Eight Octillion Dollars
This is the contents of an email I composed soon after arriving at work on May 7, 2004. My son David was ten at the time, soon to be eleven. My daughter Dani had been in the orphanage for two days, but we didn’t know her yet. We were still a family of three.
I was not usually the one to take David to school. I was usually at work by the time school started, and I picked him up from an after-school day care. But, for reasons lost in the mists of time, May 7 was different, or this post wouldn’t exist. The text has been preserved from that time, math errors intact.
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In the car, David asked me if anybody had a googol dollars. I said, “No, nobody has a googol dollars.”
“Is there a googol dollars in the whole world?”
“No, there’s not a googol dollars in the whole world, even if you took every kind of money and converted it to dollars. In fact, there wouldn’t even be a googol cents.”
So, he indicated that there might be a googol dollars in a few years, and I said no. Not if the US Treasury printed hundred dollar bills as fast as it could. Not if they built a new skyscraper just for printing hundred dollar bills.
“What about if they had a hundred skyscrapers?”
“Still not enough.”
“What if they had a billion years?”
I paused. “I’ll have to think about that,” I said. “I’ll have an answer for you when I pick you up today.”
“No, make it a hundred skyscrapers in each state.”
“Okay, how many stories on each skyscraper? A hundred?”
“Yeah, a hundred.”
“Okay.”
“But what if the government owed somebody a googol dollars?”
“It would be fake, because nothing in the world is worth a googol dollars.”
“What if it was a bunch of things?”
“The whole world together isn’t worth a googol dollars.”
“So you could buy the whole world for a googol dollars?”
It was time for him to get out of the car, so I just said “Yes”, as he left, then said, “Bye.”
And he toddled off into that school.
So, on the way to work, I worked on it. It went something like this:
We have, maybe a hundred printing presses on a floor, and a hundred floors — ten thousand printing presses per building.
We have a five thousand buildings in the United States (fifty times a hundred) — fifty million printing presses in the United States.
Maybe each printing press can print a thousand hundred-dollar bills per second. — fifty billion hundred dollar bills per second — five trillion dollars per second.
Five times six is thirty, so we have thirty trillion times ten — three hundred trillion dollars per minute.
Three times six is eighteen, so we have eighteen hundred trillion times ten — eighteen quadrillion dollars per hour.
With 25 hours a day (easier to multiply in your head), that makes eighteen hundred quadrillion divided by four — nine hundred quadrillion, four hundred fifty quadrillion dollars per day.
Similarly, we’ll allow 400 days per year. Back to eighteen hundred, times a hundred more, eighteen thousand — which makes eighteen quintillion dollars a year.
Now, in a billion years, we just add three more groups of zeros — sextillion, septillion, octillion — eighteen octillion dollars.
Funny, I got eight octillion in the car. Must have lost the leading one somewhere.
But the result is the same. That is, I believe, this number:
18,000,000,000,000,000,000,000,000,000 — that is, eighteen times ten to the twenty-seventh power.
That’s nothing close to this number:
10,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000 — that is, ten to the hundredth power.
It takes a lot to get through a hundred orders of magnitude.
Make them trillion dollar bills, and you only get another ten digits. You’re up to the thirty-seventh power. Make the presses print a trillion bills a second, and you add nine more — forty-six digits. Make it five trillion buildings, which I think would pretty much cover the planet, and give each one a trillion stories, and you have nineteen more to add to the total — sixty-five. Have a trillion planets in a trillion galaxies doing the same thing, and you add 24 digits to the total — eighty-nine. Let’s squeeze that ten out of eighteen, and we’re up to 1.8 times ten to the ninetieth power.
So, let’s harness the power of ten billion parallel universes, and we’re pretty much there. Over a googol dollars could be printed in a billion years if you had ten billion parallel universes, each with a trillion galaxies, each with a trillion planets, each with five trillion trillion-story buildings with a hundred printing presses on each floor, each printing trillion-dollar bills at a rate of a trillion per second.
I thought I’d let you know so one of us would remember to give David the answer.
Aren’t numbers fun?
