It was from Miss Rabbage at High Ham Primary School that I first heard the story of the wheat and the chessboard.
To a boy who was familiar with wheat being harvested into hessian bags by an old Massey Harris combine harvester and who tended toward a literalist view of anything he was told, the story was confusing. Having played chess, he knew that squares on chessboards were not very big, how would anyone ever fit more than a few dozen grains on square? Wheat poured from a bag quickly spread across the stone floor of the grain store, wheat poured onto a wooden board would similarly spread much wider than the square upon which it was poured.
There are many versions of the story, which is attributed the the 13th Century Islamic scholar Ibn Khallikan. Most of the retellings have been much modernised, some even including words like “billions” and “kilograms” (the word “billion” appeared in the late-17th Century and “kilograms” were adopted as a measure at the end of the 18th Century). The nearest version I can remember from the times of Miss Rabbage goes like this:
“A wise old ruler wanted to reward his servant for an act of extraordinary bravery. The servant said:
‘Master I ask you for just one thing. Take your chessboard and place on the first square one grain of wheat. On the first day I will take this grain home to feed my family. On the second day place on the second square two grains for me to take home. On the third day cover the third square with four grains for me to take. Each day double the number of grains you give me until you have placed wheat on every square of the chessboard. Then my reward will be complete.’
The wise old ruler replied:
‘This sounds like a small price to pay for your act of incredible bravery, I will ask my servants to do as you ask immediately.’
It didn’t take long for primary school children to work out that the wise old ruler had not made a very wise decision.
Spending hours of my summer holiday on the Ancestry website, I found branches of the family tree that were very long, the earliest definite date being the birth of a forebear on 25th October 1564.
Ancestry told me that one man called Mark Burge from the Somerset village of Stogumber was my 11th great grandfather. It was when I wondered how many people there could be in the family tree, and how many great grandparents I might have, that I remembered the wheat and the chessboard.
If there were 8 of the first great grandparents, I worked out that there could be as many as 8,192 of the 11th great grandparents. As for the total in the tree, if I was on the first square (2^0), my two parents on the second, my four grandparents on the third, then there would be eight of my first great grandparents, thus, I think the calculation would be:
It seems rather a lot, more resembling a dense patch of gorse than a tree.