Zero (0)
Oct 22, 2019 16:54:51 GMT
Post by Evola As He Is on Oct 22, 2019 16:54:51 GMT
One of our two main aims in the following study is to address this more or less rhetorical question asked by R. Guénon in 'The Crisis of the Modern World' :"Why have the experimental sciences received a development in the modern civilization such as they have never received at the hands of any other civilization before? Our answer, or rather our clarification, is not rhetorical in any way.
The French orientalist E. Renan, "one of the most widely read authors of the mid- to late nineteenth century", "brought to a wide public the findings of linguists and philologists. His 'Life of Jesus' (1865) has been described as the most widely read work in France at the time, next to the Bible itself. (...) one of its central messages was 'religious' in a way that paradoxically gave support to traditional Christian attitudes towards Jews. That message also echoed points made by Kant and the German liberal Protestant theologians whom Renan had studied : Christ had founded a genuinely universal religion, "the eternal religion of humanity, the religion of the spirit liberated from priesthood, from all cult, from all observance, accessible to all races, superior to castes, in one word absolute." Judaism, on the other hand, remained tribalistic ; "it contained the principle of a narrow formalism, of fanaticism, disdainful of strangers." Renan used the word 'race' copiously, if in bewilderingly diverse senses, from a synonym for 'type,' to a social and economic group, to a physical category (...) In some of his writings, Semitic inferiority in a cultural sense is a pervasive theme (particularly because of Semitic tribalism and intolerance), but he also considered the Semites and the Aryans to be part of the same "white race"(while of a different "physical type"). He described modern Jews as being perfectly capable of becoming modern citizens with other enlightened, modern men. In other passages, however, he laid historical responsibility on the Jews for the destructive intolerance introduced into the world through Christianity and Islam. (…) But Renan also praised the Semitic contribution to civilization. The very idea of human solidarity, of equality before one god, was, he wrote : "The fundamental doctrine of the Semites, and their most previous legacy to mankind", even if paradoxically contradicted by the Jewish notion of a Chosen people. He further spoke of both the modern European Aryans and the Semites as noble, in contrast to the inferior races outside Europe." ('Modern Anti-Semitism and the Rise of the Jews', A.S. Lindemann) In the introduction to his five-volume 'History of the People of Israel', he wrote : "For a philosophic mind, that is to say for one engrossed in the origin of things, there are not more than three histories of real interest in the past of humanity: Greek history, the history of Israel, and Roman history... Greece in my opinion has an exceptional past, for she founded, in the fullest sense of the word, rational and progressive humanity. Our science, our arts, our literature, our philosophy, our moral code, our political code, our strategy, our diplomacy, our maritime and international law, are of Greek origin... Greece had only one thing wanting in the circle of her moral and intellectual activity, but this was an important void; she despised the humble and did not feel the need for a just God... Her religions were merely elegant municipal playthings; the idea of a universal religion never occurred to her. The ardent genius of a small tribe established in an outlandish corner of Syria [i.e. The Israelites] seemed to supply this void in the Hellenic intellect [by giving birth to Christianity]."
One of the two main characteristics of nineteenth century scientism lies in that passage : a Philosemite anti-Semitism based on religious grounds and on a cultural determinism strongly influenced by a racial determinism of the zoological order ; and the belief in the Greek origins of modern European science : both tendencies were interconnected. Taine, whilst being more consistent and clear-headed than Renan in his assessment of the Semitic races on the typological and spiritual plane [with them, "metaphysics are lacking, religion can only conceive of a God-King who is all-consuming and solitary"], is just as blinded as him, when it comes to evaluating their abilities in the scientific domain : "[with them], science cannot come into being, the spirit is too rigid and complete to reproduce the delicate ordering of nature (...)". In many respects, Bernal, in his famous controversial 'Black Athena', has showed that scientific 'Eurocentrism' derives from a pre-scientist and pre-Darwinist fabrication of ancient Greece, whilst not having seen that it originates essentially in a non European spirit and world-outlook.
Like many nineteenth century scientist and racist, Renan claimed that "Islam and science – and therefore, by implication – Islam and modern civilization were incompatible with each other. (...) Renan admitted indeed the existence of a so-called Arabic philosophy and science, but they were Arabic in nothing but language, and Greco-Sassanian in content. They were entirely the work of non-Muslims in inner revolt against their own religion ; by theologians and rulers alike they had been opposed, and so had been unable to influence the institutions of Islam. This opposition had been held in check so long as the Arabs and Persians had been in control of Islam, but it reigned supreme when the Barbarians – Turks in the east, Berbers in the west – took over the direction of the umma. The Turks had a "total lack of the philosophic and scientific spirit", and human reason and progress had been stifled by that enemy of progress, the State based on a revelation. But as European science spread, Islam would perish (...) ('Arabic Thought in the Liberal Age, 1798-1939, A.H. Hourani).
"This is how a very large number of books on science and religion, as well as those dealing with the history of science, M. Iqbal states in 'Science and Islam', depict the eight hundred years of scientific activity in Islamic civilization. Most accounts actually reduce this time period to half its length by a summary death sentence, which turns this tradition to an inert mass some time in the twelfth century. This is the prevalent view of nonspecialists, who have never touched a real manuscript with their hands and who have never looked at an Islamic scientific instrument of surpassing aesthetic quality and dazzling details, displaying a mastery of complex mathematical theorems. The extent of the entrenchment of this view makes it almost an obligation of anyone writing a new work on Islam and science to first examine evidence supporting this view. When one makes that attempt one finds that all roads lead to Ignaz Goldziher, the godfather of the 'Islam versus foreign sciences' doctrine (...) Goldziher's attitude toward Islam was formulated in the background of the colonization of the Muslim world by European powers that had, in turn, presented Islam as a spent force that could only be derided and vilified. (...) Religion was thus seen as an inhibitor of science. This was first seen in reference to Christianity, but soon this initial recasting of the role of Christianity in Europe was enlarged to include all religions, Islam being particularly chosen for its perceived hostility toward rational inquiry. The idea that Islam was inherently against science was thus nourished under specific intellectual circumstances then prevalent in Europe, and it was in this general intellectual background that the first echoes of the 'Islam against science' theory [which, as matter of fact, many Muslims, whether of Arabic stock or not, still uphold] are heard."
R. Guenon's considerations on science and the Renaissance are worth reading again in the light of these clarifications. While stating first that, at that time, "Men were indeed concerned to reduce everything to human proportions, to eliminate every principle of a higher order, and, one might say, symbolically to turn away from the heavens under pretext of conquering the earth ; the Greeks, whose example they claimed to follow, had never gone as far in this direction, even at the time of their greatest intellectual decadence, and with them utilitarian considerations had at least never claimed the first place, as they were very soon to do with moderns" ; while stating further that "(...) what is called the Renaissance was in reality not a re-birth but the death of many things ; on the pretext of being a return to the Greco-Latin civilization, it merely took over the most outward part of it, since this was the only part that could be expressed clearly in written texts (...)", the fact remains that he is convinced that "some of the origins of the modern world may be sought in 'classical antiquity' ; the modern world is therefore not entirely wrong in claiming to base itself on the Greco-Latin civilization and to be a continuation of it" ('The Crisis of the Modern World'), about which he acknowledged himself in his correspondence that he did not know much. In this case, he would therefore have been well inspired to turn to Mecca, not to pray, but to think. For that "most outward part" of the Greco-Latin civilisation that the Renaissance took over, more precisely, turns out to be constituted by views originating in non Aryan races.
"At the beginning of the twelfth century no European could expect to be a mathematician or an astronomer, in any real sense, without a good knowledge of Arabic ; and Europe, during the earlier part of the twelfth century, could not boast of a mathematician who was not a Moor, a Jew, or a Greek." ('A History of Mathematics', C.B. Boyer). "Whether in architecture , agriculture, art, language, law, medicine, music, or technology, the considerable influence of the Arab civilisation on medieval Europe and its determinant role in the genesis of Renaissance was only acknowledged fully in the twentieth century. For instance, its influence on education is enormous : "The origins of the college lies in the medieval Islamic world. The madrasah was the earliest example of a college, mainly teaching Islamic law and theology, usually affiliated with a mosque, and funded by Waqf, which were the basis for the charitable trusts that later funded the first European colleges. The internal organization of the early European college was also borrowed from the earlier madrasah, like the system of fellows and scholars, with the Latin term for fellow, socius, being a direct translation of the Arabic term for fellow, sahib. Madrasahs were also the first law schools, and it is likely that the "law schools known as Inns of Court in England" may have been derived from the madrasahs which taught Islamic law and jurisprudence. If a university is assumed to mean an institution of higher education and research which issues academic degrees at both undergraduate and postgraduate levels, then the Jami'ah which appeared from the 9th century were the first examples of such an institution. The University of Al Karaouine in Fez, Morocco is thus recognized by the Guinness Book of World Records as the oldest degree-granting university in the world with its founding in 859 by Fatima al-Fihri. However, the madrasah differed from the medieval university of Europe in several important respects, namely that the degree took the form of a license (ijazah) which "was signed in the name of the teacher, not of the madrasa". In other words, "the authorization or licensing was done by each professor, not by a group or corporate body, much less by a disinterested or impersonal certifying body". The first colleges and universities in Europe were nevertheless influenced in many ways by the madrasahs in Islamic Spain and the Emirate of Sicily at the time, and in the Middle East during the Crusades. The origins of the doctorate dates back to the ijazat attadris wa 'l-ifttd ("license to teach and issue legal opinions") in the medieval Islamic legal education system, which was equivalent to the Doctor of Laws qualification and was developed during the 9th century after the formation of the Madh'hab legal schools. To obtain a doctorate, a student "had to study in a guild school of law, usually four years for the basic undergraduate course" and ten or more years for a post-graduate course. The "doctorate was obtained after an oral examination to determine the originality of the candidate's theses," and to test the student's "ability to defend them against all objections, in disputations set up for the purpose" which were scholarly exercises practiced throughout the student's "career as a graduate student of law." After students completed their post-graduate education, they were awarded doctorates giving them the status of faqih (meaning "master of law"), mufti (meaning "professor of legal opinions") and mudarris (meaning "teacher"), which were later translated into Latin as magister, professor and doctor respectively. The term doctorate comes from the Latin docere, meaning "to teach", shortened from the full Latin title licentia docendi meaning "license to teach." This was translated from the Arabic term ijazat attadris, which means the same thing and was awarded to Islamic scholars who were qualified to teach. Similarly, the Latin term doctor, meaning "teacher", was translated from the Arabic term mudarris, which also means the same thing and was awarded to qualified Islamic teachers. The Latin term baccalaureus may have also been transliterated from the equivalent Arabic qualification bi haqq al-riwaya ("the right to teach on the authority of another"). According to Professor George Makdisi and Hugh Goddard, some of the terms and concepts now used in modern universities which have Islamic origins include "the fact that we still talk of professors holding the 'Chair' of their subject" being based on the "traditional Islamic pattern of teaching where the professor sits on a chair and the students sit around him", the term 'academic circles' being derived from the way in which Islamic students "sat in a circle around their professor", and terms such as "having 'fellows', 'reading' a subject, and obtaining 'degrees', can all be traced back" to the Islamic concepts of Ashab ("companions, as of the prophet Muhammad"), Qara'a ("reading aloud the Qur'an") and Ijazah ("license to teach") respectively. Makdisi has listed eighteen such parallels in terminology which can be traced back to their roots in Islamic education. Some of the practices now common in modern universities which Makdisi and Goddard trace back to an Islamic root include "practices such as delivering inaugural lectures, wearing academic robes, obtaining doctorates by defending a thesis, and even the idea of academic freedom are also modelled on Islamic custom." The Islamic scholarly system of fatwa and ijma, meaning opinion and consensus respectively, formed the basis of the "scholarly system the West has practised in university scholarship from the Middle Ages down to the present day."[102] According to Makdisi and Goddard, "the idea of academic freedom" in universities was "modelled on Islamic custom" as practiced in the medieval Madrasah system from the 9th century. Islamic influence was "certainly discernible in the foundation of the first delibrately-planned university" in Europe, the University of Naples Federico II founded by Frederick II, Holy Roman Emperor in 1224". (http://en.wikipedia.org/wiki/Islamic_contributions_to_Medieval_Europe)
G. Sarton, the well-known Harvard historian of science, wrote, in his 'Introduction to the History of Science' : "The scientific advances of the West would have been impossible had scientists continued to depend upon the Roman numerals and been deprived of the simplicity and flexibility of the decimal system and its main glory, the zero. Though the Arab numerals were originally a Hindu invention, it was the Arabs who turned them into a workable system; the earliest Arab zero on record dates from the year 873, whereas the earliest Hindu zero is dated 876. For the subsequent four hundred years, Europe laughed at a method that depended upon the use of zero, "a meaningless nothing." Had the Arabs given us nothing but the decimal system, their contribution to progress would have been considerable. In actual fact, they gave us infinitely more. While religion is often thought to be an impediment to scientific progress, we can see, in a study of Arab mathematics, how religious beliefs actually inspired scientific discovery."
As P. Berlinghoff and F.Q. Gouvea put in 'Math through the Ages', "Of the knowledge which these sages [the Eastern ones] imparted to Western man, the elements of mathematics were an integral part. Hence, to trace the impress of mathematics on modern culture, we must turn to the major Near Eastern civilizations."
"The Babylonians used a special symbol to separate the 5 and 3 in the former case but failed (sic) to recognize that this symbol could also be treated as a number, that is, they failed (re-sic) to see that zero indicates quantity and can be added, subtracted and used generally like other numbers." (ibidem) In other words, zero was still used as a mere placeholder by the Babylonians.
"In around 500AD [in India] Aryabhata devised a number system which has no zero yet was a positional system. He used the word "kha" for position and it would be used later as the name for zero. There is evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. It is interesting that the same documents sometimes also used a dot to denote an unknown where we might use x. Later Indian mathematicians had names for zero in positional numbers yet had no symbol for it. The first record of the Indian use of zero which is dated and agreed by all to be genuine was written in 876." (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html).
"It is quite possible that the zero originated in the Greek world, perhaps at Alexandria, and that it was transmitted to India after the decimal positional system has been established there. (...). With the introduction, in the Hindu notation, of the tenth numeral (...), the modern system of numeration for integers was completed. Although the Medieval Hindu forms of the ten numerals differ considerably from those in use today, the principles of the system were established. The new numeration, which we generally call the Hindu system, is merely a new combination of three basic principles, all of ancient origin : (1) a decimal base ; (2) a positional notation ; and (3) a ciphered form for each of the ten numerals. NOT ONE OF THESE THREE WAS DUE ORIGINALLY TO THE HINDUS, but it presumably is due to them that the three were first linked to form the modern system of numeration." ('History of Mathematics', C.B. Boyer). As a matter of fact, according to D. Smeltzer ('Man and Number', Adam and Charles Black, London, 1953), "They [The Hindus] did not, it would seem, think of it [the zero] as denoting a number but as indicating an empty space. The idea of regarding nothingness or emptiness as a number is at least as difficult as the idea of representing emptiness by a symbol."
"We now come to considering the first appearance of zero as a number. Let us first note that it is not in any sense a natural candidate for a number. From early times numbers are words which refer to collections of objects. Certainly the idea of number became more and more abstract and this abstraction then makes possible the consideration of zero and negative numbers which do not arise as properties of collections of objects. Of course the problem which arises when one tries to consider zero and negatives as numbers is how they interact in regard to the operations of arithmetic, addition, subtraction, multiplication and division. In three important books the Indian mathematicians Brahmagupta, Mahavira and Bhaskara tried to answer these questions." (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html) Their answers turn out to be either clumsy or bluntly wrong. Errors pile up. Obviously, they were not quite in their element.
The ninth century Arab scholar Muhammad Ibn Musa Al-Khwarizmi, on the other hand, was in his element, when he wrote 'On the Hindu Art of Reckoning', which describes the Indian place-value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, and is the first work to use zero as a place holder in positional base notation. He wrote two books, that one - on arithmetic - and the other on solving equations, which, we are told, were translated into Latin in the twelfth century and circulated throughout Europe. The Latin translations often began with "Dixit Algorizmi", meaning "Al-Khwarizmi said". Many Europeans learned about the decimal place system and the essential role of the zero from these translations. The popularity of this book as an arithmetic text gradually led its title to be identified with the methods in it, giving us the word 'algorithm'. In Al-Khwarizmi, many historians of science, who, for most of them, are not mathematicians, like to think that zero is "not yet thought of as a number ; it is just a place holder." As remarkably well seen by an Arab scholar, "The ancient mathematicians, including the Greeks, considered the number to be a pure magnitude. It was only when al-Khwarizmi (…) conceived of the number as a pure relation [as a 'function'] in the modern sense that the science of algebra could take its origin." This recognition of numbers as 'pure relation' was the key for unlocking the door of algebra. The absence of quantity (0) was acknowledged as a quantity in its own right.
"Historians believe that al-Khwarizmi was born in the city of Baghdad in present day Iraq (Calinger, 199). While little is known about his private life, al-Khwarizmi's work and contributions to mathematics have largely survived the ages relatively intact. The exception is a book of arithmetic in which the original cannot be found; there is, however, a Latin translation of this work as well as other Arab references that cite the missing treatise. Al-Khwarizmi was a member of the House of Wisdom in Baghdad, a society established by the caliph for the study of science (Al-Daffa, 23). According to Al-Daffa, during al-Khwarizmi's life, much of the area between the Mediterranean and India was ruled by al-Mamun, an Islamic caliph who had consolidated his position in a protracted civil war. After pacifying the area under his control, al-Mamun became a patron of the sciences. He instituted the House of Wisdom to both translate the works of Byzantine and Greek scientists as well as to conduct research into various realms of science. Al-Mamun also built a library in Baghdad to house these works; this was the first large collection of scientific information constructed since the Library of Alexandria's erection several centuries before. Finally, al-Mamun constructed a lavish astronomical observatory in Baghdad for the use of Muslim astronomers. Within a short period of time, Baghdad became the new center for learning in the Mediterranean world (Al-Daffa, 23-34). This interest in Greek Hellenistic thought represented a tremendous change from previous Islamic ideology. This might lead one to ask why such seemingly sensible steps represent such a rapid departure from Islamic thought as well as what was the impetus for such a dramatic change ? The first idea to consider is that there had always been a fundamental difference from Greek and Islamic thought. The most important difference was a matter of religion. The classical Greeks and Romans believed in many Gods and the later, after Rome had Christianized the Mediterranean, they believed in a Holy Trinity (Smith, 340). These ideas directly conflicted with the Islamic belief of the one true God, Allah (Smith, 222). As a result, in the seventh century CE, when the disciples of Mohammed began their conquest of the Middle East, North Africa and Spain, the Muslims destroyed much of the work and knowledge of those that they conquered (Smith, 230). Their extreme Islamic fundamentalism blinded the Arabs to the advanced scientific contributions of their neighbors. The initial conquests of Islam lasted well into the eighth century CE, just a generation or two prior to the birth of al-Khwarizmi and al-Mamun. Therefore, as a matter of time, al-Khwarizmi and al-Mamun are not far removed from the zealous invaders of the past. The drastic change in Islamic attitudes toward western science might be a byproduct of the religion itself. Muslims live their lives according to the rules and precepts set forth in the Qu'ran (Koran). This book dictates all aspects of a Muslim's life and death. For example, the Qu'ran dictates that Muslims must pray several times a day toward the city of Mecca as well as giving precise rules of inheritance when one dies (Smith, 236). Both of these tasks require advanced knowledge of mathematics. Mathematics are used in the study of cartography, astronomy and geography. Knowledge of astronomy would have been critical for determining which direction to pray or for ascertaining the beginning of Ramadan (which is based largely on the phases of the moon). Other, less concrete, applications of math would have been required in order to properly divide up estates (Berggren, 63). In a sense, after the zeal of Islam aided in the destruction of knowledge, it realized just how useful that knowledge might have been for its own purposes. As a result, al-Mamun created the House of Wisdom to restore and research the answers to the scientific questions that plagued the administration of his empire." (http://209.85.135.104/search?q=cache:NRiM8OVXxwYJ:www.math.ohio-state.edu/~czorn/work_and_research/hist_algebra.pdf+khwarizmi+zero&hl=en&ct=clnk&cd=2&gl=uk)
It appears that al-Khwarizmi's work was influenced by Greek, neo-Babylonian and Indian sources with the Indians supplying the number system, the Babylonians supplying the numerical processes and the Greeks supplying the tradition of rigorous proof. He assimilated and systematised these three elements in a synthesis which was congruent with the Arabic view on mathematics, and he did it with other contemporary Arab mathematicians, of whom Abd al Hamid ibn Turk. What is interesting, incidentally, is the criterion which is used by some Arab scholars themselves to impugn his title of "Father of algebra" : "(…) according to ibn Al Nadim, "Al-Khwârazmî's Algebra contains a very short section on commercial transactions", whereas "Abd al Hamîd ibn Turk wrote an independent book devoted to this subject. It seems quite certain that in the field of algebra itself too, just as in the field of commercial transactions, it was Abd al Hamîd ibn Turk who wrote the longer and more detailed treatise." www.muslimheritage.com/topics/default.cfm?TaxonomyTypeID=12&TaxonomySubTypeID=62&TaxonomyThirdLevelID=-1&ArticleID=657).
"In Europe, the introduction of the new system met with considerable resistance and there was antagonism between the algorists using the "art of al-Khowarazmi" [those who promoted the Hindu-Arabic numeral system and the algorithms for written calculations and, thus calculated with a zero ; also called Gerbecists, in honour of Gerbert d'Aurillac, who became pope Sylvester II in the end of the tenth century, and who is the first European scholar known to have taught using the Hindu-Arabic numeration system] and the abacists [those who wrote in Roman numerals and used an abacus for calculation, as well as duodecimal Roman fractions] who continued to use the methods of the counting board."
"In 1299 the bankers of Florence were forbidden to use Arabic numerals and were obliged instead of using Roman numerals. (...) Although the Hindu-Arabic system of numeration "had been rejected by some, Italian merchants of the twelfth century recognized its superiority for computational purposes. These merchants became noted for their knowledge of arithmetic operations and developed methods of double-entry bookkeeping [completely unknown until then, and even more so, in ancient Rome]. (...) the forms of the Hindu numerals were not fixed, and the variety of forms gave rise to ambiguity and fraud (...). Outside of Italy, most European merchants kept accounts in Roman numerals until at least 1550 (and most colleges and monasteries until 1650!) ('Sherlock Holmes in Babylon and Other Tales of Mathematical History', M. Anderson, V.J. Katz, R.J. Wilson) "(...) the result is this prolonged struggle [between abacists and algorists] was inevitable. The [Arabic] numerals became a kind of secret code (yes, a cipher), used by merchants and by businesspeople who were willing to evade the laws and the secret arts – after all, the numbers were there, and they were fast and easy to use. Finally, by about the beginning of the sixteenth century, they were here to stay, though there were still those who double-checked their computations on an abacus just to be sure (there are still many places where the abacus is preferred to the computer or calculator because the work done on either of those isn't visible, while the computations worked out on an abacus can be seen by anyone who cares to watch.)" "In the end, B. Crumpacker goes on with the self-satisfied stupidity of a shareholder who knows his shares are skyrocketing ('Perfect Figures'), the numerals were irresistible. (...). Those numbers are elegant in their simplicity and versatility. There are only ten of them, but those ten can make billions". One specific work was instrumental in communicating the Hindu-Arabic numerals to a wider audience in the Latin world : that of Leonardo Pisano, "known to history as Fibonacci, [who] studied the works of Kāmil and other Arabic mathematicians as a boy while accompanying his father's trade mission to North Africa on behalf of the merchants of Pisa. In 1202, soon after his return to Italy, Fibonacci wrote Liber Abbaci ('Book of the Abacus'). Although it contained no specific innovations, and although it strictly followed the Islamic tradition of formulating and solving problems in purely rhetorical fashion, it was instrumental in communicating the Hindu- Arabic numerals to a wider audience in the Latin world" (http://www.britannica.com/EBchecked/topic/14885/algebra/231066/Commerce-and-abacists-in-the-European-Renaissance)
"Even though it would take centuries for the world to accept zero, al-Khwarizmi had produced a number system similar to the one used worldwide today (Mathematics and Astronomy). The main differences were al-Khwarizmi's skepticism of the existence negative numbers and the difference between al-Khwarizmi's symbols and the modern Arabic numbers (it would take several centuries of evolution before numerals began to take a form familiar to the twenty-first century reader)." Basically, much of the House of Wisdom's work and research was directed toward a practical end. "Al-Khwarizmi did not set out to found a new branch of mathematics when he wrote Al-Jabr wal Muqabala. In the introduction to the work, he declares his intent in very practical terms (...) : "A short work on Calculating by (the rules of) Completion and Reduction 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 all 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." Al-Khwarizmi wanted his work to help people solve mathematical dilemnas in their everyday lives." ('Al Khwarizmi', C. Brezina). "Even today, many of the inheritance laws in Arab countries are based on the inheritance laws outline in the Qu'ran. This calls for an official to divide up the deceased person's possessions according to certain proportions based on the relationship of the beneficiary to the deceased (Mathematics and Astronomy). Using al-Khwarizmi's new methods of calculation and geometric representation, the local governments were better able to handle the affairs of the deceased. According to The Free Arab Voice: Because of the Qur'an's very concrete prescriptions regarding the division of an estate among children of a deceased person, it was incumbent upon the Arabs to find the means for very precise delineation of lands. For example, let us say a father left an irregularly shaped piece of land-seventeen acres large-to his six sons, each OAA of whom had to receive precisely one-sixth of his legacy. The mathematics that the Arabs had inherited from the Greeks made such a division extremely complicated, if not impossible. It was the search for a more accurate, more comprehensive, and more flexible method that led Khawarazmi to the invention of algebra. (Mathematics and Astronomy)" (http://209.85.135.104/search?q=cache:NRiM8OVXxwYJ:www.math.ohio-state.edu/~czorn/work_and_research/hist_algebra.pdf+khwarizmi+zero&hl=en&ct=clnk&cd=2&gl=uk)
At this point, the fundamental difference between mathematics in the Greek world and mathematics in the Arab world and, more generally, between the Greek scientific spirit and the Arab scientific spirit should be clear. The following considerations will make it even clearer.
"The Egyptians and Babylonians made numerous practical applications of their mathematics. Their papyri and clay tablets show promissory notes, letters of credit, mortgages, deferred payments, and the proper apportionment of business profits." "But it is a mistake – no matter how often it is repeated - to believe that mathematics in Egypt and Babylonia was confined just to the solution of practical problems. (...) Instead we find, upon closer investigation, that the exact expression of man's thoughts and emotions, whether artistic, religious, scientific, or philosophical, involved then, as today, some aspects of mathematics. In Babylonia and Egypt the association of mathematics with painting, architecture, religion, and the investigation of nature was no less intimate and vital than its use in commerce, agriculture, and construction."
On the other hand, "Arithmetic, said Plato, should be pursued for knowledge and not for trade. Moreover, he declared the trade of a shopkeeper to be a degradation for a freeman and wished the pursuit of it to be punished as a crime. Aristotle declared that in a perfect state no citizen should practice any mechanical art. Even Archimedes, who contributed extraordinary practical inventions, cherished his discoveries in pure science and considered every kind of skill connected with daily needs ignoble and vulgar. Among the Boeotians there was a decided contempt for work. Those who defiled themselves with commerce were excluded from state office for ten years."
"A second contribution of the Greeks consisted in their having made mathematics abstract. (...) The Greek eliminated the physical substance from mathematical concepts and left mere husks. They removed the Cheshire cat and left the grin. Why did they do it ? Surely, it is far more difficult to think about abstractions than about concrete things. One advantage is immediately apparent – the gain in generality. A theorem proved about the abstract triangle applies to the figure formed by three match sticks, the triangular boundary of a piece of land, and the triangle formed by the earth, sun, and moon at any instant. The Greeks preferred the abstract concept because it was, to them, permanent, ideal, and perfect, whereas physical objects are short-lived, imperfect, and corruptible."
"The Greeks put their stamp on mathematics in still another way that has had a market effect on its development, namely, by their emphasis on geometry. Plane and solid geometry were thoroughly explored. A convenient method of representing quantities, however, was never developed nor were efficient methods of reckoning with numbers. Indeed, in computational work they even failed (sic) to utilize techniques the Babylonian had created. Algebra in our present sense of a highly efficient symbolism and numerous established procedures for the solution of problems was not even envisioned. So marked was this disparity of emphasis that we are impelled to seek the reasons for it. There are several(...) in the classical period industry, commerce, and finance were conducted by slaves. Hence the educated people, who might have produced new ideas and new methods for handling numbers, did not concern themselves with such problems. Why worry about the use of numbers in measurement if one doesn't measure, or in trading if one dislikes trade ? Nor do philosophers need the numerical dimensions of even one rectangle to speculate about the properties of all rectangles.
Like most philosophers the Greeks were star-gazers. They studied the heavens to penetrate the mysteries of the universe. But the use of astronomy in navigation and calendar reckoning hardly concerned the Greeks of the classical period. For their purposes, shapes and forms were more relevant than measurements and calculations, and so geometry was favored.
The twentieth century seeks reality by breaking matter down – witness our atomic theories. The Greeks preferred to build matter up. For Aristotle and other Greek philosophers the form of an object is the reality to be found in it. Matter as such is primitive and shapeless ; it is significant only when it has a shape."
We repeat, both for those who are interested in Evola's 'influences' and for those who haven't read him for a while : "Matter as such is primitive and shapeless ; it is significant only when it has shape."
"Because the Greeks converted arithmetical ideas into geometrical ones and because they devoted themselves to the study of geometry, that subject dominated mathematics until the nineteenth century, when the difficulties in treating irrational numbers on an exact, purely arithmetical basis were finally resolved. In view of the clumsiness (sic) and complexity of arithmetical operations geometrically performed, this conversion was, from a practical standpoint, a highly unfortunate one. The Greeks not only failed (sic) to develop the number system and algebra which industry, commerce, finance, and science must have, but they also hindered the progress of later generations by influencing them to adopt the more awkward geometrical approach. Europeans became so habituated to Greek forms and fashions that Western civilization had to wait for the Arabs to bring a number system from far-off India."
As far as Romans are concerned, many histories of mathematics, whether ancient or modern ones, do not even mention them. In 'A Short Account of the History of mathematics', W.W. Rouse Ball wrote : "There is (...) very little to say on the subject. (...) There were, no doubt professor who could teach the results of Greek science, but there was no demand for a school of mathematics. Italians who wished to learn more than the elements of the science went to Alexandria or to places which drew their inspiration from Alexandria. The subject as taught in the mathematical schools at Rome seems to have been confined in arithmetic to the art of calculation (no doubt by the aid of the abacus) and perhaps some of the easier parts of the work of Nicomachus, and in geometry to a few practical rules ; though some of the arts founded on a knowledge of mathematics (especially that of surveying) were carried to a high pitch of excellence." In 'Mathematical Thought from Ancient to Modern Times', M. Kline wrote : "Roman mathematics hardly warrants mention. The period during which the Romans figured in history extends from 750 B.C. to A.D. 476, roughly the same period during which the Greek civilisation flourished. Moreover (...), from at least 200 B.C. onward, the Romans were in close contact with the Greeks. Yet in all of the eleven hundred years there was not one Roman mathematician ; apart from a few details this fact in itself tells us virtually the whole story of Roman mathematics." According to F. Cajori, for whom the fact that a people is not interested in the slightest in mathematics is beyond mathematical logic and imagination ('A History of Mathematics'), "Nowhere is the contrast between the Greek and Roman mind shown forth more distinctly than in their attitude toward the mathematical science. The sway of the Greek was a flowering time for mathematics, but that of the Romans a period of sterility. In philosophy, poetry, and art, the Roman was an imitator (sic). But in mathematics he did not even rise to the desire for imitation. The mathematical fruits of Greek genius lay before him untasted. In him, F. Cajori goes on - without asking himself how come it never occurred to such a "practical people" as the Romans to apply the mathematical knowledge they had received from other peoples to solve everyday life, practical problems, as did the Arabs later - a science which had no direct bearing on practical life could awake no interest. As a consequence, not only the higher geometry of Archimedes and Apollonius, but even the Elements of Euclides, were neglected. What little mathematics the Romans possessed did not come altogether from the Greeks, but came in part from more ancient sources", of which the Etruscan ones. The same thing goes for what is typically described as 'Roman technology'.
The mathematical and, more generally, scientific spirit which resurfaced in the Middle Ages through the so-called 'rediscovery' of Greco-Roman texts by European scholars was, unsurprisingly, not the Greek one, not the Roman one, but the practical Asian one, and, just as unsurprisingly, those who popularised 'algorism' in the thirteenth century either belonged to the bourgeois stratum or were churchmen. The emphasis was so much on the practical applications of knowledge that a shift occurred from experience to experimentation and, ultimately, to experiments of laboratory, into which science has been sinking since the late Middle Ages. Even someone who, like Eeves in 'Foundations and Fundamental Concepts of Mathematics', is convinced that "the ancient Greeks found in deductive reasoning the vital element of the modern mathematical method" cannot but acknowledge that they "transformed the subject [mathematics] into something vastly different from the set of empirical conclusions worked out by their predecessors. The Greeks insisted that mathematical facts must be established, not by empirical procedures, but by deductive reasoning ; mathematical conclusions must be assured by logical demonstration rather than by laboratory experimentation."
The Arabs introduced and developed the experimental method. In 'The Making of Humanity', Briffault stressed that : "The debt of our science to that of the Arabs does not consist in any startling discoveries of revolutionary theories. Science owes a great deal more to Arab culture, it owes its existence... The Greeks systematised, generalised and theorised, but the patient ways of investigation, the accumulation of positive knowledge, the minute methods of science, detailed and prolonged observation and experimental enquiry, were altogether alien to the Greeks temperament… What we call science arose in Europe as a result of a new spirit of inquiry, of new methods of investigation, of the methods of experiment, observation and measurement, of the development of mathematics in a form unknown to the Greeks. That spirit and those methods were introduced into the European world by the Arabs". In the meantime, from the fall of the Roman Empire to the early Middle Ages, the Church did its best to conceal the Greek scientific spirit by preventing the works that embodied it from acting as a basis and as an axis for western science. For example, under pope Gregory the Great, all scientific studies were not allowed in Rome ; the study of ancient original works from Greece and Rome were forbidden and the Palatine library founded by Augustus Caesar was burnt down.
In that context, it's no wonder that "During the Renaissance, there was a dramatic change among Christian intellectuals from one that focused on the contemplation of God;s work to one that focused on the responsibility of the Christian for caring for his fellow humans. The active life of service to mankind, rather than the contemplative life of reflection on God's character and works, now became the Christian ideal for many. As a consequence of this new focus on the active life, Renaissance intellectuals turned away from the then-dominant Aristotelian view of science, which saw the inability of theoretical sciences to change the world as a positive virtue. They replaced this understanding with a new view of natural knowledge, promoted in the writings of such men as Johann Andreae in Germany and Francis Bacon [who became acquainted with alchemy from Latin translations of Arabic writings] in England, which viewed natural knowledge as significant only because it gave mankind the ability to manipulate the world to improve the quality of life. Natural knowledge would henceforth be prized by many because it conferred power over the natural world." ('Science and Islam') The asianisation of the European scientific spirit was completed.
It is also extremely interesting that the one credited for introducing the experimental method in alchemy is the Muslim alchemist, astrologer, astronomer, chemist, engineer, geologist, philosopher, physician and physicist Abu Musa Jābir ibn Hayyān, known in Europe as Geber, and whose writings and treatises on alchemy are quoted by Evola in 'The Hermetic Doctrine' (the research of the most celebrated nineteenth century historian of chemistry M. Berthelot would tend to show that not all works held to have been written by Jabir are actually his, but a contemporary European alchemist's]. Note that he was also deeply interested in mysticism. "The first essential in chemistry", he stated, "is that you should perform practical work and conduct experiments, for he who performs not practical work nor makes experiments will never attain the least degree of mastery." He stated this almost 500 years before, almost in the same terms, Descartes did.
"The Arabs, of course, started out with the chemical knowledge of the Egyptians, Chaldeans, Persians, and Greeks, which was made up more of the occult, the magical, and superstitions (sic) than of chemical science as we know it. Arabic chemistry, however, was not content with those borrowed crudities (sic), but initiated experimentation in a primitive form. It attempted to find a way for the prolonging of life to which the word 'elixir' testifies. Arab chemists, also, experimented with the transmutation of the baser metals into the precious ones." ('The Contribution of the Arabs to Education', K.A. Totah)
In the light of what has just been exposed, another typical excerpt from 'The Crisis of the Modern World' is worth quoting : "it is not for its own sake that Westerners in general cultivate science as they understand it; their primary aim is not knowledge, even of an inferior order, but practical applications, as may be inferred from the ease with which the majority of our contemporaries confuse science and industry, so that by many the engineer is looked upon as a typical man of science."
In the light of the considerations we have made in previous posts on Islam as a typically and essentially lunar religion, it may not be a luxury to have a look at 'The Mathematical Miracle of the Koran': www.submission.org/miracle/moon.html
P.s. : it is commonly taught and, therefore, believed, taken as granted that, from the sixth to the tenth century, many of the works of classical Greco-Roman authors were translated into Syriac by Arab scholars and translated back into Latin (from Arabic) from the tenth to the thirteenth century (by that century, there were many variants – Arabic to Spanish, Arabic to Hebrew, Greek to Latin, or combinations such as Arabic to Hebrew to Latin), during which they were reintroduced in the West. As to exactly how those Arab scholars got hold of those manuscripts, no one seems to know. Basically, no one seems to possess the 'originals'.
The French orientalist E. Renan, "one of the most widely read authors of the mid- to late nineteenth century", "brought to a wide public the findings of linguists and philologists. His 'Life of Jesus' (1865) has been described as the most widely read work in France at the time, next to the Bible itself. (...) one of its central messages was 'religious' in a way that paradoxically gave support to traditional Christian attitudes towards Jews. That message also echoed points made by Kant and the German liberal Protestant theologians whom Renan had studied : Christ had founded a genuinely universal religion, "the eternal religion of humanity, the religion of the spirit liberated from priesthood, from all cult, from all observance, accessible to all races, superior to castes, in one word absolute." Judaism, on the other hand, remained tribalistic ; "it contained the principle of a narrow formalism, of fanaticism, disdainful of strangers." Renan used the word 'race' copiously, if in bewilderingly diverse senses, from a synonym for 'type,' to a social and economic group, to a physical category (...) In some of his writings, Semitic inferiority in a cultural sense is a pervasive theme (particularly because of Semitic tribalism and intolerance), but he also considered the Semites and the Aryans to be part of the same "white race"(while of a different "physical type"). He described modern Jews as being perfectly capable of becoming modern citizens with other enlightened, modern men. In other passages, however, he laid historical responsibility on the Jews for the destructive intolerance introduced into the world through Christianity and Islam. (…) But Renan also praised the Semitic contribution to civilization. The very idea of human solidarity, of equality before one god, was, he wrote : "The fundamental doctrine of the Semites, and their most previous legacy to mankind", even if paradoxically contradicted by the Jewish notion of a Chosen people. He further spoke of both the modern European Aryans and the Semites as noble, in contrast to the inferior races outside Europe." ('Modern Anti-Semitism and the Rise of the Jews', A.S. Lindemann) In the introduction to his five-volume 'History of the People of Israel', he wrote : "For a philosophic mind, that is to say for one engrossed in the origin of things, there are not more than three histories of real interest in the past of humanity: Greek history, the history of Israel, and Roman history... Greece in my opinion has an exceptional past, for she founded, in the fullest sense of the word, rational and progressive humanity. Our science, our arts, our literature, our philosophy, our moral code, our political code, our strategy, our diplomacy, our maritime and international law, are of Greek origin... Greece had only one thing wanting in the circle of her moral and intellectual activity, but this was an important void; she despised the humble and did not feel the need for a just God... Her religions were merely elegant municipal playthings; the idea of a universal religion never occurred to her. The ardent genius of a small tribe established in an outlandish corner of Syria [i.e. The Israelites] seemed to supply this void in the Hellenic intellect [by giving birth to Christianity]."
One of the two main characteristics of nineteenth century scientism lies in that passage : a Philosemite anti-Semitism based on religious grounds and on a cultural determinism strongly influenced by a racial determinism of the zoological order ; and the belief in the Greek origins of modern European science : both tendencies were interconnected. Taine, whilst being more consistent and clear-headed than Renan in his assessment of the Semitic races on the typological and spiritual plane [with them, "metaphysics are lacking, religion can only conceive of a God-King who is all-consuming and solitary"], is just as blinded as him, when it comes to evaluating their abilities in the scientific domain : "[with them], science cannot come into being, the spirit is too rigid and complete to reproduce the delicate ordering of nature (...)". In many respects, Bernal, in his famous controversial 'Black Athena', has showed that scientific 'Eurocentrism' derives from a pre-scientist and pre-Darwinist fabrication of ancient Greece, whilst not having seen that it originates essentially in a non European spirit and world-outlook.
Like many nineteenth century scientist and racist, Renan claimed that "Islam and science – and therefore, by implication – Islam and modern civilization were incompatible with each other. (...) Renan admitted indeed the existence of a so-called Arabic philosophy and science, but they were Arabic in nothing but language, and Greco-Sassanian in content. They were entirely the work of non-Muslims in inner revolt against their own religion ; by theologians and rulers alike they had been opposed, and so had been unable to influence the institutions of Islam. This opposition had been held in check so long as the Arabs and Persians had been in control of Islam, but it reigned supreme when the Barbarians – Turks in the east, Berbers in the west – took over the direction of the umma. The Turks had a "total lack of the philosophic and scientific spirit", and human reason and progress had been stifled by that enemy of progress, the State based on a revelation. But as European science spread, Islam would perish (...) ('Arabic Thought in the Liberal Age, 1798-1939, A.H. Hourani).
"This is how a very large number of books on science and religion, as well as those dealing with the history of science, M. Iqbal states in 'Science and Islam', depict the eight hundred years of scientific activity in Islamic civilization. Most accounts actually reduce this time period to half its length by a summary death sentence, which turns this tradition to an inert mass some time in the twelfth century. This is the prevalent view of nonspecialists, who have never touched a real manuscript with their hands and who have never looked at an Islamic scientific instrument of surpassing aesthetic quality and dazzling details, displaying a mastery of complex mathematical theorems. The extent of the entrenchment of this view makes it almost an obligation of anyone writing a new work on Islam and science to first examine evidence supporting this view. When one makes that attempt one finds that all roads lead to Ignaz Goldziher, the godfather of the 'Islam versus foreign sciences' doctrine (...) Goldziher's attitude toward Islam was formulated in the background of the colonization of the Muslim world by European powers that had, in turn, presented Islam as a spent force that could only be derided and vilified. (...) Religion was thus seen as an inhibitor of science. This was first seen in reference to Christianity, but soon this initial recasting of the role of Christianity in Europe was enlarged to include all religions, Islam being particularly chosen for its perceived hostility toward rational inquiry. The idea that Islam was inherently against science was thus nourished under specific intellectual circumstances then prevalent in Europe, and it was in this general intellectual background that the first echoes of the 'Islam against science' theory [which, as matter of fact, many Muslims, whether of Arabic stock or not, still uphold] are heard."
R. Guenon's considerations on science and the Renaissance are worth reading again in the light of these clarifications. While stating first that, at that time, "Men were indeed concerned to reduce everything to human proportions, to eliminate every principle of a higher order, and, one might say, symbolically to turn away from the heavens under pretext of conquering the earth ; the Greeks, whose example they claimed to follow, had never gone as far in this direction, even at the time of their greatest intellectual decadence, and with them utilitarian considerations had at least never claimed the first place, as they were very soon to do with moderns" ; while stating further that "(...) what is called the Renaissance was in reality not a re-birth but the death of many things ; on the pretext of being a return to the Greco-Latin civilization, it merely took over the most outward part of it, since this was the only part that could be expressed clearly in written texts (...)", the fact remains that he is convinced that "some of the origins of the modern world may be sought in 'classical antiquity' ; the modern world is therefore not entirely wrong in claiming to base itself on the Greco-Latin civilization and to be a continuation of it" ('The Crisis of the Modern World'), about which he acknowledged himself in his correspondence that he did not know much. In this case, he would therefore have been well inspired to turn to Mecca, not to pray, but to think. For that "most outward part" of the Greco-Latin civilisation that the Renaissance took over, more precisely, turns out to be constituted by views originating in non Aryan races.
"At the beginning of the twelfth century no European could expect to be a mathematician or an astronomer, in any real sense, without a good knowledge of Arabic ; and Europe, during the earlier part of the twelfth century, could not boast of a mathematician who was not a Moor, a Jew, or a Greek." ('A History of Mathematics', C.B. Boyer). "Whether in architecture , agriculture, art, language, law, medicine, music, or technology, the considerable influence of the Arab civilisation on medieval Europe and its determinant role in the genesis of Renaissance was only acknowledged fully in the twentieth century. For instance, its influence on education is enormous : "The origins of the college lies in the medieval Islamic world. The madrasah was the earliest example of a college, mainly teaching Islamic law and theology, usually affiliated with a mosque, and funded by Waqf, which were the basis for the charitable trusts that later funded the first European colleges. The internal organization of the early European college was also borrowed from the earlier madrasah, like the system of fellows and scholars, with the Latin term for fellow, socius, being a direct translation of the Arabic term for fellow, sahib. Madrasahs were also the first law schools, and it is likely that the "law schools known as Inns of Court in England" may have been derived from the madrasahs which taught Islamic law and jurisprudence. If a university is assumed to mean an institution of higher education and research which issues academic degrees at both undergraduate and postgraduate levels, then the Jami'ah which appeared from the 9th century were the first examples of such an institution. The University of Al Karaouine in Fez, Morocco is thus recognized by the Guinness Book of World Records as the oldest degree-granting university in the world with its founding in 859 by Fatima al-Fihri. However, the madrasah differed from the medieval university of Europe in several important respects, namely that the degree took the form of a license (ijazah) which "was signed in the name of the teacher, not of the madrasa". In other words, "the authorization or licensing was done by each professor, not by a group or corporate body, much less by a disinterested or impersonal certifying body". The first colleges and universities in Europe were nevertheless influenced in many ways by the madrasahs in Islamic Spain and the Emirate of Sicily at the time, and in the Middle East during the Crusades. The origins of the doctorate dates back to the ijazat attadris wa 'l-ifttd ("license to teach and issue legal opinions") in the medieval Islamic legal education system, which was equivalent to the Doctor of Laws qualification and was developed during the 9th century after the formation of the Madh'hab legal schools. To obtain a doctorate, a student "had to study in a guild school of law, usually four years for the basic undergraduate course" and ten or more years for a post-graduate course. The "doctorate was obtained after an oral examination to determine the originality of the candidate's theses," and to test the student's "ability to defend them against all objections, in disputations set up for the purpose" which were scholarly exercises practiced throughout the student's "career as a graduate student of law." After students completed their post-graduate education, they were awarded doctorates giving them the status of faqih (meaning "master of law"), mufti (meaning "professor of legal opinions") and mudarris (meaning "teacher"), which were later translated into Latin as magister, professor and doctor respectively. The term doctorate comes from the Latin docere, meaning "to teach", shortened from the full Latin title licentia docendi meaning "license to teach." This was translated from the Arabic term ijazat attadris, which means the same thing and was awarded to Islamic scholars who were qualified to teach. Similarly, the Latin term doctor, meaning "teacher", was translated from the Arabic term mudarris, which also means the same thing and was awarded to qualified Islamic teachers. The Latin term baccalaureus may have also been transliterated from the equivalent Arabic qualification bi haqq al-riwaya ("the right to teach on the authority of another"). According to Professor George Makdisi and Hugh Goddard, some of the terms and concepts now used in modern universities which have Islamic origins include "the fact that we still talk of professors holding the 'Chair' of their subject" being based on the "traditional Islamic pattern of teaching where the professor sits on a chair and the students sit around him", the term 'academic circles' being derived from the way in which Islamic students "sat in a circle around their professor", and terms such as "having 'fellows', 'reading' a subject, and obtaining 'degrees', can all be traced back" to the Islamic concepts of Ashab ("companions, as of the prophet Muhammad"), Qara'a ("reading aloud the Qur'an") and Ijazah ("license to teach") respectively. Makdisi has listed eighteen such parallels in terminology which can be traced back to their roots in Islamic education. Some of the practices now common in modern universities which Makdisi and Goddard trace back to an Islamic root include "practices such as delivering inaugural lectures, wearing academic robes, obtaining doctorates by defending a thesis, and even the idea of academic freedom are also modelled on Islamic custom." The Islamic scholarly system of fatwa and ijma, meaning opinion and consensus respectively, formed the basis of the "scholarly system the West has practised in university scholarship from the Middle Ages down to the present day."[102] According to Makdisi and Goddard, "the idea of academic freedom" in universities was "modelled on Islamic custom" as practiced in the medieval Madrasah system from the 9th century. Islamic influence was "certainly discernible in the foundation of the first delibrately-planned university" in Europe, the University of Naples Federico II founded by Frederick II, Holy Roman Emperor in 1224". (http://en.wikipedia.org/wiki/Islamic_contributions_to_Medieval_Europe)
G. Sarton, the well-known Harvard historian of science, wrote, in his 'Introduction to the History of Science' : "The scientific advances of the West would have been impossible had scientists continued to depend upon the Roman numerals and been deprived of the simplicity and flexibility of the decimal system and its main glory, the zero. Though the Arab numerals were originally a Hindu invention, it was the Arabs who turned them into a workable system; the earliest Arab zero on record dates from the year 873, whereas the earliest Hindu zero is dated 876. For the subsequent four hundred years, Europe laughed at a method that depended upon the use of zero, "a meaningless nothing." Had the Arabs given us nothing but the decimal system, their contribution to progress would have been considerable. In actual fact, they gave us infinitely more. While religion is often thought to be an impediment to scientific progress, we can see, in a study of Arab mathematics, how religious beliefs actually inspired scientific discovery."
As P. Berlinghoff and F.Q. Gouvea put in 'Math through the Ages', "Of the knowledge which these sages [the Eastern ones] imparted to Western man, the elements of mathematics were an integral part. Hence, to trace the impress of mathematics on modern culture, we must turn to the major Near Eastern civilizations."
"The Babylonians used a special symbol to separate the 5 and 3 in the former case but failed (sic) to recognize that this symbol could also be treated as a number, that is, they failed (re-sic) to see that zero indicates quantity and can be added, subtracted and used generally like other numbers." (ibidem) In other words, zero was still used as a mere placeholder by the Babylonians.
"In around 500AD [in India] Aryabhata devised a number system which has no zero yet was a positional system. He used the word "kha" for position and it would be used later as the name for zero. There is evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. It is interesting that the same documents sometimes also used a dot to denote an unknown where we might use x. Later Indian mathematicians had names for zero in positional numbers yet had no symbol for it. The first record of the Indian use of zero which is dated and agreed by all to be genuine was written in 876." (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html).
"It is quite possible that the zero originated in the Greek world, perhaps at Alexandria, and that it was transmitted to India after the decimal positional system has been established there. (...). With the introduction, in the Hindu notation, of the tenth numeral (...), the modern system of numeration for integers was completed. Although the Medieval Hindu forms of the ten numerals differ considerably from those in use today, the principles of the system were established. The new numeration, which we generally call the Hindu system, is merely a new combination of three basic principles, all of ancient origin : (1) a decimal base ; (2) a positional notation ; and (3) a ciphered form for each of the ten numerals. NOT ONE OF THESE THREE WAS DUE ORIGINALLY TO THE HINDUS, but it presumably is due to them that the three were first linked to form the modern system of numeration." ('History of Mathematics', C.B. Boyer). As a matter of fact, according to D. Smeltzer ('Man and Number', Adam and Charles Black, London, 1953), "They [The Hindus] did not, it would seem, think of it [the zero] as denoting a number but as indicating an empty space. The idea of regarding nothingness or emptiness as a number is at least as difficult as the idea of representing emptiness by a symbol."
"We now come to considering the first appearance of zero as a number. Let us first note that it is not in any sense a natural candidate for a number. From early times numbers are words which refer to collections of objects. Certainly the idea of number became more and more abstract and this abstraction then makes possible the consideration of zero and negative numbers which do not arise as properties of collections of objects. Of course the problem which arises when one tries to consider zero and negatives as numbers is how they interact in regard to the operations of arithmetic, addition, subtraction, multiplication and division. In three important books the Indian mathematicians Brahmagupta, Mahavira and Bhaskara tried to answer these questions." (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Zero.html) Their answers turn out to be either clumsy or bluntly wrong. Errors pile up. Obviously, they were not quite in their element.
The ninth century Arab scholar Muhammad Ibn Musa Al-Khwarizmi, on the other hand, was in his element, when he wrote 'On the Hindu Art of Reckoning', which describes the Indian place-value system of numerals based on 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0, and is the first work to use zero as a place holder in positional base notation. He wrote two books, that one - on arithmetic - and the other on solving equations, which, we are told, were translated into Latin in the twelfth century and circulated throughout Europe. The Latin translations often began with "Dixit Algorizmi", meaning "Al-Khwarizmi said". Many Europeans learned about the decimal place system and the essential role of the zero from these translations. The popularity of this book as an arithmetic text gradually led its title to be identified with the methods in it, giving us the word 'algorithm'. In Al-Khwarizmi, many historians of science, who, for most of them, are not mathematicians, like to think that zero is "not yet thought of as a number ; it is just a place holder." As remarkably well seen by an Arab scholar, "The ancient mathematicians, including the Greeks, considered the number to be a pure magnitude. It was only when al-Khwarizmi (…) conceived of the number as a pure relation [as a 'function'] in the modern sense that the science of algebra could take its origin." This recognition of numbers as 'pure relation' was the key for unlocking the door of algebra. The absence of quantity (0) was acknowledged as a quantity in its own right.
"Historians believe that al-Khwarizmi was born in the city of Baghdad in present day Iraq (Calinger, 199). While little is known about his private life, al-Khwarizmi's work and contributions to mathematics have largely survived the ages relatively intact. The exception is a book of arithmetic in which the original cannot be found; there is, however, a Latin translation of this work as well as other Arab references that cite the missing treatise. Al-Khwarizmi was a member of the House of Wisdom in Baghdad, a society established by the caliph for the study of science (Al-Daffa, 23). According to Al-Daffa, during al-Khwarizmi's life, much of the area between the Mediterranean and India was ruled by al-Mamun, an Islamic caliph who had consolidated his position in a protracted civil war. After pacifying the area under his control, al-Mamun became a patron of the sciences. He instituted the House of Wisdom to both translate the works of Byzantine and Greek scientists as well as to conduct research into various realms of science. Al-Mamun also built a library in Baghdad to house these works; this was the first large collection of scientific information constructed since the Library of Alexandria's erection several centuries before. Finally, al-Mamun constructed a lavish astronomical observatory in Baghdad for the use of Muslim astronomers. Within a short period of time, Baghdad became the new center for learning in the Mediterranean world (Al-Daffa, 23-34). This interest in Greek Hellenistic thought represented a tremendous change from previous Islamic ideology. This might lead one to ask why such seemingly sensible steps represent such a rapid departure from Islamic thought as well as what was the impetus for such a dramatic change ? The first idea to consider is that there had always been a fundamental difference from Greek and Islamic thought. The most important difference was a matter of religion. The classical Greeks and Romans believed in many Gods and the later, after Rome had Christianized the Mediterranean, they believed in a Holy Trinity (Smith, 340). These ideas directly conflicted with the Islamic belief of the one true God, Allah (Smith, 222). As a result, in the seventh century CE, when the disciples of Mohammed began their conquest of the Middle East, North Africa and Spain, the Muslims destroyed much of the work and knowledge of those that they conquered (Smith, 230). Their extreme Islamic fundamentalism blinded the Arabs to the advanced scientific contributions of their neighbors. The initial conquests of Islam lasted well into the eighth century CE, just a generation or two prior to the birth of al-Khwarizmi and al-Mamun. Therefore, as a matter of time, al-Khwarizmi and al-Mamun are not far removed from the zealous invaders of the past. The drastic change in Islamic attitudes toward western science might be a byproduct of the religion itself. Muslims live their lives according to the rules and precepts set forth in the Qu'ran (Koran). This book dictates all aspects of a Muslim's life and death. For example, the Qu'ran dictates that Muslims must pray several times a day toward the city of Mecca as well as giving precise rules of inheritance when one dies (Smith, 236). Both of these tasks require advanced knowledge of mathematics. Mathematics are used in the study of cartography, astronomy and geography. Knowledge of astronomy would have been critical for determining which direction to pray or for ascertaining the beginning of Ramadan (which is based largely on the phases of the moon). Other, less concrete, applications of math would have been required in order to properly divide up estates (Berggren, 63). In a sense, after the zeal of Islam aided in the destruction of knowledge, it realized just how useful that knowledge might have been for its own purposes. As a result, al-Mamun created the House of Wisdom to restore and research the answers to the scientific questions that plagued the administration of his empire." (http://209.85.135.104/search?q=cache:NRiM8OVXxwYJ:www.math.ohio-state.edu/~czorn/work_and_research/hist_algebra.pdf+khwarizmi+zero&hl=en&ct=clnk&cd=2&gl=uk)
It appears that al-Khwarizmi's work was influenced by Greek, neo-Babylonian and Indian sources with the Indians supplying the number system, the Babylonians supplying the numerical processes and the Greeks supplying the tradition of rigorous proof. He assimilated and systematised these three elements in a synthesis which was congruent with the Arabic view on mathematics, and he did it with other contemporary Arab mathematicians, of whom Abd al Hamid ibn Turk. What is interesting, incidentally, is the criterion which is used by some Arab scholars themselves to impugn his title of "Father of algebra" : "(…) according to ibn Al Nadim, "Al-Khwârazmî's Algebra contains a very short section on commercial transactions", whereas "Abd al Hamîd ibn Turk wrote an independent book devoted to this subject. It seems quite certain that in the field of algebra itself too, just as in the field of commercial transactions, it was Abd al Hamîd ibn Turk who wrote the longer and more detailed treatise." www.muslimheritage.com/topics/default.cfm?TaxonomyTypeID=12&TaxonomySubTypeID=62&TaxonomyThirdLevelID=-1&ArticleID=657).
"In Europe, the introduction of the new system met with considerable resistance and there was antagonism between the algorists using the "art of al-Khowarazmi" [those who promoted the Hindu-Arabic numeral system and the algorithms for written calculations and, thus calculated with a zero ; also called Gerbecists, in honour of Gerbert d'Aurillac, who became pope Sylvester II in the end of the tenth century, and who is the first European scholar known to have taught using the Hindu-Arabic numeration system] and the abacists [those who wrote in Roman numerals and used an abacus for calculation, as well as duodecimal Roman fractions] who continued to use the methods of the counting board."
"In 1299 the bankers of Florence were forbidden to use Arabic numerals and were obliged instead of using Roman numerals. (...) Although the Hindu-Arabic system of numeration "had been rejected by some, Italian merchants of the twelfth century recognized its superiority for computational purposes. These merchants became noted for their knowledge of arithmetic operations and developed methods of double-entry bookkeeping [completely unknown until then, and even more so, in ancient Rome]. (...) the forms of the Hindu numerals were not fixed, and the variety of forms gave rise to ambiguity and fraud (...). Outside of Italy, most European merchants kept accounts in Roman numerals until at least 1550 (and most colleges and monasteries until 1650!) ('Sherlock Holmes in Babylon and Other Tales of Mathematical History', M. Anderson, V.J. Katz, R.J. Wilson) "(...) the result is this prolonged struggle [between abacists and algorists] was inevitable. The [Arabic] numerals became a kind of secret code (yes, a cipher), used by merchants and by businesspeople who were willing to evade the laws and the secret arts – after all, the numbers were there, and they were fast and easy to use. Finally, by about the beginning of the sixteenth century, they were here to stay, though there were still those who double-checked their computations on an abacus just to be sure (there are still many places where the abacus is preferred to the computer or calculator because the work done on either of those isn't visible, while the computations worked out on an abacus can be seen by anyone who cares to watch.)" "In the end, B. Crumpacker goes on with the self-satisfied stupidity of a shareholder who knows his shares are skyrocketing ('Perfect Figures'), the numerals were irresistible. (...). Those numbers are elegant in their simplicity and versatility. There are only ten of them, but those ten can make billions". One specific work was instrumental in communicating the Hindu-Arabic numerals to a wider audience in the Latin world : that of Leonardo Pisano, "known to history as Fibonacci, [who] studied the works of Kāmil and other Arabic mathematicians as a boy while accompanying his father's trade mission to North Africa on behalf of the merchants of Pisa. In 1202, soon after his return to Italy, Fibonacci wrote Liber Abbaci ('Book of the Abacus'). Although it contained no specific innovations, and although it strictly followed the Islamic tradition of formulating and solving problems in purely rhetorical fashion, it was instrumental in communicating the Hindu- Arabic numerals to a wider audience in the Latin world" (http://www.britannica.com/EBchecked/topic/14885/algebra/231066/Commerce-and-abacists-in-the-European-Renaissance)
"Even though it would take centuries for the world to accept zero, al-Khwarizmi had produced a number system similar to the one used worldwide today (Mathematics and Astronomy). The main differences were al-Khwarizmi's skepticism of the existence negative numbers and the difference between al-Khwarizmi's symbols and the modern Arabic numbers (it would take several centuries of evolution before numerals began to take a form familiar to the twenty-first century reader)." Basically, much of the House of Wisdom's work and research was directed toward a practical end. "Al-Khwarizmi did not set out to found a new branch of mathematics when he wrote Al-Jabr wal Muqabala. In the introduction to the work, he declares his intent in very practical terms (...) : "A short work on Calculating by (the rules of) Completion and Reduction 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 all 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." Al-Khwarizmi wanted his work to help people solve mathematical dilemnas in their everyday lives." ('Al Khwarizmi', C. Brezina). "Even today, many of the inheritance laws in Arab countries are based on the inheritance laws outline in the Qu'ran. This calls for an official to divide up the deceased person's possessions according to certain proportions based on the relationship of the beneficiary to the deceased (Mathematics and Astronomy). Using al-Khwarizmi's new methods of calculation and geometric representation, the local governments were better able to handle the affairs of the deceased. According to The Free Arab Voice: Because of the Qur'an's very concrete prescriptions regarding the division of an estate among children of a deceased person, it was incumbent upon the Arabs to find the means for very precise delineation of lands. For example, let us say a father left an irregularly shaped piece of land-seventeen acres large-to his six sons, each OAA of whom had to receive precisely one-sixth of his legacy. The mathematics that the Arabs had inherited from the Greeks made such a division extremely complicated, if not impossible. It was the search for a more accurate, more comprehensive, and more flexible method that led Khawarazmi to the invention of algebra. (Mathematics and Astronomy)" (http://209.85.135.104/search?q=cache:NRiM8OVXxwYJ:www.math.ohio-state.edu/~czorn/work_and_research/hist_algebra.pdf+khwarizmi+zero&hl=en&ct=clnk&cd=2&gl=uk)
At this point, the fundamental difference between mathematics in the Greek world and mathematics in the Arab world and, more generally, between the Greek scientific spirit and the Arab scientific spirit should be clear. The following considerations will make it even clearer.
"The Egyptians and Babylonians made numerous practical applications of their mathematics. Their papyri and clay tablets show promissory notes, letters of credit, mortgages, deferred payments, and the proper apportionment of business profits." "But it is a mistake – no matter how often it is repeated - to believe that mathematics in Egypt and Babylonia was confined just to the solution of practical problems. (...) Instead we find, upon closer investigation, that the exact expression of man's thoughts and emotions, whether artistic, religious, scientific, or philosophical, involved then, as today, some aspects of mathematics. In Babylonia and Egypt the association of mathematics with painting, architecture, religion, and the investigation of nature was no less intimate and vital than its use in commerce, agriculture, and construction."
On the other hand, "Arithmetic, said Plato, should be pursued for knowledge and not for trade. Moreover, he declared the trade of a shopkeeper to be a degradation for a freeman and wished the pursuit of it to be punished as a crime. Aristotle declared that in a perfect state no citizen should practice any mechanical art. Even Archimedes, who contributed extraordinary practical inventions, cherished his discoveries in pure science and considered every kind of skill connected with daily needs ignoble and vulgar. Among the Boeotians there was a decided contempt for work. Those who defiled themselves with commerce were excluded from state office for ten years."
"A second contribution of the Greeks consisted in their having made mathematics abstract. (...) The Greek eliminated the physical substance from mathematical concepts and left mere husks. They removed the Cheshire cat and left the grin. Why did they do it ? Surely, it is far more difficult to think about abstractions than about concrete things. One advantage is immediately apparent – the gain in generality. A theorem proved about the abstract triangle applies to the figure formed by three match sticks, the triangular boundary of a piece of land, and the triangle formed by the earth, sun, and moon at any instant. The Greeks preferred the abstract concept because it was, to them, permanent, ideal, and perfect, whereas physical objects are short-lived, imperfect, and corruptible."
"The Greeks put their stamp on mathematics in still another way that has had a market effect on its development, namely, by their emphasis on geometry. Plane and solid geometry were thoroughly explored. A convenient method of representing quantities, however, was never developed nor were efficient methods of reckoning with numbers. Indeed, in computational work they even failed (sic) to utilize techniques the Babylonian had created. Algebra in our present sense of a highly efficient symbolism and numerous established procedures for the solution of problems was not even envisioned. So marked was this disparity of emphasis that we are impelled to seek the reasons for it. There are several(...) in the classical period industry, commerce, and finance were conducted by slaves. Hence the educated people, who might have produced new ideas and new methods for handling numbers, did not concern themselves with such problems. Why worry about the use of numbers in measurement if one doesn't measure, or in trading if one dislikes trade ? Nor do philosophers need the numerical dimensions of even one rectangle to speculate about the properties of all rectangles.
Like most philosophers the Greeks were star-gazers. They studied the heavens to penetrate the mysteries of the universe. But the use of astronomy in navigation and calendar reckoning hardly concerned the Greeks of the classical period. For their purposes, shapes and forms were more relevant than measurements and calculations, and so geometry was favored.
The twentieth century seeks reality by breaking matter down – witness our atomic theories. The Greeks preferred to build matter up. For Aristotle and other Greek philosophers the form of an object is the reality to be found in it. Matter as such is primitive and shapeless ; it is significant only when it has a shape."
We repeat, both for those who are interested in Evola's 'influences' and for those who haven't read him for a while : "Matter as such is primitive and shapeless ; it is significant only when it has shape."
"Because the Greeks converted arithmetical ideas into geometrical ones and because they devoted themselves to the study of geometry, that subject dominated mathematics until the nineteenth century, when the difficulties in treating irrational numbers on an exact, purely arithmetical basis were finally resolved. In view of the clumsiness (sic) and complexity of arithmetical operations geometrically performed, this conversion was, from a practical standpoint, a highly unfortunate one. The Greeks not only failed (sic) to develop the number system and algebra which industry, commerce, finance, and science must have, but they also hindered the progress of later generations by influencing them to adopt the more awkward geometrical approach. Europeans became so habituated to Greek forms and fashions that Western civilization had to wait for the Arabs to bring a number system from far-off India."
As far as Romans are concerned, many histories of mathematics, whether ancient or modern ones, do not even mention them. In 'A Short Account of the History of mathematics', W.W. Rouse Ball wrote : "There is (...) very little to say on the subject. (...) There were, no doubt professor who could teach the results of Greek science, but there was no demand for a school of mathematics. Italians who wished to learn more than the elements of the science went to Alexandria or to places which drew their inspiration from Alexandria. The subject as taught in the mathematical schools at Rome seems to have been confined in arithmetic to the art of calculation (no doubt by the aid of the abacus) and perhaps some of the easier parts of the work of Nicomachus, and in geometry to a few practical rules ; though some of the arts founded on a knowledge of mathematics (especially that of surveying) were carried to a high pitch of excellence." In 'Mathematical Thought from Ancient to Modern Times', M. Kline wrote : "Roman mathematics hardly warrants mention. The period during which the Romans figured in history extends from 750 B.C. to A.D. 476, roughly the same period during which the Greek civilisation flourished. Moreover (...), from at least 200 B.C. onward, the Romans were in close contact with the Greeks. Yet in all of the eleven hundred years there was not one Roman mathematician ; apart from a few details this fact in itself tells us virtually the whole story of Roman mathematics." According to F. Cajori, for whom the fact that a people is not interested in the slightest in mathematics is beyond mathematical logic and imagination ('A History of Mathematics'), "Nowhere is the contrast between the Greek and Roman mind shown forth more distinctly than in their attitude toward the mathematical science. The sway of the Greek was a flowering time for mathematics, but that of the Romans a period of sterility. In philosophy, poetry, and art, the Roman was an imitator (sic). But in mathematics he did not even rise to the desire for imitation. The mathematical fruits of Greek genius lay before him untasted. In him, F. Cajori goes on - without asking himself how come it never occurred to such a "practical people" as the Romans to apply the mathematical knowledge they had received from other peoples to solve everyday life, practical problems, as did the Arabs later - a science which had no direct bearing on practical life could awake no interest. As a consequence, not only the higher geometry of Archimedes and Apollonius, but even the Elements of Euclides, were neglected. What little mathematics the Romans possessed did not come altogether from the Greeks, but came in part from more ancient sources", of which the Etruscan ones. The same thing goes for what is typically described as 'Roman technology'.
The mathematical and, more generally, scientific spirit which resurfaced in the Middle Ages through the so-called 'rediscovery' of Greco-Roman texts by European scholars was, unsurprisingly, not the Greek one, not the Roman one, but the practical Asian one, and, just as unsurprisingly, those who popularised 'algorism' in the thirteenth century either belonged to the bourgeois stratum or were churchmen. The emphasis was so much on the practical applications of knowledge that a shift occurred from experience to experimentation and, ultimately, to experiments of laboratory, into which science has been sinking since the late Middle Ages. Even someone who, like Eeves in 'Foundations and Fundamental Concepts of Mathematics', is convinced that "the ancient Greeks found in deductive reasoning the vital element of the modern mathematical method" cannot but acknowledge that they "transformed the subject [mathematics] into something vastly different from the set of empirical conclusions worked out by their predecessors. The Greeks insisted that mathematical facts must be established, not by empirical procedures, but by deductive reasoning ; mathematical conclusions must be assured by logical demonstration rather than by laboratory experimentation."
The Arabs introduced and developed the experimental method. In 'The Making of Humanity', Briffault stressed that : "The debt of our science to that of the Arabs does not consist in any startling discoveries of revolutionary theories. Science owes a great deal more to Arab culture, it owes its existence... The Greeks systematised, generalised and theorised, but the patient ways of investigation, the accumulation of positive knowledge, the minute methods of science, detailed and prolonged observation and experimental enquiry, were altogether alien to the Greeks temperament… What we call science arose in Europe as a result of a new spirit of inquiry, of new methods of investigation, of the methods of experiment, observation and measurement, of the development of mathematics in a form unknown to the Greeks. That spirit and those methods were introduced into the European world by the Arabs". In the meantime, from the fall of the Roman Empire to the early Middle Ages, the Church did its best to conceal the Greek scientific spirit by preventing the works that embodied it from acting as a basis and as an axis for western science. For example, under pope Gregory the Great, all scientific studies were not allowed in Rome ; the study of ancient original works from Greece and Rome were forbidden and the Palatine library founded by Augustus Caesar was burnt down.
In that context, it's no wonder that "During the Renaissance, there was a dramatic change among Christian intellectuals from one that focused on the contemplation of God;s work to one that focused on the responsibility of the Christian for caring for his fellow humans. The active life of service to mankind, rather than the contemplative life of reflection on God's character and works, now became the Christian ideal for many. As a consequence of this new focus on the active life, Renaissance intellectuals turned away from the then-dominant Aristotelian view of science, which saw the inability of theoretical sciences to change the world as a positive virtue. They replaced this understanding with a new view of natural knowledge, promoted in the writings of such men as Johann Andreae in Germany and Francis Bacon [who became acquainted with alchemy from Latin translations of Arabic writings] in England, which viewed natural knowledge as significant only because it gave mankind the ability to manipulate the world to improve the quality of life. Natural knowledge would henceforth be prized by many because it conferred power over the natural world." ('Science and Islam') The asianisation of the European scientific spirit was completed.
It is also extremely interesting that the one credited for introducing the experimental method in alchemy is the Muslim alchemist, astrologer, astronomer, chemist, engineer, geologist, philosopher, physician and physicist Abu Musa Jābir ibn Hayyān, known in Europe as Geber, and whose writings and treatises on alchemy are quoted by Evola in 'The Hermetic Doctrine' (the research of the most celebrated nineteenth century historian of chemistry M. Berthelot would tend to show that not all works held to have been written by Jabir are actually his, but a contemporary European alchemist's]. Note that he was also deeply interested in mysticism. "The first essential in chemistry", he stated, "is that you should perform practical work and conduct experiments, for he who performs not practical work nor makes experiments will never attain the least degree of mastery." He stated this almost 500 years before, almost in the same terms, Descartes did.
"The Arabs, of course, started out with the chemical knowledge of the Egyptians, Chaldeans, Persians, and Greeks, which was made up more of the occult, the magical, and superstitions (sic) than of chemical science as we know it. Arabic chemistry, however, was not content with those borrowed crudities (sic), but initiated experimentation in a primitive form. It attempted to find a way for the prolonging of life to which the word 'elixir' testifies. Arab chemists, also, experimented with the transmutation of the baser metals into the precious ones." ('The Contribution of the Arabs to Education', K.A. Totah)
In the light of what has just been exposed, another typical excerpt from 'The Crisis of the Modern World' is worth quoting : "it is not for its own sake that Westerners in general cultivate science as they understand it; their primary aim is not knowledge, even of an inferior order, but practical applications, as may be inferred from the ease with which the majority of our contemporaries confuse science and industry, so that by many the engineer is looked upon as a typical man of science."
In the light of the considerations we have made in previous posts on Islam as a typically and essentially lunar religion, it may not be a luxury to have a look at 'The Mathematical Miracle of the Koran': www.submission.org/miracle/moon.html
P.s. : it is commonly taught and, therefore, believed, taken as granted that, from the sixth to the tenth century, many of the works of classical Greco-Roman authors were translated into Syriac by Arab scholars and translated back into Latin (from Arabic) from the tenth to the thirteenth century (by that century, there were many variants – Arabic to Spanish, Arabic to Hebrew, Greek to Latin, or combinations such as Arabic to Hebrew to Latin), during which they were reintroduced in the West. As to exactly how those Arab scholars got hold of those manuscripts, no one seems to know. Basically, no one seems to possess the 'originals'.