When I was in high school, I read a book called Infinity: Beyond the Beyond the Beyond. I don’t remember much about it, but I’ll never forget the title. The concept of infinity in its … well, infiniteness… can keep my mind occupied for a long time. And the idea of going “beyond the beyond” — and then beyond that! — provided more delicious food for thought. I sometimes think about that title and the mind-candy of endlessness when I’m speaking at a school, as I was last week in West Chester, PA, and someone asked, “What’s the biggest number?” It’s a question I often hear. The conversation usually goes something like this:

Child: What’s the biggest number in the whole wide world?

David: Do you think there is such a thing as the biggest number?

Audience: half “Yes,” half “No”

David: Will someone please tell me what you think the biggest number is.

Children, variously: billion, trillion, quadrillion, quintillion, googol, googolplex, etc.

David: Hang on. Let’s suppose you think “quintillion” is the biggest number. Then what about “quintillion-and-one”? Isn’t that bigger? And if that’s the biggest, what about “quintillion-and-two” — even bigger, right?

This usually leads to a triumphant retort about an enormous number familiar to many children (much less familiar to their parents and teachers):

Child: Googol has to be the biggest!

David: What’s a googol?
Many children know that “googol” is the name for a very large number — a one followed by a hundred zeros. This is an exciting concept. In my book G is for Googol: A Math Alphabet Book, I tell the story of how “googol” got its name from a nine-year old boy. Surely it is tempting to call googol “the biggest number,” but that’s a non-starter.

Me: If you think googol is the biggest number, then what about googol-and-one? Or two googol? Or a googol googol?

Almost inevitably, at this point someone proffers an even bigger number, “googolplex.” It is true that the word “googolplex” was coined [Read more…]