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About this blog


This blog is for general random musings, related and unrelated to fic :) The title comes from the W.B. Yeats poem that also inspired my username, "Aedh Wishes for the Cloths of Heaven."

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iterated algorithms: over and over and over

Recently, my mind has been in a bit of a disarray.  A large part of it is because I'm at this precipice in my life where lots of changes are happening very quickly. My family and I just moved into a new house after living in the same apartment for ten years. I'm going to head off to college in the fall, 500 miles away from my twin sister, and I've never been apart from her for more than a couple days. My brother's moving in July for his new job. And there's just the general instability that comes with depression, plus my natural discomfort with big changes. (I think everyone is a little afraid of big changes. Humans are rather complacent creatures in that way).  Whenever I'm feeling so disarrayed, I like to fall back on science.  I'm sure some of you don't see science and math as very comforting hahaha. For me, science and math are concrete and stable; they're distanced enough from emotion that I can use them to process my feelings in a sort of calm and rational manner—which is what I'm going to attempt to do in this post. I'm keeping the science and math jargon very simple, but if I'm being honest, the ideas I'm presenting here are very intuitive, so I don't think anyone will have any trouble following along. I realize that it might be a bit boring for people who aren't as STEM-oriented, so I've included some really pretty gifs and images to entertain you   In my English class this year, I read a fantastic play by Tom Stoppard called Arcadia. Arcadia is about... many things, but one of the topics it discusses is iterated algorithms. I think the phrase "iterated algorithm" is another example of Scientists Making Things Sound Unnecessarily Complicated, so I'll break it down. The word "algorithm" has been convoluted so much by Scientists Making Things Sound Unncessarily Complicated; we've forgotten how to define it in simplistic terms because our view is completely clouded by computer scientists going insane with all sorts of crazy formulas. In very simple terms, an algorithm is just a series of step—a procedure. Generally algorithms are supposed to solve problems, but I have a sort of algorithm for procrastinating on homework, so that's certainly not always the case  The word "iterated" is probably much more familiar to everyone. In conjunction, an iterated algorithm is just a series of steps that continuously repeats, or a cycle, where what you get out, you put back in.  Here's a very simple example of an iterated algorithm, written in functional notation:  fn+1 = fn + fn-1, n > 2, f0 = 0, f1 = 1  That's an example of Mathematicians Making Things Look Unnecessary Complicated. All that notation means is that in the sequence, every term is the sum of the two terms before it. (I probably could've just written that, but I really love functional notation. That's a post for another day, though.)  If you're unfamiliar with the sequence, it goes like this:  f0 = 0 f1 = 1 f2 = 1 f3 = 2 f4 = 3 The sequence should be coming together now—if you've never seen it before, this sequence is called the Fibonacci Sequence, and it's a pretty famous seqeunce. If you plot it, it sort of looks like this: Remarkably, this pattern is found everywhere in nature: in the spiral of a sunflower, in the petals of a rose, in the shape of the Milky Way, in your face—the list goes on! (Sidenote: this (Youtube, so M) is a really cool video describing how to find Fibonacci spirals in pinecones!) If you ever needed proof that science is magical, you don't need to look further than the Fibonacci sequence. I find there's some beauty in the fact that all these different objects in nature can be united by a sequence—a very simple sequence too, if you recall the functional notation. That's kind of amazing—and really comforting, that amidst all the complexity and mess in my life, there's something that can be as simple and beautiful as the Fibonacci sequence.  But the Fibonacci sequence is just one example of an iterated algorithm. There's so many others, and I'd just like to highlight a few others (with more pretty pictures!).  There's this misconception that math can't be beautiful (bah!) and I'm here to forever dispel that idea. My evidence: fractals!  if you don't know what a fractal is, here's an example:   (Let's be honest—you cannot objectively say that that isn't absolutely beautiful.)  Fractals are geometric curves that are "self-similar" across all scales, which means that if you were to zoom into that image, you'd see the same pattern. That means that it's cyclical, a never-ending pattern—which means that fractals are created by iterated algorithms. Each iteration of the algorithm plots a new point, and with enough points, you get a pretty image. The below gif demonstrates this with a fractal called the Koch snowflake. The gif demonstrates how to draw it, but the simple algorithm is this: you draw an equilateral triangle. Then, on each side, draw another, smaller equiltateral triangle, with the side of the original as its base. Then repeat with each new equilateral triangle. With enough iterations, you'll get something that resembles a snowflake! (You should try drawing it, it's super easy and requires no artistic talent whatsoever!)   In the center of the first fractal image is one of my favorite fractals; it's called the Mandelbrot set. I'm always a little amused when I see it because it sort of resembles a snowman with little baby hands, heh. The gif below demonstrates the "self-similar" aspect of the Mandlebrot set: The equation for the Mandelbrot set is the following:  zn+1 = zn2 + C, where z0 = C and C is the number of points in the complex plane for which the orbit of zn+1 does not tend to infinity  Erm.... yeah, I would try to translate that, but I don't fully understand it myself. It's rather complex (haha, math pun!). But the beauty of iterated algorithms is that the exact equation doesn't really matter. The process for drawing it is still the same. You take an x-value, plug it into the equation, and then plot the y-value. Then you take your y-value and set that as your new x-value, and repeat the process on and on. All that changes is the equation in the middle—it can be as simple as the equation for the Fibonacci sequence, or as complicated as the above equation for the Mandelbrot set. The below gif demonstrates how the Mandelbrot set is created:      With enough iterations, the image of the Mandelbrot set becomes clearer and clearer—just like with the Koch snowflake, demonstrating that this process really is universal.  The thing about the Mandelbrot set, and the Koch snowflake, is that there's a limitation to how many iterations you can go through by hand. If you tried to draw out the Koch snowflake, you'd quickly run into a space problem that would thus limit the number of iterations that you can do. The Mandelbrot set has a similar complexity problem; it didn't become clearly defined until the 1950s, when computers started taking off and suddenly humans had much more power in their hands. Sometimes, this idea is really frustrating to me. Iterated algorithms are supposed to be never-ending—they are supposed to be inherently limitless. But that's all theoretically. Nothing bears out in practice what it promises incipiently—there's always factors beyond our control. As a scientist, this is unbearingly frustrating; can you imagine running an experiment knowing that there were factors you couldn't control that could possibly invalidate all of your findings? As a human, this is unbearingly frustrating. I've always struggled to come to term with the fact that free will is, honestly, a bit of an illusion; anything could happen anytime, and even if I don't meet my untimely demise in the next week, there's always the ominous promise of an inescapable death. There's always that thought in the back of my head that there just isn't enough time—which makes all the changes I'm experiencing at the moment all the more terrifying.  It's okay, though—iterated algorithms are slowly helping me to come to terms with the spontaneity and disorder of life and how much is generally beyond my control.  Think of it this way: beyond the realm of STEM, what other processes emulate iterated algorithms?  I started to think about this and was amazed by the number of things I could think of. In Arcadia, the final scene features a waltz between the characters—the waltz is a perfect example of an iterated algorithm. You start off where you end, and continue, seamlessly, gracefully. On a larger scope, isn't history a sort of an iterated algorithm? After all, history repeats itself. This phrase is often used as negatively, as a warning. "Great, the Nazis are back again—history really does repeat itself." But I think that there's some sort of comfort to be found in this idea, too, that things that are lost are bound to turn up again because history repeats itself. There might not be enough time in my life, but everything I discover and learn and experience will be picked up by future generations, and the search for meaning will continue.  This also means that change isn't final—because you can always retrace the algorithm. Everything I've lost isn't actually lost; it's just hiding somewhere in the algorithm. This gives me comfort as a means of fighting the impermanence of life.  So, I guess, that begs the question of what to do now, in my life at this exact moment, where so many things are spiraling and so many uncontrollable forces are acting on me.  I think that all that's left to do is keep on iterating. Keep drawing, and keep looking for the larger pattern, the beauty in what I'm creating—and keep trusting that a greater pattern will indeed emerge.  I didn't mean to get so nihilistic at the end and I think this post also spiraled out of control at some point. This is my near-midnight brain talking now, haha. I hope some of this was entertaining/interesting/hopefully also comforting to any of you, and would love to hear your thoughts. Do you know of any other iterated algorithms? (Remember: broaden your mind. They're everywhere.) Do you have general advice for dealing with lots of monumental changes happening very quickly? Does anyone else find comfort like this in math and science, or am I just weird? Did you like the pretty pictures?!  (...okay, I'm shutting up now. Thanks for reading. <3)          




stories written by computers

Hello   I’ve been researching machine creativity and I ran into a few interesting articles that I wanted to share with everyone! If you don’t know, machine creativity is exactly what it sounds like it is: teaching computers how to create art in any form. It’s a very complicated field, because if you think about it, all computers are are mega-powerful calculators with lots of memory. How in the world could they write stories and poems and draw pictures?  The answer is through math!  I know that that may seem a little counterintuitive because math is literally one of the most concrete things out there and I think everyone would agree that art is the exact opposite. But there’s always an underlying logic behind all the art that we create; though our brains work in mysterious ways, every facet of a story/artwork we created is always the result of a decision tree—whether subconsciously or consciously, we always intend to make the decisions that we do when creating art. Decision trees are really good for computers—computers love decision trees since they’re essentially just big conditionals, and conditionals are only true/false, and that’s binary, so that makes computers very very happy   Anyway, I was researching some of the things that computers have created, and found about something called NaNoGenMo (National Novel Generating Month), which is like NaNoWriMo, but instead of you writing the novel, you write code to generate a novel. I think it’s a really cool idea and there were some very amusing examples in this Medium post. My favorite was “Twide and Twejudice”, which is Pride and Prejudice but with Tweets as the dialogue   But let’s be real, those novels really aren’t that comprehensible. I did a little more digging around and found something even cooler, a web app called word.camera, which takes in a picture and then outputs a poem based on what’s happening in the picture. (Just so you know, this is definitely not an easy thing to teach a computer to do!).  Machine creativity isn’t limited only to the written word, though; as I said before, machines have been to taught how to create all sorts of art. The coolest, in my opinion, is the visual art. For instance, Google DeepDream is a research project by Google which looks at any arbitrary image you give it and finds other images inside it. Here’s an example: It’s kinda beautiful, right? And definitely a little surrealistic. Essentially, DeepDream reverses the process of recognizing objects in order to create objects that aren’t there.  Even cooler, Sony CSL is leading a project to develop AI that can create music—they’ve already generated a song called “Daddy’s Car”, which is...a little odd, but that’s understandable, considering it’s coming from a computer haha!  Anyway, this was very random, but something that I thought would be interesting to share  In particular, this was interesting for me because I’m always trying to reconcile the two sides of my creativity, the science side and the writing side. I guess, in the end, the two sides aren’t all that different! In the end, whether I’m writing a fic or writing code, I am just stringing words together to create some sort of meaning. 




what's your mythology?

This is a phrase that one of the English teachers at my school uses often, and I think it's such a profound phrase. What's my mythology? What are the stories that make up me--the stories that make up my dreams, my fears, my hopes? What are the stories that capture my humanness?  Whenever I sit down to write anything, I always try to consider this question. What are my characters' mythologies? How can I write them? Mythologies are not just "headcanons" I have about these characters; they're questions about the characters that have been spun into stories, they're the characters' fears and dreams embodied. They're the characters' imaginations. Isn't that crazy, that a story can capture a character's imagination?  I shuffle through the hundreds of stories in their mythology, the stories that speak their dreams and imaginations, looking for one that I can tell.  Sometimes, there's one that sticks out easily.  That was the case for "keyframe". I sorted through all of the stories in Regulus's mythology, stories that focus around his heroism and bravery, his sadness... and this story, about Pandora, immediately shined. My goal with this story was to showcase his fear, his dreams--to describe a singular moment that captured all the conflicting forces that guided him for his whole life: the forces of obligation, family, fear, hope, and love. The first two are negative forces but the last two are positive forces--so what remained, after the opposing forces canceled out, was his fear, and this was the guiding principle in that story: fear of death, of ashaming his family, of the punishment for rebelling, and of the regret that would haunt him if he didn't rebel.  Other times, I see three or four stories.  This was the case for "courage". Neville's mythology is filled with love, with innocence, with courage, with hope, and with tragedy. But the three stories I saw spoke about his shame and fear, the antonym to his courage--and I was fascinated. I knew I had to share this, this human side of the hero. (That phrase, "human side of the hero", is essentially one of the themes of the collection "War Stories" as a whole). One story spoke about his shame about being inadequate, about not living up to the legacy his parents left him. Another story spoke about his inability to share what he felt with his children--this one makes my heart hurt. The final story spoke about the intense fear he felt during his last year at Hogwarts. I spun the stories together, taking threads from each story, and the result was "courage"--a testament to the courage it takes to even admit fear and mistakes, and a different perspective on Neville's heroism.  And sometimes, I don't see whole stories, but fragments of stories.  This was the case for "china doll." Cho's mythology is sort of in pieces for me; I see moments for her where she is victorious and strong and moments where she's weak and broken--I wanted to capture all of that in one story. And I wanted to introduce parts of her mythology that are often forgotten: her heritage, her parents. I threaded out one story from her mythology which was a Chinese legend she had heard; this was my attempt to capture her dreams. Then I collected some fragments of other stories in her mythology: trauma after the war, pain after Cedric, the feeling of flying, and, her mother, the force that tried to keep her together. These were her fears, her dreams, her emotions.  I hope to continue sorting through these characters' mythologies, finding stories that convey their soul, or if there isn't one already existing, creating stories that can do that. I wanted to share this because it's a different perspective that's allowed me to get closer to my characters; now, by diving deep into their emotions and histories and dreams and fears and their souls as a whole, I can find a story about them that really speaks their soul. 




four seasons, four loves

The title is a reference to Avatar: The Last Airbender   One of the things and astonished seven-year-old me the most when I moved to Massachusetts to California was the fact that Massachusetts actually has four seasons. In California, it's more like you've got 2 seasons: one incredibly hot, wildfire-igniting, bone-melting summer, and the rest of the year being a little wetter and little less hot. Oh, and if you live in San Francisco, there's always fog, so you might not even notice the difference in the seasons haha.  Massachusetts is much different; we have four beautiful seasons (though with global warming, some of those seasons are stretching out a little bit). I'll start with autumn,  as that's the one we're in right now  AUTUMN New England is famous for autumn foliage and I can attest that it really is beautiful, in certain places. Where I live, it's sort of just crusty brown leaves. But I love waking up and seeing the sun rise; there's always a pretty feathery pink in the sky that melts into orange and yellow and it's just gorgeous. Also, it's really only chilly in the morning, but only enough to call for a sweater, so there's a nice mix between summer and winter here.  Regardless, I feel like autumn is a bit overrated. But maybe that's because for me, it's associated with school starting again   WINTER When I first moved to Massachusetts, winter was easily my favorite season, and for exactly one reason: snow. I'd never seen anything like it! The first snowfall, my face was pressed against my window the entire time. Now, after having shoveled way too much and almost frozen my butt off, I'm not so fond of winter anymore. In recent years, winter hasn't been so severe; we've had sporadic snowfall, a couple major storms--definitely more manageable than five or six years ago. But it's still annoying!  SPRING If I had to pick a favorite season, it would probably be between spring and summer. Spring is beautiful in Massachusetts; there's lots of pretty flowers and there's always a sense of growth and change, which is really nice. I dislike all the rain, but that, much like the snow, is very sporadic. Unfortunately, spring is very short here in Massachusetts; there's definitely a stretched out winter here.  SUMMER  Maybe because it's my default state, being from India and having grown up in California, summer is my favorite season. I don't mind the heat; I love it  I'm always cold so summer is awesome. Summer in MA is never too hot, but just hot enough to feel really good. I like summer too because time seems to slow down with the longer days, which is great since my life seems to be permanently stuck on fast-forward in all the other seasons. 



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