To Explain the World: The Discovery of Modern Science (5 page)

This leads to problems in communication. Mathematicians have told me that they often find the literature of physics infuriatingly vague. Physicists like myself who need advanced mathematical tools often find that the mathematicians’ search for rigor makes their writings complicated in ways that are of little physical interest.

There has been a noble effort by mathematically inclined physicists to put the formalism of modern elementary particle physics—the quantum theory of fields—on a mathematically rigorous basis, and some interesting progress has been made. But nothing in the development over the past half century of the Standard Model of elementary particles has depended on reaching a higher level of mathematical rigor.

Greek mathematics continued to thrive after Euclid. In
Chapter 4
we will come to the great achievements of the later Hellenistic mathematicians Archimedes and Apollonius.

3

Motion and Philosophy

After Plato, the Greeks’ speculations about nature took a turn toward a style that was less poetic and more argumentative. This change appears above all in the work of Aristotle. Neither a native Athenian nor an Ionian, Aristotle was born in 384 BC at Stagira in Macedon. He moved to Athens in 367 BC to study at the school founded by Plato, the Academy. After the death of Plato in 347 BC, Aristotle left Athens and lived for a while on the Aegean island of Lesbos and at the coastal town of Assos. In 343 BC Aristotle was called back to Macedon by Philip II to tutor his son Alexander, later Alexander the Great.

Macedon came to dominate the Greek world after Philip’s army defeated Athens and Thebes at the battle of Chaeronea in 338 BC. After Philip’s death in 336 BC Aristotle returned to Athens, where he founded his own school, the Lyceum. This was one of the four great schools of Athens, the others being Plato’s Academy, the Garden of Epicurus, and the Colonnade (or Stoa) of the Stoics. The Lyceum continued for centuries, probably until it was closed in the sack of Athens by Roman soldiers under Sulla in 86 BC. It was outlasted, though, by Plato’s Academy, which continued in one form or another until AD 529, enduring longer than any European university has lasted so far.

The works of Aristotle that survive appear to be chiefly notes for his lectures at the Lyceum. They treat an amazing variety of
subjects: astronomy, zoology, dreams, metaphysics, logic, ethics, rhetoric, politics, aesthetics, and what is usually translated as “physics.” According to one modern translator,
¹
Aristotle’s Greek is “terse, compact, abrupt, his arguments condensed, his thought dense,” very unlike the poetic style of Plato. I confess that I find Aristotle frequently tedious, in a way that Plato is not, but although often wrong Aristotle is not silly, in the way that Plato sometimes is.

Plato and Aristotle were both realists, but in quite different senses. Plato was a realist in the medieval sense of the word: he believed in the reality of abstract ideas, in particular of ideal forms of things. It is the ideal form of a pine tree that is real, not the individual pine trees that only imperfectly realize this form. It is the forms that are changeless, in the way demanded by Parmenides and Zeno. Aristotle was a realist in a common modern sense: for him, though categories were deeply interesting, it was individual things, like individual pine trees, that were real, not Plato’s forms.

Aristotle was careful to use reason rather than inspiration to justify his conclusions. We can agree with the classical scholar R. J. Hankinson that “we must not lose sight of the fact that Aristotle was a man of his time—and for that time he was extraordinarily perspicacious, acute, and advanced.”
²
Nevertheless, there were principles running all through Aristotle’s thought that had to be unlearned in the discovery of modern science.

For one thing, Aristotle’s work was suffused with teleology: things are what they are because of the purpose they serve. In
Physics
,
³
we read, “But the nature is the end or that for the sake of which. For if a thing undergoes a continuous change toward some end, that last stage is actually that for the sake of which.”

This emphasis on teleology was natural for someone like Aristotle, who was much concerned with biology. At Assos and Lesbos Aristotle had studied marine biology, and his father, Nicomachus, had been a physician at the court of Macedon. Friends who know more about biology than I do tell me that Aristotle’s writing on animals is admirable. Teleology is natural for
anyone who, like Aristotle in
Parts of Animals,
studies the heart or stomach of an animal—he can hardly help asking what purpose it serves.

Indeed, not until the work of Darwin and Wallace in the nineteenth century did naturalists came to understand that although bodily organs serve various purposes, there is no purpose underlying their evolution. They are what they are because they have been naturally selected over millions of years of undirected inheritable variations. And of course, long before Darwin, physicists had learned to study matter and force without asking about the purpose they serve.

Aristotle’s early concern with zoology may also have inspired his strong emphasis on taxonomy, on sorting things out in categories. We still use some of this, for instance the Aristotelian classification of governments into monarchies, aristocracies, and not democracies but constitutional governments. But much of it seems pointless. I can imagine how Aristotle might have classified fruits:
All fruits come in three varieties—there are apples, and oranges, and fruits that are neither apples nor oranges.

One of Aristotle’s classifications was pervasive in his work, and became an obstacle for the future of science. He insisted on the distinction between the natural and the artificial. He begins Book II of
Physics
⁴
with “Of things that exist, some exist by nature, some from other causes.” It was only the natural that was worthy of his attention. Perhaps it was this distinction between the natural and the artificial that kept Aristotle and his followers from being interested in experimentation. What is the good of creating an artificial situation when what are really interesting are natural phenomena?

It is not that Aristotle neglected the observation of natural phenomena. From the delay between seeing lightning and hearing thunder, or seeing oars on a distant trireme striking the water and hearing the sound they make, he concluded that sound travels at a finite speed.
⁵
We will see that he also made good use of observation in reaching conclusions about the shape of the Earth
and about the cause of rainbows. But this was all casual observation of natural phenomena, not the creation of artificial circumstances for the purpose of experimentation.

The distinction between the natural and artificial played a large role in Aristotle’s thought about a problem of great importance in the history of science—the motion of falling bodies. Aristotle taught that solid bodies fall down because the natural place of the element earth is downward, toward the center of the cosmos, and sparks fly upward because the natural place of fire is in the heavens. The Earth is nearly a sphere, with its center at the center of the cosmos, because this allows the greatest proportion of earth to approach that center. Also, allowed to fall naturally, a falling body has a speed proportional to its weight. As we read in
On the Heavens
,
⁶
according to Aristotle, “A given weight moves a given distance in a given time; a weight which is as great and more moves the same distance in a less time, the times being in inverse proportion to the weights. For instance, if one weight is twice another, it will take half as long over a given movement.”

Aristotle can’t be accused of entirely ignoring the observation of falling bodies. Though he did not know the reason, the resistance of air or any other medium surrounding a falling body has the effect that the speed eventually approaches a constant value, the terminal velocity, which does increase with the falling body’s weight. (See
Technical Note 6
.) Probably more important to Aristotle, the observation that the speed of a falling body increases with its weight fitted in well with his notion that the body falls because the natural place of its material is toward the center of the world.

For Aristotle, the presence of air or some other medium was essential in understanding motion. He thought that without any resistance, bodies would move at infinite speed, an absurdity that led him to deny the possibility of empty space. In
Physics,
he argues, “Let us explain that there is no void existing separately, as some maintain.”
⁷
But in fact it is only the terminal velocity of a
falling body that is inversely proportional to the resistance. The terminal velocity would indeed be infinite in the absence of all resistance, but in that case a falling body would never reach terminal velocity.

In the same chapter Aristotle gives a more sophisticated argument, that in a void there would be nothing to which motion could be relative: “in the void things must be at rest; for there is no place to which things can move more or less than to another; since the void in so far as it is void admits no difference.”
⁸
But this is an argument against only an infinite void; otherwise motion in a void can be relative to whatever is outside the void.

Because Aristotle was acquainted with motion only in the presence of resistance, he believed that all motion has a cause.
*
(Aristotle distinguished four kinds of cause: material, formal, efficient, and final, of which the final cause is teleological—it is the purpose of the change.) That cause must itself be caused by something else, and so on, but the sequence of causes cannot go on forever. We read in
Physics
,
⁹
“Since everything that is in motion must be moved by something, let us take the case in which a thing is in locomotion and is moved by something that is itself in motion, and that again is moved by something else that is in motion, and that by something else, and so on continually; then the series cannot go on to infinity, but there must be some first mover.” The doctrine of a first mover later provided Christianity and Islam with an argument for the existence of God. But as we will see, in the Middle Ages the conclusion that God could not make a void raised troubles for followers of Aristotle in both Islam and Christianity.

Aristotle was not bothered by the fact that bodies do not always move toward their natural place. A stone held in the hand does not fall, but for Aristotle this just showed the effect of
artificial interference with the natural order. But he was seriously worried over the fact that a stone thrown upward continues for a while to rise, away from the Earth, even after it has left the hand. His explanation, really no explanation, was that the stone continues upward for a while because of the motion given to it by the air. In Book III of
On the Heavens
, he explains that “the force transmits the movement to the body by first, as it were, tying it up in the air. That is why a body moved by constraint continues to move even when that which gave it the impulse ceases to accompany it.”
¹⁰
As we will see, this notion was frequently discussed and rejected in ancient and medieval times.

Aristotle’s writing on falling bodies is typical at least of his physics—elaborate though non-mathematical reasoning based on assumed first principles, which are themselves based on only the most casual observation of nature, with no effort to test them.

I don’t mean to say that Aristotle’s philosophy was seen by his followers and successors as an alternative to science. There was no conception in the ancient or medieval world of science as something distinct from philosophy. Thinking about the natural world
was
philosophy. As late as the nineteenth century, when German universities instituted a doctoral degree for scholars of the arts and sciences to give them equal status with doctors of theology, law, and medicine, they invented the title “doctor of philosophy.” When philosophy had earlier been compared with some other way of thinking about nature, it was contrasted not with science, but with mathematics.

No one in the history of philosophy has been as influential as Aristotle. As we will see in
Chapter 9
, he was greatly admired by some Arab philosophers, even slavishly so by Averroes.
Chapter 10
tells how Aristotle became influential in Christian Europe in the 1200s, when his thought was reconciled with Christianity by Thomas Aquinas. In the high Middle Ages Aristotle was known simply as “The Philosopher,” and Averroes as “The Commentator.” After Aquinas the study of Aristotle became the center of university education. In the Prologue to Chaucer’s
Canterbury Tales
, we are introduced to an Oxford scholar:

A Clerk there was of Oxenford also . . .

For he would rather have at his bed’s head

Twenty books, clad in black or red,

Of Aristotle, and his philosophy,

Than robes rich, or fiddle, or gay psaltery.

Of course, things are different now. It was essential in the discovery of science to separate science from what is now called philosophy. There is active and interesting work on the philosophy
of
science, but it has very little effect on scientific research.