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The first natural philosopher, according to Hellenic tradition, was Thales of Miletus, who flourished in the 6th century bce. We know of him only through later accounts, for nothing he wrote has survived. He is supposed to have predicted a solar eclipse in 585 bce and to have invented the formal study of geometry in his demonstration of the bisecting of a circle by its diameter. Most importantly, he tried to explain all observed natural phenomena in terms of the changes of a single substance, water, which can be seen to exist in solid, liquid, and gaseous states. What for Thales guaranteed the regularity and rationality of the world was the innate divinity in all things that directed them to their divinely appointed ends. From these ideas there emerged two characteristics of classical Greek science. The first was the view of the universe as an ordered structure (the Greek kósmos means “order”). The second was the conviction that this order was not that of a mechanical contrivance but that of an organism: all parts of the universe had purposes in the overall scheme of things, and objects moved naturally toward the ends they were fated to serve. This motion toward ends is called teleology and, with but few exceptions, it permeated Greek as well as much later science.

Thales inadvertently made one other fundamental contribution to the development of natural science. By naming a specific substance as the basic element of all matter, Thales opened himself to criticism, which was not long in coming. His own disciple, Anaximander, was quick to argue that water could not be the basic substance. His argument was simple: water, if it is anything, is essentially wet; nothing can be its own contradiction. Hence, if Thales were correct, the opposite of wet could not exist in a substance, and that would preclude all of the dry things that are observed in the world. Therefore, Thales was wrong. Here was the birth of the critical tradition that is fundamental to the advance of science.

Thales’ conjectures set off an intellectual explosion, most of which was devoted to increasingly refined criticisms of his doctrine of fundamental matter. Various single substances were proposed and then rejected, ultimately in favour of a multiplicity of elements that could account for such opposite qualities as wet and dry, hot and cold. Two centuries after Thales, most natural philosophers accepted a doctrine of four elements: earth (cold and dry), fire (hot and dry), water (cold and wet), and air (hot and wet). All bodies were made from these four.

The presence of the elements only guaranteed the presence of their qualities in various proportions. What was not accounted for was the form these elements took, which served to differentiate natural objects from one another. The problem of form was first attacked systematically by the philosopher and cult leader Pythagoras in the 6th century bce. Legend has it that Pythagoras became convinced of the primacy of number when he realized that the musical notes produced by a monochord were in simple ratio to the length of the string. Qualities (tones) were reduced to quantities (numbers in integral ratios). Thus was born mathematical physics, for this discovery provided the essential bridge between the world of physical experience and that of numerical relationships. Number provided the answer to the question of the origin of forms and qualities. Aristotle and Archimedes

Hellenic science was built upon the foundations laid by Thales and Pythagoras. It reached its zenith in the works of Aristotle and Archimedes. Aristotle represents the first tradition, that of qualitative forms and teleology. He was himself a biologist whose observations of marine organisms were unsurpassed until the 19th century. Biology is essentially teleological—the parts of a living organism are understood in terms of what they do in and for the organism—and Aristotle’s biological works provided the framework for the science until the time of Charles Darwin. In physics, teleology is not so obvious, and Aristotle had to impose it on the cosmos. From Plato, his teacher, he inherited the theological proposition that the heavenly bodies (stars and planets) are literally divine and, as such, perfect. They could, therefore, move only in perfect, eternal, unchanging motion, which, by Plato’s definition, meant perfect circles. The Earth, being obviously not divine, and inert, was at the centre. From the Earth to the sphere of the Moon, all things constantly changed, generating new forms and then decaying back into formlessness. Above the Moon the cosmos consisted of contiguous and concentric crystalline spheres moving on axes set at angles to one another (this accounted for the peculiar motions of the planets) and deriving their motion either from a fifth element that moved naturally in circles or from heavenly souls resident in the celestial bodies. The ultimate cause of all motion was a prime, or unmoved, mover (God) that stood outside the cosmos.

Aristotle was able to make a great deal of sense of observed nature by asking of any object or process: what is the material involved, what is its form and how did it get that form, and, most important of all, what is its purpose? What should be noted is that, for Aristotle, all activity that occurred spontaneously was natural. Hence, the proper means of investigation was observation. Experiment, that is, altering natural conditions in order to throw light on the hidden properties and activities of objects, was unnatural and could not, therefore, be expected to reveal the essence of things. Experiment was thus not essential to Greek science.

The problem of purpose did not arise in the areas in which Archimedes made his most important contributions. He was, first of all, a brilliant mathematician whose work on conic sections and on the area of the circle prepared the way for the later invention of the calculus. It was in mathematical physics, however, that he made his greatest contributions to science. His mathematical demonstration of the law of the lever was as exact as a Euclidean proof in geometry. Similarly, his work on hydrostatics introduced and developed the method whereby physical characteristics, in this case specific gravity, which Archimedes discovered, are given mathematical shape and then manipulated by mathematical methods to yield mathematical conclusions that can be translated back into physical terms.

In one major area the Aristotelian and the Archimedean approaches were forced into a rather inconvenient marriage. Astronomy was the dominant physical science throughout antiquity, but it had never been successfully reduced to a coherent system. The Platonic-Aristotelian astral religion required that planetary orbits be circles. But, particularly after the conquests of Alexander the Great had made the observations and mathematical methods of the Babylonians available to the Greeks, astronomers found it impossible to reconcile theory and observation. Astronomy then split into two parts: one was physical and accepted Aristotelian theory in accounting for heavenly motion, and the other ignored causation and concentrated solely on the creation of a mathematical model that could be used for computing planetary positions. Ptolemy, in the 2nd century ce, carried the latter tradition to its highest point in antiquity in his Hē mathēmatikē syntaxis (“The Mathematical Collection,” better known under its Greek-Arabic title, Almagest).