had not quite gone out. Socrates was dead, but Plato, the student of Socrates, kept his memory alive by writing dialogues in which Socrates appeared as a character.

Plato (427 B.C. - 317 B.C.) was an Athenian aristocrat, descended from the early kings of Athens. His real name was Aristocles, but he was called by his nickname, Platon (meaning “broad”) because of his broad shoulders. After the death of Socrates, Plato left Athens, saying that the troubles of the city would never end until a philosopher became king. (He may have had himself in mind!) He travelled to Italy and studied under the Pythagoreans. In 387 he returned to Athens and founded a school, which was called the Academy because it stood on ground which had once belonged to a Greek named Academus. Plato developed a philosophy which was based on the idealism of the Pythagoreans. In Pythagorean philosophy, a clear distinction was made between mathematical ideas and their physical expression. For example, geometry was considered to deal, not with real physical objects, but with idealized figures, constructed from lines of perfect straightness and infinite thinness. Plato developed and exaggerated the idealism of Pythagoras. In Plato’s philosophy, the real world is corruptible and base, but the world of ideas is divine and eternal. A real table, for example, is an imperfect expression of the idea of a table. Therefore we ought to turn our eyes away from the real world and live in the world of ideas.

Plato’s philosophy was just what the Athenians wanted! All around them, their world was crumbling. They gladly turned their backs on the unpleasantness of the real world, and accepted Plato’s invitation to live in the world of ideas, where nothing decays and where the golden laws of mathematics rule eternally.

By all accounts, Plato was an excellent mathematician, and through his influence mathematics obtained a permanent place in education. Aristotle

Plato’s favorite student was a young man from Macedon named Aristotle. Plato called him “the intelligence of the school”. He was born in 381 B.C., the son of the court physician of the king of Macedon, and at the age of seventeen he went to Athens to study. He joined Plato’s Academy and worked there for twenty years until Plato died. Aristotle then left the Academy, saying that he disapproved of the emphasis on mathematics and theory and the decline of natural science. Aristotle traveled throughout the Greek world and married the sister of the ruler of one of the cities which he visited. In 312 B.C., Philip II, who had just become king of Macedon, sent for Aristotle and asked him to become the tutor of his fourteen-year-old son, Alexander. Aristotle accepted this post and continued in it for a number of years. During this period, the Macedonians, under Philip, conquered most of the Greek city-states. Philip then planned to lead a joint Macedonian and Greek force in an attack on the Persian Empire. However, in 336 B.C., before he could begin his invasion of Persia, he was murdered (probably by an agent of his wife, Olympia, who was jealous because Philip had taken a second wife). Alexander then succeeded to his father’s throne, and, at the head of the Macedonian and Greek army, he invaded Persia. Aristotle, no longer needed as a royal tutor, returned to Athens and founded a school of his own called the Lyceum. At the Lyceum he built up a collection of manuscripts which resembled the library of a modern university.

Aristotle was a very great organizer of knowledge, and his writings almost form a one-man encyclopedia. His best work was in biology, where he studied and classified more than five hundred animal species, many of which he also dissected. In Aristotle’s classification of living things, he shows an awareness of the interrelatedness of species. This interrelatedness was later brought forward by Darwin as evidence for the theory of evolution. One cannot really say that Aristotle proposed a theory of evolution, but he was groping towards the idea. In his history of animals, he writes:

“Nature proceeds little by little from lifeless things to animal life, so that it is impossible to determine either the exact line of demarcation, or on which side of the line an intermediate form should lie. Thus, next after lifeless things in the upward scale comes the plant. Of plants, one will differ from another as to its apparent amount of vitality. In a word, the whole plant kingdom, whilst devoid of life as compared with the animal, is yet endowed with life as compared with other corporial entities. Indeed, there is observed in plants a continuous scale of ascent towards the animal.”

Aristotle’s classification of living things, starting at the bottom of the scale and going upward, is as follows: Inanimate matter, lower plants and sponges, higher plants, jellyfish, zoophytes and ascidians, molluscs, insects, jointed shellfish, octopuses and squids, fish and reptiles, whales, land mammals and man. The acuteness of Aristotle’s observation and analysis can be seen from the fact that he classified whales and dolphins as mammals (where they belong) rather than as fish (where they superficially seem to belong).

One of Aristotle’s important biological studies was his embryological investigation of the developing chick. Ever since his time, the chick has been the classical object for embryological studies. He also studied the four-chambered stomach of the ruminants and the detailed anatomy of the mammalian reproductive system. He used diagrams to illustrate complex anatomical relationships - an important innovation in teaching technique.

Aristotle’s physics and astronomy were far less successful than his biology. In these fields, he did not contribute with his own observations. On the whole, he merely repeated the often-mistaken ideas of his teacher, Plato. In his book On The Heavens, Aristotle writes: “As the ancients attributed heaven and the space above it to the gods, so our reasoning shows that it is incorruptable and uncreated and untouched by mortal troubles. No force is needed to keep the heaven moving, or to prevent it from moving in another manner. Nor need we suppose that its stability depends on its support by a certain giant, Atlas, as in the ancient fable; as though all bodies on high possessed gravity and an earthly nature. Not so has it been preserved for so long, nor yet, as Empedocles asserts, by whirling around faster than its natural motion downward.”

Empedocles (490 B.C. - 430 B.C.) was a Pythagorean philosopher who studied, among other things, centrifugal forces. For example, he experimented with buckets of water which he whirled about his head, and he knew that the water does not run out. The passage which we have just quoted shows that Empedocles had suggested the correct explanation for the stability of the moon’s orbit. The moon is constantly falling towards the earth, but at the same time it is moving rapidly in a direction perpendicular to the line connecting it with the earth. The combination of the two motions gives the moon’s orbit its nearly-circular shape.

Empedocles had thus hit on the germ of the idea which Newton later developed into his great theory of universal gravitation and planetary motion. In the above passage, however, Aristotle rejects the hypothesis of Empedocles. He asserts instead that the heavens are essentially different from the earth, and not subject to the same laws. Aristotle believed celestial bodies to be composed of a fifth element - ether. This, he thought, was why the heavens were not subject to the laws which apply to earthly matter. He thought that for earthly bodies, the natural motion was a straight line, but for celestial bodies the natural motion was circular because “one kind of motion is divine and immortal, having no end, but being in itself the end of other motions”; and motion in a circle is “perfect, having no beginning or end, nor ceasing in infinite time.”

This doctrine, that the motion of celestial bodies must be uniform and circular, was a legacy from Plato. In fact, Plato had placed before his Academy the problem of reconciling the apparently irregular motion of the planets with the uniform circular motion which Plato believed they had to have. In a famous phrase, Plato said that the problem was to “save the appearances”.

The problem of “saving the appearances” was solved in a certain approximation by Eudoxis, one of Plato’s students. He imagined a system of concentric spheres, attached to one another by axes. In this picture, each sphere rotates uniformly about its own axis, but since the spheres are attached to each other in a complex way, the resulting motion duplicates the complex apparent motion of the planets. Aristotle accepted the system of Eudoxis, and even added a few more spheres of his own to make the system more accurate. In making a distinction between the heavens and the earth, Aristotle gave still another answer to the question of which things in the universe change and which are permanent: According to Aristotle, the region beneath the sphere of the moon is corrupt and changeable, but above that sphere, everything is eternal and divine. Change is bad, permanence is good - that is the emotional content of the teaching of Plato and Aristotle, the two great philosophers of the rapidly-decaying 4th century B.C. Greek civilization.

Besides writing on biology, physics and astronomy, Aristotle also discussed ethics, politics and literary criticism, and he made a great contribution to western thought by inventing a formal theory of logic.

His writings on logic were made popular by St. Thomas Aquinas (1225- 1274), and during the period between Aquinas and the Renaissance, Aristotle’s logic dominated theology and philosophy. In fact, through his work on logic, Aristotle became so important to scholastic philosophy that his opinions on other subjects were accepted as absolute authority. Unfortunately, Aristotle’s magnificent work in biology was forgotten, and it was his misguided writings on physics and astronomy which were influential. Thus, for the experimental scientists of the 16th and 17th centuries, Aristotle eventually became the symbol of wrongness, and many of their struggles and victories have to do with the overthrow of Aristotle’s doctrines.

Even after it had lost every vestige of political power, Athens continued to be a university town, like Oxford or Cambridge. Plato’s Academy continued to teach students for almost a thousand years. It was finally closed in 529 A.D. by the Emperor Justinian, who feared its influence as a stronghold of “pagan philosophy”. Aristotle’s Lyceum continued for some time as an active institution, but it soon declined, because although Athens remained a center of moral philosophy, the center of scientific activity had shifted to Alexandria. The collection of manuscripts which Aristotle had built up at the Lyceum became the nucleus of the great library at Alexandria. The books of Plato and Aristotle survived better than the books of other ancient philosophers, perhaps because Plato and Aristotle founded schools. Plato’s authenticated dialogues form a book as long as the Bible, covering all fields of knowledge. Aristotle’s lectures were collected into 150 volumes. (Of course, each individual volume was not as long as a modern printed book.) Of these, 50 have survived. Some of them were found in a pit in Asia Minor by soldiers of the Roman general Sulla in 80 A.D., and they were brought to Rome to be recopied. Some of the works of Aristotle were lost in the West, but survived during the dark ages in Arabic translations. In the 12th and 13th centuries, these works were translated into Latin by European scholars who were in contact with the Arab civilization. Through these translations, Europe enthusiastically rediscovered Aristotle, and until the 17th century, he replaced Plato as the philosopher.

The influence of Plato and Aristotle was very great (perhaps greater than they deserved), because of their literary skill, because so many of their books survived, because of the schools which they founded, and because Plato and Aristotle wrote about all of knowledge and wrapped it up so neatly that they seemed to have said the last word.

Chapter 3: THE HELLENISTIC ERA.

Suggestions for further reading

1. Roger Ling, The Greek World, Elsevier-Phaidon, Oxford (1976).
2. Bertrand Russell, History of Western Philosophy, George Allen and Unwin Ltd., London (1946).
3. Michael Grant (editor), Greek Literature, Penguin Books Ltd. (1976).
4. George Sarton, History of Science, Oxford University Press (1959).
5. Morris Kline, Mathematics in Western Culture, Penguin Books Ltd. (1977).
6. E.T. Bell, Men of Mathematics, Simon and Schuster, New York (1937).
7. Isaac Asimov, Asimov’s Biographical Encyclopedia of Science and Technology, Pan Books Ltd., London (1975).
8. O. Neugebauer, The Exact Sciences in Antiquity, Harper and Brothers (1962).

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