Science as natural philosophy

China

As has already been noted, astronomy seems everywhere to have been the first science to emerge. Its intimate relation to religion gave it a ritual dimension that then stimulated the growth of mathematics. Chinese savants, for example, early devised a calendar and methods of plotting the positions of stellar constellations. Since changes in the heavens presaged important changes on the Earth (for the Chinese considered the universe to be a vast organism in which all elements were connected), astronomy and astrology were incorporated into the system of government from the very dawn of the Chinese state in the 2nd millennium bce. As the Chinese bureaucracy developed, an accurate calendar became absolutely necessary to the maintenance of legitimacy and order. The result was a system of astronomical observations and records unparalleled elsewhere, thanks to which there are, today, star catalogs and observations of eclipses and novae that go back for millennia.

In other sciences too the overriding emphasis was on practicality, for the Chinese, almost alone among ancient peoples, did not fill the cosmos with gods and demons whose arbitrary wills determined events. Order was inherent and, therefore, expected. It was for humans to detect and describe this order and to profit from it. Chemistry (or, rather, alchemy), medicine, geology, geography, and technology were all encouraged by the state and flourished. Practical knowledge of a high order permitted the Chinese to deal with practical problems for centuries on a level not attained in the West until the Renaissance.

India

Astronomy was studied in India for calendrical purposes to set the times for both practical and religious tasks. Primary emphasis was placed on solar and lunar motions, the fixed stars serving as a background against which these luminaries moved. Indian mathematics seems to have been quite advanced, with particular sophistication in geometrical and algebraic techniques. This latter branch was undoubtedly stimulated by the flexibility of the Indian system of numeration that later was to come into the West as the Hindu-Arabic numerals.

America

Quite independently of China, India, and the other civilizations of Europe and Asia, the Maya of Central America, building upon older cultures, created a complex society in which astronomy and astrology played important roles. Determination of the calendar, again, had both practical and religious significance. Solar and lunar eclipses were important, as was the position of the bright planet Venus. No sophisticated mathematics are known to have been associated with this astronomy, but the Mayan calendar was both ingenious and the result of careful observation.

The Middle East

In the cradles of Western civilization in Egypt and Mesopotamia, there were two rather different situations. In Egypt there was an assumption of cosmic order guaranteed by a host of benevolent gods. Unlike China, whose rugged geography often produced disastrous floods, earthquakes, and violent storms that destroyed crops, Egypt was surpassingly placid and delightful. Egyptians found it difficult to believe that all ended with death. Enormous intellectual and physical labour, therefore, was devoted to preserving life after death. Both Egyptian theology and the pyramids are testaments to this preoccupation. All of the important questions were answered by religion, so the Egyptians did not concern themselves overmuch with speculations about the universe. The stars and the planets had astrological significance in that the major heavenly bodies were assumed to “rule” the land when they were in the ascendant (from the succession of these “rules” came the seven-day week, after the five planets and the Sun and the Moon), but astronomy was largely limited to the calendrical calculations necessary to predict the annual life-giving flood of the Nile. None of this required much mathematics, and there was, consequently, little of any importance.

Mesopotamia was more like China. The life of the land depended upon the two great rivers, the Tigris and the Euphrates, as that of China depended upon the Huang He (Yellow River) and the Yangtze (Chang Jiang). The land was harsh and made habitable only by extensive damming and irrigation works. Storms, insects, floods, and invaders made life insecure. To create a stable society required both great technological skill, for the creation of hydraulic works, and the ability to hold off the forces of disruption. These latter were early identified with powerful and arbitrary gods who dominated Mesopotamian theology. The cities of the plain were centred on temples run by a priestly caste whose functions included the planning of major public works, like canals, dams, and irrigation systems, the allocation of the resources of the city to its members, and the averting of a divine wrath that could wipe everything out.

Mathematics and astronomy thrived under these conditions. The number system, probably drawn from the system of weights and coinage, was based on 60 (it was in ancient Mesopotamia that the system of degrees, minutes, and seconds developed) and was adapted to a practical arithmetic. The heavens were the abode of the gods, and because heavenly phenomena were thought to presage terrestrial disasters, they were carefully observed and recorded. Out of these practices grew, first, a highly developed mathematics that went far beyond the requirements of daily business, and then, some centuries later, a descriptive astronomy that was the most sophisticated of the ancient world until the Greeks took it over and perfected it.

Nothing is known of the motives of these early mathematicians for carrying their studies beyond the calculations of volumes of dirt to be removed from canals and the provisions necessary for work parties. It may have been simply intellectual play—the role of playfulness in the history of science should not be underestimated—that led them onward to abstract algebra. There are texts from about 1700 bce that are remarkable for their mathematical suppleness. Babylonian mathematicians knew the Pythagorean relationship well and used it constantly. They could solve simple quadratic equations and could even solve problems in compound interest involving exponents. From about a millennium later there are texts that utilize these skills to provide a very elaborate mathematical description of astronomical phenomena.

Although China and Mesopotamia provide examples of exact observation and precise description of nature, what is missing is explanation in the scientific mode. The Chinese assumed a cosmic order that was vaguely founded on the balance of opposite forces (yin–yang) and the harmony of the five elements (water, wood, metal, fire, and earth). Why this harmony obtained was not discussed. Similarly, the Egyptians found the world harmonious because the gods willed it so. For Babylonians and other Mesopotamian cultures, order existed only so long as all-powerful and capricious gods supported it. In all these societies, humans could describe nature and use it, but to understand it was the function of religion and magic, not reason. It was the Greeks who first sought to go beyond description and to arrive at reasonable explanations of natural phenomena that did not involve the arbitrary will of the gods. Gods might still play a role, as indeed they did for centuries to come, but even the gods were subject to rational laws.