Discussing the concept of "infinity" can be an eye-opening experience!

In our family, we have a going-to-bed ritual. We ask each other, "How much do I love you?" The answers are always filled with giggles as we declare: "A googol? A googol and one? A googolplex? Double a googolplex! I love you 'til infinity!"

One evening, my three-year-old, in his usual stalling-tactic mode, asked me one more question: "Mom how many words are there in the English language?" I answered, "Well, I guess there are about 600,000 and a few more are added each year." Then we talked about other languages. He pondered for a while and then asked, "Isn't there a name for each number?" Now that was a good question — good enough to talk about and, of course, delay going to bed for at least another 10 minutes.

I'd never thought about this. If we have a name for each number, and numbers go on and on, then the number of words (or combinations of words) could be infinite as well. I'd been taught that there are a set or finite number of words in a language. As usual, it took a young child to get me to think outside of the box and use my own imagination. After this awakening (for me) we had many interesting discussions that emerged from teaching my child the abstract concept of infinity.

Start off by asking your child, "What is the biggest number you can think of? What is that number plus one?" Soon your son or daughter will get the idea that there is always one number bigger. Demonstrate that infinity is NOT a number; it cannot be defined; it is NOT finite. If there were such a number, then we could easily add one more to it, or double it, and then it would not be infinity. The word infinity comes from the Latin infinitas, or "unboundedness." Infinity is the concept of going on and on without a limit, the endless, no boundaries ... forever.

Use your imagination! Even though you can never define infinity, you can imagine it! And you can have fun together trying to imagine infinity. You and your child can imagine adding one more grain of sand to a beach. Imagine a really fun day — could you think of one more fun thing to do? And then another, and another ... Would you want that day to go on forever?

Talk about large numbers you know of. Young children love the names of large Numbers, like a googol (10¹⁰⁰). They also enjoy making up names for other large numbers. Can you count the number of grains of salt in a teaspoon, a bucket, the world? Discuss the number of odd or even numbers, negative numbers, points on a line, tangents of a circle.

Bring up the concept of time. How long does it take to write out a googol? Can you write out a googolplex? (No!) How many seconds are in a day, a year, a millennium? How long has the Earth been around? How many stars are in the universe? What is a light year?

If you keep getting larger, you can also keep getting smaller. How small is an atom? How many atoms are in the universe? Is there a googol of matter in the universe? Does anyone know for sure? What do scientists really know?

Cycles that seem to go on forever are another interesting discussion — the water cycle, the cycle of life on our planet, the life cycle of a star.

Look at the symbol for infinity. What does it mean to you? Could anyone skate around in a figure 8 forever? What a about a racecar driving down an infinity-shaped track?

Imagine a building with an infinite number of floors. How high up would it go? Past the moon? How long would it take to get down the elevator? What if one more floor were added? Who would wash all those windows?

Hold up two mirrors facing each other. How many reflections are there? If the mirrors are large enough, you can demonstrate an infinite number of reflections of your child — infinite tongues, infinite waving hands, infinite smiles.

Infinity is an exciting concept, and learning about infinity can lead to big discoveries for children of all ages. It opens our eyes and minds to the concept of time, life cycles, molecular particles, large numbers and the magnitude of the universe. There are so many questions that can get everyone THINKING. You can never reach infinity, but you CAN have googols of fun trying.