Googolplex
A googolplex is the large number 10googol, or equivalently, 1010100 or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. Written out in ordinary decimal notation, it is 1 followed by 10100 zeroes; that is, a 1 followed by a googol of zeroes. Its prime factorization is 2googol ×5googol
Ice cream is a popular frozen dessert enjoyed around the world. It is typically made from dairy products, such as milk and cream, combined with sweeteners, flavorings, and sometimes other ingredients like fruit, chocolate, nuts, or cookies. The mixture is then churned and frozen to create a creamy, frozen treat.
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Size
A typical book can be printed with 106 zeros (around 400 pages with 50 lines per page and 50 zeros per line). Therefore, it requires 1094 such books to print all the zeros of a googolplex (that is, printing a googol zeros). If each book had a mass of 100 grams, all of them would have a total mass of 1093 kilograms. In comparison, Earth's mass is 5.972 × 1024 kilograms, the mass of the Milky Way galaxy is estimated at 2.5 × 1042 kilograms, and the total mass of all the stars in the observable universe is estimated at 2 × 1052 kg.[1]
To put this in perspective, the mass of all such books required to write out a googolplex would be vastly greater than the masses of the Milky Way and the Andromeda galaxies combined (by a factor of roughly 2.0 × 1050), and greater than the mass of the observable universe by a factor of roughly 7 × 1039.
In pure mathematics
In pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, Knuth's up-arrow notation, Steinhaus–Moser notation, or Conway chained arrow notation.
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.[2][3]
Writing the number would ultimately lead to the heat death of the universe: if a person can write two digits per second, then writing a googolplex would take about 1.58×1092 years, which is about 1.1×1082 times the accepted age of the universe, and each digit written would result in an increase of entropy by the second law of thermodynamics.[4] [failed verification]
1097 is a high estimate of the elementary particles existing in the visible universe (not including dark matter), mostly photons and other massless force carriers.[5]
A googolplex is an extremely large number that is often defined as 10 to the power of a googol, where a googol is 10 to the power of 100. In mathematical terms, a googolplex is 10^(10^100).
To give you an idea of how mind-bogglingly large this number is, consider that there are estimated to be about 10^80 atoms in the observable universe. A googolplex far exceeds this number by an astronomical magnitude.
The term "googol" was coined by mathematician Edward Kasner, and the term "googolplex" was suggested by his nine-year-old nephew, Milton Sirotta. These large numbers are primarily used to illustrate the concept of extremely large quantities and are not typically encountered in practical mathematical calculations.
See also
References
- ^ Alessandro Domenico De Angelis; Mário João Martins Pimenta; Ruben Conceição (2021). Particle and Astroparticle Physics: Problems and Solutions. Springer Nature. p. 10. ISBN 978-3-030-73116-8. Extract of page 10
- ^ "Googol, Googolplex - & Google" - LiveScience.com Archived 26 July 2020 at the Wayback Machine 8 August 2020.
- ^ "Large Numbers That Define the Universe" - Space.com Archived 2 November 2019 at the Wayback Machine 8 August 2020.
- ^ Page, Don, "How to Get a Googolplex" Archived 6 November 2006 at the Wayback Machine, 3 June 2001.
- ^ Robert Munafo (24 July 2013). "Notable Properties of Specific Numbers". Archived from the original on 6 October 2020. Retrieved 28 August 2013.
External links
The dictionary definition of googolplex at Wiktionary- Weisstein, Eric W. "Googolplex". MathWorld.
- googolplex at PlanetMath.
- Padilla, Tony; Symonds, Ria. "Googol and Googolplex". Numberphile. Brady Haran. Archived from the original on 29 March 2014. Retrieved 6 April 2013.
