Difference between revisions of "CSC103: DT's Notes 1"
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If you answered 31 days, then congratulations! Indeed, if it doubles in size every day, then after Day 30 it will be twice half the size of the lake, so it will have covered the whole lake! This simple example shows the powerful nature of exponential growth. It took the lily 30 days to cover 50% of the lake, but it takes in only 1 day to cover the other 50%. | If you answered 31 days, then congratulations! Indeed, if it doubles in size every day, then after Day 30 it will be twice half the size of the lake, so it will have covered the whole lake! This simple example shows the powerful nature of exponential growth. It took the lily 30 days to cover 50% of the lake, but it takes in only 1 day to cover the other 50%. | ||
| − | There are many such puzzles in our cultures that attempt to demonstrate the extraordinary power of exponential growth through seemingly impossible feats. Another is the story | + | There are many such puzzles in our cultures that attempt to demonstrate the extraordinary power of exponential growth through seemingly impossible feats. Another is the story rice on the chessboard as told by David R. Henderson and Charles L. Hooper<ref name="rice">David R. Henderson and Charles L. Hooper, ''Making Great Decisions in Business and Life'', Chicago Park Press, 1st edition, March 12, 2007.</ref>: |
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| − | Let's stay with this second example and write down the number of the square followed by the quantity of grains: | + | :::In a time of hunger, the Emperor of China wanted to repay a peasant who had saved the life of his child. The peasant could have any reward he chose, but the Emperor laughed when he heard the silly payment the foolish peasant selected: rice on a chessboard. The peasant wanted one grain of rice on the first square, doubling to two on the second, doubling to four on the third, and so on. After the Emperor agreed, his servants brought one bag of rice into his court and began tediously counting rice. Soon, he called for more and more bags of rice... |
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| + | Of course it is impossible to grant such as wish, as the number of grains that would have to be put on the 64th square of the 8-by-8 chessboard is 2<sup>64</sup>, or 18,446,744,073,709,551,616, much more than the quantity of rice produced on earth in a single year. | ||
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| + | Let's stay with this second example and write down the number of the square followed by the quantity of grains of rice: | ||
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Revision as of 19:16, 30 September 2013
--© D. Thiebaut 08:10, 30 January 2012 (EST)
