by Isaac Asimov
Seduced by the success of the axioms in developing a system of geometry, the Greeks came to think of the axioms as “absolute truths” and to suppose that other branches of knowledge could be developed from similar “absolute truths.” Thus in astronomy they eventually took as self-evident axioms the notions that (l) the earth was motionless and the center of the universe, and (2) whereas the earth was corrupt and imperfect, the heavens were eternal, changeless, and perfect. Since the Greeks considered the circle the perfect curve, and since the heavens were perfect, it followed that all the heavenly bodies must move in circles around the earth. In time, their observations (arising from navigation and calendar making) showed that the planets do not move in perfectly simple circles, and so the Greeks were forced to allow planets to move in ever more complicated combinations of circles, which, about 150 A.D., were formulated as an uncomfortably complex system by Claudius Ptolemaeus (Ptolemy) at Alexandria. Similarly, Aristotle worked up fanciful theories of motion from “self-evident” axioms, such as the proposition that the speed of an object’s fall was proportional to its weight. (Anyone could see that a stone fell faster than a feather.)
Now this worship of deduction from self-evident axioms was bound to wind up at the edge of a precipice, with no place to go. After the Greeks had worked out all the implications of the axioms, further important discoveries in mathematics or astronomy seemed out of the question. Philosophic knowledge appeared complete and perfect; and for nearly 2,000 years after the Golden Age of Greece, when questions involving the material universe arose, there was a tendency to settle matters to the satisfaction of all by saying, “Aristotle says…” or, “Euclid says…”
THE RENAISSANCE AND COPERNICUS
Having solved the problems of mathematics and astronomy, the Greeks turned to more subtle and challenging fields of knowledge, One was the human soul.
Plato was far more interested in such questions as What is justice? or, What is virtue? than in why rain falls or how the planets move, As the supreme moral philosopher of Greece, he superseded Aristotle, the supreme natural philosopher. The Greek thinkers of the Roman period found themselves drawn more and more to the subtle delights of moral philosophy and away from the apparent sterility of natural philosophy, The last development in ancient philosophy was an exceedingly mystical “neo-Platonism” formulated by Plotinus about 250 A.D.
Christianity, with its emphasis on the nature of God and His relation to man, introduced an entirely new dimension into the subject matter of moral philosophy that increased its apparent superiority as an intellectual pursuit over natural philosophy. From 200 A.D, to 1200 A.D., Europeans concerned themselves almost exclusively with moral philosophy, in particular with theology. Natural philosophy was nearly forgotten.
The Arabs, however, managed to preserve Aristotle and Ptolemy through the Middle Ages; and, from them, Greek natural philosophy eventually filtered hack to Western Europe. By 1200, Aristotle had been rediscovered. Further infusions came from the dying Byzantine empire, which was the last area in Europe to maintain a continuous cultural tradition from the great days of Greece.
The first and most natural consequence of the rediscovery of Aristotle was the application of his system of logic and reason to theology, About 1250, the Italian theologian Thomas Aquinas established the system called “Thomism,” based on Aristotelian principles, which still represents the basic theology of the Roman Catholic Church. But Europeans soon began to apply the revival uf Greek thought to secular fields as well,
Because the leaders of the Renaissance shifted emphasis from matters concerning God to the works of humanity, they were called “humanists,” and the study of literature, art, and history is still referred to as the “humanities.”
To the Greek natural philosophy, the Renaissance thinkers brought a fresh outlook, for the old views no longer entirely satisfied. In 1543, the Polish astronomer Nicolaus Copernicus published a book that went so far as to reject a basic axiom of astronomy: he proposed that the sun, not the earth, be considered the center of the universe, (He retained the notion of circular orbits for the earth and other planets, however.) This new axiom allowed a much simpler explanation of the observed motions of heavenly bodies, Yet the Copernican axiom of a moving earth was far less “self-evident” than the Greek axiom of a motionless earth, and so it is not surprising that it took more than half a century for the Copernican theory to be accepted.
In a sense, the Copernican system itself was not a crucial change, Copernicus had merely switched axioms; and Aristarchus of Samos had already anticipated this switch to the sun as the center 2,000 years earlier. I do not mean to say that the changing of an axiom is a minor matter. When mathematicians of the nineteenth century challenged Euclid’s axioms and developed “non-Euclidean geometries” based on other assumptions, they influenced thought on many matters in a most profound way: today the very history and form of the universe are thought to conform to a non-Euclidean geometry rather than the “commonsense” geometry of Euclid. But the revolution initiated by Copernicus entailed not just a shift in axioms but eventually involved a whole new approach to nature, This revolution was carried through in the person of the Italian Galileo Galilei toward the end of the sixteenth century.
EXPERIMENTATION AND INDUCTION
The Greeks, by and large, had been satisfied to accept the “obvious” facts of nature as starting points for their reasoning. It is not on record that Aristotle ever dropped two stones of different weight to test his assumption that the speed of fall is proportional to an object’s weight. To the Greeks, experimentation seemed irrelevant. It interfered with and detracted from the beauty of pure deduction. Besides, if an experiment disagreed with a deduction, could one be certain that the experiment was correct? Was it likely that the imperfect world of reality would agree completely with the perfect world of abstract ideas; and if it did not, ought one to adjust the perfect to the demands of the imperfect? To test a perfect theory with imperfect instruments did not impress the Greek philosophers as a valid way to gain knowledge.
Experimentation began to become philosophically respectable in Europe with the support of such philosophers as Roger Bacon (a contemporary of Thomas Aquinas) and his later namesake Francis Bacon. But it was Galileo who overthrew the Greek view and effected the revolution. He was a convincing logician and a genius as a publicist. He described his experiments and his point of view so clearly and so dramatically that he won over the European learned community. And they accepted his methods along with his results.
According to the best-known story about him, Galileo tested Aristotle’s theories of falling bodies by asking the question of nature in such a way that all Europe could hear the answer. He is supposed to have climbed to the top of the Leaning Tower of Pisa and dropped a 10-pound sphere and a l-pound sphere simultaneously; the thump of the two balls hitting the ground in the same split second killed Aristotelian physics.
Actually Galileo probably did not perform this particular experiment, but the story is so typical of his dramatic methods that it is no wonder it has been widely believed through the centuries.
Galileo undeniably did roll balls down inclined planes and measured the distance that they traveled in given times. He was the first to conduct time experiments and to use measurement in a systematic way.
His revolution consisted in elevating “induction” above deduction as the logical method of science. Instead of building conclusions on an assumed set of generalizations, the inductive method starts with observations and derives generalizations (axioms, if you will) from them. Of course, even the Greeks obtained their axioms from observation; Euclid’s axiom that a straight line is the shortest distance between two points was an intuitive judgment based on experience. But whereas the Greek philosopher minimized the role played by induction, the modern scientist looks on induction as the essential process of gaining knowledge, the only way of justifying generalizations. Moreover, the scientist realizes that no generalization can be allowed to s
tand unless it is repeatedly tested by newer and still newer experiments—the continuing test of further induction.
The present general viewpoint is just the reverse of the Greeks. Far from considering the real world an imperfect representation of ideal truth, we consider generalizations to be only imperfect representatives of the real world. No amount of inductive testing can render a generalization completely and absolutely valid. Even though billions of observations tend to bear out a generalization, a single observation that contradicts or is inconsistent with it must force its modification. And no matter how many times a theory meets its tests successfully, there can be no certainty that it will not be overthrown by the next observation.
This, then, is a cornerstone of modern natural philosophy. It makes no claim of attaining ultimate truth. In fact, the phrase “ultimate truth” becomes meaningless, because there is no way in which enough observations can be made to make truth certain and, therefore, “ultimate.” The Greek philosophers recognized no such limitation. Moreover, they saw no difficulty in applying exactly the same method of reasoning to the question What is justice? as to the question What is matter? Modern science, on the other hand, makes a sharp distinction between the two types of question. The inductive method cannot make generalizations about what it cannot observe; and, since the nature of the human soul, for example, is not observable by any direct means yet known, this subject lies outside the realm of the inductive method.
The victory of modern science did not become complete until it established one more essential principle—namely, free and cooperative communication among all scientists. Although this necessity seems obvious now, it was not obvious to the philosophers of ancient and medieval times. The Pythagoreans of ancient Greece were a secret society who kept their mathematical discover ies to themselves. The alchemists of the Middle Ages deliberately obscured their writings to keep their so-called findings within as small an inner circle as possible. In the sixteenth century, the Italian mathematician Niccolo Tartaglia, who discovered a method of solving cubic equations, saw nothing wrong in attempting to keep it a secret. When Geronimo Cardano, a fellow mathematician, wormed the secret out of Tartaglia on the promise of confidentiality and published it, Tartaglia naturally was outraged; but aside from Cardano’s trickery in breaking his promise, he was certainly correct in his reply that such a discovery had to be published. Nowadays no scientific discovery is reckoned a discovery if it is kept secret. The English chemist Robert Boyle, a century after Tartaglia and Cardano, stressed the importance of publishing all scientific observations in full detail. A new observation or discovery, moreover, is no longer considered valid, even after publication, until at least one other investigator has repeated the observation and “confirmed” it. Science is the product not of individuals but of a “scientific community.”
One of the first groups (and certainly the most famous) to represent such a scientific community was the Royal Society of London for Improving Natural Knowledge, usually called simply the “Royal Society.” It grew out of Informal meetings, beginning about 1645, of a group of gentlemen interested in the new scientific methods originated by Galileo. In 1660, the society was formally chartered by King Charles II.
The members of the Royal Society met and discussed their findings openly, wrote letters describing them in English rather than Latin, and pursued their experiments with vigor and vivacity. Nevertheless, through most of the seventeenth century, they remained in a defensive position. The attitude of many of their learned contemporaries might be expressed by a cartoon, after the modern fashion, showing the lofty shades of Pythagoras, Euclid, and Aristotle staring down haughtily at children playing with marbles and labeled “Royal Society.”
All this was changed by the work of Isaac Newton, who became a member of the society. From the observations and conclusions of Galileo, of the Danish astronomer Tycho Brahe, and of the German astronomer Johannes Kepler, who figured out the elliptical nature of the orbits of the planets, Newton arrived by induction at his three simple laws of motion and his great fundamental generalization—the law of universal gravitation. (Nevertheless, when he published his findings, he used geometry and the Greek method of deductive explanation.) The educated world was so impressed with this discovery that Newton was idolized, almost deified, in his own lifetime. This majestic new universe, built upon a few simple assumptions derived from inductive processes, now made the Greek philosophers look like boys playing with marbles. The revolution that Galileo had initiated at the beginning of the seventeenth century was triumphantly completed by Newton at the century’s end.
MODERN SCIENCE
It would be pleasant to be able to say that science and human beings have lived happily ever since. But the truth is that the real difficulties of both were only beginning. As long as science remained deductive, natural philosophy could be part of the general culture of all educated men (women, alas, being rarely educated until recent times). But inductive science became an immense labor—of observation, learning, and analysis. It was no longer a game for amateurs. And the complexity of science grew with each decade. During the century after Newton, it was still possible for a man of unusual attainments to master all fields of scientific knowledge. But, by 1800, this had become entirely impracticable. As time went on, it was increasingly necessary for a scientist to limit himself to a portion of the field with which he was intensively concerned. Specialization was forced on science by its own inexorable growth. And with each generation of scientists, specialization has grown more and more intense.
The publications of scientists concerning their individual work have never been so copious—and so unreadable for anyone but their fellow specialists. This has been a great handicap to science itself, for basic advances in scientific knowledge often spring from the cross-fertilization of knowledge from differ ent specialties. Even more ominous, science has increasingly lost touch with nonscientists. Under such circumstances, scientists come to be regarded al most as magicians—feared rather than admired. And the impression that science is incomprehensible magic, to be understood only by a chosen few who are suspiciously different from ordinary mankind, is bound to turn many youngsters away from science.
Since the Second World War, strong feelings of outright hostility toward science were to be found among the young—even among the educated young in the colleges. Our industrialized society is based on the scientific discoveries of the last two centuries, and our society finds it is plagued by undesirable side effects of its very success.
Improved medical techniques have brought about a runaway increase in population; chemical industries and the internal-combustion engine arc fouling our water and our air; the demand for materials and for energy is depleting and destroying the earth’s crust. And this is all too easily blamed on “science” and “scientists” by those who do not quite understand that while knowledge can create problems, it is not through ignorance that we can solve them. Yet modern science need not be so complete a mystery to nonscientists. Much could be accomplished toward bridging the gap if scientists accepted the responsibility of communication—explaining their own fields of work as simply and to as many as possible—and if nonscientists, for their part, accepted the responsibility of listening. To gain a satisfactory appreciation of the developments in a field of science, it is not essential to have a total understand ing of the science. After all, no one feels that one must be capable of writing a great work of literature in order to appreciate Shakespeare. To listen to a Beethoven symphony with pleasure does not require the listener to be capable of composing an equivalent symphony. By the same token, one can appreciate and take pleasure in the achievements of science even though one does not oneself have a bent for creative work in science.
But what, you may ask, would be accomplished? The first answer is that no one can really feel at home in the modern world and judge the nature of its problems—and the possible solutions to those problems—unless one has some intelligent notion of what science is up to.
Furthermore, initiation into the magnificent world of science brings great esthetic satisfaction, inspiration to youth, fulfillment of the desire to know, and a deeper appreciation of the wonderful potentialities and achievements of the human mind.
It is to provide such initiation that I have undertaken to write this book.
PART I
The Physical Sciences
Chapter 2
* * *
The Universe
The Size of the Universe
There is nothing about the sky that makes it look particularly distant to a casual observer. Young children have no great trouble in accepting the fantasy that “the cow jumped over the moon”—or “he jumped so high, he touched the sky.” The ancient Greeks, in their myth telling stage, saw nothing ludicrous in allowing the sky to rest on the shoulders of Atlas, Of course, Atlas might have been astronomically tall, but another myth suggests otherwise, Atlas was enlisted by Hercules to help him with the eleventh of his famous twelve labors—fetching the golden apples (oranges) of the Hesperides (“the far west”—Spain?), While Atlas went off to fetch the apples, Hercules stood on a mountain and held up the sky, Granted that Hercules was a large specimen, he was nevertheless not a giant. It follows then that the early Greeks took quite calmly to the notion that the sky cleared the mountaintops by only a few feet
