The rice and chessboard problem: why exponential growth fools your brain
The lily pond riddle: why exponential growth gives almost no warning
Lily pads cover a pond, and every day there are twice as many. The pond is full on day 30. On which day was it half full? The quick answer is wrong, and the right one shows why anything that doubles looks harmless until the very end.
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1
It is Miva, Rono's neighbour. She teaches maths, and when she hears about the rice, she has a riddle for you.
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2
It is about a pond. On day 1, there is one lily pad on it. Every day, the number of pads doubles. On day 30, the pond is full.
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3
When was the pond half full? You answer at once: day 15, half of 30. Your brain did it again: it cut a straight line in two.
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4
Miva shakes her head. The pads double every day. So the day before the pond was full, it was half full: day 29.
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5
Go back a few more days. On day 25, the pads cover only 3 parts in 100 of the pond. A walker would see a pond with a few leaves. Five days later, there is no water left to see.
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6
So the size of the pads today tells you little. What tells you more is how fast they double. Here it is once a day. This time is called the doubling time.
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7
Rono goes quiet. On his fridge hangs the bill of his credit card. Miva tells him that a debt can grow like her lily pads.
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Quick check
A pond with a head start.
Show the answer
Day 29. Starting with 2 pads is like starting one doubling ahead, so everything happens one day sooner.
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Go further
Where the riddle went, and real ponds.