One hot Sunday afternoon, Isha was throwing around a crazy ball at home, and a conversation started about the nice pattern it made with its each bounce. Rajeev being a big fan of Mathematics, started talking about the relationship between the different heights, each being half of the previous height.
There was once a King who was very fond of chess. Over time, he became quite good at it and started winning competitively (by sheer merit and not from sycophancy). For the thrill of it, he started playing the game with prize monies. He was fair too. If he won, the opponents gave him a coin or two or some fruit or vegetable from their garden. If the opponent won, he rewarded them with gold!
One day, an old man came to the palace and challenged the King to a game of chess. The king readily agreed. The old man, of course, beat the King. The King asked him, “What would you like for prize money?'. The old man said, “Just give me some rice so I needn’t worry about food for what’s left of my time here". The King felt quite insulted and said, “You’ve done what only a few have been able to and when others ask me for gold and land, all you want is rice!! Ask for something else.” But the old man was insistent. The king finally relented and said, “All right! How much rice would you like?” The old man said “O King! Just place the rice grains on the chess board using the following arrangement: 1 grain on the first square, 2 on the second, 4 on the third, 8 on the fourth and so on doubling the number of grains for each subsequent square"
The king described this arrangement to the head of the granary and asked him to get a bag of the best rice in the kingdom. Now the granarian obviously had a knack for numbers and a few minutes after he heard about the arrangement, quietly said, “O King! Am afraid you won’t be able to keep your word”. The King was puzzled and furious, “How’s that even possible? All this old man wants is a few grains of rice!” The granarian drew a chess board and explained, “The number of grains on the nth square is 2^(n-1). So for the last square alone, the number of grains is 2^63 and the total number of grains would be 264-1=18.44*1018
A grain of rice weighs about 25 milligrams or .025 grams. So 18.44*1018 grains of rice weigh
(18.44*1018)*(.025 grams)=4.612*1017 grams or 461 billion metric tons. (At 2016 worldwide rice production levels, this would take a 100 years!)
The silence was palpable and the King, needless to say, was shocked. The King turned to look at the old man who with a mischievous smile revealed his true identity - it turned out to be none other Lord Krishna, “Don’t worry, O King! You and your kingdom can pay this debt over time”. And thus began the tradition of offering rice payasam to Krishna.
We then sat down as a family with Kullakkar red rice and decided to try this out ourselves. We then spent a whole hour (in complete silence) doing a spiral arrangement using a simple doubling rule. 1 grain at the centre, 2 next to it, 4 after that and so on. After the 5th square, we started counting in fives, learnt to count fives in different ways and thus went until the 11th square. A practice in mindfulness and fine-motor skills as we picked and place each grain carefully.
It was quite fascinating to experience Mathematics, Mythology and Mindfulness meet so spontaneously!
Story paraphrased by Rajeev from www.singularitysymposium.com/exponential-growth.html
Some of the weight calculations were taken from www.wyzant.com/resources/blogs/291843/the_classic_chessboard_problem