Interesting -   -Tails that add up

Interesting - -Tails that add up

ChessbrotherJon
ChessbrotherJon
Jan 21, 2016, 5:37 PM |
1

We Are The World

 


 

 
The Unbearable Quickness of Doubling

Sometimes called deterministic chaos, or more commonly the  power of exponential growth. I prefer a term coined  

 

'The unbearable quickness of doubling', or even better I like to think it of as 'how quickly things can get out of control 


According to George Gamow, chess was invented by Sissa ben Dahir, Wazir of the court of King Shiram. King Shiram loved the game so much that he offered Sissa any reward he could name. Perhaps trying to impress the king with his mathematical skills, Sissa asked for some rice,
  one grain on the first square of the chessboard,
  two on the second,
  four on the third,
  eight on the fourth,

  and so on,

each square's amount being the double of the previous square's.

How much rice did Shiram owe Sissa?

The last square would contain 263 grains of rice.

This is a large number:

263 = 9,223,372,036,854,775,808

Suppose Shiram had tried to stack the rice of this last square in a column, each grain lying on top of the one below it. A grain of rice is about 1 mm thick. How high a column of rice would Shiram have obtained?   

In fact, if he could have stacked them this way, Shiram would have obtained a column of rice

one light year tall,

one-quarter of the way to the nearest star after the sun.

Obviously, Shiram could not give Sissa the reward he requested. What do you suppose was the outcome? Let's just say an important lesson is "Don't be a smart-alek."