Wednesday, December 14, 2011

Just How Big Is a Billion?

Today's post has nothing to do with writing, really...

But I had a fascinating conversation with our six-year-old son a couple of nights back, and I've returned to thinking about it a couple of times recently. It's stuck with me enough that I felt compelled to write about it.

We were talking about big numbers, specifically about a googol (a one followed by 100 zeros). He asked if anyone had ever counted to a googol. I said that I didn't think so, and then we go to talking about how high a person could count in a lifetime.

Here's what we said:
  • Assume you can count one number a second. (Probably aggressive.)
  • And you start the moment you're born. (Obviously not happening.)
  • And you never sleep. (Ditto)
  • And you keep going until you're 100. (Optimistic)
Obviously, that's a ridiculous proposition, on any number of levels. But, still, let's go with it. How high do you think you could count? Don't cheat and do the math. Just guess. Ready?

Follow me below the jump for the answer.

A bit of white space for those who came to this post directly rather than from the blog front page...

Answer is below....


86,400 seconds in a day. 365 days in a year. Over 100 years that's 3.15 billion seconds. So, our hypothetical counting iron (wo)man would get slightly over 3 billion before they croaked.

Folks, that's a long way from a googol.

Then my son asked "Well, what if there was someone else who followed when the first person died. How high would they count?" And we talked about how they'd get another three billion, bringing the total to... six billion. After 100 years.

Do that 1000 times over 100,000 years. Guess what. You're at three trillion now. And you're 100,000 more years away from not three quadrillion... no. You're 100,000 years away from six trillion. (Which -- just to tie this in ever so slightly with writing science fiction, is the approximate number of miles in one light-year. Space, as Douglas Adams said, is indeed "mind-bogglingly big.")

That terabyte hard drive you just bought for under $100 at some big box store -- start counting the bytes on it today one and a time and you're wrapping up in the year 35,011 or so.

We throw around millions and billions and trillions in daily life and I think it's easy to lose sight of just how big those numbers are. I know I hadn't given these big numbers any concrete sense in my own mind any time recently. And it took a simple question from a six-year-old to make me realize just how big a billion is.


  1. Simple questions from six year olds are what keep us living, in many ways, my friend.

  2. Isn't that the truth, Bill? Our little ones frequently give me cause to ponder things I might otherwise not think about. Thanks for stopping by and reading!

  3. My kids asked for a googol toys today. Besides being kind of greedy, I told them it's an insane request. They would never have time to play with all of them, and the Earth wouldn't be able to contain them, and all life would be buried under what the Earth could contain, so we would all die, and nobody, including my kids, would ever play with toys again. My kids probably think I'm just a Scrooge.

  4. LOL, Stan. And, after reading this, I just had to check... The estimated number of atoms in the "observable" universe (with is a very technical term and doesn't seem to have much at all to do with telescopes and such...) is...


    So a fraction of a fraction of a fraction of a googol.

    So even if every "toy" was a single atom, the universe might just run short of fulfilling their request. How about that!

  5. Just have to love those simple questions from kids. The thing to think about now, we have 7 billion people on the planet. That's a whole lotta people.

  6. Hi, Denise, thanks for stopping by! Yes, you're absolutely right -- it's a staggering number of people when you stop to think about it. And more arriving every day!

  7. Thanks, I'll use this in my astronomy class. And I loved your recently published Nanoism story.

  8. Thank you, on both counts, Diane. Very flattering that you'd like to use this in your astronomy class! I hope that your students find it interesting.