Ideas
Page 53
But Gupta dominance didn’t endure. The fifth generation of the dynasty, Skanda Gupta, was the last. Soon after his accession in 455, the Hunas (or Huns) massed on his northwest frontier and the cost of resistance drained the Gupta treasury. After Skanda’s death in 467, the empire declined rapidly and, just before 500, Toramana, the Huna leader, took the Punjab, while his son later absorbed Kashmir and the Gangetic plain. By the middle of the sixth century Gupta glory had entirely faded. Half a century of fragmentation followed until, in 606, a line of later Guptas, not related to the imperial clan, emerged. The most remarkable of these was the first, Harsha Vardhana, who sought once again to unify all of north India. Like Chandra Gupta I, his brilliance was recognised and recorded at the time, once by a Brahman courtier, Bana, who wrote a hagiographical life of Harsha, Harsha Carita, as well as a more discerning record, by yet another visiting Buddhist pilgrim from China. This was Xuan Zang, whose journey, In the Footsteps of the Buddha, took him to Harsha’s India between 630 and 644.
Harsha expanded his empire, but we remember him now as much for the fact that he was a poet as well as a warrior, for the fact that he rescued his sister as she was about to follow her husband on to the funeral pyre, and most of all for the important innovations in religious and philosophical ideas that occurred during his reign. It was under Harsha’s rule that Hinduism grew so much in popularity, at the expense of Buddhism, taking on its ‘classical’ form of worship, or puja. This entails the faithful bringing offerings–fruit, candies, other delicacies–to the sculptures or other images of the gods in the temples, together with the performance of certain secret rituals, all having to do with ‘female power’, or shakti, which have come to be known as Tantric. Tantrism is almost certainly a very old form of worship, associated with the ancient mother goddess, but just how and when its orgiastic nature began isn’t clear. The basic beliefs of Tantrism are very different from either orthodox Hinduism or Buddhism and their very popularity, say some scholars, must attest to the fact that the ideas are very ancient. The basic belief was that true worship of the mother goddess could be achieved only by sexual intercourse (maithuna). In time this led to group intercourse, often performed at so-called ‘polluted’ cremation grounds. These episodes were also associated with the breaking of other taboos, such as eating meat and drinking alcohol.42
Tantrism affected (some would say infected) Buddhism as well, leading in the seventh century to a third form, after Hinayana and Mahayana. This was Vajrayana (‘Vehicle of the Thunderbolt’), which introduced as its most powerful divinities a number of female saviours, known as taras, who were the consorts of ‘weaker’ Buddhas and Bodhisattvas.43 In other words, Tantric Hinduism and Tantric Buddhism both exalted the female principle, regarding this as the highest form of divine power.
Tantric worship became secret and secretive because its practices were unacceptable to many of the orthodox, but its intimate connection with yoga added to its popularity. Yoga was practised because control of breathing and the body were essential components for the proper performance of maithuna. And yoga, as a system of thought, now emerged as a more codified organisation of beliefs, with the ‘eight-fold’ path of ‘royal yoga’, raja yoga. These eight paths were: self-control, the observance of proper conduct, the practice of correct posture (asana), breath control (prana), organic restraint, mind steadying, the perfect achievement of deep meditation (samadhi), and the absolute freedom of kaivalya.44
But yoga was only one of six schools of classical Hindu philosophy which emerged at the time of Harsha Vardhana. These six were generally grouped in three couplets. Yoga, for instance, was coupled with Samkhya, or the ‘Numbers School’, which may also be of ancient origin. According to the Samkhya philosophy, the world consists of twenty-five basic principles, all but one of which are ‘matter’ (prakriti), the other being purusa–man, spirit or self. In this system there is no creator, nothing divine, all matter is eternal, uncaused. But all matter has three qualities in varying degrees–it is either more or less truthful, more or less passionate, more or less dark. The mix of these qualities determines how virtuous or noble something is, how inert, cruel, strong or bright and so on.45 The twenty-four forms of matter show some measure of evolution, in that they begin with prakriti, which ‘brings forth’ intelligence (buddhi), from which arises what we would call ego-sense (aham kara), giving rise to mind (manas). From mind the five senses emerge, and from them the five sense organs and the five organs of action. Underneath all matter lie the five elements–ether, air, light, water, earth. Purusa, the sense of being an individual, with one’s own spirit, carries with it the idea that all people are equal but at the same time all are different. Salvation is achieved only when a person realises the basic separation between purusa and prakriti, which enables the spirit to cease suffering and attain complete release. These very mystical ideas clearly overlap with Platonism and Gnostic beliefs from Greece and Alexandria.46
The other two couplets of classical Hindu philosophy are Nyaya/Vaisesika and Purva-mimansa/Vedanta. The Nyaya philosophy (or vision, darshana in Hindi) means ‘analysis’ and it teaches salvation through knowledge of sixteen categories of logic. These categories include syllogism, debate, refutation, quibbling, disputation and so on. Coupled with Nyaya, Vaisesika means ‘individual characteristics’ and is known as India’s ‘atomic system’ since its basic premise is that the material universe emerges from the interaction of individual atoms that make up the four elements–earth, water, fire and air. Vaisesika also envisages non-atomic entities (dravyas), such as soul, mind, time and space. Once again, perfect knowledge leads to salvation, when the ‘self’ is released from matter and therefore from the cycle of death and rebirth. Nyaya, like yoga, is a system of behaviour, or way of thinking, whereas Vaisesika, like Samkhya, is a set of explanations as to how matter and mind are organised and are different from one another.47
Purva-mimansa (‘early inquiry’) was a form of fundamentalism, which took the Rig Veda as literal truth and therefore insisted that salvation could only be achieved by precise re-enactment of the Soma sacrifice.48 The emphasis on ritual, and the absence of new ideas, seems to have ensured that Purva-mimansa lost adherents as time went by. In strong contrast, Vedanta (‘end of the Vedas’, and sometimes called ‘later inquiry’, Uttara-mimansa), has become India’s most influential philosophical system, developing many subsidiary forms that have appealed to a wide range of thinkers and intellectuals down the ages, and not only in India. Again in contrast to Purva-mimansa, Vedanta takes its starting point from the speculations of the Upanishads, rather than Rig Vedic sacrifice, and seeks a synthesis of all seemingly contradictory Hindu scripture. It posits the existence of the ‘Absolute Soul’ in all things.
The most successful Vedanta teacher, and the second most-revered person in Indian history, after the Buddha himself, was Shankara (c. 780–820). He was a Brahman who, during his short career, wandered from his Kerala home to the Himalayas developing his idea that our world is an illusion (maya), and that the one reality was Brahman, or Atman, the world-spirit or soul.49 Shankara’s most famous doctrine was Advaita (literally, ‘no second’, or, as we would say, monism). In Advaita, Shankara maintained that nothing in the phenomenal universe is real, everything is a secondary emanation from the one ‘ultimate, absolute being’, the ‘impersonal neuter entity’ known as the Brahman, which had three attributes, being (sat), consciousness (chit) and bliss (ananda). Brahman, for Shankara, was unchanging and eternally stable and for Westerners sounds very mystical, like a cross between Plato’s The One and Aristotle’s Unmoved Mover.50 Everything else in the universe, because it was at some level unreal, was subject to change. In humans, this takes the form of samsara, transmigration.
In one of his poems, Kalidasa mentions a revolving water-spray, for cooling the air. In antiquity and the Middle Ages, Hindu ingenuity was second only to Chinese, reflected also in the fact that, by the first century AD, Hindu doctors had perfected twenty kinds of knives for differe
nt surgical procedures. At the same time, their mathematicians conceived the notion of the rasi, a ‘heap’ of numbers, which recalls an ancient Egyptian idea that may be regarded as the ancestor of the algebraic concept of x, for an unknown quantity.
In India, as in Egypt, mathematics appears to have begun with temple-building, where a system of ropes of different lengths was used for the laying out of holy sites, for the construction of right-angles and for the correct alignment of altars. This lore was set down in a series of Sulvasutras, sulva referring to the ropes or cords used for measurement, and sutra meaning a book of rules or aphorisms relating to a ritual or science.51 Three versions of the Sulvasutras, all in verse, are extant, the best-known bearing the name of Apastamba. They are dated to anywhere between the eighth century BC and the second century AD. For that reason, we cannot be certain whether the ideas were originally worked out in India, or taken from Mesopotamia or the Hellenistic world. But Indian arithmetic certainly began in the temple: sacred formulas were conceived, for example, for the number of bricks to be used on altars.52
More reliably dated are the Siddhantas, ‘systems’ (of astronomy), of which there are five versions, all written around the turn of the fifth century, and which were early examples of the Sanskrit revival. Here too Hindu scholars insist that the ideas in the Siddhantas are original, whereas others see definite signs of Greek influence.53 Whatever the truth of this, it was in the Siddhantas that the Hindus refined and expanded the trigonometry of Ptolemy. In the opinion of H. J. Winter, ‘Hindu mathematics is undoubtedly the finest intellectual achievement of the subcontinent in medieval times. It brought alongside the Greek geometrical legacy a powerful method in the form of analysis, not a deductive process building upon accepted axioms, postulates, and common notions, but an intuitive insight in the behaviour of numbers, and their arrangement into patterns and series, from which may be perceived inductive generalisations, in a word algebra rather than geometry…The quest for wider generalisation beyond the limits of pure geometry led the Hindus to abandon Ptolemy’s methods of reckoning in terms of chords of a circle and to substitute reckoning in sines, thereby initiating the study of trigonometry. It is to the philosophical mind of the Brahman mathematician engrossed in the mystique of number that we owe the origin of analytical methods. In this process of abstraction two particularly interesting features emerged, at the lower end of achievement the perfection of the decimal system, and at the higher the solution of certain indeterminate equations.’54 Ptolemy’s trigonometry had been based on the relationship between the chords of a circle and the central angle they subtended. The authors of the Siddhantas, on the other hand, adapted this to the correspondence between a half of a chord and half of the angle subtended by the whole chord. And this was how the predecessor of the modern trigonometric function known as the sine of an angle came about.55
The second innovation of the Indians was the invention/creation of Hindu numerals. This was primarily the work of the famous Indian mathematician Aryabhata, introduced at the beginning of this chapter. In 499 he produced a slim volume, Aryabhatiya, written in 123 metrical verses, which covered astronomy and, for about a third of its length, ganitapada, or mathematics.56 In the latter half of this work, where he is discussing time and spherical trigonometry, Aryabhata uses a phrase, in referring to numbers used in calculation, ‘from place to place each is ten times the preceding’. ‘Local value’ had been an essential part of Babylonian numeration but they didn’t use a decimal system. Numeration had begun in India with simple vertical strokes arranged into groups, a repetitive system which was retained although the next move was to have new symbols for four, ten, twenty and one hundred. This Kharosthi script gave way to the so-called Brahmi characters, referred to earlier, which was similar to the Ionian Greek system, as follows:
From this arrangement two steps are needed to arrive at the one we use today. The first is to grasp that under the positional system only nine ciphers are needed–all the others, from I onwards in the above table, can be jettisoned. It is not certain when this move was first made but the consensus of mathematical historians is that it was taken in India, perhaps developed along the border between India and Persia, where remembrance of the Babylonian positional system may have sparked its use with the Brahmi alternative, or on the border with China, which had a rod system:
This may also have suggested the contraction to nine ciphers.57
The earliest literary reference to the nine Hindu numerals is found in the writings of a Syrian bishop called Severus Sebokt. It will be recalled from Chapters 11 and 12 that Justinian had closed the Athenian philosophical schools in the sixth century, whereupon some of the Greek scholars decamped to Syria (while some went to Gondeshapur). It may be that Sebokt was irritated by the fact that these Greeks looked down on learning elsewhere for ‘he found it expedient to remind those who spoke Greek that “there are also others who know something”’.58 To underline his point, he went on to refer to the Hindus, their discoveries in astronomy and in particular ‘their valuable methods of calculation, and their computing that surpasses description. I wish only to say that this computation is done by means of nine signs.’59
Note the mention of nine signs, not ten. At that point, evidently, the Hindus had not yet taken the second crucial step to the modern system–notation for the zero symbol. According to D. E. Smith, in his history of mathematics, ‘the earliest undoubted occurrence of a zero in India is in an inscription of 876’–in other words, more than two centuries after the first mention of the use of the other nine numerals. It is still not certain where the zero was first introduced, and the concept of nought, or emptiness, was independently arrived at by the Mayans, as we shall see in a later chapter. Joseph Needham, the Cambridge-based historian of Chinese science, favoured China as a source of the zero. ‘It may be very significant,’ he wrote, ‘that the older literary Indian references simply use the word “sunya”–emptiness, just as if they are describing the empty spaces on Chinese counting boards.’60 A Cambodian inscription of 683 uses the dot or bindu to represent zero, while an inscription on Bangka island (off the coast of Sumatra) of 686 shows the closed ring.61 But this is no doubt the result of Hindu influence, and it does seem that it was the Indians who first used all three of the new elements which are the basis of our counting system: a decimal base, a positional notation, ciphers for ten, and only ten, numerals. And this was in place by 876.
Nowadays, we use the simple goose egg, 0, for zero. At one stage it was assumed that the zero originally derived from the Greek letter omicron, the initial letter of the word ouden, which means ‘empty’. This is no longer accepted–sometimes a dot was used, sometimes an upside-down version of our letter h.62
The final important innovation introduced by Indian mathematicians is the system known as gelosia multiplication and long division. Gelosia is an Italian word. After the system–also called lattice multiplication–was invented in the twelfth century, it was taken to China and the Arab world, from where it entered Italy in the fourteenth and fifteenth centuries. The lattices appeared to resemble the gratings, or gelosia, used on Venetian windows. Here is an example of lattice multiplication.
In this example, 456 is multiplied by 34, to produce the answer, 15,504. The single digits are multiplied, those along the top by those down the left-hand side, and the product written in the squares, divided by a diagonal. There is thus nothing more onerous in one’s head than multiplying single digits. Then one simply adds the diagonal lines, beginning top right and carrying over, to get the final result.63
India was unaware of the advent of Islam until the early eighth century, and might have remained so for much longer but for an incident in AD 711, when the plundering of a richly laden Arab ship as it passed the mouth of the Indus so incensed the Umayyad governor of what is now Iraq that he launched a military expedition of six thousand Syrian horses and the same number of Iraqi camels against the rajas of Sind.64 This force soon conquered Brahmanabad, where the infidel
s the Muslims found there had to convert or be killed. This early ferocity didn’t last. The Arabs soon realised there were too many Hindus to exterminate, and second, Muslim scholars studied the extensive Hindu religious literature, and as a result allowed Hindus dhimmi status, a protected belief system alongside Judaism and Christianity (provided of course they paid the special tax, the jizya).65
Islam had conquered the Middle East so rapidly that it might have been expected to have the same effect in India, but it did not, as is revealed today by the existence of Muslim Pakistan and Bangladesh alongside Hindu India where, however, there are also several million Muslims. The military side of the Muslim conquest of northern India falls outside the scope of this book. It is enough to say that, over the centuries, Turks and Afghans were more involved than Arabs, and that the main forms of Islam in India were Sunnis and Sufis. Sufism received a boost in 1095 when al-Ghazali resigned from the chair of divinity at the Nizamiyah academy in Baghdad, to lead the life of a Sufi (though poetry also made Sufism popular). By the twelfth century, Sufis were divided into several different silsilas (orders), each led by a pir or preceptor and each centred on a khanqah or hospice, which attracted men from all over who were seeking the spiritual life.66 To begin with, the khanqahs subsisted on charity but, as with Buddhist monasteries in Chinia, many evolved into very prosperous communities.