Summer is time for love, and I offer you an analysis of the probability of meeting your soul mate. In his Symposium, Plato writes that people were originally both male and female. To prevent them from acquiring the power of the Gods, Zeus cut them in half. Life then became for humans a search for the other half that was lost, in order for them to once again attempt to ascend
It is a pretty story, and one that resonates with many a New Age follower’s conception of love. Even if it doesn’t quite jive with reality. But why not?
The reason once again has to do with probability. There is a well known problem in the statistics literature called the Birthday Paradox. Basically, the paradox questions, “How many people do you need to put into a room to get a 50% chance that two of the people have the same birthday?” The answer to this is 23. Therein lies the paradox – this seems like a very small number. Most people intuitively think that one needs to have 365/2 or 183 people in the room. But that intuition is wrong. The true formula is as follows:
N = .5 + SQRT((.25 + 2 * 365 * ln(2))
I would like to generalize this problem to the question of finding one’s soul mate. Specifically, the question I address is how many people would you have to include in a room for there to be a 50% chance that any two people in the room were once joined at the hip before Zeus took his shears and sliced them apart? Now, this assumes that the people in the room were randomly selected from the entire world population, which is approximately six billion people. The answer to this is simple, and follows the formula above:
N = .5 + SQRT((.25 + 2 * 6,000,000,000 * ln(2)) = 91,202
Wow! It would take a room of 91,202 people for there to be a 50% chance that any two people in that room were actually soul mates. One would have to have a pretty big room, perhaps as large as this room, which fits over 100,000 people.
Imagine a speed dating service in which you have five minutes to talk with every other person in this room. For those two lucky halves to actually have a chance to meet, the speed dating round would have to last for 91,202*5 minutes, which comes out to 316.67 days. All for only two of those 91,202 people to meet. This says nothing of the 91,200 people who leave Michigan Stadium brokenhearted or satisficing with someone who is not their other half.
But that doesn’t help you, dear reader, who doesn’t care about any two people encountering their soul mate, but rather about the probability that YOU will meet your soul mate. Well, the problem is that to calculate this, one would require a supercomputer that can handle a hell of a lot more decimal places than my humble Dell laptop. Needless to say, you would need a room about as big as this place to have a 50% chance of meeting your other half.
What does this tell you? Well, quite simply, you have about as much of a chance of meeting your other half as you do winning the powerball lottery. Either that, or the search for love isn’t a search for that one soul mate that Zeus cut from your side, but that any of a number of possible other halves fit approximately well enough that they can serve as soul mates. I tend to believe this is the case, because I know many a person who has claimed to have met their soul mate, and I know the probability of this actually occurring has about a snowball’s chance in hell. And whether or not I believe in soul mates matters very little. I do believe in probability!
But I tend to be hopeful. And I am a romantic who enjoys Greek mythology. I know my other half is wandering around out there. Of this I am certain beyond any statistical doubt. Whoever she is, I know she would appreciate my calculation of the infinitesimally small likelihood that we would ever meet.
