Who is the inventor?

The NYT has a story on the invention of the first sound recorder that brings out some important ideas about how difficult it is to credit an invention to a particular individual even today.

“It’s rare that you’ve got a major breakthrough that wasn’t developed by multiple people at about the same time,” said Mark Lemley, professor of intellectual property at Stanford Law School.

……

Whom we credit with an invention often has less to do with who came up with an idea, and more to do with who translated it into something usable, accessible, commercial. Garages and laboratories, workbenches and scribbled napkins are filled with brilliant ideas unmatched with determination, resources and market sensibilities, said Jack Russo, a Silicon Valley intellectual-property lawyer.

The New York Times March 30, 2008

Edison …Wasn’t He the Guy Who Invented Everything?

See also this NYT story on Édouard-Léon Scott de Martinville’s recording which is now audible again

Hear also:

BBC story

Da Vinci’s Evolution

Leonardo made two seminal contributions to the understanding of evolution. The first was an accurate description of fossil formation and the second his recognition of anatomical similarities among animals and humans, an early precursor to the field of comparative anatomy. Both findings would be important in presenting evidence for evolution many hundreds of years later. His findings, however, would lie undiscovered with little impact on succeeding scientific thought until long after his death.

But before we go into that it is interesting, I think, to understand the prevailing conditions in his time, if only to better appreciate his incredible contribution.

Long before Leonardo, during what are now called the Dark Ages, which extended from about 500-1000 CE after the fall of the Roman Empire, Greek and Roman science was largely forgotten in Western Europe. By the sixth century AD the scientific traditions of Ancient Greece had largely petered out, but the Greeks had left behind important texts. Philosophical and scientific teaching during this time was based upon the few copies and commentaries of these ancient Greek texts that remained in Western Europe after the collapse of the Western Roman Empire.

In the seventh century, powerful Muslim armies inspired by the new religion of Islam, in successive invasions conquered the peoples of the Middle East, North Africa and Southern Europe. As they built their vast empire, they not only spread Islam and Arabic, but also appreciated the Greek learning they came across in the ancient texts of Greek Science and philosophy in the Byzantine libraries. The Arabs translated all the important philosophical and scientific works into Arabic and assimilated much of the science of Antiquity into their culture.

In contrast to the Romans, Arab scholars not only assimilated the Greek knowledge but added to it their learning from other cultures such as from the Far East as well as their own commentaries and interpretations, further advancing the gains made by Greeks. New versions of ancient texts with added knowledge were housed in huge libraries across the Islamic empire. Towards the tail end of the Islamic influence, in Moorish Spain for example, the great libraries of Cordoba alone contained some six hundred thousand manuscripts!

For two centuries between 750 and 950, the caliphs of the Abbasid dynasty, centred in Baghdad, supported a mammoth translation effort. Greek works translated into Arabic include Euclid’s geometry, Ptolemy’s astronomy, the medical works of Galen and Hippocrates and the pharmacopoeia of Dioscorides. The caliphs understood the importance of scholarship to their expanding empire. As the reach of the Islamic world spread, stretching from northern India to Spain, they absorbed as much knowledge as they could from each conquest. In Persia and India, unlike Greece, the scientific traditions were still very much alive. And so it was to Persian and Indian scholars that the translators turned when they needed to make scientific, as well as linguistic, sense of the old Greek manuscripts (see previous post). Such expertise was vital because the caliphs wanted their acquired knowledge to deliver practical as well as intellectual benefits to their empire: from monumental architecture and city planning to medical care and transport.

Baghdad, as the capital of the Abbasid empire had been a center of learning for the 8^th and 9^th centures but saw the beginnings of a decline starting at the end of this period. The city’s early meteoric growth slowed due to troubles within the Caliphate, including relocations of the capital to Samarra (during 808–819 and 836–892), the loss of the western and easternmost provinces, and periods of political domination by the Iranian Buwayhids (945–1055) and Seljuk Turks (1055–1135). Nevertheless, the city remained one of the cultural and commercial hubs of the Islamic world until February 10, 1258, when it was sacked by the Mongols under Hulagu Khan. The Mongols massacred most of the city’s inhabitants, including the Abbasid Caliph Al-Musta’sim, and destroyed large sections of the city including its libraries and centers of learning. The sack of Baghdad put an end to the Abbasid Caliphate, and caused some scholars to move west and Spain became the greatest center of Islamic learning and technical knowledge. This moving to a more westerly location would have dramatic consequences for Christian Europe as we will see later.

At around the same time, the great Buddhist university of Nalanda that had operated for over five hundred years from 427 CE to 1197 CE was sacked by Muslim armies under the Pashtun/Turkic invader Bakhtiyar Khilji in 1193. This event is seen as a milestone in the decline of Buddhism in India. In contrast to the Arabs these invaders cared little for the university or the fact that it was a leading center of learning and a majority of the historic texts and scrolls in the university were destroyed at this time.

Nalanda had been one of the world’s first residential universities with dormitories for over 10,000 students and 2,000 teachers. The university was considered an architectural masterpiece, and was marked by a lofty wall and one gate. On the grounds were lakes and parks. The library was located in a nine storied building where meticulous copies of texts were produced. The subjects taught at Nalanda University covered every field of learning from science, astronomy, medicine, and logic to metaphysics, philosophy, Samkhya, Yoga-shastra, the Vedas, and the scriptures of Buddhism. The university attracted pupils and scholars from Korea, Japan, China, Tibet, Indonesia, Persia and Turkey. The Tang Dynasty Chinese pilgrim Xuanzang left detailed accounts of the university in the 7th century. The destruction of the temples, monasteries, centers of learning at Nalanda and northern India were probably responsible for the demise of ancient Indian scientific thought in mathematics, astronomy, alchemy, and anatomy.

As Nalanda and Baghdad died, the 12th century in Europe began an age of fresh and vigorous life: the epoch of the Crusades, of the rise of towns, and of the earliest bureaucratic states of the West, it saw the culmination of Romanesque art and the beginnings of Gothic; the emergence of the vernacular literatures; the revival of the Latin classics and of Latin poetry and Roman law; the recovery of Greek science, with its Arabic additions, and of much of Greek philosophy; and the origin of the first European universities.

During the Renaissance of the 12th century, the increased contact with the Islamic world in Spain and Sicily, the Crusades, the Reconquista, as well as increased contact with Byzantium, allowed Europeans to seek and translate the works of Hellenic and Islamic philosophers and scientists, especially the works of Aristotle, Euclid, Ptolemy, Plotinus, Geber, al-Khwarizmi, Rhazes, Abulcasis, Alhacen, Avicenna, Avempace, and Averroes, among others.

The Renaissance was so called because it was a “rebirth” of certain classical ideas that had long been lost to Europe. It has been argued that the fuel for this rebirth was the rediscovery of ancient texts that had been forgotten by Western civilization, but were preserved in some monastic libraries and in the Islamic world, and the translations of Greek and Arabic texts into Latin. Renaissance scholars such as Niccolò de’ Niccoli and Poggio Bracciolini scoured the libraries of Europe in search of works by such classical authors as Plato, Cicero and Vitruvius. Additionally, as the reconquest of the Iberian peninsula from Islamic Moors progressed, numerous Greek and Arabic works were captured from educational institutions such as the library at Córdoba, mentioned above. The works of ancient Greek and Hellenistic writers (such as Plato, Aristotle, Euclid, Ptolemy, and Plotinus) and Muslim scientists and philosophers (such as Geber, Abulcasis, Alhacen, Avicenna, Avempace, and Averroes), were imported into the Christian world, providing new intellectual material for European scholars. Particularly in the case of mathematical knowledge, some of the work of Muslim scholars was itself a compilation or translation of the earlier work of Indian mathematicians.

Greek and Arabic knowledge was not only assimilated from Spain, but also directly from the Middle East. The study of mathematics was flourishing in the Middle East, and mathematical knowledge was brought back by crusaders in the 13th century. The decline of the Byzantine Empire after 1204 – and its eventual fall in 1453 – led to a sharp increase in the exodus of Greek scholars to Italy and beyond. These scholars brought with them texts and knowledge of the classical Greek civilization which had been lost for centuries in the West and they transmitted the art of exegesis.

By the fifteenth century, even the western outposts of the Islamic world had shrunk considerably under military pressure from Western Europe — the last Muslim forces were forced out of Spain in 1492, the year Christopher Columbus reached America. When the Christian armies won territory during he crusades, their spoils often included the works of Arab scholars. Among the treasures left behind by the Moors in Toledo was one of the finest Islamic libraries filled with precious Arabic translations of Greek scientific and philosophical texts. The occupying Christian forces included Christian monks who set about translating the ancient texts into Latin. A hundred years later this learning was available to the west once again.

As the European Renaissance got under way this accumulated Islamic knowledge was sucked up by powers on the rise, such as Spain and France. Many Arabic works had by then been translated into Latin, but the sources themselves were neglected. Although European libraries and museums collected Arabic scripts, they sat in obscurity as they were largely indecipherable. Over time these trophies of ancient Islam were taken even farther afield to Russia and the United States. India, formerly under Islamic rule, is estimated to have 50,000 such manuscripts.

It was into this environment that Leonardo da Vinci who was fond of describing himself as omo sanza lettere (“an unlettered man”) arrived on April 15, 1452. Born as the illegitimate son of an ambitious and later well connected notary, Piero da Vinci, and a peasant girl, Caterina, Lenoardo spent his early days in Vinci in the company of his uncle Francesco. Francesco, only sixteen years older than Leonardo inculcated in him an understanding and respect for the nature around. Although Leonardo attended one of the customary sculo d’abasco which taught children how to read, write and enough mathematics to survive as a merchant, as an illegitimate child he would be denied entry to a scuola di lettere, a prerequisite to university.

Leonardo made up for this lack of formal education by striving constantly to educate himself in his later life. He learnt Latin to access the manuscripts in the libraries of the time, consulting scholars and assembling a considerable personal library. After his uncle Francesco’s death, Lenoardo moved to Florence to be with his father, who introduced him to his friend, renowned artist and craftsman, Verrocchio. Close to Verrocchio’s workshop was the bottega of the brothers Polliaiolo whose paintings were known for their vivid renderings of muscular bodies. They derived their knowledge of human musculature and anatomy through frequent dissections that it is speculated Leonardo must have watched. At the age of twenty, by then a master painter he was admitted into the guild of painters known as Compagnia di San Luca in 1472. Fortuitously this guild was included in the guild of physicians and apothecaries, which was based at the hospital of Santa Maria Nuova and which allowed him to perform his anatomical dissections.

One of Leonardo’s defining legacies was the synthesis of art and science and he not only brought the knowledge of science to the arts, refining perspective and adding mathematics to drawing, but also brought his keen powers of observation and his skill in the arts to the fields of natural history, anatomy, engineering and architecture.

Now that we have a sense for his time and environs, I would like to return to Leonardo’s two main contributions regarding evolution, the fossil record and comparative anatomy.

Fossils: As I mentioned at the beginning of this article, Leonardo was one of the first scholars to express a relatively modern view of fossils. The fossil record remains first and foremost among the databases that document changes in past life on Earth. Fossils provide the dimension of time to the study of life. Some of the most basic observations about fossils and the rock record were made long before Charles Darwin formulated his theory. The fossil record clearly shows changes in life through almost any sequence of sedimentary rock layers. Successive rock layers contain different groups or assemblages of fossil species.

Leonardo was well acquainted with the rocks and fossils (mostly Cenozoic mollusks) found in his native north Italy having at least observed them during his service as an engineer and artist at the court of Lodovico Sforza, Duke of Milan, from 1482 to 1499. His biographer Vasari wrote that “Leonardo was frequently occupied in the preparation of plans to remove mountains or to pierce them with tunnels from plain to plain.”

Leonardo made many observations on mountains and rivers, and he grasped the principle that rocks can be formed by deposition of sediments by water, while at the same time the rivers erode rocks and carry their sediments to the sea, in a continuous grand cycle. He wrote:

“The stratified stones of the mountains are all layers of clay, deposited one above the other by the various floods of the rivers. . . In every concavity at the summit of the mountains we shall always find the divisions of strata in the rocks.”

Leonardo appears to have grasped the law of superposition, which would later be articulated fully by the Danish scientist Nicolaus Steno in 1669: in any sequence of sedimentary rocks, the oldest rocks are those at the base. He also appears to have noticed that distinct layers of rocks and fossils could be traced over long distances, and that these layers were formed at different times:

“. . . the shells in Lombardy are at four levels, and thus it is everywhere, having been made at various times.”

Nearly three hundred years later, the rediscovery and elaboration of these principles would make possible modern stratigraphy and geological mapping.

Leonardo understood that marine fossils found in the mountains around Tuscany were the remains of ancient life forms, and that they provided evidence that ancient seas once covered areas that are now dry land. In Leonardo’s day there were at least two main hypotheses of how it was that shells and other living creatures were found in rocks on the tops of mountans. Some believed the shells to have been carried there by the Biblical Flood; others thought that these shells had grown in the rocks. Leonardo had no patience with either hypothesis, and refuted both using his careful observations. Concerning the second hypothesis of shells growing in rocks, he scathingly wrote:

 

 

“such an opinion cannot exist in a brain of much reason; because here are the years of their growth, numbered on their shells, and there are large and small ones to be seen which could not have grown without food, and could not have fed without motion — and here they could not move.”

Leonardo also refused to believe the prevailing view that fossils were simply carried to their present destinations by the biblical deluge and he suspected a much older earth than the Bible described.

“As to those who say that shells existed for a long time and were born at a distance from the sea, from the nature of the place and of the cycles, which can influence a place to produce such creatures — to them it may be answered: such an influence could not place the animals all on one line, except those of the same sort and age; and not the old with the young, nor some with an operculum and others without their operculum, nor some broken and others whole, nor some filled with sea-sand and large and small fragments of other shells inside the whole shells which remained open; nor the claws of crabs without the rest of their bodies . . .”(ref)

Indeed, Leonardo doubted the very existence of a single worldwide flood, noting that there would have been no place for the water to go when it receded. He also noted:

 

“if the shells had been carried by the muddy deluge they would have been mixed up, and separated from each other amidst the mud, and not in regular steps and layers — as we see them now in our time.”

 

He noted that rain falling on mountains rushed downhill, not uphill, and suggested that any Great Flood would have carried fossils away from the land, not towards it. He described sessile fossils such as oysters and corals, and considered it impossible that one flood could have carried them 300 miles inland, or that they could have crawled 300 miles in the forty days and nights of the Biblical flood.

 

So, how did those shells come to lie at the tops of mountains? Leonardo’s answer was remarkably close to the modern one: fossils were once-living organisms that had been buried at a time before the mountains were raised:

 

“it must be presumed that in those places there were sea coasts, where all the shells were thrown up, broken, and divided. . .”

 

Where there is now land, there was once ocean. It was possible, Leonardo thought, that some fossils were buried by floods — this idea probably came from his observations of the floods of the Arno River and other rivers of north Italy — but these floods had been repeated, local catastrophes, not a single Great Flood. To Leonardo da Vinci, as to modern paleontologists, fossils indicated the history of the Earth the scale of which extends far beyond human records. As Leonardo himself wrote:

“Since things are much more ancient than letters, it is no marvel if, in our day, no records exist of these seas having covered so many countries. . . But sufficient for us is the testimony of things created in the salt waters, and found again in high mountains far from the seas.”

Obvious as this may be today, in 1508, recognizing fossils as the remains of once living creatures was not a view shared by a majority and in fact in direct opposition to the prevailing scientific thought. As late as 1691 British biologist John Ray denied such an idea.

Comparative Anatomy: Leonardo da Vinci started his observations on the anatomy of the human body at the time he was apprenticed to Andrea del Verrocchio, who insisted that all his pupils learn anatomy. As Leonardo da Vinci became successful as an artist, he was given permission to dissect human corpses at the hospital Santa Maria Nuova in Florence. Later da Vinci dissected in Milano at the hospital Maggiore and in Rome at the hospital Santo Spirito (the first mainland Italian hospital). From 1510 to 1511 Leonardo da Vinci collaborated with the doctor Marcantonio della Torre (1481 to 1511). In 30 years, Leonardo da Vinci dissected 30 male and female corpses of different ages. Together with Marcantonio, da Vinci prepared to publish a theoretical work on anatomy and made more than 200 drawings. From this experience of anatomy and his observations of animals, Leonardo noticed the striking similarities in form and structure between humans and other animals:

“It is an easy matter to men to acquire universality, for all
terrestrial animals resemble each other as to their limbs, that is
in their muscles, sinews and bones; and they do not vary excepting
in length or in thickness, as will be shown under Anatomy.”

From The Notebooks of Leonardo Da Vinci (translated by Jean Paul Richter 1888)

Much later a scientific study of comparative anatomy and embryology to understand evolution was carried out by Carl Gegenbaur, who died over a century ago in 1903. Gegenbaur a senior colleage of Ernst Haeckel put forth his views in his book Grundzüge der vergleichenden Anatomie (1859; Elements of Comparative Anatomy) which became the standard textbook, at the time, of evolutionary morphology, emphasizing that structural similarities among various animals provide clues to their evolutionary history. Carl Gegenbaur noted that the most reliable clue to evolutionary history is homology, the comparison of anatomical parts which have a common evolutionary origin.

This article is based in part on Fritjof Capra’s excellent new synthesis, The Science of Leonardo: Inside the Mind of the Great Genius of the Renaissance.

Post Zero

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 132^nd 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 17^th 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 21^st 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 21^st 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.

Understanding the role of knowledge in human development

This blog is about trying to understand the origins, transference and use of knowledge by groups to adapt to the environment around them. I use each of these terms in their broadest possible terms, thus environment would include not just other human groups, but also the flora, fauna and inanimate world around.