The final step
In my mind, endings are always grand. They’re filled with balloons, confetti, and a large banner attached to the ceiling that says “We Will Miss You! Best Physics Teacher Ever!” I felt the need to honour my endings so much so that I threw myself a going-away party when I shifted schools after the 8th grade.
But soon after that, I started to detest endings; I realised that they weren’t always joyful affairs like the guard of honour Sachin got in his last test. Sometimes, endings are underwhelming, sans celebration, like how Dhoni retired with a simple Instagram post. They are silent odes that express a sense of gratitude, accompanied by a resolution to move on to other things. That’s what this article aims to be - an ode to Riot and Intricate Connections.
It’s been one heck of a ride. In all honesty, Intricate Connections has been nothing less than a godsend. It’s been a place for me to write whatever’s on my mind. In a world where we have to change ourselves to fit in, it’s been the singular place where I could simply be me without feeling pressure to put on a facade, simply talk about things I want to talk about like maths and science instead of what I’m supposed to be talking about, like college essays require me to. It’s been the place where I’ve written about both my peaceful 11 am thoughts and my insane 2 am epiphanies. It’s been the place that has allowed me to grow as both a writer and a thinker, and it’s taught me the importance of consistency. And I wouldn’t have had it any other way.
And as I write this article at 4 am, things have finally come back full circle. Everything works out in the end, huh?
My final article for Riot would be incomplete without a callback to several motifs that I’ve developed throughout the column. The rants about the evolution of entropy marking the arrow of time (cue “Shut up nerd”) and the quirky mathematical anecdotes about the Collatz conjecture have been all that I have lived for. Intricate Connections would be as incomplete as Gödel’s theorem without consistent references to the heat death of the universe (sadistic? I know). At Its Essence, it’s Perfect.
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I have a confession to make.
When Riot began, we were given the task of coming up with a name for our columns, and I took the longest. It took me a week - or maybe even more - to give this place a name. Nothing seemed to... fit. I want to show you a list of names that I had conceived of, along with abridged comments on each of them courtesy my beloved fellow editor and brilliant best friend, Shravan. Here goes -
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Cathartic Nonsense: gives me chaotic vibes that are kinda comforting too. kind of an oxymoron but I think that fits pretty well! only complaint is that the word cathartic is a bit aggressive, but I don't mind it
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Numbing Silence: gives me emotionless robot-ish vibes, sort of like the moment before an earthquake. sounds like something Oppenheimer would say. very creepy.
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A Solitary Tear: melancholy. MELANCHOLY. guilt about being unable to cry. sad vibes, complex emotions. also not 100% your vibe.
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Perplexed Chaos: not exactly "pretentious" but big grammar vibes. chaos is a bit on the nose but otherwise I like it.
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Chaotic Cohort: not bad, but I feel like this is more of a whatsapp group name than a solo column name
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Mundanity: simple, one-worded. a nice distraction/stand-out from the other parts of riot that are focused on chaos, kind of a straight man character (like someone who remains composed amidst chaos and eccentricity)
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Intricate Connections: feels like a column about discovery and learning. gives off the same vibes as your starry night article, I love this one. seems scientific but also very creative and free
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I want a revelation: gives off a similar vibe to "intricate connections'', but a little less whimsical and more strong because angelica immediately comes to mind, and she's a very firm character. If you're going for something tough, I think this is great.
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Don't Get Me Wrong: simple but very general, and not very easy to find what your column is about. but definitely does give me some refined grammar vibes.
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A Spark of Inspiration: like this one, fits with our logo, pretty general but also seems kinda focused on creativity
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The Inevitable Arrow of Time: what the frick-
As you can see, I was very confused. I didn’t really have a clear idea of what my column was going to focus on; I only knew that I would write what I thought was important to talk about and that my column would have a recurrent interest in STEM. But I didn’t want to be limited by that.
Maybe what took me a week was that I was looking for perfection all along.
Honestly, I can’t tell you exactly why I chose Intricate Connections. It never really felt right either. But it grew on me. And I think I know why.
Notice how it says ‘Intricate Connections’ and not ‘Intricate Things’ or ‘Intricate Objects’; subconsciously, I included what was most important to me. Considering things in isolation just wasn’t that intriguing; it was the relationships and bonds between them that interested me. Making random connections between a merry-go-round and a black hole seemed more like me. And it is these bonds and connections in Riot that have kept me going, day in and day out.
So this is a thank you to those bonds. Without the people at Riot, I doubt we would have been able to make something half as amazing. I don’t know what I would have done without you.
And to everyone who is reading this, whether this is the first time you’re reading my writing or the last, the pleasure’s been all mine.
the next Step
It’s that time of the year again with snowflakes, eggnog, and Spotify Wrapped releases. My Spotify Wrapped said I listened to almost 15 thousand minutes of music consisting of 42 genres, and my top artist was Taylor Swift. Spotify Wrapped announcements mark the beginning of the end, and it was the end of quite a tough year. I don’t want to take this article in the direction of ‘an end means new beginnings’; instead I’d like to take this some other way. 2022 brought with it memories - moments to cherish for a lifetime.
Sometimes, I don’t think I perceive time. At least I don’t like to perceive time. Time is just this concept that keeps going on and on and never stops. It’s the inevitable direction of entropy increase that leads to the eventual heat death of the universe (that was my last physics platitude, I swear). Most of my time is filled with boredom, so I just filter that time out of my memory. But there are some moments when I feel actual emotions (I think I should reassure you here that I’m not Wall-E). And to me, those are the moments worth remembering.
There were different kinds of moments - happy, sad, angry, scary, disgusting, and many more. There was the time I organised an economics fest at school that was proclaimed as ‘the best organised fest in our history’ by our principal. There was the time I received my rejection letter from Columbia University. There was the time I didn’t do as well as I thought I would at the American Math Competition. There was the time I proposed to the girl I liked. And finally, there was the time I tried beer for the first time.
My year was just a string of these moments, making memories that will stay with me forever. Some of them I will hold on to, while some of them I will let go because they aren’t worth remembering forever. The time in between also has some moments, some details that I remember, but I could not summon them to the front of my mind upon request. In my memory, this year was just a haze of countless times like these.
Sometimes, I felt the need to capture a moment as it was, like taking a picture that’ll be framed forever in my mind. It’s those momentous pictures that captured a fleeting moment, long texts that felt like a warm 5-minute long hug, and adorable voice recordings that were music to my longing ears that will keep me company in the days to come.
I also know these moments aren’t the last that are to come, not by a long shot. I might have to purge a part of my memory stick to allow space for new moments to find their place. It’s going to be tough at times, heartbreaking even, but that’s alright. I’m just going to focus on the next moment I have to add to my seemingly infinite string.
My Spotify Wrapped told me I was a Nomad. Let’s see where the next moment takes me.
one step at a time
Winter’s almost here, and it’s my favourite time of the year. Sure; in Bangalore, there isn’t much of a ‘winter’ winter compared to somewhere like Delhi or Shimla, but a mild winter always feels somewhat like a blessing. It’s the time when it’s cold enough for me to snuggle up with a cup of coffee and postpone baths by a week (for legal reasons, I bathe everyday), but not cold enough for me to have one of my trademark sneeze fests. It’s the season of gajar ka halwa and green grapes. And birthdays! There are four birthdays in my family in December, so there’s almost always a slice of chocolate cake waiting for me in the fridge.
Another thing that winter brings with it is fog. I can’t see much in the fog, and it’s scary. But it’s also thrilling. Just the other day, I woke up and there was a thick fog in my area. It was so bad that I wasn’t able to see my neighbours’ house properly. One night it exists, and the next morning it’s not visible. The only thing I could see was the faint neon light of an isolated lamppost in the distance. Even something like a building wasn’t constant and permanent, and just the thought of that felt so scary.
When I’m in the car while we’re driving through a dense fog on a cold, winter morning, I always feel on edge. In Bangalore, you really cannot trust the direction of traffic - even though King George III established left-side driving all across India (the gem of my soul - if you haven’t watched Hamilton, you should), you can always expect to see a Swiggy delivery person riding a bike on the wrong side of the road. All the fears pop up. What if someone drives into our lane without signalling that they are going to? What if someone ordered something from Swiggy nearby? What if?
It’s difficult to take even one step forward when walking through a fog. You don’t know what lies ahead, what awaits you in the ether. It could be good, it could be bad. But Murphy’s law always seems to overpower, and you end up staying in the same place.
Allow me to take a small detour here; it may seem like either one of us is being stupid, but trust me, it’ll start to make sense towards the end. Sometimes, I’m faced with a complicated maths problem where I know the solution, like one of those “Show that” questions where I’m given the right answer and I need to prove it. At first, like everyone else, I’m entirely flummoxed. Often, there’s absolutely no connection between the question and the supposed answer and I usually spend a good couple of minutes contemplating the possibility that the creator of the question was high while making it. It’s around this time that I notice something, a flash of insight, and I begin my journey to solve the question.
Even if it feels like I’m going in the wrong direction, I just dive in, head first. I just keep doing something and hope it takes me the right way. I simply keep going. On average, it takes me about three sessions of pulling my hair out, five of washing my face, and eight of walking around the room aimlessly to clear my head. But finally, I reach the answer I’m supposed to. Turns out, it was all worth it. All the frustrating wrong directions and methods were worth it in the end.
In the fog, it’s not that you don’t know what lies ahead, you just can’t see what lies ahead. You know the building is there, it exists, you saw it last night. You can’t see it right now, but that doesn’t mean it’s gone. Even though you might not see where your next step is going to take you, at least you’re moving.
Taking the wrong direction is not the end of the world. Sometimes, you go the wrong way. It happens, it’s a part of life. All you have to do at that point is retrace your steps and follow another way. Eventually, you’ll find your own right direction. You might have to traverse five wrong paths to do that, or at times, even a hundred, but you’ll find your right direction eventually.
You can’t see where you’re going, but you’re going somewhere. That’s progress. You don’t need to see it all, what lies in store for you a hundred metres down the road; you only need to know where your next step lies. Keep running or walking or crawling. You’re moving. You’re growing. You’re taking it one step at a time. Focus on the next step. And take it. Just keep moving. And it’ll all work out in the end.
I did not write this article while eating cake, I promise.
Just a number
Say the word ‘triskaidekaphobia’ thirteen times. If you do have triskaidekaphobia, by the end of it, I wouldn’t be surprised if you were hyperventilating on the floor.
Why is there such a word only for the number 13? It has a special word, but the fear of any other number is just generalised as ‘numerophobia’ (which I develop in the face of some whacky binomial theorem question in a math exam. Don’t ask).
I find that quite offensive, to be honest. My relationship with the number 13 stretches back a long way - some might even say from the time I was born. My birthday is the 13th of December, so obviously, this number is dear to me. Thus, call it premature or whatever you want, whenever this number is portrayed to be something to be scared of, it feels like a jab through my childish chest.
In second grade, my birthday fell on a Friday. There was this weird buzz around school, kids murmuring at the back of lines, the words of which I couldn’t quite make out. Someone suddenly shouted, “It’s the Devil’s Day today!”, and that got me wondering, “Was I the Devil?” Admittedly, it was not a great thought for an 8-year old with an aversion to horror and gore.
In fact, many people around the world are scared of the number 13. Some buildings purposely have only floors till 12 to avoid having the 13th. Most aeroplanes don’t have the 13th seat. The famous London Eye has 32 capsules in its periphery that are labelled until 33 because the number 13 is omitted.
Puzzled by this seemingly irrational yet universal fear, I went back and researched the reason why the number 13 is so often shunned. The lore traces back to the evening of the Last Supper, where the thirteenth man to be sitting at the table was Judas Iscariot, the supposed betrayer of Jesus Christ. The number 13 refers to this betrayal of the thirteenth member who sits at the table. Given the fact that this superstition emerged aeons ago and it is still followed today, it gave the fear some amount of validity. But it’s still just a number.
I reflected a little on my relationship with fears. I have a fear of fish, I remembered, something I discovered when I visited an aquarium with my friends. I never really thought this would be a genuine fear for me because I never had any extreme emotions towards any kind of animal. But that day when I was faced with the catfish staring right at my face, the irrational fear came to life, manifesting in the form of heavy and laboured breathing.
It then struck me that fears aren’t supposed to be rational. As long as it is real, it is a fear and should be treated like any other fear - with caution. I might fear many things I haven’t even explored yet. Fears are personal, and questioning as to why one has a particular fear won’t help in alleviating it. It’s not just a number; it’s a fear.
Fears don’t make you weak; they make you human. And there is nothing more human than having a fear that you can’t quite make sense of. Irrational fears are human.
On that note, however, I will be dressing up as the number 13 this Halloween, so this is an open warning of caution to all the triskaidekaphobics out there.
Another Life
Have you ever gotten lost at an amusement park as a child? It’s not a very pleasant experience, I must say.
Unknown faces of fast-paced strangers move in a chaotic, turbulent flow around you, while you’re at its vortex, stationary and perplexed. Everyone seems to just take a fleeting glance at you and move on, while you strain your neck upwards and attempt to discern a familiar face in the intimidatingly unfamiliar crowd. There are none for ages on end.
Finally, you make your way towards a clearing devoid of the bustling crowd and try to remember where you last saw your parents. After a time that feels like hours, you see your panicked parents running towards you, calling out your name with a hint of relief on their faces. All is well.
That’s how we feel when we’re trying to search for extraterrestrial life in the universe at the moment, with a couple of key differences - there is no bustling crowd, it’s simply radio silence; we haven’t found the parents yet, they might just be drifting off somewhere; and if sometime in the future we do end up finding them, along with a sense of relief there might come another emotion - fear.
While the prospect of finding alien life might sound exciting, it’s only naive to think that extraterrestrial life will not be threatening to humans as a species. Some might not, but when I picture a UFO landing on Earth with alien organisms swarming out, I don’t picture them with a white flag and doughnuts, but rather with machinery and weapons (and of course, their non-opposable thumbs). If you imagine it to be something else, please let me know.
Nevertheless, the search for alien life is continual and persistent. The fact that they might be dangerous to us doesn’t mean we stop looking for them altogether. The thrill of adrenaline, right?
However, while some researchers and Elon Musk believe that intelligent life other than us exists in this universe, others postulate that this might not be the case. There is a popular theory doing the rounds of the scientific community called the Great Barrier. It states that at some point during the evolution of microorganisms to the complex organisms that we are today, life had to cross multiple barriers in the process. Be it the ability to make chlorophyll so that plants could synthesise their own food or the ability to move from one place to another to survive adverse weather conditions, these evolutionary mechanics made life on Earth more complex than it previously was. Scientists think that while our race could cross all of those barriers successfully, we might have just gotten lucky to have crossed them all; meanwhile, other forms of potentially intelligent life might not have been able to overcome one of those barriers, leading to their extinction.
But I simply think it’s incredibly narcissistic of us to believe that there is no intelligent life in this universe other than us. While you might find me having a hearty laugh at the recent news that life on Mars has been discovered (owing to the fact that I am pessimistic enough to think that we won’t find alien life during my lifetime), I certainly believe they’re there. Somewhere in the depths of the unexplored realms of the cosmos lies some intelligent life outside our species. Chances are that they’re 3 headed, 5 eyed, and 7 footed, with an appearance that scares the living hell out of every toddler in the world. But they’re there.
They have to be.
dumb ways to die
Formal warning: reading further than this might lead to long-lasting existential crises.
Welcome back folks, and it’s that time of the month again where we attempt to answer another one of our age-old questions that have absolutely zero impact on us - how are we going to die?
Quite the nihilistic conundrum isn’t it?
I’m not talking about you and me here, I’m talking about this universe as the whole - where and how will it end?
Proponents of scientific theory propose three major ways in which the universe could end - The Heat Death, The Big Crunch, or The Big Rip. While I am aware that these terms might just sound like the superpowers of your favourite Marvel or DC superheroes, I assure you, none of these ways to die are as pretty.
Just to base some context of the universe, I’d like to show you this infographic.
This picture basically shows us the knowledge about the universe and everything it contains. Trying to even venture into the unknown unknowns is nonsensical, so let’s have a look at the blue region for now. In recent years, scientists discovered this thing called dark energy. But we don’t know what it is. All we know about it is that it exists. That’s all. And it is the sole reason the Big Bang happened and life as we know it was created nearly 14 billion years ago. It is also the sole reason life as we know it is going to end.
Let’s start off slow with the most depressing way to die amongst the three. The one thing we know about dark energy is that it causes the expansion of the universe to either accelerate outwards or inwards. However, if there is a balance, the expansion will continue, but at a uniform rate. Stars and galaxies will begin to move further and further apart, and the universe will reach its maximum entropy - absolute randomness with particles all over the place, but yet unable to form new stars. Matter will become so diffuse that stars won’t be able to reproduce, and after aeons of agonising stillness, the universe will simply fade away into nothingness - The Heat Death occurs.
The Heat Death
A second way for the universe to end gruesomely is the Big Rip. Hypotheses are floating around that if dark energy is too concentrated, then the universe’s expansion will begin to accelerate further than it is now. Soon, stars will begin to get further and further away and eventually reach a point where new stars aren’t able to form due to the lack of concentrated matter in an area. No new stars will form once the old ones are dead. Galaxies and solar systems will be ripped apart from each other, almost down to every last atom. But this process is far more accelerated than the Heat Death - the universe will be physically ripped apart into tiny shreds. It’s like when you try to pull apart Play-Doh to make your dream sand castle, but never put the separated pieces together; they just stay apart. Forever.
The Big Rip
And finally, coming to my favourite. The Big Crunch is when the matter in the universe will dominate the ambient energy present, and instead of pulling it apart, matter will try to force it inward. Distant galaxies, like the Andromeda and the Milky Way, will start to come together and clash, over and over again. At the end, the universe will become something like a hot furnace where you cook your pizza in, except there won’t be any escape hole to take the pizza out. The universe will become a singular point, just like how it started off. The reason I am rooting for this is 1) poetic justice of things returning to the way they used to be and 2) I imagine that since we’ll all technically just be a singular point at the end, it’ll feel like we’re all in a big, universe-wide hug.
The Big Crunch
The various deaths of the universe
While I am aware of the fact that I might have click-baited some of you guys into reading this with the title since it advertises this to be about one of the greatest video games ever created, I am writing this article with something else in mind.
I just want to remind you that this end is not going to come for at least a couple billion years from now, and considering the way we’re treating our planet right now, it doesn’t seem like the human race would last that long. If you worry about what’s to come in our future and how it’ll all end, what will happen to the here and now?
If we’re so stuck up about the fear we have for what the future holds for us, we’ll forget about what we do have in the present. While worrying about the future will make us work towards making it a better future, worrying so much that it makes us numb is not going to accomplish anything. If worrying about your college admissions makes you work towards improving your grades and your profile, then please go ahead and do that. But if excessive stress about whether you will get into the college of your dreams or not puts you knee-deep in anxiety, it’s probably not the best option to pick.
Pathways
My dad always told me that every problem can be solved in five different ways. Every problem has five distinct solutions. And five here was the lower bound. Let’s take an example -
5x - 4y = 9
3x + 2y = 23
The above problem is a set of simultaneous equations. Quick side note - simultaneous equations now give me PTSD since they were central to the one question on my end of terms that I wasn’t able to solve and I will never be able to live that down. But, as you can see, I’m over that now.
Anyways, back to the math (whenever someone says this, it gives me goosebumps). The problem can be solved in a number of different ways. Firstly, there’s the good old algebraic way, where we could either substitute one variable into another equation or cancel it out from both equations altogether to get to an answer. This method is fairly simple and straightforward; something a majority of students would use, and rightfully so.
Another interesting way to solve the problem is using the Cartesian plane. The two equations each represent a line on the plane. Just punch the equations into renowned graphing calculator Desmos and find the intersection point, and lo and behold! There you have it, the answer with minimal effort from your side. I call this the lazy approach, but don’t get me wrong, I find myself using this method on more occasions than I’d like to admit.
A third method of solving the problem that I found out was quite an interesting one. It uses vectors and matrices. One can start off by taking the coefficients of the variables in the equation and substituting them into a 2x2 matrix. This matrix will then be multiplied with an unknown vector with the variables in it, while the output vector will simply be the constants on the other side of the equation. Solving that equation of vector algebra will give out the answer. I’ve got to say that this method took my primitive brain on a rollercoaster ride (that, by the way, I thoroughly enjoyed), since the idea of connecting simple simultaneous equations to complex vector algebra seemed unfathomable to me.
But then I was stuck. I couldn’t find another method. I was capped at three. It was frustrating.
It was even more frustrating because there were more. I knew it. There had to be. There were always at least five.
Whenever you feel like you’re stuck, take a step back and evaluate your situation. Objectively. Whenever you feel like you don’t have anything to do other than the three options in front of you, which all seem bad, take a step back and look at the big picture. Where is it that you are and where is it that you have to be. And a straight-line path is the shortest distance from one point to another, but you might have that covered already in your three options. That doesn’t mean it’s the only path. There are many more.
Mostly, at least five. There will almost always be at least five.
And I found another.
There’s an old method that was developed by Aryabhatta back in the day called Kuttaka. It was a method used to find integral solutions to equations in two variables, which could apply in this case. After finding the set of solutions for one, the same process can be done with the other, and intersection of the solution sets will be the unique answer to the pair of simultaneous equations. The Kuttaka method is a little complicated, but people interested could check it out here - https://en.wikipedia.org/wiki/Ku%E1%B9%AD%E1%B9%ADaka.
I found another.
Notice how I never really told you what the answer to the question was. Because that’s where the metaphor ends. In most aspects of math, no matter what you hear from the plethora of motivational speakers, there’s usually one right answer. Which one of the five paths you take to the answer is almost immaterial to the answer itself; preference is the only differentiator. However, in life, which one of the five paths you take matters after all. Each path leads you to a different secret cave, the depths of whose darknesses can only be discovered by venturing down its path, committing to unraveling its mysteries.
But however many paths you think there are for you to choose from, there’s always another obscured one. So look out for that one. Who knows, that may be the one you want to traverse.
Anyways, I’m off to break my head over a fifth solution method for my problem. See you on the other side.
rainbows and more
I was always in love with rainbows. Everywhere I looked, I wanted things to be colourful - like a rainbow. Rainbow pastries, rainbow cakes, rainbow coloured keychains on my bag, rainbow coloured tabs for sections in my maths notebook, you name it. My mom always used to chide me for this habit, for the fact that I didn’t have a colour taste and just put all the colour I could fathom into anything I saw. Immaturity.
But then I grew up. And I also developed an astute sense of colour (our Duchess of Design breathes a sigh of relief). The urge of putting a rainbow into everything went away. And so did my childhood.
During that period, though, the rainbow came to symbolise something else, something more universal, something that spurred what can only be called a paradigm shift in the course of history. I learnt it to also be the pride flag. And I was flummoxed.
Rainbows used to symbolise childlike innocence. But now they symbolised pride, a concept I didn’t understand, and I don’t think I do till this day. It felt confusing to have the same symbol for two different things. Those two meanings couldn’t coexist, could they?
Here’s what I get when I think of the concept of pride. I think of it to be the freedom to love anyone you want to, irrespective of gender or sexuality. It means the ability to freely express your own gender or sexuality. There are no fixed categories one falls into when it comes to gender or sexual orientation - it’s more of a histogram rather than a bar graph (I couldn’t help myself, I’m sorry). And it has taken me a much longer time than I would have liked to get that completely. And I’ll give it to you, pride means so much more than that. It could mean something completely different for you, probably something I haven’t quite understood yet. But I’m learning, or at least trying to learn.
Gay marriage still isn’t legal in most countries in the world, and there’s a long way to go before that is fixed. People around the world haven’t come out to their friends and family about their gender and sexuality in the fear of being judged and ridiculed about it. Looking at the current situation, I have no doubt that it’ll take some time to be fixed. But what appals me is how these issues popped up in the first place.
As children, we never really cared about who people chose as their significant other. But as we grew up, that changed. It started to matter. It started to affect how we saw the things and people around us. And that change, those eyebrows we started to raise and those hushed voices we started to hear when we saw two girls holding hands, is everything pride stands against.
So the two symbols of the rainbow aren’t very different after all. Pride is a representation of freedom for anyone to love whoever they want - men, women, non-binary people, even rainbows.
Happy pride month.
The ups and downs
I’ve never really fancied trigonometric functions.
When I was first introduced to the soh cah toa definition of trig functions, I thought I learnt everything there was to learn. It seemed easy enough. I rushed to Khan Academy from my quick access toolbar, like a duck to water, and tried out a trig worksheet. The first question - Calculate sin(45°). I was stumped.
To calculate the value of a trig function, you needed a right-angled triangle, right? So how can we do it with just one angle?
But then, the unit circle definition of trig functions presented itself to me, and all was well. Although inverse trig function identities continue to baffle me to this day, I’m going to keep that aside in the interest of time and space (spacetime? Don’t mind if I do).
Taking a closer look at the graphs of trigonometric functions, I’ve always found them to be rather quirky, to say the least. Even the simplest one, the sine function. They’re all repetitive, like they’re stuck in some kind of a rut.
At first, it goes up. And then comes back down. But then it goes up again. Only to come back down. It’s periodic in nature, just like your mundane daily routine during the pandemic.
The only problem happens when you look at it too closely rather than looking at the big picture. If you zoom in enough on a trough, it’ll almost look like a straight line - a straight line on -1. If you zoom in enough on a peak, it’ll also look like a straight line - a straight line on +1. It’ll seem like it never ends.
But both of those things, a peak and a trough, they don’t stay that way. That’s the definition of a periodic function - eventually, a peak moves forward and becomes a trough and likewise for a trough.
Thing is, you can transform these functions as well. Increasing a sine function’s amplitude makes the peaks go higher and the troughs even lower. Increasing its period effectively makes its peaks and troughs last longer, in essence, stretching the function itself. The most beautiful thing, though, is shifting entirely. Translating the function up by 1 unit makes it go from 2 to 0 and back to 2, but never below 0.
If you think that trig functions are reserved for textbooks and blackboards, I’ve got news for you. Life is a sine function in itself. It has its own peaks and troughs - peaks where you think nothing can go better, and troughs where you think nothing could be worse. But it’s periodic; it always goes back. After a peak, there’s always a trough; and after a trough, there’s always a peak. It might not be as regular as the function makes it out to be, but it happens. Give it some time.
The beauty of it is that the peaks and troughs are mutually dependent on each other. Without any one of them, the sine function will cease to exist.
But you can always translate the function. We all have our ups and downs in life, and that’s what makes life so. But by translating your function upwards, the ups of life will go even higher, while the downs might become a little less horrible. If the peak is a raise, make it a promotion next time. If the trough is a D in your exam, make it a C next time.
If f(x) = sin(x) is the function of your life, you would want it to be f(x) + 1. So make it that way.
Do you see that I despise transformations?
Stages of love
The ubiquitous perception of Valentine’s Day is that it is only celebrated on one day, the 14th of February. But that, my friend, is a naive mindset. You see, I believe Valentine’s Day is one of the few “festivals” that is celebrated in stages (the other well-known one is exemplified by the popular carol “12 Days of Christmas”). Largely, there are 5 phases that Valentine’s Day is spread over, and I’m going to waste the next five minutes of your life explaining them to you. Strap on, it’s going to be terrible.
Just a side note to all the couples out there - some parts of this might be applicable to you as well, but largely, this is for the single crowd, which is clearly the dominant population in society. Also, you suck. I mean, it’s fine. I don’t care. It’s okay. On that topic...
Phase 1: Denial
This isn’t as heavy as it sounds, don’t worry. It’s for that time of the year towards the end of January but it’s not quite February yet and you just cannot accept that it is the New Year already and almost a month has passed while all you have done is eat Maggi Magic Masala straight out of the packet at 2am and watch reruns of Tom and Jerry on Cartoon Network. It doesn’t feel like the New Year yet, but time flies so quickly. It’s in that awkward, limbo time between Christmas and Valentine’s Day with Republic Day just around the corner. Meanwhile, you’re still eating the leftover popcorn from Lohri.
Also, you are completely oblivious about Valentine’s Day.
Phase 2: Fear
First week of February.
You have just realised Valentine’s Day is around the corner. And you don’t have a date yet.
Panic mode sets in. Scenes of last year flash in front of you as you see the less mature, “kid” version of you putting yourself out there just to get beaten down. Frightening, isn’t it? You come to a concrete resolve that you won’t be alone this time of the year again. Some potential dates are mapped out, and you prepare a strategy to impress them (Note: I am being a little liberal using the plural form “dates”, but I have never achieved such a high stature).
Phase 3: Anxiety
The week leading up to the 14th.
You’ve narrowed it down to one person you’re going to ask on the 14th and you’re pulling out all the stops, with a bar of Dairy Milk Silk Oreo and a two-tiered chocolate cake with icing you’ve prepared yourself. A little, or rather, quite significant voice of reason inside you begs you to listen to it; you’re in denial of it (nice how things come around, isn’t it). Full preparation to impress her is underway and you finally convince yourself that there is a small, tiny, minuscule chance that she might say yes.
Phase 4: Show-time
14th February
She says no. You go back home.
Phase 5: Coping
The week after the 14th.
Happiness is hard to find. It feels like your world has just been turned upside down and you don’t quite know how to deal with it completely. The little things that gave you joy before don’t seem to excite you anymore. You don’t have any motivation to do the hundred assignments that are pending in your assignments tab (because, of course, you had that motivation prior to the heartbreak as well). You go through the five stages of grief all over again, if not for the person you wanted to impress then for the time you wasted in pulling out all the stops. It doesn’t feel like life will be normal anytime soon.
Or you just return to the same oblivious, shameless fool you were. Either works.
In essence, what I’m trying to say is that Valentine’s Day is just a concept imposed upon us by society and we shouldn’t let it dictate the terms of our life to such an extent. It’s just another traditional festivity and we shouldn’t really care about it this much. Care about it as much as you care about Kannada Rajyotsava - little to not at all (the only difference being you don’t get a holiday on Valentine’s Day but we can live with that). St. Valentine doesn’t deserve so much popularity in society and it’s time we get that.
Anyways, I hope everyone has a great Valentine’s Day, and if you’re single and Netflix-ing and chilling, I’m right there with you.
Republic Day: A Parade of Pointless Shenanigans
I never understood the point of Republic Day.
Imagine this, I’m in the process of writing a tad less than 145,000 word long book over the course of three years, and I finally finish it. However, the book doesn’t get published for another three months from now. Am I going to celebrate more on the day I finished writing the book, or the day it gets published? Wait no, in hindsight, I would probably celebrate more three months later because it gets commercially available then, so forget I was trying to make a point there! The previous contrast has nothing to do with Republic Day and the Constitution and any uncanny resemblance to the same is unintended!
Well, that went out the window.
Anyways, the only real perk of Republic Day, anyone would agree, is the well-deserved holiday we get from it. Although it’s on Wednesday this time around, which is a very odd day considering it is in the middle of the week, hey, a holiday is a holiday, so no complaints from here. Being an Economics student, I know that having something in short supply increases its value. I guess a lot of economic theory was put into deciding nationally-mandated holidays, so kudos to the sadist human being who designed the system in this way. Also, being a student of the IBO without any religious or festive holidays, the system works even better.
The Beating Retreat is one of those traditions which stirs up a patriotic sentiment in me. However unrelated the Retreat is to the point of Republic Day, it’s still one of those things that is iconic. The Beating Retreat conveniently happens on the Rajpath, which is flanked on both sides by the Rashtrapati Bhavan, just so that the President can watch the parade from his balcony in his PJs. The highlight of the show, however, are the fighter jets that fly overhead. All the loop-de-loops they conduct never fail to leave me in awe. Also, air pollution.
The awards given out after all the ceremonies of Republic Day are the most bizarre functions you can ever imagine. Hear me out, of course they’re one of the most prized civilian honours in India, but their classification baffles me. The Padma Vibushan is the second highest civilian honour in India while the Padma Bushan is the third highest civilian honour. The only difference between these two is that the former is awarded for “exceptional and distinguished service” while the latter is awarded for “distinguished service of a high order”. That makes as much sense as the IBO marking the topmost marking band for “satisfactory analysis of a diagram” with the second highest band being marked for “appropriate analysis of a diagram”.
Anyways, like I was trying to say, to me, Republic Day makes the least sense out of the three national holidays in our country. But as long as I get a state-mandated holiday along with a complimentary snack box at the apartment’s flag hoisting, you will not see me complaining. My point is, if you enjoy Republic Day festivities, by all means, lead the way. My only advice is don’t read into the thing too much because that rabbit hole is hard to escape from. But if not, just enjoy your holiday (it’s a bonus if you’re NOT a student of the IBO). :)
Small Wins
Let’s face it - 2021 was shit for everyone, probably even more so than 2020.
With the increase in general anxiety level throughout the year due to the second wave, I think it’s fair to say that physical health wasn’t the only thing that got ruined.
Looking back, I think the years 2020 and 2021 can just be removed from the everlasting continuum of time. The passage of time in these two years was tough. Just when your eyes start burning and you wonder when this teacher is going to get out of your screen, you realise only forty minutes are over of your seven-hour long school day and start contemplating the entire point of your existence.
And yes, I’ve seen those memes (which can be better termed as conspiracy theories) floating around the internet, that 2021 stands for “2020 won” and 2022 stands for “2020 too”.
I’m not going to go on a rant on what was wrong with the last two years because I fear that if I start, I’ll never stop. Even though they were absolutely pointless, I wanted to take a moment to acknowledge the wins I had this year, however little or huge they might have been.
First of all, I got my IGCSE results back in August, and I got 9 A*, which is the highest possible grade you can get (just wanted to mention that I beat Shravan here, but he did get more A’s than me :)). But surprisingly, I wasn’t thrilled, I wasn’t ecstatic, I wasn’t jumping around my room hyperactively - I was simply relieved. 9th and 10th grade were hard-fought for me, and shifting to an international school that had a worldwide reputation for breeding cocky students didn’t make it easier for me. I still have the mail from my coordinator announcing my result pinned in my inbox and it will stay there till the time I get over it. When I saw my result, it felt like the air inside my lungs was the same as the air outside. I felt at peace.
Next in line, we have the time I painted my wall. Granted, it wasn’t a perfect piece of artisanship, but it was mine. And it lasted for a while; it went for almost 4-5 months without being spoiled (a quick shoutout to my brother for denting the wall without even realising it, kudos to you). The wall itself isn’t much of a prize, but I’m proud of the effort I put into it. An upside to painting it was that my workout for that day was over, so all-in-all, not complaining.
Boy, I had a really tough time coming up with this list. I’m not very good at remembering the good times that I had, and people often yell at me for not remembering stuff we did together. So for the third point on the list, I’m including every single second that I spent with my friends (in real life, not online, but don’t think you needed that clarification). All the meetups, all the get-togethers we had over the past year were absolutely wonderful, even though they all seem like this blur of unadulterated happiness for me. Even at the lowest of my lows, what kept my chin up was the hope of more such meetups and get-togethers.
I’ve said it multiple times and I will say it again - 2021 sucked. Congrats to everyone who made it through, with or without a smile on your face.
But that doesn’t mean there weren't some good times along the way. I feel that taking the time out to recognise the good stuff that you did in the year may reduce the pain and hardship you experienced along the way, if not erase it altogether. I did. Now your turn.
Mediocre
When people are born, they don’t have anything much going for them, other than their differently-organised set of genes. They’re born exactly in the same way as everyone else. Nothing special. Nothing different. Nothing better. All the same. Just average.
I, too, was perfectly normal (I hope. You can never be too sure when your parents constantly joke about bringing back the wrong baby from the baby room).
But somewhere along the way, things changed. I wasn’t normal anymore. I wasn’t average. I was deemed to be above average. Everyone around me told me I was above average. And I knew that as well (if that felt like a flex to you, keep reading).
I have always been above my classmates in most regards when it comes to academics. Consistently scoring above average in most exams, that felt normal to me. I could do things that other people around me just couldn’t do.
Even when it came to sports, I was placed in the category that was above average. I could play a whole lot of sports fairly decently, well enough to be mistaken for a semi-serious player.
But when it comes to being the absolute best at something, I falter. Take any discipline you like, any academic subject, any sport. There’s always this one person in my grade who is better than me at that thing. And it annoys me, it always has. I love math, but there has always been this one person in my grade who can solve problems quicker and more accurately than me. I love cricket, but there have always been a couple of people in my grade who play better than me. I’m never the best at anything. But I’m just about there.
I have always told myself that I was the typical example of “jack of all trades; master of none”, and over the years, it has proved to be true.
To offer an explanation to this, the strongest theory I’ve had is that I always seem to settle, I always seem to be happy with where I am at that moment. And I don’t know why exactly that is the case. It’s probably because I haven’t had a strong passion for anything till now. And I’ve been told that it’s alright and I will figure it out. It’s been five years since I first heard that, but I still haven’t found anything. But I’ve been told it happens to everyone.
But I’m not “everyone”. I am not average. I am not mediocre. So why do I always tend to settle?
I don’t have an answer to that yet. I will get back to you when I get it.
And I will get it.
To Prove the Unprovable
My dad always told me that if you encounter a roadblock or a problem anywhere, five ‘Why’s can get you to your answer - if you repeatedly question why you made a silly mistake in the final step of an insanely simple arithmetic problem (which I’ve never ever done before, believe me), you will arrive at the root cause of that mistake. Asking those questions will lead you to these axiomatic statements, which have to be true. If it’s a mistake you make in an excruciatingly simple test, the answer to that fifth ‘Why’ will show you what you have to work on to improve in the future.
Gödel’s theorem works in a similar way. Many of you might not have heard of it since it is one of those few mind-numbingly complex concepts that hasn’t been adulterated by wannabe science-fiction writers (Whew!) According to traditional mathematics, there are two kinds of statements - true or false. And for both these kinds of statements, there are definitive proofs. However, according to the Austrian mathematician Kurt Gödel, there existed these true statements that were unprovably true; they laid the foundation for mathematics and were essentially everywhere. If one started to make these unprovably true statements axioms, then it would create a ton of other unprovable statements below that one that have to be true. He called it the “Incompleteness theorem”.
A hole was torn through mathematics, with long-standing unproven conjectures actually turning out to be unprovably true. Some mathematicians tried to cleverly sidestep this hole by just ignoring it altogether - ignorance is bliss, they say. Others were worried that their entire life’s work would have been futile (don’t we all love an existential crisis). A few of them even dedicated the rest of their lives to finding some of these unprovably true statements - and there were millions!
Inexplicable truths are all around us, and not just in mathematics. There are these inexplicable truths in my life, and I don’t know why they’re there, but they’re there. The definitive statements are just those actions and things that happen in my life that have a solid rationale behind them, but the unprovably true statements are those things that are just there but don’t have any reason to be there. Especially the people around me - some have seen me at my worst and my best. They have inspired me and motivated me to keep on going, no matter what. They’re like oatmeal; they sustain me.
This article, like most others of mine, may just seem like a dumbfounded attempt at writing something profound, but to me, this feeble attempt of an article just serves to appreciate my inexplicable truths manifested as the people around me. They’re like the mismatched pieces in the jigsaw puzzle of my life - clearly not perfect for me, but they’re the ones that make me whole. Without them, I am simply incomplete.
I love you all, you know who you are.
Horror movies and why i Adore them
A fairly familiar situation hovers into view. The 8x8 chessboard makes me feel safe and guarded. There’s just one problem - when I reach the end, it expands. When I reach the end again, it expands again. After all the frantic chaos trying to catch an escape route, I stand on an infinite floor of chess boards with me standing at the apex of it all. The more I hurry around, the larger the infiniteness I see. I try to find something - a door, a secret hatch, a ladder which will airlift me out of here; I find nothing. I return to the place I started from, lay down, and wait for the chaos to engulf me. That was a glimpse of my nightmares.
I hate horror movies. I cannot watch a horror movie without broad daylight and a blindfold just in case I need it. Actually, scratch that - I cannot watch a horror movie (The article title is making real sense right now, isn’t it?) Till date, I’ve never watched a horror movie from start to finish, only sporadic parts of them, but trust me, those sporadic parts were enough to scare the bejeezus out of me. So that’s me. My friends, on the other hand, have laughed at movies like Anabelle and Conjuring, so you get where my reluctance to watch a horror movie with them comes from.
Horror movies stimulate a part of one’s brain which is responsible for the ‘flight-or-fight’ response. People who like that emotion, in turn like horror movies as well.
Now that we’ve gotten that crucial scientific point of discussion out of the way, let me talk about horror movies and my nightmares. I watched Squid Game a while back, and this list wouldn’t be complete without the doll from ‘Red Light, Green Light’. All I remember from that nightmare was the doll 2 inches away from my face when I opened my eyes, and that was enough for me to not sleep that entire night.
One prerequisite of having nightmares I want to address here is that you have to be able to sleep first. And get REM sleep. That does explain why I haven’t seen quite as many nightmares in the past couple of years, but that is a problem for another day.
Another one of the frequent nightmares I have had is just a recurrent symbol of sharks. Just sharks generally swimming, swashing around me, while I lay in the focus of it all, paralysed. One incident I vividly remember - I am in a public pool; it’s fairly shallow, about 6ft in depth (shallow for me, I meant). And I’m doing whatever anyone does in a public pool (not pee). All of a sudden, the familiar ground beneath me is taken away, as a shark erupts from the surface, plunging its shiny, white teeth into my skin. I woke up covered in sweat.
There was this one nightmare I remember about hot air balloons. My family and I were on a trip to Coorg, where we were supposed to board a hot air balloon from the top of a cliff. Not sure if the travel manager suggested this, but we were supposed to climb onto the hot air balloon while it was in the air. My grandfather went first, and he jumped onto the platform pretty easily. Next was my grandmother, and she made it in as well. But slipped off the edge. I woke up with a start.
So, those were a couple of nightmares that come to my mind. Others are there too, but they drift off as instantly as they come. And most of the ones I forget come from cliched horror movies. To end, I just want to say one thing - to the people I am going to be spending Halloween with, this year and in the future, if you’re planning to watch a horror movie in the dark at 12 am, please let me know in advance so that I can schedule a conveniently-timed doctor’s appointment then. Anyways, happy trick-or-treating!
WHAT ARE THE ODDS?
Perfection is a topic upon which I have voiced my opinion on this column before. Let’s venture into that realm again. My only problem with it is that the state of something being ‘perfect’ just seems so improbable to me. Not unattainable, mind you, just improbable (there’s still a sliver of sunshine for all you perfectionists out there). But I’d like to talk about one essential factor that is required to change that improbable to attainable - luck.
I’m sure all of you have been acquainted with Murphy’s law. If not, let me just tell you that it has been the root cause of all your problems without you even being aware of it. The law states, “Anything that can go wrong, will go wrong”, with a recently added clause of “usually at the worst time”. Take a drama production, for example. Things that can go wrong include actors coming after the show started, the makeup and costume guy falling sick, one of the kids in the front row venturing onto stage to eat a prop - I think it’s safe to say that the things that can go wrong are practically infinite in number. According to Murphy’s Law, all these things can and will go wrong. It is luck that is required to reduce that figure from order of hundreds to an order of tens.
I personally hate the concept of probability and chance. When we were taught this in school, I audibly groaned. I need to know if something is going to happen or not going to happen; anything in between is so frustrating. But when I started to study quantum mechanics (oh who am I kidding, you probably know all about the quantum world from Avengers Endgame), I realised that everything can be expressed in terms of probability. While the probability of me sitting on my sofa writing this at 5 am could be close to 100%, there is a miniscule probability of me being on Mars jamming to Lungi Dance right now. This world is governed by probability and chance, and luck is the sole factor that can tip the scale in favour of one side.
Let me tell you a story. It’s about an incident I can now joke about, so brace yourselves. I liked this girl (and that’s how most disasters occur isn’t it). At least I thought I liked her. And just for context, I’d had minimal interaction with her before coming to this revelation. So instead of telling her directly, instead of building a meaningful relationship before telling her, I built my own little fantasy of how I wanted things to be. In my head. And in this fantasy, she liked me back, obviously. In the midst of switching between reality and fantasy, I actually began to think that the fantasy would come true. So when I finally told her, she said no, obviously.
Since the time I realised (or I thought) I liked her and the time I told her, nothing had changed, not even in the slightest. I had created this fantasy in my head that I hoped would come true. I hoped I would get lucky.
See, but that’s the thing, right? Despite the several (failed) attempts numerology and sun signs have had to convince me that the two of us were meant to be, ‘getting lucky’ is not about the perfect alignment of constellations at birth. It’s so much more about conscious hard work and effort put into achieving a goal you have set your eyes upon. Don’t hope to “get lucky”; go about your life in such a way that luck has no other choice but to turn in your favour. Don’t hope to “get lucky”; make your luck yourself.
Felix Felicis sounds like the most useless potion in the world.
From Ripped Jeans To DalgonA Coffee - Where did we lose ourselves?
During every single one of my Instagram scrolling sessions over the past few weeks, I have encountered at least one post with Doja Cat’s Woman playing in the background, while in the foreground, a stranger flawlessly recreates the beloved TikTok dance in their own style. A few days ago, I, too, committed the same war crime, and that will be the first and last time I hop onto an ongoing trend (unless a trend about black holes and printers comes along, I will jam to that one all day long). But that got me thinking - why do we hop onto trends in the first place? Is it because we actually like doing it, or because it looks good on our Instagram feed?
The concept of ripped jeans has always boggled me. Why would you pay a higher amount of money for less amount of actual cloth used in the jeans? I have been told by many people that the higher cost of ripped jeans arises from the extra manual labour put into it, with the finesse of the finishing stitches and what not (still doesn’t make that much sense, but I digress). Ripped jeans started as a trend in the 1970s, as a show of retaliation against society. It was actually popularised by celebrities like Madonna, and soon the entire world started wearing jeans with cuts and holes in them. When I ask people, “Why do you wear ripped jeans?” a large majority of people tend to reply with “Because it’s a trend.” End of conversation.
What’s the difference between Dalgona coffee and its normal counterpart? From personal experience, they are made in the same way, using the same ingredients, and they taste exactly the same (if anyone has uncovered the truth behind the difference, I need to talk to you right now)! Yet there was a sudden increase in popularity in Dalgona coffee last year. Not quite sure whether its cause was collective genuine interest in the coffee that just happened to come about simultaneously, or just simple boredom of the lockdown, but the trend did happen. And it spread like wildfire. But my question goes out to the people who have tried their hand at making Dalgona coffee even once - was it you who made the coffee, or the people around you?
Trends exemplify the herd mentality perfectly. When you see some people on a common trend, the automatic thought process is, “All of them are doing this, and I don’t want to be left out of the scheme of things, so let me also do it.” And this is where the problem arises.
There is no sense of self that prevails in this world anymore; all that exists is a sense of society as a whole. In a way, that is a really beneficial emotion to foster when it comes to solving issues like world hunger and global warming. Scientific discoveries that are made with an intent of advancing the knowledge of society are always useful in some form or the other. However, we get so lost in this chaotic swirl of life and the people around us that we forget about ourselves and what we enjoy doing.
Society is a puppeteer, forcing us all to dance around according to its own whims and fancies. It tells us how to act, how to behave, and even what to do with our lives. It fosters the herd mentality by virtue of its intricacies and that has altered even our primary instincts to some degree.
We have been told to develop a sense of ‘us’ rather than ‘me’ from a very young age, and it has played a major role in turning us from self-obsessed rats to empathetic human beings, but maybe thinking about ‘me’ once in a while isn’t as bad as it is shown to be. So, as for my final thoughts, I want you to remember just one thing - cut off those strings, shed its aftermath completely, and be free. Do what YOU want to do. I promise you will not be disappointed.
Black holes: The Supermassisve suckers of the universe
By now, if you’re still reading this column, you must have realised that Intricate ConnectionsTM is for the more intellectually-oriented, #iaminSTEM people. And now that 90% of my reader base has gone, I’d like to address the 10% of you who stayed. In case you haven’t noticed, I love physics. I’ve heard many people talking about black holes, trying to understand what they actually are, and more often than not, they’re probably wrong. On that note, the rest of this article is my futile attempt in explaining to you what a black hole actually is by telling you what it is not.
Full disclosure, I’d like to mention that I have no working knowledge about black holes and they will continue to boggle me for eons to come. And with that, let’s begin.
Something I feel is very similar to a black hole, but not quite, is one of those Magic 8-balls. Think about it. Both of them are spherical or at least elliptical in shape, and both of them are usually black in colour. However, one sucks gullible travellers in due to the curvature of spacetime around it, while the other sucks gullible travellers in using empty promises of a bright future (these are the same people who believe in numerology, horoscopes and sun signs. All-in-all, not complaining). Another uniting factor among the two is that Magic 8-balls work in terms of probability. When you ask it something, it gives one of ‘signs point to yes’, ‘my reply is no’, or ‘better not tell you now’, which means it has a variety of answers. A black hole too works in terms of probability, so to say. After crossing the event horizon, the answer to the question ‘Am I going to die?’ will 100% turn out to be ‘signs point to yes’.
Another thing I feel that resembles black holes is a printer. Look at it this way - both of them suck stuff in. In a printer, it’s paper. But in a black hole, it’s everything. There is no discrimination based on caste, creed, race, colour, or even size, a black hole sucks everything inside irrespective. The only difference is that printers eject that stuff out too. When you put a paper into the top of the printer, you expect it to come out from the backside. But we haven’t quite discovered where a black hole’s backside lies. There have been theories about the existence of a white hole, which does the opposite of a black hole - it only ejects stuff. Honestly, I don’t think the discovery of a white hole would be really pretty. It’ll look too much like a Gujarati uncle with diarrhea on a warm summer morning.
Coming to my third point, I believe that another thing that is very similar to a black hole is a merry-go-round at Disney World. Both of them spin around; black holes are a tad bit faster, but merry-go-rounds aren’t that far behind. Again, the difference between them lies in what they suck in - black holes suck in, well, everything, and merry-go-rounds suck in pre-adolescent children who are weirdly passionate about horses. One commonality between a supermassive black hole and merry-go-rounds is that they are anticlimactic - when you are going in, you’re very excited to see what’s going to happen, but at the end of the ride, you think ‘That’s it?’ See, black holes and merry-go-rounds are much more alike than you might think! Black holes may come in all shapes and sizes, and likewise merry-go-rounds may have either cats and dogs or Ariel figures to sit on. The underlying similarity between them - they suck.
And that ends my list. While we might think that black holes are very complex, they aren’t so different from the things we are used to after all. The only thing that is stopping any object from becoming a blackhole is the volume it occupies. If you condense anything to be small enough, it too can become a black hole. So, if you think about it, any object is not and could be a black hole simultaneously (Schrödinger is probably rofl-ing in his grave right now).
To conclude, if this article has taught you anything new about black holes or about anything in general, I’m sorry, that was not my intention, go back and read it again. If it didn’t, then I want to leave you with one last thought - You too are a black hole.
No you’re not, don’t freak out. Have a great day.
Image sources: Wikipedia, Astronomy Magazine, iStock
An Illusion
DISCLAIMER: Read at your own risk. The author of this article is not liable for the reader’s urges of destroying property. And believe me, the urges will be there.
Despite it not being #ThrowbackThursday, I’d like to take you back to the good old days in third grade when we used to play math tricks and riddles on one another. Let’s try that again, for nostalgic purposes. Pick any number under 100 you’d like. Got it? Alright, now if it’s even, halve it; if it’s odd, triple the number and add one. Got the next number? Ok, now repeat the same even-odd process again. And again. And again. Do it 116 more times just in case (Confused? Haha me too). If you remember the game correctly, at this point, the trickster, i.e. me, will guess your number. My guess - your number is either 4, 2, or 1.
I got it right, didn’t I?
It seems like a naive and deceivingly simple problem - start with any number, apply the process as shown above, and prove that it always reaches the numbers 4, 2, or 1 eventually. Believe me when I say that if you are anything like me, please, please run as far away from this problem without looking back, or else you’ll see the expression ‘3n + 1’ wherever you go - in the shower, on the streets, in history lessons where you are learning about the World Wars. When world-renowned mathematicians themselves haven’t been able to resolve this conjecture in about a century, what hope does an eleventh grader have of solving it?
I kid you not. The Collatz Conjecture, sometimes called the ‘3n + 1’ conjecture, is infamous amongst professionals for the fact that it hasn’t been solved yet. Unlike Fermat’s last theorem, every mathematician has definitely given the solution a try some time in their career, but has miserably failed.
There are only two ways in which the Collatz Conjecture can be resolved. We may find a solid proof, showing that all numbers will reach 1 eventually. The other involves us finding a self-sustaining loop, other than the 4-2-1 one, that loops around to itself eventually. But no one has succeeded in finding such a proof or a loop yet. Considering that even computers haven’t been able to solve the problem, it seems like something that’s just a little bit more difficult than your average high-school mathematics problems.
Now, if this has motivated you to try to give a crack at the Collatz Conjecture, that wasn’t my intention at all and I compel you to put that pen down. However, if you are as stubborn as me when it comes to unsolvable problems, by all means do give it a go; don’t come crying back to me when you’ve spent an entire week trying to blow your head up in frustration. Just a little piece of advice - if you want to try out different numbers to see where they land up, start with something around 2⁶⁸, since every single number below that has been proved to come back to 1 eventually.
If you have had a go at it, welcome back from a session (or multiple) of agony and repentance! I don’t blame you; the problem seems like something any third grader can understand, which is why it is so lucrative. Being so deceptively simple, it might tempt anyone to have a go at it, but in reality it’s much harder than it seems.
Things are not always what they seem to be. From the transformers, a semi-truck might actually be an alien robot. Your cute little brother might actually be a harbinger of hell. A math problem that seems like a platitude might actually be unsolvable. You might be having epic flashbacks of sleepless nights after watching the Matrix right about now, but honestly, that could be a possibility in our world too, you never know. We may never know. We haven’t found our Neo yet.
We’re surrounded by illusions. Things are not what they seem to be. Everything around us may just be another illusion. From the nib of your pen to the house you live in, it could very well be an illusion. The scary part is that we have no way of confirming whether it is an illusion or not.
Maybe our universe is an illusion.
Sources:
https://www.quantamagazine.org/why-mathematicians-still-cant-solve-the-collatz-conjecture-20200922/
A story of cricket: apartheid, preposterous rules, and a World Cup never won
Cricket. A gentleman’s game. Over the years on the 22 yards, there have been countless acts of sportsmanship and integrity shown by many players, as the true spirit of the game has been displayed on numerous occasions. Records have been made, records have been broken. But there have also been times when the exact opposite occurred. And it is these events that remain etched in the memories of the public across the world. Let me paint a picture for you.
The World Cup of 1992. Due to the 22-year long ban because of apartheid laws, South Africa’s chances of even being allowed to play in the World Cup seemed dim. After countless roundtable discussions between the ICC and the South African Cricket Board (CSA), they were finally given the permission to participate, but not without a catch. In South Africa, Nelson Mandela was advocating for the erasure of the apartheid laws and a referendum was supposed to take place to decide the fate of these laws. The aforementioned catch here was that the referendum was supposed to take place in the middle of the tournament. An agreement was reached but on the basis of one condition - if the referendum decided upon the removal of the laws, then the team would be allowed to continue in the tournament. If not, they were to be sent back home mid-tournament.
And so began the conquest of South Africa in the World Cup of 92. Having not played cricket at an international level for over 22 years, they were the default underdogs in all of their matches. With that label, however, came a certain kind of attitude - the ‘nothing to lose’ kind. Since any game they play might be the last one they ever play, they were the most potent opposition for any side. Contrary to popular support, they won match after match, after match. Snowplowing everyone in their wake, soon enough they were in the knockout stages of the tournament, where they had to face the daunting opposition of England in their semi-final match.
Before we move ahead, let me give you some context. There were two fabulous rules put in place by the ICC ahead of the World Cup that had the power to make or break games on their own. The first one was called the rain rule. It dictated that if during the second innings, rain interrupted play and overs were forced to be cut down, then the least productive overs of the first innings, that is, the overs in which the least runs were scored, were to be declared null and void, and the target would be changed accordingly. I could not underscore the stupidity of this rule even if I tried.
The second rule was regarding the broadcasting rights of the tournament. In those days, broadcasters were the ones that gained a lot of revenue from the World Cup tournaments from advertising rights (amongst other stuff), which eventually fed into the pocket of the ministries. As a result of this, the World Cup organisers of 1992 had passed over all control over the timings of the match to the broadcasting agencies. At face value, this doesn’t seem like a bad rule. But I urge you to read ahead.
Returning to the timeline we left off. South Africa was supposed to face England in their semi-final match, but the results of the nationwide referendum were scheduled to come in just a few days prior to the match. To their great relief, 66.7% of South Africans had voted against the apartheid laws. A nation was redeemed. It was like South African cricket was given a lifeline, something that they could savour for the rest of eternity. It was only fitting that they should bring home the final cherry on top to celebrate their triumph - the World Cup trophy.
And thus the match began. The norm at the time was batting first if you won the toss, but the South African captain Kepler Wessels opted to bowl first, raising many eyebrows. As the match progressed, it seemed to be an encounter of equals, as both sides traded blow for blow. The broadcasting company, however, had other plans. Since they had a fixed deadline of 6:10 pm that the first innings had to adhere to, South Africa could only complete 45 overs out of their 50 over quota. To extend the innings further, the company had to pay a little extra fee, and obviously, they were more inclined towards earning a little more money than letting an international World Cup semi-final be extended for a little bit, weren’t they? So, at the end of their innings, England posted a score of 252/6 in their 45 overs, posing South Africa with a target of 253.
When South Africa came out to bat, they looked to be in trouble in the 27th over, reeling at 131/4. Jonty Rhodes and McMillan steadied the innings and brought them on the cusp of a World Cup final ticket when they needed a fairly attainable 22 runs off 13 balls.
And then, it started to rain.
12 minutes. It rained for 12 minutes. And that 12 minutes of rain was enough to foil the hopes of 39 million South African fans.
There was a special reserve day for all the knockout matches organised by the ICC, but even if the matches were to be postponed, the broadcasting company still had to suffer a fee. They couldn’t let an insignificant World Cup hamper their profit margins now could they? They had to finish the match before 10:10. And thus, the rain rule inevitably came into play.
At first, one over was reduced, which eventually increased to two. The least productive overs from the first innings, i.e. two superb maiden overs bowled by Pringle, were to be voided. The scoreboard quickly changed from an achievable 22 off 13, to a hard-but-not-impossible 22 off 7, to a speechless 22 off 1. In just over the span of 12 minutes, South Africa had gone from vindicated heroes and hopeful champions to an insignificant footnote in the pages of history. A dejected McMillan came onto the field to play the final ball of the innings and knocked it around for a single. Even the English players recognised the injustice and apologised to the South Africans personally. England had won by 19 runs.
The clock stood firm at 10:08.
As an updated version of the rain rule, cricket matches now use the D/L method to settle games interrupted by rain. In an article I read, the author advocated for the fact that if the D/L method were to be used in the England-South Africa scenario, McMillan would still have to score an impossible 12 runs off 1 ball. And that’s true. But that’s not the point of it all. Hearts were broken, dreams were shattered, and saying ‘the D/L method wouldn’t have solved things either way’ isn’t something you can argue about.
The tournament had ended. Imran Khan had led Pakistan to victory in the final against England. Meanwhile, South Africa returned home heartbroken. They had fought against all odds to achieve vindication, only to fall back harder at the hands of bureaucracy. An endless abyss had formed at the bottom of their stomachs, filled with broken hearts and shattered dreams, something that couldn’t be filled. Within it lay agony, sorrow, and the remembrance of a trophy never won.
PERFECTION
Apple has announced the release of its new iPhone, iPhone 13! Shocker! It wasn’t long ago, I think around October last year, when Apple released its iPhone 12. And within another year, lo and behold, the brand new, not-a-cheap-attention-seeking-tactic, definitely-not-a-capitalism-driven-venture, iPhone 13! Interestingly, both the iPhone 12 and 13 have those rectangular edges, reminding us of the good old days of the iPhone 5s. Apple did take a short excursion into the realm of the rounded rectangle designs, which lasted for almost 6 versions of the iPhone, but now they’re back with the most-treasured rectangular design that they claim to be better than ever before (I wouldn’t completely trust that last part though)!
Coincidence? More like planned obsolescence.
Dating back to the early nineteenth century, planned obsolescence emerged from, interestingly, the lamp industry. Over the years, lamps became more and more energy efficient, as many of them lasted for more than 2400 hours. The lamp industry flourished, and as research succeeded, it began to feed the pockets of the large multinationals of the time - Philips, General Electric, and Osram, to name a few. Essentially, capitalism reigned supreme. Not for long though; it did bite them in the ass later on (whew, close save).
Since lamps lasted for more and more hours, consumers took a while to come back to replace their fused out lamps. This time gap eventually became so significant that sales in the industry as a whole started to see a dip, and panic struck. The capitalism-driven machine had run out of fuel, and ironically, it was those large corporations who decided to step in and manifest an alliance called the Phoebus Cartel. Essentially, the job of the Cartel was to ensure that no lamp that was produced lasted for more than 1000 hours. Eventually, people ran out of lamps faster than they used to and came back for their replacements, and the Cartel merrily pocketed their profits. The normalcy of capitalism was reintroduced (as it apparently should be?).
So just to flesh out all the details, the idea behind planned obsolescence revolves around worsening a certain product for your own benefit. At first, it’s glaringly counterintuitive. Why would a producer manufacture worse goods on purpose to dissatisfy their consumers? In the case of Apple, it’s purely a marketing and sales tactic, which intends to keep the consumers on for the ride. Launching new models of the iPhone every year makes the users think that their old ones have become obsolete and coerces them to buy the new one, ensuring that Apple rakes in steady, high profit.
In the world of economics and business, everything can be improved. The iPhone, laptops, food products, beverages, cars, heavy machines, everything. There’s always room for improvement in anything you make. Likewise, in the world of people, there’s always room for improvement in any sphere of life.
The Phoebus Cartel is in every one of us.
It’s deep-rooted. Whether it’s there by pure happenstance, or it was wired in by some superior Creator, I do not know. But I know it’s there. It builds flaws into us, tears us down, even breaks us into pieces at times. It destroys lives in the name of some long sought after ‘future improvement’.
But flaws aren’t necessarily bad. Without our flaws, we would just be some dull, monotonous, perfectionist versions of ourselves. And what’s the point of living in some perfect world where everyone is the best version of themselves? Growth, self-improvement and discovering oneself is what drives happiness.
Your flaws make you who you are. Your flaws make up your identity. It’s what makes you unique. It’s what makes you different from everyone else. Because let’s face it, no one is perfect.
But that’s what makes our world perfect.
AT ITS ESSENCE
Curling up with a good book and a cup of chai in my hand is something of a tradition for me when it rains outside. The pitter-patter of the rain, mixed with the smell of petrichor, emanates a feeling of calmness within me. That calming, soothing rain, however, could also be the one responsible for uprooting trees, flooding river banks, and tearing families apart. Harsh, relentless, and all-consuming. The shift from a serene drizzle to a full-blown thunderstorm only requires a gentle nudge from its surroundings, and that’s when lightning and tempests take over.
In the 21st century, the world of technology has grown leaps and bounds, and at some point, social media came into existence. When it was first introduced, people marvelled at it, revered it, even, as though it was some sort of god-given gift that descended onto our plane one day. It could connect people from all around the world, enable communication, and act as a haven for sharing one’s thoughts and ideas. Nowadays, it’s seen as an outright curse by a vast majority of people, as they try to battle and raise awareness about social media addiction and the harmful side effects of spending too much time on social media.
One day, let’s say, you meet someone on the internet and you hit it off immediately. Both of you text each other everyday, and your apprehension of talking to a stranger from the internet goes away as you begin to talk freely. Your conversations are always lively, and you decide you’re going to meet in real life. When that day finally arrives, they feel like a completely different person. Your online and tinder dates may be starkly different from what they are in real life. And that just goes to show that people may be very active on social media, trying to portray a very optimistic personality, while in real life, they may be entirely different. While the two of you may be totally hitting it off virtually, they just don’t feel like the same person in person. But that’s neither your fault, nor is it theirs. It’s just… there.
Bear with me for a moment as I talk about my one true love - physics (Well, if you think about it, physics is an all-consuming, all-encompassing discipline that can never be truly ‘talked about’- shut up nerd). To begin with, light used to act like a wave, as proved by Thomas Young’s double slit experiment that resulted in an interference pattern, and that’s what people believed for more than a century. Then, Einstein came along and performed an experiment regarding the photoelectric effect, which eventually proved that light also behaved like a particle at times. Physicists were at a crossroads when they came across this phenomenon and were shocked to find out that light could behave in more than one manner simultaneously. Eventually, they concluded that light could act as both a particle and a wave, and now, escaping this universal fact is next to impossible.
Now, you might be wondering where I am going with this (as am I). These aspects, attributes, and dualities I have listed above aren’t limited to just these realms of reality. It is an innate characteristic that is weaved into the very fabric of nature. No action, no behaviour, no response is ever uninfluenced by that object or organism’s environment. If you put someone in an online environment, they tend to behave differently than they would in real life. When put in a party full of strangers, people may act reserved and reticent, while with their close friends, they are absolutely jubilant and not afraid to let their hair down. And that is just an inevitable conclusion.
Scenarios make or break people. When you put yourself in easy situations, you won’t experience any self-growth, and before you know it, you would have wasted time you can never get back. When you push yourself out of your comfort zone, that’s when self-improvement occurs and you become better. every. single. day.
curiosity and the educational system
“A bimetallic strip consists of two metals joined together lengthwise. When heated, the strip bends. They are normally used in thermostats and fire alarms,” reads the textbook. I learn it. Three months later, the question paper asks, “What is a bimetallic strip?” I write - A bimetallic strip consists of two metals joined together lengthwise. When heated, the strip bends. They are normally used in thermostats and fire alarms. A few miles away, someone is actually manufacturing a fire alarm using a bimetallic strip, but I can’t do the same since I’m only familiar with a minuscule aspect of the bigger picture.
It’s physics class and the teacher is explaining the mechanics of the bimetallic strip to us.
He says, “When heated, the
bimetallic strip bends,” as it states
in the definition.
I ask, “But why does it bend?”
“Upon heating, both the metals
expand, but one expands more
than the other, and because they
are joined together, the strip
bends to one side,” he responds.
A moment of silence.
“But why does one metal
expand more than the other?”
“It is because one metal has a
higher responsiveness to heat
than the other, causing it to
expand more.”
“But why is one more responsive
than the other?”
Awestruck silence. I don’t hear a response. Finally I hear -
“You don’t need this for now;
you will learn this next year.”
I’d be lying if I said that I hadn’t been in these two scenarios at least a million times over. I’m completely sure that you have been in that situation too. On numerous occasions, I’ve heard the phrases “You don’t need this right now” or “That’s not in your syllabus, don’t bother yourself with it”. And for children who study solely for exams, that’s by far the best thing they can hear. I’ve been in a situation when I’m ecstatic about not having to study another complicated topic in further depth.
If that’s what education is all about, that’s it! Life’s absolutely perfect. The only thing people have to do in their educational career is learn the entire textbook by-heart, vomit that knowledge onto the answer script, get impeccable scores, and pass out with flying colours. It’s that simple.
Now, I want you to ask yourself, what does a machine do? Machines have circuit boards, wires and cables to connect all the internal machinery inside of them, but at the fundamental level, they’re black boxes. We give them something to do, they perform certain hardwired processes on it, and they give us something in return. Take a moment to think about the example of tests I gave earlier, and you’ll start to see a similarity between machines and us. Students are given textbooks by teachers, we are then hardwired to learn the entire textbook by-heart, and then give out mugged-up answers on the test in return. Where is the inquisitorial mind? Where is the critical thinking part of the mind? Where is the curiosity? Missing.
As we all must know, kids ask a lot of questions all the time. “Why is the sky blue?” “Why shouldn’t I touch fire?” “Why can’t I make a mess out of my room?” Once in a while, they come up with a question that even adults can’t answer plainly. It takes them a while to think of the answer; maybe even a little bit of research would be required. Simple child-like curiosity takes them to places that adults can only imagine. The innocence of these kids, unbound by the ‘customs’ and ‘norms’ of society, helps them think about things that are imperceivable to adult minds. These norms and customs are so deep-rooted in adult minds that it hinders their innate instincts of curiosity. Did that inherent instinct just get lost in the process of growing up?
Or were we forced to give it up?
Nowadays, technology is taking a major leap, with new products being developed, manufactured and introduced into the market every week. Where in that process of the conception, manufacturing, and selling of a new technological device did we start to mimic the machine itself? I know where that answer lies, and I think you do too.
