Googol

From Wikipedia, the free encyclopedia

This article is about the large number. For the Internet company and search engine, see Google. For the author, see Nikolai Gogol.

A googol is the large number 10¹⁰⁰, that is, the digit 1 followed by one hundred zeros (in decimal representation). One googol is written as: 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. The term was coined in 1920 by nine-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. Kasner popularized the concept in his book Mathematics and the Imagination.

A googol is of the same order of magnitude as the factorial of 70 (70! being approximately 1.198 googol, or 10 to the power 100.0784), and its only prime factors are 2 and 5 (100 of each). In binary it would take up 333 bits.

The googol is of no particular significance in mathematics, but is useful when comparing with other incredibly large quantities such as the number of subatomic particles in the visible universe or the number of possible chess games. Kasner created it to illustrate the difference between an unimaginably large number and infinity, and in this role it is sometimes used in teaching mathematics.

The Internet search engine Google was named after this number. Larry Page, one of the founders, was fascinated with mathematics and "Googol," even during high school. They ended up with "Google" due to a spelling mistake.^[1]^[2]

The word "google" or "googol," regardless of spelling, suggests the wide-eyed look of a baby, and the comic strip character Barney Google who began appearing in the 1910s.

1 Writing out a googol
2 The shrinking googol
3 Googolplex
4 Googol and comparable large numbers
5 Miscellaneous
6 See also
7 References
8 External link

[edit] Writing out a googol

A googol can be written in conventional notation as follows:

1 googol = 10¹⁰⁰ =

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

Its "conventional" English number name is ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale, or ten sexdecilliard on the Peletier long scale.

[edit] The shrinking googol

When it was named in 1920, the googol was undeniably large. However, with the invention of fast computers and fast algorithms, computation with numbers the size of a googol has become routine. For example, even the difficult problem of prime factorization is now fairly accessible for 100-digit numbers. However, computations of a googol steps are still completely out of reach.

[edit] Googolplex

Main article: googolplex

A googolplex is 1 followed by a googol of zeroes, or ten raised to the power of a googol:

$\mbox{googolplex} = {10}^{\mbox{googol}} = {10}^{({10}^{100})} .$

[edit] Googol and comparable large numbers

A googol is greater than the number of particles in the observable universe, which has been variously estimated from 10⁷⁹ up to 10⁸¹.^[3]^[4]
A little googol is 2¹⁰⁰, or about 1.267x10³⁰, while a little googolplex is $2^{2^{100}}$ or about $10^{3.8 \times 10^{29}}$ .
Avogadro's number, 6.0221415x10²³, can loosely be thought of as the number of carbon atoms in twelve grams of elemental carbon, and is perhaps the most widely known large number from chemistry and physics. Avogadro's number is much less than a googol.
Black holes are presumed to evaporate because they faintly give off Hawking radiation; if so, a supermassive black hole would take about a googol years to evaporate.^[5]
Seventy factorial, or 70!, is just over a googol, 1.19785717 × 10¹⁰⁰. This means that there are over a googol ways to arrange seventy items (or people) in a sequence (such as a line to a concert).
The Shannon number, a rough estimate of the number of possible chess games, is very much more than a googol, around the order of 10¹²⁰.
A googol is considerably less than the number described in the ancient Greek story of The Sand Reckoner, namely $10^{8 \times 10^{16}}$ .

[edit] Miscellaneous

Googol was the answer to the million-pound question on Who Wants to Be a Millionaire? when Major Charles Ingram allegedly attempted to defraud the quiz show on 10 September 2001.
In one Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Schroeder responds "about a googol to one."
A symmetrical Googolagon with equal sides would be viewed as a circle.
In an episode of the animated series "Teenage Mutant Ninja Turtles: Fast Forward," the "Gaminator" video games system is said to have a "3 googolhertz processor."
"A googol is precisely as far from infinity as is the number one." - Carl Sagan, Cosmos