J J O’Connor and E F Robertson :(From the previous issue)From around 1022 Mahmud’s armies began to have success in taking control of the northern parts of India and in 1026 his armies marched to the Indian Ocean. Al-Biruni seems only to have been in the northern parts of India, and we are uncertain how many visits he made, but observations he made there enabled him to determine the latitudes of eleven towns around the Punjab and the borders of Kashmir. His most famous work India was written as a direct result of the studies he made while in that country.The India is a massive work covering many different aspects of the country. Al-Biruni describes the religion and philosophy of India, its caste system and marriage customs. He then studies the Indian systems of writing and numbers before going on to examine the geography of the country. The book also examines Indian astronomy, astrology and the calendar.Al-Biruni studied Indian literature in the original, translating several Sanskrit texts into Arabic. He also wrote several treatises devoted to certain aspects of Indian astronomy and mathematics which were of particular interest to him. Al-Biruni was amazingly well read, having knowledge of Sanskrit literature on topics such as astrology, astronomy, chronology, geography, grammar, mathematics, medicine, philosophy, religion, and weights and measures.Mahmud died in 1030 and he was succeeded by his eldest son Mas’ud, although not before a difficult political situation in which the two sons of Mahmud each tried to follow their father as ruler. Clearly al-Biruni was unsure who would succeed for he chose not to give a dedication in his India which appeared at this time. Better to have no dedication than to choose the wrong one! Mas’ud proved to be a ruler who treated al-Biruni more kindly than his father had done. If al-Biruni had been a virtual prisoner before, he now seems to have become free to travel as he pleased. Mas’ud was murdered in 1040 and succeeded by his son Mawdud who ruled for eight years. By this time al-Biruni was an old man but he continued his enormous output of scientific works right up to the time of his death.The total number of works produced by al-Biruni during his lifetime is impressive. Kennedy estimates that he wrote around 146 works with a total of about 13,000 folios (a folio contains about the same amount as a printed page from a modern book). We have mentioned some of the works above, but the range of al-Biruni’s works cover essentially the whole of science at his time. Kennedy writes :-… his bent was strongly towards the study of observable phenomena, in nature and in man. Within the sciences themselves he was attracted by those fields then susceptible of mathematical analysis. We have mentioned al-Biruni’s astronomical observations many time above. It is worth noting that he had a better feel for errors than did Ptolemy. In [66] the author comments that Ptolemy’s attitude was to select the observations which he thought most reliable (often that meant fitting in with his theory), and not to tell the reader about observations that he was discarding. Al-Biruni, on the other hand, treats errors more scientifically and when he does chose some to be more reliable than others, he also gives the discarded observations. He was also very conscious of rounding errors in calculations, and always attempted to observe quantities which required the minimum manipulation to produce answers.One of the most important of al-Biruni’s many texts is Shadows which he is thought to have written around 1021. Rosenfel’d has written extensively on this work of al-Biruni. The contents of the work include the Arabic nomenclature of shade and shadows, strange phenomena involving shadows, gnomonics, the history of the tangent and secant functions, applications of the shadow functions to the astrolabe and to other instruments, shadow observations for the solution of various astronomical problems, and the shadow-determined times of Muslim prayers. Shadows is an extremely important source for our knowledge of the history of mathematics, astronomy, and physics. It also contains important ideas such as the idea that acceleration is connected with non-uniform motion, using three rectangular coordinates to define a point in 3-space, and ideas that some see as anticipating the introduction of polar coordinates.The book details the mathematical contributions of al-Biruni. These include: theoretical and practical arithmetic, summation of series, combinatorial analysis, the rule of three, irrational numbers, ratio theory, algebraic definitions, method of solving algebraic equations, geometry, Archimedes’ theorems, trisection of the angle and other problems which cannot be solved with ruler and compass alone, conic sections, stereometry, stereographic projection, trigonometry, the sine theorem in the plane, and solving spherical triangles.Important contributions to geodesy and geography were also made by al-Biruni. He introduced techniques to measure the earth and distances on it using triangulation. He found the radius of the earth to be 6339.6 km, a value not obtained in the West until the 16th century. His Masudic canon contains a table giving the coordinates of six hundred places, almost all of which he had direct knowledge. Not all, however, were measured by al-Biruni himself, some being taken from a similar table given by al-Khwarizmi. The author remarks that al-Biruni seemed to realise that for places given by both al-Khwarizmi and Ptolemy, the value obtained by al-Khwarizmi is the more accurate.Al-Biruni also wrote a treatise on time-keeping, wrote several treatises on the astrolabe and describes a mechanical calendar. He makes interesting observations on the velocity of light, stating that its velocity is immense compared with that of sound. He also describes the Milky Way as… a collection of countless fragments of the nature of nebulous stars. Topics in physics that were studied by al-Biruni included hydrostatics and made very accurate measurements of specific weights. He described the ratios between the densities of gold, mercury, lead, silver, bronze, copper, brass, iron, and tin. Al-Biruni displayed the results as combinations of integers and numbers of the form 1/n, n = 2, 3, 4, … , 10.Many of al-Biruni’s ideas were worked out in discussions and arguments with other scholars. He had a long-standing collaboration with his teacher Abu Nasr Mansur, each asking the other to undertake specific pieces of work to support their own. He corresponded with Avicenna, in a rather confrontational fashion, about the nature of heat and light. In, eighteen letters Avicenna sent to al-Biruni in answer to questions that he had posed are given. These letters cover topics such as philosophy, astronomy and physics. Al-Biruni also corresponded with al-Sijzi. The paper contains a letter that al-Biruni wrote to al-Sijzi (translated into English in which contains proofs of both the plane and spherical versions of the sine theorem. Al-Biruni says were due to his teacher Abu Nasr Mansur.Finally we should say a little about the personality of this great scholar. In contrast with the works of many others, we find out a lot about al-Biruni from his writings. Despite the fact that no more than one fifth of his works have survived, we get a clear picture of the great scientist. We see a man who was not a great innovator of original theories, mathematical or otherwise, but rather a careful observer who was a leading exponent of the experimental method. He was a great linguist who was able to read first hand an amazing number of the treatises that existed and he clearly saw the development of science as part of a historical process which he is always careful to put in proper context. His writings are therefore of great interest to historians of Science.It appears clear that, despite his many works on astrology, al-Biruni did not believe in the ‘science’ but used it as a means to support his serious scientific work. A devout Muslim, he did write religious texts to suit his patrons particular sect. He shows no prejudice against different religious sects or races, but he does have strong words to say about various acts they committed. For example the Arab conquerors of Khwarazm destroyed ancient texts – what sin could be worse than that to the scholar as dedicated to learning and history as was al-Biruni. On the Christian faith al-Biruni considered the doctrine of forgiveness, writing in India :-Upon my life, this is a noble philosophy, but the people of this world are not all philosophers. … And indeed, ever since Constantine the Victorious became a Christian, both sword and whip have been ever employed. An indication of the sarcasm that he employed against those he saw to be foolish we give the reply that he made to a religious man who objected to the fact that an instrument which al-Biruni was showing him to determine the time for prayers had Byzantine months engraved on it. Al-Biruni reports in Shadows that he said to him:-The Byzantines also eat food. Then do not imitate them in this! (Concluded) (Internet)
