Google googol for lots of 0s

photo by Gerd Altmann

Kids around here recently celebrated their 100^th day of the school year by partaking in various activities revolving around the number 100.  In honor of that auspicious event, we are checking out what happens when you get 100 zeros to play follow-the-leader with a 1.

Googol!

In 1938, mathematician Edward Kasner was searching for a name for a number he had in mind to illustrate the thought-level difference between infinity and numbers that are not actually infinite but just seem to go on forever by virtue of being ridiculously huge.

The number he envisioned was 1 followed by 100 zeroes, which you can either write all the way out, or express like this: 10¹⁰⁰.  But what to name this crazy big number?

As Kasner was out on a stroll with his 9-year-old nephew Milton Sirotta, he asked the youngster for an opinion.  Milton – proper purveyor of nine-year-old wisdom (don’t underestimate it!) – thought that a pretty ridiculous number should have a funny-sounding name, so he fatefully suggested “googol.”  And it stuck.

How big is that, really?

Let me tell you, googol is big.  Googol is greater than the number of atoms in the known universe.  If you labeled the universe’s subatomic particles with sequential numbers, you’d run out of matter bits before you got to googol.

If you started counting by ones at the moment of the Big Bang and spoke one number per second from then until now, you would only be about halfway to counting to googol.

Be glad for that big number, though, for around googol is the number of years we expect to pass before the heat death of the universe -- a ridiculously long existence expressed by a ridiculously large number.

But googolplex knows what from big!

Young Milton went on to suggest an even bigger number – googolplex – which he described as writing a 1 followed by zeroes until you get tired of writing.  Kasner thought there should be a little more definition there, but googolplex ended up being plenty big indeed – it’s defined as a 1 followed by a googol of zeroes.

How much is a googolplex?  I’ve seen it described thus: take the universe and pack it full with specks of dust.  Give each speck a number assignment (1, 2, 3, etc.).  Now reassign each speck a new number.  Keep going…the amount of different numbering combinations you could get out of a speck-stuffed universe is approaching the range of a googolplex.

How about Google?

Word has it that the search engine giant got its name during a meeting when its founders were brainstorming and looking for available domain names.  To give an impression of the company’s hoped-for far-reaching web presence, someone suggested “googol,” and the person typing in potential domain names typed “google” – presumably just an outright misspelling – and that’s where Google comes from. 

Similarly the folks at Google thought it would be cute to call their headquarters the GooglePlex.  Yeah, it’s cute.

And finally…

There’s a video here that reviews all this and then shows how a universe that’s googolplex meters wide would be so big that the subatomic particles would run out of possible arrangements of themselves before running out of space to arrange in, and would therefore have to repeat some permutations exactly, resulting in your ability to have tea with yourself…if you could find yourself in a googleplex-meter-wide universe, that is.