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The Aryabhatiya reveals frustratingly little about its author, though Aryabhata does tell us when he was born—in the form of a brainteaser: “When sixty times sixty years and three quarters of the yuga had elapsed,” he says, “twenty three years had passed since my birth.” The answer, if you know your yugas—a Hindu time unit lasting between twelve and forty-eight centuries—is 476 CE.
This playfulness is characteristic of the twenty-three-year-old’s work. “There’s a lot in the Aryabhatiya which is fun and ingenious,” Professor Kim Plofker, a historian of Sanskrit mathematics at Union College in New York State, says. “Aryabhata is one of the early Indian scientists that I think it would have been most interesting to work with personally, if you were the caliber of student who understood what he was getting at, because he’s clearly a very creative and audacious and innovative mind.”
Aryabhata most likely taught at Kusumapura, a scholarly center close to present-day Patna on the banks of the river Ganga, or Ganges, in northeast India. He lived toward the end of the Gupta dynasty, a supposed “golden age” of artistic creation and intellectual discovery much celebrated in Indian nationalist history.
The sciences flourished, too, and Aryabhata was certainly a product of this moment. As Plofker puts it, “The type of computation Aryabhata was doing—applying trigonometry and other sophisticated mathematics to astronomical calculations—had been done for at least several centuries before him.” While many of the insights attributed to Aryabhata are his own, she adds, “they are not confined to innovations of his own. Like every mathematician, astronomer, or scientist that we know of, he stood on the shoulders of giants.”
Some of Aryabhata’s ideas would prove too awkward for his fellow astronomers to accept. Though he didn’t put forward a heliocentric model of the universe, his idea of a rotating earth was sufficiently radical that it embarrassed his followers. They shared with early Western astronomers a belief that the sky was the moving element. What’s more, it wasn’t easy to reconcile Aryabhata’s theory with the cosmology found in Vedic and post-Vedic Sanskrit texts. So, in later editions of his work, his disciples did him what they thought was the favor of editing out or correcting what they believed to be his mistakes.
Knowledge of the paths and alignments of the planetary spheres has long played a central role in how people in India order their lives (when to get married, when to start a business, and so on) and it still does today. Despite the radicalism of some of Aryabhata’s cosmology, his techniques to predict planetary movements proved useful for very conventional tasks, such as calculating the correct time to hold religious rituals, and for trying to divine future prospects—uses of astronomical knowledge that remain popular.
The idea that the planets have some influence over terrestrial events is an Aristotelian one. Ptolemy had a whole treatise on astrology, the Tetrabiblos, and it is clear that Hellenistic influences brought such ideas to India. They took deep root and gave mathematicians such as Aryabhata a very practical social utility. In Aryabhata’s time, mathematicians did their calculations on boards covered with dust, and their work was known, unglamorously, as dhulikarman—“dust work.”
Like other early Indian scientific disciplines, the principles underlying dhulikarman calculations were part of an oral tradition, and the sutras of a tract such as the Aryabhatiya were meant to be memorized. As a further mnemonic aid, Aryabhata created his own alphabetic system in which letters took the place of numbers, creating unpronounceable “words.” Their purpose was to represent very large integers in a few syllables, thereby making them much easier to remember than long strings of digits.
It is a method reminiscent of Panini’s (3) invention of code to express his rules. According to Christopher Minkowski, Boden professor of Sanskrit at Oxford, Aryabhata was “unique in the concision with which he expresses his texts.” This capacity to distill technical principles and data into crystalline phrasing was something much prized by certain Indian intellectual traditions. Aryabhata, Minkowski says, “is able to present, in just a very limited number of verses, all sorts of mathematical ideas. So in thirty-two verses he deals with the decimal place value system, squares, cubes, square roots, cube roots, triangles—all that and more. In thirty-two verses, it’s a lot of mathematics, but there is a great deal of art in the way that he expresses himself in Sanskrit.”
It’s revealing to compare Aryabhata with Isaac Newton, who also expressed some of his discoveries in natural language. Newton chose quite simple Latin to do this (not much like the complex Sanskrit used by Indian mathematicians), but he also expressed his laws in the form of equations: notations that developed into a universal symbolic language, in a way that mathematics in the Sanskrit tradition never did.
In the Western tradition, mathematics sits at the very top of the pyramid of human knowledge. It’s the paradigmatic science, the one by which reality can be abstracted into fundamental truths. Yet this wasn’t so in India, where mathematical reasoning was just one among several forms of knowledge, and certainly not superior to the understanding of language—as Panini had established. Unlike Euclid, Aryabhata and his tradition didn’t give much importance to establishing axioms and deducing proofs.
In fact, like grammar, early Indian mathematics seems to have been concerned primarily with the way things worked in real life. Take, for example, the notion of a sphere. For Aryabhata and his successors, a sphere was like an iron ball: it had to have flat surfaces, “for only thus can it be stable on level ground,” as the Indologist Johannes Bronkhorst has put it. “Classical Indian geometry,” he added, “like grammar, describes objects that exist in the material world, not abstractions.” In other words, mathematical calculations were taken as true if they corresponded well to the real world, whether or not they could be proven in some abstract way. The results mattered more than the methods used to get to them. This means that it’s often difficult to follow Aryabhata’s reasoning, even as one is impressed by his conclusion. As Plofker says, “Euclid is more like modern mathematics because the modern mathematics we do nowadays is still essentially Greek: it’s axioms, proposition, proof, structure. The Aryabhatiya is not playing the same intellectual game, so to speak. It’s got its own set of rules for the mathematics that it’s doing and what it’s creating.”
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Aryabhata’s ideas, translated into Arabic, were influential to later generations of Islamic astronomers and mathematicians. And in India, several schools of astronomers and mathematicians—the latter mainly located in the southern state of Kerala—developed his insights. However, because he wasn’t working within the framework of his Western counterparts, his ideas didn’t feed directly into the global stream of scientific discovery (in the way that, say, Newton’s did). Despite the significance of the Aryabhatiya, for a long time its author remained in relative obscurity, even on the subcontinent.
It was only when science and technology began to flourish in modern India that his reputation got a relaunch. Indian scientists, trained in Western techniques, nevertheless wanted their own national lineage. According to Professor U. R. Rao, a senior scientist at the Indian Space Research Organization, who oversaw that first satellite project, the mission helped restore Aryabhata’s reputation. “There was a great realization of our own past,” Rao says. “It was a forgotten chapter of our history, and that was changed completely.”
The launch of the Aryabhata satellite was only a partial success, however. After five days in space, the satellite stopped transmitting. Still, India’s first step in a space program has already put an Indian spacecraft in orbit around Mars, at a lesser cost than some Hollywood science-fiction movies, and it helped bring popular attention to India’s long-neglected heritage of scientific thinking—including, of course, the thinking of Aryabhata. Today, his reputation is even a little overblown. Some people claim he invented zero; identified gravity a thousand years before Newton; and more. None of this is true.
Gaining a more historically a
ccurate appreciation of the achievements of early Indian mathematics and science is just beginning. Only in recent decades have we begun to study seriously the wealth of India’s ancient treatises. When it comes to the ocean of Sanskrit science, the boat of our historical knowledge has only just set forth.
8
ADI SHANKARA
A God Without Qualities
Eighth century CE
Day dawns in the South Indian pilgrimage town of Sringeri, in Karnataka. It’s a brief moment of stillness and cool. Walking sleepily in the half-light, I’m startled by something coiled on a veranda: a snake that, from the looks of it, is drowsy, too. But as my eyes adjust to the rising light, I look again and laugh: it’s not a snake—merely a coiled rope, left behind by a man who’s been fixing the tiled roof.
This bit of self-deception—mistaking a rope for a snake—is an occasional false alarm in Indian life. It’s also among the most well-known, even hackneyed, examples cited in Indian philosophical thought. Its purpose is to show that, although the sensory world is out there, our imaginations sometimes intervene between us and reality. Our minds, in other words, are tricksters. At the same time, what we perceive (the snake superimposed on the rope) has real power. As another famous example from Indian philosophy runs, even someone who only thinks he has been bitten by a snake can die from shock.
Mistakings pervade Hindu philosophy, which is full of metaphors of concealment and obscuration. Many serve as examples of maya, the reality that substantially and unarguably presents itself to us but whose true nature remains elusive because of the limitations of our consciousness. Push aside this slippery, illusory world and something pure and constant is revealed: god, the divine, or the universal spirit, Brahman.
Although the varieties of Hinduism defy doctrinal unity, maya and Brahman are essential parts of a philosophical vision that many people now identify with the religion. In large part, we owe this vision to Adi Shankara, a religious thinker (perhaps the nearest that Hinduism has to a theologian) who, roughly twelve hundred years ago, transformed Hindu beliefs and practices, established temples and schools across the subcontinent, and in many ways laid the foundations of modern Hinduism, which is now the third-largest religion in the world.
In Europe, the eighth century was the era of Charlemagne’s bloody expansion of Christendom, through campaigns against the Saxons, Saracens, Moors, and Slavs, and of his ascension to Rome’s Christian imperium. Shankara’s roughly contemporaneous efforts to establish a monastic order and assert his religious vision in India were vastly different: his was an intellectual struggle, prosecuted through debates across the subcontinent. At the heart of Shankara’s interpretation of Hinduism is an idea that remains as powerful as it is paradoxical: nirguna Brahman, “a god without qualities.”
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The narrow roads to Sringeri wind up through the Sahyadri Hills, past miles of laboriously tended coffee plantations, stands of palm, and splays of bamboo. Here, in this remote temple town, Shankara is said to have founded his first Hindu monastery, or mutth—one of four he would establish, along with various temples, at the cardinal points of the subcontinent: at Badrinath, in the Himalayan foothills of the north; at Puri, on the Bay of Bengal in the east; at Dwarka, where the Gulf of Kutch opens into the Arabian Sea, in what is now the western state of Gujarat; and here at Sringeri, in the south.
Shankara, or Shankaracharya as he was also known, supposedly began traveling across India at a young age. As with so many of these ancient figures, there’s uncertainty and dispute about his early life. It’s generally reckoned that he was born in the eighth century, in the Malabar region of southern India, now in the state of Kerala. Some religious biographies, written in verse several hundred years after Shankara’s death, claim that the deity Shiva appeared to Shankara’s parents in a dream and gave them the choice of producing a son who was “all-knowing and virtuous but short-lived” or one who would live long but “without any special virtue or greatness.” They opted for the former, and named their precocious child Shankara, another name for Shiva. As promised, the boy turned out to be a prodigy, but was just thirty-two when he died.
It was said that Shankara had to hear something only once to remember it, and that he had mastered the four Vedas, the oldest Hindu scriptures, by the age of eight. Around the same time, or possibly even earlier, Shankara declared his desire to become a sannyasi, an ascetic, wandering monk. This announcement scandalized his by-then-widowed mother. In the traditional life cycle of a Hindu male, sannyas (renunciation of the world) is the fourth and final stage. A boy first has to grow to be a student and then an adult householder, and then later withdraw into hermetic retirement. Only after that can he take the final step and become a religious wanderer.
But Shankara prevailed, and, by the age of sixteen, with half his life already spent as an ascetic, he was producing sophisticated scriptural commentaries and articulating a radical new version of what eventually became known as Hinduism. He remained devoted to his mother, though. After she died, Shankara returned home intending to perform the death rites, but his community refused to let him. Only a householder could do the rites, they said—not a sannyasi. It was a painful snub, and perhaps the pivotal incident that turned Shankara against high Brahminical rituals and toward what he considered the undervalued inner wisdom of post-Vedic texts.
In celebratory biographies such as the Shankara-Vijayas, or the “Conquests of Shankara,” the earliest of which date from around the fourteenth century, Shankara is portrayed as more than just a wandering religious figure. He is miraculous in physique as well as deeds: a face like the full moon, a broad chest, arms so long they reached his knees, and fingernails the color of blood. But what really awed people was his capacity for intellectual jousting and dialectic victories over scholarly rivals. The most dramatic was over the venerable pandit Mandana Misra, an old-style believer in ritual recitation of mantras and japas. These were sounds, conveying no meaning as such, but considered purifying because they were believed to have been handed down by the gods.
A dying sage directed Shankara to meet Mandana: he told Shankara to look for a big house, surrounded by walls and with a tall locked gate, where parrots could be heard chanting Vedic mantras. Shankara triggered yogic powers to leap into the courtyard, and after exchanging insults by way of introduction, he and Mandana decided to debate the validity of their beliefs. Mandana’s wife was chosen as umpire. She placed two fresh flower garlands around their necks, declaring that whichever garland faded first would indicate the loser.
The disputations went on for eighteen days. Finally, Mandana’s flowers wilted, and he conceded defeat. His wife took up the challenge and thought she had found a subject for debate that would surely flummox the celibate Shankara: the art of love. Shankara asked for a month to investigate. Using his yogic powers once more, he entered the body of a king, proved a quick student at gathering the necessary knowledge, and returned to claim victory.
Shankara turned now to spreading his message across the country, arguing down rivals one by one. According to one of the Shankara-Vijayas, he continued his “merciless refutation of all hostile creeds and philosophies: the teachings of the Tathagata [the Buddha (1)] became lifeless, the school of Kumarila became silent, the Naiyayika philosophy became weak and paralyzed, and the Kapila’s system also followed suit.”
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In Shankara’s day, there existed a range of religious sects devoted to various gods, sects that followed distinct practices, from animal sacrifice and fire rituals to tantric sex and magic. These beliefs, along with Buddhism and a range of other philosophical schools, sustained a world of debate and controversy, and challenged the Brahminic tradition.
Shankara aimed to bring some order to this profusion of belief and practice, both orthodox and heterodox. By his time, Sanskrit texts of the Vedas existed alongside oral versions, and the canon had expanded to include a collection of two hundred broadly philosophical works known as the Upanishads. Also known a
s the Vedanta (literally, “after Vedas” or “at the Vedas’ end”), the Upanishads ventured answers to questions posed in the Vedas: Where did we come from? Why are we here? Where do we go? Shankara seized on these writings and turned them, through his commentaries, into a powerful new doctrine.
According to Jonardon Ganeri, a professor of philosophy at New York University, “Shankara’s ambition as a thinker was to provide a unified, coherent reading of the great plurality and diversity of the Hindu scriptures.” Ultimately, Ganeri says, this project was a moral one: “I think of Shankara as a theologian, interpreting canonical religious texts as providing the foundation around which a moral vision is organized.”
For Shankara, the focus of this vision was the jnana, or “knowledge,” contained in the Vedas and Vedanta that revealed the essential unity of the cosmos. “Shankara thought there was just one real entity, Brahman, the fundamental grounding principle of the universe,” Ganeri says. “Everything else—all the apparent distinctions and differences in the world, including differences between different individual selves—is illusory.” Perhaps most radically, Shankara held that the distinction between self (atman) and the divine (Brahman), which appears so evident in the sensory world of maya, was also a misapprehension. This was the core of the monist doctrine that Shankara systematized. It is now known as Advaita Vedanta—that is, “non-dualist” Vedanta—because it does not recognize two substances in the universe, but only one.
As a result of this tenet, Vedic Hinduism had to be newly formulated, and turned away from popular forms of worship, which, according to Shankara, misunderstood the individual spirit’s path to liberation. Obsession with rituals had to be replaced by asceticism, celibacy, the giving up of family life, and an intellectual rigor that could help others grasp the truth that the seeking person divined. Instead of mantras, Shankara prescribed meditative reflection, through which each individual could pierce the veil of maya and come to recognize the identity between his or her own essence and the universal spirit. Once we grasp that oneness with the eternal, Shankara said, we attain moksha, or release from the cycle of life and death.
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