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.