Based on T.E. Rihll, Greek Science (Oxford University Press, 1999), and Olaf Pedersen, Early Physics and Astronomy (Cambridge, 1993)
One of the [Egyptian] priests, a very old man, said, “O Solon, Solon, you Greeks are always children: there is not such a thing as an old Greek.” And on hearing this Solon asked, “What do you mean by this saying?” The priest replied, “You are young in soul, every one of you. For you possess not a single belief that is ancient and derived from old tradition, nor is your understanding grey with age.” — Plato, Timaeus
The Greeks freely acknowledged their intellectual debt to older civilizations: they had acquired elements of mathematics and astronomy from the Babylonians, and the rudiments of geometry from the Egyptians. But beginning in the seventh century BC, the Greeks developed a new kind of thinking.
For some reason a few Greeks living on the margins of the Greek world (and thus simultaneously on the margins of other worlds) began to think that natural phenomena, such as the seasons, eclipses, rainfall and so on were physical consequences or effects of other physical phenomena or causes. Bit by bit, Zeus was relieved of thunderbolt duty, Poseidon of earthquakes, Apollo of epidemic disease, Hera of births, and the rest of the pantheon of gods were pensioned off or abstracted, to become symbols of natural phenomena rather than the wilful and larger-than-life but all-too-human characters which populate and sometimes dominate Greek literature.1
Explaining physical phenomena in natural terms was just one aspect of the Greeks’ newfound insistence on rationality. For the Babylonians and the Egyptians, mathematical and geometrical results were generalizations from examples, or concepts that were understood intuitively. The Greeks replaced these methods with formal logic. For them, the deductive proof became the only acceptable basis for a result. Pythagoras’s theorem illustrates the difference between these approaches.
The mathematical fact that we call Pythagoras’ theorem was known to the Babylonians at least 1200 years before Pythagoras was born. Why then do we call it Pythagoras’ theorem? Because facts and theorems are different. The mathematical fact antedates him, but the theorem is his. And herein lies the difference between Greek activities, which we are calling science, and what went before or elsewhere, which we do not call science. The Babylonians observed a mathematical regularity, and compiled or calculated tables of similar regularities. The Greeks…observed this mathematical regularity, and proved geometrically that it holds for all particular cases.2
Another aspect of Greek rationality was their attempts to organize data according to some logical scheme. Aristotle’s sorting of animal and plant life according to form or function is one example. Astronomical theories — which began with the Greeks — are another.
Why was it the Greeks who laid the foundations of science? A few hypotheses have been put forth, but none is entirely persuasive.
The first philosophers lived in the Ionian city of Miletus, on the western edge of Asia Minor. It was part of a complex trading network, and its inhabitants would have had frequent interactions with Phoenicians, Mesopotamians, and Egyptians, as well as with Greeks from the mainland. Their exposure to different religions, customs, and modes of thought might have made them less dogmatic and more willing to explore novel ideas.
The Greeks in general were fiercely independent. Many of them lived under non-authoritarian governments, which accustomed them to forming their own judgements. The centrality of trade to Miletus likewise accustomed its people to independence of thought and action. Greek philosophy strongly favoured this disposition.
One of the major features of Greek science is that most of its practitioners were autodidacts. Even those who studied under a philosophical giant seem, with very few exceptions, not to have been content to follow a path laid down by a predecessor. They wished to carve out their own path, citing predecessors’ views when it suited them, and ignoring them likewise. They did not so much stand on their predecessors’ shoulders as knock them down, step over them, and go elsewhere.3
The three pathbreaking Milesian philosophers — Thales, Anaximander and Anaximenes — proposed distinctly different ideas, as did the three great Athenian philosophers — Socrates, Plato and Aristotle.
Finally, there is the role of religion. The Greeks worshipped a great many gods, many of them local, but they had “no sacred writings and no dogmas.”4 The core of their religious activity was not a profession of faith, but the performance of rituals and participation in public festivals. These two factors — the absence of a fixed ideology, and an emphasis on outward performance — might have given Greek philosophy enough leeway to establish itself.
Greek science might not have been constrained by organized religion, but it was not itself free of moral considerations.
All ancient theories on nature were part and parcel of theories on god, the good, and much else besides. The ancient emphasis on the good, the perfect, the form, or similar notions might be compared with the modern hankering after the god of quantification: in both cases there is a tendency to try to import into everything something highly valued in the society which produces it…For the ancients, the virtues (especially goodness and justice) seem to have had a role similar to our numbers, providing an idealized scale against which all real things could be measured, a conceptual rock in a sea of shifting sand.5
For this reason, concepts that seemed rational to the ancient Greeks do not always sound rational to us.
Thales (c. 626-548 BC) is said to have proved some simple geometric theorems, such as that a circle’s diameter divides the circle into equal areas. This claim, if true, would imply that Thales invented the deductive proof. Even if he did not, there is little doubt that the deductive proof was devised and perfected by Greek philosophers.
For Pythagoras (c. 570-495 BC) and his followers, mathematics had spiritual overtones. They believed that a person was “a divine soul entombed in a material body, enslaved by corporeal baseness and impurity as well as by intellectual darkness and ignorance.”6 They also believed that numbers connected the spiritual and material realms. The discovery of harmonics seemed to justify this belief. The sounds produced by vibrating strings harmonize only when the ratio of the strings’ lengths is very simple — 3:4 or 2:3 or 1:2. The reduction of such a complex phenomenon as music to simple numbers seemed to imply the possibility of liberation from the material world.
The Pythagoreans organized their studies into pure and applied subjects. Number theory was pure; music was its application. Geometry was pure; astronomy was its application. This division would become the quadrivium, the framework for advanced studies in Europe until well into the Middle Ages.
The first proof of Pythagoras’s Theorem would not have been “mathematical” in our sense of the word, because the early Greeks lacked both symbols for arithmetic operations and any knowledge of algebra. The proof might well have involved the physical manipulation of tiles.7 The conversion of a thousand-year-old empirical regularity into a general rule was a significant achievement, but it had an unexpected impact on the course of Greek mathematics. The Pythagoreans, investigating the implications of the Theorem, discovered that the ratio of the length of a square’s diagonal to the length of its side cannot be represented by any ratio of whole numbers. The discovery that some quantities cannot be expressed as ratios
…meant that the fundamental Pythagorean concept of number as the nature of things had to be discarded, involving, in turn, a strengthening of geometry…In geometry, such incommensurable quantities were perfectly acceptable, and Greek mathematicians concluded that geometrical entities are of a more general nature than those which can be represented by numbers or ratios of numbers. Against this background mathematicians gradually turned their attention more and more to geometry, and the result of the development was a very considerable advance within the field.8
Greek mathematicians attempted to turn geometry into a single structure that began with the simplest concepts and progressed to the most difficult results. The culmination of this research program was Euclid’s Elements (written c. 300 BC).
Geometry had originally dealt with practical problems such as the area of a field, but it became the study of dimensionless points, infinitely extended lines, and other abstractions. Plato, following the lead of Socrates, believed that such abstractions underlay every imaginable thing, from circles to apples to justice. Each thing had an ideal or a form, and examples of the thing encountered in the material world were debased and imperfect versions of the ideal. True knowledge for Plato was knowledge of the ideals, not of their worldly counterparts. His philosophy diminished the value of sensory experience — of observation — and emphasized abstract thinking in its place.
The Greek philosophers were conscious of the world’s diversity. They were also aware that the world changed continually: new things appeared, existing things disappeared. The pervasiveness of change led Heraclitus to claim that you cannot step into the same river twice.9 The philosophers asked whether some simple structure underlay all of this complexity. The earliest philosophers speculated that every material entity was built up from, and dissolved back into, a single substance. For Thales, this substance was water; for Anaximenes, air; for Heraclitus, fire. This theory was superseded by two others, four-element theory and atomism. Both theories were well-developed by the time of Plato (c. 428-338 BC) .
The Four Elements
The theory of the four elements began with Empedocles (c. 494-434). He hypothesized that all things were composed of four fundamental substances, namely fire, air, water, and earth. Two more material substances acted as catalysts: “love” united the fundamental substances and “strife” separated them.10 These six substances were eternal: they could not be created or destroyed. The mixing of fire, air, water, and earth under the influence of “love” gave rise to material objects, and their separation under the influence of “strife” brought about the objects’ dissolution. This theory seemed capable of explaining natural phenomena.
When a piece of fresh wood is thrown into a fire it is split up into four constituents: the fiery element appears in the flames, the air element in the smoke, the watery element as tar and the earthy element in the ashes.11
Plato discarded “love” and “strife” but kept the four fundamental substances. He called them “elements,” which originally meant letters. The implication was that material things were analogous to words, both being formed by their respective elements.
Aristotle (384-322 BC) combined the theory of the four elements with the idea, from Hippocratic medicine, that material bodies have four fundamental qualities: hotness, dryness, coldness, and wetness. Since nothing can embody both a quality and its opposite, only four pairings of qualities are possible. Aristotle claimed that each element embodies one pair, with one of the qualities being dominant (D) and the other secondary (S). He imagined earth to be dry (D) and cold (S), water to be cold (D) and moist (S), air to be moist (D) and hot (S), fire to be hot (D) and dry (S). In this theory the elements themselves are malleable.
Under the influence of adequate causes one element can be transformed into another. If, for example, water is heated by fire, the hotness will destroy the coldness of water and replace it, while at the same time the secondary property — moistness — of water will be promoted to a dominant position. A new element is now created, with moistness as the dominating and hotness as the secondary property, that is air, as happens when water is transformed into steam.12
Although the elements can be transformed, they can be neither created out of nothing nor dissolved into nothing. As in the earlier theories, material objects are created and destroyed by the mixing and separation of the elements.
By the combinations of elements, according to Aristotle, all the known substances of nature are produced, each in such a way that it is quite impossible to distinguish the pure elements. Two elements unite when their mutual attraction, due to their common qualities, is stronger than the repulsion of their opposite qualities. Thus fire and earth may combine to form embers because both are dry, and their dryness can, when circumstances are favourable, keep them together, overcoming the repulsion between the coldness of the earth and the hotness of the fire. But because there are opposite qualities in all compound substances, these substances are inevitably less stable and must, eventually, dissolve again into their constituent elements.13
The theory of the four elements provided the foundations for Aristotle’s depiction of the universe. The earth lay at the center, unmoving, while the sun, the moon, the wandering stars (planets) and the fixed stars rotated around it. The fixed stars were held in place by a crystalline sphere, while the sun, the moon, and each of the wandering stars had its own crystalline sphere. These spheres were concentric, with the lunar sphere being the innermost one. Aristotle divided the universe into the sublunary (below the moon) and the supralunary (beyond the moon). The sublunary universe was the domain of the four elements.
Earth and water were supposed to be provided with a special quality called gravity, while air and fire possess an opposite quality called levity…Gravity was defined as an inherent tendency in heavy bodies to move towards the centre of the world, which is the natural place for the heavy bodies, while levity was considered an opposite tendency for movement away from the centre. If all hindrances are removed, it was argued, a body dominated by the element earth must move downwards along a straight line towards its natural place at the centre. If a substance is dominated by the element of fire, it is light by nature and performs a natural motion upwards towards the natural place of light bodies, that is, the inner surface of the sphere of the Moon. In between are the natural places of water outside the earth, and air inside the fire. The elements air and water were considered to be media, because they are placed in the middle between the extremes of earth and fire, which explains the subdivision of the elementary world into four sublunary spheres between the centre of the world and the sphere of the Moon.14
Thus, the sublunary universe consisted of four nested spheres of elements: the sphere of earth at the center, followed by the spheres of water, air, and fire.
Humans were part of the sublunary universe, so their lives and health were governed by the four elements. Empedocles asserted that health depended upon the proper balance of the elements within the body. Hippocrates refined this concept by arguing that the body contained four humours, each dominated by one of the elements, and health hinged upon their balance. The humours were blood (dominated by fire), yellow bile (air), phlegm (water), and black bile (earth). Galen (c. 130-199 AD), the greatest of the Greek physicians, argued that the balance of these humours influenced a person’s disposition. An excess of blood made him sanguine, of yellow bile made him choleric, of phlegm made him phlegmatic, and of black bile made him melancholic.
The supralunary bodies appeared to be perfect, unchanging and eternal, their paths through the heavens repeating endlessly. They were so different from anything found in the sublunary world that Aristotle declared them to be made of a different substance, which he called ether. Ether’s natural motion was circular, the only regular motion that repeated itself indefinitely. This claim was problematic from the beginning: the astronomical observations already available to the Greeks were incompatible with simple circular orbits.
The theory of the four elements would greatly influence the development of western science. Exposure to this theory and its offshoots, primarily through the works of Aristotle, inspired Europeans to adopt a scientific view of the world. But the theory was entirely wrong, and it eventually became an obstacle that European scientists had to overcome in order to make further progress. Like the Greeks themselves, European scientists had to knock down their predecessors, step over them, and go elsewhere.
The cosmology based on nested spheres of the four elements persisted until about 1500, when evidence from the New World made it untenable. The idea of crystalline spheres was not abandoned until Tycho Brahe determined that the path of the comet of 1588 passed through the imagined spheres. The perfection of the heavenly bodies, and the associated claim that they were materially different from the earth, was not questioned until Galileo observed mountains on the moon (1609) and spots on the sun (1612). The idea that health hinged upon the balance of the humours, and the associated therapies of bloodletting and purging, persisted into the eighteenth century. It was gradually abandoned as knowledge of human anatomy developed, shifting attention toward less fanciful therapies.
Atomism, developed by Leucippos (born c. 500 BC) and Democritos (c. 460-370 BC), reduced the number of fundamental substances to one:
The world is made of two parts, the full and the empty, the vacuum. The fullness is divided into small particles called atoms. The atoms are infinite in number, eternal, absolutely simple; they are all alike in quality but different in shape, order, and position. Every substance, every single object, is made up of those atoms, the possible combinations of which are infinite in an infinity of ways.15
The existence of empty space is crucial to this theory. The atoms move through space, colliding with each other. These collisions lead to the formation of groups. Every material object is made up of these groups, and all of their sense properties — colour, smell, taste, temperature — follow from the configuration of the groups.
Atomism was a deterministic theory. For Leucippos,
Nothing happens in vain [without reason], everything has a cause and is the result of necessity.16
Democritos emphasized that this causality extends even to our thoughts. Humans do not have free will. We believe that we do because we are unaware of the complex atomic interactions that determine our thoughts.
Aristotle says that Thales, having observed the attraction of metal filings to a magnet, concluded that “all things are full of gods.” It is likely that he meant not that each thing had a soul, but that everything shared “some kind of life-principle.”17 Democritos seems to have held a similar view, but for him, the life-principle (like everything else) was an emergent phenomenon.
Democritos did not conceive a spirit distinct from matter, but some groups of atoms he thought were subtler than others, and he conceived a whole gamut of such groups from the heaviest and most earthly to the lightest and most ethereal. The soul (or vital principle, pysche) is corporeal and made of the lightest atoms (like fire) and the most mobile (spherical in shape for greater mobility). There is a share of these lightest atoms (that is, souls) in everything; this idea enabled the early atomists to explain sensations, thoughts, and psychologic phenomena of every kind…The whole universe is animated (besouled), but there are no gods.18
Confronted with competing theories, the disputatious Greek philosophers took sides, and most of them chose the theory of the four elements. Atomism became so little regarded that none of the works of Leucippos and Democritos have been preserved.
Atomism was revived by Epicurus (341-270 BC), who made it the foundation of his moral philosophy. We are nothing but atoms, he said, coming briefly together and then separating again. No part of us will survive death. Although death itself is inescapable, a part of the natural order, there is no afterlife and certainly no god to judge us in an afterlife. The only thing that remains to us is our fleeting existence in the material world, when our only concerns should be the pursuit of pleasure and the avoidance of pain. Epicurus did not, however, advocate unbridled sensualism. He believed that a great deal of unhappiness came from the too avid pursuit of pleasures that would, in the end, prove unsatisfying. (He believed that sexual attachment and marriage were often pleasures of this kind.) Moderating or abandoning one’s desires is the more certain route to happiness, and tranquility and friendship are the greatest goods. Epicurean philosophy had many adherents among educated Greeks and Romans up to the third century AD, by which time Christianity — philosophically, the mirror image of Epicureanism — was strongly ascendant.
Bodies at Rest and in Motion
Bodies at rest were of interest to the Greeks because their properties underlay two common tools, the balance and the lever. Nevertheless, Archimedes’ exploration of them, On the Equilibrium of Planes, is almost purely theoretical. It begins with a series of postulates about balances that, like Euclid’s axioms, are taken to require no proof. The first postulate, for example, states that equal weights at equal distances are in balance, but that equal weights at unequal distances are not. In the latter case the weight that is more distant from the fulcrum will sink. The postulates also introduce a novel idea, the center of gravity. Archimedes (c. 287-212 BC) then uses the postulates to prove a number of theorems. He formally develops the law of the lever — a lighter weight can shift a heavier weight if it is farther from the fulcrum — which builders would have been aware of for centuries. Archimedes’ goal was to explain what he had already observed.
On Floating Bodies is organized in the same fashion, beginning with simple observations and then developing more complicated results. Archimedes implicitly introduces the idea of specific gravity, considering the behaviour of objects that are lighter or heavier than an equal volume of water. For example, he argues that if a lighter-than-water body is placed in water, it will sink to the depth at which it displaces an amount of water that weighs as much as the body itself. This observation, too, would have been something that people had accepted without understanding: a heavily laden boat rides more deeply than a lightly laden boat.
The Greeks were interested in mechanics, and their machines often developed in advance of the underlying theory. Hero of Alexandria (c. 10-70 AD) wrote a textbook for engineers in which he described the simple machines — the lever, the windlass, the screw, the wedge, and the pulley. The engineers in turn built an array of machines, including looms, olive presses, locks and keys, hoists, gear mechanisms, and water clocks.
The Greeks found the behaviour of bodies in motion to be more puzzling. “Is it absurd to discuss such questions,” Aristotle asked, “while the principle escapes us?”19
Aristotle recognized three kinds of motion. The first kind was natural motion:
There is the downward fall of heavy bodies; this is due to a force existing in the body called gravity. In addition, there is the rise of light bodies like smoke and fire. This is due to a similar inner force, levity. A body is always either heavy or light. Gravity and levity are mutually exclusive qualities… When there are no external obstacles to the motion, the natural motion will cause the bodies to seek their “natural place.” For the heavy bodies this is the center of the world, while to the fire, for example, it is a spherical shell just inside the lunar sphere and adjacent to it. The third type of natural motion is the rotation of the heavenly bodies.20
The second kind was voluntary motion, the deliberate movement of living things. The third and most puzzling kind was forced motion, when an external force opposes natural motion, as it does when a heavy object is lifted. What made forced motion so puzzling was that it was believed to require a continuing force.
When, for instance, one lifts a weight or pulls a carriage there is no problem in finding the origin of the force. But when a stone is thrown, it becomes more difficult, at least from the moment when the stone has left the hand. The force cannot be seated in the stone, as in this case it could perform only its natural downward motion. Nor can it come directly from the hand, as the physics of Antiquity does not accept the possibility of action or force at a distance. Aristotle then advances the theory that moving force is transmitted from the hand to its adjacent layers of air, from these layers to the neighbouring ones, and so on, until it reaches the stone.21
Aristotle adhered to the four-element theory in part because it assumed that all space was filled was some infinitely divisible element. The atomic theory, by contrast, permitted space to be absolutely empty, which would have prevented the transmission of force.
John Philoponus (c. 490-570 AD) proposed the first persuasive alternative to Aristotle’s theory:
When a stone is thrown it will continue its motion because a certain immaterial moving force was impressed upon it during the short time when the stone was in contact with the hand. This force is supposed to exist after the immediate contact has ceased.22
The impressed force was a property of the body itself, like its colour or hardness. It was, however, a temporary property: a thrown stone would fall to the ground when the impressed force was exhausted, leaving only the stone’s natural motion. This idea became known as impetus theory, and some form of it was still current in fourteenth-century Europe.23
Aristotle had also argued that heavier objects fell faster than lighter ones, but Philoponus — without benefit of a leaning tower — argued that this claim was visibly untrue. There were other simple but instructive experiments as well. Strato (c. 335-270 BC) learned that falling bodies accelerate by watching the rain:
If one observes water pouring down from a roof and falling from a considerable height, the flow at the top is seen to be continuous, but the water at the bottom falls to the ground in discontinuous parts. This would never happen unless the water traversed each successive space more swiftly.24
He also recognized that impact is related to both weight and speed, so a longer fall leads to a greater impact.
If one drops a stone or any other weight from a height of about an inch, the impact made on the ground will not be perceptible, but if one drops the object from a height of a hundred feet or more, the impact on the ground will be a more powerful one. Now there is no other cause for this powerful impact…It is merely a case of acceleration.25
The modern rule is that impact is proportional to the square of the speed.
The Babylonians had been charting the apparent movements of the heavenly bodies for a thousand years when the Greeks began their study of the heavens. The Greeks, though, were not content with mere observation. They wondered about the nature of celestial objects, just as they had wondered about the nature of matter. And once again, they responded to a dearth of facts by speculating freely. Xenophanes (c. 570-478 BC) believed that the sun was
…a collection of fiery particles which assemble in the morning to form a radiant cloud. This cloud travels across the Earth,…only to dissolve again at night.26
Empedocles believed that the sun
… did not exist at all as a material entity. He explained day and night by the assumption that a bright and a dark hemisphere revolve around the Earth, the light from the bright hemisphere being reflected from the Earth back onto the heavens as a strongly illuminated spot which we call the Sun.27
But the philosophers also advanced hypotheses that have proved to be strikingly accurate. Thales is said to have recognized that the moon’s glow was reflected sunlight. Democritus recognized that the Milky Way was a vast collection of faint stars. Anaxagoras correctly explained solar and lunar eclipses.
The Greeks used the gnomon, an instrument of Babylonian origin, to study the apparent movements of the sun. A gnomon is a post set vertically in level ground. Changes in its shadow reveal the movements of the sun. The gnomon was used to determine the solstices: the summer solstice is the day on which the gnomon’s noon shadow is shortest, and the winter solstice is the day on which it is longest. But how is noon to be determined? Draw on the ground a north-south line that passes through the center of the gnomon. Noon is the moment when the tip of the gnomon’s shadow passes through the north-south line. How is this north-south line to be found? Inscribe on the ground a circle centered on the gnomon. The gnomon’s shadow is very long at sunrise, shortens through the morning and lengthens through the afternoon, and is very long again just at sunset. The tip of the gnomon’s shadow cuts the circle twice during the day — once in the morning and once in the afternoon. Draw a line between the points where the shadow’s tip cuts the circle. This line lies east-west, and a line perpendicular to it lies north-south. Once the solstices had been established in this fashion, the equinoxes and the lengths of the seasons could be determined.28
The solar year is the time between successive summer solstices. Thales took it to be 365 days, but later astronomers considered the possibility that it is not an even number of days.29 By the second century BC, the estimate of the solar year had been refined to 365 74/300 days (an error of about six minutes).
The gnomon gave rise to the sundial in the fourth century BC. The sundial’s hours were one-twelfth of the sun’s journey across the sky, so they were long is summer and short in winter. This way of thinking about hours persisted until the invention of the mechanical clock in the Middle Ages.
The early philosophers imagined the earth to be a disc, but by the time of Pythagoras, evidence of the earth’s curvature led to the belief that the earth is a sphere. The earth’s curvature can be deduced from the recession of the horizon as one climbs to higher elevations, or by the disappearance of land as one ventures farther from shore.30 Astronomical observation yielded further evidence:
The first real proofs of the spherical shape of the Earth are recorded in Aristotle, who showed that the Earth cannot be flat, for if one travels north or south the stars vary in their altitude above the horizon, which would not be the case on a flat Earth. Furthermore, during a lunar eclipse the earth casts a round shadow on the Moon’s surface, regardless of the position of the Sun, which is another proof of the Earth’s spherical shape.31
If the earth is a sphere, how big is that sphere? Eratosthenes (c. 275-194 BC) was the first person to answer this question. He learned that on the summer solstice, a gnomon casts no shadow at noon in the town of Syene, which lies due south of Alexandria. On the same day, a gnomon in Alexandria does cast a shadow at noon. If the sun is so far away from the earth that the light rays striking Syene and Alexandria are effectively parallel to each other, the length of the noon shadow in Alexandria can be used to determine the curvature of the earth between Syene and Alexandria. Eratosthenes calculated this arc to be 1/50th of a complete circle. He estimated the distance between Syene and Alexandria to be 5,000 stadii. The circumference of the earth is then 50 × 5,000 stadii. There is some uncertainty about the length of a stadium, but it appears that the error in Eratosthenes’ estimate is about 16%.
The mapping of the heavens developed slowly.
Even the fixed stars were “located” only in very vague terms (such as “near X is Y”) for a long time. Hesiod (Works and Days) and his contemporaries had talked of the risings and settings of the major constellations in the seventh century B.C., yet there was still no good system for identifying particular stars and where to find them in the sky five hundred years later. Then in the second century B.C. Hipparchus set about making a star catalogue, and tried to give with reasonable accuracy some locational co-ordinates — inconsistently using several different reference systems, mostly declinations — for about half of the 850 stars he identified. Ptolemy added about 170 more stars about 200 years later, and used one system of proper co-ordinates (ecliptic longitudes and latitudes) for them all. His astronomy superseded all that had gone before and became the orthodox account of the heavens for the next 1500 years.32
Hipparchus (190-120 BC) also discovered precession of the equinoxes, the centuries-long rotation of the heavens “caused by the earth’s polar axis…rotating about a true vertical axis very slowly.”33 The rate of precession is so small that Hipparchus only found it by comparing his own observations with those made by Timocharis 170 years earlier. Hipparchus estimated the rate of precession to be 1° per century; the modern estimate is 1° every 72 years.
The Babylonians and the Greeks understood the basic movements of the heavenly bodies:
(1) The planets rose and set nightly from east to west, as did all the heavenly bodies. (2) Yet they also moved in the manner of the sun, from west to east through the fixed stars. Their courses could be plotted nightly through patterns or certain constellations of stars which were called the zodiac…Each of the planets made the complete circling of the zodiac…in a different period of time. Saturn was seen to take nearly thirty years; Jupiter, twelve years; Mars, two year and six months; Mercury, Venus, and the sun, one year. (3) In the course of their encirclement of the zodiac from west to east they were seen to slow down in their easterly movement until they appeared to stop in the sky, whereupon they seemed to reverse the direction of their movement and proceed in a westerly direction from some time until they again stopped, reversing their direction once more to continue in their over-all easterly traversal of the zodiac.34
The last phenomenon — known as retrograde motion — created a loop in the planet’s apparent path.
The task that the Greeks set themselves was to construct a geometric model that would replicate all of these motions. Their bedrock model was the Pythagorean model of nested spheres with a motionless earth at the center. The fixed stars, each planet, the sun, and the moon were held in place by one of the spheres, and their movements were the result of the spheres’ steady rotation. This model conformed to a geometer’s idea of perfection, but it implied that the heavenly bodies travelled perfectly circular orbits at constant speeds, contrary to the evidence.
Eudoxus (c. 408-355 BC) was able to model retrograde motion without abandoning the assumption of uniform circular motion. Each planet’s motion are assumed to be governed by four spheres. The planet is fixed to the equator of the innermost sphere, and the spheres are linked so that the differing motions of the spheres are all communicated to the planet. The two inner spheres move at the same speed but in opposite directions. If the two spheres have the same axis of rotation, their opposing motions would hold the planet in one place. But if their axes are somewhat different, their combined motions cause the planet to follow a path that looks like the infinity symbol, ∞. Now add the outer spheres. Their speed of rotation is chosen so that the planet moves across the zodiac at the correct speed.35 This steady west-to-east movement prevents the planet from tracing out the full infinity symbol, so the planet instead follows a looping path.
Eudoxus’s model works well for the relatively slow-moving outer planets, but less well for the faster inner planets. For them, if the axes of the inner spheres are offset a small amount, the paths generated by the model have the correct amplitude (up-and-down movement), but the planet moves eastward so quickly that there are no loops. If the offset is large, the loops are recovered but the amplitude is too large.
The full system proposed by Eudoxus used 27 nested spheres. By the time of Aristotle, the number of spheres required to match the data had risen to 55. And it was still not entirely successful. The apparent sizes of the sun and the moon change, indicating that they are sometimes closer and sometimes farther from the earth. This observation cannot be replicated by any model of nested spheres centered on the earth.
Eudoxus does not comment on the physical reality of the crystal spheres, and suggests no mechanism for driving the motions of the spheres. He might well have believed that his model did no more than simulate the motions of the heavenly bodies. Aristotle, however, argued that the spheres were physical entities. Such was the reverence of European scholars for Aristotle that they held to this idea until it was disproved by Tycho Brahe at the end of the sixteenth century.
Among the Greeks there were some dissenters who argued that the basic model needed more fundamental revision. The nightly march of the fixed stars across the heavens had been attributed to the rotation of the sphere that holds them in place. Heraclides (c. 390-310 BC) suggested a simpler solution: the sphere of the stars stood still while the earth rotated on its axis once each day. The same rotation explained the rise and fall of the sun. Aristarchus (c. 310-230 BC) argued that the sun sat motionless at the center of the universe, that the earth orbited around it, and that the fixed stars were so far away that the earth’s movement along its orbit created no discernible parallax. He believed that the stars themselves did not move, which suggests that he, like Heraclides, believed that the earth rotated on its axis.
These views had few supporters, and were rejected by Hipparchus and by Ptolemy (100-170 AD). The rotation of the earth would be very fast, which seemed to be contradicted by our sense of stillness, and also by the observation that objects fall directly to the ground instead of being “left behind” by the earth’s movement. Ptolemy concluded that
There is perhaps nothing in the celestial phenomena which would count against that hypothesis…[but] from what would occur here on earth and in the air, one can see that such a notion is quite ridiculous.36
The earth’s movement along an orbit would compound the problem of speed, and the claim that the universe was so big that parallax could not be observed seemed to pile one extravagant proposition on top of another.
With these avenues of research closed off, new tools were needed to save the “nested spheres” approach. Two such tools were devised by Apollonios (c. 262-190 BC). An eccentric was a shift of a planet’s circular orbit so that it was no longer centered on the earth. An epicycle was a circular orbit for a planet that was centered not on the earth itself, but rather on a point that followed a circular orbit centered on the earth. These devices gave astronomers more degrees of freedom, allowing them to more closely replicate the data. The fiction of circular orbits was maintained, but the Pythagorean idea that the universe displayed come kind of geometrical perfection was no longer tenable.
The most complete “nested spheres” model of the universe appears in Ptolemy’s Almagest. It became the benchmark for centuries of Islamic and European scholars. It also demonstrated the possibilities of a purely theoretical approach to astronomy.
The most general feature of the Almagest is the extremely abstract geometrical character of its theories. There are very few references to the physical properties of the universe. Ptolemy succeeded in furnishing the proof that it is possible to give a complete mathematical description of planetary motions without entering on such questions as the nature of celestial matter or the forces keeping the planets in motion…Its abstract presentation contrasted strongly with the picture of a universe composed of ethereal spheres in which Aristotle had tried to embed the astronomy of Eudoxos…
Gradually, two different schools of astronomy emerged, one trying to create a physical astronomy, the other concentrating on planetary theory. Though it started in Antiquity, this debate continued throughout the Middle Ages.37
The Fate of Greek Science
Of the twenty-six philosophers named above, twenty-two lived and died before 100 BC.38 A span of just five centuries separates Thales’ simple proofs from Hipparchus’s discovery of precession. After that, the pace of Greek inventiveness slowed substantially. More than eight centuries separate Aristotle’s theory of forced motion from Philoponus’s revision of the theory.
Perhaps this slow-down was to be expected. The modern world experiences a “cascade of knowledge” in which new discoveries open the way to further discoveries. This cascade requires a certain density of knowledge. Think of solving a jigsaw puzzle. Early on, few pieces are in their proper places — perhaps just a section or two along the edge of the puzzle. More pieces are put in place based on their colour or their texture, but their positions are just guesses. Later, some of these pieces are linked together to form sections, and the sections are linked together to form an emerging picture. Solving the puzzle is easy at the end because the density of knowledge is high, and difficult at the beginning because the density of knowledge is low. We expect scientific progress to continue because our density of knowledge is high; but for the Greeks, the density of knowledge was low — so low, perhaps, that they couldn’t make further connections.
Alternatively, the Greeks might have boxed themselves in by clinging to theories that were simply wrong, like the four-element theory and the nested spheres model. What they needed was a revolution, and there was none to be had.
These hypotheses imply that the cause of the slow-down came from within science itself, but the alternative — that science was impacted by external events — is equally credible.
Greek science was, from its beginning, the product of prosperous and independent societies. Its first center of learning was Ionia. The end of philosophy there coincided with the encroachment of the Persians, who conquered all of Ionia by 540 BC. Anaxagoras, Xenophanes, and Pythagoras were all born in Ionia but chose to move to more stable jurisdictions.
Xenophanes went to Syracuse and Pythagoras to Crotone (in southern Italy), but Anaxagoras went to Athens, a wealthy city-state that prized its independence. Athens became the next center of Greek natural philosophy. The eventual slow-down of Greek science in Athens roughly corresponds to the Roman conquest of the Greek peninsula. After their victory in the Battle of Corinth (146 BC), the Romans turned Macedonia into a Roman province and politically dominated the rest of the peninsula. Athens joined in a revolt against the Romans in 87 BC. The revolt failed, much of Athens was reduced to ruins, and the Athenians themselves became poorer. Wealth and independence, the preconditions for scientific inquiry, were lost.
Upper-class Romans were disdainful of the contemporary Greeks. For them, the Greeks’ defeat in battle was proof of their inferiority. Nevertheless, the Romans admired Greek rhetoric, literature, and ethical philosophy, and they studied these subjects with the aid of Greek teachers and scholars. Natural philosophy, though, was not of interest to them unless it had immediate engineering applications. The conquerors’ lack of interest in scientific matters must have influenced the choices of capable young Greeks, leading them away from science and towards the arts.
The Romans’ interest in Greek achievements initially helped to maintain Hellenic culture in the east. The officials sent from Rome were drawn from a social elite that fluently spoke and read Greek. The official language of administration in the east continued to be Greek (except in the army, where Latin prevailed), and Greek law continued to be the norm.
The status of the Greek language began to change in the third century AD. The borders of the Roman empire were no longer secure, and military matters had acquired a new urgency. The emperors of the time tended to be military men. They were less refined than their predecessors, spoke no Greek themselves, and appointed men like themselves as their senior officials. The Greek language lost its cachet.
Greek withered away in the West even in the most cultivated circles…So learned a man as Augustine, deeply interested in Greek philosophy and theology, never mastered Greek, using translations and occasionally, it would seem, spelling out a sentence or two with the aid of a lexicon.39
As knowledge of Greek withered, so did the West’s knowledge of the science and philosophy written in that language.
The new religions that came out of the east also had an impact on Greek science. They emphasized direct engagement with a supreme being and the existence of a personal afterlife. They offered hope to people who lived simple and often bleak lives. Pragmatic doctrines like Stoicism and Epicureanism could not compete with them, but there were strands of early Greek science that could.
The Roman age saw the wide diffusion of a number of very oriental cults, the so-called mystery religions. The Egyptian worship of Isis had already begun to spread outside Egypt in the Hellenistic age and now became universal. Mithraism, a Persian cult, spread far and wide, and so also did the worship of the Phrygian Great Mother of the Gods. Judaism seems also to have become widely diffused; we hear of many proselytes in the first century. More significant for the future was the growth of Christianity. There was a steady growth of religiosity throughout the Empire…Greek philosophy also took on a more religious tone. Both the two new philosophic schools of the Roman period, Neopythagoreanism and Neoplatonism, were strongly infused with religious emotion.40
These philosophies had strong mystical themes, and their most fundamental explanations assumed the existence of spiritual or incorporeal beings. Some of their adherents (such as John Philoponus) made significant contributions to science; but the great insight of Ionian philosophy — that there is only nature, and that nature can be rationally understood — is much diluted within them.
When Christianity became the dominant religion in the West, its theologians had to decide the place of Greek philosophy. In this task they were influenced by the prior work of the Jewish philosophers of Alexandria. The most prominent of these philosophers was Philo Judaeus (early first century AD), who influenced the “religious philosophy of the late antique Greek Christians, of the Syriac Christians, of the Islamic and Jewish medieval philosophers, and finally, of Latin medieval schoolmen.”41
The early Christian scholars asserted that the Christian scriptures revealed “full and perfect wisdom.” If philosophy deviated from the scriptures, it was false. The philosophers’ willingness to debate issues was taken as further proof that their philosophy was false, while the simplicity and fixity of Christian dogma were taken to show Christianity’s truthfulness. The Christian scholars also argued that philosophy distracted Christians from more important matters.
The philosophers, even where they are not wrong, are missing the whole point of existence, the discovery of God.42
In spite of these views, the Christian scholars were able to find some value in philosophy.
If the fathers thought of revealed truth as the more certain knowledge, the early Christian father, and Philo before him, often made the important supplementary assumption that there is really only one truth, and properly conducted philosophy or human reason will also arrive at that truth.43
This idea became the “double faith doctrine”: faith can be attained through either God’s revelation or human reasoning. Thomas Aquinas was one of the many scholars who subscribed to this view.
Philo questioned one of the basic precepts of Greek science, and the Christian scholars followed his lead.
One of the fundamental views taken over by the fathers from Greek philosophy, but radically modified in the Christian writings, was that there exists in nature a generally fixed order expressible in terms of laws, for the most part immutable. This fixed order with its laws may, however, be set aside in miraculous fashion at God’s pleasure.44
The idea that God could suspend the laws of nature at any moment became known as occasionalism. It undermined the concept of cause and effect, and was an obstacle to progress in both Europe and the Islamic world.
There was a third center of Greek learning, also born of affluence: Alexandria in Ptolemaic Egypt. Among the scholars who chose to live and work there were Strato, Euclid, Aristarchus, Eratosthenes, Claudius Ptolemy, Philo Judaeus, and the mathematician Diophantus. Christianity played an active part in its downfall. Alexandria had once hosted communities of pagans, Jews, and Christians in relative peace. However, the emperor Constantine converted to Christianity in the early fourth century AD, and thereafter Roman policy tilted toward the Christians. The Christians of Alexandria came to believe that paganism could and should be suppressed, and the city’s pagans came to believe that their religion was threatened with extinction. Intermittent street fighting broke out between Christian and pagan street gangs, culminating in the Christian sacking of an ancient pagan temple, the Serapeum, in 391. The Christian fanatics were reinvigorated in 412 by the appointment of a more militant patriarch, Cyril. He first acted against the Jews, ordering their expulsion from the city. (He had no legal right to do so, but he had the power of the gangs behind him.) Cyril then targeted the pagans. Actually, he targeted one pagan: Hypatia, a mathematician and neoplatonist, Alexandria’s most respected scholar. On Cyril’s instigation, Christian hoodlums found Hypatia, mutilated her and killed her. Hypatia was among the last of Alexandria’s renowned scholars.
- T.E. Rihll, Greek Science, p. 16. It should be noted that the Greek philosophers were always a very small part of the Greek population. The vast majority of the Greeks continued to farm, make, fight and trade as they had always done, and the traditional gods continued to rule their lives. My references to “the Greeks” should almost always be understood as referring to the Greek philosophers alone. ↩
- T.E. Rihll, Greek Science, p. 18. ↩
- T.E. Rihll, Greek Science, p. 4. ↩
- George Sarton, Ancient Science through the Golden Age of Greece (Dover Publications, 1993), p. 198. ↩
- T.E. Rihll, Greek Science, p. 10. ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 16. ↩
- See Jacob Bronowski, The Ascent of Man (BBC 1973), pp. 158-60 for a possible proof. ↩
- Olaf Pedersen, Early Physics and Astronomy, pp. 18-9. ↩
- Heraclitus’s actual words are lost to us. What we know is what Plato wrote: “Heraclitus somewhere says that all things are in process and nothing stays still, and likens existing things to the stream of a river. He says you would not step twice into the same river.” This situation is not unusual: almost all of the writings of the earliest philosophers have been lost. We know of their ideas largely through scattered references to them in the work of later philosophers, who were usually more interested in buttressing their own arguments than with providing a fair and full portrayal of their predecessors’ beliefs. Our knowledge of these beliefs is therefore fragmentary, and differences of interpretation persist. ↩
- George Sarton sees the influence of the poet Hesiod here. The first act of Hesiod’s creation story was the joining of heaven and earth by Eros (Love). ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 124. ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 128. ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 128. ↩
- Olaf Pedersen, Early Physics and Astronomy, pp. 130-1. ↩
- George Sarton, Ancient Science through the Golden Age of Greece (Dover Publications, 1993), p. 253. ↩
- Quoted by George Sarton, Ancient Science through the Golden Age of Greece (Dover Publications, 1993), p. 251. ↩
- Geoffrey Kirk, John Raven, and Malcolm Schofield, The Presocratic Philosophers (Cambridge, 1983), p. 97. ↩
- George Sarton, Ancient Science through the Golden Age of Greece (Dover Publications, 1993), p. 254. ↩
- From Aristotle’s Mechanics. Quoted by T.E. Rihll, Greek Science, p. 36. ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 106. ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 107. ↩
- Philoponus, quoted by Olaf Pedersen, Early Physics and Astronomy, p. 110. ↩
- Impetus theory was promoted by the philosopher John Buridan (c. 1300-1360). ↩
- From Strato, On Motion. Quoted by Marshall Clagett, Greek Science in Antiquity (Dover, 2001), p. 70. ↩
- From Strato, On Motion. Quoted by Marshall Clagett, Greek Science in Antiquity (Dover, 2001), p. 70. ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 34. ↩
- Olaf Pedersen, Early Physics and Astronomy, pp. 34-5. ↩
- The length of the noon shadow can be used to calculate the angle at which the sun’s rays strike the gnonom. An equinox, either winter or summer, occurs when this angle is midway between the angles for the two solstices. Counting the days between a solstice and an equinox determines the length of a season — they are not all equal. ↩
- In modern terms, there is no reason to believe that the time taken for the earth to travel around the sun is an even number of earth days. ↩
- Centuries later, Samuel Coleridge would write of land’s progressive disappearance:
“The ship was cheered, the harbour cleared,
Merrily did we drop
Below the kirk, below the hill,
Below the lighthouse top.” ↩
- Olaf Pedersen, Early Physics and Astronomy, p. 45. ↩
- T.E. Rihll, Greek Science, p. 66. ↩
- T.E. Rihll, Greek Science, p. 68. ↩
- Clagett, Greek Science in Antiquity, pp. 83-4. ↩
- Two spheres are required because there are both lateral and vertical movements in the planet’s path across the zodiac. ↩
- Claudius Ptolemy, quoted by Rihll, Greek Science, p. 70. ↩
- Pedersen, Early Physics and Astronomy, p. 87. ↩
- Of the remainder, Hero was active in the first century AD, Ptolemy and Galen in the second century, and Philoponus in the fifth century. ↩
- A. H. M. Jones, “The Greeks under the Roman Empire,” Dumbarton Oaks Papers (1963), p. 13. ↩
- A. H. M. Jones, “The Greeks under the Roman Empire,” Dumbarton Oaks Papers (1963), p. 10. ↩
- Marshall Clagett, Greek Science in Antiquity, p. 130. ↩
- Marshall Clagett, Greek Science in Antiquity, p. 132. ↩
- Marshall Clagett, Greek Science in Antiquity, p. 134. Philo had written that “Moses said the same thing as Plato, only earlier and better.” (Quote is from Pollard and Reid, The Rise and Fall of Alexandria, p. 194) ↩
- Marshall Clagett, Greek Science in Antiquity, p. 138. ↩