The rice and chessboard legend is used to illustrate the magnitude of exponential functions. In scientific research, the numbers in the mathematical models can increase so exponentially that they require massive amounts of computing power to solve them. The following examples illustrate the power of doubling.
The Inventor of Chess and the Emperor of India
It is believed that chess was invented some 1,500 years ago in India, and the game's inventor so impressed the emperor that he was asked to name his reward. The inventor asked for one grain of rice on the first square of the chessboard and double that number of grains for the next square and double that for the next and so on until all 64 squares were filled.
The emperor thought it was such insignificant compensation for so marvelous a game that he agreed, only to find out that by the time the 64th square was filled, there was not enough rice in the kingdom to fulfill the request. One version of the legend claims the inventor was then beheaded.
There are stories that use wheat instead of rice, but in either case, 1 doubled 64 times yields the number 18 followed by 18 zeros.
Water Lilies on a Lake
A more visual example of doubling is water lilies on a lake. There is one water lily on day one, and they double every day. If at the end of 30 days, half the lake is filled, how many days until the entire lake is covered? The answer is 31. See quantum computing