Chapter 1 Science and the Ancient World

Why do we traditionally start a course in the history of science with the Babylonians and Egyptians rather than with the Greeks? I can think of two good reasons. First, until the 17th century astronomy and mathematics, rather than chemistry or biology, were absolutely central to the development of modern science. By bringing together observation with mathematical analysis, nature, and especially the heavens, was described numerically and geometrically, and this "style," so to speak, had an enduring legacy on how nature would be explained throughout the modern era. And, the Babylonians in particular made some astonishing contributions in mathematical astronomy that were most certainly known about by the Greeks. Secondly, in much of the Greek literature on science the Greeks saw Egypt as the source of wisdom. For example, in Plato's Timaeus, one of the most important early works on the nature of the universe, the Greeks were characterized as children with respect to the Egyptians. As Plato's character Solon discovers during a trip to the Nile delta:

To this city came Solon and was received there with great honor; he asked the priests, who were most skillful in such matters, about antiquity, and made the discovery that neither he nor any other Hellene knew anything worth mentioning about the times of old. On one occasion, wishing to draw them on to speak of antiquity, he began to tell about the most ancient things in our past of the world. About Phoroneus, who is called "the first man," and about Niobe; and after the Deluge, of the survival of Deucalion and Pyrrha; and he traced the genealogy of their descendants and, reckoning up the dates, tried to compute how many years ago the events of which he was speaking happened. Thereupon one of the priests, who was of very great age, said: O Solon, Solon, you Hellenes are never anything but children, and there is not an old man among you. Solon in return asked him what he meant. I mean to say, he replied, that in mind you are all young; there is no old opinion handed down among you by ancient tradition, nor any science which is hoary with age.⁽¹⁾

Yet, the Greeks misled themselves into thinking that Geometry had its origins in Egypt or Mesopotamia; in reality it was wholly a Greek innovation.

Our discussion of Science in the Ancient World and the Mesopotamians in particular is most difficult for a number of reasons, including the time span under consideration and the sources involved. In this section, we shall examine the period 3000-300 B.C., more elapsed time than the remainder of our narrative! And the historical explanation of this ancient world is methodologically unique, for unlike modern historians we must rely on the work of the archeologist who studies tools and artifacts and the anthropologist who studies primitive societies of the contemporary world and then projects backward.

Man existed long before the Babylonians and Egyptians. However, a revolution in the use of polished stone tools that marks the transition between the Paleolithic and Neolithic Ages took place between 8000 and 6000 B.C. This revolution may be the most significant of all the transitions we will study in terms of its impact on society.

During the paleolithic age men were food gatherers, and this activity was the occupation of every man. For tools flint was made by chipping. Between 8000 and 6000 B.C. the polished stone tool appeared, and it created a revolution in agriculture. Mixed farming, the cultivation of plants like wheat and barley, and the domestication of animals (first the goat, sheep and pig, later oxen and cows) characterized this revolution.

Man gained a new appreciation for seasonal events; he also pursued activities like brewing, bakery and pottery. Later in this period several technical advances occurred, like the smelting of copper, the development of the plow, and the invention of the sailboat. With agrarian development came the emergence of stable communities along several river valleys, which set the stage for the early history of Astronomy and Mathematics.

It was this emergence of city civilizations along certain river valleys that proved to be crucial to the development of ancient astronomy and mathematics. Three important regions were: 1) Tigris and Euphrates

2) Nile River

3) Indus Valley

It was in the confluence of the Tigris and Euphrates that we find the presence of the Sumerians who later were taken over by a Semitic people, the Akkadians. From this fusion came the empire of the Babylonians, an empire frequently threatened by its northern neighbors, the Assyrians.

In Babylonia, as in Egypt, a class of scribes emerged. (Both Civilizations developed a number system.) In the former they were tax bureaucrats and administrators, while in the latter they were sometimes called rope-stretchers because of the methods they used to survey the land after every annual flood.

The textbooks and instruction manuals of this administrative class have survived. In the case of Mesopotamia, they are small tablets of clay; Egyptians left papyrus rolls. One type of tablet that has come down to us are problem tablets, where on one side the teacher has done the problem, and on the other side the student worked on a solution. A second type of text was tabular, in which reciprocals, squares, square roots, cubes and cube roots were computed for the purpose of calculating special types of cubic equations and exponential functions. The Mesopotamians used a system characterized by a placed notation--although only the context tells you your place--and a base of 60 that has survived to the present in our use of both circle angles and the reckoning of time. One important advantage of the Babylonian number system was that one did not need to worry about special values for fractions and integers.

Egyptians on the other hand, could add, subtract, multiply, divide, and calculate simple areas, but they did not compute volumes and nowhere is there evidence that geometrical knowledge existed. In terms of astronomy, the Egyptians never developed a mathematical theory of movement of heavenly bodies. Indeed, their astronomy was static rather than dynamic; once developed, little innovation took place over the centuries. Considerable attention was paid to the calendar, however, not only because of its importance to agriculture, but also for religious festivals. Egyptians used observations related to periodic events in the heavens--the movements of the sun, moon and stars--to derive a calendar.

The Egyptians began their calendar by fixing the New Year with the flooding of the Nile (which took place in the middle of July). The Flooding took place around the time of the appearance of a prominent star on the Eastern horizon as the sun set--Sirius (Sothis).

The year was then divided by the appearance of the moon. Note that the appearance of the moon does not take place in equal time durations--sometimes 29, sometimes 30 days. This resulted in a calendar totaling 354 days. The Egyptians then inserted an extra month of 11 days which they added to the end of the year. Egyptians also divided the day into 24 equal components. At night this division took place by noting the appearance of prominent stars, which established the time unit of the decan.

Our evidence concerning Babylonian astronomy in much more fragmentary. Babylonian observations were motivated by magic, mysticism, and astrology. Yet, the accuracy of these observations are not to be underestimated; many of the phenomena they were interested in was close to the horizon and very difficult to see with the naked eye.

By 500 B.C. the Babylonians had such a wealth of data that they began to predict phenomena, like eclipses. They did these computations from periodic tables called ephemerides. Using arithmetic progressions to describe periodically variable quantities life the velocity of the sun and moon, the angles between the ecliptic and the horizon, the latitude of the moon and the magnitude of eclipses, the Babylonians developed a theory to predict these events.

No discussion of the ancient world of the Egyptians can be complete without saying at least something about the pyramids. The ancient Greeks numbered them among the seven wonders of the world. Early Christian tradition identified them as Joseph's granaries, built, according to the book of Genesis, in anticipation of the seven years famine. Today we count some 80 major and minor pyramids dotting the West Bank of the Nile, most of them in the 55 mile stretch between Abu Roash and the Faiyum. Most of these pyramids have been thoroughly explored, studied and documented. We know they are tombs, yet they still fire our imagination. Some say that such colossal structures could not have been built with the simple tools of ancient Egypt; the builders must have levitated the huge stones in place by magic, or watched in awe as visitors from outer space lent skills that our scientist have yet to discover. Others see in the measurements of the Great Pyramid of Cheops at Giza a key to events past, present and future. And some recent writers claim to have discovered a mysterious force in the pyramidal shape itself. Inside even a table top pyramid of cardboard, they say, a razor blade keeps its edge and fruit and milk stay fresh.

Why did the ancient kings choose to be buried in tombs of pyramidal form? The answer lies in the fact that a pyramid is an expression of evolving religious ideas. In its purest form it is almost literally a sunburst turned to stone.

One concept that never changed throughout Egyptian history was the need to preserve the dead body from decay so that the spirit of its owner could reenter it at will. That is the reason for the burial mounds of the first dynasty Egypt that gradually evolved to the 4th dynasty pyramids.

The pyramid itself dominated a large assemblage of buildings and open courts in a walled enclosure. The buildings, like the pyramid, were faced with fine white limestone brought from a quarry at Tura in the hills East of the Nile. One key building was the mortuary temple, for here priests conducted regular services on behalf of the dead king.

To move the stone blocks into place, the Egyptians used neither wheels nor draft animals, but sledges hauled by men. In some tomb paintings there are scenes of oxen drawing blocks from a quarry, but animals weren't precise enough to use on the pyramid itself. Fewer than a dozen men could manhandle a pyramid building block into place; this can be deduced from a famous scene from the tomb of XIIth Dynasty noble Dhutohotep, in which 172 men drag a colossal statue, many times larger than any pyramid block. The essential ingredient to building a pyramid therefore was steady, dedicated labor and a high degree of social planning. And money -- lots of money, in the form of food and shelter for the pyramid workers.

As the Egyptians had their successes, so did they have their failures. Sekhem-khet's successor, Kha-ba, is believed to have built the so-called "Layer" pyramid at Zawiet el Aryan. Here the Egyptians tried a different form of construction, layering vertical piles of stone into a step pyramid shape. It didn't work, and the Layer pyramid today is a low mound of rubble, whereas Zoser's step pyramid still stands at Saqqara.

One claim often made by theorists who believe the Great Pyramid at Giza has powers and attributes beyond the mundane is that the angle of the pyramids's sides is of special mystical significance. Khufu, son of Sneferu, built the Great Pyramid with sides angling up at 51 degrees, 52 minutes. Yet there is no standardization of slope angle among the other pyramids. If the angle of the Great Pyramid were of such cosmic significance, the Egyptians surely would have repeated it in subsequent pyramids -- but they didn't. Virtually every shade of angle from as shallow as 43 degrees to as steep as 65 degrees occurs in pyramids other than Khufu's.

The Great Pyramid is unique not only in that it incorporated pi proportionally but also the constant proportion known during the Renaissance as the Golden Section, designated by phi or 1.618. If the 356 cubits of the Pyramids apothem are divided by half the base, or 220 cubits, the result is 89/55, or 1.618. Phi, like pi, cannot be worked out arithmetically, but only with the use of a compass and a straight edge. With the incorporation of the Golden Section, The Great Pyramid provides an effective system for translating spherical areas into flat ones. The subtlety of the Pyramids's projection lies in the fact that when viewed from the side, the laws of perspective reduce the actual area of a face (mathematically oversized) to the correct size for the projection, which is the Pyramid's cross-section. What the viewer saw, and sees, with the aid of perspective is the correct triangle. The key to the geometrical and mathematical secret of the Pyramid, so long a puzzle to mankind, was actually handed to Herodotus by the temple priests (Heliopolos) when they informed him that the pyramid was designed in such a way that the area of each of its faces was equal to the square of its height.

In short, the Egyptians developed a numerical system and a calendar, while the Babylonians developed numerical methods and empirical astronomy. These two civilizations formed the starting point of the Greeks, who by the 5th century B.C. began to speculate about the nature of the heavens and the world around them.

Greek Science: The Pre-Socratics, Plato and Aristotle

While both the Babylonian and Egyptian cultures of the period 3000-300 B.C. made interesting contributions to the development of modern astronomy, mathematics and medicine, I have chosen not to spend considerable time on this part of the ancient period. But why should one emphasize the Greeks rather than other ancients? Because they left an indelible imprint on our way of thinking about natural phenomena, about the way we explain the world around us. And contrary to what the Greeks thought about being intellectual descendants of the Egyptians, their contributions to the development of modern science were unique and revolutionary. As historian Otto Neugebauer has maintained, until the Age of Newton, all astronomy merely consisted of "modifications, however ingenious, of Hellenistic astronomy." The kinds of questions about nature that we ask and the framework of the answers that we give have their ultimate origins in Greek Civilization.

Three features of Greek science emerged between 500 B.C. and 300 B.C. and had a lasting significance for future developments. They were:

a) The Greeks were the first to banish the mythical gods from explanations about nature. They tried to give a natural account of nature.

b) The Greeks saw the world around them as orderly and as possessing an inherent harmony.

c) And they described this harmony in mathematical terms, and in particular geometrical terms after about 300 B.C.

Beginning around 600 B.C. a number of Greek philosophers--presocratic philosophers as they were called--began to explain nature in terms of the so-called arche'--the primary material from which all things are made. Unlike traditional accounts like Genesis 2:7 where "the Lord God formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living being," they explained natural phenomena without referring to anthropomorphic gods. Rather, they constructed a world made from a material substance, the arche'. For Thales, the arche' was water--for Anaximander it was the boundless--for Anaximines it was air--for Heraclitus it was fire. Thus, Anaximander saw creation not as an act of a god or gods, but the separation of fire, water, air and earth from his arche', the boundless. We would say today that these philosophers were materialists in that they constructed a world made of a material substance and reductionists in that they reduced all phenomena to material things. The significance of this conceptual shift away from the sometimes whimsical and capricious gods towards naturalistic explanations cannot be underestimated, for all of modern science is based on this intellectual foundation.

It is also to be noted that Thales explored electrical and magnetic phenomena. For example, he found that amber, after being polished with a piece of wool or fur, attracts light objects like feathers,, bits of dried grass and straw. Thales came to the conclusion that his rubbing the amber made it magnetic. He also noted that when he picked up lodestone(an iron ore with a silvery finish, also called magnetite), it attracted pieces of iron, whether it was rubbed or not.

Concurrent with the activities of these so-called pre-Socratics, another group of Greek thinkers, the Pythagoreans, also began to explain nature without resorting to the gods, but instead of using a substance, or matter, they used numbers. They ultimately played a crucial role in Greek developments related to science. Aristotle described the Pythagoreans as devoting

themselves to mathematics; they were the first to advance this study, and having been brought up in it they thought its principles were the principles of all things. Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into being -- more than in fire and earth and water (such and such a modification of numbers being justice, another being soul and reason, another being opportunity -- and similarly almost all other things being numerically expressible); since, again, they saw the attributes and the ratios of the musical scales were expressible in numbers; since, then all other things seemed in their whole nature to be modeled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of things, and the whole heaven to be a musical scale and a number. And all the properties of numbers and scales which they could show to agree with the attributes and parts and the whole arrangement of the heavens, they collected and fitted into their scheme.

Pythagoras was born in Ionia and resided in South Italy (560-480 B.C.). He was the founder of a brotherhood that lasted through the entire Greek period. While it is very difficult to get a clear picture of his brotherhood, one thing is clear: Pythagoras did not prove Pythagoras' theorem as outlined in Euclid.

While we know almost nothing of Pythagoras we do know that he wrote two treatises now lost, Transmigration of Souls and Mathematics and Natural Philosophy. And within the brotherhood there existed two levels--the listeners and the mathematikar--those people who were allowed to speak and make contributions. For the Pythagoreans, harmony in life was associated with the number, and number theory was critically important. The first four numbers could represent everything that was present in the universe.

However, by 400 B.C. or so a great theological crisis shook and ultimately split the brotherhood. The Pythagoreans had asserted as a central tenant of their philosophy the idea that numbers were discrete entities that delineate and define space. Yet, in studies of the Pythagorean theorem, the diagonal could not be expressed in terms of the side as a ratio of whole number integers.

This discovery proved to be a great turning point in the history of Greek thought and accounts for the changing of Greek tradition from number theory to geometrical theory. Indeed, this failure of the Pythagoreans led to the rise of Platonic thought concerning nature, a view that had enormous significance all the way to the Scientific Revolution of the 1600s.

Plato was the student of Socrates, a philosopher who had called for the ideals of beauty, truth, goodness and justice during a time in Greek history when Athenian society was being critiqued because of its failures during the Peloponnesian War (431-404 B.C.) with Sparta. Socrates' ideas were carried over by his pupil Plato into the physical world, where the good, the virtuous and the just were tied to a world of geometrical figures, the tetrahedron, the cube, the pyramid and the octahedron. For Plato the universe was divine, and this divinity was reflected in the circular and regular movement of the heavens.

However, Plato's ideas with the universe didn't fit with observations. Plato was puzzled with certain aspects of the path of heavenly bodies, particularly the motions of the planets. To the observer, the planets did not move with regularity for

1) They did not move with uniform motion.

2) Their brightness can vary (distance from earth varies).

3) Their motion was not circular but looping.

To circumvent this dilemma, Plato explained these discrepancies by stating that these apparent anomalies in planetary motion were the result of observers who were being misled by their senses; he steadfastly maintained that the universe was divine and that circular motion was the only true and proper way of representing the trajectory of these bodies. Plato would have a powerful influence on those who followed him, especially Eudoxus of Cnidus and Aristotle, both of whom attempted to provide comprehensive accounts of all the main features of the movements of the heavenly bodies.

Eudoxus of Cnidus (384-322 B.C.) probably did research at Plato's Academy. He was a leading figure in the formalizing of geometry, and he probably wrote an Elements of Geometry which Euclid would later develop. Eudoxus claimed that the motion of planets cannot be simply described by using one, perfect circular trajectory. For Eudoxus, a planet's motion was the consequence of a combination of a number of circular motions. Thus, the complex paths of the sun, moon and planets were produced by simple circular movements of a number of concentric spheres. The earth is at rest at the common center of all the spheres, but their axes are inclined to one another and they rotated at different, though uniform rates. Thus, for each of the five known planets he postulated four such spheres, the planet itself being placed on the equator or innermost sphere.

While one sphere accounted for the movement of the planet through the sky from east to west, and the second explained the motion of the planet along the Zodiac, it is the third and fourth spheres that were most remarkable, for they were used to explain the planets' retrogradations. These two spheres rotated at equal speeds but in opposite directions, and their combined movement produced a three dimensional figure 8. Eudoxus' theory explaining the looping motion of the planets and variations in the apparent diameter of the moon and brightness of the planets. It is an idea of great significance, because Aristotle would take it (a geometrical solution) and give it a physical significance!

One of the greatest figures in the history of science, along with Galileo, Newton and Einstein, Aristotle was born in 384 or 383 B.C. and died in 322 B.C. He studied almost 20 years at Plato's Academy and probably taught there for some years. After leaving the Academy he was tutor of Alexander the Great before the young prince embarked on his campaign of world conquest. As founder of the Lyceum at Athens, which continued many years after his death, Aristotle made an important contribution to education in the Ancient World. He planned and organized far reaching projects of empirical research, supported by Alexander and carried out by himself and his students, which led to many basic discoveries in the fields of the natural sciences. His most important works related to the sciences were On the Heavens, On Coming Into Being and Passing Away, the Physics, De historia animalium, De partibus animalium, and De generatione animalium.

In Aristotle's On the Heavens the author took Eudoxus' geometrical interpretation and gave it a physical significance. Aristotle developed a physics for the heavens that was different from that on the earth. He claimed that heavenly bodies were distinguished by uniform circular motion, in contrast with characteristic motion on earth that was linear and directed either away from or toward it's center. For Aristotle the earth was at the center of the universe, and the four basic material elements were in the process of moving to their natural places.

Between the sphere of the moon and the sphere of the fixed stars were approximate spheres of Mercury, Venus, Sun, Mars, Jupiter and Saturn, all made of a material not found inside the sublunary sphere, a fifth element.

Aristotle's scientific ideas on matter and the universe dominated philosophical thought until the 16th century. His earth-centered universe would not be challenged until Copernicus' 1543 treatise; and his theory of the four elements until Paracelsus' works of the same time (1540). He was the dominant figure in the history of ancient and early modern science, and proved to be unassailable until Galileo crystallized the so-called Scientific Revolution.

Aristotle's understanding of matter--his use of four elements to describe it--was outlined in his work On Coming Into Being and Passing Away. His four elements--Air, Fire, Earth, and Water--would last long into the 18th century, for it was only in the 1770s that Antoine Lavoiser conclusively proved that air is composed of a mixture of substances, thus proving Aristotle wrong. The big problem for Aristotle, however, was how to account for change, and he did this in an ingenious way. With each element he attached two qualities that could be recognized by the senses:

fire--dryness, hotness

water--moistness, coldness

air--moistness, hotness

earth--dryness, coldness

In perfect form, a particular element contained its two qualities to a maximum degree. But in the substances of everyday life this perfection was never reached; rather the elements could change by modifying their qualities. Thus earth, in its ultimate degree possessed perfect dryness and coldness, but by abstracting coldness and substituting hotness it might be transmuted into fire. And indeed, this idea of transmutation, an idea that obsessed alchemists after Aristotle, was fueled by an Aristotlean idea of material change as represented by a diagram that was often found in the alchemical literature.

A teleological point of view--that is that the character of nature is being directed toward an end or shaped by a purpose--permeates the whole of Aristotle's work. Aristotle opened up main fields of inquiry--comparative anatomy and physiology, embryology, customs of animals, geographical distribution, ecology--and in each field he assembled the relevant facts, described and discussed them, and drew philosophic conclusions. His Historia animalium contains all the zoologic observations collected by Aristotle. Amazing insights included

* Aristotle said correctly that dolphins were air-breathing mammals and not fish, as people believed.

*It was originally thought that the hyena was a hermaphrodite, that is both a male and a female in the same animal. Aristotle showed there were male hyenas and female ones, just like other mammals.

* He saw that in a honeybee hive, there was only one queen, though he called it the "king" or "leader." His descriptions of hive life were not bettered until the 1700s.

* He described how a cuttlefish digested its food.

* He realized that animal parts or organs were suited to do certain jobs, such as long legs for fast running. He said "Nature makes the organs to suit the work they have to do."

Aristotle also made some errors, understandable given the fact that he had no microscope and a limited geographical range for his investigations. For example he asserted that

* He believed that some young animals appeared from mud and water without parents. He failed to see their eggs, which are so tiny.

* He thought a goat would be a male or female depending on the way the wind blew when the parents mated.

* He stated that the site of intelligence was the heart, not the brain.

In Aristotle's De partibus animalium physiological processes and tissues are dealt with. Aristotle referred to six kinds of tissue

1) blood

2) fat

3) marrow

4) brain

5) flesh

6) bone

For Aristotle every living being is made up of matter and soul, and while the above mentioned book dealt with matter, De anima focused on the soul, and thus De anima is a treatise on psychology. For Aristotle all things had a

1) nutritive soul--a soul that guides their nutrition and material life

2) sentient soul--enables one to feel

3) appetitive and locomotive soul

and in some higher animals man

4) rational soul

Aristotle asserted that every living body was animated, and that the soul cannot be detached from the body. In the case of each individual all parts are united for the greatest good of its wholeness and are intelligently organized in view of that end. He wrote "nature never makes anything that is superfluous." And, in the opinion of Aristotle this soul was seated in the heart. He came to this conclusion from his embryological observations in which the heart appeared ahead of all other organs.

Aristotle also contributed to the development of ideas both in taxonomy and in embryology. He formulated a scala naturae, a ladder of nature in which species do not change, which did not imply evolution, but rather a means of illustrating the fundamental unity and order of nature. Thus, the animal kingdom was divided into bloody/bloodless categories. In his embryology studies, contained in De generatione animalium, he not only introduced the comparative method in embryology, but also distinguished between primary and secondary sexual characteristics.

Aristotle is the key figure in this history of ancient science and indeed one of a handful of leading thinkers and doers in the entire history of science from the dawn of man to the present. His work in virtually every scientific field--from biology to physics to chemistry to astronomy--became a cornerstone of Western Science until the Scientific Revolution. And indeed his methodology, his reliance upon close observation and interdisciplinary bent, remain with us today.

Greek Science and Its Decline

Let us now turn to the last phase of ancient science, a period that began with the transformation of Greece from a culture based on city states to the Hellenistic Empire. The era opened with the conquests of Phillip II and Alexander the Great, and thus a process of consolidation took place in which the empire encompassed the major centers of ancient civilization.

As a whole, this period is most difficult to characterize. On one hand, it was a period of decline and the rise of superstition. Yet, it also witnessed the high point of science in antiquity. It is clear that the history of ancient science does not correlate perfectly with the history of Greek Civilization, a not uncommon phenonenon when we extend our analysis forward in time to the present century.

Certainly the most significant intellectual achievement of this period was the systematic development of geometry. Euclid, working c.300 B.C. in Alexandria, brought together the theorems and propositions that had been accumulating during the previous century in his 13 books of the Elements. The form of this book is very important, as it was influential down to the 18th century; for example, Newton's Mathematical Principles was written in classical Euclidian form.

The Elements contains more than what is normally conceived of in terms of geometry--the author also deals with ratios, the nature of numbers and proportions. In his method of proof, two concepts are employed--analysis and synthesis. In analysis, one assumes what is to be proved, and then one works backwards to principles that are accepted (by definition) or to an already proven theorem. The method of synthesis is the classic method of proof of Euclid, where one starts with definitions and postulates, and subsequently works forward. Thus, principles are used to deduce further principles.

What were Euclid's definitions, axioms (commonly accepted to be true) and postulates about construction?

1) a line joins two points

2) a circle can be drawn from any center

3) all right angles are equal

4) parallel line postulates: conditions of

interior angles

These same methods would be employed by Appolonius and Archimedes in later work.

Studying under Euclid's successors at Alexandria, Appolonius of Perga (b. 262 B.C.) earned the reputation of being the "Great Geometer." His best known work was Conic Sections, which was modeled after the Elements in terms of its logical layout and framework. Conic Sections critically and thoroughly examined the various curved sections of solid cones, including the ellipse, parabola and hyperbola. In about 240 B.C. a Greek astronomer in Egypt, Erastsothenes, made an exciting discovery. He found that when the Sun was directly overhead in one city, Syene, it cast a shadow in another city, about 500 miles(800 km) to the North. Erastsothenes figured that this meant Earth's surface curved. he also thought Earth was a ball about 25,000 miles(40,000km) around. Hipparchus later studied Earth's shadow when it eclipsed the Moon. From the size of the Moon, he decided it must be about 240,000 miles (384,000 km) from Earth.

Of far more fame than Appolonius, Erastsothenes, or Hipparchus however, was Archimedes, born in 287 B.C. in Syracuse on the island of Sicily.

Archimedes, like Appolonius, was trained at Alexandria, and his career combined studies that were both theoretical and practical. His work On Floating Bodies established the science of hydrostatics, and his theorems on the lever were fundamental to the discipline of mechanics. An inventor and improvisor of considerable talent, he is credited with the device known as the Archimedean screw to raise water as well as compound pulleys and cogwheels. Of course there is the famous story of Archimedes and the crown of gold, a crown that was discovered to contain a base metal by measuring the volume displaced in water. Legend also has it that during the Roman siege of Syracuse Archimedes directed an array of mirrors against a fleet of Roman ships located in the harbor, thus being an early practitioner of the star wars concept of directed energy focused on target. Whether this is true or not, it is most certain that the Romans killed Archimedes during the sack of Syracuse in 212 B.C.

Clearly one reason for the advancement of science during the Hellenistic Period and the work of Euclid was the establishment of two institutions, the Library and the Museum. Located at the crossroads of the ancient world -- Alexandria, Egypt -- these institutions so critical to the development of ancient science were certainly not isolated from the mainstream of the ancient world. Alexandria was at the very hub of Mediterranean and indeed world commerce, tying together the Sudan and Somalia with France, Germany, Russia and England as such products as elephants, precious metals, furs, amber and tin were all for sale.

The Library and Museum were founded around 280 B.C. Like Plato's Academy and Aristotle's Lyceum, the Museum was a community of scholars working, and to some extent, living together; there were common meals for the members of the Museum, as at the Library and Academy. But the Museum differed from them in that it was not primarily a teaching institution, and that instead of being self-supporting, it entirely depended on funds from the Ptolemies, the rulers in Egypt and North Africa. They not only built the Library and Museum and the complex of buildings associated with them in the royal quarter of Alexandria, but also paid regular stipends to such officials as the Librarian and grants to other scholars. And the Library had manuscripts, to the tune of almost half a million in 235 B.C., rising to 700,000 during the rule of Julius Caesar.

Among those who held official posts at the Museum were Erastsothenes of Cyrene, the geographer who measured the circumference of the earth. And it was only in Alexandria that the dissection of human bodies was under taken on any scale in antiquity. What motivated the Ptolemies to support research? Partly there were practical reasons, as in the case of Philo (studies on air) who received patronage to perfect the machines of war. Archimedes took geometrical knowledge and perfected practical apparatus that included: lenses, siege catapults possessing a 200 m range, and his well known Archimedean screw for raising water.

In many cases the chief reasons for encouraging scientists to come and work in Alexandria was simply the prestige attached to their research. Although such mathematicians as Archimedes of Syracuse and Appolonius of Perga wrote principally for other mathematicians, they sometimes dedicated their treatises to notable heads of state, doing so in some cases not merely out of fact, but in a way that shows they expected their work to be understood. The Ptolemies tried to attract distinguished scientists to Alexandria for much of the same reasons as they collected texts of the masterpieces of Greek literature, namely to add luster to their own reputations.

The effects of this kingly patronage should not be exaggerated. It would certainly be wrong to assume that every major scientist who is recorded as having worked in Alexandria was subsidized by the Ptolemies. Moreover, the patronage was often capricious. The first 3 Ptolemies were generous in their support of science, but later members of the dynasty were often less so, and some positively discouraged scientists from living in Alexandria. The Museum continued its existence down to the 5th century A.D., but its fortunes fluctuated from one generation to another.

Despite the institutionalization of science during this era, a marked decline that took place after 100 B.C. or so is a most difficult problem to understand. It is certain that there occurred a decline in the commitment to scholarly work. Erudition rather than scholarship became fashionable, and perhaps the root of this change in the perceived value of science can be traced to the values within Roman Society.

The Roman mentality that began to dominate the Western world by 100 B.C. or so tended to emphasize existing knowledge rather to encourage creative thought. Romans emphasized organization and as an agrarian and warrior based society were decidedly anti-intellectual and generally lacked a speculative imagination (they were doers, not thinkers; engineers, not scientists).

In terms of calendrical reckoning, the Romans used a lunar calendar with the months Januarius, Februarius, Martius, Aprilis, Maius, Junius, Quintilis, Sextilis, September, October, November and December. Since lunar months were shorter than months as we know them today, a 13th month was added in some years, and this extra month was called by the Romans Mercedonius. When Julius Caesar became ruler of Rome, the calendar was a whole season off, as December was coming at the end of summer. To correct this Ceasar made the months agree with the seasons by adding 80 extra days to the year 46 b.C. That year was thus 445 years long, the longest year in history and it was also called the "year of confusion." Next, Caesar stopped using the old lunar calendar. Rather, he shifted to a solar calendar, based on the length of time it takes the earth to orbit the sun. Every fourth year an extra day was added to February. But the calendar was far from perfect, for it was based on the assumption that the year was exactly 365 days and 6 hours long. In actuality the length of the year is 365 days, 5 hours, 48 minutes and 46 seconds, but this small difference of 12 minutes would eventually lead to a cylindrical crisis in the early 1500s, as by then the calendar was ten days off and Church Holidays were not coming at the right time. The problem proved to be the fateful stimulus for Copernicus to rethink not only the reckoning of the days and years, but the very nature of the universe itself.

The Romans had a concrete sense of reality. It is a fact that Latin is a very different language than Greek. Latin lacks an abstract vocabulary and it is infinitely more difficult to philosophize in Latin compared to Greek. The basic Roman mentality valued learning for display. This attitude reinforced the concept of the Handbook, and the Romans became the greatest Encyclopedists of all time. Among the most significant authors and their works were:

Varo (116-27 B.C.)

On Agriculture

The Book of the Nine Disciplines

Vitruvius (114-27 B.C.)

Architecture

Celsus

Treatise on Medicine

The last century B.C. and first A.D. produced very little original work. During the 2nd century A.D., however, two major figures emerged who in many ways represent the culmination of ancient science--Ptolemy and Galen.

Ptolemy's Mathematical Composition, known since the middle ages by its Arabic name Almagest (the greatest) is the most comprehensive treatise on astronomy coming down from antiquity.

We know very little about Ptolemy. He lived in Alexandria, and conducted his observations between 127 to 141 A.D. For Ptolemy, mathematics yielded unshakable knowledge. The purpose of study was not merely to obtain knowledge, but also to appreciate the beauty and order of the heavenly bodies, and indeed Ptolemy claimed that astronomy improved men's characters:

of all studies this one especially would prepare men to be perceptive of nobility both of action and of character: when the sameness, good order, proportion and freedom from arrogance of divine things are being contemplated, this study makes those who follow it lovers of this divine beauty and instills, and as it were makes natural, the same condition in their soul.

Ptolemy asserted that the earth was fixed, and at the center of the universe. He felt that the main task of the astronomer was to explain the apparent irregularities in planetary motions in terms of combinations of uniform circular motions. To do this Ptolemy borrowed ideas from Appolonius and Hipparchus, who used the so-called epicycle, where a Planet P moves around the circumference of the epicycle, whose center C itself moves around the circumference of the deferent circle, the center being E. This model could be used to explain the retrogradation of the planets.

For example, to explain the motion of the moon, Ptolemy assumed that it moved on an epicycle which is carried around the deferent circle; the center of the deferent was not the earth itself, but a point which itself revolved on a small circle with the earth as its circle.

For planets, Ptolemy modified the original epicyclic model. The planet was imagined as moving on an epicycle, the center of which moved around a deferent circle. The center of this circle is fixed, but it did not coincide with the earth. Not only does the planet move with retrograde motion, but also it has its greatest speed near the apogee (when it is furthest away from the earth).

Having set out the main elements of his theory, Ptolemy then proceeded to give a systematic account of each planet in turn. He determined for each planet, by calculations based upon observations: 1) the size of the planet, 2) the planets eccentricity, 3) tables from which the longitudinal position of the planet can be computed and 4) the magnitudes and durations of the retrogradations of each planet.

Of course, the fundamental weakness of the Almagest was that by using the doctrine of the equant, it could be asserted that the movement of heavenly bodies was not explained in terms of combinations of regular circular motions. Copernicus would criticize Ptolemy exactly in this way.

Galen (129 A.D.-199 or 200)

Galen's chief work was in biology and medicine, but he was also known as a philosopher and philogist. In his treatise that the best doctor is also a philosopher, he asserted that philosophy was an essential part in the education of a physician for three reasons: 1) the doctor must be trained in the scientific method, 2) it is the task of philosophy to study nature, and the whole theoretical side of biology--the investigation of the constituent elements of the body and the functions of the organs, for example, the cures under this heading, and 3) there is an ethical reason for the doctor to study philosophy, since, in the opinion of Galen, the profit motive is incompatible with a serious devotion to the art. The doctor must learn to despise money.

Galen's physiology was highly speculative, based on the interaction of the contrary qualities of the four Aristotlean elements. However, his descriptions of both anatomical structures and physiological processes show evidence of sustained and minute observation. From his texts, particularly On Anatomical Procedures, Galen preferred to perform dissections on human subjects, but such opportunities were rare. For his studies, Galen used a variety of animals, including pigs and kids, but normally he worked with Barbary apes.

Above all, Galen insisted on practice in dissection. Just as the great 16^th century anatomist Vesalius was to do, Galen castigated arm-chair professors who practiced their anatomy out of books. He insisted on care and precision. In describing the dissection of the muscle leading into the armpit he wrote:

in passing laterally to the false ribs, if you are careless you may tear away the head of the small muscle which, I said, runs into the armpit and was unnoticed by anatomists. . . this runs up to the armpit, where its fibers converge into a narrow fleshy strand. If you strip away its expanded lower origins in the skin, you will find that the fleshy part extended to the armpit is rent. If on the one hand you are diligent and seek the point from which it is torn and do not find it, you will be full of doubt, as I was at first. But, on the other hand, if you are careless and easy-going (as our anatomical predecessors were in many of their operations), holding this fleshy sheet to be of no account, you will cut or tear it away from the underlying tissues and throw it away. As to the need for exercising precision in removing the skin there, enough has now been said.

In some cases, dissection was not sufficient for Galen's purposes. To investigate vital processes, dissection must be performed, although he recommends that before proceeding to dissect the live animal, the operations should be practiced on a dead one. In Anatomical Procedures, he describes the vivisection of the heart and lungs which he carried out first to observe the beauty of the heart and arteries and secondly, to study the effect of constructing the heart artificially.

With the work of Ptolemy and Galen, ancient science truly reached its highpoint. Yet, long before the time of their work, the emphasis upon curiosity, and the creation of new knowledge concerning nature and the universe had no longer a central place in Civilization. Indeed, after the intense period of creative activity, c. 300 B.C., ancient science had entered a general decline, a decline that became more and more recognizable by 300 A.D. Why this decline, this erosion, in the quality and quantity of scientific thought? Of course, one reason was the nature of the Roman mentality, as previously discussed. And as the Empire came under more and more pressure from barbarians outside its border, convulsions and dislocations were not exactly conducive to the promotion of abstract thought that was seen as having an end unto itself. Nevertheless, the rise of Christian religion also played a part in the decline of science, especially after Christianity became institutionalized within the Roman Empire.

In the first centuries after the death of Christ, the west turned to the east for its philosophy and religion. It was during this upsurge of religious interest that Christianity took root in Rome. It appealed to a cross-section of classes, including artisans, peasants and intellectuals.

St. Augustine, St. Ambrose, and St. Jerome were all trained in Roman schools. St. Augustine, a former skeptic, was the first to take note of the tension between the world of reason and the world of faith. This new tension was to be between the world of ideas, thought to be located in the soul, and the world of appearances, or we could say between the world of the spirit and the world of the flesh.

While early Christian attitudes towards inquiry concerning nature varied, influential writers like Augustine (354-430) made clear that detailed knowledge of natural science is irrelevant and dangerous:

It is enough for the Christian to believe that the cause of all created things, whether heavenly or earthly, whether visible or invisible, is none other than the goodness of the Creator, who is the one true God.

And this idea had been echoed prior to Augustine by one of the early church fathers, Tertullian (c. 200 A.D.) who saw philosophy as a threat to the Christian and rejected it:

What then has Athens to do with Jerusalem, the Academy with the Church, the heretic with the Christian? We have no need of curiosity after Jesus Christ, nor of research after the Gospel. When we believe, we desire to believe first, that there is nothing else that we should believe.

For the faithful then, faith was more important than reason or observation; and once Christianity was adopted as the official religion of the emperor, pagan philosophers had to deal with legal sanctions and the closing of their academies. Further, church careers in this era were for more lucrative than the careers of doctors, for example.

The Christian religion took over the administrative network of the empire by about 300 A.D. Thus the organizational structure of the early church--with the Bishop playing a crucial role--was patterned after the Roman Empire.

Christian Culture reflected the encyclopedic nature of Rome during its decline. Early monastic scholars generated knowledge in terms of Pliny and Varo. Typical of the period was the work of Isidore of Seville. He wrote a great two volume work called Etymologies. Isidore, who lived in Spain before the Mohammaeden invasions, had his encyclopedic compendium transmitted throughout the Christian world.

But Christianity was only one of several reasons for the decline of science in the West. With the collapse of Rome, the ideals of ancient science would be assimilated by the Islamic world, where religious beliefs would be coupled with philosophical inquiry and not only restore the Greek tradition concerning inquiry about nature but improve upon the ideals of Aristotle, Galen, Ptolemy, and others.

While we have been discussing for the most part the place of scientific thought in the ancient world, some time might be spent in dealing with engineering (applied science) and technological innovation during the same period. During this general period of scientific decline within the Greek and Roman Empires several important technical innovations--the screw to pump water, the piston to pump water, undershot and overshot water wheels, the crossbow and catapult, various cranes and hoists--were developed and applied to the solution of practical problems. Four men whose contributions in mechanics or engineering particularly stand out: 1) Ctesibius of Alexandria (c. 270 B.C.), 2) Philo of Byzantium (c. 200 B.C.), Marcus VITRUVIUS Pallio (c. 25 B.C.), and 4) Hero of Alexandria (c. 60 A.D.). All of these men wrote on mechanical subjects, and although Ctesibius book is lost, we have parts of Philo's so-called Mechanical Collection, VITRUVIUS' On Architecture, and a number of Hero's works, including On Pneumatics, On Artillery Constructions, and On the Construction of Automata.

At times, one is astonished by the sophistication in terms of design of these mechanisms associated with the Ancient World. From the ability to harness power through the use of gears, to the use of pulleys, pistons, and chains, to Hero's totally mechanically driven puppets out of wood, the Ancients had taken aspects of theoretical geometry and had succeeded in constructing useful devices. But, the Ancient World never progressed past a certain stage of development, and this question preoccupies historians to this very day.

Why did the ancient world remain static in nature, never evolving into a more industrial society. In part the answer lies in the fact that the Greeks and Romans were dependent largely on human and animal power, and therefore were limited in what actually could be done to control their environment. Water wheels were expensive, and were also at their best in the fast flowing streams of Northern Europe, not in the areas of Southern Italy or Greece. While steam power was demonstrated in a device by Hero, the technology to cast pistons and efficiently convert reciprocating to circular motion was non-existent. So the lack of power was a stumbling block.

So too was the presence of a large number of slaves. How would slavery hinder the adoption of new technology? And at times inferior views concerning the status of the engineer slowed progress.

At the heart of the matter, however, was the fact that in Roman times wealth was seen as a means to an end rather than an end itself. The idea of using mass production was totally alien to a civilization in which the nation's progress was quite uneven. Roman society and leadership was centered on a small elite who sought to exploit and control the majority who were economically unable to be an integral component of the Empire's economy.

In conclusion, we can say that while an absolute connection between science and society in the case we just examined did not exist, certainly a strong link between societal values and priorities was present in a declining Roman Empire. And one wonders if things would have been different and science would have been nourished would the decline have been arrested. In our own present society similar kind of values and priorities also exist, and perhaps we should take heed to the lessons of history.