Biographical encyclopedia
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1 [3] THALES THALES [3] in the problem. No rules are given for solving a particular type of problem for all possible sets of conditions. Perhaps it is assumed that the reader will work out the rule for himself from the cases given. Perhaps the rules are given on some other papyrus not yet found, or possibly forever lost. Perhaps the priestly caste kept the general rules a secret, just as the followers of Pythag oras [7] many years later were to keep certain mathematical discoveries secret. Certainly, considering the technical pro ficiency of the Egyptians in mathe matics (for the builders of the pyramids could by no means have been mathe matical novices) it is hard to believe that generalization did not exist. Nevertheless the fact remains that there is no documentary sign of general ization in mathematics until the time of Thales [3], who lived a thousand years after Ahmose. [3] THALES (thay'leez) Greek philosopher Bom: Miletus, 624 b . c .
b .
. The later Greeks considered Thales the founder of Greek science, mathe matics, and philosophy, and they cred ited to him the origin of almost every branch of knowledge. It is hard to say how much of this is later embroidery. He is supposed to have been bom of a Phoenician mother, though this is doubted by some. Perhaps the legend only signifies that he was educated in Eastern science. Certainly he visited Egypt and probably Babylonia. It may be that what seemed to the Greeks a multiplicity of achievement was simply the lore of the more ancient peoples. For instance, the single deed that most secured his reputation, according to the tale told a century and a half later by the Greek historian Herodotus, was his prediction of an eclipse of the sun, an eclipse which then proceeded to take place in the very year for which it was predicted. (When it occurred it fright ened the Medes and Lydians, who were on the point of advancing into battle, and convinced them of the beauties of peace. They signed a treaty and the ar mies returned home.) Modem astro nomical research showed that the only eclipse that took place in Asia Minor in Thales’ time was on May 28, 585 b .
., so that the aborted battle is the first human historical event that can be dated with certainty to the exact day. Nevertheless Thales’ feat seems not so miraculous when we consider that the Babylonians had worked out systems for the accurate prediction of lunar eclipses at least two centuries before his time. His ability to predict this solar eclipse, and to the year rather than to the day, was, therefore, almost certainly acquired in the East. Thales was the first Greek to maintain that the moon shone by reflected sunlight and this, too, may rep resent Babylonian lore. Thales also borrowed Egyptian geome try, but here he made a fundamental ad vance. He converted it into an abstract study, being the first man we know of to consider it as dealing with imaginary lines of zero thickness and perfect straightness, rather than with actual lines, thick and imperfect, scraped in the sand or scratched on wax. (If the Egyp tians or Babylonians had already made this advance, it is still true that Thales was the first to place such views on rec ord in a form that has reached us, via the works of later philosophers.) Thales seems also to have been the first to go about proving mathematical statements by a regular series of argu ments, marshaling what was already known and proceeding step by step to the desired proof as inevitable conse quence. In other words, he invented de ductive mathematics, which was to be systematized and brought to a high pol ish two and a half centuries later by Euclid [40], Certain specific geometric theorems were later supposed to have been discov ered by him; for instance, that the diam eter of a circle divides it into two equal parts, that vertical angles are equal, and that the base angles of an isosceles trian gle are equal. He was also supposed to have mea sured the height of an Egyptian pyramid 2 [3] THALES ANAXIMANDER [4] by comparing the length of its shadow to that of the shadow of a stick of known size—which represents the concept of trigonometry. In the physical sciences, he was the first to study magnetism. More impor tant, he is the first man we know of who asked the question: Of what is the uni verse made? and to answer it without in troducing gods or demons. His own answer was that the funda mental stuff (the “element,” we would now say) of the universe was water, and the earth was only a flat disc floating on an infinite ocean. This answer was a most reasonable guess for the times, since it was clear that life, at least, depended on water. But the question itself was far more important than the answer, for it inspired later philosophers, who flour ished in the same region, near Miletus, among them Anaximander [4], Anaxi menes [5], and Heraclitus [10], to specu late on the same subject. It was this line of thought that led eventually, after two thousand years of painful intellectual struggle, to modern chemistry. Thales in addition to being a philoso pher was, according to later tradition, a practical man of affairs. In politics he shrewdly urged a political union of the various Greek cities of Ionia (the mod ern southwest coast of Turkey), of which Miletus was one, for self-defense against the encroaching non-Greek king dom of Lydia. This, the following cen turies amply demonstrated, was the only way the Greeks could defend themselves against the surrounding nations. How ever, the Greek passion for disunity rose triumphant over all and was the cause of the country’s ruin. Aristotle [29] said that Thales, stung by jibes to the effect that if he were so wise, it was strange that he wasn’t rich, quietly bought up the olive-presses in Miletus and surrounding territory in a year when his knowledge of weather told him the olive crop would be a good one. Charging monopoly prices for the use of the presses, he grew rich in one season. Then, having proved his point, he aban doned business and returned to the world of the mind. This may have been invented merely to point a moral. If so, Plato [24] in vented another tale to point another moral. While walking along and studying the stars, Plato said, Thales fell into a well. An old woman coming in response to his cries, helped him out, but said with contempt, “Here is a man who would study the stars and cannot see what lies at his feet.” Already in the time of Plato and Aris totle, two and a half centuries after Thales, the old philosopher’s views were remembered imperfectly and made the subject of legend. In valuing philosophical speculation over the practical applications of science, Thales set the tone for later Greek think ing. As a result the work of Greek engi neers and inventors was largely ignored by later Greek writers and badly under estimated, in consequence, by all later generations. We have only very slight in formation about Thales’ younger con temporary, Eupalinus [8], who in his way may have been as accomplished a sage.
In later centuries, when the Greeks made up lists of the “seven wise men,” Thales was invariably placed first. [4] ANAXIMANDER (a-nak'si-man-der) Greek philosopher
b . c .
ab o u t 546
b . c . Like Thales, whose pupil he was, Anax imander helped introduce the science of the ancient East to Greece. He was the first Greek to make use of the sun dial, for instance, which had been known for centuries both in Egypt and Bab ylonia. No better timekeeper was to be found until the days of Ctesibius [46], over three centuries later. Anaximander was also the first to attempt to draw a map of the whole earth as he knew it. He recognized that the heavens re volved about the Pole star and so he pic tured the sky as a complete sphere and not merely as a semispherical arch over the earth. For the first time the notion of spheres invaded astronomy; this was to culminate eventually in the sophisticated
[5] ANAXIMENES PYTHAGORAS [7] (but erroneous) picture of the universe drawn up by Ptolemy [64]. He also recognized that the earth’s surface must be curved, to account for the change in the position of the stars as one traveled. He felt a north-south cur vature was enough, however, so he pic tured the earth as a cylinder about an east-west axis with a height one-third its diameter. The notion of a spherical earth had to wait several decades for Pythag oras [7] and his followers. Anaximander’s idea of the basic ele ment of the universe was far more mysti cal than Thales’ plain and undramatic notion that it was water. Anaximander envisaged a formless mass that was both the source and the destination of all ma terial things. He called this unobservable substance apeiron, meaning infinite. Nev ertheless, he conceded this much to water—he thought life originated there. In this he was quite correct. The treatise Anaximander wrote de scribing his views is thought to be the first work of consequence in Greek prose. His works are now lost. [5] ANAXIMENES (an'ak-sim'ih-neez) Greek philosopher Born: Miletus, about 570 b . c .
b .
. Little is known about Anaximenes ex cept that he may have been a pupil of Anaximander [4], and that he believed air to be the fundamental element of the universe. By compression, he supposed, it could take on the form of water and, eventually, earth. By rarefaction, it heats and becomes fire. He is supposed to have been the first Greek to distinguish clearly between planets (such as Mars and Venus) and stars and to have maintained that the rainbow was a natural phenome non rather than a goddess. [6] XENOPHANES (zee-nof'uh-neez) Greek philosopher Born: Colophon, Ionia, about 570 B.C.
Died: about 480 b . c . Like Pythagoras [7], his contemporary, Xenophanes left Ionia after 545 b . c . when Persia had conquered the region. He settled in the town of Elea. He wrote on Pythagorean doctrine, but was less mystical than most of the school. He did not believe in transmigration of souls or in the primitive Greek gods but in a monotheism not at all characteristic of Greek thought. He guessed that earth might be the fundamental element of the universe, but he is best known for his theory, derived from the fact that seashells were some times found on mountain heights, that the physical characteristics of the earth changed with time. Mountains, he main tained, must have originally been cov ered by the sea and, with time, risen to their present heights. This was a remarkable forecast of later geologic thinking, but it remained an isolated ray of light until Hutton [297], twenty-three centuries later, founded geology and made sober sense of Xenophanes’ seemingly wild guess. [7] PYTHAGORAS (pih-thag'oh-rus) Greek philosopher
about 560 b .
. Died: Metapontum (in southern Italy), about 480 b .
. Pythagoras, like the other early sages of Greece, was reputed to have traveled widely in Egypt and the East, and he may well have done so. He is also re ported to have studied under Anax imander [4] or even under Thales [3] himself.
However, the first event in his life that seems reasonably certain is his departure from Samos in 529 b . c . and his emigra tion to Croton in southern Italy. (By that time the coasts of southern Italy and eastern Sicily had been colonized by the Greeks and the region remained Greek in culture well into the Middle Ages.) Pythagoras’ move, according to tradition, was brought about by the harsh, one- man rule over Samos on the part of the tyrant Polycrates. Whatever the cause, the move extended the philosophic and 4 [7] PYTHAGORAS PYTHAGORAS [7] scientific tradition—begun by Thales at the eastern rim of the Greek world—to the far west of the Greek world. In Croton, Pythagoras broke with the rationalism of the east-Greek tradition and founded a cult marked by secrecy, asceticism, and mysticism. The cult, Pythagoreanism, forbade, for instance, the poking of fire with an iron poker and the eating of beans. It also taught the doctrine of the transmigration of souls. There is a story, for instance, that Pythag oras ordered a man to stop beating a dog, claiming he recognized the voice of a dead friend of his. This may merely have been a humane impulse on Pythag oras’ part—or it may have been invented by the cult’s many enemies to cast ridi cule upon it. In many ways Pythagoreanism was like the mystery cults prevalent in Greece then and afterward, but it differed from them in the interest the followers of Pythagoras had in mathe matics and astronomy. The cult achieved important political power in Pythagoras’ later years and was usually to be found on the side of the aristocrats. Even dur ing the lifetime of Pythagoras, however, the democrats had started to gain the upper hand in southern Italy and the cult began to suffer persecution. Pythag oras was exiled from Croton about ten years before his death. Pythagoreanism survived as an active cult for only a cen tury after its founder’s death. The unpopularity it brought upon it self by its political activity resulted in a violent wave of persecution that spread over all the Greek world. By 350 b . c . Pythagoreanism was wiped out. The influence of its ideas, however, has lasted into modern times, and Pythagoras re mains the most famous of the earlier Greek philosophers. It is he, indeed, who is supposed to have coined the word “philosopher.” Because of the secrecy shrouding the beliefs of Pythagoreans, it isn’t always easy to tell what they were, or how much of what was attributed to them by later Greek writers is correct. In particu lar, it is hard to say for what Pythagoras himself was responsible, and what was originated by his many disciples, espe cially Philolaus [19]. The greatest scientific success at tributed to Pythagoras was in his study of sound. He found that the strings of musical instruments delivered sound of higher pitch as they were made shorter. Furthermore he found that the rela tionship of pitch could be simply cor related with length. For instance, if one string was twice the length of another, the sound it emitted was just an octave lower. If the ratio of the strings was three to two, the musical interval called a fifth was produced, and if it was four to three, the interval called a fourth was produced. Increasing the tension of the strings also raised the pitch. Thanks to these observations, the study of sound was the one branch of physics in which Greek views remained unaltered in mod ern times. This study may have led Pythagoras to the belief that the whole universe rested on numbers and their relationship, for he (or his followers) proceeded to invest numbers with all sorts of mystic significance. Today these notions seem foolish, but they did encourage the inves tigation of the mathematical properties of the numbers. For instance, it was the Pythagoreans who discovered that the square root of two (that is, the number which, multiplied by itself, gives a prod uct of exactly two) could not be ex pressed as the ratio of two numbers. No conceivable fraction, however compli cated, will give the product of two when multiplied by itself. Here was a very simple concept that could not be put into whole numbers. How then could numbers account for something as complicated as the whole universe? The Pythagoreans were sup posed to have vowed themselves to se crecy concerning such “irrational num bers” lest outsiders scoff. It slipped out anyway and there is a story that the Pythagoreans executed one of their fel lows whose tongue had wagged too freely on the subject, though this may be another slander circulated by the anti- Pythagoreans. Pythagoras is most famous, perhaps, for having been the first to work out the 5 [8 ] EUPALINUS HECATAEUS [9] proposition (by strict mathematical de duction) that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of its sides. This is still known as the Pythagorean theorem. Pythagoras was the first Greek to rec ognize that the morning star (Phos phorus) and the evening star (Hesperus) were in fact one star. After his time it was called Aphrodite, and we know it now as the planet Venus. He was also the first to note that the orbit of the moon is not in the plane of the earth’s equator but is inclined at an angle to that plane. He was the first man known to us who taught that the earth was spherical. He was also the first Greek philosopher to point out that the sun, moon, and vari ous planets did not partake of the uni form motion of the stars, but that each had a path of its own and was at a different distance from the earth. Thus began the notion that in addition to the heavenly sphere that Anaximander had postulated, separate spheres had to be provided for the various planets. For seven hundred years thereafter, the num ber of spheres necessary to account for the planetary movements was to multi ply, and over twenty-one hundred years passed before Kepler [169] wiped them out. [8] EUPALINUS (yoo-puh-ly'nus) Greek architect Born: Megara (20 miles west of Athens); flourished in the sixth century b . c . It is obvious that the ancients pos sessed their share of great engineers, for some of their feats of construction were as great as anything we can do today, considering the primitive nature of the tools and techniques available to them. It is a pity that we know so little of them. Except for the semilegendary Im hotep [I], nothing is known about indi vidual pre-Greek engineers, and very lit tle is known about engineers in Greece’s golden age. An exception is Eupalinus, whose name is at least attached to a specific accomplishment. He specialized in water systems, building one for his na tive city in Megara about 530 b . c . Later, he was engaged by Polycrates, the tyrant of the Aegean island of Samos, to build an aqueduct there. For this project, Eu palinus had to tunnel through a hill for over half a mile. The ancients were profoundly impressed that Eupalinus started the tunnel at both ends and the two halves met only a couple of feet ofi center. [9] HECATAEUS (hek-uh-tee'us) Greek traveler Born: Miletus, about 550 b . c .
b .
. Hecataeus carried on the rationalist tradition of Thales [3] and applied it par ticularly to the surface of the earth. He traveled widely through the Persian Em pire (which in his time dominated Asia Minor) and wrote a book on Egypt and Asia which, however, has not survived. In Egypt he is supposed to have become aware of the true stretch of previous his tory when the Egyptians showed him records going back hundreds of genera tions. Hecataeus continued the work, begun by Anaximander [4], of attempting to map the world. He divided the land area into a northern half (Europe) and a southern half (Asia) with the east-west structures of the Mediterranean Sea and the Caucasus Mountains forming the di viding line. Both continents were drawn as semicircles and the whole was en circled by Oceanus, the “ocean river.” The Greeks, however, were not the out standing travelers and explorers of the time. That honor was held by the far less articulate (and therefore less advertised and less remembered) Phoenicians, of whom Hanno [12] bears off the palm, if the vague remnants of his tale are to be credited. Hecataeus rationalized history as well as geography, writing the first Greek ac count of the deeds of men which did not accept gods and myths at face value. In fact, Hecataeus took a skeptical and downright scornful view of myths. His 6
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