Pathfinders

by Jim Al-Khalili

  On theology, al-Bīrūni held a view that is still a point of contention in the world today: he stated that the Qur’an ‘does not interfere with the business of science nor does it infringe on the realm of science’. Like the earlier scholars of al-Ma’mūn’s Baghdad, al-Bīrūni was, it seems, more than able to separate his rationalist approach to scientific enquiry from his religious beliefs.

  Al-Bīrūni’s best-known, if not most important, achievement in science was his famous determination of the circumference of the earth from an ingenious measurement of the height of a mountain. (The method had been mooted by al-Ma’mūn’s astronomer Sanad two centuries earlier – but we only have al-Bīrūni’s account of it.) His experiment was carried out between 1020 and 1025 while on his travels with the Ghaznavid Sultan Mahmūd in north-west India. During his time at a fort in a place called Nandna, in modern Pakistan and about 60 miles south of Islamabad, he observed a high mountain to the west.10 It was exactly what he had been looking for because it overlooked the flat Punjabi plains that stretched out as far as the eye could see, enabling him to fix the angle of the line of sight to the horizon very accurately when looking out from the top of the mountain.

  I shall describe his technique in detail, for it requires no more than elementary geometry, and yet is astonishingly ingenious. In his Determination of the Coordinates of Cities, al-Bīrūni begins his description of the method by referring back to the famous measurements carried out first by Eratosthenes and later repeated by al-Ma’mūn’s astronomers. Then, with his legendary sharp wit, he writes the immortal lines: ‘Here is another method for the determination of the circumference of the Earth. It does not require walking in deserts.’11 His first step is to determine accurately the height of the mountain while standing on the flat plain near its base. He has a square board of sides one cubit (roughly 20 inches) and ruled with equal divisions along its edges. (If you are not mathematically inclined you may want to skip the next few paragraphs.)

  Al-Bīrūni’s method for measuring the height of a mountain by geometric means (comparing ratios of sides of similar triangles).

  Call the square board ABCD and stand it vertically on edge C as in the diagram. From D, hang a ruler that can swivel freely. First, make sure that the side BC is in line with the peak of the mountain (point E) and then fix the square in this position. Now rotate the ruler so that it is also pointing along a line with the mountain peak and hence cuts the side AB at some point, G. We now have two similar triangles: ADG and CED (because both are right-angled at A and C, and both have equal angles ADG and CED since the lines CE and DA are parallel). So, we can now equate the ratios of sides such that AG : AD = CD : CE. Since three of these sides are known, we can work out the fourth length, CE.

  Next, let a small stone drop freely from the corner D and mark where it lands, at H, then measure the distance along the ground, HC, with the now detached ruler. Now we can compare two other right-angled triangles: DCH and CEF, where F is the (inaccessible) point marking the base of the mountain directly below E. We note that since angles DCH and ECF add up to 90 degrees (since DCE is a right angle) then angle DCH must equal angle CEF (as angles ECF and CEF also add up to 90 degrees). So the two triangles DCH and CEF are also similar and we can again compare ratios of sides: CH : CD = EF : EC. Again, we have just one unknown side: EF, the height of the mountain.

  In practice, the length AG will be very small because the lines of sight to the mountain peak along CBE and DGE will be almost parallel. But al-Bīrūni assures us that he was able to make this careful measurement.

  With the mountain’s height now known, he can use this value to work out the size of the radius of the earth. But he must first climb to the top of the mountain, with an astrolabe accurate enough to measure very small angles. In his writing, al-Bīrūni describes two different mathematical ways of determining the radius. I shall explain it here using a third method, which amounts to the same thing.

  From the top of the mountain, the angle of dip of the horizon, TAH, from the horizontal AH is measured. (Note that al-Bīrūni determines the horizontal by using a plumb line to find the vertical.) He found this angle to be 34 minutes of arc (just over half a degree). Because the angle ATO is a right angle (since the line AT is a tangent to the circle – a geometrical theorem that Euclid has taught generations of schoolchildren for two millennia), then the angles TAH and TOA are equal. Now all that is needed is some elementary trigonometry. The cosine of the angle TOA is equal to the ratio OT : OA, where OT is the radius of the earth. But OA = OB + BA, where OB = OT = the radius, and BA is the known height of the mountain. Thus, the only unknown quantity involved is the radius of the earth and a little rearranging will give us its value. Al-Bīrūni was very familiar with the use of trigonometric tables. He calculated the radius of the earth to be 12,803,337 cubits, which, when multiplied by twice pi, gives a value for the circumference of the earth that is within 1 per cent of the modern value – just under 25,000 miles.

  It is often recorded how remarkably accurate the value arrived at by al-Bīrūni was, closer than anyone had achieved in the past. But the fact is that there are a number of uncertainties, such as an accurate definition of the cubit and the Arabic mīl, and the fact that all these calculations assume an exactly spherical earth (whereas we know the circumference to be greater around the bulge of the Equator than it is round the poles). What is remarkable about al-Bīrūni’s method, therefore, is not the closeness of his result to the modern value but the ingenuity of the method itself and the care needed to measure the quantities accurately, particularly the very small angles.

  Al-Bīrūni’s method for calculating the circumference of the earth.

  I shall not discuss al-Bīrūni’s many contributions to other scientific disciplines, but feel it is important to mention briefly his work in earth sciences. Travelling widely in India, al-Bīrūni not only made a detailed study of its geography, history and culture, he also wrote tellingly on its geology. He discovered that the subcontinent was once a sea before it became land,12 but thought that this was due to the gradual build-up of alluvium rather than the correct and far more dramatic continental drift:

  But if you see the soil of India with your own eyes and meditate on its nature, if you consider the rounded stones found in earth however deeply you dig, stones that are huge near the mountains and where the rivers have a violent current: stones that are of smaller size at a greater distance from the mountains and where the streams flow more slowly: stones that appear pulverized in the shape of sand where the streams begin to stagnate near their mouths and near the sea – if you consider all this you can scarcely help thinking that India was once a sea, which by degrees has been filled up by the alluvium of the streams.13

  He has also been described as the first anthropologist, having written detailed comparative studies on the religions and cultures of the peoples he encountered over a wide swathe of Asia.

  If one were forced to choose between the three giants of medieval science, Ibn al-Haytham, al-Bīrūni and Ibn Sīna, as to who was the greatest of all then I can do no better than to refer to the historian George Sarton, in his definitive Introduction to the History of Science. Given that the three men lived at the same time, he defines the first half of the eleventh century as the ‘Age of al-Bīrūni’.

  I end this chapter as I began, with another quotation from al-Bīrūni, in which he defends the pursuit of scientific knowledge against anti-scientific attitudes in the societies he encountered – still an issue in many parts of the world to this day:

  The extremist among them would stamp the sciences as atheistic, and would proclaim that they lead people astray in order to make ignoramuses, like him, hate the sciences. For this will help him to conceal his ignorance, and to open the door for the complete destruction of sciences and scientists.14

  If these sentiments, which so eloquently make the case for rationalism, are the most important legacy of Arabic science, then this underrated and little-known Persian genius was ce
rtainly its greatest advocate.

  13

  Andalusia

  During the most splendid period of Islamic Spain, ignorance was regarded as so disgraceful that those without education concealed the fact as far as possible, just as they would have hidden the commission of a crime.

  S. P. Scott, History of the Moorish Empire in Europe

  The Strait of Gibraltar that separates the south-west tip of Europe from the continent of Africa is named after the Rock of Gibraltar, from the Arabic Jebel Tāriq (or ‘Tāriq’s mountain’), the huge limestone promontory overlooking the Mediterranean. Tāriq ibn Ziyad was the Umayyad general who crossed over into Spain in 711 CE, extending Islamic rule into Europe. On reaching land and confronting the forces of the Christian Visigoths, he is said to have burned his army’s ships in the harbour to stop his men from fleeing back to Africa. In a speech to his soldiers, famous right across the Arabic-speaking world to this day, he is supposed to have said: ‘Men, where can you flee? The sea is behind you, and the enemy in front of you. There is nothing for you, by God, except for truth and strength of character.’ The victory of Tāriq’s army marked the beginning of the Muslim conquest of Spain and almost eight hundred years of Islamic religious and cultural influence in the lands known as Andalusia.

  But this influence was far more than simply that of an occupying power. At its height, the golden age of the city of Córdoba in central Spain rivalled that of Baghdad for its riches, culture and size, even its great library. During the relatively short period of the so-called Andalusian Umayyad caliphate (929–1031), Córdoba became the most important city in Europe and saw wonderful achievements in science every bit as rich and varied as those under the Islamic dynasties of the East.

  Before I discuss some of these scientific achievements and the leading characters responsible, such as the ninth-century inventor Ibn Firnas, the tenth-century surgeon al-Zahrāwi and the twelfth-century philosopher Ibn Rushd, I shall hurry through a brief history of Andalusia. I cannot do it justice in just a few pages, nor will I apologize for neglecting to cover the wonderful art and culture of the period, for mine is still a story about science, and that story is an easier one for me to tell. The reason for this is that the golden age of Arabic science in Spain did not last very long. So concentrated was it in time, in fact, that most of the leading scientists, physicians and philosophers worthy of mention were contemporaries. All were of course products of a somewhat different Islamic culture, far from the Abbāsids of the Middle East and Persia.

  Possibly most importantly, in the broader discussion of the scientific achievements of medieval Islam, it was mainly via Spain that we see the transmission of Arabic science into Europe, a process that took longer than the two-century duration of the translation movement which brought Greek science to the Arabs.

  The official Umayyad caliphate’s rule in the East had been ended by the Abbāsids in a famous battle on the banks of the river Zab near Mosul in Iraq on 25 January 750 CE. To ensure that they did not try to claw back their power, the Abbāsids ordered the massacre of every member of the Umayyad royal family. But they were not as thorough as they had hoped. One young Umayyad prince by the name of Abd al-Rahmān, a grandson of an earlier caliph, managed to escape. Together with his close companion Bedr, this 16-year-old prince evaded the Abbāsid guards by swimming across the Euphrates. With the help of tribes still loyal to the Umayyads, Abd al-Rahmān made his way to Egypt and eventually across North Africa and into Spain. By 756, with courage and intelligence, he had slowly built up a power-base, capturing first the city of Seville, and then Córdoba, defeating the Abbāsid governor there and making it his new capital. He immediately proclaimed himself the first Umayyad amīr of Andalusia, Abd al-Rahmān I, refusing to recognize the Abbāsid caliphate in Baghdad. To begin with, there was open and widespread hostility among the Arabs of Spain towards anything coming from the Abbāsid capital, which was seen as being dominated by degenerate non-Arabs (Persians) and, by extension, not true Muslims.

  It was not until the reign of Abd al-Rahmān’s great-grandson, Abd al-Rahmān II (r. 822–52), that peace and prosperity, and with them an intellectual awakening, began to take root. Thus, at the same time that al-Ma’mūn was setting up his House of Wisdom in Baghdad, Córdoba was also tentatively seeing the first green shoots of scholarship. Abd al-Rahmān II dedicated himself to attracting the very best scholars his generous patronage could buy in the hope of rivalling Baghdad as a centre of learning. But modernization would come only slowly, and Abd al-Rahmān II had to bring about change cautiously.

  Culturally, Córdoba first tried to imitate Baghdad, and its people loved to hear from travellers arriving from the East about the latest stories, fashions and songs. One of the first to join Abd al-Rahmān’s court was an Iraqi musician by the name of Ziryāb (Blackbird) – nicknamed from his dark complexion, beautiful singing voice and fine appearance. A jealous music teacher had driven Ziryāb out of Baghdad, so he had made his way to Córdoba in 822 where Abd al-Rahmān hired him at a handsome salary. Ziryāb would take Islamic Spain by storm and quickly became a cultural icon, introducing the Córdobans to the very latest ideas from metropolitan Baghdad, from music and eating customs to hairstyles, perfumes and deodorants – he even oversaw the development of toothpaste, which was to become very popular across Spain. Not only did he become the arbiter of taste in ninth-century Andalusia, a cornerstone of Spanish music and art, he was also a generous patron of the sciences.1

  By the late ninth century, Andalusians had obtained Arabic copies of several of the translated Greek texts as well as the work of some of the great figures of ninth-century Baghdad, such as al-Khwārizmi and al-Kindi. The philosophy of the Mu’tazilite movement had reached Spain from the East during the reign of Abd al-Rahmān II, but had made very little impact to begin with. However, by the second half of the ninth century, travellers from the East were starting to be noticed, to the extent that they began to be subject to persecution by the still conservative Andalusian establishment.

  The true golden age of Andalusia is considered to have begun with the reign of Abd al-Rahmān III in 929.2 This ruler would not be satisfied with the title of amīr and instead elevated himself to full caliph, putting his power and prestige on a par and in direct competition with the caliphate in Baghdad. In the early years of his reign he was preoccupied with putting down the many dynastic wars, uprisings and tribal revolts that had been going on for decades. All were eventually crushed and he was able to unite the whole of Spain. In many ways, Abd al-Rahmān III was a ruler in the mould of the great Harūn al-Rashīd of Baghdad a century earlier. Like Baghdad, Córdoba was now a vast and glorious city: the largest, most prosperous, and certainly the most cultured, in Europe.

  It was Abd al-Rahmān’s son, al-Hakam (r. 961–76), who would warrant an even stronger comparison with an Abbāsid counterpart, this time with al-Rashīd’s son, the great al-Ma’mūn himself. Just like al-Rashīd and al-Ma’mūn, these Andalusian rulers now had the luxury of peace and prosperity, with scholars enjoying their generous patronage. Al-Hakam, mirroring al-Ma’mūn’s obsession with books, would use the vast sums of money at his disposal to satisfy his own obsession. He would send men to the East to obtain copies of all the books they could lay their hands on, enabling him to build a great library within the royal palace next to the Great Mosque of Córdoba, which would soon hold almost half a million books – the largest library in Christian Europe at the time had no more than a few hundred manuscripts. Al-Hakam employed many scribes to make copies of all books brought back. The philosopher Ibn Hazm records that the library catalogue alone filled forty-four volumes of fifty folios each.3 Of course, the difference between Córdoba and Baghdad was that there was little in the way of a translation movement here, for most of the books that al-Hakam acquired were in Arabic already.

  The most famous legacy of the rule of this father and son was a palace-city complex built a few miles outside Córdoba, known as Medinat al-Zahrā’ (the word medina meaning
‘city’; see Plate 12). It was begun by Abd al-Rahmān III in 936, but the origin of its name is lost in the mists of time. Some say it was to please his mistress, Zahrā’, whose statue stood over the main entrance; others, that it was named after the Prophet’s daughter, Fātimat al-Zahrā’. This second explanation seems the more likely, for the newly self-declared caliph was keen to show his subjects, and the world, his power and religious credentials. The building of the palace city began at a time when Abd al-Rahmān was beginning to turn his attention to expansion into North Africa, which was at this point under the control of the Shi’a Fātimid dynasty, also named after the Prophet’s daughter. Therefore, another possible explanation for the name is the desire of the Sunni Umayyads to antagonize the Fātimids.

  Al-Zahrā’ has been called the ‘forgotten Versailles of the Middle Ages’, but it was not the first such palace city to be built in the Islamic world: the Abbāsid Caliph al-Mu’tasim (younger brother of al-Ma’mūn) had founded the city of Sāmarra in 836, 80 miles north of Baghdad, when he had to leave the capital after its populace revolted against his hated Turkish guard. At the time, Sāmarra was referred to as Surra man Ra’a (‘Delighting Him Who Sees It’).4 The famous spiral cone minaret (malwiyya) of the great mosque of Sāmarra remains today one of the most iconic legacies of the medieval world (see Plate 00). The mosque itself was in its day the largest in the world.