Do the numbers googol and googolplex really exist?
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.