Kids Thinking About Infinity

My son said this, when he was about three. He was playing with coins at the time, from his piggy bank, as kids do (if you have a small child, you know that coins never stay in the piggy bank, and somehow, despite Canada not minting pennies for years, there is ALWAYS a penny on the floor…)

Specifically, he said,

I have infinity money, I have more than I can count!

For a three year old, this is about as good a definition of infinity as you can get. You can never count that high. The only problem is, he was considering a very finite pile of money at the time. If he knew how to count those coins he would have. In grade one, they have spent a lot of time counting by different coins. Money is as good a context as any (and he counted a big bag of change recently, in order to get a fidget spinner-getting toys is a powerful motivator for mathematics in the early years).

We made this fun little video about counting. There was actually 100 teddy bears. When kids are little, and you ask about really big numbers, they say “4”. I tried this. They know one, two, and have maybe an idea of many. When they bigger, they might say “10”.

We tried writing out numbers on paper, and my trick was always adding a zero each time. Then I filled a paper with zeros after a leading “1”.

You can do this with kids:

“what’s the biggest number you know?”

They might say, “one million”, to which your reply, “I will just add one, and now we have ‘one million and one’”. This game could literally go on forever.

I just read Eugenia Cheng’s great book called “Beyond Infinity”, which is a great tour of concepts surrounding the infinite. She talked about some beginning ideas about infinity. All kids have had these ideas at some point.

Here they are:

Infinity goes on forever.
Infinity is bigger than the biggest number.
Infinity is bigger than anything we can think of.

And:

If you add one to infinity, it’s still infinity.

Some grade 7s said something that encompasses all of these ideas.

We want kids to play with infinity. We want them to wonder about the infinite. They can come up with insights like this, if we let them.

Why is the Hilbert Hotel not on elementary school curricula worldwide? Why don’t we walk in on the first day of grade 2 and ask,

“What’s the biggest number you know?”

See what happens. Kids are born to wonder, because they are human. Humans are born to think, and we have developed a powerful tool called mathematics to help us think. Math classrooms are thinking classrooms.

Try this one with kids. It’s my new favourite thing to get kids thinking about billions.

Bill Gates is 57. How much money would he have to give away every day, to give away his fortune by age 70? 80? 90?

If you dropped a hundred dollar bill in front of Mr. Gates, would he pick it up?

Now, think about how much infinity money actually is…more than has ever been minted or printed, on this Earth, from now until the end of the Universe. That’s a lot of money!