I was just idly flipping through Facebook, as I am prone to doing instead of going to bed like I should have three hours ago, when I saw a thing where someone wrecked their motorcycle and ended up falling down an open manhole. One of the comments on this was something along the lines of how unlucky that person must have been. That comment reminded me of one of my favorite Fun Math Tricks™. By that I mean, one of those weird things that the world does that most people don’t realize. This particular one is called the Law of Truly Large Numbers. (Not to be confused with the Law of Large Numbers, which is completely different, but also relevant).
The thing that makes science possible is that the universe is predictable. If you do the same thing under the same circumstances, you can predict the result with relative certainty. Let’s start by flipping a coin. Assuming everything is fair and there’s no wonkiness in play, there’s an equal chance that any flipped coin will come up either heads or tails. There’s no real way to predict the result of any particular coin toss. The result of a single toss (again, assuming everything is perfectly random) is unpredictable.
However, if you toss that coin 10 times, or 100 times, or 1000 times, the results ARE predictable. Over 10 flips, you may get a perfect 5/5 split, or a less than perfect 6/4, or maybe even a rare 7/3. But flip it 100 times and you’re likely to come out a lot closer to even. And over a thousand flips, you’re probably going to come out less than one percentage point from dead even. This is the Law of Large Numbers. A single event may be unpredictable, but many events over time are extremely predictable.
But what about the Law of TRULY Large Numbers? This has to do with the fact that we as humans don’t process numbers above 1000 really well. They are outside our everyday range of experience, so we don’t really viscerally understand what they mean. This is especially true when we get into the range of millions and billions. When people want to indicate that something is really rare, they say it’s “one in a million”. But here’s the thing. New York City has a population of more than 8 million people, so something with a one in a million chance happens to someone 8 times EVERY DAY there. Tokyo has a population of 32 million. The United States has a population of 328 million. For something that’s supposed to be rare, one in a million chances pop up all the time. This is the Law of Truly Large Numbers.
So why talk about this here? This isn’t a science blog, it’s a charity blog. I wanted to talk about this here because when something uncommon and good occurs, people sometimes refer to it as a ‘miracle”. Now, I’m not here to debunk miracles. I’m perfectly fine with the hand of the divine acting in the world. What I do want to do is point out that with the Law of Truly Large Numbers, things that we might refer to as miracles aren’t really that uncommon. In fact, they happen all the time. But then again, so do things like people wrecking their motorcycle and falling in an open manhole. Why? Because the world is big, and things happen all the time. What matters is where you are standing.
The Law of Truly Large Numbers tells us that uncommon things happen all the time. But there’s more to it than that. Sometimes miracles are truly random events, but sometimes miracles result from the actions of humans. Someone finding a kidney donor match is a miracle. Someone getting food and shelter when they truly need it is a miracle. Sometimes just getting cab fare at the right time is a miracle.
The Bard once wrote, “there is nothing either good or bad, but thinking makes it so” (Hamlet, Act 2, Scene 2, 249-250). What may be a simple act of kindness that requires little to no effort on one person’s part could be another person’s miracle. Your good deed may turn out to be exactly what someone else needs. That’s the great thing about the Law of Truly Large Numbers. You never really know what is going to happen. You can only be sure that it will. And its sibling, the Law of Large Numbers means that even if one good deed doesn’t make a miracle, if you do it long enough, eventually it will.
Who said math was evil?
