Mathematics and the Imagination

Mathematics and the Imagination is a book written by and .Kasner and Newman. "Mathematics and the Imagination" Originally published by Simon and Shuster, 1940. Dover Edition published in 2001. ISBN 978-1556151040 It was originally published by Simon and Shuster in 1940 and Dover edition was published in 2001.
In the first chapter "New names for old", googol is defined as "1 followed by a hundred zeros" (p.20). In p.23, it is explained that googol was invented by a child (Dr. Kasner's nine-year-old nephew), and the child gave a name for a still larger number googolplex. "It was first suggested that a googolplex should be 1, followed by writing zeros until you got tired." However as the definition is not well-defined, Kasner modified the definition to "The googolplex then, is a specific finite number, with so many zeros after the 1 that the number of zeros is a googol."
In the second chapter "Beyond the google", Eddington's number is explained as \(136 \cdot 2^{256}\) (p.32), which is an estimate of the exact numbers of protons / electrons in the universe by Sir Arthur Eddington at that time. Skewes number is explained as \(10^{10^{10^{34}}}\) (p.32) and the total possible number of moves in a game of chess is shown as \(10^{10^{50}}\) (p.32). He then writes that pointed out that "if we imagine the entire universe as a chessboard, and the protons in it as chessmen, and if we agree to call any interchange in the position of two protons a "move" in this cosmic game, then the total number of possible moves, of all odd coincidences, would be Skewes' number: \(10^{10^{10^{34}}}\)" (pp.32-33). In pp.33-34, he cites "The Sand Reckoner" by Archimedes.
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Category:Literature