What if everyone had only one soul mate?

What if everyone actually had only one soul mate, a random person somewhere in the world?

—Benjamin Staffin

What a nightmare that would be.

But what if we did have one randomly-assigned perfect soul mate, and we couldn’t be happy with anyone else? Would we find each other?

We’ll assume your soul mate is set at birth. You know nothing about who or where they are, but—as in the romantic cliché—you’ll recognize each other the moment your eyes meet.

Right away, this raises a few questions. For starters, is your soul mate even still alive? A hundred billion or so humans have ever lived, but only seven billion are alive now (which gives the human condition a 93% mortality rate). If we’re all paired up at random, 90% of our soul mates are long dead.

That sounds horrible. But wait, it gets worse: A simple argument shows we can’t just limit ourselves to past humans; we have to include an unknown number of future humans as well. See, if it’s possible for your soul mate to be in the distant past, then it also has to be possible for soul mates to be in the distant future. After all, your soul mate’s soul mate is.

So let’s assume your soul mate lives at the same time as you. Furthermore, to keep things from getting creepy, we’ll assume they’re within a few years of your age.

With the same-age restriction, most of us have a pool of around half a billion potential matches.

But what about gender and sexual orientation? And culture? And language? We could keep using demographics to try to break things down further, but we’d be drifting away from the idea of a random soul mate. In our scenario, you don’t know anything about who your soul mate will be until you look into their eyes. Everybody has only one orientation—toward their soul mate.

The odds of running into your soul mate are incredibly small. The number of strangers we make eye contact with each day is hard to estimate. It can vary from almost none (shut-ins or people in small towns) to many thousands (a police officer in Times Square). Let’s suppose you lock eyes with an average of a few dozen new strangers each day. (I’m pretty introverted, so for me that’s definitely a generous estimate.) If 10% of them are close to your age, that’s around 50,000 people in a lifetime. Given that you have 500,000,000 potential soul mates, it means you’ll only find true love in one lifetime out of ten thousand.

Luckily, XKCD found a way to make things easier. If you want to read more, click here.