Infinity is a funny thing. When I was a kid, my mom always used to tell me that she loved me to the moon and back infinity times. Not long ago, it occurred to me that she might as well have said she loved me to the grocery store and back infinity times, or the width of a hair and back infinity times, or to the edge of the galaxy and back infinity times. It's all exactly the same distance. But I guess some infinities sound larger than others.
My kids, especially my 5-year old son, have started using the word infinity to describe everyday things, which almost always produces an amusing mental image in my head. For example, my son will say that he wants a snack and he would like infinity popsicles please, and of course I have to picture the entire known universe filled with popsicles, and then some.
A few days ago, I fixed our Nintendo Wii, which was making a horrible grinding noise, and today it started making the noise again. I told my son that it shouldn't take me very long to fix it again this time, and I should be able to fix it more permanently because I got some practice last time. He said he hoped I wouldn't be fixing the Wii for infinity days... or worse, infinity years.
Of course, infinity years is not at all worse than infinity days. I asked him, "Do you know when you could use the Wii if I had to fix it for infinity days?" He said he didn't know, and I said, "Never!" And I said the same for infinity years. Then I reassured him that it probably wouldn't take anywhere close to that. Then again, whether it takes me one hour or three days, either possibility is equally close to infinity years, which is to say, nowhere close.
My kids also don't tend to use a million or a billion to stand in for a very large number. They usually say a googol. The other day I was remarking to my wife that a googol is probably much larger than the number of atoms in the observable universe, and she wasn't convinced. I did a back of the envelope estimate and came up with about 10^80 atoms in the universe, which by sheer dumb luck turns out to be very close to the actual best estimate we have. And a googol is 100,000,000,000,000,000,000 times larger than that.
So ten times the observable universe is still nowhere close to a googol atoms. One billion observable universes is still about 100,000,000,000 times less. You have to take one hundred billion billion observable universes to get about one googol atoms. And that is equally distant from infinity as the number of atoms in my pinky fingernail. Infinity is a funny thing.
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