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Revision as of 05:56, 28 September 2023 view sourceJPxG (talk | contribs)Edit filter managers, Autopatrolled, Administrators118,965 edits →Size: literally 10e-30 to 10e60. how could this possibly be original research?!Tags: Mobile edit Mobile web edit Advanced mobile edit← Previous edit Revision as of 19:03, 30 October 2023 view source 27 is the best number (talk | contribs)Extended confirmed users1,419 edits Added infoboxTag: 2017 wikitext editorNext edit →
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{{short description|Large number defined as ten to the 100th power or ten to the 100th power}} {{short description|Large number defined as ten to the 100th power or ten to the 100th power}}
{{distinguish|text=] or ]}} {{distinguish|text=] or ]}}
{{infobox number

| number=10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
| cardinal = googol
| ordinal text = googolth
| multiplying text =
| numeral =
| factorization = <math>2^{100}\times 5^{100}</math>
| divisor =<math>2^{100}\times 5^{100}</math>
| roman =
}}
A '''googol''' is the ] '''10<sup>100</sup>'''. In decimal notation, it is written as the ] 1 followed by one hundred ]s: <!-- Do not use ], it breaks mobile -->'''10,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000'''. Its ] is '''10 duotrigintillion'''. (The short scale names are standard in the English-speaking world.) A '''googol''' is the ] '''10<sup>100</sup>'''. In decimal notation, it is written as the ] 1 followed by one hundred ]s: <!-- Do not use ], it breaks mobile -->'''10,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000,{{wbr}}000'''. Its ] is '''10 duotrigintillion'''. (The short scale names are standard in the English-speaking world.)


Revision as of 19:03, 30 October 2023

Large number defined as ten to the 100th power or ten to the 100th power Not to be confused with Google or Nikolai Gogol. Natural number

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A googol is the large number 10. In decimal notation, it is written as the digit 1 followed by one hundred 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. Its systematic name is 10 duotrigintillion. (The short scale names are standard in the English-speaking world.)

Etymology

The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner. He may have been inspired by the contemporary comic strip character Barney Google. Kasner popularized the concept in his 1940 book Mathematics and the Imagination. Other names for this quantity include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.

Size

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 put in perspective the size of a googol, the mass of an electron, just under The time allocated for running scripts has expired., can be compared to the mass of the visible universe, estimated at between The time allocated for running scripts has expired. and The time allocated for running scripts has expired.. It is a ratio in the order of about 10 to 10, or at most one ten-billionth of a googol (0.00000001% of a googol).

Another way of illustrating the immense size of a googol is to picture the Frontier supercomputer, which as of 2022 is the most powerful supercomputer in the world and measures 680 m (7,300 sq ft), almost exactly the same size of a basketball court with run-offs and sidelines. The Frontier is capable of making 1,102,000 TFLOPs (1.1 quintillion calculations per second). If the supercomputer was shrunk down to the size of an atom (for reference, a typical grain of sand might have 37 quintillion atoms), and if every atom in the observable universe (~The time allocated for running scripts has expired. atoms total) was as powerful as a Frontier supercomputer, it would take approximately 100 seconds of parallel computing to manually add up all the digits The time allocated for running scripts has expired. like an adding machine (instead of using shorthand calculations).The time allocated for running scripts has expired.

Carl Sagan pointed out that the total number of elementary particles in the universe is around 10 (the Eddington number) and that if the whole universe were packed with neutrons so that there would be no empty space anywhere, there would be around 10. He also noted the similarity of the second calculation to that of Archimedes in The Sand Reckoner. By Archimedes's calculation, the universe of Aristarchus (roughly 2 light years in diameter), if fully packed with sand, would contain 10 grains. If the much larger observable universe of today were filled with sand, it would still only equal 10 grains. Another 100,000 observable universes filled with sand would be necessary to make a googol.

The decay time for a supermassive black hole of roughly 1 galaxy-mass (10 solar masses) due to Hawking radiation is on the order of 10 years. Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future.

A googol is considerably smaller than a centillion.

Properties

A googol is approximately 70! (factorial of 70). Using an integral, binary numeral system, one would need 333 bits to represent a googol, i.e., 1 googol = 2 ( 100 / l o g 10 2 ) {\displaystyle 2^{(100/\mathrm {log} _{10}2)}} ≈ 2. However, a googol is well within the maximum bounds of an IEEE 754 double-precision floating point type, but without full precision in the mantissa.

Using modular arithmetic, the series of residues (mod n) of one googol, starting with mod 1, is as follows:

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 the OEIS)

This sequence is the same as that of the residues (mod n) of a googolplex up until the 17th position.

Cultural impact

Widespread sounding of the word occurs through the name of the company Google, with the name "Google" being an accidental misspelling of "googol" by the company's founders, which was picked to signify that the search engine was intended to provide large quantities of information. 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"; however, no suit was ever filed.

Since October 2009, Google has been assigning domain names to its servers under the domain "1e100.net", the scientific notation for 1 googol, in order to provide a single domain to identify servers across the Google network.

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 a confederate in the studio audience.

See also

Notes

  1. ≈1.1979×10

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References

  1. The time allocated for running scripts has expired. (retrieved March 17, 2015)
  2. The time allocated for running scripts has expired. Extract of page 120
  3. The time allocated for running scripts has expired. The relevant passage about the googol and googolplex, attributing both of these names to Kasner's nine-year-old nephew, is available in The time allocated for running scripts has expired.
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  10. The time allocated for running scripts has expired. See in particular equation (27).
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External links

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  • The time allocated for running scripts has expired.
  • Googol at PlanetMath.
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