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 mathemetician (Matthew Googol?) came up with.
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Does a googol exist? Sure, it's a number, just 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/mailba g/mgazilli.html.)
The nephew also suggested a much larger number called googolplex, which he described as 1 followed by as many zeroes as you courld 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 10^110 ... This is larger than a googol but much less than a googolplex.
And I don't want anyone worrying about the accuracy of these numbers--we're using comparative analogy, not precise calculations.
