Googol

A googol is the large number 10100. 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.

Concept

The term was coined in 1920 by 9-year-old Milton Sirotta (1911–1981), nephew of U.S. mathematician Edward Kasner.[1] Kasner popularized the concept in his 1940 book Mathematics and the Imagination.[2] 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.

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 give a sense of how big a googol really is, the mass of an electron, just under 10−30 kg, can be compared to the mass of the visible universe, estimated at between 1050 and 1060 kg.[3] It is a ratio in the order of about 1080 to 1090, or only about one ten-billionth of a googol (0.00000001% of a googol).

Carl Sagan pointed out that the total number of elementary particles in the universe is around 1080 (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 10128. 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 1063 grains. If the much larger observable universe of today were filled with sand, it would still only equal 1095 grains. Another 100,000 observable universes filled with sand would be necessary to make a googol.[4]

The decay time for a supermassive black hole of roughly 1 galaxy-mass (1011 solar masses) due to Hawking radiation is on the order of 10100 years.[5] Therefore, the heat death of an expanding universe is lower-bounded to occur at least one googol years in the future.

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 ≈ 2332.19280949, or exactly . 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 is found:

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)

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,[6] which was picked to signify that the search engine was intended to provide large quantities of information.[7] 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;[8] 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.[9][10]

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.[11]

See also

References

  1. ^ Bialik, Carl (June 14, 2004). "There Could Be No Google Without Edward Kasner". The Wall Street Journal Online. Archived from the original on November 30, 2016. (retrieved March 17, 2015)
  2. ^ Kasner, Edward; Newman, James R. (1940). Mathematics and the Imagination. Simon and Schuster, New York. ISBN 0-486-41703-4. Archived from the original on 2014-07-03. The relevant passage about the googol and googolplex, attributing both of these names to Kasner's nine-year-old nephew, is available in James R. Newman, ed. (2000) [1956]. The world of mathematics, volume 3. Mineola, New York: Dover Publications. pp. 2007–2010. ISBN 978-0-486-41151-4.
  3. ^ Elert, Glenn; et al. "Mass of the Universe". Archived from the original on 2017-07-23.
  4. ^ Sagan, Carl (1981). Cosmos. Book Club Associates. pp. 220–221.
  5. ^ Particle emission rates from a black hole: Massless particles from an uncharged, nonrotating hole, Don N. Page, Physical Review D 13 (1976), pp. 198–206. doi:10.1103/PhysRevD.13.198. See in particular equation (27).
  6. ^ Koller, David (January 2004). "Origin of the name "Google"". Stanford University. Archived from the original on July 4, 2012. Retrieved July 4, 2012.
  7. ^ "Google! Beta website". Google, Inc. Archived from the original on February 21, 1999. Retrieved October 12, 2010.
  8. ^ "Have your Google people talk to my `googol' people". Archived from the original on 2014-09-04.
  9. ^ Cade Metz (8 February 2010). "Google doppelgänger casts riddle over interwebs". The Register. Archived from the original on 3 March 2016. Retrieved 30 December 2015.
  10. ^ "What is 1e100.net?". Google. Archived from the original on 9 January 2016. Retrieved 30 December 2015.
  11. ^ 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.

External links

Ban number

In recreational mathematics, a ban number is a number that does not contain a particular letter when spelled out in English; in other words, the letter is "banned." Ban numbers are not precisely defined, since some large numbers do not follow the standards of number names (such as googol and googolplex).

There are several published sequences of ban numbers:

The aban numbers do not contain the letter A. The first few aban numbers are 1 through 999, 1,000,000 through 1,000,999, 2,000,000 through 2,000,999, ... The word "and" is not counted.

The eban numbers do not contain the letter E. The first few eban numbers are 2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66, 2000, 2002, 2004, ... (sequence A006933 in the OEIS). The sequence was coined in 1990 by Neil Sloane. Coincidentally, all the numbers in the sequence are even.

The iban numbers do not contain the letter I. The first few iban numbers are 1, 2, 3, 4, 7, 10, 11, 12, 14, 17, 20, 21, 22, 23, 24, 27, 40, ... (sequence A089589 in the OEIS). Since all -illion numbers contain the letter I, there are exactly 30,275 iban numbers, the largest being 777,777.

The oban numbers do not contain the letter O. The first few oban numbers are 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 23, 25, 26, ... (sequence A008521 in the OEIS). Since "thousand" and all the -illion numbers contain the letter O, there are exactly 454 oban numbers, the largest being 999.

The tban numbers do not contain the letter T. The first few tban numbers are 1, 4, 5, 6, 7, 9, 11, 100, 101, 104, 105, 106, 107, 109, 111, 400, 401, 404, 405, 406, ... (sequence A008523 in the OEIS).

The uban numbers do not contain the letter U. The first few uban numbers are 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, ... (sequence A089590 in the OEIS).

Double exponential function

A double exponential function is a constant raised to the power of an exponential function. The general formula is , which grows much more quickly than an exponential function. For example, if a = b = 10:

Factorials grow more quickly than exponential functions, but much more slowly than doubly exponential functions. However, tetration and the Ackermann function grow faster. See Big O notation for a comparison of the rate of growth of various functions.

The inverse of the double exponential function is the double logarithm ln(ln(x)).

Edward Kasner

Edward Kasner (April 2, 1878 – January 7, 1955) was a prominent American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jew appointed to a faculty position in the sciences at Columbia University. Subsequently, he became an adjunct professor in 1906, and a full professor in 1910, at the university. Differential geometry was his main field of study. In addition to introducing the term "googol", he is known also for the Kasner metric and the Kasner polygon.Kasner's PhD dissertation was titled The Invariant Theory of the Inversion Group: Geometry upon a Quadric Surface; it was published by the American Mathematical Society in 1900 in their Transactions.

English numerals

English number words include numerals and various words derived from them, as well as a large number of words borrowed from other languages.

Google Search

Google Search, also referred to as Google Web Search or simply Google, is a web search engine developed by Google LLC. It is the most used search engine on the World Wide Web across all platforms, with 92.74% market share as of October 2018, handling more than 3.5 billion searches each day.The order of search results returned by Google is based, in part, on a priority rank system called "PageRank". Google Search also provides many different options for customized search, using symbols to include, exclude, specify or require certain search behavior, and offers specialized interactive experiences, such as flight status and package tracking, weather forecasts, currency, unit and time conversions, word definitions, and more.

The main purpose of Google Search is to hunt for text in publicly accessible documents offered by web servers, as opposed to other data, such as images or data contained in databases. It was originally developed by Larry Page and Sergey Brin in 1997. In June 2011, Google introduced "Google Voice Search" to search for spoken, rather than typed, words. In May 2012, Google introduced a Knowledge Graph semantic search feature in the U.S.

Analysis of the frequency of search terms may indicate economic, social and health trends. Data about the frequency of use of search terms on Google can be openly inquired via Google Trends and have been shown to correlate with flu outbreaks and unemployment levels, and provide the information faster than traditional reporting methods and surveys. As of mid-2016, Google's search engine has begun to rely on deep neural networks.Competitors of Google include Baidu and Soso.com in China; Naver.com and Daum.net in South Korea; Yandex in Russia; Seznam.cz in the Czech Republic; Yahoo in Japan, Taiwan and the US, as well as Bing and DuckDuckGo. Some smaller search engines offer facilities not available with Google, e.g. not storing any private or tracking information.

Within the US, as of July 2018, Microsoft Sites handled 24.2 percent of all search queries in the United States. During the same period of time, Oath (formerly known as Yahoo) had a search market share of 11.5 percent. Market leader Google generated 63.2 percent of all core search queries in the United States.

Googolplex

A googolplex is the number 10googol, or equivalently, 10(10100). Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes, that is, a 1 followed by a googol zeroes.

Guggol

Googol (Persian: گوگل‎, also Romanized as Gūggol; also known as Gūk Gol and Qokgol) is a village in Chehel Chay Rural District, in the Central District of Minudasht County, Golestan Province, Iran. At the 2006 census, its population was 1,787, in 436 families.

History of Google

The Google company was officially launched in 1998 by Larry Page and Sergey Brin to market Google Search, which has become the most used web-based search engine. Page and Brin, students at Stanford University in California, developed a search algorithm at first known as "BackRub" in 1996. The search engine soon proved successful and the expanding company moved several times, finally settling at Mountain View in 2003. This marked a phase of rapid growth, with the company making its initial public offering in 2004 and quickly becoming one of the world's largest media companies. The company launched Google News in 2002, Gmail in 2004, Google Maps in 2005, Google Chrome in 2008, and the social network known as Google+ in 2011, in addition to many other products. In 2015, Google became the main subsidiary of the holding company Alphabet Inc.

The search engine went through numerous updates in attempts to combat search engine optimization abuse, provide dynamic updating of results, and make the indexing system rapid and flexible. Search results started to be personalized in 2005, and later Google Suggest autocompletion was introduced. From 2007, Universal Search provided all types of content, not just text content, in search results.

Google has engaged in partnerships with NASA, AOL, Sun Microsystems, News Corporation, Sky UK, and others. The company set up a charitable offshoot, Google.org, in 2005. Google was involved in a 2006 legal dispute in the US over a court order to disclose URLs and search strings, and has been the subject of tax avoidance investigations in the UK.

The name Google is a variant of googol, chosen to suggest very large numbers.

James R. Newman

James Roy Newman (1907–1966) was an American mathematician and mathematical historian. He was also a lawyer, practicing in the state of New York from 1929 to 1941. During and after World War II, he held several positions in the United States government, including Chief Intelligence Officer at the US Embassy in London, Special Assistant to the Undersecretary of War, and Counsel to the US Senate Committee on Atomic Energy. In the latter capacity, he helped to draft the Atomic Energy Act of 1946. He became a member of the board of editors for Scientific American beginning in 1948. He is also credited for coining and first describing the mathematical concept "googol" in his book (co-authored by Edward Kasner) Mathematics and The Imagination.

Large numbers

Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions. The term typically refers to large positive integers, or more generally, large positive real numbers, but it may also be used in other contexts.

Very large numbers often occur in fields such as mathematics, cosmology, cryptography, and statistical mechanics. Sometimes people refer to numbers as being "astronomically large". However, it is easy to mathematically define numbers that are much larger even than those used in astronomy.

List of PlayStation games (M–Z)

This is a continued list of games for the Sony PlayStation video game system.

Mathematics and the Imagination

Mathematics and the Imagination is a book published in New York by Simon & Schuster in 1940. The authors are Edward Kasner and James R. Newman. The illustrator Rufus Isaacs provided 169 figures. It rapidly became a best-seller and received several glowing reviews. Special publicity has been awarded it since it introduced the term googol for 10100, and googolplex for 10googol. The book includes nine chapters, an annotated bibliography of 45 titles, and an index in its 380 pages.

Names of large numbers

This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.

The following table lists those names of large numbers that are found in many English dictionaries and thus have a claim to being "real words." The "Traditional British" values shown are unused in American English and are obsolete in British English, but their other-language variants are dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America; see Long and short scales.

Indian English does not use millions, but has its own system of large numbers including lakhs and crores.

English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see indefinite and fictitious numbers.

Orders of magnitude (numbers)

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities. Each number is given a name in the short scale, which is used in English-speaking countries, as well as a name in the long scale, which is used in some of the countries that do not have English as their national language.

Power of 10

In mathematics, a power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:

1, 10, 100, 1,000, 10,000, 100,000, 1,000,000, 10,000,000. ... (sequence A011557 in the OEIS)

Rayo's number

Rayo's number is a large number named after Agustín Rayo which has been claimed to be the largest named number. It was originally defined in a "big number duel" at MIT on 26 January 2007.

Secretary problem

The secretary problem is a problem that demonstrates a scenario involving optimal stopping theory. The problem has been studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.

The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.

The problem has an elegant solution, and the shortest rigorous proof known so far is provided by the odds algorithm (Bruss 2000). An easy analysis implies that the optimal win probability is always at least (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality (2003). The optimal stopping rule prescribes always rejecting the first applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the stopping rule, because the probability of stopping at the best applicant with this strategy is about already for moderate values of . One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.

Sirota

Sirota, Sierota, Sirotta or Syrota (Russian or Ukrainian: сирота, meaning orphan) is a gender-neutral Slavic surname that may refer to:

Alexander Sirota (born 1976), Ukrainian photographer

Anton Sirota (born 1976), Slovak scientist

Beate Sirota (1923–2012), American performing arts director

Benny Sirota (?–?), one of the founders of the Troika Pottery in St Ives, Cornwall, UK in 1962.

David Sirota (born 1975), American writer

Gershon Sirota (1874–1943), Ukrainian musician

Leo Sirota (1855–1965), Ukrainian pianist

Louanne Sirota (born 1970), American actress

Lyubov Sirota (born 1956), Ukrainian writer

Milton Sirotta (1911–1981), American who coined the word "googol"

Nick Sirota (born 1984), American ice hockey player

Ruslan Sirota (born 1980), Ukrainian musician

Svyatoslav Syrota (born 1970), Ukrainian football player and administrator

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