How long would it take to count to decillion

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.

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My son likes large numbers (like septillion, googol and googolplex) and once asked me how long it would take to count to septillion (which is 1 followed by 24 zeros).  I told him it would take longer than the age of the universe to do that, so he started working his way down.  He asked me about counting to one million.  I did a little math (assuming one number per second) and got about 11-12 days . . . but then thought, the large numbers (like 658,243) take more than a second to say.

Looked on the web a little to see if anyone else had done a more sophisticated calculation.  Lots of calculations were like my own (assuming one number per second).  Others acknowledge that it would take longer for large numbers and made assumptions about what that would be.  But nothing definitive, so I thought I’d make one.  This counting calculator is based on the number of syllables in every number and counts all the syllables you’d have to pronounce in order to count from one to one million (or other numbers).

There is also a Spanish and Espanol number version of the calculator.

If the calculator is not self-explanatory, there are several steps to follow:

1. First time yourself counting to 20.
2. Based on your time, the calculator determines your counting rate in syllables per second (there are 32 syllables in the numbers between one and twenty).  You can try to count the number of syllables yourself.
3. Specify what number you’d like to count to, the default is one million but you can specify one billion or any number below one trillion.
4. Specify how many hours per day you think you can count.  Remember you need to eat and sleep and take breaks too.
5. Push the button and it’ll tell you how long it takes to count to your target number.

You can vary different parameters (counting speed, hours per day and target number) to see how long counting might take. (Spoiler, if you count to large numbers, it can take a very long time!)

I also decided to plot the number of syllables in each number between one and a million.  Not totally straightforward to plot one million points in an interactive fashion (where you can hover over the plot to see what numbers have how many syllables) so I ended up making a static image in R. It also shows the cumulative average number of syllables when counting up from one to the numbers below one million.

Update: I tried to upgrade this calculator from going up to 1 trillion to handling a septillion, but I found out that Javascript can only hand up to about 9 quadrillion before breaking down.  This mini-calculator now goes up to about 9 quadrillion.

Program and Data: The program was written in Javascript and runs locally in your browser.  The static plots were generated in R (R Studio) from the output of the Javascript program.

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