The train finally stopped. After hours of sitting, she was free. She had been desperately waiting to arrive, checking the time and location again and again. Yet, when the moment came, she didn’t rush to get up, grab her bag, and leave. If it wasn’t for the young man beside her who wanted to slip out fast, she might have stayed longer. Did she really want to leave, or just like knowing she could?

Stepping out of the station, the first smell of the city hit her: weed. “Yukh. I missed this,” she muttered. Taxi drivers stared into her eyes, shouting offers. Too tired to even say no, she pretended not to hear and dragged her suitcase away. Its wheels rattled loudly on the dotted sidewalks. In airports and stations, a suitcase glides with ease. But out here, every meter was a fight, like a punishment for not taking a taxi.

As she walked past the stores, something caught her eye. Evening was settling in; shops were closing. One clothing store had forgotten to dress the mannequin after selling its shirt. Its bare chest stood awkwardly in the window. She smiled, amused by the silly scene, and quickly snapped a photo. She thought of a funny caption and opened her messenger. But he wasn’t pinned anymore. They weren’t talking. Her smile faded. The suitcase noise no longer bothered her.

She gave a fake smile to the concierge, pulled out her keys, and unlocked the door. “Hello,” she whispered into the empty apartment. The thirsty dieffenbachia in the corner seemed to greet her back in silence. She tossed her keys onto the table, the usual spot. For her, home was a place where you could throw things down without thinking: keys on the table, clothes on the floor, yourself on the couch.

Back in her small, safe room at last. A place where tears never needed a reason, and even if they did, the room had plenty stored. It had seen her try so hard for an exam she still failed. It had seen her heartbreak after countless late-night chats and flirty hours that blurred into dawn. It had been there through happy-ending movies on her laptop, while her own stories never seemed to end that way.

to be continued…

Physics and its laws are generally considered to be discovered, not invented. Humans observed the universe, invented math, and over hundreds of years gradually uncovered the rules that govern the world we live in.

These laws are mostly bulletproof. They're effectively true and practically proven. Yes, Newton’s laws of motion break down at relativistic speeds or quantum scales, but in everyday life, physics laws are astonishingly reliable, with no known exceptions within their domains. For example, the Laws of Thermodynamics have never been violated. They’re solid as a rock.

But, funny enough, the reverse isn’t always true. Even though we extracted these rock-solid laws from the fabric of nature, not everything around us behaves so predictably. Some things are completely random or so chaotic that you can’t find even the tiniest consistent pattern to call it a law. But what about those things in life that seem solid?

---

Long-distance relationships are... brutal. Before I experienced one myself, I was pretty sure I couldn’t handle it. In my opinion, it’s like stripping away most of the beautiful parts of a healthy relationship, intimacy, physical touch, lovely looks, going out, deep conversations, and compressing what’s left into a fragile, often misunderstood form of communication, texting.

It takes a lot of effort, energy, and dedication from both sides. I truly admire the people who manage to keep it going. Because the truth is, when you're thousands of kilometers apart, there’s almost nothing you can do.

I spent months in a long-distance relationship. As I expected, it was incredibly hard not being able to hug the person I loved, hold her hand, smell her hair, or even just look into her eyes instead of a screen. The separation was real. Solid. Bulletproof. Until one night.

You know how your phone automatically goes to sleep if you don’t touch the screen for a while? Some apps, like YouTube, prevent that from happening when you’re watching videos. But most apps, including Telegram, don’t stop the phone from sleeping.

Except… there’s a special case.

When you send a GIF to someone in Telegram, as long as it’s playing on the active screen of the chat and hasn’t been scrolled away, Telegram prevents the phone from going to sleep. I suppose the developers thought users might want to watch GIFs like they do videos, without constantly tapping the screen.

One night, we were talking. It was late in her time zone. I sent a GIF. It was delivered and seen. But no reply came. I waited. Still nothing. A few minutes later, I asked her a question. It was instantly seen, like she was still there, in the chat. But again, no response. A few more minutes passed. Another message. Seen, but nothing back.

And that’s when it hit me.

She had fallen asleep in the middle of our conversation. There was no winding down, no good night. We were mid-conversation. But exhaustion took over, and she drifted off with the chat still open and the GIF still auto-playing on the screen.

As soon as I realized what had happened, I started sending dot messages “.” one after another, nudging the GIF further and further up in the chat window. Once the GIF was out of view, Telegram had no reason to keep the phone awake. I had just a few seconds left. I sent one last message: Love you. Good night. And then, her phone finally went to sleep, just like her. Nothing was delivered or seen after.

It’s hard to describe, and even harder to believe, but that moment felt like magic. Like I had actually watched her fall asleep, gently leaned in to kiss her forehead, pulled the blanket up, and whispered goodnight in her ear, from 9,891 kilometers away.

Who would’ve thought something as intimate as a kiss or a hug could transcend that kind of distance? It was, by every known measure, impossible until that night.

So yeah, I believe there is always an exception. Even in situations that seem as unbreakable as the laws of nature, life sometimes finds a loophole. A way to make the impossible happen.

I love physics and its rules. But I love it even more when life doesn’t always follow them.

This is my first single-qubit quantum circuit I wrote today:

dev = qml.device("default.qubit", wires=1)
@qml.qnode(dev)
def apply_hxh(state):
    if state:
        qml.PauliX(wires=0)
    qml.Hadamard(wires=0)
    qml.PauliX(wires=0)
    qml.Hadamard(wires=0)
    return qml.state()
print(apply_hxh(0))
print(apply_hxh(1))

It applies a sequence of Hadamard–X–Hadamard gates with optional initial X to a single qubit and returns the resulting quantum state.

I started learning quantum mechanics out of pure enthusiasm. I have absolutely no purpose whatsoever from learning quantum computation. Not everything in life should carry a purpose. To be more precise, not everything in life should start with a purpose. It's not always obvious how a specific path leads to something great.

I believe that's one of the key differences between theory and practice. Mathematicians and engineers. Usually, engineers are building something or improving what they've built. There is always some clear outcome expected after their work. But mathematicians are solving problems or proving theorems that do not have any application at all (for now). They discover new lands we have not yet called home. The fun part is, the technologies engineers use today are the result of the work done by these enthusiastic theorists.

I think this general principle applies to life, too. Our time on Earth is far too short to learn everything or to explore ideas today with the guarantee they'll be useful years down the line. But every now and then, diving into a new science, hobby, or activity completely at random can open doors in ways you’d never imagine. That’s exactly what I’m doing right now.

"The Intouchables" is a great, heart-warming movie that tells the true story of a beautiful friendship.

The film closes with the song "Una Mattina" by Ludovico Einaudi. It's a lovely piano piece. But recently, I realized there's something about that song that makes me listen to it over and over. I'll find myself randomly pulling out my phone in the middle of the day, searching for it on Spotify, and hitting play.

The piece itself is good, but maybe not what you'd call a masterpiece. If you hear it for the first time, you might just think, "Okay, that's nice," and move on. It's not the most amazing piano music in the world or something that immediately gets stuck in your head. So why is it so different for me?

I think it's because those notes don't just carry the music; they carry the entire movie and the good feelings that came with it. Those notes tell a story. Every time the song plays, the final scene of the movie replays in my mind, and I remember how good I felt.

So, maybe the key to making something special is a story, whether it's real or fictional. We see extreme examples of this when ordinary items sell for thousands of dollars at auctions. Winston Churchill's half-smoked cigar (literally trash) was once sold for £12,000.

But what about people? Does hearing someone's life story make them special to us, like that simple piano piece became special to me? Not necessarily.

After all, not every story is special to everyone. Even though Churchill's cigar sold for a fortune, I wouldn't pay a dollar for it. It's not special to me. I think it's the same when you meet someone new. Sure, I'm curious to hear your life story, just like I'm open to watching a new movie, but it doesn't mean it will be special to me. Not yet.

As time goes on and you spend more time with someone, you start creating your own story. You're making your own movie together.

This movie doesn't just have a soundtrack, the music you listen to together. It also has smells, like the scent left on your shirt after a long hug. It has tastes, like your kisses and the food you ate the night of your first kiss. And it has sense of touch, like the feeling when you cafune her.

The scenes of this movie become your memories. That’s the point when everything about that person becomes special. All of your time and experiences together get compressed into these ordinary things: a song, a scent, a taste, a touch.

"Una Mattina" is special to me because it's a sweet capsule of a movie that's one hour and 52 minutes long. But I have other capsules, simple things I own, that hold entire movies stretching for months or years. Unlike "The Intouchables," none of those movies ended well.

And that's why little things are breaking my heart, each in their own unique way.

I've always been fascinated by mathematics. I was never exactly at the top of my class. Not a math prodigy in school or university, but something about the elegance of math and how it underpins the very fabric of nature has always blown my mind.

Sure, when most people hear "math," they think of calculus, integrals, or Fourier transforms, topics that were often despised and quickly forgotten after finals. We rarely use them directly in day-to-day life, or so it seems. But if you dig a little deeper, you’ll find that math quietly powers almost everything around us.

Take Shazam, for instance. The app that magically tells you what song is playing in a noisy cafe. It relies on the Fourier transform to break sound into its frequency components. Or consider ChatGPT. At its core, it runs on complex neural networks and transformers, which are essentially large-scale matrix operations, a pure expression of mathematical beauty.

The deeper you dive into math and computer science, the more you start seeing everything as a system to be modeled, optimized, or hacked. Years ago, I had this idea to exploit ride-hailing pricing algorithms using chaos theory. Another time, I used Laplace’s theorem to improve how to rate and choose products to buy. It started as a personal hobby, but when I casually shared these ideas on a second Twitter account, people loved them. They followed, engaged, and began using what I built. It was and still is a fun and surprisingly rewarding experience.

Then something shifted.

While reading Algorithms to Live By, a particular chapter on sorting caught my attention. It explored how we organize and rank things in life, and naturally, it brought up sports leagues. The whole purpose of a league, after all, is to figure out who the best teams are, efficiently. Computer science gives us several optimized approaches for that: single elimination, Swiss-system, etc. Formats that avoid unnecessary comparisons.

So why on earth do leagues like the NBA or LaLiga use round-robin formats where every team plays every other team? From an algorithmic standpoint, it's wasteful. It's inefficient.

Then came the golden line of the chapter:

Well, minimizing the number of games isn't actually in the league's interest. In computer science unnecessary comparisons are always bad, a waste of time and effort. But in sports that's far from the case. In many respects, after all, the games themselves are the point.

Leagues use long, complex formats not because they’re efficient, but because they’re fun. Because they build narratives. Because they generate moments. The goal isn’t speed; it’s engagement, entertainment, and sustainability.

And that’s when I realized: sometimes, math doesn’t need to win.

That moment felt like something new. For once, the powerful tools I’d always trusted didn’t really matter. And you know what? That was okay. Not everything needs to be faster. Not everything needs to be smarter. Sometimes, we just want to enjoy.

Show me the longer home route so I can finish that song I love. Recommend me a movie that's nothing like what I usually watch, maybe I’ll discover something unexpected. Find me that overpriced hardcover book, even though my Kindle is fully charged, just because I want to feel the pages in my hands.

Maybe life isn't always about being fast, cheap, or efficient. Maybe sometimes, the best choice is not to optimize at all. Just let it be. Forget the tools. Forget the rules. Just live. Who cares?