It was a busy couple of centuries.
AL-KHWRIZM +
ALGORITHM = ALGEBRA
The ancient root of the word algorithm is little understood today, despite its ubiquitous usage to describe the magic formula behind everything from the Google search engine to NASA spacecraft.
Mystery solved.
Muhammad ibn Msa al-Khwrizm is the father of modern mathematics. His name lives on in English, in mangled form, in the word algorithm.
We know very little about al-Khwrizm’s life. His name suggests he was born in the region of Khwarazm in what is now Uzbekistan. There are clues that he was a Zoroastrian who may have converted to Islam.
We know a lot about al-Khwrizm’s work as a scholar in al-Mansur’s court in Baghdad. He introduced what were then called “Hindu numerals” to the Muslim world. He also produced an important astronomical chart that made it possible to calculate the positions of the sun, the moon, and the major planets and to tell time based on stellar and solar observations.
Al-Khwrizm’s most important contribution to science was a groundbreaking mathematical treatise: Al-Kitab al-Mukhtasar fi hisab al-jabr wa’l-muqabala. The title translates as The Compendium on Calculation by Restoration and Balancing, but the book is most often referred to as al-jabr, or algebra. His treatise was a combination of mathematical theory and practical examples related to inheritances, property division, land measurements, and canal digging. He was the inventor both of quadratic equations and mathematical word problems. Some of his word problems became classics, which meant they were still giving students grief several centuries later.
The golden age of Islam created new states, cities, and academic disciplines. This Islamic renaissance was built on the backs of thousands of slaves, servants, and prisoners, who worked as miners extracting gold, along with silver, copper, and lead, from vast precious metal reserves under the Middle Eastern desert. These minerals were originally brought to Earth by meteorites from outer space. In the seventh century, with no major agricultural or industrial resources, mining and exporting gold bullion enabled the Islamic empire to trade with the rest of the world—and served as the means to mint a new Islamic currency.
AN ARABIAN MINE
JAMAL, A SLAVE IN HIS LATE TWENTIES FROM Northern Africa, awakens at the morning call on his sleeping mat in the miners’ barracks. He quickly cleans up and kneels for the morning prayer. After a brief meal, he carries a lantern and his pick and walks with his fellow miners the two hundred yards from their barracks. Near the entrance of the tunnel, the men form a line. Just as he has done every morning for the last ten years, Jamal lights his lantern and checks that it has sufficient oil as he readies himself to enter the Mahd al-Dhahab mine. He’ll be underground for the remainder of the day, not returning to the surface until after sunset.
At the mouth of the mine, Jamal sees the owner-operator, a prominent man of the local Quarashi tribe, known to the men as al-Hajjaj. Jamal averts his eyes when al-Hajjaj barks orders at the men to make haste, pointing at the newer of two tunnel entrances. As if we don’t know which tunnel to enter, thinks Jamal as a current of fear travels up his spine. New tunnels bring extra danger to miners since there is still rock to break apart and rubble to be cleared before picks can be used to extract gold nuggets from new veins—yet to be found.
Jamal leads his gang until they reach the spot where they finished yesterday fifty meters underground. He takes up his pick and begins to loosen an area of rock from the low ceiling ahead of him, working at the same crevice for several hours, handing loose rock back to the man behind him, who hands it to the next man, continuing until the rock reaches the wagon at the rear of the line used to bring rock up to ground level, where it will be inspected for traces of gold.
Suddenly Jamal hears the dreaded sound of loose rock falling behind him, followed by muffled sounds of panic. He freezes with his pick in midair. As more rocks fall from above, Jamal crouches on the ground, with his arms over his head, praying for the collapse to stop, or for his death to come quickly. When the dust from falling rock clears and it grows quiet again in the tunnel, Jamal realizes he’s alive and alone on the wrong side of a collapsed pile of debris. He calls out several times, but gets no response.
Jamal then begins the difficult work of removing the stones that separate him from the only exit from this tunnel, not sure how much rock has fallen. He has no idea whether he is the only survivor of this collapse, or its only victim. Jamal tells himself not to think, just to keep going, and be thankful for the fact that he still has a working lantern. Rock by rock, beginning with the least precarious, his work continues slowly and carefully.
When enough loose stones have been cleared, Jamal braces himself on his haunches and picks up a rock as big as a man’s head, noticing it is heavier than the others. He twists his torso to drop the rock behind him, turning it over, about to put it down, when he thinks to bring the rock up to eye level for closer inspection. Unbelieving at first, Jamal brings the lantern closer, amazed to see a shiny piece of gold nugget buried deep inside the now-split piece of ore. Jamal’s excitement is immediately tempered by the thought that he may not live to celebrate this important find—the first sizable nugget to come from the new tunnel. He calls out again to the others, hoping to be heard. When he is greeted by silence again, Jamal’s spirit falls; tired and hopeless, he lies down on the mine floor, just as the oil in his lantern runs out, leaving him in total darkness.
On the other side of the collapsed tunnel, other miners scramble to remove fallen rock from the legs and torsos of partially buried miners. So much rock has fallen and so many are buried; things don’t look good for Jamal.
At daylight, back at the mouth of the mine, a large crowd has gathered to watch and wait for news of the trapped miners. Owner-operator al-Hajjaj directs a party of rescuers, who carry miners out of the tunnel one by one, some writhing in pain but still alive, others lying dead on stretchers.
Finally, the last man to be pulled out is placed on the ground by his rescuers. It is Jamal, covered with dirt and sweat, but smiling as he holds up the piece of ore with its nugget of gold. Shouts and cheers are heard from the other miners in the crowd.
The next day, again at daybreak, Jamal’s piece of gold is stocked by another worker on a camel that is then led away for the trip to the Mahd al-Dhahab smelting operation. Jamal, proud of his find, stands again at the head of the line of miners, preparing to reenter the same tunnel from which he was rescued the day before.
Gold mining was dangerous and backbreaking work.
One Arabian mine, the Mahd al-Dhahab (Cradle of Gold), is 155 miles southeast of Medina and 170 miles northeast of Mecca, the major religious centers of the Islamic world. Still in business today, Mahd al-Dhahab produced 1.5 million ounces of gold from more than a million tons of ore in historic times.
IN 750 CE, THE ARMIES OF Abu al-Abbas defeated the last of the Umayyad caliphs in a series of bloody battles. Now a new caliph, and a new dynasty, sat on the throne of Damascus.
Some men in al-Abbas’s position would have hunted down the remaining members of the old dynasty to ensure no heirs remained to lay claim to the throne. Instead, the new caliph invited the surviving Umayyads to a feast. At first, his guests perched nervously on the cushioned benches in the dining hall of the Abbasid family estate in Damascus. Servants moved around the room, offering them tidbits of spiced meat, honeyed dates, and fresh oranges. Wine flowed without regard to the Prophet’s prohibition on alcohol. Skilled slaves played tamburs in the background. Slowly, the Umayyads relaxed and began to enjoy al-Abbas’s hospitality. They didn’t notice when someone gave an unobtrusive signal.
Suddenly, the servants stripped off their robes, displaying the armor beneath. Someone screamed. The Umayyads sprang to their feet. Some ran to the doors, which had been blocked. Others fought back as best they could, unarmed men against armored solders.
ABD AL-RAHMAN
ESCAPES DAMASCUS
Abd al-Rahman and h
is younger brother escaped from al-Abbas’s slaughter together. As al-Rahman later described it:
Joined by my freed man, Badr, we reached the bank of the Euphrates, where I met a man who promised to sell me horses and other necessities; but while I was waiting he sent a slave to find the Abbasid commander. Next we heard a noise of the troops approaching the farmhouse; we took to our heels and hid in some gardens by the Euphrates, but they were closing in on us. We managed to reach the river ahead of them and threw ourselves into the water. When they got to the bank they began shouting “Come back! You have nothing to fear.” I swam and my brother swam.
Al-Rahman made it across the river. His brother was captured and killed.
One young Umayyad prince, Abd al-Rahman, not yet twenty, survived the slaughter. He fled through the North African deserts toward present-day Spain—the newest, most distant, and most neglected province of the Islamic empire. When al-Rahman finally reached his goal, five years later, he deposed the ruling governor in the name of the Umayyad dynasty.
SPAIN HAD BECOME PART OF the Islamic empire forty years earlier when a band of Muslim invaders from North Africa defeated the last of its Visigoth rulers. By 720 CE, Muslims had conquered most of the Iberian Peninsula. A cluster of small Christian kingdoms managed to hold a narrow strip of the desolate country in the northeast, an area so wild that not even the Romans had managed to subdue it completely. The conquerors named the region al-Andalus, the land of the Vandals, and chose the old Roman city of Córdoba as their capital. By the standards of the vast Islamic empire ruled from Damascus by the Umayyad caliphs, the new province was poor, backward, and unattractive. Just like the rest of Medieval Europe.
Abd al-Rahman and his Umayyad successors brought the technical, cultural, and commercial benefits of the Islamic world to al-Andalus. The previously impoverished country literally blossomed under their rule. Muslims brought Arab technologies for making the most of scarce desert resources to the semi-arid climate of the Iberian Peninsula. Dams and irrigation systems weren’t the only change. Muslims also introduced new crops that would transform Europe’s diet, including rice, sugar, oranges, lemons, spinach, melons, and eggplant. By the tenth century, the Arab agricultural revolution had transformed Spain into the wealthiest, and best-fed, region of Europe.
More productive land allowed more workers to move to the cities and work as specialized craftsmen. Soon Spanish luxury goods were traded throughout the Muslim world, including musical instruments from Seville, leather goods from Córdoba, and steel weapons from Toledo. As the prosperity of Muslim Spain grew, its cities became oases of luxury, wealth, tolerance—and learning.
THE WORLD’S
FIRST AVIATOR
875 CE. Sixty-five-year-old scientist Abbas Ibn Firnas leapt off the top of the Rusafa palace of Córdoba in a device made of feathers attached to a wooden frame. He had designed the hang glider himself after hours of watching birds in flight. For several minutes he glided on the air currents, able to adjust his altitude and steer toward his targeted landing spot. The gliding was wonderful; the landing was rough. Ibn Firnas was badly injured in the crash. After he was pulled out of the wreck, he claimed that he hadn’t paid enough attention to the way birds use their tail feathers; if he’d only added a tail apparatus to the glider, he’d have been just fine.
Abbas Ibn Firnas is not well-known in the West, but he is honored as the first aviator in the Arab-speaking world. Both a moon crater and the Ibn Firnas Airport in Baghdad are named after him.
Abd al-Rahman’s successors consciously chose to create a city that would rival Baghdad in the pursuit of the arts and sciences. They actively recruited scholars, poets, musicians, and artists, offering them tempting incentives to leave the comfortable metropolises of the Abbasid empire for the wild west of Spain. They sent agents to the older cities of the Muslim world to purchase copies of important books. They funded libraries, hospitals, and research. The royal library alone held some 400,000 books at a time when the largest library in Christian Europe had only 640 books in its catalog. By the reign of Abd al-Rahman III in the tenth century, the Benedictine nun, Rosita, would describe Córdoba, the region’s capital, as “the ornament of the world . . . it was wealthy and famous and known for its pleasures and resplendent in all things, especially for its seven streams of wisdom.”
AS 1999 DEMONSTRATED AGAIN, people get very nervous when a millennium is about to end. In 999 CE, many European Christians believed the world would end in a matter of months. Signs of the apocalypse had been reported throughout Europe: eclipses, rains of blood, Viking attacks. Amid this fear, Gerbert d’Aurillac, archbishop of Ravenna, soon to be Pope Sylvester II, sat at his tilted writing desk, composing a letter in response to an urgent request from his friend, Adalbold, bishop of Utrecht: “In these geometrical figures which you have already received from us, there was a certain equilateral triangle, whose side was thirty feet, height twenty six, and according to the product of the side and the height the area is three hundred ninety.”
Pope Sylvester II
The apocalypse could wait. The question of how to find the area of a triangle was more important—and more difficult.
By the middle of the tenth century, rumors of the studia Arabum began to reach curious minds in Europe.
The Dark Ages were no longer quite so dark, but education was still limited in terms of both who was educated and what they learned. Charlemagne’s reforms had created monastic and cathedral schools designed to train boys for service in the Church, for running a large estate, or for running a large estate for the Church. In a time when even nobles were often illiterate, reading, writing, and the simple arithmetic possible in Roman numerals represented giddy heights of intellectual achievement. In theory, more advanced students moved on to the seven liberal arts of the classical world: the trivium of grammar, rhetoric, and dialectic; and the quadrivium of arithmetic, geometry, astronomy, and music. In practice, there was no one in France qualified to teach the quadrivium in 967 CE, when Gerbert was ready to advance. If he wanted to learn more, he would have to go to Spain, where the “seven streams of wisdom” flowed freely.
Gerbert, later known as the Scientist Pope, was the first and the most infamous of the handful of European scholars who made their way to Spain and Sicily to study the black arts of mathematics and astronomy. Just as in Baghdad, the early interest was in these fields of study. Gerbert tried to introduce Arabic numbers and the art of algebra on his return. (And was accused of practicing “Saracen magic” for his pains.) Adelard of Bath, who followed him more than a hundred years later, translated Euclid’s Elements into Latin and wrote treatises on using the astrolabe and Ibn Firnas’s version of al-Khwrizm’s astronomical chart.
The Europeans’ first attempts at learning the studia Arabum were stumbling. Gerbert and his friends struggled with the simplest problems in geometry. Adelard’s translation of Euclid included more than seventy transliterations from the Arabic when there was no Latin word to describe the concept. Europe’s first real access to Arabic learning came in 1085, when the Christian ruler Alfonso VI captured Toledo from the Muslims. Under the rule of “Alfonso the Wise,” the city became the center of an informal school of translation, similar to that in ninth-century Baghdad. By the thirteenth century, texts translated into Latin from Greek and Arabic were finding their way to the new universities of Oxford and Paris.
Islam had set the West on the path to the Renaissance and the rise of modern science. English philosopher and mathematician Roger Bacon summed up the role of the East in keeping civilization alive during Europe’s Dark Ages when he wrote, “Philosophy is drawn from the Muslims.”
JUNE 8, 793 CE. FOR MORE THAN a hundred years, the monastery of Saint Cuthbert had been a sanctuary for learning. It was also a storehouse of riches. Golden crosses and crosiers gleamed in its lavishly appointed chapels. Illuminated manuscripts filled its library. Tapestries decorated its walls.
The Dark Ages were no longer quite so dark . . . Islam had set the
West on the path to the Renaissance and the rise of modern science.
Situated on the tidal island of Lindisfarne off the east coast of England, the monastery’s inhabitants had been sheltered from the fighting between local chieftains that was a regular part of life in the British Isles. When three strange ships landed directly on the beach, it excited no more than curiosity. Then bands of armed men poured out of the ships, and the violence began. Monks and villagers alike tried to defend the settlement, but the raiders beat them back. They pillaged houses and religious buildings, taking food as well as treasures. They seized cattle and took captives for ransom or sale as slaves. According to the British cleric Alcuin, the Vikings left “the church of St. Cuthbert spattered with the blood of the priests of God, despoiled of all its ornaments.” The raiders left as quickly as they had come, leaving the island’s remaining inhabitants in shock.
THE ATTACK ON LINDISFARNE was the beginning of the “Viking Age.” Sometime in the eighth century, the Norse people of Scandinavia began to produce light, fast ships that could sail across open seas and travel inland up rivers using either oars or sails. Soon after, Viking raiders began to harry the coasts of Europe. The first targets of those who went “a-viking” were unprotected settlements on the coast or near the mouths of navigable rivers.
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