The Shah and the Sage
Copyright 2005 by Jeff Suzuki
For East Kingdom Coronation in 2005 there was an Arts and Sciences display where “Persian” themed entries were requested. I thought about writing up the mathematics of Umar al-Khayyami (I hear he was a poet, too...), but decided that a treatise on solving cubic equations using intersecting conic sections was a bit ambitious for a competition.
I cast about for ideas, and eventually remembered the story about the inventor of chess and the reward he asked from the king. The result was this song...
The music is “Schiarazula Marazula”, often known as the SCA Maltese Bransle. I think it's worth pointing out that this is now the third filk I've written to this music. One day I'll actually write a good filk to it...
When the game of chess was first made by a Persian sage, The Shah said "Name a boon that I can give you as a wage." The wise man said "Quit thoughts of war and let your armies rest, And work to give your people law and health and happiness." The Shah said "That I cannot do, so name another prize. Pearls or gold or tracts of land or maidens with green eyes." The wise man said "If you'd prefer, I'll take this as my due, Just give to me what follows from this task I ask of you." "Starting in the first square of the chess board's sixty-four, Place a single grain of rice then take a stately tour, On ev'ry square put twice as much as the one you've just passed, And when you've filled each square this way give me what's on the last." The first square held but one small grain, the second only two. The third held four, the fourth held eight and so the number grew. The queen's rook, so important for the game that ends "Checkmate!" The count of grains it space contained: one hundred twenty-eight. Two hundred fifty-six grains filled the first square of the pawns. Five hundred twelve the next and so the doubling grains went on. The last square of the row had grains whose number was this great: Two and thirty thousand, seven hundred sixty-eight. The queen rook's pawn moved one square on and found a crowded space. Eight million grains and more were packed into that tiny place. A pile so high reached to the sky and topped the minaret, The shah sent servants to the store for more rice bags to get. If a pawn tried to land on the third square from the queen. Eight bags of rice did fill the space––a wonder to be seen. If it went on one square beyond, behold what waited there: Four thousand bags of rice did not suffice to fill that square. The vizier told the storehouse to send up ten thousand bags. The next square took up most of them and tongues began to wag. The shah was bound to keep his word, and grant the wise man's boon. But at this rate the doubling bags would reach far past the Moon. The shah said "It will cost me less to grant your first desire." The wise man said "That's true, but know the cost of battle's higher." And so the Shah quit thoughts of war and let his armies rest, And worked to give his people law and health and happiness.
Chess was probably invented in India, but several features, including the term checkmate (shah maht, the king is dead) are Persian.
The last square would contain 263 grains: approximately 9 x 1018.
I assumed 108 grains per cubic meter. Depending on the size of your board, your chess squares are probably around 10 cm2 in area; if the eight million (actually 8,388,608) grains on QR3 were put into such a square, the pile would be about 84 meters tall.
I assumed about 8 bags per cubic meter (yes, they're very big bags) and about 16 million grains per bag. The square referred to (Q4 in modern terminology) contains 134,217,728 grains, or about 8 bags.
The square beyond would be Q5 in modern terms. If Q4 held 8 bags, then Q5 would hold 4096 bags.
If Q5 holds 4096, the “next square” (to be filled) is K5, with 8192 bags.
The last square would hold about 550 billion bags of rice. If each bag were 1/4 meter thick, the stack would form a pile 137 million kilometers high. The Moon is only about 400,000 kilometers way; the pile of rice would reach nearly to the sun.
