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To: Maurice Winn who wrote (35622)	7/1/2003 11:24:10 PM
From: marcos	Respond to of 74559

There was a huge burst of commerce and science when the moros took Spain, they say ... also before that, when the greeks came, and in between when phoenician towns boomed for a while .... then when the moros were kicked out there came a surge of exploration and trade that provided mixing, which is what it takes to make thrive a lot of things, with ideas at the top of the list .... not that the spanish themselves benefited from the mixing, because they refused to mix in real terms, felt that their 'god' had 'chosen' them [really, and said so in those terms, the writings exist still] .... but they spun off mixing to others ... sort of like Globalstar i guess, only different ... anyway it's the mixing that does the trick ... post cut short, called to chauffeur duty, cheers

To: Maurice Winn who wrote (35622)	7/2/2003 9:01:00 AM
From: smolejv@gmx.net	Respond to of 74559

<'english' [didn't they actually start out as 'arabic'?] letters > ...I don't know where they came from, but they are handy. Let me quote in excerpts from Carl B. Boyer, "History of Mathematics", (a standard reference book): During the first century of the Arabic conquests there had been political and intellectual confusion, ... The Arabs were at first without intellectual interest, and they had little culture, beyond a language, toimpose on the peoples they conquered. ... But by 750 the Arabs were ready to have history repeat itself, for the conquereors became eager to absorb the learning of the civilizations they had overrun. by 766 we learn that an astronomical-mathematical work, known to the Arabs as the "Sindhind", was brought to Baghdad from India. ... A few years later, perhaps about 775, the Siddhanta was translated into Arabic, and it was not long afterward (ca. 780) that Ptolemy's astrological "Tetrabiblos" was translated into Arabic from the Greek ... [page 226] The first century of the Muslim empire had been devoid of scientific achievement. This period (from about 650 - 750) had been, in fact, perhaps the nadir in the development of mathematics, for the Arabs had not yet achieved intellectual drive, and concern for learning in the other parts of the world had pretty much faded. Had it not been for the sudden cultural awakening in Islam during the second half of the eighth centrury, considerably more of the ancient science and mathematics would have been lost. To Baghdad at that time were called scholars from Syria, Iran, and Mesopotamia, including Jews and Nestorian Christians; under three great Abbasid patrons of learning -- al-Mansur, Haroun al-Rashid, and al-Mamun -- the city became a new Alexandria. During the reign of the second of these calliphs, ... , part of Euclid was translated. ... Mohammed ibn-Musa al-Khwarizmi, ..., who died sometime before 850, wrote more than a half dozen astronomical and mathematical works, of which the earliest were probably based on the Sindhind derived from India. Besides ... [he] wrote two books on arithmetic and algebra which played very important roles in the history of mathematics. ... In this work, based presumably on an Arabic translatoin of Brahmagupta, al-Khwarizmi gave so full an account of the Hindu numerals that he probably is responsible for the widespread but false impression that our system of numeration is Arabic in origin. Al-Khwarizmi made no claim to originality in connection with the system, the Hindu source if which he assumed as a matter of course; ... [pages 227-228] Through his arithmetic, al-Khwarizmi's name has become a common English word; through the title of his most important book, Al-jabr wa'l muqabalah, he has supplied us with an even more popular household term. From this title has come the word "algebra", for it is from this book that Europe later learned the branch of mathematics bearing this name. Diophantus sometimes is called "the father of algebra", but this title more appropriately belongs to al-Khwarizmi. It is true that in two respects the work of al-Khwarizmi represented a retrogression from that of Diaophantus. First, it is on a far more elementary level than that found in the Diophantine problems and, second, the algebra of al-Khwarizmi is thoroughly retorical, with none of the syncopation found in the Greek Arthmetica or in Brahmagupta's work. Even numbers were written out in words rather than symbols! It is quite unlikely that al-Khwarizmi knew of the work of Diophantus, but he must have been familiar with at least the astronomical and computational portions of Brahmagupta; yet neither al-Khwarizmi nor other Arabic scolars made use of syncopation or of negative numbers ... [page 228]