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Not to be confused with goggol.

Googol is a very well-known large number, equal to 10100 or 1 followed by 100 zeroes.[1] It is also called "ten duotrigintillion".

Coined in the year 1920,[2] it has become very famous as a generic example of a large number , and is what the field of googology is named after.

History

The term was coined by Edward Kasner's nine-year-old nephew, Milton Sirotta in 1920. It was first published in a book co-written by Kasner Mathematics and the Imagination in the 1940's. The name was most likely influenced by name of the title character of the American comic strip Barney Google and Snuffy Smith, which was very popular at the time. Barney Google's name was in turn inspired by Vincent Vickers' 1939 children's book The Google Book.

Properties

The googol is equal to ten duotrigintillion in the short scale, or ten sexdecilliard in the long scale.[3] Googol can be expressed as {10,100} in BEAF, or as E100, E100#1, or E2#2 in Hyper-E notation.

Sbiis Saibian has given the alternative name guppyding.[4]

Aarex Tiaokhiao coined the names unoohol, 100-noogol, and booiolplex for this number.[5]

Username5243 coined the name goodolplex for this number, and it's equal to 10[1]10[1]2 in Username5243's Array Notation.[6]

SuperJedi224 coined the name decigol for this number.[7]

Size

There are a mere 1080 elementary particles in the observable universe, so googol has little use when measuring real-world quantities. However. it is still much less than the number of Planck volumes in the observable universe (which is about 10183), so it still has some real-world meaning. Sbiis Saibian showed that a googol particles in a tightly packed sphere would still have a diameter of 5.6 quadrillion meters, or half a light-year.[8]

A cube with edge length 35mm contains about a googol Planck volumes.[9]

Googol is comparable to some numbers produced by combinatorics. For example, 70 factorial (the number of ways 70 distinct objects can be arranged in a row) is about 20% larger than 10100.

A googol seconds is about a sexvigintillion (1081) times the estimated age of the universe. A googol angstroms is approximately 100 trevigintillion light-years.

It takes approximately 317 novemvigintillion years to count to a googol one integer at a time. Counting by googols, half googols, or duotrigintillions, of course, one could count there faster but it is not considered kosher in hide-and-seek or googology.

Approximations in other notations

Notation Lower bound Upper bound
Scientific notation $$1\times10^{100}$$
Arrow notation $$10\uparrow100$$
Steinhaus-Moser Notation 56[3] 57[3]
Copy notation 9[100] 1[101]
Chained arrow notation $$10→100$$
Taro's multivariable Ackermann function A(3,329) A(3,330)
Pound-Star Notation #*(8,8,2,3,1,7,1)*9 #*(15,0,2,10,2,1)*12
BEAF {10,100}
Bashicu matrix system (0)(0)(0)(0)(0)[1333] (0)(0)(0)(0)(0)[1334]
Bird's array notation {10,100}
Hyperfactorial array notation 69! 70!
Strong array notation s(10,100)
Fast-growing hierarchy $$f_2(323)$$ $$f_2(324)$$
Hardy hierarchy $$H_{\omega^2}(323)$$ $$H_{\omega^2}(324)$$
Slow-growing hierarchy $$g_{\omega^{\omega^2}}(10)$$

Cultural impact

The definition of googol, googolplex, and similar numbers eventually branched into the field of googology, the study of, nomenclature of, and creation of notations for large numbers.

Larry Page and Sergey Brin, the founders of the Google search engine, named their company after a pun on googol, as their goal is to cache the mass of data that makes up the World Wide Web.[10]

Googology Wiki has a tongue-in-cheek goal to reach 10100 articles.

Sources

Googol and related numbers
-minutia group
n-ary numbers with multipliers
Eyelash mite group: eyelash mite-speck · eyelash mite-crumb · eyelash mite-chunk · (binary/ternary/octal)eyelash mite · eyelash mite-bunch · eyelash mite-crowd · eyelash mite-swarm
Dust mite group: dust mite-speck · dust mite-crumb · dust mite-chunk · (binary/ternary/octal)dust mite · dust mite-bunch · dust mite-crowd · dust mite-swarm
Cheese mite group: cheese mite-speck · cheese mite-crumb · cheese mite-chunk · (binary/ternary/octal)cheese mite · cheese mite-bunch · cheese mite-crowd · cheese mite-swarm
Clover mite group: clover mite-speck · clover mite-crumb · clover mite-chunk · (binary/ternary/octal)clover mite · clover mite-bunch · clover mite-crowd · clover mite-swarm
Pipsqueak group: (binary/ternary/octal)pipsqueak
Little squeaker group: (binary/ternary/octal)little squeaker
Small fry group: (binary/ternary/octal)small fry
Guppy group: (binary/ternary/octal)guppyspeck · (binary/ternary/octal)guppycrumb · (binary/ternary/octal)guppychunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)guppy(bit/byte)
Minnow group: (binary/ternary/octal)minnowspeck · (binary/ternary/octal)minnowcrumb · (binary/ternary/octal)minnowchunk · (ternary)minnow(bit/byte)
Goby group: (binary/ternary/octal)gobyspeck · (binary/ternary/octal)gobycrumb · (binary/ternary/octal)gobychunk · (ternary)goby(bit/byte)
Gogol group: (binary/ternary/octal)gogolspeck · (binary/ternary/octal)gogolcrumb · (binary/ternary/octal)gogolchunk · (ternary/quadternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)gogol(bit/byte)
Jumbo shrimp group: (binary/ternary/octal)jumbo shrimp
Lightweight group: (binary/ternary/octal)lightweight
Ogol group: (binary/ternary/octal)ogolspeck · (binary/ternary/octal)ogolcrumb · (binary/ternary/octal)ogolchunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)ogol(bit/byte)
Tiny twerpuloid group: (binary/ternary/octal)tiny twerpuloid
Googol group: (binary/ternary/octal)googolspeck · (binary/ternary/octal)googolcrumb · (binary/ternary/octal)googolchunk · (ternary/quaternary/quinary/duodecimal/hexadecimal/vigesimal/sexagesimal)googol(bit/byte) · googolbunch · googolcrowd · googolswarm
Eceton group: ecetonspeck · ecetoncrumb · ecetonchunk · ecetonbunch · ecetoncrowd · ecetonswarm
Numbers with base-multipliers
Numbers with -plex