Googol is a very well-known large number, equal to 10100 or 1 followed by 100 zeroes. It is also called "ten duotrigintillion" using the short scale.
Coined in the year 1920,100 it has become very famous as a generic example of a large number , and is what the field of googology and the search engine Google are named after.
Contents
- 1 History
- 2 Properties
- 3 Sizeedit | edit source
- 4 Cultural impact
History
The term was coined by Edward Kasner's nine-year-old nephew, Milton Sirotta in 1920. It was perhaps first published in New Names in Mathematics (1937). 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.
In 1998, the search engine Google was founded, which was named after this number. Their company being named after a large number represents the enormous size of the internet.
Properties
The googol is equal to ten duotrigintillion in the short scale, or ten sexdecilliard in the long scale. 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.
Aarex Tiaokhiao coined the names unoohol, 100-noogol, and booiolplex for this number.
Username5243 coined the name goodolplex for this number, and it's equal to 10[1]10[1]2 in Username5243's Array Notation.
SuperJedi224 coined the name decigol for this number.
Sizeedit | edit source
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 10185), 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.
A cube with edge length 35mm contains about a googol Planck volumes.
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.
The time it takes for the black hole TON 618 to fully decay due to hawking radiation is about a googol years.
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.
Googology Wiki has a tongue-in-cheek goal to reach 10100 articles, which is probably impossible.
Googol was the subject of the £1 million question in a 2001 episode of the British version of the quiz show Who Wants To Be A Millionaire?, where contestant Charles Ingram cheated his way to the jackpot with the assistance of an aide in the audience.
- May 9, 2013
- #1
MathJakob 1615
Just curious, for a start I don't think there is enough hard drive space in the world to document the number but if a computer could printout 100billion 0's a second, how many years would it take before the computer had printed out the full number?
I have no idea how to possibly work this out, I tried using wolfram but I don't even know to type lol.
- May 9, 2013
- #2
Mark44 Mentor Insights Author 36,5548,541
MathJakob said: Just curious, for a start I don't think there is enough hard drive space in the world to document the number but if a computer could printout 100billion 0's a second, how many years would it take before the computer had printed out the full number?
A Googol is 10100, which is 1 followed by 100 zeroes.
I have no idea how to possibly work this out, I tried using wolfram but I don't even know to type lol.
How big is a Googolplex?
- May 9, 2013
- #3
SteamKing Staff Emeritus Science Advisor Homework Helper 12,8091,670
All your answers are here:
//en.wikipedia.org/wiki/Googolplex
- May 9, 2013
- #4
MathJakob 1615
Mark44 said: A Googol is 10100, which is 1 followed by 100 zeroes.
How big is a Googolplex?
Googolplex is [tex]10^{googol}[/tex]
Also no SteamKing that does not answer my question unfortunately. It mentions nothing about a computer being able to printout or run through 100billion 0's per second.
I know there is not enough room to write the number out, but if there was, how long would it take a computer printing 100billion 0's per second?
- May 9, 2013
- #5
Mark44 Mentor Insights Author 36,5548,541
MathJakob said: Googolplex is [tex]10^{googol}[/tex]
100 billion is 1 X 1011 (by American reckoning, with 1 billion being 1,000 million).MathJakob said:
Also no SteamKing that does not answer my question unfortunately. It mentions nothing about a computer being able to printout or run through 100billion 0's per second.
I know there is not enough room to write the number out, but if there was, how long would it take a computer printing 100billion 0's per second?
This problem isn't hard if you write the numbers in scientific notation.
- May 10, 2013
- #6
SteamKing Staff Emeritus Science Advisor Homework Helper 12,8091,670
The googolplex = 10^(10^100)
If there isn't enough material (and enough atoms) in the universe with which to print the value, its pretty safe to say that the time required > the age of the universe.
- May 10, 2013
- #7
MathJakob 1615
You're not listening to what I'm saying... I'm not talking about printing the number out onto physical objects, I said this many many times. I simply want to know, if a computer can read 100 billion 0's per second, then how many years will that computer take, until it's read through the entire number.
How hard is it to get an answer around here... I'm terrible at maths cmon guys.
Last edited: May 10, 2013
- May 10, 2013
- #8
phyzguy Science Advisor 5,0542,054
It's not that hard. A googolplex is 10^(10^100). If you print out 10^11 zeros per second, then it will take
t = 10^(10^100) / 10^11 = 10^(10^100-11) = 10^(10^100) seconds
t = 10^(10^100) / (3*10^18) = 10^(10^100-18.5) = 10^(10^100) years
Where the last equality in each line is approximate, since I'm ignoring 11 (or 18.5) compared to a googolplex. However, this is a very, very good approximation.
So the answer is that it will take a googolplex seconds or a googolplex years, both of which are about the same, and both of which are an incomprehensibly long time.
,
- May 10, 2013
- #9
jbriggs444 Science Advisor Homework Helper 11,4956,131
phyzguy said: It's not that hard. A googolplex is 10^(10^100). If you print out 10^11 zeros per second, then it will take
t = 10^(10^100) / 10^11 = 10^(10^100-11) = 10^(10^100) seconds
t = 10^(10^100) / (3*10^18) = 10^(10^100-18.5) = 10^(10^100) years
That's how long it would take to count to a googolplex. The challenge at hand is how long it would take to print a googolplex.
That does not take 1010100 operations. It only takes 10100 operations. SteamKing has already referenced a page that provides a time estimate. The only difference is that his reference used an assumption of two zeroes per second rather than 100 billion.
- May 10, 2013
- #10
phyzguy Science Advisor 5,0542,054
My mistake. So let me re-do my estimate:
t = 10^(100) / 10^11 = 10^(100-11) = 10^89 seconds
t = 10^(100) / (3*10^18) = 10^(100-18.5) = 3*10^81 years
Still an extremely long time, but not so incomprehensible.
- Jan 27, 2016
- #11
Brian121268 10
so that's 30 sexvigintillion years, (3,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years) or 1/10 novemvigintillion seconds, (100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 seconds) if the math is correct. according to //bmanolov.free.fr/numbers_names.php
I guess. my brain shuts down after 6 zero
I assume that is how long it takes for the computer to do it. If so, my best guess as to how long it would take to count out is: Go get in your car right now. Start driving, any direction, at about 75 mph. Now drive to the very edge of the universe. Return home. You might have done it by now. If not, you may need to repeat.
Last edited: Jan 27, 2016