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 

Twin Paradox (Part I)


At 8.00 am, UK time, the voice of the mother reached the twins. For the inexperienced observer, a mirror situated in the middle of the room would not change the sight of the two young men getting out of bed. Genetic coincidence, the same house, the same school, and all the factors that shape a person played a role in this, but in quite an unusual way. After all, Albert and Isaac were quite different from each other.

The moment the zygote containing both of them had split into two, they stopped being the same, due simply to the impenetrability of their bodies. They could never be in the same place at the same time. Ever. From that first moment, the variation of nutrients in different points of her mother’s womb made them unique and distinct. The alikeness between them was actually something learned.

From the moment their parents first talked to the twins, they always told them they were different: they would go through different experiences, listen to teachers who would explain they were different, and date girls who would swear they were different. As everyone had insisted so much on how different they should be, the only way the twins could be independent from what other people said and thought, was to be as similar to each other as possible. So they unconsciously tried to act the same while they were together, and then lived completely unrelated lives when they separated.

That morning, after having identical breakfasts and exchanging equally incomprehensible monosyllables with their mother, they left the house taking opposite paths. They both knew what the other was up to, and they both knew they didn’t want each other’s company.

Isaac had just gone through a break-up, and for him nothing made sense. I don’t want to say that there wasn’t anything in the world he could relate to. No, not at all. What I mean is that nothing, doing nothing, being nothing, made complete sense to him. That empty silence filled him and fulfilled him. He just longed for the day to consume itself until he could go back to bed and sleep, not to feel, not to do, not to be. It was the exhaustion of just being there during his waking life that got him tired at the end of the day, and gave him a peaceful sleep, free of painful dreams.

This was surprisingly easy for him to do. As long as nothing posed a challenge, as long as nothing was unexpected and his body didn’t have to react to any stimulus, he was just fine. He looked for a quiet coffee place and sat there, his back towards the clock, friend and enemy at the same time.

There was a strange beauty in the normally ugly streets. He was there, contemplating them with no rush or urgency. His sight wasn’t going to change in hours, so he could appreciate colours he wouldn’t normally see, faces he would ignore, gestures that would remain invisible.

At some point, he realized it was dark already. It all had happened so slowly he hadn’t realized how much the streets had changed. It was only when the street lights switched on, that he turned around and faced the clock, marking 6.40 pm, UK time, same time for UK time zone.

He was fortunately late for dinner, and he rushed towards home, getting there at 7.00 pm. UK time, same time for UK time zone, considering the watches are perfectly synchronized with Greenwich official time.

At the other side of the city, Albert aimed for a productive day, and opened his physics book at the library. Now, if you wonder why a person would wake up at 8 am on a Saturday to study physics outside the exam period, and you can only think of one reason, that’s the one. So he needed to learn something, at least the words that would make him sound like he knew something.

Among all the concepts that didn’t catch his fragile attention, the entropy stood out as something more tangible. Entropy, the measure of disorder or homogeneity, of those things getting more messy and more mixed in our life. Entropy as the measure of how fast things get mixed, how fast first love happens, how fast a relationship breaks up. That he could understand.

He didn’t wait to learn the applications or implications of the concept. The moment he grasped slightly what entropy was, he couldn’t wait longer, and he ran with that certainty to Suzy’s place. He looked at the streets, almost with the same attention that at the same time his brother Isaac was looking at them. They saw the streets in the same way, but for different reasons. Isaac couldn’t stand being anywhere else, Albert would have never forgiven himself being anywhere else.

Suzy opened the door and invited him to enter. He opened his notebook. She opened his shirt. And in a minute there were no notebooks, no clothes, and no one else in the world. Their skins on the couch, the hands on the shoulders, the foreheads together. So many things happening, and yet for a minute no one made a move.

Second part and scientific rationale coming next week.

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

The Fillers (Part II)

Burning Field.png

Dear son,

We are safe one more day. After many losses, much pain and hunger, we rest at the headquarters. Tools and weapons have come to help us, but nothing gets easier out there.

Last month Fillers cornered us on Millennium bridge. I pushed, punched, made my way out, but Helen didn’t move. I thought the stress had finally got to her, but she knew better than I did. “Their skin”, she said. It wasn’t easy to pay attention to the ten faces that were suffocating us, yet I saw what she meant. Apart from especially empty, those faces were especially shiny. The few sun rays that came through the clouds reflected on them with a thousand glitters. Worth looking at, not worth dying for. I grabbed Helen’s hand and jumped into the Thames.

Helen had an idea, but she didn’t have the time or the energy to do something with it; none of us did. Still, every night she would go to bed later, and wake up earlier every morning. Two weeks later she held a pair of filtered glasses on her hand. They were nothing short of a marvel. The image of a person was no different, but the Fillers looked shiny through them, even in the darkest nights. Quite handy when you have to choose whether to shoot a running silhouette. It was a little victory, a compensation for past and future defeats.

The following week a huge mass of Fillers followed us to a potato field. We had barely collected some food when they came upon us. The potatoes would entertain them, but they would also make them multiply. With a can of gas and a couple of matches we burned the work of months. The explosives didn’t hurt, either. The fire got rid of some Fillers, but the rest followed us, not because they were angry, but because the only food within a five-mile radius was in our bags.

We ended up in prison. While burning crop fields was a crime a long time ago, now it’s considered humanitarian work. Prisons, however, are among the few places that still hold in one piece. This one was still full: nobody had given any order regarding the prisoners. Now the Fillers had come to the gates, and there was only one way out.

“You have to get them out. Now!”, I said to them.

“But we didn’t receive any order from the government”, said one of them.

“There’s almost no government left”, added Helen.

The guards nodded, but didn’t make a move. Nobody knew what to do, so I stood in the middle of the cell block and shouted at prisoners and guards alike.

“Listen to me! I don’t care what you did, nobody does, not any more. Whatever your crimes were, you’ve paid enough for them. We all have. We did some wrong in our lives, but we also did some good. If we deserved to be punished, we now deserve to be rewarded. But make no mistake: our reward is not a comfortable life. Our reward is this chance to fight!”

The guards opened the cells. Angry prisoners burst out of them looking for blood. Thankfully it wasn’t our blood they were after. They too had lost many loved ones to the Fillers.

It wasn’t an easy fight. Every time we took down a Filler six others surrounded us. I punched and I kicked until I was out of breath, and then I kept fighting. It was around midnight when we made it to the other side of the burned field. We ran once again away from the danger. That open field was our reward.



The Science behind the Story

The Fillers stand as a metaphor for cancer cells again, and all the considerations from part I still apply. The first new bit in this post refers to Targeted Cancer Therapy. This approach consists of creating new drugs that target only cancer cells, in contrast to chemotherapy. Normally these drugs act on the surface of cancer cells. That is why in the story the detection of Fillers through filtered glasses depends on the reflection of light on their skin.

Burning the fields in the story compares to Hormone therapy. This treatment reduces the natural production of some hormones that cancer cells use to grow. Inevitably this is also harmful to the healthy cells that use these hormones for their regular functioning.

Finally, the prison incident refers to Immunotherapy treatments. Most of these treatments stimulate white cells in the body. However, some of them also use viruses that fight cancer cells, and also make white cells more active (hence the pep talk to the criminals/viruses, who had caused some trouble before, and the confused guards/white cells).

Photo from Wikimedia Common, Public Domain.

The Fillers

guy dark room

I love you, son. I thought I’d write that first. I don’t know how much time I have left.

Fillers have surrounded this abandoned house. Their breath condensates on the other side of the window. They don’t want to enter, yet they’ll still burst the door open. Helen and I left some Slime at a corner in Soho. The place was empty for a minute. Then Fillers came out of nowhere, rushing after us. I’m sure the Slime got to them, but it’s still dark and too early for it to react to sunlight. If I don’t make it out of here, I want you to know how this war is, how to fight when your hands can hold a weapon.

I was one of the first to spot a Filler. He bumped into me and everyone else on that street. He didn’t turn back, or listen to the angry shouts. He kept going, and kept eating from his shopping bag. He looked like any other man, he moved like any other man, but he didn’t listen or talk. He just ate and walked.

It wasn’t long until more of them appeared. They didn’t attack us, but they didn’t stop at anything to get their food. An unconscious force drove them around with no direction or purpose, and dragged them to consume more and more. They didn’t acknowledge each other, either. And yet, their women got pregnant faster than I’d ever seen. They gave birth in the street, and their children walked half an hour later.

Experts talked about an infection, others about some change in climatic conditions. The truth is nobody had a clue, and nobody dared to attack them. They were still human, or so we thought.

One day a crowd of them took Trafalgar Square. A few people got trapped between them. Fillers just took the space and squeezed men and women until they couldn’t shout any more, suffocating them, making them bleed from the pressure. That was the call to action governments were waiting for, but it was already too late.

The army first got rid of the ones on the coast. Soldiers dragged Fillers with bulldozers into the sea until they all drowned under the water. Some people said it was inhumane, but son, you should have seen the Fillers’ empty faces. They didn’t fight, they didn’t struggle. They just died as they had lived: trying to consume everything around them.

Filler pregnant women were the next target, as there were so many of them. People attacked pregnant women without asking first if they were still human. That’s where we lost your mum and your sister. Many women fell that day, and there was no one to blame but the anonymous crowd. No woman got pregnant after that, and our numbers went down ever since that day, while theirs grew and grew without control.

Then came the RT units. They bombed every place where Fillers gathered. They got many of them, but some of us, too. Still many Fillers were dispersed among us, and we had to fight them one by one.

A month later Helen came up with the Slime. Son, you must learn how to use it: it’s no toy to play with. Only use it at night time, away from the sun. Spread it through areas taken by Fillers until they get their hands on it. They won’t even notice. Then, the light from the Sun will burn them. Just remember it will also burn you during the day, as it has burnt so many of us already. You’ll learn the rest with time.

The door is about to give way, but it’s still holding. The first ray of sunlight is coming through the windows, and some flames are lighting our way. We’re still in the fight. It’s time to go for a morning run. I love you, son.

The Science behind the Story

The Fillers in the story are a metaphor for cancer cells. It is important to understand that cancer is not an infection, but a group of damaged cells that grow without control. Normally the symptoms appear when that large set of cells interfere with the normal functioning of an organ. As the Fillers in the story, they take the space and the resources without directly attacking healthy cells.

Pushing the Fillers into the sea compares to curative surgery. When the cancer is located in a certain area and hasn’t spread around the body, this can be a very successful treatment.

Attacking pregnant women reflects how chemotherapy attacks cells that are dividing fast. As cancer cells divide very quickly, this treatment gets rid of many of them. Regrettably, it also attacks other cells that divide often in the body. This is why the main character’s wife is also attacked in the story, or why hair cells are damaged in patients undergoing chemotherapy.

The bombing from the RT military units is a reference to radiotherapy. In this case cancer cells are attacked by radiation. While it eliminates many cancer cells in an area of the body, it also inevitably damages healthy tissue.

Finally, the Slime is a reference to a technique called Neutron Capture Therapy. This approach consists of taking a harmless substance, normally boron, and attach it to the cancer cells. Then, the tumour is irradiated with neutrons, that are not dangerous to human tissue, either. When the neutrons meet the boron atoms, a reaction occurs and radiation is emitted, damaging only the cells around, that is, the cancer cells. The problem with this technique is that delivering the boron accurately to the cancer cells is still difficult to achieve.

Some of these techniques and many others have worked very effectively to heal many cancers, and this is the reason why life expectancy has increased so much during the past years. However, as the main character in the story, we are all still in the fight.

Photo from Pixabay. Used with license Public Domain CC0.

Love by Numbers



At 8.05 am, under a 64% cloudy sky and facing a wind of 21 miles per hour, Najwa’s hand rose again between 52 kilograms of luggage, trying to hail a taxi. Drivers kept on picking up people who were faster than her, or ignoring her due to the extensive amount of luggage they’d have to carry.

At the other side of the road Alex rushed into a taxi pushing aside, 80% involuntarily, a man as old as the finest French wine available in the corner store. He was late for an important job interview in which he’d definitely have succeeded, considering the other candidates had broken a leg and run over the interviewer’s dog, respectively. But the 20% that voluntarily pushed the man generated a feeling of guilt that made Alex go back at a slow motion speed and open the door for him. He looked around for the next available taxi, but it was already too late.

He wasn’t late for his interview. Actually, if and only if he had taken the next taxi, a leaf falling from the 37th tree of Hamill street would have hit a little wasp that, disoriented by it, would have flown against the windscreen of a slow driver’s car, causing him to speed up 2 miles per hour, just enough to allow him to get to the next traffic light on time. That event would have avoided a traffic jam, with the global result that Alex would have got to the company building 5 minutes and 37 seconds before his appointment and, after a brief introduction to the woman in the help desk, he’d have arrived to the door of the interviewing room 2 minutes, 12 seconds and half a sigh before the stipulated time. He definitely wasn’t late that way.

He was late though, because he looked at the other side of the road and spotted a graceful hand waving among a mountain of suitcases. As if moved by a rush of 150 milligrams of noradrenaline, he crossed the road at three quarters of the greatest speed ever reached by man, with his heart beating at one ninth the rate of a hummingbird’s. That was unnoticed by Najwa until he hit one of her suitcases with the force of an average sea wave reaching the shore, causing it to tilt half the angle he’d have leaned in to kiss her.

She turned to him and started an insult, moved by the intense anger triggered in the amygdala of her brain. That activity disappeared exponentially fast as Alex got into the middle of the road risking being hit by a taxi that would have killed him four times due to several injuries in the head, the lungs, the liver and the femoral vein. The heart would have been left intact, though.

But the taxi eventually stopped as the driver swore at an average speed of 4.3 words per second. Alex opened the car trunk and started putting the luggage inside as Najwa’s mouth opened to form a 90% perfect circle. He approached her and they stared at each other for a 3 second-long eternity, finally interrupted by the 440 Hertz of the taxi horn.

700 milligrams of oestrogen later, she realized she was 28 minutes, 49 seconds and two potential kisses behind schedule, so she entered the taxi carrying her last suitcase. The driver started the car, and sped off, his stress level at a dangerous 82%.

Najwa looked through the window at the stranger, who was disappearing at half a broken heart a minute. She tore off the label of her suitcase, on which her phone number was written, and threw it out of the window. Regrettably, the combined speed of the taxi and the 21 mile per hour wind was nearly twice the maximum speed Alex could have run, and the paper flew away and away…

… until a 90% happy old man, very improbably the one Alex offered the taxi to, grabbed it from the air and handed it to our 40-milliliters-of-sweat-hero. After all, we cannot rely only on numbers, C4N W3?

Photo: Números by Public Domain Pictures, used with license Public Domain CC0.

The Sky in their Eyes


Adam’s philosophy was literally to always look forwards. Every morning he would get on the 7:54 train, sit down and catch up with the yellow press. He wouldn’t look away from his newspaper until the electronic voice announced his stop. After the day of work and before the sunset, he would sit on his couch, looking straight at his TV. Violent scenes and crimson blood would keep him from going out.

One regular Friday morning Adam walked into the station, bought his newspaper, and headed to the platform. What was normally a friendly empty space was now full of young people who had not yet seen their beds. Adam pushed, and squeezed, and turned around the crowd to approach the rails.

When the train finally came, the crowd dragged him inside, making him drop his paper on the way. Stuck as he was between the people, he couldn’t even take his phone out to read something. He couldn’t even look forwards, as an angry drunk woman stood in front of him. She didn’t look like the kind of person who enjoys staring. So for the first time in a long time, Adam looked sideways.

At his side was Kailee, a Hawaiian girl with blue eyes and bags under them. Adam was aware his first thought was selfish: “What is this person doing in my train?”

The answer to this question was something of a mystery even for Kailee. She went with friends to a concert the past night. The crowd separated them in the middle of the band’s most famous song. She met a cute guy, and ran away from him because he was singing the lyrics wrong. She found her friends again, had a fight because she felt abandoned, and went back into the crowd. She ended up in the train station earlier than she wanted to be. The drunk scary woman pushed her half a meter as she stepped into the train, and that’s where Adam spotted her. Kailee looked into his eyes. Unused to the human contact, Adam turned his head away.

Close to him he spotted Jovann, a short guy with dark blue eyes. A girl had dragged him to the concert, where he had found out she was there to meet somebody else. He stormed away from her, and bumped into a childhood friend. He spent the night with him and remembered their childhood dreams. A girl in the group kissed him in the middle of her musical ecstasy. Then a fight at the end of the concert separated Jovann from his old friend and the new girl. Unable to find them, he walked back to the train station, got in the train, and looked at Adam, who once again looked away.

Sky was not coming from the concert. She had woken up early in the morning, got a cup of tea and got it spilled on her blouse by the pushing crowd. She had missed her 7:48 train and ended up on the 7:54 train that Adam never missed. When their eyes met, Adam couldn’t look away, not this time. Sky’s look seemed to say “I don’t normally spill tea on my blouse”, and Adam’s said “I don’t have anything to do with them”. Sky smiled in understanding. Adam wanted to say something romantic, he really did:

“I dropped my newspaper” was all that came out.

“I missed my train” was her reply.

All his life looking forward, and now Adam couldn’t keep his head straight. Those blue eyes scared him and drew him closer at the same time.

“I’m, I’m glad you missed that train”.

“Me, too”.

One must add for the sake of romantic consistency that if Adam had looked a bit further between the faces, he would have spotted Violet, who was coming back from the concert. Although Adam and Violet would have been attracted to each other at first, she soon would have found him insensitive. “You don’t see me like I am at all!” would have been her final sentence before breaking their fleeting relationship. So it was quite fortunate for Adam to look at Sky instead.

The Science behind the Story

This story answers the classic childhood question “Why is the sky blue?”. The light coming from the sun is a mix of all colours. When this light hits the atmosphere molecules it gets scattered in different directions. However, cool colours like blue and violet are around 10 times more scattered than warmer colours like yellow and red. That is why when we look at the sun, most of the light that comes straight to us is yellow. This is the yellow press that Adam looks at, or in the physical scenario, looking straight into the sun. Please never look straight into the sun!

At sunset, the light goes through more air and the effect is even more pronounced, so the light turns more reddish. This is the crimson blood and the violence Adam watches in the evening shows.

The blue and violet light gets scattered away from us at first, but then it comes back and we see it coming from the sky, rather than from the sun itself. That is why in the story people have gone through lots of random events to get to Adam’s train, but eventually their blue eyes meet Adam.

And the final question: why is the sky not violet? Because just like Adam, we are less sensitive to this colour. There is also less violet in the light coming from the sun, and some of it gets absorbed by the atmosphere, too. This is portrayed by people blocking Adam’s view in the story.

So next time your kids ask you why the sky is blue, tell them Adam’s story and don’t just reply “cause I say so”.


Photo from Pixabay, used with license CC0 Public Domain.

Rigilusburgh Warriors


In the old city of Rigilusburgh, as the legend says, the finest warriors were trained day and night to protect the city. Among them, and as always, there were cowardly and brave soldiers. The brave dreamt of future battles where they would fight with honour, while the coward were quite happy to stay around, showing off and pretending they were eager to go to war. The brave were calm by nature and did not need anyone to tell them what to do, but some insecure cowards came around, and the courage of the brave was such, and the energy of their speech was such, that the coward became brave just by listening to them. However, the brave lived a solitary tough life, and sometimes that was too much to bear. Over-weighed by worries and inexistent battle, they became cowards themselves, and came back to find refuge in the crowd.

One day, because of the prosperity of the city, the soldiers were forced to expand and colonize new territories. They all started together, the brave and the coward, but at the very front of the army, where there were not that many warriors, the brave found themselves alone, some of them becoming cowards, the others finding it difficult to convince others. This allowed the coward to gain advantage. However, close to the front there were still some brave soldiers who tried to call for the ones who were behind them, and made them speed up a bit, because they still could see the new territory, free of human activity, free of cowards.

Regrettably, at some point, the cowards took so much advantage, that the foremost brave soldier could not see the new territory any more, it was all full of cowards. That was a sad day. There was no point in trying to call the others to find a land he could not see. At that point, he decided to slow down and regroup with the other brave soldiers in order not to disappear completely. From that moment on, the brave advanced slowly inside the mass of cowards, trying to convince as many of them as possible, and trying not to become cowards themselves.

Suddenly, the danger came, the enemy gates were reached, and then all the cowards that had thought too much of themselves died easily at their enemies’ hands. They called for the braves, they begged for them to come, but they were far behind, and the Rigilsburgh soldiers died, and the city knew nothing about them.

It was only after some time that the brave slowly caught up and finally found the enemy. All their cowardly friends were piled up at the gates while the enemies laughed from above. That offence ought to be avenged, and it would be indeed. They were brave soldiers from Rigilsburgh after all. They grouped, they fought, they took their bows and arrows, their shields and swords, and the heads of the enemies were rolling down the walls before the night came. The brave soldiers took the wall and saw what laid in front of them. A land infested with enemies, a land for the braves to conquer, and endless battle to fight.

As the braves defeated the enemy, a few cowards joined them after the wall, but most of the territory was still dangerous, and the bodies at the wall put most of them off, so it was only a few of them that were not coward enough to join the brave, and waited there for the moment to become brave themselves, to live in this land of endless battle.

The Science behind the Story

This story, and part of the following explanation, are included in my PhD thesis, published by the University of Edinburgh in 2013. Only a few minor corrections have been added.

I worked on a project that involved the propagation of bacteria that were either susceptible to an antibiotic (coward) or resistant to it (brave). There is a mechanism by which this resistance can be transferred from a resistant bacteria to a susceptible one. It is called horizontal gene transfer, and it involves an exchange of genetic material between individuals of the same generation. In the story this process is represented by the brave convincing the coward.

Sometimes the resistance to the antibiotics is lost, or a brave soldier becomes a coward. This process happen without interaction with other cowards (when the soldiers feel alone). The motion of the warriors correspond to the diffusion of the bacteria, while the growth in the new territory corresponds to bacteria multiplication.

At the very front of the army, the process of brave soldiers becoming cowardly is more intense than the convincing of cowards, and as a result the cowards win advantage. However, there are some brave soldiers in front of the coward mass, and that is why they pull the rest of the brave population, calling for them. Or in scientific terms, the resistant bacteria drag the others forward so long as they are not overtaken by the majority of the susceptible ones.

Nevertheless, the moment the braves are overcome by the cowards front, they slow down and all the brave population goes at a slower speed. This corresponds to the propagation of resistant and susceptible bacteria without any antibiotics barrier.

Finally, when the antibiotic barrier/the enemy is reached, it is only the braves who can continue, and now expand at a much larger speed, happy to fight and live in the new environment, free of cowards. However, there are some cowards who still join them in a small quantity. The susceptible bacteria or the cowardly soldiers would not be able to live in this dangerous environment by themselves, but a few of them survive on the shadow of the braves.

For more on the science of the story, see also the original research paper.


Drawing by Iantresman at en.wikipedia [Public domain], via Wikimedia Commons. PD-US.Source: William Howitt, John Cassell, John Cassell’s Illustrated History of England: From the earliest period to the reign of Edward the Fourth., Editor: John Frederick Smith, Publisher W. Kent and Co., 1857. Page 6.

Quantum Break-up



Two weeks ago at this time I was still with Naomi. There was surprise, anger, sadness, and now all I’m left with are questions. When did the whole thing go bad? When did love turn to hate? When was I wrong? When was I right? The more I think about it, the more I blame the whole thing on her. It was all her fault, yet something bugs me.

“What the hell are you worrying about? She was a bitch!” said Rachel, who had always been on my side, even when she shouldn’t have.

“You really think so?”, I asked hopeful.

“She slapped you, for God’s sake! You know what I’d do if a guy slapped me?”

“She saw me kissing Mary.”

“She saw Mary kissing you.”

“I’m not sure any more. Every time I think of that night-”

“I was there! One second and you pushed her away, how’s that your fault?”

“I know.”

“What’s wrong with you? She shouts at you, she leaves you outside waiting in the rain, and she slaps you. Don’t spend one more second thinking of her”.

Everything Rachel said was true, and so was everything I’d ever told her. Yet, it wasn’t the first time I had that feeling I couldn’t articulate something. Right as she was, Rachel hadn’t been there all the time. She hadn’t seen us in private. She had missed so many inexplicable intimacies, and those unspoken details were now dancing inside my head.

Tony had been a good friend these past weeks. He was playing the neutral game, meeting both of us, but he was Naomi’s friend long before I met him. We all knew he was going to stick with her.

“Just apologise” was his first conclusion.

“Excuse me?” was my reply.

“Apologise to her. Text her or something. Say you’re sorry and then forget the whole thing”.

I wondered if he just wanted to finish our friendship fast, or if he also wanted to date her in the near future.

“Sure. Here it goes. -Naomi, I’m sorry you slapped me. Your hand must really hurt after that. Also, staying in your warm flat at 2 am must have been a pain. You could have been down at the door with me feeling the rain on your skin-.”, I said.

“Who started all this? Who was the one not texting, the one saying I’m too busy?”, he replied.

“Are you really comparing these things?”

“I’m just saying she was lovely to you before you started not returning her calls.”

“You’re telling me everything would have been alright if I had picked up the phone?”

“Yes! That’s exactly what I’m telling you.”

“And she wouldn’t have slapped me, either.”

“Can you really blame her after kissing Mary?”

“She kissed me!”

“So what? You’d been talking to her for an hour leaving your girlfriend alone in a party where she didn’t know anyone else.”

I had to leave the room. This is the kind of bullshit I don’t need to listen to. If it was something I could really blame myself for, I’d take it. I really would. But not this crap. My friend Rachel was right, my soon to be ex-friend Tony wasn’t. That was it. Yet why was there something inside my head still wondering? In these moments of confusion Claire always helped.

Claire’s days were perfectly planned from 8.00 am to 11.59 pm. She wouldn’t waste any time, but she would spend it with me every time I called her. I met her at her lab.

“I don’t know, Claire, I just feel I’m missing something.”

She pointed at her experiment.

“This is a quantum system. Before I send light to take the measurement, it’s in a mixed state. Let’s say it’s not red, or blue, or green. It’s all of it at the same time.”

“Claire, I appreciate you-”

“When I send the light, I can see it with clarity. It’s only blue. Yet, if somebody else had repeated the experiment in the same circumstances, it would be only red.”


“The thing is that once I see it blue, I can’t stop seeing it blue.”

“Claire! I’m not in the mood today. I don’t want to learn all this shit.”

“I’m just trying to help.”

“I know you are, I’m just, ah, forget it.”

I got up from there and left the room. Claire was my last hope to understand, and she was just telling me all this crap about the mixed state, and seeing it blue and somebody else seeing it red, and this, oh, shit. I turned on my feet and came back to the lab. She was already knee-deep in calculations.

“When you said quantum system, you meant relationship?”, I asked.

“Yup”, she replied, still looking at her papers.

“And when you said light, you meant break-up?”


“Was I being a moron?”

“You’re starting to get it.”

“So if I see it blue, could I stop seeing it blue?”

“No, you’ve lost that mixed state. The break-up made it disappear.”

“And another person would see it red?”

“They would.”


“So you learn. If you repeat the experiment with identical systems, sometimes you see it red, others blue, others green. You find out the quantity of them in the total mix.”

“But there are no identical Naomis. All I can see it’s blue.”

“You’d better learn from the blue, then.”

I’d better.

The science behind the story

This story is slightly different to previous ones, as the concept is itself explained in the story through Claire. To put it all in a nutshell, a quantum measurement makes the system go into one defined state. However, before we take that measurement, the system could be in several possible states. That’s why Schrödinger’s cat is often used as a metaphor, as it could be alive and dead inside its box before we look at it. In the story the break-up of a couple is used as an irreversible separation of perspectives. For a comprehensive approach to quantum measurements, see the Wikipedia page.


Photo from Pixabay, used with license CC0 Public Domain.