Significance – Large and Small Numbers

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Significance

Here’s a question: what do you get when you add one to a million? The answer: still a million.

Well, precisely speaking, it’s a million and one. But in the real world, it’s hardly ever necessary to be that precise. Let me put the question another way: what do you get when you add a drop of water to a full sink? The answer: still a full sink. Even if the amount of water in the sink to begin with is exactly a million times the amount in the drop, it does not change the fact that the full sink at the end is indistinguishable from the full sink at the beginning, and we call it and treat it as the same thing.

When adding a drop of water to a sinkfull, the drop is insignificant. But a single drop on a microscope slide  makes all the difference in the world. By itself, the drop is neither significant nor insignificant; we need context in order to say one way or the other.

This is a neat concept for science, but it leads to a troubling everyday question: when do your and my individual actions matter? Is there any real reason for me to personally recycle my plastics, or vote, or be a conscientious consumer? There will only be a significant impact if lots of people do it. One more or one less won’t make a difference.

This is the part where I should say, “Of course an individual’s contribution makes a difference.” And if enough people believe it, large numbers of people will do good things and a real difference will be made. There are times when a lie like this is the simplest, most harmless way to make good things happen, and I’m all for this message being spread. But here on A Scientist’s Fiction, we boldly face the truth head-on, not letting ourselves be distracted by wishful thinking. The question isn’t, “Why is it true that an individual’s contribution makes a difference?” The question is, “How do we argue that individuals should do the right thing, given the fact that an individual’s contribution does not make a difference?”

First, we should note that there are many times when individual actions do make a difference. Like a drop of water under a microscope, taking time out of your day to spend on another person, even a mere smile as you pass them by, can make a world of a difference for that person. That alone makes it worth it.

But even on the collective scale where individual actions don’t make a difference, there is still a reason to do the right thing. That reason is because you and I want to be good people. We want to be the kind of people who are responsible with our environment, with our economy, with our government. Even if taking your own bag to the grocery store is not going to make a dent in the world’s plastic problem, it is the kind of thing a good person does. It’s not just about plastic anymore, it’s about building habits of responsibility that help you in every aspect of your life. And if you can’t recycle, or if you aren’t sure which politician is the right one, the pressure is off. One person not being perfect isn’t the end of the world. So let’s do what we believe is right, regardless of whether that particular choice makes a difference in the grand scheme of things.