Exponential growth is difficult for the human mind to comprehend! Chess was invented in India some 2500 years ago by people who loved math and numbers. A ruler of a kingdom was so impressed by chess, he offered a payment to the inventor. The inventor asked for a payment in grains of wheat placed onto the chessboard as follows. One grain on the first square, two grains on the second square, four grains on the third square, and so on. The ruler, apparently not comprehending the geometric series, waived him off with his hand. However, this amount of wheat exceeds all the grain ever produced by humanity or 264 -1.
Why is it so hard to comprehend exponential growth? It is because
1) People haven't learned math well?
2) People don't practice math and forget?
3) People can't imagine big numbers?
Or maybe all of the above?
India produced great mathematicians and I'm sure this fable was passed along through the generations to teach young kids to think about numbers and put their mind to great use.
Okay, so chess isn't your thing. Here's another brainteaser. If you take a regular sheet of A4 paper and fold it 102 times, how thick will it be? Maybe as big as your wallet you think. Well, it would be thicker than the Universe!
In my experience, I see people struggle with the math, as well as imagining very small or very large things. If an A4 piece of paper is cut in half, then in half, and so on it will get too small to cut after about 7 or 8 cuts. But if we could keep cutting it in half 31 times, then it would be as small as an atom. An atom is "uncuttable" so this is one way to introduce students to the concept of an atom.
In other words,
½ x ½ x ½ x ½ .... is a very small number.
