Geek Trivia: Double (trouble) figures

What's the largest number ever put to practical use in mathematics -- a figure so significant that it dwarfs a centillion, a googolplex, and even the total number of atoms in the known universe?

When you see the word googleplex, odds are good that you have one of three reactions:

  • What's a googleplex?
  • Hey, that's Google's headquarters.
  • Somebody doesn't know how to spell that number.

Yes, as many of you undoubtedly are aware, Google, the search engine-powered media giant, is a clever misspelling of googol, a number represented by a one with 100 zeroes behind it (10100). Google, Inc. extended the quirky pun by naming its major company offices Googleplexes after another number, the googolplex, which is a one with a googol zeroes behind it. (That is, 10^10100 or, in what passes for mathematic humor, 10googol.)

Okay, so where did the word googol come from? After all, it doesn't fit into the more familiar etymology of large numbers laid out with Greco-Latin roots such as quad- for quadrillion (1015), oct- for octillion (1027), or dec- for decillion (1033).

These terms conform to the short scale of long numbers, which is the primary English language system for naming numbers, wherein each power of 1,000 has its own [root] + -illion designation. (This is opposed to the large scale, which names every power of one million.)

A googol doesn't fit into this system because it's not a recognized number in orthodox mathematics. In the short scale, 10100 is actually 10 duotrigintillion.

Mathematician Edward Kasner coined the term googol in his 1940 book Mathematics and the Imagination. More properly, Kasner's nephew coined the term when asked to make up a memorable name for a one with 100 zeroes behind it. That same nephew also coined the term googolplex, with Kasner supplying the ten to the googol definition. Both terms have since slipped in the popular consciousness, with one or the other often named as the "biggest number there is."

In truth, the largest designated number in the short scale is the centillion (10303). The mathematics world considers any number larger than a one with 303 zeroes behind it to be infinite, at least for all reasonable purposes. That's not to say that mathematicians don't use numbers larger than the centillion, just that these numbers usually defy description -- and sometimes even scientific notation.

Such is the case for the largest number ever put to practical mathematical use -- one so large it dwarfs the number of atoms in the universe.


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