The so-called Arabic numerals used in most parts of the world today were developed in India. The Indian system of place-value notation was far more efficient than the unwieldy numerical systems of Egyptians, Greeks, and Romans, and the invention of zero was a profound intellectual achievement. Indeed, it has to be ranked as one of the most important and influential discoveries in human history. This system is used even more widely than the alphabet derived from the Phoenicians (see Chapter 4) and is, in one sense, the only truly global language.
In its fully developed form the Indian method of arithmetic notation employed a base-10 system. It had separate columns for ones, tens, hundreds, and so forth, as well as a zero sign to indicate the absence of units in a given column. This system makes possible the economical expression of even very large numbers. And it allows for the performance of calculations not possible in a system like the numerals of the Romans, where any real calculation had to be done mentally or on a counting board.
A series of early Indian inscriptions using the numerals from 1 to 9 are deeds of property given to religious institutions by kings or other wealthy individuals. They were incised in the Sanskrit language on copper plates (see below). The earliest known example has a date equivalent to 595 c. e. A sign for zero is attested by the eighth century. Other textual evidence leads to the inference that a place-value system and the zero concept were already known in the fifth century.
This Indian system spread to the Middle East, Southeast Asia, and East Asia by the seventh century. Other peoples quickly recognized its capabilities and adopted it, sometimes using indigenous symbols. Europe received the new technology somewhat later. Gerbert of Aurillac, a French Christian monk, spent time in Spain between 967 and 970, where he was exposed to the mathematics of the Arabs. A great scholar and teacher who eventually became Pope Sylvester II (r. 999-1003), he spread word of the “Arabic" system in the Christian West.
Knowledge of the Indian system of mathematical notation eventually spread throughout Europe, in part through the use of a mechanical calculating device—an improved version of the Roman counting board, with counters inscribed with variants of the Indian numeral forms. Because the counters could be turned sideways or upside down, at first there was considerable variation in the forms. But by the twelfth century they had become standardized into forms close to those in use today. As the capabilities of the place-value system for written calculations became clear, the counting board fell into disuse. The abandonment of this device led to the adoption of the zero sign—not necessary on the counting board, where a column could be left empty—by the twelfth century. Leonardo Fibonacci, a thirteenth-century C. E. Italian who learned algebra in Muslim North Africa and employed the Arabic numeral system in his mathematical treatise, gave additional impetus to the movement to discard the traditional system of Roman numerals.
Why was this marvelous system of mathematical notation invented in ancient India? The answer may lie in the way in which its range and versatility correspond to elements of Indian cosmology. The Indians conceived of immense spans of time—trillions of years (far exceeding current scientific estimates of the age of the universe as approximately 14 billion years old)—during which innumerable universes like our own were created, existed for a finite time, then were destroyed. In one popular creation myth, Vishnu is slumbering on the coils of a giant serpent at the bottom of the ocean, and worlds are being created and destroyed as he exhales and inhales. In Indian thought our world, like others, has existed for a series of epochs lasting more than 4 million years, yet the period of its existence is but a brief and insignificant moment in the vast sweep of time. The Indians developed a number system that allowed them to express concepts of this magnitude.
Copper Plate with Indian Numerals
This property deed from western India shows an early form of the symbol system for numbers that spread to the Middle East and Europe and that today is used all over the world. (Facsimile by Georges Ifrah. Reproduced by permission of Georges Ifrah.)
Wall Painting from the Caves at Ajanta, Fifth or Sixth Century c. e.
During and after the Gupta period, natural caves in the Deccan were turned into complexes of shrines decorated with sculpture and painting. This painting depicts one of the earlier lives of the Buddha, a king named Mahajanaka who lost and regained his kingdom, here listening to his queen, Sivali. While representing scenes from the earlier lives of the Buddha, the artists also give us a glimpse of life at the royal court in their own times. (Benoy K. Behl)
Scholastic arrangements in them are worthy of observation____The cities and towns of this country are the
Greatest of all in the Middle Kingdom. The inhabitants are rich and prosperous, and vie with one another in
The practice of benevolence and righteousness____The
Heads of the Vaishya families in them establish in the cities houses for dispensing charity and medicines. All the poor and destitute in the country, orphans, widowers, and childless men, maimed people and cripples, and all who are diseased, go to those houses, and are provided with every kind of help.3
Various kinds of evidence point to a decline in the status of women in this period (see Diversity and Dominance: Relations Between Women and Men in the Kama Sutra and the Arthashastra). In all likelihood, this was similar to developments in Mesopotamia from the second millennium b. c.e., in Archaic and Classical Greece, and in China from the first millennium b. c.e. In those civilizations, several factors—urbanization, the formation of increasingly complex political and social structures, and the emergence of a nonagricultural middle class that placed high value on the acquisition and inheritance of property—led to a loss of women’s rights and an increase in male control over women’s behavior.
Over time, women in India lost the right to own or inherit property. They were barred from studying sacred texts and participating in the sacrificial ritual. In many respects, they were treated as equivalent to the lowest class, the Shudra. As in Confucian China, a woman was expected to obey first her father, then her husband, and finally her sons (see Chapter 6). Indian girls were married at an increasingly early age, sometimes as young as six or seven. This practice meant that the prospective husband could be sure of his wife’s virginity and, by bringing her up in his own household, could train and shape her to suit his purposes. The most extreme form of control of women’s conduct took place in parts of India where a widow was expected to cremate herself on her husband’s funeral pyre. This ritual, called sati°, was seen as a way of keeping a woman “pure.” Women who declined to make this ultimate gesture of devotion were forbidden to remarry, shunned socially, and given little opportunity to earn a living.
Some women escaped these instruments of male control. One way to do so was by entering a Jainist or Buddhist religious community. Status also gave women more freedom. Women who belonged to powerful families and courtesans who were trained in poetry and music as well as in ways of providing sexual pleasure had high social standing and sometimes gave money for the erection of Buddhist stupas and other shrines.
Sati (suh-TEE)
World History
