googol n : a cardinal number represented as 1 followed by 100 zeros (ten raised to the power of a hundred)

English

Etymology

Made up in 1938 by the nine year old Milton Sirrota, the nephew of mathematician Edward Kasner.

Pronunciation

• Rhymes: -uːɡəl

Cardinal number

1. The number 10100; 1 followed by 100 zeros.

Translations

• French: gogol
• Swedish: googol
• Russian: гугол

Derived terms

• Google
• googolplex

A googol is the large number 10100, that is, the digit 1 followed by one hundred zeros (in decimal representation). The term was coined in 1938 by 9-year-old Milton Sirotta, nephew of Edward Kasner (Kasner 1989, pp. 20-27; Bialik 2004). Kasner then extended the term to the larger "googolplex." Kasner popularized the concept in his book Mathematics and the Imagination (1940).

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. A googol has 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. Edward 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.

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 official 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.

Googolplex

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

10googol = 10(10100).

In the documentary Cosmos, physicist and broadcast personality Carl Sagan estimated that writing a googolplex in numerals (i.e., "1,000,000,000...") would be physically impossible, since doing so would require more space than the known universe occupies.

Thomen's number, named for ancient mathematical philosopher Robbeas Thomen, is the number googolplex raised to the power of one googolplex:

googolplexgoogolplex = (1010100)1010100.

Of course, at the time this number was concieved by Thomen, such notation was far advanced. Thomen believed that at this number, mathematics became superimposed against supernatural philosophy as numbers this big cannot possibly apply to humankind but to the gods themselves. At the time Thomen concieved possibility for such a number, most civilizations had not even incepted zero into their number systems. This makes Thomen's number incredibly conceptually advanced for its time.

Googol and comparable large numbers

A googol is greater than the number of atoms in the observable universe, which has been variously estimated from 1079 up to 1081 . Less than a googol Planck times have elapsed since the Big Bang (the current figure stands at around 8×1060 Planck times). From the previous two figures, it can be seen that a list of where every particle is at every possible discernible unit of time since the Big Bang would contain over a googol entries, but still far less than a googolplex: around 8 × 10140.

A little googol is 2100 (about 1.268), or 1,267,650,600,228,229,401,496,703,205,376, while a little googolplex is 2^ or about 10^.

Avogadro's number, 6.02214179, is exactly the number of 12C atoms in 12 grams (0.012 kg) of unbound 12C in its ground state. It is perhaps the most widely known large number from chemistry and physics. Avogadro's number is less than the fourth root of 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.

Seventy factorial, or 70!, is "just 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, 10120, a rough lower bound on the number of possible chess games, is more than a googol.

A googol is considerably less than the number described in the ancient Archimedes' story of The Sand Reckoner, namely \left((10^8)^\right)^=10^. But it should be noted that the system invented by Archimedes is reminiscent of a positional numeral system with base 108, so that Archimedes' number could be written \left[\left((10)^\right)^\right]_=\left[10^\right]_, that is, one googol in base 108

On a practical level, googol is perhaps the most worthless number in existence (next to the Shannon number).

In popular culture

Googol was the answer to the million-pound question: "A number one followed by 100 zeros is known by what name?" on Who Wants to Be a Millionaire? when Major Charles Ingram allegedly attempted to defraud the quiz show on 10 September 2001. The other options were a megatron, a gigabit or a nanomole.

Googol is one of the 336 vocabulary words in the board game Balderdash, and their definition on the back of the card is "The number one followed by 100 zeros."

In the January 23, 1963 Peanuts strip, Lucy asks Schroeder what the chances are of them getting married, and Schroeder responds "Oh, I'd say about 'googol' to one."

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

The company name Google is a misspelling of the word "Googol" made by founders Larry Page and Sergey Brin, as described in the book The Google Story by David A. Vise.

See also

• Large numbers
• Names of large numbers
• Googolplex

References

External links

• History from the Google website
• "Tridecabillion" by Paul Niquette

astronomical number, billion, decillion, duodecillion, googolplex, infinitude, infinity, jillion, large number, nonillion, novemdecillion, octillion, octodecillion, quadrillion, quattuordecillion, quindecillion, quintillion, septillion, sexdecillion, sextillion, tredecillion, trillion, undecillion, vigintillion, zillion