The Fire Within the Eye
A Historical Essay on the Nature and Meaning of Light

Princeton University Press

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At the very beginning the King made engravings in
the supernal purity. A spark of blackness emerged in the
sealed within the sealed, from the mystery of En-Sof, a
mist within matter, implanted in a ring, no white,
no black, no red, no yellow, no color at all.
(Zohar [15.sup.a])

1. Prospectus

I came out of the darkness into my dark house and switched on the light. Instantly, I saw in front of me the fireplace with a tall old chair beside it. I saw the chair; that is to say, if someone wants to argue about it, I saw a familiar pattern of lines, colors, and textures that I recognized as the chair. Light came into my eyes, the chair came into my mind. But why the chair? Why not an aardvark or a bicycle? Try again. Not just light but an image carried by light came into my eyes; then something happened, and not just a chair came into my mind but a particular chair, located about ten feet in front of me. Perhaps it is not obvious how all this happened, or how it could happen so quickly.

We can study the mystery of vision most efficiently by breaking it down into small questions: What is light? Where does it come from? How does it carry an image into my eye? What is an image, anyhow? What happens inside an eye? Is an eye something like a camera, or is it more of a cerebral mechanism? What happens in my brain when my eyes see something? And finally, when it has happened, how does that chair get into my consciousness, my mind? But this is the modern style; by the time I have asked these questions I have already done much of the thinking that took twenty-five hundred years. Thought is integral. It grows in open air and is packaged later. Experience comes first: switch, light, see chair, all at once. Then, in an inquiring mind, a sense of curiosity: how did this happen?

The pages that follow will tell in a leisurely way how we arrived at our modern questions about light and vision and will suggest some answers. They will show, for example, how some people argued cogently that what passes through the pupil of the eye travels outward, not inward, while others maintained for centuries that nothing travels at all. Those ideas are no longer current, but I will have failed in my purpose if they seem to you absurd. And even if they seem a bit naive, so will our best thoughts, no doubt, after we have gone.

But why ask such questions at all? Well, for one thing, you can't hope to fit people with glasses or help their ophthalmia or make a telescope if you don't know what is going on, but behind that there stands another reason, the one Aristotle puts at the start of his Metaphysics: "All men naturally desire knowledge." We specially value knowledge of things that are important to us, as means to wise action and inner satisfaction. Then Aristotle continues, "Above all the other senses, sight helps us to know things and reveals many distinctions." Light enables vision and vision enables knowledge and action; it represents creative power. For minds touched by the Bible, the command "Let there be light" was the beginning of everything. It was not just that one could now see; light somehow energized the act of creation that transformed a dark, wet, chaotic half-existence into sea, land, a sunlit garden, a man and a woman.

The history of light is a long story which I intend to make longer still with many digressions. The first few chapters will be concerned with light as a means of seeing and knowing and as active power. We begin with some historical background, together with basic philosophical notions that for many centuries guided both questions and answers. We will see how light came to represent in people's minds the truth of an ideal world of which ours is only a moving model, in which the words "God is light" are a simple statement of fact. We will also have to discuss the physics of light. This starts early but will not become a dominant theme until the second half of the book.

Most of the ideas we shall first encounter originated, as far as we know, among the thinkers of the ancient Greek world. At least, they have come down to us with Greek names attached to them. The next few sections introduce some of the personalities and the ideas they put forth to explain both vision (their primary concern) and the nature of light. Out of this it will begin to become clear what the ancients thought was important in their philosophy of the created world.

2. The Roots of Matter

The name of Athens shines in history. Twice she led other nations in the defense of Greece when the Persians tried to conquer it. Later Athens became very rich and attracted writers and artists. She did not, however, produce many of them, or many of the thinkers who made the name of Greece immortal. They tended to come from the periphery, the shores of the Eastern Mediterranean, the Aegean, and the Black Sea.

From about 600 B.C.E. certain men around this rocky perimeter were identified by their reputation for wisdom. They were not professors like Plato and Aristotle, who lived two hundred years later. Many were civic leaders who had proved they were smart by solving political or military problems or by getting rich, or all three, so that people paid attention to what they said. They discoursed about the world, about Nature and the great questions of human life. Some wrote books, all of which disappeared after a while in the upheavals that destroyed the libraries of Athens, Pergamon, Alexandria, and smaller centers. We have only fragments of those books, chosen by later writers to illustrate some point of vocabulary or grammar or, more often, an opinion. We should never read one of these fragments in the belief that it is what the author actually wrote. But such as they are, by the beginning of the twentieth century scholars had collected them, arranged them, translated them, and begun to theorize about the intellectual culture from which they arose. It is dangerous work. From the fifth century on, we know much about the Greek world. For earlier times, the history that has been put together could be significantly changed by the discovery of only a few new fragments.

As far as we know, the first place where wise men achieved a special status was the city of Miletus, on the west coast of Asia Minor south of Ephesus. To the east was the kingdom of Lydia, which at the beginning of the sixth century was absorbed by the Persian empire. Nothing is left of Miletus now but a huge Roman theater and the remains of a public square paved in marble, but in its prime it controlled most of the trade along the northern coast and into the Black Sea, and in the sixth century it was the richest city of the Greek world. It was perhaps here that natural philosophy first caught the interest of the educated public. This is the philosophy that looks upward and asks questions about stars and clouds and winds and weather, and downward at things on earth, and wonders what they are made of and what principles explain the ways in which they change.

We live in a world of huge variety. Look around at the different things you can see, various solid materials, perhaps some liquids, and of course there is the air, which you feel but cannot see. Materials change. Living things grow and die, wood rots, iron rusts, liquids evaporate. Is there anything we can say about all these materials and processes in general? Are the various substances fundamentally different and continually changing their nature, or are they manifestations of some principle that does not change? A man named Thales, one of the first Milesian philosophers, suggested that water is the fundamental principle, though we do not know how he went on from there. Aristotle reports the suggestion and explains that for Thales Nature is life, and life needs water. What Thales proposed can be judged a bad guess if you wish, but the question he asks is not trivial, and physicists have pursued it ever since. At present they find themselves in a cloudy world inhabited by particles with names like quarks and gluons. Questions like "What is light?" and "How do I see the world around me?" must extend back into the night of time, but the first record of them comes from Miletus.

Other thinkers continued the Milesian game. I shall mention only the three who contributed theories of light and vision: Empedocles, Leucippus, and Democritus.

Empedocles (c. 495-435 B.C.E.) lived in Akragas, a large city on the south coast of Sicily that is now known as Agrigento. Pindar, who also lived there, called it the fairest city of men, and its massive temples of yellow limestone still stand among almond groves along the shore. Empedocles was well known, a leader of the colony's democratic forces, an orator, and tradition says he was also a doctor. He taught that matter is eternal and changes only its forms: "Before now I was born a boy and a maid, a bush and a bird, and a dumb fish leaping out of the sea." He wore fine clothes: "a purple robe and over it a golden girdle, ... slippers of bronze and a Delphic laurel wreath." He glittered as he addressed his followers or walked the streets, and when he wrote down his philosophy it was in stately hexameters. Thales had one fundamental material principle; Empedocles has four, which eternally unite and separate and move about as the world goes its way. They are not substances, not things; he calls them roots and names them after figures from mythology: Zeus, Hera, Aidoneus (i.e., Hades), and a weeping nymph, Nestis. In a sense these are the elements of matter, and Aristotle, writing a century later, calls them Fire, Earth, Air, and Water. Nobody knows for certain which was which, but Nestis doubtless represented Water. The third-century (C.E.) biographer Diogenes Laertius says that Zeus is Fire and Hera is Earth, but whatever they were, the old writers understood that they are modes of existence, not substances, and that by themselves they have no properties. Because of their abstract nature I write them with capital letters. Earth is not dug with a spade, Fire is not hot, Water is not wet. We never encounter them in pure form because they represent extreme tendencies--Fire tries to move upward, Water and Earth try to move downward, Air tries to move sidewise, and if there is any hope of explaining the immense variety of natural substances it must be in terms of balances between contrasting principles.

Things made from these roots do not just sit there. Empedocles sees that change is everywhere and nothing lasts forever, so he introduces two further principles, Love and Strife. Love draws the roots together, and Strife tears them apart. In Nature they produce fixity and change; what we know as birth and death are only rearrangements. Concerning light, Aristotle says Empedocles taught that it travels at immense speed "between the Earth and its surrounding space,"' but he mentions him only to contradict him, and this is all we know. We shall discuss Empedocles's theory of vision in Chapter 2.

3. Atoms and Emptiness

Miletus was conquered and destroyed by King Darius of Persia in 494 B.C.E. It lost its rich hinterlands but started to rebuild itself as destroyed cities usually do, and a child named Leucippus was born there about twenty years later. By the time he grew up the city had recovered enough so that people had time to listen to a very original thinker. We know little about him, but Aristotle, though he did not believe in atoms at all, credits Leucippus with inventing them. Atoms represent another attempt to identify a permanent reality that underlies and explains the changing world. Leucippus's atoms are too small to see, infinite in number and in the variety of their shapes and sizes, and they move in empty space. We shall see in a moment why atoms have no place in Aristotle's philosophy of substance and change, but the particular point on which he concentrates his objection is empty space. The trouble really is that there was no way of talking about it that made sense. The atomists used the word kenon, meaning empty, but this is an adjective. They could of course say "the empty," and they did, but the phrase acquired the sense of "nonbeing," and then it was hard to answer questions like "Exactly what is nonbeing?" or "Would you please point to an example of it?" Today we would say they were talking about space, but they had no word for that. (The situation was similar in Greek arithmetic, which used a clumsy system akin to Roman numerals, apparently because a positional notation like ours or the Babylonians' requires a zero, a symbol that represents nothing at all.) Leucippus did not try to define the empty, causing critics to judge that he was a very poor philosopher, but imagined atoms moving in it, combining and separating so as to create the substances and the processes that surround us. They follow no plan, and whatever is combined today will some day separate. Atoms do not go where they want to go or where the gods want them to go. Instead, they follow their logos, which can be thought of as a necessity arising from the order and fitness of things. The only fragment we have from Leucippus says "Nothing happens at random; everything happens out of reason and by necessity," and this is the first suggestion that at some level of its structure the behavior of matter is governed by laws that are not violated. I used the word "law," but that metaphorical comparison with a legal statute came later, as did the notion of inviolability.

The second atomist was Democritus, a few years younger than Leucippus. He lived in Abdera, on the north shore of the Aegean near the border of Macedonia and is said to have traveled widely, perhaps to the Persian empire to learn astronomy from the Chaldeans, perhaps as far as India. One may suppose he visited Leucippus in Miletus.

Democritus saw some of the deeper implications of atomism, in particular how the theory deals with questions concerning what is really true. Suppose I sit in a room, reading. You come in from outside and remark how dark it is inside. It doesn't seem dark to me. We may both understand perfectly well why we don't agree, but how to explain the situation in exact language?--Even at this early time people wanted to use words exactly. What is the room, really: light, dark, or neither? Democritus answers by saying that questions like this are not questions of fact. He does not mention light, but "sweet exists by convention, bitter by convention, color by convention; in reality there are only atoms and emptiness" (fragment 9). Because this is an important point, let me make clear by an example what he is saying. The letters C-A-T do not look like a cat. The word "cat" does not sound like the noise a cat makes, but when we see the letters or hear the word we know the conventions that tell us what is meant. Long afterward, the German physicist and physiologist Hermann von Helmholtz wrote, "Our sensations are for us only symbols of the objects of the external world, and correspond to them only in some such way as written characters or articulate words correspond to the things they denote."

We cannot know atoms or emptiness, and if what we think we sense is only a convention, what can we know? Democritus continues, "We know nothing in reality, for truth lies in the abyss" (fragment 117). By now, twenty-five hundred years later, we know something about how to explain our sensations, but as to the truth about how things actually are, Democritus speaks for us all.

The atom was a stupendous invention, but it was only one small item in the Mediterranean supermarket of ideas. Plato bought it, but in Timaeus, the book where he discusses it, he reinterprets it in his own comprehensive system until it is almost unrecognizable. In Aristotle's metaphysics, on the other hand, a thing's properties belong to it as a whole, so that he cannot use the idea at all. Atoms mostly sat on the shelf until there was use for them in someone's philosophy. To tell that story I will jump a century, over Plato and Aristotle, who have little to do with it, and return to them shortly.

Epicurus (c. 342-270) was born to a prosperous Athenian family on the island of Samos, not far from Miletus. Like other young men of his class he studied and traveled, and in 307 he came to Athens, where he founded an institution that was something between a school and a social club. It met in his house and garden, where his followers, men and women and even slaves, sought a revivifying philosophy as Athenian greatness in art and political power faded into twilight. Epicurus tried to make his pupils see that fate and gods are not to be feared, that the gods are content and not vindictive, that enlightened people should ignore the supernatural and concentrate on living a life that is honest and frugal, serene and happy. Much of his argument rested on the teachings of Democritus.

How does Democritus enter this peaceful garden? His atoms and things made of them are impersonal, ethically neutral, and unaffected by supernatural forces. If there is a drought it is because atoms of wind have blown away atoms of cloud, and not because a god is angry. If something goes wrong you should work to make it better instead of killing a sheep. The simple machinery of atoms explains why real life has nothing to fear from malice on Olympus. It is not that gods don't exist, only that their existence is of a higher order. They are not concerned about us and will not bother us. "It is impossible," he writes, "to dispel our anxieties and enjoy our pleasures if we do not understand the nature of the universe and if we allow things learned from myths to frighten us."

The world runs by the operation of impersonal forces, but do we? That would be going too far, for there is no use in teaching a rule of life to someone who cannot freely choose to follow or reject it. And besides, we all know how it feels to make a free choice between alternatives. Epicurus uses rather strange terms to explain how this happens. He says that atoms have two kinds of motion: free fall, and motion imparted by a collision. Both, presumably, are rule-governed, but from time to time there is a third kind, a "swerve" that allows atoms to click together forming associations that would not otherwise have happened. These random events break the causal chain, but how he thought they allow free will we do not know, for his book On Choice and Avoidance is lost. All we have is a mysterious explanation given by the Roman poet Lucretius in his epic-length poem De rerum natura, or "Concerning the Nature of Things," written about 50 B.C.E. This is an account of Epicurean philosophy in more than seven thousand hexameter lines, clearly designed for immortality, and its fundamental purpose is to teach that Nature is impersonal and gods are not to be feared. We are lucky to have a very fine verse translation by Rolfe Humphries [1968].

Lucretius writes that particles go where they are sent, but "now and then they move a little from their path, barely enough so that one could say they are deflected." These are the words that promise each of us a certain freedom from causal constraints: "How does our will escape the chains of fate--this will through which we move forward as we please, swerving in our motion not at determined times or places but where our mind carries us?" Though our bodies are made of atoms we are not mechanical dolls. We make our own choices.

There is no occasion here to say more about the poem, and there can be no substitute for reading it, but I will pull out of it a few physical insights that have some bearing on light. First, the reality of atoms. Everything we have from Epicurus is in general terms, but a poem is best when it is specific. Lucretius gives examples of phenomena that atoms explain: the force of wind, the diffusion of a scent, and the drying of clothes on the line. Either the water departs a wet shirt invisibly, particle by particle, or else it simply ceases to exist, but Lucretius will not allow the latter. Nothing, he says, comes from nothing or vanishes into nothing.

Lucretius also gives some explanations that have not endured: he has atoms of heat, cold, and sound, but these sensations are now explained as the result of atomic motions and are not themselves atoms. From the properties of matter he deduces that the atoms of hard substances are firmly hooked together whereas those of a liquid are round and roll against one another. The atoms inside a lemon have sharp points. We can hear what is happening in the next room; therefore the particles of sound are small enough to go through a wall. Intelligible speech consists of a sequence of sounds, and so we must imagine a stream of these little particles, all different. The particles of light can pass through transparent substances. But now a difficulty arises. When we look at something we do not see it in temporal sequence as when we hear words; rather, we see it all at once, and so the thing that comes to our eyes must have some special character that makes it different from sound and allows it to create a picture in our mind that is different at each moment. But what is this thing? How Epicurus and Lucretius answered that difficult question will be told in Chapter 2 when we discuss theories of vision.

Outside a small circle, people greeted the philosophy of Epicurus with the special rage and scorn reserved for those who question prevailing beliefs. References in later philosophy are almost all contemptuous. We rarely use the term "epicure" to praise someone. The Stoic philosopher Epictetus, writing shortly after Lucretius, summarizes what most people thought of the Epicurean principle in a single sentence: "Eat, drink, and satisfy your passion for women; relieve yourself, and snore." Perhaps he is right; nowhere in Epicurus is there any mention of the tears and promises with which we try to change our bad ways and make ourselves better than we are.

Lucretius does not speak of gods or suggest any general rule for living, but particles swerve and we are not bound by fate, and the last two books of De rerum natura are devoted to simple, causal explanations of events that were then, and are still by many people, regarded as signs of wrath in Heaven: eclipses, thunder, lightning, waterspouts, earthquakes, and volcanoes. Not all the explanations still fly, but the principle does: exhaust every natural explanation before turning elsewhere.

Empedocles, Leucippus, and Democritus were all alive during the Periclean age, the middle of the fifth century. At the same time, in Athens, the four playwrights Aeschylus, Sophocles, Euripides, and Aristophanes were at work, the Parthenon was going up, and Socrates walked the marketplace. And as that shining age drew to a close, Plato was born.

4. Plato's Philosophy of Ideas

Every town laid out before the modern age has an open place, agora in Greek, forum in Latin, where markets were held and public business was transacted. In Athens, most of the time, the agora must have looked like a county fair in an old Currier and Ives print. The ground was dusty or muddy as the case might be, and most of it was covered with wooden booths where shopkeepers sold the things city-dwellers need. That is how it looked. Ordinarily it was also full of sound, for it was where men met to argue about people and news and politics and everything else in their world. Before printing, there was the voice. In the agora teachers of eloquence and argument, called sophists, attracted students by offering to uphold either side of a vexed question. Politicians made their noise, and in the crowd an ill-favored man with snub nose and bulging eyes, shabbily dressed, barefoot in most weather and generally regarded as a quibbling bore, joined group after group, listening for a while and then upsetting the easy flow of platitudes by asking exactly what they meant.

Sometimes Socrates was the center of his own circle, which Plato (427-347) joined in his twentieth year to discuss questions that are simple to ask and hard to answer. What is virtue? What is justice? It is easy enough to give examples of each, or of their contraries, but the questions remain. Each example of justice is unlike the rest; the more examples you give the harder it becomes to say what they have in common. It was the same question, in the moral order, that Thales had asked about matter. Examples are not enough, said Socrates, and the question is important, for only he who knows what justice is can be just. Then what is it? First of all, it is a word, needed because we need to capture thoughts in language so they can be understood and discussed. But a word ought to mean the same thing every time; it must refer to something. What does it refer to?

Before people awoke to questions like this, the specific was all. Aeschylus and Sophocles had put questions of justice and duty at the center of dramas depicting the world of myth, but myth is always specific; it describes the individual case and leaves us to deduce the generality. Myth begins the language of metaphor.

Philosophers before Plato, trying to express their ideas about nature, faced similar problems, and they tended to use terms such as Empedocles's four roots with mythological names, controlled by Love and Strife. Plato was of the last generation of Athenians who were at home in myth and familiar with its language. He understood that leaders of a modern state must find some other way to talk, but still, the old one was so natural to him that when he tried to explore the true meaning of words he tended to start with a myth.

The dialogues Plato writes usually have Socrates in the middle of them, arguing, insisting, changing tactics, laughing, walking away, but the upper regions of his talk are probably all Plato's. Imagine a realm of existence, Plato sometimes calls it the Heaven above Heaven, which never changes. It is populated by what he calls eide, translated variously as Forms or Ideas, one eidos called Virtue, another called Justice, another called simply the Good, and so on. Perhaps every word which in our world denotes a definite concept has its counterpart in that Heaven of Heavens. The world we live in is an imperfect version of that Heaven, imperfect because things here change all the time, and the examples of virtue and justice we encounter are never the same, never quite pure, never unmixed with their opposites. But still it is possible for a prepared and properly educated person, from time to time, to pierce through the barrier between the two worlds and discern the reality that shines above our cloudy air. In his effort to achieve consistency, never successful, Plato at one point tries to furnish his Heaven of Heavens with the Ideas of beds and tables, adding, as Aristotle says, that of course the objects around us are different from the ideal ones from which they get their names, but "it is because they participate in an Idea that objects of the same kind have the same name." A critic might say that Plato was having problems with words, that instead of solving them the Ideas raised more and worse problems; later he retreats and is not sure that he can have any material objects in Heaven without, as he says, "tumbling into a bottomless pit of nonsense."

A person about to recite a myth does not announce "I am going to tell you a myth." Instead, a story begins. Presently it reaches its end and stops, but myth never exhausts its meanings; that is why it endures. Plato did not present his mythical world of Ideas as a consistent doctrine that hearers were supposed to accept or reject; it was a way of talking about problems important to him and his friends and followers. Plato's myth is not important for the theory of light and vision to be described in the next chapter, but its influence on later thought through figures like Plotinus and Saint Augustine will become obvious as we go along. Myths in Plato's Phaedo and Republic speak to his readers through their imaginations and remain in their minds as pictures. One in The Republic is essential to our story. It is known as the Myth of the Cave, and I will sketch it because it provides a picture that has helped many generations to think about the world of Ideas.

Imagine, says Socrates, that there are men imprisoned in a cave with a low opening to the outer world along its side, but the prisoners are chained so that though daylight is at their shoulder they cannot see it. A fire is kept lighted behind them and in front of it people pass back and forth carrying various objects, so that all the prisoners can see is moving and flickering shadows cast on the wall in front. These shadows, being all they can see, define the world of their words and thoughts, so that when they believe they are naming a thing they are naming only its shadow. But suppose one of them were suddenly freed and made to look out at the real world beside him. His eyes would be dazzled and hurt by the light, he would see nothing familiar, nothing he saw would make any sense, and he would want to sit down again and face the familiar shadows. Only gradually, taken from the cave, would he learn how the world really looks and what is really in it.

The soul, says Socrates, is like an eye. When it looks toward the Heaven of truth and beauty it knows them and understands them, but when it looks into our world of becoming and passing away it has no knowledge but only opinions that change and change again. The Good is to the soul as the sun is to the eye, and Plato carries the analogy further: just as the sun sustains all of Nature's life and growth, so the Good, through its action in the ideal world, is the cause of all things in our world; "it causes their state of being, though the Good itself is stronger and more venerable than being."

Let us try to read these words not just as a metaphorical statement of Plato's view of the Good but, as many read them afterward, an inspired utterance that explains why the world exists and opens the Good to human understanding. We are not to take it literally but rather to look for the deeper truth it expresses. If we do this, we may be led to ponder what it implies about the Nature and powers of light. If the Good is the highest element of the Ideal world, fructifying every other form of existence, does it not seem to follow that the sun occupies an analogous position in our own world? If so, its powers extend as far beyond its effects on the eye as the powers of the Good extend beyond ordinary goodness. This was how it seemed to many of Plato's followers, and even centuries later we shall find them attributing powers to light far exceeding those suggested by experience and common sense.

Alfred North Whitehead says somewhere that all later Western philosophy can be read as footnotes to Plato. Though this need not be seen as a desperately serious remark, it at least describes the historical weight and persistence of Plato's words. His successors molded his ideas and adopted them to their own purposes and in doing so kept them alive. Plato isolated the Good in a domain inaccessible to ordinary experience, but Platonists were followed by Neoplatonists. In Egypt, six hundred years later, one of them named Plotinus saw Good pervading the universe, emanating from the world's unitary principle, the One, in a sort of radiation like the sun's. The One is the origin of all being, but it cannot be analyzed or described, because to analyze is to divide into parts, and even a description would tend to focus on one or another aspect of something that does not have different aspects. It brings warmth and life, and at the same time it manifests the world's goodness and intelligible order. Its radiation spreads perfection over every level of existence; its power is both physical and ideal, and the light by which the sun pours its blessings onto the Earth shares in that power.

Dante imagines this light in Book XXVIII of the Paradiso. He stands at the edge of the Empyrean sphere, from which

    I saw a point that shone with light so keen,
    the eye that sees it cannot bear its blazing;
    the star that is for us the smallest one
    would seem a moon if placed beside this point.

The light is spiritual light, and the point is a spiritual point; but it is a point, for before Dante, Saint Thomas wrote that God is perfectly simple, he is not mixed with anything else, he has no parts, and a point, as Euclid defined it long ago, is that which has no parts.

Neoplatonic doctrines flowing from Plotinus's luminous vision spread over the Greek world. Later on in this book we shall find them in early Christian philosophy exemplified by the Gospel of Saint John and in the early Church Fathers' explanations of the command "Let there be light." In the ninth century, Arabic translations of Plotinus and his successors and commentators opened a channel through which Neoplatonic thought flowed into Mesopotamia and North Africa. We shall find it in the writings of Alkindi of Kufa, whose work, appearing in Latin in the twelfth century, inspired the Englishmen Robert Grosseteste and Roger Bacon and their followers to think of light as a physical power. Finally, in sixteenth-century Italy there was a resurgence of Neoplatonic philosophy, almost unrecognizable under a veil of magic charms and delightful ritual, that started when Marsilio Ficino translated Plotinus. We shall touch some of these branches of Plato's great tree but only touch them; to go farther would need many chapters and someone who has read more than I have.

5. Aristotle's Philosophy of Desire

In the western suburbs of Athens there was a grove of trees adorned by fountains and walks; near it an old gymnasium. The place was called Akademe, and for many years men had taken study and exercise there. About 387, Plato established a school which endured on this spot, with some hiatuses and many changes of direction, for some 925 years, until Justinian closed all the pagan schools. This was the world's first institution of higher learning; I would call it the first university. It is said that Plato put a sign over the gate, "Let no one ignorant of mathematics enter here." In fact, very distinguished mathematicians worked and taught there, but I do not think that the sign was supposed to be taken literally. Plato was announcing that everything would be discussed here in the cool and analytical style of mathematics. Athenians and foreigners, some of them future commanders and statesmen and a few of them women, came here to study how to think and speak and act.

Aristotle (384-322 B.C.E.) was never an Athenian. He was born in Stagira, on the border of Macedonia, came to Athens at nineteen to study with Plato at the Academy, and stayed there till he was almost forty. He found Plato teaching mathematics and expounding his version of what the leaders of a state should know, much of it expressed in the poetic language of Ideas. Aristotle and the other young scholars loved Plato and his talk of an ideal world but could find no way to express its meaning in coherent terms, and for them it remained a myth. Their task was to find some other explanatory framework with which to express the same exalted thoughts. For philosophic discussion they wanted a language that conveyed its message without symbol or metaphor, using words that meant the same every time they were used. This was something new in the Greek world, and it separated Aristotle's followers from scholars who preferred to think like Plato.

Aristotle's knowledge and intelligence were legendary, and people expected that when Plato died he would succeed him as director of the Academy. For some reason, perhaps his nationality, he was not chosen and went back north. A few years later he was tutoring the young son of Philip of Macedon while Philip conquered Greece, but when Philip died and Alexander became king, Aristotle moved back to Athens and established his own school, the Lyceum, on the grounds of another old gymnasium. It too had a grove of trees, and in time Aristotle's followers became known as peripatetics, people who walk around. The Lyceum must have had lecture halls also, where students scratched on wax tablets while a teacher read from a bundle of notes. What we have of Aristotle's writings seems to be mostly those notes, uneven in quality and sometimes no more than aids to memory, collected and edited and finally published after many adventures and changes of hands. They cover a staggering range of subjects: medicine, physiology, comparative anatomy, metaphysics, psychology, politics, logic, meteorology, physics, cosmology, ethics, literary criticism, and many topics in biology and natural history.

For years after Greece surrendered its political power to the Roman Empire people still went to Athens to study, bringing books and knowledge home with them. But as the Empire declined and the great libraries disappeared, few but Greeks remembered their language, and outside a few centers of learning most of the old books were lost. Of Aristotle, the logical works had been translated into Latin and every educated Roman had to study them. Several of Plato's dialogues seem to have been translated, but the only one that survived into the middle ages is the first part of one called Timaeus which describes the structure of the world in mythic terms. It was not until the twelfth century that scholars from northern Europe traveling in Moorish Spain discovered complete Arabic translations of works they had heard of but thought they would never see. The braver ones learned Greek and Arabic, and in the next two hundred years a great flood of translated Greek and Arabic philosophical and scientific writing, accompanied by brilliant Arabic commentaries, arrived in Europe; it is hard to imagine how we would be thinking and living today if this had not happened. Now began the age of Aristotle's influence in Europe. Until the scientific renaissance of the seventeenth century, and in some places later than that, the language of science was largely Aristotelian, and we must learn some of it.

First, what does the physical world consist of? It consists of substances, specific and individual. This pencil is a substance. Do I see the substance? No, I see only some of its qualities--size, shape, color--and it has others, such as weight, that I perceive in other ways. The pencil itself has an identity independent of all the qualities by which we know it, and that is its substance. Substance is Aristotle's answer to the question "What is it that persists as the world changes?" As the pencil gets shorter it is still the same pencil, the same substance. The qualities that enable us to identify this substance as a pencil--including what it does--are called its properties, and the sum of these properties, what we can know and understand about the pencil, is called its form. But a pencil has other qualities. It may be long or short, hot or cold, sharp or blunt, and it might be on this table or in the other room. Qualities such as these, which are not essential to its being a pencil, are called accidents.

The pencil is made of wood and other kinds of matter, but each kind consists of a mixture of elements. Aristotle proposes three elements in his Physics and four in On Generation and Corruption; the second view prevailed, and Empedocles's four roots became idealized substances, like the earth, air, fire, and water we know, but purer. They consist of prime matter together with the properties that make it become one element or another. There is only one kind of prime matter and, by itself, it has no qualities at all and hence no independent existence. It is not made of atoms, for atomicity would be a kind of property.

Finally comes essence, the inner nature of a thing that is responsible for all its properties; we use it today in the Aristotelian sense if we say that some act is the essence of futility.

The formulas get messy when one tries to apply them in specific cases. For example, because one can identify and talk about a particular form, one can even call certain forms substances. This extra complexity will be necessary later when we think about perception, for Aristotle taught that the world is perceived through the soul, and that the soul is such a form.

But Nature consists of more than forms and substances; it consists of processes as well. Nature doesn't just sit there, it also happens, and it is here that Aristotle's explanation of the world departs sharply from our own. Things change for many reasons--because they are hammered or heated or pushed around, but also because they are urged toward perfection as plants grow upward, by their own inner natures. Matter, says Aristotle, desires form "as the female desires the male or the ugly the beautiful." A peach ripens because its material yearns toward a certain perfect form of ripeness. In Aristotelian jargon the ripe peach has a material cause and a formal cause. But if you allow it, the peach continues past perfect ripeness because the larger plan of the universe requires that fruit should fall and rot and propagate the species. That is why a fruit exists in the first place, its final cause as Aristotle says; and there is a fourth, trivial kind of cause called efficient: if the branch is shaken the peach falls.

But of course not all changes are possible. A green peach never develops into a ham sandwich. In its green state it holds a potentiality that strives to actualize its own kind of ripeness. Most changes can be described in terms of transitions of this kind. Aristotle's arguments and distinctions are delicate and exact and can be found in Book IX of the Metaphysics, but these simple remarks will suffice for what comes later.

We have seen why things happen, but how do they happen? In Aristotle's system this was an important question because one of his basic principles is that everything that moves (he counts any kind of change as motion) is being moved by something else that is itself in motion. Book VIII of the Physics contains a long and uncomfortable discussion of this claim. Many instances are obvious, but when a peach drops to the ground, where is the mover? It is the process of natural growth that produced the peach at the end of its twig. But obviously there must be an exception to Aristotle's principle. Motion must originate somewhere in an Unmoved Mover, or Prime Mover, that causes change without itself changing. It lies outside the sphere that carries the fixed stars; "it thinks that which is most divine and precious; and it does not change, for change would be change for the worse, and this would already be a motion." It causes change by being loved; in Dante's words, this is "the love that moves the sun and the other stars." That is, it causes motion in the sphere that carries the fixed stars, and this motion cascades down through the spheres below it that carry the planets, until it reaches the domain of the four elements that make the Earth and everything on it.

The definitions and ideas briefly sketched here are worked out at length in Aristotle's Physics and Metaphysics, their purpose was to enable natural philosophy to do its job of explaining Nature, starting with substances and properties and potentialities. One says: the peach tends to fall because it is largely composed of Earth, and that is what Earth does. This is plausible, and it applies to heavy things we have handled, but does it apply to everything that is heavy? What makes us think that the element Earth always has this property? It is time to look for a moment at what we know about the world, and how we know it.

6. What Is Science, and How Do You Know It Is Right?

When Aristotle distinguishes between art and science he is only putting into words a distinction that had long existed in people's minds. Science (episteme) is certain knowledge, and he starts with a definition of the word "know": "We all suppose that what we know is not capable of being otherwise.... Therefore an object of knowledge exists necessarily and is eternal, for things that are necessary in the unqualified sense are all eternal; and things that are eternal are ungenerated and imperishable." The tentative, the provisional, the approximate have no place in Aristotle's episteme, only unchanging first principles or knowledge gained from them by logical deduction. In this sense a science of accidents is impossible: sunlight falls on a stone and it becomes warm, but warmth is an accidental property, and there is no use trying to explain it from first principles because warmth comes and goes, while first principles do not come and go. They refer only to what remains, to substances and the properties that define them.

Scientific knowledge, in Aristotle's view, is knowledge of causes. It is universal and invariable. On the other hand, experience is neither, and the evidence of our senses is not always reliable. No two cases of epilepsy are exactly alike; thus there can be no science of epilepsy. In fact, our world contains very little knowledge that would qualify as episteme. We need other categories of knowledge. One is opinion, doxa, which "deals with that which can be otherwise than it is." Another is art, techne. It is "a capacity to make, involving a true course of reasoning. All art is concerned with coming into being." Farming and building are arts, and so is medicine. Art is learned by experience, whereas episteme, if it does not follow logically from other episteme, must be intuited or guessed. An example is the proposition, "The shape of the heavens is of necessity spherical: for that shape is most appropriate to its substance and is also primary by nature." Such a judgment does not follow from observation; it is, to put it bluntly, a guess, but one of which Aristotle was absolutely certain, and on it his whole cosmology is founded. Science, which traded in this kind of knowledge, was loftier than any art, and its contemplation, known as theoria, was considered the highest form of activity.

Understanding this way of thinking, we can see why Greek explanations of Nature are so abundant in unsupported hypotheses. Aristotle was one of the few who admitted that this is what they were, and he admits it quite often when he refers to "the science we are seeking." In modern science hypotheses are usually suggested by experiment and, if possible, tested by experiment. But what is an experiment? To experiment on something we change it in some way--perhaps heat it--and see what happens. Aristotle would say we play with accidents, not substance, and only skate on the surface of episteme. For thinkers of antiquity and the middle ages, hypothesis belonged to science; experiment and opinion belonged to art, and they existed in separate worlds. During the seventeenth century, the period known as the scientific revolution, they drew closer together, but as we shall see, it was not until two centuries later that something like the modern scientific viewpoint developed.

What are the first principles, and where do they come from? When Aristotle proposes to explain the appearance of the heavens and the motions of stars, he declares that the universe is contained in a sphere, but he does not just say this and then go on to deduce the consequences, for the rest of the chapter lists his reasons for thinking so: the geometrically simple nature of a sphere, the fact that the universe revolves around us, the fact that the Earth at its center is also a sphere, and so on. None of these proves the principle, but they add up to a conviction, and for the parts of his system that might conceivably be otherwise Aristotle never claims any more. His Posterior Analytics is a book on making error-free deductions from first principles. In its final chapter he has to face the problem of where first principles come from. Ultimately, he says, intuition extracts them from our experience of many particulars, out of which one universal truth "come[s] to rest in the soul." In a wonderful figure he tells how it feels as the many become one, "as in a battle, when a rout occurs, if one man makes a stand another does and then another, until a position of strength is reached." Think of the great scientific principles, natural selection for example. The more general and inclusive they are, the more likely they are to have arisen in a single act of intuition. But scientists have become skeptical of any principle reached in this way. Examine it from every side, consider alternatives, think of observations that put it to the test; finally, try to devise an experiment by which it stands or falls. And ten years later, reopen the question in the light of new knowledge. But this kind of thinking came much later.

I should add that in the middle ages another question was raised: is a "science" of physics even possible? The problem is that whereas episteme is based on necessary connections, it is not obvious that anything in Nature happens necessarily. Thunderstorms may have a cause, but no two are alike. There is no use producing a watertight argument to prove that tides must be highest at the time of full and new moons if it turns out that this is not always the case. Only very slowly have people become convinced that there is necessity in Nature, and that one can usually find some explanation for an apparent exception.

These paragraphs have introduced a few bits of Aristotelian lore that will be useful as we go along. Aristotle himself never regarded his theory as complete. His works show that he saw most of the difficulties very clearly, and of course his efforts to deal with them tended to make things more complicated. He spoke of "the science we are seeking," never of "the science we have found." For him, though, substances and forms and the rest had a real existence outside the mind. I have tended to present them more as devices that enable language to be used in a consistent way. During the middle ages people who held the first interpretation were called realists, while the others, who said no, substance and form are only names of concepts, were nominalists. The nominalists finally won, but the language remains, and so do various questions that are asked in it. People asked, for example, "Is light a substance or an accident?"--Substantia aut accidens? Some of the controversies that will occupy this book turn on that question. Later we shall find several reasoned answers, but people went on arguing. In Chapter 10 we shall see how modern physicists create a paradox when they treat light as accidens in their theory but speak of it as if it were substantia.

Why does anything happen? The world around us is in continual motion (remember that motion, for Aristotle, includes any kind of change--the rising moon, a burning fire, a blossoming rose). What drives potentiality to become actuality? I have mentioned the principle with which Aristotle begins Book VII of his Physics, which seems so natural that it is hard to see how any reasonable person could doubt it:

Everything that is in motion must be moved by something.

But this, as we have seen, leads to an infinite regress unless one postulates an Unmoved Mover at the beginning of it all, for whose sake the heavenly spheres turn, bringing motion and change to the Earth below. Aristotle says little about how motion is transmitted from the outermost sphere--which, being largest, moves the fastest--down through the successive planetary spheres to the Earth--which does not move as a whole but suffers various other changes. That the spheres affect what happens on Earth was obvious. Anyone can see that the sun controls the seasons and the moon controls the tides, but how is it done? It was a long time before anyone attempted a serious answer to this great scientific question, and the first answer, when it came ([sections] 3.6), was more concerned to explain the stars' effects on humanity than on seasons and tides. But still, no one doubted the effects.

(C) (C) 1997 PRINCETON UNIVERSITY PRESS All rights reserved. ISBN: 0-691-04332-9

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