Zero, One, and Infinity

Posted on August 15, 2010


The concept of infinity is useful in mathematics, but doesn’t have many practical applications in everyday life. In fact, it tends to cause problems. For example, if you had an infinite number of ping pong balls, each with a different numeral, and you gave away all of the even-numbered balls, you’d still have an infinite number of ping pong balls. If you had an infinite number of amoebas and each one split in two, you’d still have an infinite number of amoebas. (And this is ignoring the fact that you can’t have an infinite number of things: where would you put them?)

Now picture the number line and that gap between Zero and One. How many numbers are there in the gap? Another endless string, rational and irrational numbers. For every two values, there’s always another value in the space between them. In order to move from Zero to One, then, we have to pass through an infinite number of numbers. This idea is the premise for many theoretical puzzles — paradoxes — all based on the idea that you can never take an infinite number of steps. But in reality, every gap contains its own infinity, and we traverse those gaps routinely, whenever we scratch our nose or walk across the street to visit a lonely neighbor.

Which brings us, at long last, to my intended topic: The change that can occur when you move from complete absence to a single presence. From having Zero to having One.

Sometimes I try to comprehend what it would be like to be the only survivor of a nuclear war. Assuming I had enough food, water, and breathable air, and could find some decent shelter, the next greatest challenge would be loneliness. Like prisoners who are put into solitary confinement for long periods of time, I imagine that being alone would eventually drive me insane. Wandering from place to place in search of other survivors, I would gradually lose hope as it became apparent that either no one else is alive or the others are so far away that I’ll never be able to reach them. But what if I did find another person? Just one. What difference would it make? Zero people, or one person. The difference, you already know, would be enormous. In fact, the difference would be immeasurable. Infinite.

Back to solitary confinement. For some reason, you’ve been sent to prison. Worse, you’re thrown into a small cell in the basement, out of hearing range of anyone else. Your food is sent to you on a conveyor belt. A single light bulb burns for three hours a day. Your cell consists of a cot, pillow, blanket, toilet, and sink. There are no sounds. Nothing moves, except you. There is no mirror, no window to the outside. How long would you last before you lost your mind? Now add one item. A book. Would it matter whether it was a novel or a biography? Even a chemistry textbook would be infinitely better than no book at all. That single volume could keep your mind from shattering. You would read every word, slowly, repeatedly. The book would become your whole world.

We have a coat closet in our house that’s filled with all kinds of outerwear. Adding or removing one item would probably go unnoticed. But what if I were outside in the middle of winter and I had no coat? The wind is howling and the temperature is zero. Would an increase of one degree matter at all? No. But one coat would make a big difference.

There are people who own ten homes. There are other people who have nowhere to live. To whom would the addition of one house make the greatest impact? How much would you appreciate the eleventh home? How much would you appreciate the first? You’re crossing the desert. You have one gallon of cold water, or you have no gallons of cold water. Tremendous difference. Life and death.

Do you have friends? People who really know you, I mean, or at least try to know you. If you had a hundred casual friends and acquaintances, would you trade them all for one person who paid close attention, asked questions, and actually listened to the answers and remembered them? What kind of difference does it make to have one person know you, rather than none?

I wrote a post recently in which I said I’ve let go of my delusions about changing the world. But I know better. I can change the world for someone. I can find someone who has Zero and help them to have One. That could change the person’s entire life. 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.