Thursday, July 10, 2008

A Googolplex, More Or Less

Has nothing to do with a search engine, just so there’s no misunderstanding right at the start. You see, there is a number with the name “googol,” which shows up as a “1” with a hundred zeros behind it. A “googolplex” is a one with a googol of zeros behind it.

One googol is presumed to be greater than the number of elementary particles in the observable universe. Therefore a list of the state of every particle at every measurable unit of time since the Big Bang would have nowhere near a googolplex entries.

Since a googolplex is one followed by a googol zeroes, it would not be possible to write down or store a googolplex in decimal notation, even if all the matter in the known universe were converted into paper and ink or disk drives. Indeed, if you had an unlimited supply of ink and paper, you would need around 10 to the power of 20 universes to fully write it down.

Thinking of this another way, consider printing the digits of a googolplex in unreadable, one-point font. (Newspapers are usually 9-point.) The distance to write the digits would be about 4.7 × 10 to the power of 69 times the diameter of the known universe. The time it would take to write such a number also renders the task implausible: if a person can write two digits per second, it would take around 1.1 × 10 to the power of 82 times the age of the universe to write down a googolplex.

(This information is from Wikipedia and looks reliable.)


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