THE BIRTH OF SCIENCE
NATURAL SCIENCE IN THE WEST was born in Greece approximately five centuries before the birth of Christ. It was conceived by the coming together of two great ideas. The first was that reason could be systematically employed to enlarge our understanding of reality. In this regard, one might say that the Greeks invented “theory.” For instance, while literature is as old as writing, and politics as old as man, political theory and literary theory began with the Greeks. So too did the study of logic and the axiomatic development of mathematics. One of the earliest Greek philosophers, Heraclitus (540–480 B.C.), taught that the world was in constant flux, but that underlying all change is Reason, or Logos.
The second great idea was that events in the physical world can be given natural—as opposed to supernatural, or exclusively divine—explanations. The pioneer of this approach was Thales of Miletus (625–546 B.C.), who is said to have explained earthquakes by positing that the earth floated on water. He is most famous for speculating that water is the fundamental principle from which all things come. Thales was thus perhaps the first thinker to seek for the basic elements (or in his case, element) out of which everything is made. Others proposed different elements, and eventually the list grew to four: fire, water, earth, and air.
The search for the truly fundamental or “elementary” constituents of the world has continued to this day. In 1869, Mendeleev published his periodic table of chemical elements (which at that point numbered sixty-three). Later, the atoms identified by chemists were found to be composed of subatomic particles, which are now studied in the branch of science known as elementary particle physics. Today it is suspected that these particles are not truly elementary but are themselves manifestations of “superstrings.” If this present speculation proves to be correct, it will vindicate Thales’ intuition that there is but a single truly fundamental “stuff” of nature. In fact, as we shall see, this dream of theoretical unification and simplification has been progressively realized with each of the great advances of modern science.
The idea of “atoms” was the most remarkable and prescient of all the ancient Greek scientific ideas. It was proposed first by Leucippus (fifth century B.C.) and Democritus of Abdera (c. 460–370 B.C.). The Nobel laureate Richard Feynman, in his great Lectures on Physics, wrote,
If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence were to be passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis . . . that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.1
Of course, the rudimentary version of atomism proposed by Leucippus and Democritus was not a scientific theory in our modern sense. It could not be tested, and it led to no research program, but rather remained, as did most of Greek natural science, at the level of philosophical speculation.
ARCHIMEDES (c. 287–212 B.C.), one of the great figures of mathematical history, was born in Syracuse, Sicily. He discovered ways of computing the areas and volumes of curved figures, methods that were further developed by Torricelli, Cavalieri, Newton, and Leibniz in the seventeenth century in order to create the field of integral calculus. Unlike most Greek mathematicians of antiquity, Archimedes was deeply interested in physical problems. He was the first to understand the concept of “center of gravity.” He also founded the field of hydrostatics, discovering that a floating body will displace its own weight of fluid, while a submerged body will displace its own volume. He used the latter principle to solve a problem given to him by King Hiero of Syracuse, namely, to determine (without melting it down) whether a certain crown was made from pure or adulterated gold. Hitting upon the solution while in the public baths, he ran naked through the streets shouting “Eureka!” (“I have found it!”), the eternal cry of the scientific discoverer.
Archimedes was also the discoverer of the principle of the lever, boasting, “Give me a place to stand and I will move the earth.” Legend has it that he helped defend Syracuse from a Roman siege during the Second Punic War by inventing fantastic and ingenious weapons, such as the “claw of Archimedes,” and huge focusing mirrors to ignite ships. According to Plutarch, “[Archimedes] being perpetually charmed by his familiar siren, that is, by his geometry, neglected to eat and drink and took no care of his person; . . . [he] was often carried by force to the baths, and when there would trace geometrical figures in the ashes of the fire, and with his fingers draw lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science.” During the siege of Syracuse, in spite of standing orders from the Roman general that the great geometer not be harmed, Archimedes was struck down by a Roman soldier while drawing geometrical diagrams in the sand. His last words were, “Don’t disturb my circles.”
The beginning stage of any branch of science involves simple observation and classification. Not surprisingly, much of Greek natural science consisted of this kind of activity. At times it was more ambitious and sought for causes and principles, but these principles were for the most part philosophical. In other words, they were not formulated into scientific laws in the modern sense. One thinks of Aristotle’s principle that “nothing moves unless it is moved by another.” This was meant as a general statement about cause and effect. It did not allow one to predict anything, let alone to make calculations.
It is interesting that the Greeks, for all their tremendous achievements in mathematics, did not go far in applying mathematics to their study of the physical world—astronomy being the major exception. This should not surprise us. It is perhaps obvious that the world is an orderly place, as opposed to being mere chaos; but the fact that its orderliness is mathematical is very far from being obvious, at least if one looks at things and events on the earth, where there is a great deal of irregularity and haphazardness. The first person to conceive the idea that mathematics is fundamental to understanding physical reality—rather than pertaining only to some ideal realm—was Pythagoras (c. 569–c. 475 B.C.). This insight was perhaps suggested to him by his research in music, where he discovered that harmonious tones are produced by strings whose lengths are in simple arithmetical ratios to each other. In any event, Pythagoras and his followers arrived at the idea that reality at its deepest level is mathematical. Indeed, Aristotle attributed to the Pythagoreans the idea that “things are numbers.” This assertion may seem extreme, and doubtless did to Aristotle, but to the modern physicist it appears both profound and prophetic.
It is in the motions of the heavenly bodies that the mathematical orderliness of the universe is most apparent. This has to do with a number of circumstances. First, interplanetary space is nearly a vacuum, which means that the movements of the solar system’s various bodies are unimpeded by friction. Second, the mutual gravitation of the planets is small compared to their attraction to the sun, a fact that greatly simplifies their motion. In other words, in the solar system nature has provided us with a dynamical system that is relatively simple to analyze. This was vital for the emergence of science. In empirical science it is important to be able to isolate specific causes and effects so that they are not obscured or disrupted by extraneous and irrelevant factors. This normally has to be done by conducting “controlled” experiments (experiments, for instance, that allow one to compare two systems that differ in only one respect). Usually, it is only in this way that one gets a chance to observe interesting and significant patterns in the data. But it did not occur to the ancient Greeks to perform controlled experiments—or, for the most part, experiments of any kind. It is therefore very fortunate that they had the solar system to observe.
The first application of geometry to astronomy seems to have been inspired by Pythagorean ideals. Pythagoras himself suggested that the earth is a perfect sphere. Later, Eudoxus (c. 408–c. 355 B.C.) proposed a model in which the apparently complex movements of the heavenly bodies resulted from their motion in perfectly circular paths. These Pythagorean principles—that theories should be mathematically beautiful and that they should explain complex effects in terms of simple causes—have been tremendously fruitful in the history of science. But they are not sufficient. The mathematical approach of these earlier astronomers lacked a key ingredient, namely the making of precise measurements and the basing of one’s theories upon those measurements. In this respect Hipparchus (C. 190–C. 120 B.C.) far exceeded his predecessors and transformed astronomy into a quantitative and predictive science. He made remarkably accurate determinations of such quantities as the distance of the moon from the earth and the rate at which the earth’s axis precesses (the so-called precession of the equinox, a phenomenon that he discovered). After Hipparchus, the development of ancient Greek astronomy reached its culmination in the work of Ptolemy (c. 85–c. 165), whose intricate geocentric model of the solar system was to be generally accepted for the next fifteen centuries.
The Greeks’ attraction to mathematics was a double-edged sword. On the one hand, it had incalculable benefits for science. The Greeks’ most enduring scientific legacy lay in their mathematics and mathematical astronomy. On the other hand, this attraction to mathematics reflected a tendency (seen very markedly in Plato) to disdain the world of phenomena for a more exclusive focus on the realm of the ideal.
We find quite the opposite tendency in Aristotle. Aristotle was very much interested in phenomena of every kind, and (in contrast to many of his later epigones) engaged in extensive empirical investigations, especially in biology. He was undoubtedly one of the greatest biologists of the ancient world. His legacy in physics, however, is more ambiguous—indeed, on the whole, perhaps negative. There are several reasons for his comparative failure as a physicist. First, there is the fact, already remarked on, that terrestrial phenomena are hard to sort out. Among many other complications, they involve large frictional forces, which resulted in Aristotle being fundamentally misled about the relationship between force and motion. Second, Aristotle appreciated neither the true nature of mathematics nor its profound importance; his genius lay elsewhere. Third, Aristotle’s approach to the physical sciences was philosophical; in his thought there is no bright line between physical and metaphysical concepts. This would not have created so many problems for later thought—problems discussed in more detail below—had it not been for the very brilliance and depth of Aristotelian philosophy.
HIPPARCHUS (c. 190–120 B.C.) is considered the greatest observational astronomer of antiquity. Little is known of his life except that he was born in Nicaea, located in present-day Turkey, and spent most of his life on the island of Rhodes. What distinguished him from his predecessors was his application of precise measurements to geometrical models of astronomy. Not only did he make extensive measurements; he also made use of the voluminous astronomical records of the Babylonians, which dated back to the eighth century B.C. This long span of data allowed him to compute certain quantities with unprecedented accuracy.
Hipparchus created the first trigonometric tables, which greatly facilitated astronomical calculations, and developed or improved devices for astronomical observation. He also compiled the first star catalogue, which gave the positions of about one thousand stars. Though he worked on many problems, such as determining the distance to the moon, he is most famous for discovering the “precession of the equinox” and correctly attributing it to a wobbling of the earth’s axis of rotation. Newton later showed that this wobbling was caused by the gravitational torque exerted by the sun and moon on the earth’s equatorial bulge.