*How* much rice?

When I was young, I heard the story of the rice and the chessboard.

King Shihram of India was an oppressive tyrant. One of his subjects, Sissa ibn Dahir, invented the game of chess as a strategic (and social) training tool, and the king was so pleased that he asked Sissa what reward he wanted. Sissa’s answer was that the king should put one grain of rice (or wheat, in some versions) on the first square of a chessboard, two grains on the second square, four grains on the third square, eight grains on the fourth square, and so on, doubling the number of grains of rice with each square.

The King thought he had gotten off easy, but the simple math of exponential increase demonstrated that Sissa was no fool: the total weight of rice would exceed the weight of all living things on earth and make a heap larger than Mount Everest.

I always wondered just how much rice that was, but back then we didn’t have Wikipedia, and I don’t think such an “inconsequential” article would have made it into the Brittanica. Now, however, all is different.

An illustration of the operating principle is below:

The abbreviations refer to Mega (million), Giga (billion), Tera (trillion), Peta (quadrillion), and Exa (quintillion).

This principle was used by Ray Kurzweil who coined the term “The Second Half of the Chessboard,” referring to the point at which an exponentially growing factor begins to have a significant economic impact on an organization’s overall business strategy. The example above shows that the first square of the second half contains more rice than the entire first half combined.

Mathematically, the total number of grains of rice can be expressed as

(or so I’m told), which resolves to 264 – 1 (or so I’m told.) Dammit Jim, I’m a linguist, not a mathematician.

On the entire chessboard there would be 264 − 1 = 18,446,744,073,709,551,615 grains of rice (that’s 18.4 quintillion), weighing 461,168,602,000 metric tons, which would be a mountain of rice larger than Mount Everest. This is around 1,000 times the global production of rice in 2010 (464,000,000 metric tons).

Looking at the amazing Humphrys map comparing the heights of various mountains, look at how tiny St. Peter’s cathedral is in comparison (click the map for full size).

Even had King Shihram been able to pay, Sissa would have had difficulty finding a place to put his reward. And that’s a whole lot of sushi.

The Old Wolf has spoken.

3 responses to “*How* much rice?

  1. Pingback: So just how much sushi is that? | Playing in the World Game

  2. «The example above shows that the first square of the second half contains more rice than the entire first half combined.»

    In fact, every single square on the chess board contains the sum total of all the previous squares combined, plus one. This includes the first square, which has no squares before it, but still contains one grain of rice.

  3. Pingback: Squandering Resources Manifesto – Squandering Resources

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