Finding the missing piece

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 Mount Olympus.

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.

Bayesian bar hopping, Einsteinian insanity, and the seduction of soft science

A few months ago I was having dinner with a friend, a professor of physics. We'll call him professor base-rate-neglect. He's one of those hard science jerks who always reminds me that the social sciences are soft sciences. I'm used to claims like these from idiots like him. But, still, I love the guy. So professor BRN was complaining about his love life, or lack thereof. "I don't get it. I'm smart. I'm fairly attractive. I have a good job. But I can't seem to meet women."

Experimentaholic replies, "Well, how are you trying to meet them? Or rather, how have you met the women you've dated most recently?"

Dr. BRN says, "I met Kelly at a bar. That ended horribly. I met Jen at the park. Ended terribly. I met Susan at the bookstore. Ended because she moved to Oregon."

Experimentaholic: "Well, have you ever heard of a guy names Thomas Bayes?"

BRN: Sure. He did Bayes Theorem. I forget about what it says, though. I hated statistics. It's soft math.

Experimentaholic: I hate it when you people say that. Especially since I will use soft math to solve your problems. Bayes dealt with a statistical problem having to do with where billiard balls would end up resting on a table. I think this directly relates to your problem.

BRN: This is why I don't trust you soft scientists. Soft thinking. Billiard balls. What do billiard balls have to do with my love life?

Experimentaholic: More than you'd think. I won't go into the gory details of marginal and conditional probability, because you probably slept through stats. But let me ask you another question. How many times per week do you do any of these activities?

BRN: Well, I might seem a bit like an alcoholic, but I probably go out to bars three times per week. I go running on the weekend, and probably go to the bookstore once a month or so.

Experimentaholic: Okay. Think for a minute. So you go to bars 12 times a month, and you got one hit and 11 misses. You go running four times a month, and you get one hit and three misses. You go to the bookstore once a month, and you get one hit, no misses. Do you get where I am going with this?

BRN: Not really.

Experimentaholic: Dude, for every time you go to the bar each year, say, there is a less than one percent chance you are going to meet someone. Why? Because you head to the bar 144 times per year, and only have one relationship to show for it. You go running 36 times per year, and you have one relationship to show for it. That means the probability of you meeting someone while running is around 2 percent. Now, you go to the bookstore 12 times a year, and you have one relationship to show for it. That's an 8 percent chance that every time you go to the bookstore, you'll meet someone.

It seems as if you're doing everything backwards. What would Thomas Bayes do, if he either were alive today or not a Presbyterian minister, or not a [explicative deleded] lush like you? He would be going to the bookstore 3 times a week, going running twice a week, and avoiding bars altogether. Man, you got your strategies mixed up. All because you are ignoring the base rates - or the hits and misses - of your strategies of meeting people.

BRN: I never thought of it that way.

Experimentaholic: I know you think that my kind of science is soft, and that psychology is bullshit. I think a lot of psychology is bullshit too. But I am forcing you to do a little experiment. I don't care if you keep going to bars three times a week, you're a lush after all, and the tenure track thing is stressful. Drown yourself in beer. But I am forcing you to go to the bookstore three times a week. An hour at the bookstore, perusing the shelves, and let's see how your love life changes.

BRN: We'll see. I'll have to think about it.

Experimentaholic: Think all you want. It's the fact that you're not thinking about base rates that makes you miserably unhappy and sitting here complaining to me, and going home alone to your miserable apartment and crying your lonely self to sleep.

BRN: Whatever, you [explicative deleted] soft scientist.

Now, I haven't seen BRN for a little while, and I just received the following email from him.

Experimentaholic:

Yo, man. Sorry I've been out of touch, but the most amazing thing happened. So at first, I basically ignored your little "experiment" and kept doing what I always do. I thought, "You're dumb, and what do you know?" Then, a few weeks later, after a pretty bad hangover, I decided to try your little experiment. For two weeks, I went to the bookstore three times a week. During the third week, I'm sitting there, reading a copy of Dawkins's The God Delusion, when this totally gorgeous woman walks up and says that she loved that book. We started chatting, and she is a biology grad student at [redacted] university. We totally hit it off, and she gives me her number. I call a few days later, we go out on a date, and you know where this is heading. Long story short, I'm seeing this girl. It's been five weeks now, and I am totally falling for her. Man, I can not believe that a psychologist of all people could [increase the frequency of his sexual encounters]. I thought you soft scientists were idiots. Next time we get together, dinner's on me.

My response?

I guess it takes a psychology professor to remind a physics professor that Einstein defined insanity as "doing the same thing over and over again and expecting different results." Perhaps there is something to soft science after all? Either way, I will relish the dinner. And I look forward to meeting the new lady.

Experimentaholic saves the day.