Peering at Infinity

Infinity is such a fun, crazy, mind-expanding, mind-boggling concept. It’s a topic that some kids will gleefully try wrapping their thoughts around. I’ve been noodling on how to play with it in a rich and interesting way with pre-schoolers. (If you have ideas, please share.) In the meantime, though, I’m finding ways to touch on it with my 9-year-old.

In my search for preschool appropriate infinity material, I found the book The Cat in Numberland by Ivar Ekeland and illustrated by John O’Brien. This is the story of a hotel for numbers whose capacity seems limitless, even as more guests arrive. It is based on an idea originally conceived of by mathematician David Hilbert to explain Georg Cantor’s understanding of infinity.  Hmm. Sounds very mathy, doesn’t it? It is. And it’s also very accessible…that was the point of David Hilbert’s idea for the Hotel Infinity – to make the mathematical concept of infinity accessible to us regular folk.  Infinity is so much more interesting and deep and rich than simply being “on and on forever.” Maybe you remember a bit of that from Calculus. Maybe not. No worries. What’s important right now is that this book is an easy and delightful way to dive into the mathematical infinite with your child.

By the way, this book is written as a short chapter book, and there are engaging illustrations on every page. Read it, or just look at the pictures!

Ekeland cleverly touches on mathematical concepts by explaining how the numerical guests at the hotel can – or can’t – play together. The story begins with the integers (the counting numbers.) The numbers love playing addition, subtraction, and multiplication, but they don’t all like division because some of them cannot play. The odd numbers cannot play division with 2, for example. Then one day Zero shows up, whom everyone wants to play with (and who loves all operations except for division), and the Hotel Infinity, which is already full, must find room for the new guest. Thus begins Ekeland’s tour of infinity. Witness to the numerical escapades is the hotel cat, who observes all the activity with curiosity and confusion.

When I started to read this book to the 9-year-old, I thought we’d break it up into one or two chapters a night. I was tired and wanted to get this kid to bed. But as soon as we began, it was clear that he was into it. He lingered on pages to dig into the detailed illustrations (on p. 25, check out the Roman numeral for one million two hundred thirty-four thousand five hundred sixty-seven!) He made connections back to this TedEd video that he likes to watch.  He looked over the mathematical expressions on each page to check that they were correct. He loved this book, and we ended up reading the whole thing in one sitting…and going to sleep a little later than planned.

I wondered how the 5-year-old would like the book. What would he connect with? His first comment was that some of these number-people have big butts. (Yes, the backsides of the long numbers stretch out quite a bit.) Then when he realized that the Hotel Infinity stretched up forever, he said “No way! That’s impossible!” But he stuck with it and particularly enjoyed the illustrations showing the numbers “playing” together. We talked about the minus sign…he didn’t understand the term “minus” but he did understand “take away”, so we talked about different ways to say the same thing. When Zero arrived at the hotel, he excitedly remembered the multiples of 10 that he had played with at school. It took us a long time to read just two chapters of the book because we stopped to observe and wonder and remember a lot.

The next day we picked up with Chapter 3, and I learned so much about the 5-year-old by observing his comments and reactions. First, he is NOT interested in algebraic concepts right now. As I lingered  to explain the page that demonstrated numbers taking the place of letters and letters taking the place of numbers, he clearly said to me:

“I am not listening anymore, Mom. Get back to reading.”

Um. Okay. Excellent self-reflection, Son.

But then, when I read a very long number to him, he looked at me and came up with his own very long number: 5,354. And he explained to me:

“Mom. The 4 is the units. And the 5 is the tens. And the 3 is the hundreds. And the other 5 is the thousands. Yes.”

Do you know what just happened there?? I just found out what he’s learning in school! He just connected something we were doing at home to something he is doing at school…and that reinforces everyone’s hard work! Yes. A morning well-spent.

I wonder what Chapter 4 will bring.

(Mathematically…as with many thoughtful things, the simple activity of reading this book is rich with benefits. Most obviously, there is the topic itself. The Cat in Numberland introduces a way to understand one kind of infinity…and ends with a teaser that hints at others. It also touches on mathematical operations and algebraic concepts in playful ways that can clarify and deepen your child’s understanding of the material…or simply introduce the material for the first time. Beyond that, though, the simple act of reading this kind of book with your child will reinforce the ideas that math is interesting, math is universal, and math is important. It will reinforce at home what she is (or will be) learning at school. It will reinforce to him that math is alive and interesting and engaging. And, if nothing else, it’s awfully nice to snuggle and read a book together no matter what it’s about. )