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/~czor\
n/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."
http://www.muslimheritage.com/topics/default.cfm?TaxonomyTypeID=12&TaxonomySubTy\
peID=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-aba\
cists-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/~czor\
n/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':
http://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'.