- Googolplex
A

**googolplex**is the number 10^{googol}, which means it's a 1 followed by agoogol of zeros (i.e. 10^{100}zeros).:1 googolplex:= 10^{googol}:= $10^\{10^\{100,!$:= 10^{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}In the documentary "",astrophysicist and broadcast personalityCarl Sagan estimated that writing a googolplex in numerals (i.e., "10,000,000,000...") would be physically impossible, since doing so would require more space than the known universe occupies.In 1938,

Edward Kasner 's nine-year-old nephew Milton Sirotta coined the term "googol "; Milton then proposed the further term "googolplex" to be "one, followed by writing zeroes until you get tired". Kasner decided to adopt a more formal definition "because different people get tired at different times and it would never do to have [the boxer champion] Carnera be a better mathematician than Dr. Einstein, simply because he had more endurance". [*cite book | last = Kasner| first = Edward | authorlink = Edward Kasner| year = 2001 | title = Mathematics and the imagination | publisher = Dover Publications | location = Mineola, NY*]**How big is a googolplex?**One

googol is presumed to be greater than the number of elementary particles in the observable universe, which has been variously estimated from 10^{79}up to 10^{81}. A googol is also greater than the number ofPlanck time s elapsed since theBig Bang which is estimated at around 8 × 10^{60}.Since a googolplex is "one followed by a googol zeroes," it would not be possible to write down or store a googolplex in

decimal notation , even if all the matter in the known universe were converted into 0's. Indeed, if you had an unlimited supply of ink and paper, you would need around 10^{20}times the current age of universe to fully write down a googolplex.Thinking of this another way, consider printing the digits of a googolplex in unreadable, one-point font.

TeX one-point font is .3514598 mm per digit, which means it would take about 3.5 × 10^{96}meters to write in one-point font. The known universe is estimated at 7.4 × 10^{26}meters indiameter , which means the distance to write the digits would be about 4.7 × 10^{69}times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around 1.1 × 10^{82}times theage of the universe to write down a googolplex.Thus in the physical world it is difficult to give examples of numbers that compare closely to a googolplex. In analyzing

quantum state s andblack hole s, physicist Don Page writes that "determining experimentally whether or not information is lost down black holes of solar mass ... would require more than 10^{1076.96}measurements to give a rough determination of the final density matrix after a black hole evaporates". [*http://arxiv.org/pdf/hep-th/9411193*] In a separate article, Page shows that the number of states in a black hole with a mass roughly equivalent to theAndromeda Galaxy is in the range of a googolplex. [*[*]*http://www.fpx.de/fp/Fun/Googolplex/GetAGoogol.html How to Get A Googolplex*]In

pure mathematics , the magnitude of a googolplex is not as large as some of the specially defined extraordinarilylarge number s, such as those written withtetration ,Knuth's up-arrow notation ,Steinhaus-Moser notation , orConway chained arrow notation . Even more simply, one can name numbers larger than a googolplex with fewer symbols, for example,9

^{99999}, is much larger.This last number can be expressed more concisely as

^{6}9 usingtetration , or 9↑↑6 usingKnuth's up-arrow notation .Some

sequence s grow very quickly; for instance, the first two Ackermann numbers are 1 and^{2}2=4; but then the third is^{33}3, a [*http://mathworld.wolfram.com/PowerTower.html power tower*] of threes more than seven trillion high.Yet, much larger still is

Graham's number , perhaps the largestnatural number mathematicians actually have a use for.A googolplex is a gigantic number that can be expressed compactly because of nested exponentiation. Other procedures (like tetration) can express large numbers even more compactly. The natural question is: what procedure uses the smallest number of symbols to express the biggest number? A

Turing machine formalizes the notion of a procedure or "algorithm ", and abusy beaver is the Turing machine of size n that can write down the biggest possible number [*http://mathworld.wolfram.com/BusyBeaver.html*] . The bigger n is, the more complex the busy beaver, hence the bigger the number it can write down. For n=1, 2, 3, 4 and 5 the numbers expressible are not huge, but research as of2008 shows that for n=6 the busy beaver can write down a number at least as big as $4.640\; imes10^\{1439\}$. [*http://www.drb.insel.de/~heiner/BB/index.html*]**External links***Who Can Name the Bigger Number? http://www.scottaaronson.com/writings/bignumbers.html

*Comparing googolplex to numbers similar in size: http://home.earthlink.net/~mrob/pub/math/numbers-15.html#l_p1_1000e100

*The Biggest Numbers in the Universe: http://www.strangehorizons.com/2001/20010402/biggest_numbers.shtml

*Knownprime factor s of googolplex + n (0 <= n <= 999): http://www.alpertron.com.ar/GOOGOL.HTM

*Another Googolplex page: http://www.procrastinators.org/googolplex.html

*A humorous C program to count to a googolplex: http://www.fpx.de/fp/Fun/Googolplex/

*The Challenge of Large Numbers http://www.fortunecity.com/emachines/e11/86/largeno.html

*Googolplex is "inconceivable" but still "describable": http://jimvb.home.mindspring.com/hamlet.htm**ee also***

Large numbers

*Names of large numbers **References****External links***

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*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**googolplex**— ☆ googolplex [go͞o′gôl pleks΄, go͞o′gälpleks ] n. [ GOOGOL + L plex, fold] the number 1 followed by a googol of zeros; 10 to the power googol … English World dictionary**Googolplex**— Googol [ˈguːgɔl] ist eine Bezeichnung für die Zahl 10100. Das entspricht einer 1 mit 100 Nullen, ausgeschrieben: 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… … Deutsch Wikipedia**Googolplex**— Se ha sugerido que este artículo o sección sea fusionado con Gúgol (discusión). Una vez que hayas realizado la fusión de artículos, pide la fusión de historiales aquí. Un googolplex es un número desmesuradamente elevado que corresponde a 10… … Wikipedia Español**Googolplex**— Gogolplex Le gogolplex (googolplex en anglais) est défini comme le nombre 10 élevé à la puissance gogol. Il peut être noté : 10gogol, Pour la seconde notation, il faut préciser que … Wikipédia en Français**googolplex**— noun Date: 1938 the figure 1 followed by a googol of zeros equal to 10googol … New Collegiate Dictionary**googolplex**— /gooh gawl pleks , gol , geuhl /, n. a number that is equal to 1 followed by a googol of zeros. [1935 40; GOOGOL + PLEX] * * * … Universalium**googolplex**— [ gu:g(ə)lplɛks] cardinal number equivalent to ten raised to the power of a googol … English new terms dictionary**googolplex**— goo·gol·plex … English syllables**googolplex**— goo•gol•plex [[t]ˈgu gəlˌplɛks[/t]] n. math. a number that is equal to 1 followed by a googol of zeros, expressed as 10^googol • Etymology: 1935–40 … From formal English to slang**googolplex**— /ˈgugəlplɛks/ (say goohguhlpleks) noun the number 10 raised to the power of a googol … Australian English dictionary