Dante’s millions

“As I write, the London world championship is tied at 3½-3½, after seven games. In striving to move ahead, the challenger, Fabiano Caruana, has been the victim of the awesome mathematics of chess. According to the statisticians there are more possible moves in chess games than there are atoms in the observable universe. Ten to the power of 70 is the official estimate. As someone with a good Italian name and ancestry, Fabiano may be familiar with Dante’s Paradiso. In Canto 28 the poet writes: ‘Ed eran tante, che ‘l numero loro, Piu che ‘l doppiar de li scacchi s’inmilla.’ In other words, the number of angels or intelligences in the heavens far exceeds the immense number created by placing a piece of corn on the first square of the chessboard and doubling each time until square 64 is reached. The number of grains on this square alone will be 18,446,744,073,709,551,616 and the total number of grains on the chessboard will be 36,893,488,147,419,103,231.” […]    –Raymond Keene, The Spectator, November 24, 2018