A MULTIPLICATION PROBLEM
EACH MORNING when we wake up, mankind has increased by a number equal to the population of a city the size of Lausanne or Heidelberg. During the next forty years it will grow by about 30,000 metropolitan cities, or 3,000 cities of more than a million people, or 200 giant cities such as New York.
The legendary inventor of the game of chess is supposed to have offered it for sale to a maharaja, who asked him to set the price. The answer was: one kernel of wheat for the first square, two for the second square, four for the third, eight for the fourth, and so on, doubling the number of grains for each succeeding square on the board. The maharaja, very happy to have the game for what seemed so little, agreed. But in all of India, in all the world, there was not enough wheat to pay the inventor. The first twenty squares brought the price to more than a million kernels of wheat; the first half of the board, thirty-two squares, brought it to more than two thousand million. One may safely assume that if the maharaja's mathematicians continued their computations they did it solely for exercise. The total price came to 18,446,744,073,709,551,615 kernels of wheat.
Such are the surprises provided by the simple process of duplication. As matters stand now, mankind doubles its number every forty years. In 1961 the population of the world surpassed the three thousand million mark. In 2000 there will be roughly six thousand million. If this rate of increase keeps up, there will be 100 thousand million people on earth in 2160, which means that one single uninterrupted city area would cover all habitable land. Six hundred years from now, each one of the 150 thousand million human beings would be allotted just a little more than one square yard. Seven hundred years from now, six people would have to share this square yard; and in seventeen hundred years from now, the total weight of mankind would equal that of the planet on which they live.
One would get dizzy trying to add up further. Fortunately, the increase in population is not merely a matter of arithmetic. At some point the human avalanche will stop -- through intelligent reasoning we hope, and not through a catastrophe. When and where the