The fall of the Roman empire ushered in the period known as the Dark Ages—a time of great change and uncertainty, with new empires created in the aftermath. Much of the original scientific knowledge from the ancient world was lost to the West, but kept alive by Islamic astronomers in the East. The period also saw new advances in astronomy and mathematics, thanks to enlightened scientists such as Omar Khayyam.
In 1900 the wreck of a Greek ship was discovered off the island of Antikythera. The vessel was dated to about 80 BC. The ship alone was a valuable archaeological find, but amongst the cargo was an object that has puzzled scientists and archaeologists for years. It consisted of a frame containing a set of brass wheels, very similar to the mechanism of a clock but a thousand years before its time, and quite unlike anything else ever discovered. The best explanation so far is that the mechanism was an astronomical device used to calculate the positions of the planets—an advanced version of an instrument known as the astrolabe, which was also used to predict eclipses and to follow the motion of the Moon. The device was an isolated find, but if we accept the antiquity of the Antikythera instrument then we must accept that Greek and Roman technology in the ancient world was far in advance of what had previously been thought.
The traditional date for the fall of the Roman empire is usually cited as 476 when Romulus Augustus (reigned 475–76), the de facto emperor of the Western Roman empire, was deposed by Odoacer (435–93). The mighty Roman empire that had lasted so long and that had eventually brought Christianity to the Western world, was finally overthrown by people the Romans called the barbarians. The centuries that followed became known as the Dark Ages. Rome became divided into two empires: the East and the West. The Western empire fared badly; it became a feudal, agrarian society, and after a few generations much of the knowledge passed down from the ancient world was never used and in many cases was lost. The Eastern empire, the Byzantine empire centered on Constantinople, fared much better. Manuscripts and other forms of knowledge from the library at Alexandria found their way to the East where many scripts were copied and translated into Arabic so that they could be studied by Islamic scholars.
For more than a century after the fall of Rome the Islamic empire seemed content with its boundaries, but after the flight of the prophet Mohammed (570–632) from Mecca in 622 the empire began to expand. The city of Alexandria survived Rome by nearly two centuries, but in 641 it finally succumbed to the Arabian invaders. The sacking and burning of the great library, the greatest store of knowledge in the world, is often quoted as the barbaric work of Islam, but centuries later it transpired that this was not quite the case. Many of the manuscripts resurfaced, sometimes as the originals in Greek or Latin, sometimes as Arabic translations. When the period of military expansion was complete, the Islamic scholars became great admirers of the civilizations of the past, and were keen to retrieve as much knowledge as they could from the ancient world. Within a hundred years the Islamic empire dominated the whole of the Middle East. The empire spread westward across Asia Minor, into Egypt, and across the north of India as far as the border of China. It also spread to the west along the southern shores of the Mediterranean, and in 771 the Moors crossed the Straits of Gibraltar and settled in the region called Andalusia in southern Spain.
Andalusia was once part of the Roman empire. Scipio Africanus (236–183 BC) conquered the region in 210–206 BC, and it eventually became the Roman province of Baetica. This province flourished under Roman rule and was the birthplace of the emperors Trajan (c.56–117) and Hadrian (76–138) and the writers Lucan (39–65) and Seneca (c.3 BC–AD 65). Roman rule lasted there until the Vandals, closely followed by the Visigoths, overran the region in the fifth century. Thus when the Moors arrived in the eighth century Andalusia already had an impressive Roman history—but it was not a history well known to the local people; it had all happened long before living memory.
Very little is known about the state of astronomy in the centuries immediately after the fall of Rome, but by the ninth century we see the first appearance of the fruits of Arabian knowledge. The earliest-known astrolabes, for example, appear in Islam, and an example from Damascus still survives from about 830. One of the astrolabe’s uses was to determine the elevation of celestial objects above the horizon. It comprised two or more flat metal discs with calibrated scales, attached so that both, or all, the discs could rotate independently. For early navigators and astronomers it served as a star chart, a compass, a clock and a calendar. It survived for centuries and it had no equal as a navigational device until the introduction of the sextant in the 18th century. The Danjon astrolabe is what is known as a portable solstitial armillary, modified for observations of the stars. The instrument is suspended by a small hook or eye, and it consisted initially of a single ring that hung in a vertical plane. Pivoted at the center of the ring was a rod equal in length to the ring diameter, carrying sights at either end. It could be aligned on a star or a planet, with an angular scale inscribed on the armillary ring to show the object’s altitude.
Many important advances in the field of mathematics were made in the Islamic world. One of the simplest, but most significant, ideas was the introduction of a symbol for the number zero, making possible the Arabic system of numerals with a base of ten. It is the system used almost exclusively today. To appreciate what a great step forward this represents we need only look at the problems of multiplication and division thrown up by the Roman numeral system that was widely used in the West at that time. Arabian mathematics went much further than just devising the numerical system we use today. They also introduced algebra, the system of mathematics where unknown quantities are represented by symbols. Equations could be manipulated algebraically to simplify many mathematical calculations.
We know the names of many of the early Islamic astronomers, and we even know a little about their work, but it is not until the ninth century that we can identify individual astronomers and their contributions to knowledge. Albategnius (c.850–929) was one of the earliest of the Islam school. He was an Arabian nobleman born in Batan in Mesopotamia, and he became the leading astronomer and mathematician of his time. He drew up improved tables for the motion of the Sun and the Moon. He knew that the Earth’s orbit around the Sun was an ellipse, and he measured its eccentricity. He also measured the inclination of Earth’s equator to its orbital plane and he made an estimate of the number of days in the year. Albategnius made his observations over a period of 40 years from his observatory in Rakku, and they were summarized in his book Movements of the Stars, published in Europe long afterward in 1537. His estimate of the year was so accurate that it was used by European astronomers in the 16th century for the Gregorian reform of the Julian calendar.
Albategnius was followed two generations later by the astronomer Al Sufi Abd al-Rahman. He was born in 903 and lived for 83 years. He was another Persian nobleman, also known by the Latinized name Azophi. He published a work called the Book of the Fixed Stars, which first appeared in about 964. It included a catalog of 1018 stars, giving their approximate positions, magnitudes and colors. It obviously owed much to Ptolemy’s Almagest, but it also contained many Arabic star names that are still in use today, although sometimes in a corrupted form. An interesting entry is the earliest-known reference to the Andromeda Galaxy, our closest galaxy. It was also at about this time that a Persian mathematician and astronomer called Abul Wafa (940–97) studied and described geometrical constructions using only a straight edge and a fixed compass. He later dubbed his instrument a “rusty compass” because it never changed its radius. Wafa also pioneered the use of the trigonometrical functions; he compiled tables of sines and tangents at intervals of 15 arc-minutes, and he seems to be the first to have used the secant and cosecant functions. Much of his work was carried out as part of an investigation into the complex orbit of the Moon.
In the early centuries it is always difficult, and usually impossible, to differentiate between astronomers and astrologers because there was only a fine boundary between them. Astrologers were keen to know the positions of the planets as accurately as possible in order to help them formulate their predictions. The astrologer al-Birini flourished at the end of the first millennium. He was born just before sunrise on September 4, 973 at the city of Kath on the River Oxus, in what is now Uzbekistan. He was interested in all branches of learning and was fluent in six languages. In 998 he moved to Gurgan on the Caspian Sea where he completed his first major work called The Chronology of Ancient Nations. He also wrote a Book of Instruction in the Elements of the Art of Astrology, dedicated to a high-ranking woman called Rayhanah. It begins with sections on geometry and arithmetic, then describes the astronomy of Ptolemy and also includes a detailed section on the use of the astrolabe. The remainder of the book concentrates on astrology and shows how many of the world’s events and disasters were forecast in the stars.
In about 1000 the Arab mathematician and physicist Alhazen (c.945–c.1040) wrote the first important book on optics since the time of Ptolemy. He rejected the older notion that light was emitted by the eye in favor of the view accepted today—that light is emitted from a source like the Sun, or reflected from an object, and then gathered into the eye. His Treasury of Optics was written at the end of the first millennium, but it was not published in Latin until 1572, over 500 years later, giving another example of how long some of the Arabic texts survived and how they came to be known in Europe. He described lenses, plane and curved mirrors and colors. Alhazen was also an engineer. He made an expedition to southern Egypt, sponsored by the caliph al-Hakim (985–1021), where his mission was to study possible ways of controlling the waters of the Nile. He soon realized that what he had undertaken was impossible and that the Nile could not be easily tamed. He also realized that when the bad news reached the caliph he would be executed for having failed in his task. Alhazen feigned madness upon his return. He kept up the pretense for many years until the death of the caliph in 1021.
We must also give a mention to the astronomer Arzachel (1028–87), who lived in the Andalusian region of Spain. He was the foremost “Spanish-Arab” astronomer of his time. He carried out a series of observations at Toledo, and he presented his work in the Toledan Tables. He corrected geographical data from the time of Ptolemy, and in the 12th century his tables were translated into Latin. Arzachel was the first to prove conclusively that there was a small precession of the Earth’s orbit relative to the stars. He measured a precession of 12.04 seconds of arc per year—a brilliant and accurate piece of observation and remarkably close to the modern accepted value of 11.8 seconds. In a later chapter we shall look at the much smaller precession of the orbit of Mercury and its importance to astronomy. Arzachel invented a novel form of flat astrolabe, known as a safihah, details of which were published in Latin, Hebrew and several European languages. His work was well known to Copernicus who, in his De Revolutionibus Orbium Coelestium, quotes Arzachel and Albategnius and acknowledges his debt to their work.
We now come to the best-known and the most-honored of the Persian astronomers. He was the astronomer-poet Omar Khayyam, who lived from 1044–1122. The name khayyam means “tentmaker” in Arabic, and there is some evidence that his father was indeed a tentmaker and that he himself practiced this trade for a short time.
A Persian nobleman called Nizam ul Mulk was educated at the same school as Omar Khayyam, in Nishapur, the provincial capital of Khurasan. Nizam described his first meeting with Omar Khayyam:
When I first came there I found two other pupils of mine own age newly arrived, Hakim Omar Khayyam, and the ill fated Ben Sabbah. Both were endowed with sharpness of wit and the highest natural powers; and we three formed a close friendship together. When the Imam rose from his lectures, they used to join me, and we repeated to each other the lessons he had heard. Now Omar was a native of Nishapur, while Hasan Ben Sabbah’s father was one Ali, a man of austere life and practice, but heretical in his creed and doctrine.
Omar Khayyam attended other institutions of learning, including those at Bukhara, Balkh, Samarkand and Isphahan, but he lived in Nishapur and Samarkand in Central Asia for most of his life. On the accession of Din Malik Shah (1055–92) as sultan of Jalal, Omar Khayyam was appointed court astronomer with an observatory in Esfahan. Other leading astronomers were brought to the court, and for about 18 years Omar Khayyam supervised his team of astronomers to produce work of very high quality. During this time Khayyam was responsible for compiling astronomical tables, and he contributed to a calendar reform in 1079. He calculated the length of the year as 365.24219858156 days—a grossly over-accurate figure quoted to a precision not even achievable today. It is correct as far as the fifth decimal place, but it is almost certainly built upon the work of Albategnius a century before him, who in turn had access to the work and observations of Ptolemy and the Alexandrian scholars.
Omar Khayyam is one of the select group of astronomers who also made original contributions to the advance of mathematics. A good example is his work on algebra, which became known throughout Europe in the Middle Ages. His skill as a mathematician was legendary in his time. In his book on algebra he classified many algebraic equations based on their complexity. When he came to study the cubic equation he identified no less than 13 different forms. He went on to discover a geometrical method to solve cubic equations by finding the intersection of a parabola with a circle. He studied probability, including what we now call binomial probability, and he produced figures for what we know as Pascal’s triangle. He questioned whether or not a ratio should be regarded as a number. To put his work into perspective it must be said that the Romans also had the means to solve the cubic equation and they, too, used a geometric method, so Khayyam’s method was probably a derivation from an earlier method. It is also well known that in the third century BC the Alexandrian mathematician Apollonius wrote a treatise on the conic sections. This was also known to the Arabians, but very few could master the ancient texts and Omar Khayyam’s contribution is seen as a new development to an old problem. He extended Euclid’s work by giving a new definition of ratios and showed how to handle the multiplication of ratios. He also contributed to the theory of parallel lines.
Omar Khayyam not only made original contributions to science but also to literature. In fact he is better known as a poet than as an astronomer, and he is certainly the best-known Arabian poet in the Christian world. His fame is due to the Englishman Edward Fitzgerald (1809–83) who translated into English the Rubaiyat of Omar Khayyam, a collection of 100 short, four-line poems, and then published them in 1859. The English version of the Rubaiyat has gone to several editions. This is in spite of the fact that a lot is lost by the translation into English. It has to be said that Edward Fitzgerald took a few liberties in his translation and to help with the marketing, and he wrote the first stanza entirely on his own!
Wake, For the Sun, who scattered into flight
The Stars before him from the field of night,
Drives Night along with them from Heav’n, and strikes
The Sultan’s Turret with a Shaft of Light.
The Rubaiyat contains very little astronomy, and when it does it is only in support of the philosophy:
LXXII
And that inverted bowl they call the sky,
Whereunder crawling cooped we live and die
Lift not your hands to it for help—for it
As impotently moves as you or I.
His best-known quatrain came when he was pondering the past and the future of the universe. He decided that it was impossible to change the past. He was able to express his thoughts far better than most:
LXXXI
The moving finger writes; and, having writ,
Moves on: nor all your piety and wit
Shall lure it back to cancel half a line.
Nor all your tears wash out a line of it.
Earlier in the chapter we had a description of Omar Khayyam as a pupil by one of his contemporaries. We now have an account of the mature Omar Khayyam, the teacher, as described by one of his pupils, Khwajah Nizami of Samarkand, who relates the story:
I often used to hold conversations with my teacher, Omar Khayyam, in a garden; and one day he said to me, “My tomb shall be in a spot where the north wind may scatter roses over it.” I wondered at the words he spake, but I knew that his were no idle words. Years after, when I chanced to revisit Nishapur, I went to his final resting place and lo! It was just outside a garden, and trees laden with fruit stretched their boughs over the garden wall, and dropped their flowers upon his tomb, so that the stone was hidden under them.
Omar Khayyam’s ten books and 30 monographs have survived. These include books on mathematics, algebra, geometry, physics and metaphysics.
For centuries, the Spanish had been eager to expel the Moors from southern Spain. In the 11th century the fabled warrior El Cid (c.1040–99) fought to drive out the Moors. In this endeavor he had the backing of the pope, who wished to convert the Arabs to Christianity. El Cid was considered the perfect Christian knight: chivalrous, gentle and magnanimous in his conquests. But nothing could be further from the truth; he terrorized the Arabs with his night raids. He and his men raped innocent women, pillaged and plundered the houses and mosques and gave no quarter. In 1135 the Muslim city of Toledo fell to the Spanish. Rumors spread about new finds in Toledo, and inquisitive travelers came to see what they could plunder. It became obvious to the educated that a great center of culture and civilization existed there. It was also obvious to the unbiased observer that it was the Europeans, not the Moors, who were the barbarians in southern Spain.
In England, not long after the Norman conquest, a monk called Adelard of Bath (c.1080–c.1152) heard a rumor that rare manuscripts had been discovered in a part of Spain. Copyists and translators from all over Europe were soon on their way to Spain to try to gain access to the knowledge. Adelard was lucky. He found his way to Toledo and there, to his joy and amazement, he discovered a wonderful library where he was able to procure rare documents for his own use. Others heard of Adelard’s success and followed him across the Pyrenees and into Spain.
In 711 Muslim Arabs under the leadership of Tariq ibn Ziyad (died 720) crossed the Strait of Gibraltar from Tangier and invaded southern Spain, ending the Visi-gothic rule there. Henceforth Andalusia’s history was closely linked with that of Morocco and the North African coast until the end of the 15th century.
It is fascinating to ask how long it took after the fall of Rome for knowledge to grow and surpass the point it had reached in the ancient world. Most historians would say that it was not until the Renaissance that mankind could claim to have gained knowledge that the ancients had not discovered. As regards astronomy, the setback was more than a thousand years. It was not until after the time of Copernicus (1473–1543) that knowledge of astronomy advanced beyond that of the ancient world.