Googolplex: Difference between revisions
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imported>Cyrobyte Undid revision 1293031755 by Ratsniffer (talk): This image is unnecessary. It doesn't even represent the number googolplex at all. |
imported>GuccizBud m →top: Copy edit ▸ Presentation (dashes), and reference to below section added. |
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{{short description|Number ten to the power of a googol}}{{ | {{short description|Number ten to the power of a googol}}{{About|the large number|Alphabet Inc's headquarters|Googleplex}} | ||
{{Use dmy dates|date=September 2020}} | {{Use dmy dates|date=September 2020}} | ||
{{pp|small=yes}} | {{pp|small=yes}} | ||
<!--IMPORTANT: Please do not try to write out a googolplex in standard form in the article.--> | <!--IMPORTANT: Please do not try to write out a googolplex in standard form in the article.--> | ||
A '''googolplex''' is the [[large number]] | A '''googolplex''' is the [[large number]] {{math|10{{sup|10{{sup|100}}}}}}, that is, {{math|10}} [[Power of 10|raised to the power]] of a [[googol]]. If written out in ordinary [[decimal notation]], it would be {{math|1}} followed by a googol (10<sup>100</sup>) {{nowrap|zeroes{{px2}}{{mdash}}{{px2}}}}a physically impossible number to write explicitly {{xref|(see: {{slink||Size}}, below)}}. | ||
==History== | ==History== | ||
In 1920, [[Edward Kasner]]'s nine-year-old nephew, Milton Sirotta, coined the term ''[[googol]]'', which is 10{{sup|100}}, and then proposed the further term ''googolplex'' to be "one, followed by writing zeroes until you get tired".<ref>{{cite journal | title = There Could Be No Google Without Edward Kasner | first = Carl | last = Bialik | journal = The Wall Street Journal Online | date = 14 June 2004 | url = https://www.wsj.com/articles/SB108575924921724042 | In 1920, [[Edward Kasner]]'s nine-year-old nephew, Milton Sirotta, coined the term ''[[googol]]'', which is 10{{sup|100}}, and then proposed the further term ''googolplex'' to be "one, followed by writing zeroes until you get tired".<ref>{{cite journal | title = There Could Be No Google Without Edward Kasner | first = Carl | last = Bialik | journal = The Wall Street Journal Online | date = 14 June 2004 | url = https://www.wsj.com/articles/SB108575924921724042 }} (retrieved 17 March 2015)</ref> Kasner decided to adopt a more formal definition because "different people get tired at different times and it would never do to have [[Primo Carnera|Carnera]] [be] a better mathematician than [[Albert Einstein|Dr. Einstein]], simply because he had more endurance and could write for longer".<ref>Edward Kasner & James R. Newman (1940) [[Mathematics and the Imagination]], page 23, NY: [[Simon & Schuster]]</ref> It thus became standardized to 10<sup>(10<sup>100</sup>)</sup>, which is usually written as 10<sup>10<sup>100</sup></sup> using the conventional interpretation for [[Order of operations#Serial exponentiation|serial exponentiation]].<ref>{{cite book |author1=Anthony J. Dos Reis |url=https://books.google.com/books?id=FFcTpMi3aKQC |title=Compiler Construction Using Java, JavaCC, and Yacc |publisher=John Wiley & Sons |year=2012 |isbn=978-1-118-11277-9 |edition= |page=91}} </ref> | ||
==Size== | ==Size== | ||
A typical book can be printed with | A typical book can be printed with one million zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires {{10^|94}} such books to print all the zeros of a googolplex (that is, printing a googol zeros).<ref>Stanford student Wolfgang Nitsche put together a website which will, provided a 94-digit volume number, generate a PDF file consisting of {{10^|6}} zero digits (with an initial one digit in volume 1), and registered an ISBN for the set: {{pb}} {{cite book| last=Nitsche |first=Wolfgang |date=August 2013 |title=Googolplex Written Out |place=Stanford, CA |isbn=978-0-9900072-0-3 |url=http://www.googolplexwrittenout.com/ |publisher=Wolfgang Nitsche }}</ref> | ||
If each book had a mass of 100 grams, all of them would have a total mass of | If each book had a mass of 100 grams, all of them would have a total mass of {{10^|93}} kilograms. In comparison, [[Earth]]'s mass is {{Val|5.97e24}} kilograms,<ref>{{Citation| last=Williams| first=David| year=2024| title=Earth Fact Sheet |website=NASA Space Science Data Coordinated Archive | publisher= National Aeronautics and Space Administration |url=https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html |access-date=2024-11-15 |archive-url=https://web.archive.org/web/20250821225050/https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html |archive-date= 2025-08-21 }}</ref> the mass of the [[Milky Way]] galaxy is estimated at {{Val|1.8e42}} kilograms,<ref>{{Citation |last=Letzter |first=Rafi |year=2019 |title=Our Large Adult Galaxy Is As Massive As 890 Billion Suns |website=Space.com |url=https://www.space.com/our-galaxy-is-so-big-good-lord.html}}</ref> and the total mass of all the stars in the [[observable universe]] is estimated at {{Val|2e52|u=kg}}.<ref>{{cite book |title=Particle and Astroparticle Physics: Problems and Solutions |author1=Alessandro Domenico De Angelis |author2=Mário João Martins Pimenta |author3=Ruben Conceição |edition= |publisher=Springer |year=2021 |isbn=978-3-030-73116-8 |page=10 |url=https://books.google.com/books?id=WXwwEAAAQBAJ}}</ref> | ||
To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the mass of the observable universe by a factor of roughly | To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the mass of the observable universe by a factor of roughly {{val|5e40}}. | ||
===In the physical universe=== | ===In the physical universe=== | ||
In the [[Public Broadcasting Service|PBS]] science program ''[[Cosmos: A Personal Voyage]]'', [[Cosmos: A Personal Voyage#Episode 9: "The Lives of the Stars"|Episode 9: "The Lives of the Stars"]], [[astronomer]] and television personality [[Carl Sagan]] estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of the [[observable universe]] is filled with fine [[Cosmic dust|dust particles]] roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different [[combinations]] in which the particles could be arranged and numbered would be about one googolplex.<ref> | In the [[Public Broadcasting Service|PBS]] science program ''[[Cosmos: A Personal Voyage]]'', [[Cosmos: A Personal Voyage#Episode 9: "The Lives of the Stars"|Episode 9: "The Lives of the Stars"]], [[astronomer]] and television personality [[Carl Sagan]] estimated that writing a googolplex in full decimal form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of the [[observable universe]] is filled with fine [[Cosmic dust|dust particles]] roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different [[combinations]] in which the particles could be arranged and numbered would be about one googolplex.<ref>{{citation |last=Goodrich |first=Ryan |date=2013 |url=https://www.livescience.com/31981-googol.html |title=Googol, Googolplex - & Google |website=LiveScience.com }}</ref><ref>{{citation |url=https://www.space.com/41721-big-numbers-universe-photos/2.html |title=Photos: Large Numbers That Define the Universe |website=Space.com |last=Saplakoglu |first=Yasemin |date=2018 |access-date=2025-09-12}}</ref> | ||
{{10^|97}} is a high estimate of the elementary particles existing in the visible universe (not including [[dark matter]]), mostly photons and other massless force carriers.<ref>{{cite web | {{10^|97}} is a high estimate of the elementary particles existing in the visible universe (not including [[dark matter]]), mostly photons and other massless force carriers.<ref>{{cite web | ||
|author=Robert Munafo | |author=Robert Munafo | ||
|date= | |website=Robert Munafo's home pages | ||
|date=2025 | |||
|title=Notable Properties of Specific Numbers | |title=Notable Properties of Specific Numbers | ||
|url=http://mrob.com/pub/math/numbers-19.html | |url=http://mrob.com/pub/math/numbers-19.html | ||
|access-date= | |access-date=2025-09-12 | ||
}}</ref> | }}</ref> | ||
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* [[Orders of magnitude (numbers)]] | * [[Orders of magnitude (numbers)]] | ||
* [[Skewes's number]] | * [[Skewes's number]] | ||
* [[Googol]] | |||
* [[Infinity]] | |||
==References== | ==References== | ||
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* {{Wiktionary-inline}} | * {{Wiktionary-inline}} | ||
* {{MathWorld | urlname=Googolplex | title=Googolplex}} | * {{MathWorld | urlname=Googolplex | title=Googolplex}} | ||
* {{cite web|title=Googol and Googolplex |url=https://www.numberphile.com/videos/googol-and-googolplex |work=Numberphile|last=Haran |first=Brady |author-link=Brady Haran |others=Padilla, Tony; Symonds, Ria |date=17 February 2012 }} | |||
* {{cite web|title=Googol and Googolplex|url= | |||
{{Large numbers}} | {{Large numbers}} | ||
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[[Category:Numbers]] | [[Category:Numbers]] | ||
[[Category:Large numbers]] | [[Category:Large numbers]] | ||
[[Category:1920s neologisms]] | |||
Latest revision as of 01:26, 6 March 2026
A googolplex is the large number 1010100, that is, 10 raised to the power of a googol. If written out in ordinary decimal notation, it would be 1 followed by a googol (10100) zeroesTemplate:Px2—Template:Px2a physically impossible number to write explicitly .
History
In 1920, Edward Kasner's nine-year-old nephew, Milton Sirotta, coined the term googol, which is 10100, and then proposed the further term googolplex to be "one, followed by writing zeroes until you get tired".[1] 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".[2] It thus became standardized to 10(10100), which is usually written as 1010100 using the conventional interpretation for serial exponentiation.[3]
Size
A typical book can be printed with one million zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires Template:10^ such books to print all the zeros of a googolplex (that is, printing a googol zeros).[4] If each book had a mass of 100 grams, all of them would have a total mass of Template:10^ kilograms. In comparison, Earth's mass is 5.97×1024 kilograms,[5] the mass of the Milky Way galaxy is estimated at 1.8×1042 kilograms,[6] and the total mass of all the stars in the observable universe is estimated at 2×1052 kg.[7]
To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the mass of the observable universe by a factor of roughly 5×1040.
In the physical universe
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 full decimal form (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than is available in the known universe. Sagan gave an example that if the entire volume of the observable universe is filled with fine dust particles roughly 1.5 micrometers in size (0.0015 millimeters), then the number of different combinations in which the particles could be arranged and numbered would be about one googolplex.[8][9]
Template:10^ is a high estimate of the elementary particles existing in the visible universe (not including dark matter), mostly photons and other massless force carriers.[10]
Mod n
The residues (mod n) of a googolplex, starting with mod 1, are:
- 0, 0, 1, 0, 0, 4, 4, 0, 1, 0, 1, 4, 3, 4, 10, 0, 1, 10, 9, 0, 4, 12, 13, 16, 0, 16, 10, 4, 24, 10, 5, 0, 1, 18, 25, 28, 10, 28, 16, 0, 1, 4, 24, 12, 10, 36, 9, 16, 4, 0, ... Template:OEIS
This sequence is the same as the sequence of residues (mod n) of a googol up until the 17th position.
See also
- Graham's number
- Names of large numbers
- Orders of magnitude (numbers)
- Skewes's number
- Googol
- Infinity
References
- ↑ Bialik, Carl (14 June 2004). "There Could Be No Google Without Edward Kasner". The Wall Street Journal Online. (retrieved 17 March 2015)
- ↑ Edward Kasner & James R. Newman (1940) Mathematics and the Imagination, page 23, NY: Simon & Schuster
- ↑ Anthony J. Dos Reis (2012). Compiler Construction Using Java, JavaCC, and Yacc. John Wiley & Sons. p. 91. ISBN 978-1-118-11277-9.
- ↑ Stanford student Wolfgang Nitsche put together a website which will, provided a 94-digit volume number, generate a PDF file consisting of Template:10^ zero digits (with an initial one digit in volume 1), and registered an ISBN for the set: Nitsche, Wolfgang (August 2013). Googolplex Written Out. Stanford, CA: Wolfgang Nitsche. ISBN 978-0-9900072-0-3.
- ↑ Williams, David (2024), "Earth Fact Sheet", NASA Space Science Data Coordinated Archive, National Aeronautics and Space Administration, archived from the original on 21 August 2025, retrieved 15 November 2024
- ↑ Letzter, Rafi (2019), "Our Large Adult Galaxy Is As Massive As 890 Billion Suns", Space.com
- ↑ Alessandro Domenico De Angelis; Mário João Martins Pimenta; Ruben Conceição (2021). Particle and Astroparticle Physics: Problems and Solutions. Springer. p. 10. ISBN 978-3-030-73116-8.
- ↑ Goodrich, Ryan (2013), "Googol, Googolplex - & Google", LiveScience.com
- ↑ Saplakoglu, Yasemin (2018), "Photos: Large Numbers That Define the Universe", Space.com, retrieved 12 September 2025
- ↑ Robert Munafo (2025). "Notable Properties of Specific Numbers". Robert Munafo's home pages. Retrieved 12 September 2025.
External links
| File:Commons-logo.svg | Wikimedia Commons has media related to Googolplex. |
- File:Wiktionary-logo-en-v2.svg The dictionary definition of googolplex at Wiktionary
- Weisstein, Eric W. "Googolplex". MathWorld.
- Haran, Brady (17 February 2012). "Googol and Googolplex". Numberphile. Padilla, Tony; Symonds, Ria.
