CONTRIBUTION OF MUSLIM SCIENTISTS IN THE FIELD OF SCIENCE AND TECHNOLOGY_05
By: Hamza Sheth
Mohammad Bin Musa al-Khawarizmi: ‘Algorizm’ (Mathematics, Astronomy)
Abu Abdullah Mohammad Ibn Musa al-Khawarizmi was born at Khawarizm (Kheva), south of Aral sea. Very little is known about his early life, except for the fact that his parents had migrated to a place south of Baghdad. The exact dates of his birth and death are also not known, but it is established that he flourished under Al- Mamun at Baghdad through 813-833 and probably died around 840 C.E.
To celebrate the 1200th birth anniversary of Muhammad bin Musa Al-Khawarizmi the former USSR issued this postal stamp pictured on top.
The terms Algebra and Algorithm are familiar to all of us but how many have heard of their founder Mohammed Al- Khawarizmi.
In Geography he revised and corrected Ptolemy's view and produced the first map of the known world in 830 CE.
He worked on measuring the volume and circumference of the earth, and contributed to work related to clocks, sundials and astrolabes.
Life:
Abu Abdallah Muhammad ibn Musa Al-Khawarizmi. The last- mentioned name (his nisba) refers to his birthplace, Khwarizm, modern Khiva, south of the Aral Sea. He was born around 780 in the town of Kath part of Khwarism. Kath is now buried in the sand. He died around 850. He was summoned to Baghdad by Caliph Al-Mamun and appointed court astronomer. From the title of his work, Hisab Al-Jabr wal Mugabalah (Book of Calculations, Restoration and Reduction), Algebra (Al-Jabr) derived its name.
Algebra symbolizes the debt of Western culture to Muslim mathematics. Ironically, when it first entered the English language it was used as a term for setting of broken bones, and even sometimes for the fractures themselves. This reflects the original literal meaning of the Arabic word al-Jabr, 'the reuniting of broken bones,' from the verb jabara 'reunite.' The anatomical connotations of this were adopted when the word was borrowed, as algebra, into Spanish, Italian and medieval Latin from one or other of which English acquired it. In Arabic, however, it had long been applied to the solving of algebraic equations. The full Arabic expression was 'Ilm aljabr wa'l muqabalah' ''the science of reunion and equations,' and the mathematician Al-Khawarizmi used aljabr as the title of his treatise on algebra.
In the twelfth century Gerard of Cremona and Roberts of Chester translated the algebra of Al-Khawarizmi into Latin. Mathematicians used it all over the world until the sixteenth century.
A Latin translation of a Muslim arithmetic text was discovered in 1857 CE at the University of Cambridge library. Entitled 'Algoritimi de Numero Indorum’, the work opens with the words: 'Spoken has Algoritimi. Let us give deserved praise to God, our Leader and Defender’.
It is believed that this is a copy of Al-Khawarizmi’s arithmetic text, which was translated into Latin in the twelfth century by Adelard of Bath (an English scholar). Al-Khawarizmi left his name to the history of mathematics in the form of Algorism (the old name for arithmetic).
Work:
Al-Khawarizmi was a mathematician, astronomer and geographer. He was perhaps one of the greatest mathematicians who ever lived, as, in fact, he was the founder of several branches and basic concepts of mathematics.
In the words of Phillip Hitti: "He influenced mathematical thought to a greater extent than any other mediaeval writer."
His work on algebra was outstanding, as he not only initiated the subject in a systematic form but he also developed it to the extent of giving analytical solutions of linear and quadratic equations, which established him as the founder of Algebra.
Hisab Al-jabr wAl-muqabala, contains analytical solutions of linear and quadratic equations and its author may be called one of the founders of analysis or algebra as distinct from geometry.
He also gives geometrical solutions (with figures) of quadratic equations, for example X2 + 1OX = 39, an equation often repeated by later writers. The ‘Liber ysagogarum Alchorismi in artem astronomicam a magistro A. [Adelard of Bath] compositus!' deals with arithmetic, geometry, music, and astronomy; it is possibly a summary of Al-Khawarzmi’s teachings rather than an original work.
His astronomical and trigonometric tables, revised by Maslama Al-Majrti (Second half of tenth century), were translated into Latin as early as l126 by Adelard of Bath. They were the first Muslim tables and contained not simply the sine function but also the tangent (Maslama's interpolation).
His arithmetic synthesised Greek and Hindu knowledge and also contained his own contribution of fundamental importance to mathematics and science. Thus, he explained the use of zero, a numeral of fundamental importance developed by the Arabs.
Similarly, he developed the decimal system so that the overall system of numerals, 'algorithm' or 'algorizm' is named after him. In addition to introducing the Indian system of numerals (nowgenerally known as Arabic numerals), he developed at length several arithmetical procedures, including operations on fractions. It was through his work that the system of numerals was first introduced to Arabs and later to Europe, through its translations in European languages.
He developed in detail trigonometric tables containing the sine functions, which were probably extrapolated to tangent functions by Maslamati.
He also perfected the geometric representation of conic sections and developed the calculus of two errors, which practically led him to the concept of differentiation. He is also reported to have collaborated in the degree measurements ordered by Al-Mamun which were aimed at measuring of volume and circumference of the earth.
Books:
Several of his books were translated into Latin in the early 12th century. In fact, his book on arithmetic, Kitab Al-Jam'a wal-Tafreeq bil Hisab Al-Hindi, was lost in Arabic but survived in a Latin translation. His astronomical tables were also translated into European languages and, later, into Chinese. His geography captioned Kitab Surat-Al-Ard,(The Face of the Earth) together with its maps, was also translated. In addition, he wrote a book on the Jewish calendar Istikhraj Tarikh Al-Yahud, and two books on the astrolabe. He also wrote Kitab Al-Tarikh and his book on sun-dials was captioned Kitab Al-Rukhmat, but both of them have been lost.
A Servant of God:
Al-Khawarizmi emphasised that he wrote his algebra book to serve the practical needs of the people concerning matters of inheritance, legacies, partition, law suits and commerce. He considered his work as worship to God.
Quotation from Al-Khawarizmi:
That fondness for science, that affability and condescension which God shows to the learned, that promptitude with which he protects and supports them in the elucidation of obscurities and in the removal of difficulties, has encouraged me to compose a short work on calculating by al- jabr and al-muqabala , confining it to what is easiest and most useful in arithmetic. [al-jabr means "restoring", referring to the process of moving a subtracted quantity to the other side of an equation; al-muqabala is "comparing" and refers to subtracting equal quantities from both sides of an equation.]
Yaqub Ibni Ishaq Al-Kindi: ‘Alkindus’ (Philosophy, Physics, Optics)
Abu Yousuf Yaqub Ibn Ishaq al-Kindi was born at Kufa around 800 C.E. His father was an official of Haroon al-Rashid. Al-Kindi was a contemporary of al-Mamun, al-Mu'tasim and al-Mutawakkil and flourished largely at Baghdad. He vas formally employed by Mutawakkil as a calligrapher. On account of his philosophical views, Mutawakkil was annoyed with him and confiscated all his books. These were, however, returned later on. He died in 873 C.E. during the reign of al-M'utamid.
Al-Kindi was born and brought up in Kufah, which was a centre for Arab culture and learning in the 9th century. This was certainly the right place for al-Kindi to get the best education possible at this time. Although quite a few details (and legends) of al-Kindi's life are given in various sources, these are not all consistent. We shall try to give below details which are fairly well substantiated.
Al-Kindi's father was the governor of Kufah, as his grandfather had been before him. Certainly all agree that al-Kindi was descended from the Royal Kindah tribe which had originated in southern Arabia. This tribe had united a number of tribes and reached a position of prominence in the 5th and 6th centuries but then lost power from the middle of the 6th century. However, descendants of the Royal Kindah continued to hold prominent court positions in Muslim times.
After beginning his education in Kufah, al-Kindi moved to Baghdad to complete his studies and there he quickly achieved fame for his scholarship. He came to the attention of the Caliph al Ma'mun who was at that time setting up the "House of Wisdom" in Baghdad. Al-Ma'mun had won an armed struggle against his brother in 813 and became Caliph in that year. He ruled his empire, first from Merv then, after 818, he ruled from Baghdad where he had to go to put down an attempted coup.
Al-Ma'mun was a patron of learning and founded an academy called the House of Wisdom where Greek philosophical and scientific works were translated. Al-Kindi was appointed by al- Ma'mun to the House of Wisdom together with al-Khwarizmi and the Banu Musa brothers. The main task that al-Kindi and his colleagues undertook in the House of Wisdom involved the translation of Greek scientific manuscripts. Al-Ma'mun had built up a library of manuscripts, the first major library to be set up since that at Alexandria, collecting important works from Byzantium. In addition to the House of Wisdom, al-Ma'mun set up observato- ries in which Muslim astronomers could build on the knowledge acquired by earlier peoples.
In 833 al-Ma'mun died and was succeeded by his brother al- Mu'tasim. Al-Kindi continued to be in favour and al-Mu'tasim employed al-Kindi to tutor his son Ahmad. Al-Mu'tasim died in 842 and was succeeded by al-Wathiq who, in turn, was succeeded as Caliph in 847 by al-Mutawakkil. Under both these Caliphs al-Kindi fared less well. It is not entirely clear whether this was because of his religious views or because of internal arguments and rivalry between the scholars in the House of Wisdom. Certainly al-Mutawakkil persecuted all non-orthodox and non-Muslim groups while he had synagogues and churches in Baghdad destroyed. However, al-Kindi's lack of interest in religious argument can be seen in the topics on which he wrote. He appears to coexist with the world view of orthodox Islam.
In fact most of al-Kindi's philosophical writings seem designed to show that he believed that the pursuit of philosophy is compatible with Islam. This would seem to indicate that it is more probably that al-Kindi became the victim of such rivals as the mathematicians Banu Musa and the astrologer Abu Ma'shar.
It is claimed that the Banu Musa brothers caused al-Kindi to lose favour with al-Mutawakkil to the extent that he had him beaten and gave al-Kindi's library to the Banu Musa brothers.
Al-Kindi was best known as a philosopher but he was also a mathematician and scientist of importance. To his people he became known as the philosopher of the Arabs. He was the only notable philosopher of pure Arabian blood and the first one in Islam. Al-Kindi "was the most leaned of his age, unique among his contemporaries in the knowledge of the totality of ancient scientists, embracing logic, philosophy, geometry, mathematics, music and astrology.
Perhaps, rather surprisingly for a man of such learning whose was employed to translate Greek texts, al-Kindi does not appear to have been fluent enough in Greek to do the translation himself. Rather he polished the translations made by others and wrote commentaries on many Greek works. Clearly he was most influenced most strongly by the writings of Aristotle but the influence of Plato, Porphyry and Proclus can also be seen in al-Kindi's ideas. We should certainly not give the impression that al-Kindi merely borrowed from these earlier writer, for he built their ideas into an overall scheme which was certainly his own invention.
Al-Kindi wrote many works on arithmetic which included manuscripts on Indian numbers, the harmony of numbers, lines and multiplication with numbers, relative quantities, measuring proportion and time, and numerical procedures and cancellation. He also wrote on space and time, both of which he believed were finite, 'proving' his assertion with a paradox of the infinite. Garro gives al-Kindi's 'proof' that the existence of an actual infinite body or magnitude leads to a contradiction. In his more recent paper [8], Garro formulates the informal axiomatics of al-Kindi's paradox of the infinite in modern terms and discusses the paradox both from a mathematical and philosophical point of view.
In geometry al-Kindi wrote, among other works, on the theory of parallels. He gave a lemma investigating the possibility of exhibiting pairs of lines in the plane which are simultaneously non-parallel and non-intersecting. Also related to geometry was the two works he wrote on optics, although he followed the usual practice of the time and confused the theory of light and the theory of vision.
Perhaps al-Kindi's own words give the best indication of what he attempted to do in all his work. In the introduction to one of his books he wrote. It is good that we endeavour in this book, as is our habit in all subjects, to recall that concerning which the Ancients have said everything in the past, that is the easiest and shortest to adopt for those who follow them, and to go further in those areas where they have not said everything.
Certainly al-Kindi tried hard to follow this path. For example in his work on optics he is critical of a Greek description by Anthemius of how a mirror was used to set a ship on fire during a battle. Al-Kindi adopts a more scientific approach.
Anthemius should not have accepted information without proof. He tells us how to construct a mirror from which twenty-four rays are reflected on a single point, without showing how to establish the point where the rays unite at a given distance from the middle of the mirror's surface. We, on the other hand, have described this with as much evidence as our ability permits, furnishing what was missing, for he has not mentioned a definite distance.
Much of al-Kindi's work remains to be studied closely or has only recently been subjected to scholarly research. For example al-Kindi's commentary on Archimedes' The measurement of the circle has only received careful attention as recently as the 1993 publication [10] by Rashed.
In chemistry, he opposed the idea that base metals can be converted to precious metals. In contrast to prevailing alchemical views, he was emphatic that chemical reactions cannot bring about the transformation of elements. In physics, he made rich contributions to geometrical optics and wrote a book on it. This book later on provided guidance and inspiration to such eminent scientists as Roger Bacon.
In medicine, his chief contribution comprises the fact that he was the first to systematically determine the doses to be administered of all the drugs known at his time. This resolved the conflic- ting views prevailing among physicians on the dosage that caused difficulties in writing recipes.
Very little was known on the scientific aspects of music in his time. He pointed out that the various notes that combine to produce harmony, have a specific pitch each. Thus, notes with too low or too high a pitch are non-pleatant. The degree of harmony depends on the frequency of notes, etc. He also pointed out the fact that when a sound is produced, it generates waves in the air which strike the ear-drum. His work contains a notation on the determination of pitch.
He was a prolific writer, the total number of books written by him was 241, the prominent among which were divided as follows:
1. Astronomy
2. Arithmetic
3. Geometry
4. Medicine
5. Physics
6. Philosophy
7. Logic
8. Psychology
9. Music
In addition, various monographs written by him concern tides, astronomical instruments, rocks, precious stones, etc. He was also an early translator of Greek works into Arabic, but this fact has largely been over-shadowed by his numerous original writings. It is unfortunate that most of his books are no longer extant, but those existing speak very high of his standard of scholarship and contribution. He was known as Alkindus in Latin and a large number of his books were translated into Latin by Gherard of Cremona. His books that were translated into Latin during the Middle Ages comprise Risalah dar Tanjim, Ikhtiyarat al-Ayyam, Ilahyat-e-Aristu, al-Mosiqa, Mad-o-Jazr, and Aduiyah Murakkaba.
Al-Kindi's influence on development of science and phi- losophy was significant in the revival of sciences in that period. In the Middle Ages, Cardano considered him as one of the twelve greatest minds. His works, in fact, lead to further development of various subjects for centuries, notably physics, mathematics, medicine and music.
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