Student: What’s the biggest number you know?
Me: Well, here’s a pretty big one. 10^10^10^10.
Student: What’s that, like a billion?
Me: Not quite. See 10^10? That’s ten billion. It’s about the number of people in the world, plus 3 bonus Indias.
Student: All right! Bonus Indias!
Me: Okay, so you can picture 10^10?
Student: Well, not really, but I know what it means. Keep going.
Me: Okay. Now 10^10^10 is a 1 followed by 10 billion zeroes. Like, turn all those people into zeroes, line them up behind a numeral 1. That’s 10^10^10.
Me: Just to write it out, you’d need about 3 million sheets of paper. That’s a 9 foot x 9 foot x 12 foot stack.
Student: But the poor trees!
Me: I know. Let’s call this number the tree-killer.
Student: Yeah. Stupid tree-killer!
Me: So picture the tree-killer. It’s a massive number. Absurd. Grotesque. Beyond imagination.
Me: Now, 10^10^10^10 is a 1 followed by a tree-killer of zeroes.
Student: Say what now?
Me: We just discussed how treekiller is the craziest, hugest, most unfathomable thing you’ve ever tried to fathom, right?
Me: Well, that unfathomable monstrosity of a number… that’s how many digits are in my number.