Sissa ibn Dahir

Sissa invents chess (Thiago Cruz, artist impression)

Sissa ibn Dahir (also: Sessa) allegedly lived in India in the third or fourth century AD and, according to legends, is considered to be the inventor of the game of chess or its original Indian form, Chaturanga .

His name is also associated with the wheat grain legend (also known as the chessboard task). The story is a "parable for the diversity of the chess game" ( Martin Beheim-Schwarzbach ), which symbolizes the inexhaustibility of possibilities and game courses in chess. The legend can be understood both as an homage to the game of chess, as an illustrative mathematical teaching example and as a socially critical work . The anecdote is often mentioned in connection with exponential functions and is the oldest example of a mathematical question relating to chess - and thus an anticipation of the field of chess mathematics .

Legend

The Indian ruler Shihram tyrannized his subjects and plunged his country into hardship and misery. In order to draw the king's attention to his mistakes without igniting his anger, Dahir's son, the wise brahmin Sissa, created a game in which the king, as the most important figure, cannot achieve anything without the help of other figures and pawns. The chess lessons made a strong impression on Shihram. He became milder and had the game of chess spread so that everyone could take note of it. In order to thank him for the clear teaching of wisdom and entertainment at the same time, he granted the brahmin a free wish. He wanted grains of wheat : he wanted one grain on the first square of a chessboard , double that on the second square, i.e. two, on the third again double the amount, i.e. four, and so on. The king laughed and was angry at the Brahmin's supposed modesty.

When Shihram asked a few days later whether Sissa had received his reward, he heard that the arithmetic masters had not yet calculated the amount of wheat grains. After several days of uninterrupted work, the head of the granary reported that he could not raise this amount of cereal grains anywhere in the empire. On all the squares on a chessboard it would be 2 ⁶⁴ -1 or 18,446,744,073,709,551,615 (≈ 18.45 trillion ) grains of wheat. Now he asked himself how the promise could be kept. The arithmetic master helped the ruler out of his embarrassment by recommending that he simply let Sissa ibn Dahir count the grain grain by grain.

There are alternative ways of telling the story, according to which it was grains of rice instead of grains of wheat.

Mathematical calculation

Using the geometrical molecular formula

${\displaystyle \sum _{i=0}^{n}2^{i}=2^{n+1}-1}$

the number of grains of wheat is calculated as follows:

${\displaystyle 1+2+4+8+\dotsb =2^{0}+2^{1}+2^{2}+2^{3}+\dotsb +2^{63}=\sum _{i=0}^{63}2^{i}=2^{63+1}-1=18.446.744.073.709.551.615}$

In words: 18 trillion, 446 trillion, 744 trillion, 73 billion, 709 million, 551 thousand, 615.

On a chessboard, the grains of wheat would be distributed as follows:

	A.	B.	C.	D.	E.	F.	G	H
8th	1	2	4th	8th	16	32	64	128
7th	256	512	1,024	2,048	4,096	8,192	16,384	32,768
6th	65,536	131,072	262.144	524.288	1,048,576	2,097,152	4,194,304	8,388,608
5	16,777,216	33,554,432	67.108.864	134.217.728	268.435.456	536.870.912	1,073,741,824	2,147,483,648
4th	4,294,967,296	8,589,934,592	17.179.869.184	34,359,738,368	68.719.476.736	137,438,953,472	274.877.906.944	549,755,813,888
3	1,099,511,627,776	2.199.023.255.552	4,398,046,511,104	8,796,093,022,208	17,592,186,044,416	35.184.372.088.832	70,368,744,177,664	140.737.488.355.328
2	281,474,976,710,656	562,949,953,421,312	1,125,899,906,842,624	2,251,799,813,685,248	4,503,599,627,370,496	9.007.199.254.740.992	18,014,398,509,481,984	36,028,797,018,963,968
1	72,057,594,037,927,936	144.115.188.075.855.872	288.230.376.151.711.744	576,460,752,303,423,488	1,152,921,504,606,846,976	2,305,843,009,213,693,952	4,611,686,018,427,387,904	9,223,372,036,854,775,808

The total amount of wheat on the chessboard would have a mass of approx. 730 billion t with a thousand grain mass of approx. 40 g. This corresponds to 1000 times the global wheat harvest in 2014/2015.

Origin of the anecdote

There is no evidence for this story in Indian sources. It is part of the Arab culture. Both the biographer Ibn Challikān (1211-1282) and the writer and poet as-Sabhādī , who lived in Baghdad in the Middle Ages , are given as origin. As-Sabhādī is said to have already given the correct solution.

See also

• History of the game of chess
• Exponential growth
• Josephspfennig

Web links

• Video about the rice grain parabola: Exponential function explained in simple terms

Individual evidence

1. ↑ Martin Beheim-Schwarzbach: The book of chess . Insel Verlag, Leipzig o. D. (1934), p. 6.
2. ^ J. Giżycki: Chess at all times. Zurich 1967, p. 113, as well as Lindörfer: The large chess dictionary. P. 311.
3. ↑ http://sv-morsbach.de/schach/geschichte.html
4. ^ Gerhard Eisenbrand, Peter Schreier, Alfred Hagen Meyer: RÖMPP Lexikon Lebensmittelchemie. 2nd edition, 2006, p. 40.
5. ↑ Statista , global wheat harvest from 2000/2001 to 2019/2020 *
6. ↑ Klaus Lindörfer: The great chess dictionary. Munich 1991, p. 311.
7. ↑ Georges Ifrah: Universal History of Numbers. Campus Verlag, Frankfurt am Main / New York 1986, ISBN 3-593-34192-1 , pp. 482-485.