The Googol, the Googolplex and Other Really Big Numbers

This article relates to Jenniemae & James

Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real 'wow, that's big,' time... Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we're trying to get across here.
- Douglas Adams, The Restaurant at the End of the Universe

Most of us can get our head around what a million looks like, but visualizing a billion, let alone a trillion can be challenging. The image to the left is what a billion dollars looks like stacked on a pallet in $100 notes. Click the image to see what a trillion dollars looks like!

But a trillion pales into numerical insignificance compared to a googol, let alone a googolplex.

What, might you ask, is a googol and why is it so called?

The story goes that prominent American mathematician Edward Kasner (1878-1955) was out walking one day with his two young nephews mulling over what to call the number 10¹⁰⁰ (that is to say the number 10 followed by 100 zeros), when nine-year-old Milton Sirotta pipes up and suggests it be called a 'googol' (from the Latin googis meaning "a lot"). Two years later, in 1940, Edward Kasner and his colleague James R Newman (the "James" in Jennimae and James) publish Mathematics and the Imagination - a non-technical book about maths which introduces the term googol to general readers for the first time.

So, what about the googolplex? To get to grips with the googolplex we first must return to that memorable day when Kasner is out walking with his nephews. As the story goes, apparently taking barely a moment to rest on his laurels from coining the 'googol,' young Milton proposes an even bigger number to be called a googolplex (plex from the Latin to fold - i.e. comprising of many parts - which gives us words such as duplex and cineplex), which would be "one, followed by writing zeroes until you get tired." Kasner liked the name but, recognizing that his young charge maybe a tad out of his mathematical depth, pointed out that writing zeroes until you get tired isn't all that scientific. So he tidied up the mathematics to define a googolplex as 10 to the power of a googol - which, as it happens, is such a big number that you would get very tired trying to write it down; in fact you'd be dead long before getting close to writing it!

It's taken me some time to get my head around what a googol is, but thanks to Carl Sagan by way of the fine folks at http://www.procrastinators.org I think I'm beginning to get a handle on it.

For starters, this is what a googol looks like:

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,
000,000,000,000,000,000,000

10 followed by a hundred zeros is certainly a big number - so big that some estimate that a googol is greater than the number of hydrogen atoms in the observable universe. But a googolpex is exponentially larger - 1 with a googol of zeros after it (or to put it another way, 10,000 x trillion x trillion x trillion x trillion x trillion x trillion x trillion x trillion).

Still not quite visualizing it? I'm not surprised! Maybe this will help: apparently, if you were to count 2 numbers a second it would take you about 1722 years to reach a googol. As for counting to a googolplex - there's a good chance the universe as we know it would have come to the end by the time you counted to that - which makes one wonder, just for a moment, did we really need a word for it?

But stop the presses; apparently there's an even bigger number coined by mathematician Ronald Lewis Graham (who, incidentally, is both past president of the American Mathematical Society and of the International Jugglers' Association), known as Graham's Number - but at this point I am totally out of my depth so am not even going to begin to attempt to describe his Very Big Number!

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

*For the purposes of this piece we have used the American definition of a billion as one thousand million, and a trillion as a million million - other countries, including much of Europe, define these terms differently.

Filed under Medicine, Science and Tech

This "beyond the book article" relates to Jenniemae & James. It originally ran in May 2010 and has been updated for the April 2011 paperback edition. Go to magazine.

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