I am trying to clean up my Inbox (you know, the whole "zero emails" goal). As I'm working on it, I've come across an old e-mail where I recorded my conversation with M. This took place a few days before his 7th birthday (hence the wintry picture up top). So I'm transferring it here for record-keeping.
He said: "I'm drawing an infinite zero". I asked him to explain.
Him: See, this is a big zero (draws). Inside of it I am drawing smaller and smaller zeros, so infinitely many. So that's infinity zero. Like our eyes and heads are infinity zeros because like eyes are round and then there are circles inside like zeros and then pupils are made of atoms. And there are like so many of them. Also, if we look for zeros around us in the universe, there are infinite many of them - planets and galaxies and atoms. Squares are also infinite but it's harder to find them 'cause like we don't have square heads or eyes or anything square in us.
Me (worried that he doesn't understand what zero really is): Ok, but you know, a square is a shape. Is zero a shape?
Him: No, it's not. It looks like circle, but zero is when there's nothing
Me (relieved): ok, so what's now?
Him: you see this wooden block? It's square and we can cut it into many squares (shows how to cut into thin squares with same area as the original wooden block)
Me: so how many squares would you get that way?
Him: a lot, depends how thin you can cut it. Can be a hundred, a thousand or more.
Me: and if we use a laser that cuts very-very thin slices?
Him: yes, can be many-many squares.
Me: what if we want infinite number of square slices? How thick would they have to be?
Him: very-very thin
Me: will they be zero thin?
Him: no, not zero. They will only get zero thin when we run out of wood. But they will be super thin almost zero and there will be infinite many of slices. So that's infinite zero.
Then he goes of to draw lots and lots of nested circles, nested squares, nested ovals, saying how all are infinite. Then he says, looking at all those nested shapes:
Him: You know, + and - always work the same in infinite circles and in infinite squares or anything else infinite.
Then he mentioned something that was "zero infinity", so I asked him to explain. Here was his explanation:
"Imagine you are on an island. It's infinitely big. But you don't see anything at all"
Me: why can't I see anything?
Him: because there isn't anything on this island. Because it's a zero infinity island.
Me: ok, my mind is officially blown, I gotta write it down.