The Calendar (22 page)

As long as time reckoners used the Latin system--or Greek, Egyptian or any other numerical system that lacked precise fractions they were forced to conclude that it was impossible to calculate a true year. This powerfully reinforced the belief in the Middle Ages that if such a number existed, it was known only to God, when in truth the number was simply beyond the capability of the symbols and numerical system in use at the time--and continued to be until the thirteenth and fourteenth centuries, when Europeans began broadly adopting the earliest versions of the modern decimal system.

The idea of using decimal fractions came to Europe from the Arabs, though they were not the first to use positional notation to write out and determine fractions. Again this distinction seems to belong to the Mesopotamians, who over the millennia figured out a fraction system based on their own positional notation scheme which gave them a precision and computing power far beyond that of any other system until the European Renaissance. But because Mesopotamia’s system was based on 60 and not on a more manageable number such as 10, their remarkable discovery was limited by the complexity of carving into clay and stone place-values in negative powers of 60, which not only are indivisible for some fractions but also quickly become long and complicated symbols to write out. For instance, the length of the year in cuneiform numerals is:

The Chinese by the third century AD had also discovered how to write fractions using their positional notation, and did so using our familiar base-10 system. But their discovery does not seem to have travelled beyond the Far East. As for the Indians, for some reason they did not develop decimal fractions, despite having base-10 positional notation for whole numbers. Instead they devised an early version of placing one number over another to represent fractions--a numerator over a denominator--that was apparently borrowed from Greek mathematicians in Alexandria, with one difference: they placed the denominator over the numerator. The bar line was introduced later by Arab mathematicians.

Of course, the vast majority of people in ancient times had little use for fractions beyond the most simple divisions of a whole. Only a handful of mathematicians and astronomers cared to be more precise--and even they tended to simply round off numbers either to the closest simple fraction or to the nearest whole. This is undoubtedly why early astronomers, from Hipparchus and Ptolemy to Aryabhata, were able to note that the 365 1/4-day year was wrong, but seemed willing to accept this rounded-off number as tolerable enough that none called for a correction, or for reforms in the official calendar.

When Aryabhata wrote his
Aryabhatiya
in 499, at the precocious age of 23, Gupta culture and learning remained at a high point. But even as he pondered pi and the position of planets, a dark cloud was fast engulfing the empire: the Huns. This eastern branch of the scourge that had hastened the crash of Rome had for years been hammering away mercilessly against the Gupta frontier to the northwest.

By the time the
Aryabhatiya
appeared, the Huns had broken through the Guptas’ main defensive lines to devastate parts of northwestern India. But unlike Rome, the Guptas, with help from the Chinese in the north, had weakened the military strength of the hordes over the years to the point that the invaders were unable to thoroughly conquer the Indians or destroy their culture. During the middle third of Aryabhata’s life the Huns set up a shaky kingdom that ruled from modern Afghanistan to central India, never reaching Kusumapura. Aryabhata lived long enough to see a coalition of Indian kings and warlords drive them back into Kashmir in 542, when he was 66 years old. He also had lived long enough to see the golden age of Gupta culture slowly eroded, even if the continuity of Indian culture was preserved.

As the political situation worsened, the spirit of open inquiry and free thinking that had thrived earlier was squelched by a turn to conservative Vedic values. This apparently got Aryabhata into some trouble with his more controversial theories, particularly his supposed hint that the earth might circle the sun. At least this seems to be the case given the vigour with which later Indian scholars, perhaps anxious to conform to the more rigid orthodoxy of the day, dismiss this theory less on academic than religious grounds.

How Aryabhata responded to his critics is unknown. But we have a clue to his true feelings, and his willingness to express them, in a short passage at the end of the
Aryabhatiya.
It reads like something Roger Bacon would have written as a fevered defence of science. ‘He who disparages this universally true science of astronomy,’ says Aryabhata, ‘which ... is now described by me in this
Aryabhatiya
, loses his good deeds and his long life.’

But unlike Bacon, Aryabhata was revered by scholars and laymen alike, during and after his lifetime. Every great Indian mathematician and astronomer who came after him used the
Aryabhatiya
as the basis for their work and acknowledged his contributions. This includes Varahamihira (505-587), a contemporary of the elderly Aryabhata* who wrote an encyclopaedia that cites the master of Kusumapura, but emphasizes astrology over astronomy--a choice Aryabhata would have rejected as unscientific.

*There may have been two Aryabhatas working at roughly the same time. Aryabhata the Elder and Aryabhata the Younger.

The great mathematician Brahmagupta (598-665) also held Aryabhata in high esteem, incorporating some of the earlier master’s works into his own--and unfortunately editing them and adding his comments to the point that it is hard to tell what belongs to Aryabhata and what to Brahmagupta, since the originals Brahmagupta worked from have been lost. Brahmagupta’s reverence did not extend to Aryabhata’s controversial ideas. Nor did it stop him from offering corrections in his
Brahinasphuta-siddhatita,
written around 628, to what he considered his predecessor’s mistakes on matters ranging from the altitude of the sun’s ecliptic to Aryabhata’s measurement of the diameter of the earth.

Aryabhata’s impact was so profound in his homeland, that in 1975 modern India honoured this ancient genius by launching a scientific satellite named the
Aryabhata
on an Indian Intercosmos rocket. Unlike the ideas of its namesake, the satellite failed after only four days and came crashing back into the atmosphere on 11 February 1992.

After Brahmagupta, India continued to produce noted mathematicians, including Bhaskara (1114-1185), considered by mathematicians to be the most brilliant in his field anywhere during the twelfth century. But he was the last true standout in medieval India.*

*In 1887 another mathematics genius was born in India, Srinivasa Ramanujan, who tragically died at the age of 33. His natural fluency and intuition with numbers has been compared to the free-ranging and eclectic style of thinking of Aryabhata and other earlier Hindu mathematicians.

All of these men contributed mightily to the evolution of concepts that three centuries after Aryabhata’s death would continue their journey to the West via a people that in Aryabhata’s era were primitives barely known to the great civilizations of the day. Living on a vast desert to the south of the empires of Persia and Byzantium, they began stirring to life only in the final years of Brahmagupta’s life, then suddenly they burst out of their desert peninsula to begin the conquest of much of the Near East and southern and central Asia. In the process they discovered and then embraced the ancient knowledge of India, Greece and Mesopotamia, creating an unlikely amassing of ideas drawn together in what became the early medieval era’s greatest centre of learning: Baghdad.

9 From the House of Wisdom to Darkest Europe

It was He that gave the sun his brightness and the moon her light, ordaining her phases that you may learn to compute the seasons and the years. God created them only to manifest the Truth. He makes plain his revelations to men of knowledge.
The Koran, c. AD 630

In 773, some 250 years after Aryabhata’s death, a delegation of diplomats from the lower Indus River Valley arrived in the new Arab capital of Baghdad. Dressed in brightly coloured silks, turbans and glittering gems, this group probably travelled by sea from the Indus delta around the desert coast of modern-day Iran and up the turquoise waters of the Persian Gulf to the port city of Abadan--some 30 miles inland now because of silt built up over the centuries. They would then have sailed up the Tigris about 200 miles to Baghdad, passing by the hot, dry banks lined with tiers of ancient, irrigated terraces and stone cities dating back to the time of Sumer and Ur, arriving at last outside the gates of al-Mansur’s magnificent city. Half a century after the Arabs had conquered the lower Indus River Valley, in 711, this delegation was one of many dispatched by local Indian authorities to the court of Caliph al-Mansur to provide him with news about their province, and to settle outstanding disputes. They also hoped to impress the great caliph, the founder of the Abbasid dynasty, with the richness and sophistication of their country by showering him with gifts--perhaps a gem-encrusted suit of armour, a flute carved out of ivory, a highly prized falcon or a silk tapestry depicting scenes from their province.

This particular delegation also brought with them an astronomer, undoubtedly having heard that al-Mansur was not only a mighty general and military ruler, but also a patron of the arts and sciences. The astronomer’s name was Kanaka. An expert on eclipses, he reportedly carried with him a small library of Indian astronomical texts to give to the caliph, including the
Surya Siddhanta
and the works of Brahmagupta (containing material on Aryabhata). Nothing more is known about this Kanaka. The first known reference to him was written some five hundred years later by an Arab historian named al-Qifti.

According to al-Qifti, the caliph was amazed by the knowledge in the Indian texts. He immediately ordered them to be translated into Arabic and their essence compiled into a textbook that became known as the
Great Sindhind
(Sindhind
is the Arabic form of the Sanskrit word
siddhanta).

No one is sure if this incident per se ever happened. But something like it must have, in order to bring the works of India into the sphere of the early Islamic scholars, whence they would travel to Christian Europe through Syria, Sicily and Arab-controlled Spain. A version of the Great Sindlhind would be translated into Latin in

1126. This was one of dozens of critical documents that would contribute to the knowledge base needed to propel Europe into the modern age, and to calculate a true and accurate year.

Kanaka allegedly visited the court of the caliph in Baghdad about a century and a half after one of the most extraordinary moments in history: the sudden maelstrom that came out of Arabia in the mid-600s. Driven by a potent fusion of religious zeal and a centuries-old martial tradition among the tribes of the desert, the armies of the Prophet Mohammed were at first a phenomenon of arms and religion, though they soon became an unlikely force for the advancement of learning. This came in part from the Prophet’s command that the faithful seek knowledge, but also because the Arabs did not follow the example of the
barbari
in the West, who had looted and destroyed the cities and provinces of Rome. Instead the Arabs assimilated the cultures of the peoples they conquered--much the same way the early, uncouth Romans had done centuries before when they eagerly embraced and absorbed the cultures they conquered in Greece and the Near East.

In a sense the Arabs arrived just in time. Most of the ancient centres of learning, and the cultures that had nourished them, were in a state of exhaustion or outright collapse by the mid-600s, after decades of warfare and internal decay. To the east the Gupta era was ending as India broke up into small kingdoms and struggled to fend off fresh onslaughts from the Huns; in the Near East a long war fought between Byzantium and Persia ended with a peace treaty in 628, leaving both empires gravely weakened; to the west the
barbari
continued to battle over what was left of Rome.

Not surprisingly, this period produced little original thinking and was a low point in intellectual output from the Himalayas to the British Isles--with some notable exceptions, such as Brahmagupta in India and a few scattered scholars still struggling to work in the Greek tradition within the Byzantine Empire. But even there the output was meagre as the rump of the old Roman Empire, pressed by enemies on all sides, had become more stridently orthodox. Indeed, for decades the imperium and Church had been repressing rival Christian sects, pagans and anyone else who did not fall in line behind an increasingly strict religious dogma--including scholars.

This religious retrenchment in Byzantium had begun under Justinian in Cassiodorus’s time. In 529 he had closed the nine-hundred-year-old Academy of Plato in Athens and had dispersed its scholars, claiming it was a hotbed of paganism.* Fearing for their lives as well as their intellectual freedom, many of these scholars had fled to Persia, where they established a kind of Academy in exile. This was a pale imitation of the original, though this community of scholars remained viable enough that when the Arabs seized Persia a century later these Greeks were able to play a major role in bringing the texts and learning of the ancient Hellenes to the attention of Arab scholars.