PODCAST:More or Less: Behind the Stats
TITLE:Are there more possible games of chess than atoms in the universe?
DATE:2024-01-20 00:00:00
URL:
MODEL:gpt-4-gizmo
This episode of "More or Less Behind the Stats," titled "Are There More Possible Games of Chess Than Atoms in the Universe," aired on January 20, 2024. Hosted by Tim Harford, it delves into the intriguing question of whether the number of possible chess games exceeds the number of atoms in the observable universe. Here are the key points:
Shannon Number: The episode introduces the Shannon number, named after computer scientist Claude Shannon, which is an estimate of the number of possible chess games. The figure is 10 to the power of 120, a number so vast it's hard to comprehend.
Chess Game Calculations: Shannon estimated this figure by considering an average chess game to last about 80 moves (40 moves for each player). He assumed each move had about 30 possible choices. By multiplying 30 choices for each move across 80 moves, he arrived at the enormous Shannon number.
Atoms in the Observable Universe: To compare this with the number of atoms in the observable universe, the episode turns to astronomer Professor Catherine Hayman's, who provides an estimate of between five to seven times 10 to the power of 79 atoms. This calculation is based on the volume of the observable universe and the average density of hydrogen and helium atoms.
Comparison of the Two Numbers: When comparing these two figures, it's clear that the number of possible chess games (10 to the power of 120) far exceeds the number of atoms in the observable universe (up to 7 x 1079). This conclusion demonstrates the incredible complexity and variability of chess as a game.
Infinite Possibilities in Chess: The episode highlights that the total number of all possible chess games is likely much higher than the Shannon number, considering that many games can extend beyond 80 moves, and there's a vast array of legal but strategically nonsensical moves.
Power of Exponentials: The discussion emphasizes the power of exponential growth in numbers, showcasing how quickly possibilities can multiply to reach staggering heights.
This episode of "More or Less Behind the Stats" presents a fascinating exploration of two seemingly incomparable realms – the vast universe and the intricate game of chess – and illustrates the surprising result that chess, in its complexity, offers more possibilities than there are atoms in the observable universe.
