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Sacred Number

44 Modern nuMBers the dawn of quantity 45 When the ancient Greeks proved that the diagonals of squares could not be expressed as fractions, it is said to have caused a crisis in their ranks, a little like the terror still experienced today by many people faced with a square root symbol. The last 400 years of human thought have transformed our conception of number. After the revolutionary adoption of Indian numerals, and with them the astonishing zero, the next piece of witchcraft was the introduction of negative numbers, thus creating a number line which vanished in two directions. Negative numbers seem simple enough to us today but they throw up a serious conundrum. Square a negative number and it becomes positive, so what are the square roots of negative numbers Mathematicians had to invent them They realized that there was another number line, that of the square roots of negative numbers, which they called imaginary numbers, labeled today with an i so i is the square root of minus one. The play between imaginary and real numbers effortlessly produces fractals, the recursive shapes we find all around us in nature. With the decimal system we use today, we can describe numbers like , or pi, the ratio between a circle s circumference and its diameter, with great accuracy. However, some of the most beautiful objects in modern mathematics simply employ repeated fractions which would have been familiar to the ancients. These capture the complex essence of square roots, the golden section , , and the exponential growth function, e.
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