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How it works : Inventions
42:
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The ancient Egyptians were among the earliest people to evolve a kind of decimal system for recording numbers. Units were written as a single vertical stroke, so that four units were recorded as four strokes. A new symbol, like an inverted letter U, was used to denote ten units, while other symbols were employed to record hundreds, thousands, ten thousands, and so on. Thus, to write a number such as ninety-eight, the ancient Egyptians had to set down eight strokes and nine symbols for the number ten. The Romans slightly improved upon this system in two ways. First, they introduced additional symbols to denote five, fifty and five hundred; and secondly, by placing a symbol of a lower value in front or behind one of higher value they showed whether it was to be added or subtracted to obtain the required number. Thus L denoted fifty, XL denoted forty (fifty less ten) and LX sixty (fifty plus ten). At much the same time the Greeks produced a numerical system in which the letters of their alphabet were written with a stroke above to indicate the numbers one to ten, and thereafter twenty, thirty and so on.
The great disadvantage of all these systems was that it was impossible to make any but the simplest arithmetic calculations. Single additions or subtractions presented no difficulty, but to multiply two large numbers was quite a different matter. The practical solution was to use a sand-table, called an abacus, named after the Greek word for sand, abax, and not to be confused with the later bead-frame of the same name first used by the Chinese. A grid was first drawn in the sand with vertical, horizontal and oblique lines. The numbers to be multiplied were then set out as marks in the sand along the top and down the side of the grid (fig 1). Each Column was then multiplied, place by place, against the other, units being recorded below the oblique line and tens above it in each square of the grid (fig 2). The oblique columns were then added and the numbers set down (fig 3) along the side and bottom of the grid. The answer obtained still had to be transliterated into Roman or Greek numerals. This unwieldy procedure made complex calculations very difficult and they were often the work of experts.
By 500 AD astronomy had reached a point where complex mathematics were essential, and this was especially true of the work being done in the cities of the Punjab, at that time a melting-pot of Hindu, Buddhist and Greek cultures. Shortly after 500 AD, according to tradition, the astronomer Aryabhata decided to replace the cumbersome marks made on the abacus by a group of symbols representing the numbers one to nine. He realized, furthermore, that the actual numerical value given to the symbol could depend upon its position. Thus the symbol for three could mean three units in the first column, thirty in the second column, three hundred in the third column, and so on. In other words, he introduced the idea of place notation that we use today, an idea already present in embryo in the practical use of the abacus. One further improvement had to be made. In using the abacus it was perfectly practical to leave a blank space in a column; and in setting the figures down as Roman numerals there was no need for the figure zero. Hence, CV is read as 105, and there is no need to record that no tens are present in the number. With place notation, however, a symbol was required to show the place was void, and the Indian scholars introduced a sign for zero, the cipher. When the Arabs conquered the Punjab shortly after 700 AD, they were impressed by the advanced state of Indian mathematics and, in 771 AD, Indian scholars were brought to Baghdad to teach the new system. Their symbols were adopted by the Arabs, who referred to them as Hindi (Hindu) or huruf alghubar (sand letters). Soon not only Arab scholars but also traders and businessmen were using Hindi symbols. Europeans were slow to learn from the Arabs. Although a few European scholars had adopted the system before 1200 AD, its general use did not gain popularity until after this date when the Hindi figures, known in Europe as Arabic figures, were introduced by Leonardo Fibonacci of Pisa. A century later, when the first true clocks began to be built, Arabic numbers were still not widely understood, and Roman numerals were used.
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Reproduced from HOW IT WORKS p1221
