Barry Farber enjoys telling the famous fable of the invention of the game of Chess and used it several times during my appearances on his show. It is not only a great story, but an example of the power of stories in teaching.
In the fable the Emperor of Persia is an inveterate chess player; loves the game and one day orders an audience for the inventor of the game, a mathematician so obscure we do not know his name in spite of the fact he deserves to be immortal.
When the man appears at court the Emperor lauds him with praise and offers “…anything you want as a reward!” The room is still as all present wonder for what he will ask. After a minute of silent consideration he says, “Your Eminence, I only ask that one grain of rice be placed on game board, then two on the next, four on the one after than, doubling in each step to the last square on the board.”
The Emperor was highly amused as the man could have asked for anything but “A few handfuls of rice?” he exclaims. The inventor smiles slowly as the Emperor assigned the task to one of his courtiers.
Two days later the Emperor’s man frantically tries to explain to him that what the chess inventor has asked for is more than all the rice ever grown! And, it is still true to this day! How can this be?
A chess board has eight ranks and eight files for 64 squares. Starting with the first we put one rice grain then two, then four, then eight and so on. This can be expressed as: 2 x 2 x 2… 64 times or 2^64, two to the 64th. Two times itself 64 times. The product is 18 followed by 18 zeros!
A million is one followed by six zeros, a billion is one followed by nine zeros, a trillion, one followed by 12 zeros. 18 followed by 18 zeros is a very big number. Let’s translate it into mass.
50 grains of rice have a mass of one gram. There are 454 grams in a pound of 22,700 rice grains. When we divide that into 18 times ten to the 18th, which is the mathematical way of saying 18 followed by 18 zeros and written as 18 x 10 to the 18th power, 10^18th, the expression is:
18 x 10^18 = 7.92 x 10^14 tons
2.27 x 10^4
Or, 792 x 10^12 which is 792 trillion pounds of rice which is probably more rice than has ever been grown by man. How does that fit with the history of rice culture?
Rice was originally a wild plant occurring only occasionally in shallow water swamps. Man started growing rice, planting, tending and harvesting it 10,000 years ago in China World rice production is 487 million tons of rice per year. If we assume starting at zero and regularly increasing we can approximate the total rice grown with an overall average times 10,000 years. That would be:
487 x 10^6 tons = 244 x 10^6 tons
2
Thus, in 10,000 years we would have grown:
244 x 10^6 x 1 x 10^4 = 244 x 10^10 tons of rice
or 2.44 x 10^12 tons in Scientific notation
This is a long way from the 7.92 x 10^14 tons on the chessboard! In fact we can find:
7.92 x 10^14 = 3.25 x 10^2
2.44 x 10^12
We find it would take us 325 times as long as we have cultured rice or 3,250,000 years to grow enough rice to fill the chessboard! So the clever mathematician got nothing! The moral of the story is, “Never make a ridiculous demand than cannot be filled.” Need we add this is why Mr. Trump will be one of our greatest Presidents as he knows not to exceed the bounds of reason in the manner of the Democrats
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