Certainly, memorizing the Koran seemed to stimulate al-Mamun’s intellectual faculties and his inquisitive nature. Unlike his older half brother and rival al-Amin, the future seventh caliph of the Abbasids was always a serious student, something his father had sought to ensure from the beginning. “Let no hour pass without giving him the benefit of some new piece of knowledge, but don’t let him be bored or overwhelmed. Don’t go too easy on him, and don’t allow him to enjoy being idle,” al-Rashid is reported to have ordered his son’s tutor.36 And al-Mamun, who reigned from 813 to 833, was later to be the driving force behind some of the greatest achievements of medieval Arab scholarship. Ibn al-Nadim’s tenth-century compendium of Arab thinkers says the caliph’s intellectual attributes defied enumeration. “We are too rich in famed traditions concerning him to go into detail when mentioning him,” al-Nadim reports.37 One Christian bishop praises al-Mamun’s talents after entering a theological debate against Muslim scholars, with the caliph serving as arbiter: “When the renowned philosopher converses with al-Mamun, incapacity of speech dries up his tongue.”38
A lifelong adept at science and philosophy, al-Mamun also took his astrology seriously, a view shaped by the cultural influences of the Persians in and around the court and soon augmented by translations of important Greek astrological texts. Among the Arabs, astrology long went hand in hand with the other sciences. One royal Baghdad astrologer dubbed it “the mistress of all sciences.”39 The astrologer had to study the nature of things and learn the changing states of animals, plants, and minerals according to the seasons. The expert practitioner of the art had to turn to complex trigonometric functions to capture the elusive movement of the planets. He needed to explore the mysteries of reflection and refraction to account for the projection of planetary rays that influenced events on the distant earth below. And he needed the utmost precision in instrumentation and timekeeping, preparing star tables accurate not just to minutes of degrees but to seconds and beyond.40 In other words, the successful astrologer needed to possess the profile of the emerging modern scientist.
Throughout the Middle Ages, kings, princes, caliphs, and sultans—Christians and Muslims alike—consistently sought the guidance of horoscopes and the astrologers who could tease these and other sophisticated readings from the complex motions of the celestial bodies. Few others could afford the full-time services of such rare and learned figures, or support the costly research and observations required for them to practice and refine their art. However, any insight into worldly events, such as a propitious time for war or a politically useful marriage, or simply on the fate of the dynasty, was seen as justifying the huge expense. Besides, many of the best astrologers doubled as valued physicians, personal counselors, or scientific advisers. This arrangement was also highly favorable to the early scientists, for the support of the local potentate offered a fair measure of protection against the more conservative theologians, distrustful of the scientists’ activities and wary that these “philosophers” might be tempted to trespass on God’s turf.
The integration of these two forces, astrology and classical science, proved a potent incentive for early Arab intellectual development. Some of Baghdad’s greatest astrologers were also important translators and editors of major scientific works, and the best among them strove to make accurate astronomical measurements and calculations in support of their prognosticators’ art. An early Abbasid text explicitly links the two, proclaiming that both God and the stars had commanded the Arabs to renew the state of the world’s learning: “The people of every age and era acquire fresh experiences and have knowledge renewed for them in accordance with the decree of the stars and signs of the zodiac, a decree which is in charge of governing time by the command of God Almighty.”41
Much of al-Mamun’s patronage for the study of the stars was no doubt driven by a royal passion for astrology, but he also evinced a healthy curiosity about the natural world and a predilection for investigation and the scientific method. During a visit to Egypt in 832, the last full year of his life, the caliph sought unsuccessfully to learn the meaning of the ancient hieroglyphs but did manage to break into the Great Pyramid of Giza, only to find that the royal tomb had long since been emptied by robbers.42 Four years earlier, the caliph launched a systematic program of astronomical studies at the first specialized observatories, established in Baghdad and Damascus, as well as the first large-scale expedition devoted to scientific experimentation.43 These endeavors reveal how the Arab scientists approached and assimilated the classical texts—as starting points for their own research and studies, not as ends in themselves. And such projects helped launch the careers of some of early Islam’s greatest scientists and intellectuals.
Caliph al-Mamun took a deep interest in the work of the scholars at the House of Wisdom, going there regularly to discuss the latest research, royal funding, and related matters directly with his experts and advisers. He also emphasized greater study of mathematics and astronomy in the work already under way. But even with a phalanx of leading scholars at his disposal, he could not always get the answers he sought. “Al-Mamun wanted to know the size of the earth, so he made some investigations about this and found that Ptolemy had stated in one of his books that the circumference of the earth was so many thousand stades,” recounts one of the caliph’s finest astronomers, Habash al-Hasib. “Thereupon he asked the interpreters about the meaning of stades and they gave different interpretations.”44
With his experts stumped, al-Mamun was determined to find out by measuring the length of one degree of the earth’s Great Circle, mapping out an ambitious scientific experiment to solve the riddle. Extending an experiment by the ancient Greek mathematician Eratosthenes, the caliph dispatched two teams of astronomers, surveyors, and instrument makers to the desert plain of Sinjar, near Mosul, where they took initial readings of the sun’s altitude before setting off in opposite directions, one group heading due north and the other due south. As they moved, they took care to note the distance they had traveled, inserting special markers into the ground along their path. When a second set of solar readings indicated they had traveled one degree along the meridian, they stopped and retraced their steps, double-checking the distance they had come.
The two independent results were then analyzed and compared, yielding a remarkably accurate final figure. Al-Mamun’s researchers’ calculation of the circumference of the earth was very close to what we know it to be today. Despite this success, one leading astronomer’s account of the mission says that the caliph’s teams could have saved themselves a lot of trouble by using one simple observation and some basic trigonometry. “There is another method for the determination of the circumference of the earth. It does not require walking in deserts,” sniffs the accomplished mathematical astronomer al-Biruni in his Determination of the Coordinates of Cities.45 Whatever the approach, medieval Arab readings of the position of the sun and the geographic coordinates of cities, determinations of time and date, and related findings were all of similarly high caliber. The early Islamic observations were not exceeded for accuracy until the time of Danish astronomer Tycho Brahe in the sixteenth century.46
When things did go wrong, al-Mamun was quick to intervene. He once used a wartime visit to Damascus to conduct a scientific fact-finding mission, after data from earlier attempts to chart the sun and the moon across the heavens from the Baghdad observatory proved grossly inaccurate. The caliph called on his Syrian advisers to find a qualified astronomer who could improve upon the Baghdad results. “Al-Mamun ordered him to make ready instruments of the greatest possible perfection and to observe the heavenly bodies for a whole year,” says Habash al-Hasib. This wealth of astronomical material was then collated, on al-Mamun’s instructions, and published “for those desirous of learning that science.”47 The chagrined Baghdad astronomers apparently concluded that their best tack was to blame their tools; a brass instrument used to take some of the faulty measurements, known as an armillary sphere, was sold for scrap in t
he stationers’ bazaar.48
The founder of Baghdad, al-Mansur, must have had high hopes when he first sent an emissary to the holy city of Arin, then the Hindu center of astronomy and mathematics, in search of Indian scholars.49 A thirteenth-century Hebrew commentary says the caliph had received word of the teachings of the Indian sciences and, having satisfied himself that such matters were not contrary to Islam, sent one of his Jewish subjects to entice the Indians to Baghdad to share their wisdom.50 But even the caliph could not have anticipated the profound effects on Muslim intellectual life that would be produced by the sudden infusion of a new and alien way of thinking about the physical world. By the early eighth century, scattered outside influences had already begun to reach the Arabs by way of early Indian and Iranian star tables. Such tables were known in Arabic as zij, from the Persian word zik, or “guiding thread,” with their orderly rows and columns suggesting the warp and woof of traditional weaving. Soon Arab astronomers, astrologers, doctors, and other men of science were regularly consulting the zij to chart the movement of the heavens and even to tell time and fix dates. The royal astrologers Mashallah and Nawbakht had relied on one such Iranian example, the zij al~Shah, to fix the date for the construction of Baghdad.51
Still, the visit of the Hindu delegation to the Abbasid court, around 771, marked a true turning point in Arab intellectual history. The Indian sages brought with them prized Sanskrit scientific texts, believed to be in part the work of the seventh-century scholar Brahmagupta and known as the siddhanta. According to a tenth-century account by the widely traveled geographer al-Masudi, the documents contained all Hindu knowledge of the spheres, the stars, mathematics, and other sciences.52 Another account notes the heavy reliance in the siddhanta on the sine function—an invaluable contribution developed by the Hindus and later seized upon and refined further by the Arabs—as the basis for all its calculations.53 By the ninth century, all six trigonometric functions—sine and cosine, tangent and cotangent, secant and cosecant—were known. Only the former was an import; the other five were Arab discoveries. This allowed the substitution of calculations in the place of geometric diagrams, paving the way for the full development of modern mathematical astronomy.54
Traditionally, Hindu scientific works were written in verse, for ease of memorization, and offered little if anything by way of explanation, procedures, or proofs. As a result, the early Arab scholars and translators were faced with two immediate challenges: to disentangle the scientific content from the stylized Sanskrit verse and then to discover for themselves the complex arithmetic and astronomical procedures implied in the text. Commentaries that could have shed much light on the latter operation were not part of the Indian largesse.55 These problems proved both short-lived and ultimately beneficial to the Abbasid quest for knowledge. They forced the Arabs to grapple with the fundamental science of the siddhanta literature rather than rely on simple imitation, and they virtually ensured that Iranian and Greek scientific traditions would over time be brought to bear on the questions at hand. In these ways, the initial Arabic translation of the siddhanta helped launch a dynamic body of work that culminated in a synthesis of classical and contemporary learning.
No one did more to advance the latest trends and then explain and popularize the results than the mathematician and astronomer Muhammad ibn Musa al-Khwarizmi. Born around 783, al-Khwarizmi was able to take full advantage of the social mobility and intellectual meritocracy that characterized early Abbasid scholarly life in Baghdad. Little is known of his exact origins, although his name suggests that he or his family originally came from Khwarazm—Khiva in present-day Uzbekistan. Al-Khwarizmi’s Muslim faith is made clear by the pious prefaces to some of his works, but his forebears may have been Zoroastrians. As a prominent researcher attached to al-Mamun’s House of Wisdom, al-Khwarizmi went on to attain rare heights in such disciplines as astronomy, arithmetic, and algebra.
Given his expertise and interests, al-Khwarizmi may well have participated in the caliph’s astronomical observations at Baghdad, or even the desert survey of the length of one degree. His work on the siddhanta, however, is more certain, for he produced around 825 an abridged version at al-Mamun’s request, as well as two famous star tables, known as the zij al~Sindhind, which were used for centuries across the Muslim world and later in Christian Europe. Today, al-Khwarizmi’s tables stand as the oldest extant example of the Islamic zij, although the surviving form has undergone significant modification in the intervening centuries. His work on the astrolabe, likewise the oldest extant Muslim example of its kind, resonated for centuries. “He was one of the masters of the science of the stars,” Ibn al-Nadim recounts. “Both before and after [confirmation by] observation, people relied upon his first and second astronomical tables known as the Sindhind.”56
The success and popularity of al-Khwarizmi’s zij helped establish the star table as a fundamental element of the Arab scientific arsenal, a fact attested to by its widespread use, its remarkable longevity, and its almost continuous refinement. More than 225 such tables were compiled in the Muslim world between the eighth and the nineteenth centuries, although roughly half of these are lost and known only through references in commentaries or other scientific works.57 Some were computed meticulously to reflect accurate data at a given location, while others were half-understood copies or sloppy redactions of earlier tables. The surviving versions of al-Khwarizmi’s tables had their astronomical data transposed for use in Spain’s Western Caliphate, where the work retained its popularity long after it had been surpassed by that of Muslim scientists in the East.
A correctly calibrated zij provided the user with all the tools needed to pinpoint the positions of the sun, the moon, and the five visible planets; to tell time day or night based on stellar or solar observations, which was especially useful for regulating Islam’s five daily prayers; and to determine the possibility of sighting the crescent moon, which marks the start of the Muslim lunar month. The star tables were indispensable for casting a horoscope without time-consuming observations, perhaps their biggest selling point. The zij could also be supplemented by the use of astronomical instruments, mostly for solving complex problems in spherical geometry and timekeeping. One thousand years after its creation, the zij al~Sindhind of al-Khwarizmi was still in use in Egypt.58
The transmission of Hindu astronomy did not, of course, take place in a vacuum but was part of the wholesale Arab campaign to absorb, master, and build upon classical knowledge. The Indians’ advanced art of reckoning—characterized by the decimal place system of nine numerals and a zero, virtually the system we use today—either accompanied the handover of the siddhanta or followed very quickly on its heels. It was certainly known within decades of the arrival of the Hindu astronomical science.59 As he did with the zij al~Sindhind, al-Khwarizmi produced a successful treatise on the use of the new system, The Book of Addition and Subtraction According to the Hindu Calculation, the first known Arabic work on the subject.
“We have decided to explain Indian calculating techniques using the nine characters and to show how, because of their simplicity and conciseness, these characters are capable of expressing any number,” al-Khwarizmi informs his readers. He then provides a detailed explanation of the positional principle of decimal notation, with reference to the Indian origin of the nine number symbols, as well as the use of the zero—“the tenth figure in the shape of a circle”—to prevent confusion over the position of the figures.60
Al-Khwarizmi’s Arabic text has been lost, but it survives in twelfth-century Latin translation, the chief vehicle by which the so-called Arabic numerals were conveyed to the West. For Muslim readers, The Book of Addition and Subtraction explained fully a system that was already in some use by the early ninth century, and within a little more than one hundred years it had led to the discovery of decimal fractions. These were used to find the roots of numbers and later to calculate the value of pi—the ratio of the circumference of a circle to its radius—correctly to an impre
ssive sixteen decimal places.61
Perhaps no work brings out the genius of al-Khwarizmi, particularly his ability to identify and master an emerging discipline or technology and then explain it fully and effectively, as much as his treatise on algebra. The Book of Restoring and Balancing—the second element of the Arabic title, Kitab al-jabr wa’l-muqabala, bequeathed the West the term algebra—was dedicated to his patron Caliph al-Mamun and wrapped in a shroud of religious and practical utility. “That fondness for science, by which God had distinguished Imam al-Mamun … has encouraged me to compose a short work, … confining it to what is easiest and most useful in arithmetic, such as men constantly require in cases of inheritance, legacies, partition, law-suits, and trade, and in their dealings with one another, or where the measuring of lands, the digging of canals, geometrical computation, and other objects of various sorts and kinds are concerned.”62
In one example, al-Khwarizmi guides the reader through the settlement of a woman’s estate after she dies and leaves a husband, a son, and three daughters. Under the prevailing inheritance rules, a husband was entitled to one quarter of the estate, and a son’s share was twice that of a daughter—an improvement over pre-Islamic Arab practice, in which women generally received nothing.63 As al-Khwarizmi shows, a relatively simple algebraic operation solves the equation for any size estate. More complex problems, including the computation of the annual religious tax, or zakat, follow.
Here, then, was the beginning of the Arabs’ study of algebra, a field in which they excelled, as demonstrated by both the large number of scholarly commentaries on al-Khwarizmi’s work and their production of many original algebra texts. Over the centuries, the pervasive influence of The Book of Restoring and Balancing can be seen in the repeated, verbatim use of several of al-Khwarizmi’s most famous examples of quadratic equations. In his typical fashion, al-Khwarizmi managed to combine Hindu and early Babylonian influence in solving such equations by the means of algebra with the Greek tradition of geometric proofs to validate the results.64 By stressing the relationship between analytic and geometric solutions to such problems and introducing the decimal place system, al-Khwarizmi, for the first time in mathematical history, established the art of analysis as a worthy discipline in its own right and put it on an equal footing with the more glamorous geometry. He also makes clear in later chapters that, his fine introductory remarks to al-Mamun notwithstanding, he is interested in algebraic theory and calculation for their own sake.65
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