Graffiti for infinity
For reckless teachers who do not hesitate to leave the classroom door open so that their students' imaginations can fly off to infinity
OF COURSE! I expect you would rather I started by telling you how tall I am, how much I weigh, and what colour my skin and my hair are. What a load of crap! I couldn't care less about any of that. Don't expect me to send you my latest selfie, either; it's none of your business if it was on an exotic beach or behind some stinking rubbish bins. You can forget it because I don't have Insta. I can't think of anything more hypocritical than a selfie on the internet. Don't expect any of that bullshit from me. The last thing my self-esteem needs is to see myself posted there with a disgustingly low number of likes that objectively quantify the immensity of my loneliness.
What I want to tell you about happened quite recently at the entrance to my high school. There I was, waiting for the door to be opened. Despite being an early September morning, the heat of the sun on my back was making me sweat badly. I impatiently listened to the still distant, dragging footsteps of the caretaker approaching desperately slowly. It was only the fact that he gave off a discreet scent of cautious intelligence that prevented me from classifying him as a troll from a Tolkien book. Double turn of the key, the creaking of the hinges and the heavy swing of the door. Now, if you were thinking that the guy would let me in with no further explanation, you must be crazy.
"You can't come in. You're late," he announced, more than predictably. Pick any big guy who is tall, fat, mean-spirited, and squint-eyed, and all you can expect him to say is "You can't come in". How original, Jesus Christ!
"Keep your hair on! I had an accident. I've got the pieces in here," I replied, showing him the tiny box that held the remains of the disaster. He hesitated so I shook it to make it clear that it was not empty.
He remained where he was, undaunted, blocking the way, apparently unmoved. Even so, small details betrayed the intensity of the desperate inner crisis he was undergoing as his neurons struggled to engage in the sort of mental reasoning to which they were unaccustomed and that may even have been beyond their cognitive abilities. Although his attitude was clearly one of total passivity, the physiognomy of the owner of that big head began to slowly mutate. The thick, bushy eyebrows, which were determined to join into one, were frowning. His eyes, small and endowed with semi-independent life, searched restlessly and individually for a safe place to focus. A vein, once invisible but now thick and violet, throbbed on his forehead with increasing intensity and rhythm. You could even hear the cogs whirring in his brain as he decided what to do. However, school gossip says that he's only messing with us, that his parsimony is feigned, and that he has a Tik-tok account that is all the rage. Just thinking about it is pathetic. You have to be very cruel to spread a rumour like that; and even crueller to graffiti it on the door of the toilets. What if it turns out to be true! The guy kills me.
"Go to the technology lab. You'll find Dr Vidal. She'll know how to repair it," he finally announced in his cavernous voice. So much drama for such a simple conclusion. What a character Polybius is! This is what we call him at school, although I don't know anyone who dares say it to his face.
As if making an infinite effort, Polybius slowly began to get out of my way until, an eternity later, my path was free. As I passed him, a serious, impassive, inquisitive blue eye never stopped scrutinizing me for a second. The other eye completely ignored me and began to follow the happy and capricious zigzags of the cloud of flies trapped in the gravitational field of his huge head. He is a real pro, the damn lord and master! Believe me, Mortimer is a novice compared to him.
You may have assumed that my institute was surrounded by bucolic garden areas, with large interior spaces, laid out along wide corridors generously bathed in natural light, and that the classrooms and laboratories were equipped with the latest pedagogical tools and technology, very up to the minute. If that's what you thought, then you're crazy. Let me remind you that this is not the United States of America or Australia; this is Europe. But not the bucolic Europe on the banks of the elegant River Cam, where educational institutions can be proud of their beautiful English Gothic architecture. This is poor Europe, in the southwest, where we still haven't decided whether we are at the bottom of the pile of the old continent, or at the top of the black one. If you ask me, I proudly vote for the second option.
My school is a former Franciscan convent. It lost its status as an ecclesiastical building after the famous confiscation by Minister Mendizábal in 1836. The unexpected availability of spaces to citizens inspired some enthusiastic local politicians to endow the city with a great public school. It was a magnificent project, with a ridiculously low budget. It is fair to acknowledge that the improvements made at that time served to adapt the building to its new purpose and, with no further work, have provided for the education of about seven generations of students so far. The following leaders of the local government, worthy acolytes of their predecessors, have managed to keep the flame of the initial spirit burning, prioritizing any initiative that would minimize budgetary costs over any other criteria, whether pedagogical or merely functional.
Since then, the only real improvements made have been that the building has been provided with electricity and running water. To make these improvements obvious to anyone who visited the educational institution, all the electrical and plumbing fixtures were clearly visible, and present in every corner imaginable. There is not a single wall that is not criss-crossed by bundles of cables in all directions right next to the water pipes. Maybe it was all intentionally designed to improve the psychomotricity of the users of the building because in some corridors and entrances to rooms you need to jump over the wiring that crosses your path as if it were a death trap. The arrival of telecommunications did nothing but add new lines of wires that happily joined the existing chaos. As is only to be expected in a country renowned for the plastic artists, these wires merely made an aesthetic contribution, and were no guarantee of efficient connectivity to internet.
Now that you have some sort of idea of the kind of mess my institute is in, you will not be surprised if I tell you that I had to cross the cloister, climb the great community staircase to the upper cloister and go up another small, dark staircase before I reached the old monastic attic room.
On my way I didn't meet a soul. The only company I had were the fragments of learned discourse that came to me through the closed doors of the classrooms I passed. These fragments were brief, fortuitous and on a wide range of subjects, and so made up a kind of disconcerting sermon that was completely empty of content although, strangely, not unpleasant on the ear. I would swear that this is how politicians prepare their electoral speeches. I know nothing more hypocritical than politics!
As I was saying, I wended my way to the attic. Inhospitable and isolated, it had been considered the most appropriate place for the brand new technology laboratory, Dr Vidal's kingdom par excellence.
I don't mean that she is a proper doctor. At least not the kind of doctor who cures you and gives you injections in the hospital. She has a doctoral degree in science from some university that I don't remember right now. Honestly, it is shameful that I don't know which one because she's constantly telling us about it. In fact, she mentions it whenever she can which, by the grace of God, happens to be very often. Some very important university, I suppose. At least for her, of course. The fact is that we are not allowed to address her with the usual terms of Mrs, Miss, or even Teacher. She is Dr. Vidal to her friends and everyone else. We students don't feel too comfortable being so formal. We refer to her as DaVinci or, if you're one of the newbies, more explicitly as the Techno teacher. Some bright spark noticed a certain homographic relationship between Dr Vidal and DaVinci, and a certain affinity between the content of her classes and the outlandish inventions of the illustrious Renaissance man. That's not to say DaVinci is a striking nickname but it caught on. I'm sure that if she found out, she would be very proud that we identify her with such an important figure.
The stairs I had just climbed led straight into
the laboratory, without any need for a hallway or door. As I say, the work on
the building had been kept to the bare minimum. She had her back to me and was writing
on the blackboard. I read
That was just typical of DaVinci. She was always writing a word, which meant God knows what, and a name. Just with that she probably had all she needed for the next class in the lab.
Other teachers would use a book. Not her. It was not her style. In fact, the experiment she prepared for the first class of every year involved burning the technology books that we had brought from home. Apparently, in the old days, pigs were slaughtered in the monastery attic and then the sausages were made. The fireplace dates back to that time. When she found it there, DaVinci simply put it to a new use. It wasn't that she didn't like the book because it was outdated or inaccurate or boring (which it was). As she said, every year she was required to choose a manual, so she tried to select the one that burned the best. It can't be said that she is a hypocritical teacher. You could use any adjective to describe one part or another of her complex personality except hypocritical. But when it came to the crunch, the so-called burning turned out to be a farce, a sham in which the flames never touched the paper, a pedagogical metaphor, a scandalous pantomime for didactic purposes. According to her, we should not let anyone decide for us which books we should read, and that we have to write our own book.
"What can I do for you? The next class is not for three quarters of an hour. Besides, you are not even in the group," she snapped without turning to look at me.
This woman freaks me out. I have no idea how she does it. But this time I decided I would give myself the pleasure of turning the tables on her.
"Good morning, Dr Vidal. I came to show you something," I said while I innocently made to move towards where she was standing next to the blackboard.
Before I could take even the first step, she was already turning abruptly towards me. Her hair twirled around her face because of the speed of her reaction; her white skin was now almost transparent; her black eyes were popping out of her head; the nostrils of her aquiline nose were dilated; her smile was frozen in a kind of wide and manic rictus. The scream that accompanied her dramatic manoeuvre began somewhere in the inaudible range of the ultrasonic scale and ended up drilling my eardrums, piercing my body from top to bottom and shaking my intestines. With my feet stuck to the ground, I apologized as casually as I could while I took the phone out of my pocket and put it in the lead box on the floor at the top of the staircase that led into the laboratory.
DaVinci is a staunch advocate of a strange theory. Our organisms are electrical entities. If they are permanently exposed to artificial electromagnetic fields, our metabolism becomes unbalanced and we are less able to respond to aggressive external agents such as viruses or bacteria. We tend to disagree with her on this point. Last year, to clarify the issue, we organized an investigation into the studies available on the internet and concluded that the World Health Organization has found no empirical evidence to prove what DaVinci tells us. Our conclusions could hardly be said to have impressed her very much, and she remained unmoved in her opinion.
"Mobiles cook your brain! It is up to you what you do with your body, but in my laboratory I do not want devilish machines. And that's it!" she concluded unilaterally and unreasonably.
DaVinci is a bit odd. You'd be crazy not to notice. However, as long as all mobiles are locked in the lead box at the entrance, she is a good teacher.
Without further ado, I went over to show her the contents of the small box in my hands. Still trying to get her breath and dignity back, she looked at it with evident disinterest.
"Broken hearts are not my speciality. Go and find Basilio. He'll know what to do. Now, please leave me alone."
As I returned to the darkness of the staircase
and retraced my steps, I could not help thinking of him, of us. I see the two
of us, him and me, sitting on the rocks listening to the waves breaking on the shore as we hold
hands and share the book. The Old Man and
the Sea, One Hundred Years of
Solitude, The Unbearable Lightness of
Being. The sun inexorably sets and deprives us of light, the playful sea
breeze ruffles our hair and turns the page over. I listen to you and me,
reading Blood Wedding.
ME: You're in a hurry?
YOU:Yes. I want to be your wife, and be alone with you, and hear no voice but yours.
ME: I want that too!
YOU: And I only want to see your eyes. And for you to hold me so tight that even if my mother, my dead mother, called me, I could not break free of you.
ME: My arms are strong. I'm going to hold you for the next forty years.
My memories vanished when I returned to the warm atmosphere of the cloister, I was blinded by the light and suddenly broke into a sweat. I took a deep breath to regain the composure I had lost for a short while. Basilio teaches Classical Literature. His subject is optional and no one has enrolled on it for years, so he's always hanging around the library, which is also in the cloister but in the opposite wing from where I was at the time. That was where I headed.
As I walked around the cloister, I could not
help stopping when I passed the management offices in the monastery's old
chapter house. If you think that I stopped in deference to authority, you're out
of your minds. It was out of respect for the graffiti on the wall not the
academics on the other side. The graffiti covered the whole wall including the doors,
notice boards, and passing cables and pipes. It just appeared there one morning
and it caused quite a commotion. The headmaster and the head of studies were
both outraged and decided to have it removed immediately. With the support of
some of the teachers, the students rebelled. In the end, the school board had
to decide on the graffiti's future. It was a very tight vote. As expected, all
those holding positions of responsibility voted to have it removed and to find
out who had done it. But they lost. The graffiti not only survived, but every
year it's touched up so it doesn't fade away.
Forbidden to forbid
knows where Quino got it from. Perhaps he found it on a wall in Buenos Aires −the
capital of the country where even little children are professional philosophers−
and decided that his Mafalda would proclaim it to the whole world. It was graffiti
that had been painted on the conscience of humanity itself and that no one will
ever be able to erase. It is destined to last forever. For infinity.
I was brought back to reality by the clock of the church bell tower next to the high school striking the quarter of an hour. I continued towards the library, which is in exactly the same place as where the monks had theirs. I would even go so far as to say that the furniture, the shelves and some of the collection were the same as the monks'. Basil might even have been around at that time. He probably used to be a monk and the friars left him behind when they fled. And I shall tell you more. If the school were suddenly closed down, it is almost certain that no one would remember to go and warn him, and who knows how long he would be locked up in there before he realized what had happened.
Next to the library entrance, on the ground of the cloister itself, there is a blackened area that must measure about a square meter that no one ever dares step on. Even newcomers to the school seem to instinctively realize the advisability of not stepping on it. The director says that the monks used to have a confessional there, just in case they needed to ask God for forgiveness for the blasphemies they had read in the books they had just consulted in the library, the only window onto the world that was open to them.
We do not believe her. She is hiding the truth. We all know that the stain is much more recent. In the 1980s, a video game machine was sent to the school by a former student who, when he finished university, had gone to the United States to do his doctorate and had stayed there to work at a software company. As he wrote in his letter, it was a gift in gratitude for the excellent training he had received at our educational institution. You've got be crazy to believe that. It was all part of a worldwide experiment. The game on the machine was none other than the sadly famous Polybius, the one that destroyed the brains of players who got addicted. Although it was only there for a few months, its power was so great that the temperature of the graphic processors burned the stone on the ground. Before the men in black turned up to take it away forever, a few students had already had time to play. There is still living proof at the school of all this. That's right. Polybius, the caretaker, was one of the students who played with the machine. And I have already told you how he ended up. Now you know where the nickname comes from. I must admit that this one is completely appropriate.
I also avoided stepping on the black stain and entered the library, a large, dark room with minimal ventilation where the old book shelves were set up in no particular order to form a maze that is impossible for the uninitiated to navigate. The convent walls are especially solid in this part of the building, efficiently isolating the library from the inevitable uproar of the school's daily activity. Entering the library is like taking a trip to a parallel universe, a calm cosmos not yet overcome by noise pollution. Although there is a table at the entrance to accommodate the person in charge, Basilio has never felt compelled to sit in the chair. Always deserted, the desk reaffirms in the visitor the sensation of having arrived at a desolate place.
"Is anyone there?" I shouted from the entrance itself to announce my presence.
Of course, I already knew there was someone and who it was. I had asked the question so I knew where to find him. I could hear the book shelves carrying my voice from aisle to aisle, as if asking each other, until the question returned to me a little later with no accompanying answer, just as it had come out of my mouth. Given the silence I had received as a response, I chose a random corridor to get lost in. After walking for a while with the occasional company of an anonymous cockroach eager to find out who was disturbing their kingdom, I tried to repeat the greeting, which returned to me, this time with an accompanying answer.
"Oh! It's you. I'm in the Contemporary Mapuche Literature section," announced a voice, which also bounced from shelf to shelf following an invisible route. It was impossible to know where it had originated.
As I did not know where the sections were, I continued walking, randomly turning right or left.
"I can't find you! My eyes aren't used to the dark and I can't see you anywhere," I said, more for the mischievous pleasure of hearing my words repeated hither and thither than in any real hope of finding my incorporeal interlocutor.
"The echo already knows how to do its job well. There's no need to help him with pleonasms!"
That's just typical of him. He loves to use words he knows perfectly well students don't understand. When I tried to look the word up on my mobile, I didn't find it in the usual pocket: I must have left it in DaVinci's lead box. Probably all for the best, I thought. I wasn't expecting anyone to get in touch with me at all that day. And I wouldn't be tempted to read his WhatsApp messages again and again, which obviously wouldn't do me any good at all. Remembering it now, the pain and the indignation overwhelmed me. He has a partner. He didn't know how to tell me. He's very sorry. What we had was just a summer romance. He has a boyfriend. Well I never!
What took me most by surprise was when I realised his profile picture had gone. How can someone be so mean? How can you have the nerve to break up using WhatsApp and block the contact all at the same time?
"I'd better look for you. Where are you?"
I swallowed, stemming my tears and rage, while I looked for a shelf that would help me to say where I was.
"In the section Altruistic Economics!"
Still under the influence of bitter memories, I failed to notice where Basilio arrived from. Tiny and stunted, his head seemed to be balanced on his scrawny neck. His tiny, inquisitive black eyes peered out at me curiously from behind nineteenth-century pince-nez glasses miraculously perched on the tip of a stylised and surprisingly long nose. I would even say that he pointed his large ears, ostentatiously separated from the skull, towards me at will, while he played with a few thin and endless whiskers that escaped rebelliously from the perimeter of his face.
"What have you decided, then?"
"I beg your pardon? What are you talking about?
"On your last visit here we agreed that when you knew what you wanted to do in life, what you wanted to do for a living, you would come and tell me."
"Oh, that. Yes, I thought that I'd try and find myself a job as a juggler in hell. With snowballs."
"It's too early to be quoting the cynic Rincewind, don't you think? I deduce that you must be here for other reasons."
Somehow he always manages to know who I am quoting. I could have sworn that I'd get him with Terry Pratchett. Without further ado, I simply lowered the box so that he could see its contents.
"I'm afraid I can't help you. Infinity is not part of my field of study. After all, I'm a poet, not a mathematician. You'll have to go down to the basement. Remember to take a gift so that they let you leave later."
"It's the mathematics seminar room in the basement not Dante's inferno," I replied with the satisfaction of knowing that I had successfully identified the literary quote.
"Follow me, I know a shortcut," he ordered, giving me an enigmatic smile that revealed two upper incisors that would barely have fit in an ordinarily sized mouth.
He turned and began to move with short but very quick steps. I wish I had noticed where I was going so I would know how to get around this maze once and for all, but I had my work cut out to follow him, so I had to make do with not losing sight of him.
Actually, he immediately got so far ahead of me that I only managed to see him when he was at the end of the corridor and about to turn left or right. He moved with such agility and speed that I could have sworn he got down on all fours to do it. The only thing I glimpsed was his tail, which he would have defined as murine, just before he disappeared around the corner. Our race ended in a corner of the library where a small opening led to a descending spiral staircase.
"Every now and again all poets need to make a furtive escape to the field of mathematics and this is my secret passageway so that I can do it with all necessary discretion," Basilio explained, waiting impatiently for me to reach the hidden corner. "You can't go wrong. All you have to do is go down and you'll find the basement you're looking for.
And with this, he disappeared without so much as a by-your-leave, and leaving me no choice but to start the descent. It was a narrow staircase poorly illuminated with a dim, sporadic light bulb. As I was going down, I wondered if I was heading to the maths seminar or if it really was a shortcut to hell. Who would I find there? Would it be Charon, Dante's boatman, or Ada Amorós, the maths teacher? I couldn't say which one would be the most dangerous.
You would probably be taken in completely by her kindly appearance. She's a person with a strong constitution, although not tall. Her head seems to be directly attached to the trunk with no need for a neck. Protected by long, arched eyebrows, her disproportionately large eyes are of such a light honey colour that they could almost be yellow and they do not seem to need to blink. Her nose, small and aquiline, was somehow the dominant feature of her physiognomy and managed to conceal her mouth, which may not even have been there. The hyperbolic, flamboyant, and generous hairstyle she favoured could well have been a deliberate provocation and the students, always eager to find an appropriate nickname for teachers, had christened her the Owl.
Despite being fascinating birds, it should not be forgotten that owls have powerful claws at the end of their legs. In Amorós' case, the claws are didactic, and you have to be very careful not to fall prey to them. Her classroom seems to have been invaded by ideas and concepts that wander in search of some distracted mind to attach to, and which have the habit of slipping into your brain without your permission. Trust me, I know what I'm saying. On this occasion the source of my conviction is not some graffiti on the back of a toilet door. It happened to me.
It all happened during the first class on a Monday morning in February. It was a rather unfortunate timetable, more suitable to being seduced by Morpheus than to attending a maths class. Still under the effects of an understandable drowsiness, I had managed to forget that I have been a man of letters all my life. Suddenly a most abstract theorem popped into my head and seized my understanding. The multitude of ideas and thoughts that usually drift happily through my mind were so horrified by the presence of that terrible mathematical concept that they fled in fear from the hippocampus. For a week, the intruder monopolised my mind and ruled over all my attempts at reasoning. It was not until I had managed to understand it and finally demonstrate it that I regained my intellectual life and the literary reasoning that so characterizes me took the upper hand once more. Damn stowaway! Even today I sometimes think that I can hear it hidden in a groove in the temporal cerebral cortex, glimpse it crouching behind the occipital lobe, smell it as if it were embedded in the olfactory bulb, always waiting for an opportunity to counterattack.
Luckily, the descent down the spiral stairs did not bring me into contact with any undesirable who I owed money, and the corridor at the foot of the stairs did indeed lead to where Basilio had said it would. Before giving Charon the chance to appear by surprise, I went into the old basement that had once been the monastic cellar, and which today was presided over by a sign that announced I was entering the Mathematics Seminar Room.
"Hi," she replied as she looked up from the book on the lectern in front of her. Please tell me that you've finally been seduced by maths. That would be some good news to start the year. If you want, I have a couple of books...which may tempt you," she said slowly, as if carefully fitting the words into the sentence one by one.
Do you now understand what I was telling you? I had hardly entered the room and she was already trying to drag me to the dark side of the force. Believe me, the less you talk to her the better, so once again I just showed her the contents of the box I was carrying so she could come to her own conclusions. To see it better, she climbed down from her perch on the stool, where she loves to rest. She walked slowly, like a fat owl that had eaten so many mice it could no longer fly.
"It's a broken heart, shattered into an infinite number of pieces. And what do you want me to do with it?"
"I was hoping you would tell me how to repair it."
"I'm afraid I can't. A broken heart can only be repaired by its owner. What's more, given the state it's in, don't be surprised if it takes you forever."
"And how will I know when I've done it, that it is my heart again?"
"As it's broken into an infinite number of pieces, it can be reconstructed an infinite number of ways. But don't worry, they're all yours, they're all equally valid. And don't forget that while you're repairing it, it might fall apart and you'll have to start all over again. Life is often nothing more than that. We spend it healing the wounds that have been inflicted on us while we are learning about ourselves, discovering who we really are. And if we're lucky, we find someone to share it with. Someone with whom we can swap pieces of a jigsaw puzzle and build a heart between the two of us. Someone who loves us. Someone we love. And someone with whom we can make our ephemeral existence a full life experience.
The Owl knows how to give advice. You have to give her that.
I was soon back in the warm atmosphere of the cloister, sweat pricking my skin again. The interior of the cloister, once a well-kept garden with a discreet fountain for washing away sins, was now a small jungle abandoned by the gardener and choked by weeds. It seemed like a good place to hide, think and decide what to do next.
That's where inspiration came to me. Suddenly I knew what I wanted to be in life. You'll say that I have lost my mind, but I want to be a piece of graffiti on a wall. Graffiti that stirs the conscience of those who see it. Graffiti that inspires children and the elderly, wise people and fools, intellectuals and politicians. A piece of graffiti for infinity.
It was almost time for the change of classes. I could have gone to my classroom. I could have gone in and acted as if nothing had happened. But I was not in the mood to be so hypocritical. Any other day I would have been, but not that day. I decided to go back to the entrance to the school. The door would be locked, of course. But the keys are always in the lock, and before any of Polybius's eyes perceived my intentions and made contact with his clumsy brain, I would be out.
"You can't go out. It's not time yet," I heard him yelling in the distance, as was more than predictable, but I already had one foot in the street. Pick any guy who's tall, big, fat, mean-spirited, and squint-eyed, and the only thing he'll say is "You're not allowed out". How original, Jesus Christ!
Before leaving, I turned and yelled as hard as I could:
stood transfixed and, for the first time since I had known him, both his eyes
agreed to look at me at the same time, staring, without blinking. I ran away. I
fled as fast as I could, without looking back.
What's wrong with you? What have you not understood? The end means that the story is over. That's all, there's nothing else. You don't need to carry on reading.
see that you're the stubborn kind. Okay, you found me out. I made it all up. In
fact, I made it all up years ago when I was still at school. That's the raw
truth: I hadn't done my homework and the nought out of ten I was about to be
given would have made my teeth
rattle. I let my imagination run wild, I know that. Of course, the
teacher did not believe my story. I was being sincere when I said that I wanted
to be a piece of graffiti that would inspire humanity to infinity. Oh, and it's
also true that it was terribly hot in that old classroom and that I was
sweating in a bad way. Nothing else. Well, just one other thing but I'm not
going to tell you. It is not my problem if you're dying to know what it is! I AM NOT GOING TO TELL YOU!
First of all, let me point out that proposals made by groups of mathematicians do not have a recognized author. This is the case, for example, of the Pythagorean School: their contributions were not signed by any mathematician in particular, but as a group of mathematicians. For this reason, today many of their ideas are attributed to Pythagoras as the visible head of the group. "Forbidden to forbid" was a slogan for the youth street protests of the late 1960s. In the absence of a specific author, I have taken the liberty of choosing one of the thinkers of the time of whom I am a big fan. I am referring to the great graphic humourist Joaquín Salvador Lavado, better known as Quino. This Argentine, son of Andalusian emigrants from Fuengirola (Malaga), managed to shake the conscience of the world from one of its forgotten corners.
The concept of infinity is abstract and difficult to understand. In mathematical terms, it represents something that has no limits or which is greater than any real or natural number.
Zeno of Elea, a philosopher who lived in the fifth century B.C., explored the concept of infinity and proposed a number of paradoxes that contradict our daily experience of physical phenomena. According to these paradoxes, Achilles, the fastest runner of his time, should not be able to overtake a turtle running just a few meters ahead of him. The reason is that Achilles, fast as he is, would take some time to get to the point where the turtle started from. In this time, the turtle, slow as it is, would have moved a certain distance. Achilles would again take some time to reach the new spot where the turtle had been. And again, the turtle would have moved a certain distance. In short, Achilles would always be behind the turtle because during the time he takes to reach the new point where the turtle had last been, it would already have moved to a new point further away.
You can experience another of Zeno's paradox with your own fingers. Place two fingers a certain distance apart, any distance you like. For example, suppose you place them 20 centimetres apart. Now divide the distance between your fingers, and bring them closer so that you halve the initial distance. That is, they are now 10 centimetres apart. Divide the distance by two again, and bring your fingers closer so that they are now 5 centimetres apart. Keep repeating the process of halving the distance between your fingers. Every time you do, they will always be half the distance they were before. The conclusion is that, although your eyes and touch tell you that sooner or later your fingers are touching, in fact it is impossible for them to touch, since you have only brought them closer and halved the distance between them. Complicated, right?
Zeno's paradoxes are based on the idea that space and time can be infinitely divided. He was the first to realize that the idea of infinity is complex. His work is the first example of infinitesimal reasoning, which was developed into infinitesimal calculus by Leibniz and Newton in the seventeenth century. George Cantor, a German mathematician who lived between 1845 and 1918, proposed that some infinities are larger than other infinities, and even assumed the existence of an infinity of infinities.
In 1924 the mathematician David Hilbert proposed the paradox of the Grand Hotel, which shows that a hotel with infinite rooms, all of them occupied, can continue to welcome new guests. It can even welcome an infinite number of new guests. That said, and with Hilbert's permission, personally I would rather stay in a less busy hotel, in case the cook has not accurately calculated the size of the guests' infinite appetite for breakfast.
If you want to learn more about infinity, a must read is A Brief History of Infinity: The Quest to Think the Unthinkable by Brian Clegg. His explanations will be equally interesting to mathematicians, philosophers or curious onlookers who want to know more.
Although in the story you have read Basilio apologises
because, as a poet, infinity is not part of his field of study, the truth is
that infinity is also present in art and poetry. Elisabeth Bartlett, an English
poet born in 1924, expressed the complexity of infinity with these verses:
Because I longed
to comprehend the infinite
I drew a line
between the known and unknown.
The concept of infinity has inspired many famous quotes. Surely you know the line quoted by Buzz in the animated film Toy Story: "To infinity and beyond". My favourite is by Stephen Hawking, who said: "In an infinite universe, every point can be regarded as the centre, because every point has an infinite number of stars on each side of it."
You see, thanks to infinity, you, the reader, whoever you are and whenever you read this text, and I, who have written it right now in Reus, are both the centre of the universe.
Urbano Lorenzo Seva, Reus 2020
Translation by John F. Bates and Urbano Lorenzo Seva