“The true logic of this world is the calculus of probabilities” – James Clerk Maxwell
Another Friday night in. I’m halfway through my third romantic comedy. I’m reaching the point of staring-at-screens-saturation. Half a meter away from my office chair or two meters from my couch, I’ve spent too many hours looking at those pixels. If Fred had been by my side, this would have been a romantic night. Too often I surprise myself missing the hopeless cases I’ve dated. Laura is about to come by. She never says no when I call her. She never says no to anyone, so she’s not coming until the end of her second party.
The buzzer rings.
“Hey, Laura, come in”.
Laura is a good enough friend to understand that my bra is too far for me to pick it up in the time it takes her to walk two flights of stairs. She comes in and gives me a hug, loving, wasted and stylish in equal measure.
“Thanks for coming. I feared you might find some company that will keep you”, I say.
“I found some company alright!”, she replies.
She left a guy in a party to come to see me in a depressive night. That makes me shed tears of gratitude.
“Don’t worry. Sam’s room wasn’t locked, and she has a really nice bed that fit the three of us.”, she adds.
The tears have suddenly evaporated.
“So, what’s wrong, little Emily?”, she asks me.
“You know what’s wrong”.
“I do. And you know what your problem is?”
“OK. Surprise you. Mmm”
I make her sit down before she falls onto the carpet.
She raises her left index ceremoniously:
“Maxwell once said “The true logic of dating is the calculus of probabilities””.
I must admit I’m a bit surprised.
“Maxwell said that?”, I ask.
“Almost word by word. You see? You’re alone and you’re thinking of getting a boyfriend. And when you get a boyfriend, you try to keep him”.
“Yeah, I tend to do that. Call me weird”.
“The problem is you’re not seeing the whole picture.”
“I see”, literally I do.
“You have a chance with every man you meet”, she explains.
“Even the orange one?
“Sure”, she goes on, “Now the chance of dating the orange guy might be too small. That’s fine. The mind of a man is a complex fluctuating entity that shifts preferences very quickly. At some point in his life, even if it’s just for one night, he’s going to be really into you. That’s where you catch him. But you need to keep yourself entertained in the meantime.”
“And what about when I’m with someone? Shouldn’t I try to keep him?”
“That’s your problem right there. The probabilities of jumping into relationships with other men are still there. If you cut them, then the probability of being dumped is bigger. But if you keep them, not only you have more chances of changing, but also jealousy will always increase your chances to keep the relationship. Then you can choose to keep it or to jump to another”.
Laura has a mathematical point.
“Is that what you do? You’re always thinking of jumping into another relationship without giving yourself to one?”
“Now you’re getting it.”
“That’s really -”
Her phone rings in the middle of our conversation.
“Hi, gorgeous. How are you? I’m, well, half an hour?”
She looks at me with a smile.
“I think I’m available?”
Her nonsense has been the most entertaining part of my night. The least I can do is to return the favour. I nod to her.
“Yes, I’m available. OK. Bye bye!” She hangs up. “Sorry, what were you saying?”
I try to pick up my train of thought.
“What you do is, I don’t know, don’t you find it a bit sad?”
For the first time of the night she stops and thinks. She raises her index ceremoniously again.
And with that she kisses me good bye and leaves me with the my third movie.
The Science behind the story
The scenario presented here illustrates a probability equation called Master equation. It’s a fundamental statistical tool that works as follows: there is a set of states (or guys) in which a system can be (or a girl can date, including the possibility of not dating anyone). At any given time, the probability of being at every given state has a certain value, for example, P(single, today)=60%, P(orange guy, today)=10%, P(guy with tie, today)=30% (let’s ignore the other three men for the sake of simplicity). These probabilities change with time, and that is what the master equation models.
Having established the probabilities for today, let’s compute the probability of being with the orange guy tomorrow. This is a sum of the following contributions:
-The probability of being single today times the probability of starting a relationship with the orange guy. Let’s say the probability of starting a relationship with him is small (5%). Then, this contribution takes the value P(single, today) x P(single → orange guy)=60% x 5%=3%.
-The second contribution comes from the probability of being with the orange guy today and stay with him (for example, 90%). This is the probability Emily normally works on: P(orange guy, today) x P(orange guy → still orange guy)=10% x 90%=9%.
-Finally the third possible scenario is the one Laura insists on. She’s with the guy with the tie today and she moves into a relationship with the orange guy tomorrow. Let’s give that jealousy probability a value of 10%, so the contribution is P(guy with tie, today) x P(guy with tie → orange guy)=30% x 10%=3%.
With these data the probability of being with the orange guy tomorrow is 3%+9%+3%=15%, so luckily for Emily is increasing. To determine the probabilities of her being single tomorrow or being with the guy with the tie tomorrow, analogous calculations apply.
All these balances are really important in stochastic processes and have a huge range of applications of statistical mechanics, biophysics and even economics.