Googolplex

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A googolplex is the number 10googol, i.e. 1010100, which can also be written as the number 1 followed by a googol zeros (i.e. 10100 zeros).

In pure mathematics, the magnitude of a googolplex could be related to other forms of large number notation such as tetration, Knuth's up-arrow notation, Steinhaus-Moser notation, or Conway chained arrow notation.

Contents

History

In 1938, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term googol, then proposed the further term googolplex to be "one, followed by writing zeroes until you get tired". Kasner decided to adopt a more formal definition "because different people get tired at different times and it would never do to have Carnera be a better mathematician than Dr. Einstein, simply because he had more endurance and could write for longer".[1] It thus became standardized to 10googol.

Size

In the PBS science program Cosmos: A Personal Voyage, Episode 9: "The Lives of the Stars", astronomer and television personality Carl Sagan estimated that writing a googolplex in numerals (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than the known universe provides.

An average book of 60 cubic inches can be printed with 5×105 zeroes (5 characters per word, 10 words per line, 25 lines per page, 400 pages), or 8.3×103 '0's per cubic inch. The observable (i.e. past light cone) universe contains 6×1083 cubic inches (1.3 × π × (14×109 light year in inches)3).

This math implies that if the universe is stuffed with paper printed with '0's, it could contain only 5.3×1087 '0's—far short of a googol of '0's. In fact there are only about 2.5×1089 elementary particles in the observable universe so even if one were to use an elementary particle to represent each digit, one still would require the universe's volume about a trillion times larger. Therefore a googolplex cannot be written out since a googol of '0's cannot fit into the observable universe.

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