This first post, about the origins and transference of the concept of zero and the modern numeral system from India to the Islamic world. This is an extract from the book “Lost History: The Enduring Legacy of Muslim Scientists, Thinkers, and Artists” by Michael H. Morgan.
Chapter 3
God in the Numeral
…and He has enumerated everything in numbers.
QUR’AN (LXXII:28)
Bangalore India, 2007 – From above and afar the capitol city of Bangalore in Karnataka state is a modernistic grid cutting the green savanna and copses of the vast Deccan plateau. The layout of the city is unusual in this part of the world for its crisp regularity. During monsoon season, huge cumulus clouds build into thunderheads in the afternoon and torrential showers pour down over the palms and scrub, over the square blocks and surveyed quadrants of a place that speaks of the new. The haze of exhaust hangs bluish in the tropic heat, evidence of the roar and tumult as traffic pulses in and out of the various centers.
The grid indicates a city atypical for this subcontinent. Bangalore is a 500-year-old center in a country that goes back thousands of years, but most of the its growth has come in the last 30 years. The vast civic park in the middle hosts the redbrick, neoclassical high court and the state legislature and library, whereas the newer streets and highways radiate out to the exploding suburbs, boxy towers and corporate parks of global capitalism.
In one of those office parks, Fahmida Khan is writing algorithms for software to support commodities trading at several exchanges around the world including Chicago and Singapore. An algorithm is a set of numerical calculations and instructions, which if carried out systematically produces a desired result. Algorithms are critical to software design, as well as modern science and engineering, enabling computers and smart electronics to sort through masses of digital data and text, calculating spatial relationships encoding and decoding confidential information – all the basic processes of modern computing, technology, commerce, and science.
Founder of her own small software shop, Fahmida’s biggest clients oare the new behemoths of Indian information technology, like Infosis and Wipro, but she is starting to get contracts from the big multinational firms too. Originally dedicated to taking on the outsourced back-office business processes of from North America and Europe, these new Indian firms are looking to move up the computing food chain, writing the software and designing the devices and circuits that will drive the next wave of global computing.
Fahmida’s algorithms create codes that turn financial data into gibberishwhen being transmitted, and then on the other side reverse the process to decode the information. For a hacker or thief the algorithms are so complicated that it would thousands of massive computers years and years trying every algorithmic permutation, out to the 132nd decimal place to finally hit on the code. So far, it is not worth trying to break the code.
Fahmida learned her skills in Silicon Valley, where she worked after attending the California Institute of Technology. She worked first at Hewlett-Packard, the grandfather of Silicon Valley firms, and later at Oracle Systems. Had she stayed at Oracle, she probably could have become a vice president or even better, and depending on her timing, left the company a multimillionaire.
But in 1998, she made a momentous decision. Having been raised from childhood to look north and west towards the wealthy countries of Europe and America and to the foreign educational centers like Cal Tech, she decided to come back home. Sacrificing income and the prestige of being with more established firms, she came home to found her own company.
Thousands of other Indians who had emigrated to America have made the decision to come home, in particular to Bangalore. Although the reverse migration has been largely in computing and software, others have begun to follow, including doctors and entrepreneurs. While they all sacrifice income, because of India’s low labor and living costs they can afford other amenities and servants that were beyond their reach in America and Europe. They can live at the top of society in India, where overseas they were part of the prosperous middle class. For a country that long languished between colonialism and a stagnated 1960’s socialism, this new class is starting an economic revolution that the old socialists could not imagine, although no one knows how far they will go.
Fahmida’s family, as reflected in her name, is Muslim. Though the details of when and how they became Muslim are lost, her ancestors were long civil servants in the service of the Mughals and then the British, and her great-grandparents settled in Bangalore in the time of the British Raj. As educated and cosmopolitan people living far south, they have been fairly remote from the periodic dislocations and strife between religions farther north. During the period of partition in 1947, they had taken to heart Gandhi’s message of interfaith harmony and had never considered moving to Pakistan or Bangladesh, unlike tens of millions who did.
And they have felt vindicated in their decision. Watching Indian Muslims rise to positions of success and power, in Bollywood, in the presidency of the country, in business and entertainment, has made them proud. And it has made them glad that they have not used their religion as the primary definer of who they are. They are Indians first, and they are glad of it.
And Fahmida’s family was so proud to see her moving to California to study, and then to hear of her success in business. Though they had the normal worries about a single Indian woman in faraway America – and they have constantly maneuvered to find her the right husband – they have given her the freedom to make her own choices.
Though Bangalore was captured by the Mughals in the 17th century – and the architecture of nearby Mysore and Bijapur reflects the stamp of the Muslim vision, with domes and minarets and pointed arches echoing to the Abbasids and Persians and Central Asians – the cityscape of Bangalore does not look particularly Muslim, nor does the name of Karnataka. Always a minority in India, though the political elite for centuries, the Muslims have been only part of the cultural and religious patchwork of South Asia. The Hindu foundation of India is the bedrock of Karnataka and elsewhere. All around the state are ancient Hindu temples like Belur and hampi. Add to that the influence of the Portuguese who traded along both Indian coasts for 500 years, and their former colony of Goa only a few hundred miles west, and finally the styles and language of the English, who considered India the prize of their colonial crown.
While Bangalore is rich and exploding, the Economy of the state, like India, is also an extreme mix of ancient capitalism and global capitalism. Even though 600 million Indians have not been touched by globalization and subsist on a level unimaginable to westerners, as you move through the remaining 400 or million or more you find rising gradations of wealth including the middle class that is now one of the largest in the world.
India’s world class technical schools have helped create a new techno-elite that feeds into the new big firms, helping transform this ancient country into a global leader in information technology.
Coming home has actually been an issue for Fahmida and her extended family. While at one level these families mourn for those who have gone away and yearn for them to return, some of the Khans, on the other hand, including her mother, had mixed feelings when faced with the reality of Fahmida back in India. Deeply indoctrinated in a sense of inadequacy derived from a fairly limited time in history – the British colonial period – the older Khans had always thought foreign was superior. British was good and American was better. So they had some heated and confused discussions with their daughter who was giving all that up to come home.
Although she would never have admitted it to them, Fahmida felt some of that, too. She had been proud of her Cal Tech degree and her work at Hewlett-Packard and Oracle. She realized that she too carried some of the prejudice of her parents, especially aout education, though not the love of things British. She respected the newness of America and how far the country had come in such a short time. She knew that that top universities in the aggregate, were without equal.
But then when she’d seen the same hint of newness in Bangalore on her return trips, the money, the office parks, the same smell and even some of the people she’d known in Silicon Valley, she had changed her thinking. She had actually thought that by coming home and helping build Bangalore, she would build India. And maybe build herself.
She has another hour before she goes to a client meeting at one of the downtown hotels. This man has flown in from Boston. His firm has done very well. Looking out the window, she sees it will probably rain before dark. That will slow down traffic.
She as one little mathematical snag to solve before she can feel good about leaving for the day. She looks up her shelf for one of the old standbys from her university days, Elements of the Algorithm, with a portrait of the old Arab or Persian mathematician al-Khwarizmi on the cover, namesake of the algorithm. She knows it had been up on her bookshelf. Did one of her colleagues grab it during lunchtime?
She needs that book. She knows the chapter she wants. She hardly ever refers to the other sections. She doesn’t remember anything about al-Khwarizmi, and its irrelevant now. There was the a foreword that told about him, maybe she read it 20 years ago in graduate school, but she doesn’t remember anything but his name. And what does it matter? Relevant history in the world of information technology only goes back about two years. Has she lost that book?
BAGHDAD, A.D. 832 – There is a thread in the tapestry of lost history made of a tstring of numbers and calculations, and these numbers, born of the highest imagination will enable many of the tapestry’s other threads to materialize.
A pivotal force in creating these numbers and formulas is a Persian man born in about 780 in the faraway town of Khiva, Khorasan province, known as Khwarizm to the Arabs, in Central Asia. He is named Mohammad al-Khwarizmi, literally Mohammad of Khwarizm.
In the eighth century, his birthplace is deep in the steppe, a way station on the Silk Road that stretches at one end from China, at the other end from Rome. Though the two ends of this spectrum have never had a direct contact, over the centuries there is a fairly regular exchange between two worlds. All this passes through Khorasan; at times the exchange is no more than a breeze, a foreign and exotic lost butterfly hanging in the air for a few seconds, then swept away.
The old trading oasis of Khiva lies south of the Aral Sea, the oasis and the sea composing two watery havens surrounded by the Garagum Desert that stretches off into nothingness. Assorted religions and cults have come through and stayed or shriveled, until Islam finally takes root. Caravans of camels and horses come out of the distant nothingness to aw down their wares and bargain, then to drink and rest, to tell stories and look up at the stars. At night the town is swallowed up by space; by day it is a green dot on the face of the yellow vastness. Although it will later become part of other countries and empires, Khiva harks back to ancient Persia, and the lean and bearded man with the long back hark carries the soul of Persia within him. And though he is named after the Prophet as many good Muslim boys are, this young man is also known to some Arabs as al-Majusi, literally the Magus or magician, leading some people to believe that his earlier faith, or that of his people, may have been Zoroastrianism, the old fire worship. Because he also draws on ancient Hebrew mathematical and astronomical texts, there are those who think his family had been Jewish.
To be named the magician will prove to be true beyond the knowledge of those who named him. This dark-haired main, with piercing brown eyes set into deep sockets and cheeks creased by leanness and weather, is a magician in other ways as well. Steeped in the tradition of faith and of magic, he yearns to find the secrets of the universe in numbers. He writes mathematical problems; he dreams numbers; he reduces every movement of his day to numbers: the numbers of steps to the bathhouse, the angle of sun to Earth and the triangle created there, and the curves of the Silk Road wandering across half the Earth.
In numbers and equations and computations spinning out of their series, he sense the hidden codes of the universe, the numerical representation of the complexity of God’s creation. And as a Muslim, in a time when it is believed that God can be revealed through reason and knowledge, he will help lead a great mathematical revolution, giving the first glimpse of a future day when the age of computers will outstrip the processing speeds and capabilities of the human mind, no matter how brilliant.
At the founding of the House of Wisdom in 832 in Baghdad, al-Khwarizmi is summoned by the Caliph al-Mamun himself to assist in the search for God in the numeral. And when he arrives there, he sees the great interpreters like Hunayun ibn Ishaq gradually decoding the formulas of Euclid’s Elements based on geometry, of Pythagoras and Ptolemy, and thoughts of Aristotle and Socrates. Others are translating Archimedes’s works such as The Sphere and the Cylinder, The Measurement of the Circle, The Equilibrium of Planes, and Floating bodies, all of which help influence Muslim thought significantly. Al-Khwarizmi will help in that effort, because he is able to read Greek and turn its meaning into Arabic.
The Central Asian man sees turbaned mathematician-astronomers working together in rooms using maps, star charts, astrotables, and other measuring instruments, thinking through problems together, checking each other’s work, poring over translations, and discussing endlessly. For a man who has often done much of his work alone and had rarely found thinkers who were his equal, to find so much intelligence and competition gathered in one place is both exhilarating and intimidating. But he knows ths is an unparalleled opportunity, and he will make as much of it as he can.
Even as the knowledge of the ancient Greeks is revealed in greater detail with each passing month, al-Khwarizmi is determined to search for mathematical knowledge wherever it can be found. He has heard of the mathematical wisdom of the early Hindus. In the time of the founding of the court of the Caliph al-Mansur, there had been a Indian astronomer in the court named Kanka, and he is said to have used a Hindu text written by a long-dead mathematician named Bhramagupta, used to calculate the position of the sun and planets, to predict eclipses and the like. Al-Khwarizmi has heard talk of this book and method, but he cannot find it. He spends days digging through the archives to try to track down the original, and he endlessly tasks the archivists and librarians to find the Sanskrit papers written by the dead Bhramagupta that the dead Kanaka had once used.
When the archivists finally return, they bring with them many treasures originally from India. And among them are the kinds of books and papers that al-Khwarizmi and the caliph yearn for, the collected knowledge and ideas of other peoples and civilizations. Among the treasures lies a 200-year old book called Brahma Sphuta Siddhanta, or Opening of the Universe. While knowing only a few words of Sanskrit, al-Khwarizmi believes this is almost certainly what he is looking for, and he has the translators set about rendering it into Arabic.
The Arabic name of the Hindu work will be Sindhind. The Hindu original will one day be lost and al-Khwarizmi’s Arabic version will also be lost, but a Latin version of is work done centuries later will survive.
And as the translators decode the old Indian text, its Sanskrit characters like magic and their impenetrable secrets one by one becoming the familiar swirl of Arabic, al-Khwarizmi is at first dumbfounded, then awed, and then gratified to the depths of his soul. Each evening he awaits the new day’s revelation of mathematics. He lies awake at night up on the roof of his quarters at the House of Wisdom as he had done when a boy in Khorsan, watching the half sphere of the heavens orbit Polaris, the middle of the southern sky shifting off to the south. At the center of the base of the hemisphere of heaven, he ponders what he has leaned the previous day, unable to sleep because of the anticipation of what he will find.
While there are countless things now revealing themselves to him from the translators pens, the one thing that stuns and shakes him the most is the Hindu character shaped like a dot, a pinpoint of blackness like negative star. This dot is the foundation of an entire vision of mathematics, of nothingness, is the source from which all higer mathematics can now spring. The nothingness of the dot will grow to become the center of the source code behind the physical universe.
Weak and drunk with the world that is now exploding in his head, al-Khwarizmi knows that mathematics has to be the code work of the divine. From the discovery of the Hindu dot that will one day be represented in much of the world by a circle and known a zero, he sees an infinite number of paths and possibilities streaking out in all directions. And he is not alone in these kinds of thoughts, for in the house of wisdom and other mathematical salons that will arise at other courts, dozens and eventually hundreds astronomical-mathematical thinkers are turning over in their minds assorted issues, each coming at the numeric mystery from a slightly different angle. Unconsciously and intuitively, the early Muslim mathematicians will create a kind of collective intelligence, feeding on each other, borrowing and stealing from one another, competing for the favors of patrons, making terrible mistakes, authoring spectacular breakthroughs. In a way, the House of Wisdom in Baghdad and similar Muslim centers will be the world’s first think tanks, an example of network computing, using networked human brains rather than machines.
And al-Khwarizmi and his colleagues are not alone in time or history, for aside from inventing, they also assimilate and aggregate much of the brilliance that has come before. From the Babylonians via the Greeks, they inherit the sexagesimal measure of time in 60 seconds and 60 minutes. Muslim astronomers and other scientists will translate these numerals into the degrees of the compass and the directions of earth and sky that will survive into the 21st century. From the Indians they will capture the astronomic importance of numbers. Via the Persians and directly from the Indians, they will capture the zero, and the breakthrough of decimal math, and the first hints at representing numbers as symbols and not as words.
Among other things, al-Khwarizmi realizes as he scribbles that the very process of writing mathematics will need to be revised. In his day there are three different methods of calculating math in the Abbasid world and its environs. There is the universal finger counting method, which serves certain basic purposes well, as in business transactions of small size. There is a more complicated version using Arabic letter characters, which is better but still not up to the task.
And there is the Hindu method, a decimal system with characters representing quantities ranging from 0 to 9, and then arranged in a combination to reach up and down into positive and negative infinity from the sources dot of zero. The Hindu numerals are the best, the only ones adequate to all the possibilities that al-Khwarizmi and his counterparts and successors see dancing in their heads: needs like calculating the area of irregular spaces; finding missing quantities using the relationship of known ones; calculating the relationship of the Earth to the sun and stars, so as to better compute the holy days as commanded by the Prophet; finding the location of Mecca so that the faithful can pray in that direction with certainly and not guesswork. The Hindu cum Muslim number system will be essential to establishing a new theory about curvature that will show how to resolve the two different universes of angles and curves. The new number system will begin to help answer the mathematical questions implicit in conical space and projections. And the Hindu-Arab numbers will be essential to 21st century questions such as the behavior of light and the properties of solids. Modern technology and civilization will not able to rise and evolve without these numbers.
In al-Khwarizmi’s mind and in the Hindu system, all spins around the dot of nothingness. Brilliant Bhramagupta had found the zero and tried to represent its emptiness and mystery in a written equation. He wrote the ultimate truth of zero to be: Zero divided by zero equals zero. And though he was wrong in that calculation, which is impossible, he was infinitely prescient in his willingness to think in new ways, which in turn threw a spark of genius to the Muslims, starting a bonfire of thought.
Two hundred years later up on that Baghdad roof, al-Khwarizmi laughs to himself. The equation of division of and by zero is absurd; it proves nothing. He laughs out loud, risking waking the others. A woman of the night calls up to him, unaccustomed to hearing laughter from this handsome, dark man and wondering if he wants company. But he is off in his thoughts.
The zero, he realizes, must be accepted on pure faith. It cannot be proven. And in terrible irony, which he considers sharing with his patron al-Mamun, he sees that the ultimate value of rationalist mathematics is pure revelation, just as god was revealed not quantified.
Pp 82-90.
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