Chaucer's Cultural Geography by Lynch Kathryn L.;

Author:Lynch, Kathryn L.;
Language: eng
Format: epub
ISBN: 1479898
Publisher: Taylor & Francis Group

II

Even though we cannot define the Arabic outlook—in Leff’s sense of the word (2–6)—any more than we can the outlook of any other cultural group, certain patterns of thought do seem to be peculiar to Arabic literature, art, music, and mathematics. These structural patterns determine Arabic principles of organization, which in turn explain the Arabic practice of enclosing tales within a framework. Typical of the medieval Arabic approach to organizing material is the way the Arabs developed and modified mathematical principles originating in Babylonia, in contrast to the way the Greek mathematicians dealt with those principles. The ancient Babylonians worked out by observation and experiment a system of mathematics that they used as a tool of trade and commerce. But because Babylonians had not devised zero as a place holder, they could not write numbers like 1, 230 without ambiguity and could not develop modern methods of addition. They handled computation by using tables similar to our multiplication tables, which they arrived at by trial and error (Kramer 1: 35–36).

In the sixth century B.C., Pythagoras studied Babylonian mathematics and rejected observation and experiment, the practical side of Babylonian computational mathematics. He dwelt instead on mathematical theory and insisted that mathematical proof be accomplished by deductive reasoning, a method that starts with a whole and deduces relations within that whole (Kramer 1: 46). His approach led to a concept of unity in which the whole has greater importance and the parts are subordinate. Irrational numbers baffled the Pythagoreans, who found a number like the square root of 2 an impossible concept. The Babylonians had used a number approximating the square root of 2 and left it at that, but the Greeks, bothered by the lack of precision, wrote irrational numbers (and all numbers) geometrically. To represent the square root of 2, the Greeks drew a line equaling the hypotenuse of a right triangle whose sides were one measure long, thereby eliminating Babylonian ambiguities. But their system of working with irrational numbers always remained geometric: they never became accustomed to dealing with irrational numbers numerically as we do or as the medieval Arabs did (Kline 32–33, 48–50, 173).

Pythagoras, voicing what had been implied in Greek thought before his time, stated emphatically that the universe is harmonious because all its parts are related to one another mathematically. Pythagorean mathematics sees underlying order in the mysterious, arbitrary, and chaotic workings of nature (Kline 147–49). Following Pythagoras, other Greek mathematicians and philosophers dealt with the theoretical, scorning the practical and utilitarian. Plato recommended the study of calculation, not for trade and utilitarian purposes, but for the sake of knowledge and truth. He thought that the study of mathematics compels the soul to a loftier region, where number theory is related to the idea of the good; that numbers should not be attached to objects in the sensible world; and that a unit should always appear as a unit and not as a group of small pieces (Republic 6.510, 7.525A–26D; see also Kline 42–46). Like Pythagoras,

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.