# Googol

Not to be confused with Google.

A googol is the large number 10100; that is, the digit 1 followed by 100 zeroes:

10,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000,­000

The term was coined in 1938[1] by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner popularised the concept in his 1940 book Mathematics and the Imagination. Other names for googol include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.

A googol has no special significance in mathematics. However, it is useful when comparing with other very large quantities such as the number of subatomic particles in the visible universe or the number of hypothetical possibilities in a chess game. Kasner used it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics. To give a sense of how big a googol really is, the mass of an electron, just under 1×10-30 kg, can be compared to the mass of the visible universe, estimated at between 1×1050kg and 1×1060 kg.[2] It is a ratio in the order of about 1080 to 1090, still much smaller than the value of a googol.

Carl Sagan points out that the total number of elementary particles in the universe is around 1080 (the Eddington number) and that if the whole universe was packed with neutrons so that there was no empty space anywhere, there would be around 10128. He also notes the similarity of the first calculation to that of Archimedes in The Sand Reckoner.[3]

A googol is approximately 70! (factorial of 70). In the binary numeral system, one would need 333 bits to represent a googol, i.e., 1 googol ≈ 2332.19280949, or exactly $2^{(100/\mathrm{log}_{10}2)}$.

The residue of googol (mod n) are

0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 4, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 16, 10, 5, 0, 1, 4, 25, 28, 10, 28, 16, 0, 1, 4, 31, 12, 10, 36, 27, 16, 11, 0, ... (sequence A066298 in OEIS)

Widespread sounding of the word occurs through its namesake, the famous internet company Google, with the name "Google" being an accidental misspelling of "googol" by the company's founders,[4] which was picked to signify that the search engine was intended to provide large quantities of information.[5] In 2004, family members of Kasner, who had inherited the right to his book, were considering suing Google for their use of the term googol.[6] However, no suit was ever filed.

The word is notable for being the subject of the £1 million question in a 2001 episode of the British quiz show Who Wants to Be a Millionaire?, when contestant Charles Ingram cheated his way through the show with the help of an accomplice.[7]

## References

1. ^ Kasner, Edward and Newman, James R. (1940). Mathematics and the Imagination. Simon and Schuster, New York. ISBN 0-486-41703-4.
2. ^ Elert, Glenn et al. "Mass of the Universe".
3. ^ Sagan, Carl (1981). Cosmos. Book Club Associates. pp. 220–221.
4. ^ Koller, David (January 2004). "Origin of the name "Google"". Stanford University. Archived from the original on July 4, 2012. Retrieved July 4, 2012.
5. ^ "Google! Beta website". Google, Inc. Archived from the original on February 2, 1999. Retrieved October 12, 2010.
6. ^
7. ^ Falk, Quentin; Falk, Ben (2005), "A Code and a Cough: Who Wants to Be a Millionaire? (1998–)", Television's Strangest Moments: Extraordinary But True Tales from the History of Television, Franz Steiner Verlag, pp. 245–246, ISBN 9781861058744.