He was also famous as a political sage, successfully urging the Milesians to resist assimilation by Croesus, King of Lydia, and unsuccessfully urging a federation of all the island states of Ionia to oppose the Lydians.
Anaximander of Miletus was a friend and colleague of Thales, one of the first people we know of to do an experiment. By examining the moving shadow cast by a vertical stick he determined accurately the length of the year and the seasons. For ages men had used sticks to club and spear one another. Anaximander used one to measure time. He was the first person in Greece to make a sundial, a map of the known world and a celestial globe that showed the patterns of the constellations. He believed the Sun, the Moon and the stars to be made of fire seen through moving holes in the dome of the sky, probably a much older idea. He held the remarkable view that the Earth is not suspended or supported from the heavens, but that it remains by itself at the center of the universe; since it was equidistant from all places on the “celestial sphere,” there was no force that could move it.
He argued that we are so helpless at birth that, if the first human infants had been put into the world on their own, they would immediately have died. From this Anaximander concluded that human beings arose from other animals with more self-reliant newborns: He proposed the spontaneous origin of life in mud, the first animals being fish covered with spines. Some descendants of these fishes eventually abandoned the water and moved to dry land, where they evolved into other animals by the transmutation of one form into another. He believed in an infinite number of worlds, all inhabited, and all subject to cycles of dissolution and regeneration. “Nor,” as Saint Augustine ruefully complained, “did he, any more than Thales, attribute the cause of all this ceaseless activity to a divine mind.”
In the year 540 B.C. or thereabouts, on the island of Samos, there came to power a tyrant named Polycrates. He seems to have started as a caterer and then gone on to international piracy. Polycrates was a generous patron of the arts, sciences and engineering. But he oppressed his own people; he made war on his neighbors; he quite rightly feared invasion. So he surrounded his capital city with a massive wall, about six kilometers long, whose remains stand to this day. To carry water from a distant spring through the fortifications, he ordered a great tunnel built. A kilometer long, it pierces a mountain. Two cuttings were dug from either end which met almost perfectly in the middle. The project took about fifteen years to complete, a testament to the civil engineering of the day and an indication of the extraordinary practical capability of the Ionians. But there is another and more ominous side to the enterprise: it was built in part by slaves in chains, many captured by the pirate ships of Polycrates.
This was the time of Theodorus, the master engineer of the age, credited among the Greeks with the invention of the key, the ruler, the carpenter’s square, the level, the lathe, bronze casting and central heating. Why are there no monuments to this man? Those who dreamed and speculated about the laws of Nature talked with the technologists and the engineers. They were often the same people. The theoretical and the practical were one.
About the same time, on the nearby island of Cos, Hippocrates was establishing his famous medical tradition, now barely remembered because of the Hippocratic oath. It was a practical and effective school of medicine, which Hippocrates insisted had to be based on the contemporary equivalent of physics and chemistry.* But it also had its theoretical side. In his book On Ancient Medicine, Hippocrates wrote: “Men think epilepsy divine, merely because they do not understand it. But if they called everything divine which they do not understand, why, there would be no end of divine things.”
In time, the Ionian influence and the experimental method spread to the mainland of Greece, to Italy, to Sicily. There was once a time when hardly anyone believed in air. They knew about breathing, of course, and they thought the wind was the breath of the gods. But the idea of air as a static, material but invisible substance was unimagined. The first recorded experiment on air was performed by a physician† named Empedocles, who flourished around 450 B.C. Some accounts claim he identified himself as a god. But perhaps it was only that he was so clever that others thought him a god. He believed that light travels very fast, but not infinitely fast. He taught that there was once a much greater variety of living things on the Earth, but that many races of beings “must have been unable to beget and continue their kind. For in the case of every species that exists, either craft or courage or speed has from the beginning of its existence protected and preserved it.” In this attempt to explain the lovely adaptation of organisms to their environments, Empedocles, like Anaximander and Democritus (see below), clearly anticipated some aspects of Darwin’s great idea of evolution by natural selection.
Empedocles performed his experiment with a household implement people had used for centuries, the so-called clepsydra or “water thief,” which was used as a kitchen ladle. A brazen sphere with an open neck and small holes in the bottom, it is filled by immersing it in water. If you pull it out with the neck uncovered, the water pours out of the holes, making a little shower. But if you pull it out properly, with your thumb covering the neck, the water is retained within the sphere until you lift your thumb. If you try to fill it with the neck covered, nothing happens. Some material substance must be in the way of the water. We cannot see such a substance. What could it be? Empedocles argued that it could only be air. A thing we cannot see can exert pressure, can frustrate my wish to fill a vessel with water if I were dumb enough to leave my finger on the neck. Empedocles had discovered the invisible. Air, he thought, must be matter in a form so finely divided that it could not be seen.
Empedocles is said to have died in an apotheotic fit by leaping into the hot lava at the summit caldera of the great volcano of Aetna. But I sometimes imagine that he merely slipped during a courageous and pioneering venture in observational geophysics.
This hint, this whiff, of the existence of atoms was carried much further by a man named Democritus, who came from the Ionian colony of Abdera in northern Greece. Abdera was a kind of joke town. If in 430 B.C. you told a story about someone from Abdera, you were guaranteed a laugh. It was in a way the Brooklyn of its time. For Democritus all of life was to be enjoyed and understood; understanding and enjoyment were the same thing. He said that “a life without festivity is a long road without an inn.” Democritus may have come from Abdera, but he was no dummy. He believed that a large number of worlds had formed spontaneously out of diffuse matter in space, evolved and then decayed. At a time when no one knew about impact craters, Democritus thought that worlds on occasion collide; he believed that some worlds wandered alone through the darkness of space, while others were accompanied by several suns and moons; that some worlds were inhabited, while others had no plants or animals or even water; that the simplest forms of life arose from a kind of primeval ooze. He taught that perception—the reason, say, I think there is a pen in my hand—was a purely physical and mechanistic process; that thinking and feeling were attributes of matter put together in a sufficiently fine and complex way and not due to some spirit infused into matter by the gods.
Democritus invented the word atom, Greek for “unable to be cut.” Atoms were the ultimate particles, forever frustrating our attempts to break them into smaller pieces. Everything, he said, is a collection of atoms, intricately assembled. Even we. “Nothing exists,” he said, “but atoms and the void.”
When we cut an apple, the knife must pass through empty spaces between the atoms, Democritus argued. If there were no such empty spaces, no void, the knife would encounter the impenetrable atoms, and the apple could not be cut. Having cut a slice from a cone, say, let us compare the cross sections of the two pieces. Are the exposed areas equal? No, said Democritus. The slope of the cone forces one side of the slice to have a slightly smaller cross section than the other. If the two areas were exactly equal, we would have a cylinder, not a cone. No matter how sharp the knife, the two pieces have unequal cross sections. Why? Because, on
the scale of the very small, matter exhibits some irreducible roughness. This fine scale of roughness Democritus identified with the world of the atoms. His arguments were not those we use today, but they were subtle and elegant, derived from everyday life. And his conclusions were fundamentally correct.
In a related exercise, Democritus imagined calculating the volume of a cone or a pyramid by a very large number of extremely small stacked plates tapering in size from the base to the apex. He had stated the problem that, in mathematics, is called the theory of limits. He was knocking at the door of the differential and integral calculus, that fundamental tool for understanding the world that was not, so far as we know from written records, in fact discovered until the time of Isaac Newton. Perhaps if Democritus’ work had not been almost completely destroyed, there would have been calculus by the time of Christ.*
Thomas Wright marveled in 1750 that Democritus had believed the Milky Way to be composed mainly of unresolved stars: “long before astronomy reaped any benefit from the improved sciences of optics; [he] saw, as we may say, through the eye of reason, full as far into infinity as the most able astronomers in more advantageous times have done since.” Beyond the Milk of Hera, past the Backbone of Night, the mind of Democritus soared.
As a person, Democritus seems to have been somewhat unusual. Women, children and sex discomfited him, in part because they took time away from thinking. But he valued friendship, held cheerfulness to be the goal of life and devoted a major philosophical inquiry to the origin and nature of enthusiasm. He journeyed to Athens to visit Socrates and then found himself too shy to introduce himself. He was a close friend of Hippocrates. He was awed by the beauty and elegance of the physical world. He felt that poverty in a democracy was preferable to wealth in a tyranny. He believed that the prevailing religions of his time were evil and that neither immortal souls nor immortal gods exist: “Nothing exists, but atoms and the void.”
There is no record of Democritus having been persecuted for his opinions—but then, he came from Abdera. However, in his time the brief tradition of tolerance for unconventional views began to erode and then to shatter. People came to be punished for having unusual ideas. A portrait of Democritus is now on the Greek hundred-drachma bill. But his insights were suppressed, his influence on history made minor. The mystics were beginning to win.
Anaxagoras was an Ionian experimentalist who flourished around 450 B.C. and lived in Athens. He was a rich man, indifferent to his wealth but passionate about science. Asked what was the purpose of life, he replied, “the investigation of the Sun, the Moon, and the heavens,” the reply of a true astronomer. He performed a clever experiment in which a single drop of white liquid, like cream, was shown not to lighten perceptibly the contents of a great pitcher of dark liquid, like wine. There must, he concluded, be changes deducible by experiment that are too subtle to be perceived directly by the senses.
Anaxagoras was not nearly so radical as Democritus. Both were thoroughgoing materialists, not in prizing possessions but in holding that matter alone provided the underpinnings of the world. Anaxagoras believed in a special mind substance and disbelieved in the existence of atoms. He thought humans were more intelligent than other animals because of our hands, a very Ionian idea.
He was the first person to state clearly that the Moon shines by reflected light, and he accordingly devised a theory of the phases of the Moon. This doctrine was so dangerous that the manuscript describing it had to be circulated in secret, an Athenian samizdat. It was not in keeping with the prejudices of the time to explain the phases or eclipses of the Moon by the relative geometry of the Earth, the Moon and the self-luminous Sun. Aristotle, two generations later, was content to argue that those things happened because it was the nature of the Moon to have phases and eclipses—mere verbal juggling, an explanation that explains nothing.
The prevailing belief was that the Sun and Moon were gods. Anaxagoras held that the Sun and stars are fiery stones. We do not feel the heat of the stars because they are too far away. He also thought that the Moon has mountains (right) and inhabitants (wrong). He held that the Sun was so huge that it was probably larger than the Peloponnesus, roughly the southern third of Greece. His critics thought this estimate excessive and absurd.
Anaxagoras was brought to Athens by Pericles, its leader in its time of greatest glory, but also the man whose actions led to the Peloponnesian War, which destroyed Athenian democracy. Pericles delighted in philosophy and science, and Anaxagoras was one of his principal confidants. There are those who think that in this role Anaxagoras contributed significantly to the greatness of Athens. But Pericles had political problems. He was too powerful to be attacked directly, so his enemies attacked those close to him. Anaxagoras was convicted and imprisoned for the religious crime of impiety—because he had taught that the Moon was made of ordinary matter, that it was a place, and that the Sun was a red-hot stone in the sky. Bishop John Wilkins commented in 1638 on these Athenians: “Those zealous idolators [counted] it a great blasphemy to make their God a stone, whereas notwithstanding they were so senseless in their adoration of idols as to make a stone their God.” Pericles seems to have engineered Anaxagoras’ release from prison, but it was too late. In Greece the tide was turning, although the Ionian tradition continued in Alexandrian Egypt two hundred years later.
The great scientists from Thales to Democritus and Anaxagoras have usually been described in history or philosophy books as “Presocratics,” as if their main function was to hold the philosophical fort until the advent of Socrates, Plato, and Aristotle and perhaps influence them a little. Instead, the old Ionians represent a different and largely contradictory tradition, one in much better accord with modern science. That their influence was felt powerfully for only two or three centuries is an irreparable loss for all those human beings who lived between the Ionian Awakening and the Italian Renaissance.
Perhaps the most influential person ever associated with Samos was Pythagoras,* a contemporary of Polycrates in the sixth century B.C. According to local tradition, he lived for a time in a cave on the Samian Mount Kerkis, and was the first person in the history of the world to deduce that the Earth is a sphere. Perhaps he argued by analogy with the Moon and the Sun, or noticed the curved shadow of the Earth on the Moon during a lunar eclipse, or recognized that when ships leave Samos and recede over the horizon, their masts disappear last.
He or his disciples discovered the Pythagorean theorem: the sum of the squares of the shorter sides of a right triangle equals the square of the longer side. Pythagoras did not simply enumerate examples of this theorem; he developed a method of mathematical deduction to prove the thing generally. The modern tradition of mathematical argument, essential to all of science, owes much to Pythagoras. It was he who first used the word Cosmos to denote a well-ordered and harmonious universe, a world amenable to human understanding.
Many Ionians believed the underlying harmony of the universe to be accessible through observation and experiment, the method that dominates science today. However, Pythagoras employed a very different method. He taught that the laws of Nature could be deduced by pure thought. He and his followers were not fundamentally experimentalists.* They were mathematicians. And they were thoroughgoing mystics. According to Bertrand Russell, in a perhaps uncharitable passage, Pythagoras “founded a religion, of which the main tenets were the transmigration of souls and the sinfulness of eating beans. His religion was embodied in a religious order, which, here and there, acquired control of the State and established a rule of the saints. But the unregenerate hankered after beans, and sooner or later rebelled.”
The Pythagoreans delighted in the certainty of mathematical demonstration, the sense of a pure and unsullied world accessible to the human intellect, a Cosmos in which the sides of right triangles perfectly obey simple mathematical relationships. It was in striking contrast to the messy reality of the workaday world. They believed that in their mathematics they had glimpsed a perfect reality, a realm
of the gods, of which our familiar world is but an imperfect reflection. In Plato’s famous parable of the cave, prisoners were imagined tied in such a way that they saw only the shadows of passersby and believed the shadows to be real—never guessing the complex reality that was accessible if they would but turn their heads. The Pythagoreans would powerfully influence Plato and, later, Christianity.
They did not advocate the free confrontation of conflicting points of view. Instead, like all orthodox religions, they practiced a rigidity that prevented them from correcting their errors. Cicero wrote:
In discussion it is not so much weight of authority as force of argument that should be demanded. Indeed, the authority of those who profess to teach is often a positive hindrance to those who desire to learn; they cease to employ their own judgment, and take what they perceive to be the verdict of their chosen master as settling the question. In fact I am not disposed to approve the practice traditionally ascribed to the Pythagoreans, who, when questioned as to the grounds of any assertion that they advanced in debate, are said to have been accustomed to reply “The Master said so,” “the Master” being Pythagoras. So potent was an opinion already decided, making authority prevail unsupported by reason.
The Pythagoreans were fascinated by the regular solids, symmetrical three-dimensional objects all of whose sides are the same regular polygon. The cube is the simplest example, having six squares as sides. There are an infinite number of regular polygons, but only five regular solids. (The proof of this statement, a famous example of mathematical reasoning, is given in Appendix 2.) For some reason, knowledge of a solid called the dodecahedron having twelve pentagons as sides seemed to them dangerous. It was mystically associated with the Cosmos. The other four regular solids were identified, somehow, with the four “elements” then imagined to constitute the world; earth, fire, air and water. The fifth regular solid must then, they thought, correspond to some fifth element that could only be the substance of the heavenly bodies. (This notion of a fifth essence is the origin of our word quintessence.) Ordinary people were to be kept ignorant of the dodecahedron.