The Art of Dating

“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, Emily!”

“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?”

“Surprise me”.

“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.”

“What 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.

Images: Men in black vector image and Men silhouettes vector, Public domain.


Twin Paradox (Part II)


Her breath on his mouth was more than Albert could take without moving, without losing control, without falling. Now I don’t say falling in love or off the couch, I mean falling into the void of what he never had experienced before, his body at the complete mercy of the first woman who touched it.

It all took what seemed like an eternity to Albert, and only a moment for Suzy. And while certainly an external observer would agree that Suzy was right on this one, he also would agree that the third time Suzy was satisfied.

After some time, better not to think how long, Suzy woke up and kissed Albert, pushing him into a more studious position. Albert, feeling himself both a clever person (probably he wasn’t) and a God of love (he definitely wasn’t that), explained to Suzy the concept of entropy, with all the clarity of mind that an 18-year-old who has just lost his virginity can reach, and that’s not a small thing to say.

Leaving Suzy satisfied in several aspects, Albert returned to the now completely different streets. The sunlight was gone, but they had never looked so bright. Without shame, without pressure, with strength, with a smile, he rushed home knowing, not caring, that he was late for dinner. He burst into the living room, and started a series of excuses that involved entropy, a couple of missed buses, terrible traffic and people he hadn’t met for a while. His mother looked at him with intergenerational misunderstanding.

-What’s wrong with you? It’s only 7.

7 pm, by anyone’s standard, at least in the UK and the UK time zone, considering the watches are perfectly synchronized with Greenwich official time, and of course assuming observers don’t move with respect to each other at a velocity comparable to the speed of light.

Albert looked at Isaac:

-It’s 7!

-I know. I thought it was like 4 or something.

-What? No! It was… it’s late.

-Well, -said the mother after her not especially busy not especially quiet day- it’s clear that whatever you might say, the clock says it’s 7. You might have thought it was another time, but the clock is always right. 7 it is.

And as she said that, she punched the table with her fist. The vibration propagated across the wall, and got to the screw that was holding the clock, making it fall.

-See what you make me do!- shouted the mother.

Albert took the clock and put it back onto the wall, observing the hands pointing at 7 and 12. He didn’t say a word for the rest of the night.

The next day, Albert’s excitement got him out of bed before his sadder half. He wandered ecstatically alone through the house and looked at the clock in the kitchen, that was marking 7. And I say 7, neither am or pm or any of the other stuff, 7 because the clock had broken the past night. But Albert knew time had passed. He had been sleeping, getting dressed, walking down to the kitchen with a smile only for himself. But what if he hadn’t done any of this? Actually, what if no one in the world had done anything at all? What if not a single atom had moved and our story was stuck in this word? What if everything stayed at rest and entropy didn’t change? What if nothing got more mixed and untidy? If the world was still, how long was it still for, and who would notice? Who could talk about time, about sadness, about entropy, about love, when nothing was happening?

Then Albert smiled, nearly as happily as the day before. Time, what we call time, all the time, is just a measure of how fast the earth rotates, but why should we accept always that references? More things had happened inside his body the past day than inside his brother’s or his mother’s. He had lived more, and it was his own clock that mattered. If it was about life, and about what he had done, he was the best judge to say how much time had passed, how much glucose he’d burnt, how much entropy he’d created, how much sex he’d had. Well, maybe Suzy had a say in that, too. But he had lived more, he had lived faster, he had got older, he had got wiser. All in one day, well, one day, you know what I mean. Glad to understand Albert looked at the clock again, taking his time.

The Science behind the Story

The concept of entropy is one of the most famous in physics. Its intuitive explanation is described in the story: “a measure of disorder or homogeneity”. So the more homogeneous a system is, the more well-spread its components are, the more clothes are around your bedroom rather than separated inside the wardrobe, the more entropy there is.

The interesting thing is that entropy always grows with time, e.g, coffee and milk mix together, but don’t separate; a hot and a cold body reach an intermediate temperature, but they don’t go back to their initial states; or a glass breaks but doesn’t repair itself spontaneously. This means entropy can be taken as a measure of time itself, that is, as time passes entropy increases, and vice versa. If nothing happened at all in the Universe, it would be difficult to define time, as we always define it as the measure of how fast something happens.

An interesting conclusion from this is that indeed a subjective measure of time might be more appropriate than an “objective” measure (like the Earth going around the Sun), because only the former accounts for the amount of processes that happen inside our bodies. The subjective measure of time relates to our body, but it’s still different to our psychological perception of time. As we know, we believe time to go faster when we’re having fun, no matter if many processes are happening inside our body or not. For more on this, see this passage.

The title of the story is actually a reference to another problem of physics, also called Twin Paradox. While that concept also deals with different time perceptions, it is included in the theory of special relativity rather than in the concept of entropy.

Picture: Public Domain Images – Time Is Running Out, License CC0 1.0