Numbers fascinate my grandson. He tries to grasp the concept of infinity. “Can we count to infinity? What is infinity plus one? Does the sum of infinite numbers produce a finite number?” The questions are endless, or should I say infinite.
Mathematics has never been my strong subject, and the concept of infinity is difficult to explain. But I too am fascinated by the concept of infinity, and at best, all I can offer is that there is a gap that exists between each number, and each gap contains it’s own infinity. Well that didn’t explain much to my inquisitive grandson. I finally found it easier to explain infinity that exists between Zero (a nothing) and One than trying to visualize the infinity in each gap. There is a gap between Zero and One, and the numbers that exist in that gap are an endless string of rational and irrational numbers. (There’s .1 and .12 and .112 and .113 and so on with an infinite collection of others.) In order to move from Zero (a nothing) to One, then, we have to pass through an infinite number of numbers.
So how do I explain it in simple terms? How do I explain the change that occurs when moving from complete absence to a single presence? How do I explain that we encounter “infinity” routinely in our daily lives? And that having Zero to having One can make an infinite difference in one’s world.
My father and I came up with a simple explanation years ago after we would share our thoughts on various episodes of “The Twilight Zone.” Some episodes left us thinking deeper into the philosophy of the known unknowns. Sometimes we tried to understand what it would be like to be the only survivor of a catastrophe that hit the earth. Assuming you, the survivor, had enough food, water, and breathable air, and could find some decent shelter, your greatest challenge would be loneliness. You’d wander around in search of other survivors, and gradually lose hope. But what if you did find another person? Just one. What difference would it make? Zero people, or one person? The difference would be enormous. In fact, the difference would be immeasurable. Infinite.
Or imagine that for some reason you are in solitary confinement. You’re in a cell, which consists of a cot, pillow, blanket, toilet, and sink. A single light bulb burns for a few hours a day. Your food is sent to you on a conveyor belt. There are no sounds. There is no mirror, no window to the outside. Nothing moves, except you. How long would you last before you became insane? Now add one item. A book. Would it matter whether it was a biography, or a fantasy novel? A chemistry or quantum physics textbook? A dictionary? Each of these would be infinitely better than no book at all. That single volume could keep your mind from disintegrating. You would read every word, every equation, slowly, repeatedly. The book would change your whole world. From Zero to One.
After our hypothetical discourse, my father and I would bring the discussion to home. He would point to the coat closet and say; “You have a coat closet in your house that’s filled with all kinds of jackets. Adding or removing one item will probably not make a difference. But what if you were outside in the middle of winter and you had no coat? One coat would make the infinite difference.” And we would continue to find examples in our daily lives that routinely made an “infinite” difference from Zero to One.
I continue the discussion with my grandson. You’re in the desert. You have no canteen of water or you have one canteen of water. A life changing difference. From Zero to One. There are people who own five homes. There are other people who have nowhere to live. To whom would the addition of one house make the greatest impact? The change from Zero to One is felt and appreciated infinitely greater.
But my grandson is at an age where larger numbers appeal to him. He says he wants to be the scientist who can change the world for more than just one. As for me, I’ll stick to changing one life at a time from having Zero to having One. And the difference for me would be just as great, because changing the world for someone would be infinitely greater than changing the world for no one. Zero to One, an infinity of numbers that fill the gap.