Millions more

Because I am fascinated by large numbers, I present here a paraphrased version of the story of the rice on the chessboard.

A man who lived in a wealthy kingdom had performed a great deed. When the King learned of this he decided to reward the man and asked him what he would like as his reward. Seeing a chessboard (8 squares on a side) in the King’s chamber he asked for one grain of rice to placed on the first square, 2 on the second square, 4 on the 3rd, 8 on the fourth and so on, to the last and 64th square. The King, not fully understanding the implications of this request, said that he would gladly reward the man as he stipulated and ordered that the rice be brought in. Things began nicely, but the amount of rice required for each square quickly became enormous. The 21st square required more than a million grains rice. The 41st square required more than a trillion grains and the ruler exhausted all the rice in all the land before he reached the 64 square.

I have created 21 images, each with twice as many pixels as the previous one, to demonstrate visually exponential growth. I have assembled them on a separate page because they are too large (2,000 x 2,000 pixels, but only 32 kilobytes) to fit the format of this blog. If I had created all 64 images the largest one would have been over 4 trillion pixels wide. On most computer screens there are 72 pixels in an inch so it would require a screen 941 miles wide to view the image at full resolution.

See my visual representation of geometric or exponential growth here. It is much more dramatic than a simple line on a graph.