Finding Zero Read Online Free Page B

then extending the numbers to the left of zero to –1, –2, –3, and onward. The number –1 is a reflection of the number +1 through a mirror placed at zero. But the zero plays many other important roles in mathematics and its applications. And some crucial equations in physics, biology, engineering, economics, and other fields use zero as the key element (Maxwell’s equations in physics are a good example).

    The ancient Babylonians developed a cumbersome number system based on 60 rather than 10, and without a real zero. In this system, ambiguities arose because of the lack of a zero, and they could only be resolved from the context. As a modern example, if someone told you that something costs six-ninety-five, you would understand it to be $6.95 if you were buying a magazine and $695 if you were purchasing an airplane ticket. With their cumbersome number system, the Babylonians were forced to make such assumptions all the time. But interestingly, vestiges of their ancient system still exist today: We have 60 seconds in a minute, 60 minutes in an hour, and the circle has 360 (6 × 60) degrees. All in all,however, the Babylonian system would be as inadequate today as doing calculations with one’s fingers and toes.
    An interesting question arises: Why use a base of 60? We have ten fingers, so base 10 makes sense, and if you insist on also counting toes, a base 20 may be useful. But 60? In 1927, the prominent Austrian American historian of science Otto Neugebauer suggested that the choice of the large base of 60 was made to address an important practical problem in using numbers in Babylonia. Often, fractions of a whole, such as 1 ⁄ 2 , 1 ⁄ 3 , 3 ⁄ 4 , and 2 ⁄ 3 , were required as measures: Perhaps someone wanted to buy half a loaf of bread, or a third of a wheel of cheese, or two-thirds of a shepherd’s pie. How could the numbers 1 ⁄ 2 , 1 ⁄ 3 , 3 ⁄ 4 , and 2 ⁄ 3 —the most commonly used fractions—be reconciled with a natural system using ten numbers abstracted from fingers? Neugebauer’s answer was that 60 is a good solution since this number is divisible by 2, 3, 4, and 10, and for this reason it was chosen as the base for the entire system. Another hypothesis is that the Babylonians knew five planets (Mercury, Venus, Mars, Saturn, and Jupiter) and that they chose their base, for cosmological reasons, to be the product of this number and the 12 (lunar) months of the year. 3
    I already knew something about the Greco-Roman number system from visiting Greece and Rome. This system, too, lacked a zero, and with it the ability of the numbers to cycle so that the same signs could be used over and over again to mean different things. The Greco-Roman system, like the Babylonian and Egyptian, had to fade away, remaining only as an elegant way of commemorating official dates or representing time on clock and watch faces.
    Then, in the thirteenth century, a system of numbers consisting of nine numerals and a round zero appeared in Europe. This innovation became popular and within a few decades took hold in all segments of educated society. Merchants, bankers, engineers, and mathematicians found that it improved their lives because they could make quicker calculations with fewer errors.
    It is believed that Leonardo of Pisa (ca. 1170–1250), better known as Fibonacci (of the famous Fibonacci sequence), was the one to bring the Hindu-Arabic numerals to Europe. He did it through his book, Liber Abaci (the book of the abacus), published in 1202 and circulated widely throughout the continent. This mathematical volume described the nine Indian figures—the digits 1 through 9—and a symbol, 0, for what Fibonacci called zephirum, meaning zero. The root of the Latin zephirum has been traced to the Arabic word for zero, sifr. So a linguistic connection is found here from the Arab zero to the new European one. And the author clearly refers to the nine