"Once upon a time, long ago there was a king who ruled a prosperous land. Poverty was unknown there and every person was gainfully employed. Hence the sight of a beggar making his way along Main Street caused quite a stir in the capital of the land. The king demanded to see this strange man. When brought to him the beggar revealed that he indeed did not have any possessions nor any money for the purchase of food. The king magnanimously offered all-you-can-eat meals for the rest of the week and clean clothes so that the beggar could continue his journey to the next land. Surprisingly, the beggar declined the royal offer and asked for a modest favor. The king demanded to know what the wish was. The beggar humbly requested a grain of rice for the first day, two on the second, four on the third day and so on - doubling the previous days contribution.
The king looked through the window at the overflowing granaries and almost accepted it when his grand vizier, remembering something that he had learnt in Elements of Numbers (Math 201 at the local University) advised his highness that he should reconsider. To calculate the implication of the wish he pulled out a dusty abacus to perform exponential calculations. He fumbled with it for a while but could not express the magnitude of the numbers involved because he ran out of beads. The king getting impatient with his vizier on such a simple wish from a poor man, officially granted the beggar the wish. Little did he know that he had sounded the death knell of his reign.
The next day the beggar came to claim his grain of rice. The townsfolk laughed at the beggar and said that he should have taken the king's kind offer for a full meal instead of the measly grain of rice. On the second day he was back for the two grains. A week later, he brought a teaspoon for the 128 grains that was due to him. In two weeks it was a non-negligible amount of half a kilo. At the end of the month it had grown to a whopping 35 tons. A few days later the king had to declare bankruptcy. That is how long it was needed to bring down the kingdom."
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"Once upon a time there was a king who loved to play chess. One day the king proposed that if anyone in his kingdom could beat him at chess, the king would grant them any reasonable wish. A poor farmer stepped forward to meet the king's challenge. Much to the king's surprise, the farmer beat the king quickly and with seeming ease. True to his word, the king agreed to grant the farmer's wish. Wanting to wish for something that seemed reasonable, the farmer suggested the following: "I propose that you place on the first square of the chess board one penny, and on the second square, two pennies, on the third, four pennies, and so forth, until the last square is reached." After a moments thought, the king granted the request, as it seemed that the farmer had, in fact, asked for very little money. As the king began to place the money on the chess board, however, he soon realized his terrible mistake. Let's see why.
The chess board consists of 8 x 8 = 64 squares. On the first row of the board, the king placed:
0.01, 0.02, 0.04, 0.08, 0.16, 0.32, 0.64, 1.28
for a total of $2.55. Notice that the amount of money is doubling between squares (exponential growth). On the second row, the king placed:
2.56, 5.12, 10.24, 20.48, 40.96, 81.92, 163.85, 327.68
Combined with the first row, there was a total of $655.35 on the board. On the third row, the king placed:
655.36, 1310.72, 2621.44, 5242.88, 10485.76, 20971.52, 41943.04, 83886.08
Combined with the first two rows, there was a total of $167,772.16 -- and there were still five rows to complete! Continuing along like this, the completed board would have contained $368,934,881,474,191,032.32. The king, of course, ran out of money well before this and was unable to keep his promise."
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"A courtier presented the Persian king with a beautiful, hand-made chessboard. The king asked what he would like in return for his gift and the courtier surprised the king by asking for one grain of rice on the first square, two grains on the second, four grains on the third etc. The king readily agreed and asked for the rice to be brought. All went well at first, but the requirement for 2n − 1 grains on the nth square demanded over a million grains on the 21st square, more than a quadrillion on the 41st and there simply was not enough rice in the whole world for the final squares."
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For an in depth analysis, see Wikipedia.
This is a Cultural Code, in reference to a parable that exists outside of the world of the novel. Clearly the parable itself is not concrete, but the concept is understood by most people. In this way it is also a Semantic Code, as it suggests an idea of rapid growth, approaching infinity, to the reader.