A Staff Report from the Straight Dope Science Advisory Board

# Do the numbers googol and googolplex really exist?

January 26, 2000

Dear Straight Dope:

Do the numbers googol and googolplex really exist? I recollect from first grade that a googol is a 1 with 100 zeroes after it. A googolplex is a google of googols (googole squared?).  Seems to me it would make sense for a google to have 99 or 102 (or some other multiple of 3) zeroes — call me old fashioned.  I seem to recollect this was a sort of concept number that some mathematician (Matthew Googol?) came up with.

Let's get something straight first. A googol is a number. A google, or rather Google, is a prosperous Internet search provider. I've never heard of a googole, and there wasn't a Mr. Googol, unless you're thinking of the Russian novelist Nikolai Gogol (1809-1852), who as far as I know never dabbled in mathematics. Judging from your letter, you seem to be a little confused on these points.

Now then. Does a googol exist? Sure, it's a number, like any other. The term was coined by the nine-year-old nephew of mathematics author Dr. Edward Kasner to describe the number 1 followed by 100 zeroes — that's 10100 in scientific notation. (For a list of names of other big numbers, see http://www.straightdope.com/mailbag/mgazilli.html.)

The nephew also suggested a much larger number called googolplex, which he described as 1 followed by as many zeroes as you could write before your hand got tired. Krasner set the definition of googolplex as 1 followed by a googol of zeroes … that is, 10googol.

In fact, of course, your hand would get tired several hundred years before writing a googol of zeroes.

To put things in perspective:

• The number of words printed since in the 500 years after the Gutenberg Bible (so, say, 1456 to 1956) is around 1017.
• If the entire universe were filled with protons and electrons so that there was no vacant space, the total number would be about 10110. That's larger than a googol but much less than a googolplex.

And I don't want anyone bugging me about the accuracy of these numbers — I'm trying to establish order-of-magnitude quantities, which is tech talk for "give you the general idea." It's not like I sat there and counted the protons.

Staff Reports are written by the Straight Dope Science Advisory Board, Cecil's online auxiliary. Though the SDSAB does its best, these columns are edited by Ed Zotti, not Cecil, so accuracywise you'd better keep your fingers crossed.

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