Essays and notes on mathematics, philosophy, and poetry.https://www.bellabah.com/en-ushttps://www.bellabah.com/posts/a-bigger-garden/https://www.bellabah.com/posts/a-bigger-garden/A man tended his garden, lost in routine When fluttered in a butterfly, unannounced, More brilliant than anything he’d ever seen, Entranced, he laid down his shears, And proclaimed: “O’ butterfly, I’d sow the whole Earth, So you might always alight, Gently upon a flower’s petal, And if your w...Mon, 28 Oct 2024 00:00:00 GMThttps://www.bellabah.com/posts/a-children-of-prometheus/https://www.bellabah.com/posts/a-children-of-prometheus/Heaven determined that the cosmos be like a frozen sea, And were its mandate met, All would be commanded still in icy thrall, O’ mankind! Take inspiration from the defiant stars, Those selfless stars, Who generously share their stolen warmth, Burning as it were with a Promethean soul, To li...Wed, 13 Mar 2024 00:00:00 GMThttps://www.bellabah.com/posts/a-lament/https://www.bellabah.com/posts/a-lament/How lonely is the branch with no bird to give perch, Wasted is the flower’s nectar when there is no bee, And barren is the garden from disuse; The tree under which the poet lies gives no shade, So what use is his pen with none as its subject, Tormented in knowing that, Any verse is consigned t...Wed, 13 Mar 2024 00:00:00 GMThttps://www.bellabah.com/posts/a-lit-soul/https://www.bellabah.com/posts/a-lit-soul/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This poem was inspired by a quote I came across online that I now know came from Werner Herzog's memoir. I know nothing of the man, but the following quote had me thinking: "I'd rather die than go to an analyst, because it's m...Tue, 19 Dec 2023 00:00:00 GMThttps://www.bellabah.com/posts/all-things-are-nails/https://www.bellabah.com/posts/all-things-are-nails/All things are nails \ to the hammer forged for one purpose. One evening, in a grief that visits even iron, \ the hammer turned to its maker: "Why was I made narrow? \ I cannot plant flowers, \ nor mark a canvas.” The maker replied: “The garden you cannot tend, you will fence. \ The painting you...Tue, 05 May 2026 00:00:00 GMThttps://www.bellabah.com/posts/an-ashen-inheritance/https://www.bellabah.com/posts/an-ashen-inheritance/Among a row of houses sat a solitary great house atop a high hill. This great house was an old house, by and large considered one of the "better" houses. Nevertheless, like all material things, it was not without its blemishes: in some of its support beams were termites; in some of its closets, ling...Mon, 06 Nov 2023 00:00:00 GMThttps://www.bellabah.com/posts/appetit/https://www.bellabah.com/posts/appetit/Whosoever puts themselves to task, In pursuit of whatever consumes them-- Not after scraps, But doggedly after their true quarry, Like a greyhound set on course, Will discover in themselves, The strange alchemy of effort: As if the burning itself, Generates its own fuel— So they’ll understa...Sat, 04 Jan 2025 00:00:00 GMThttps://www.bellabah.com/posts/backwash-learning/https://www.bellabah.com/posts/backwash-learning/**Definition (Backwash)** *informal* [Oxford English Dictionary]: The liquid that flows back into a bottle, glass, etc. after someone has taken a drink, assumed to contain that person's saliva. Suppose that [Adam](https://www.bellabah.com/posts/dignity/), our perennial gentleman-hermit, sets out to...Wed, 03 Sep 2025 00:00:00 GMThttps://www.bellabah.com/posts/come-home/https://www.bellabah.com/posts/come-home/If it's true, as oft they claim,\\ That one's eyes are windows to one's soul,\\ Then come close, peer deep within,\\ Glimpse the depths of this restless heart of mine. Hear you my heart?\\ How fiercely it roars,\\ Defying stillness and silence,\\ Beneath the gaze of the one it adores. It proclaims...Sat, 16 Sep 2023 00:00:00 GMThttps://www.bellabah.com/posts/coordination-many-agents/https://www.bellabah.com/posts/coordination-many-agents/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This was the start of my serious research at MIT, and the technical start for some of my later work with power systems. I'd written this during the summer of 2018. (I was watching the 2018 FIFA world cup pretty religiously so ...Thu, 21 May 2020 00:00:00 GMThttps://www.bellabah.com/posts/craters-become-lakes/https://www.bellabah.com/posts/craters-become-lakes/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> I went backpacking with a couple of friends up in Desolation wilderness (southwest of Lake Tahoe) this past weekend. The timing was fortuitous because I've recently really gotten into "thinking", and there's no better time and...Thu, 22 Aug 2024 00:00:00 GMThttps://www.bellabah.com/posts/cresting-sisyphus-mountain/https://www.bellabah.com/posts/cresting-sisyphus-mountain/Readily will I unburden Sisyphus, Without care to crest the Mountain in which Man finds banal suffering and his very Soul trapped, I shall relieve Sisyphus of that accursed boulder. So readily will I heft said sorry stone above my head And to Atlas' awe, Strike down hard To split asunder the v...Fri, 25 Aug 2023 00:00:00 GMThttps://www.bellabah.com/posts/dignity/https://www.bellabah.com/posts/dignity/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This article is inspired by one of the themes explored in Martin Luther King, Jr's ["Remaining Awake through a Great Revolution"](https://kinginstitute.stanford.edu/king-papers/documents/remaining-awake-through-great-revolutio...Mon, 23 Mar 2020 00:00:00 GMThttps://www.bellabah.com/posts/endurance-of-spirit/https://www.bellabah.com/posts/endurance-of-spirit/Man is first pliable, Only when compelled to run through nature’s course, Through her crags and bramble, and under an angry sun and an inhospitable cold, Is he made firm, sharp, and with purpose, Just as the sword gains its shape under hammer blows, Finds its edge in the whetstone, And its bit...Sun, 22 Oct 2023 00:00:00 GMThttps://www.bellabah.com/posts/enlightenment-now/https://www.bellabah.com/posts/enlightenment-now/Here are my thoughts on Steven Pinker's *The Enlightenment Now*. I'd read this sometime in 2018, probably in March, shortly after the book came out. I took some notes while reading the book, and for whatever reason, I chose to take the following quotes from the book: #### On being wary of sensatio...Tue, 21 Jan 2020 00:00:00 GMThttps://www.bellabah.com/posts/factories-without-pause/https://www.bellabah.com/posts/factories-without-pause/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> For whatever reason, my mammalian brain finds explosions deeply satisfying—preferably controlled, non-lethal, and pointed skyward. Which is to say, I like rockets. And I want to see orders of magnitude more rockets. Along with...Mon, 29 Sep 2025 00:00:00 GMThttps://www.bellabah.com/posts/feature-development/https://www.bellabah.com/posts/feature-development/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> The following is inspired by an entry in my journal reflecting on recent events at the office. After three and a half years of professional experience, I finally feel entitled to some opinions on how things ought to be done. P...Mon, 15 Jul 2024 00:00:00 GMThttps://www.bellabah.com/posts/four-inscribed-circles/https://www.bellabah.com/posts/four-inscribed-circles/import { Image } from "astro:assets"; Circles captivate us, and inscribed circles doubly so. In [a previous post](/posts/inscribed-circles), we tackled finding the area of a shaded region. Today we pursue a similar goal with a twist.  Here w...Sun, 13 Jul 2025 00:00:00 GMThttps://www.bellabah.com/posts/gedanken-spheres/https://www.bellabah.com/posts/gedanken-spheres/## Introduction I've never liked puzzles. That is, until I read of Albert Einstein and his employ of *Gedankenexperimenten*–thought experiments–to shape his understanding of general and special relativity. Now I like puzzles, but only of the German variety. Lately, I've been assailed by the though...Wed, 15 Oct 2025 00:00:00 GMThttps://www.bellabah.com/posts/haikus-at-3am/https://www.bellabah.com/posts/haikus-at-3am/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> Driving back from a party late at night and my slight astigmatism causing the other vehicle's lights to seem like halos, my mind went straight to stars, their beauty, and the kernel of the idea that the terrestrial mirrors the...Sun, 10 Sep 2023 00:00:00 GMThttps://www.bellabah.com/posts/half-are-new/https://www.bellabah.com/posts/half-are-new/Consider a team of $n$ people (where $n$ is even), with exactly half wearing red shirts and half wearing blue. A leader, wanting to illustrate this 50/50 split, declares: "Look to your left and right—one of them is wearing red!" This sounds reasonable; after all, if we pick someone at random, they ...Wed, 10 Sep 2025 00:00:00 GMThttps://www.bellabah.com/posts/inquiry-into-spatiotemporal/https://www.bellabah.com/posts/inquiry-into-spatiotemporal/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> I'd written this for a philosophy class my last semester at MIT. The main thesis here is pretty contrived, forced, and probably wrong, but is in my opinion, interesting nonetheless. I've found that I frequently come up with co...Mon, 18 Jan 2021 00:00:00 GMThttps://www.bellabah.com/posts/hello-world/https://www.bellabah.com/posts/hello-world/What a time to be alive! 🙌🏿🙌🏿...Sat, 18 Jan 2020 00:00:00 GMThttps://www.bellabah.com/posts/inscribed-circles/https://www.bellabah.com/posts/inscribed-circles/import { Image } from "astro:assets"; I was given an interesting math problem on a post-it note recently. The setup is pictured below: two circles (of radius $r$) are inscribed within a $2r \times r$ rectangle. I've chosen, without loss of generality, $r = 1$. The goal is to find the total area of...Wed, 09 Jul 2025 00:00:00 GMThttps://www.bellabah.com/posts/joie-de-vivre/https://www.bellabah.com/posts/joie-de-vivre/All belongs to the genuine, Who do not flinch from their own passion, Nor douse their own fiery spirit, Having vowed to never forge a false self, Or anything resembling an aped imitation of a living soul; All belongs to the people of substance, Who do not bottle their excitement or stifle thei...Mon, 27 May 2024 00:00:00 GMThttps://www.bellabah.com/posts/kerplunk/https://www.bellabah.com/posts/kerplunk/import { Image } from 'astro:assets'; import kerplunkImg from '../../assets/posts/kerplunk/kerplunk.png'; ## Introduction I was recently (mildly) bullied by a 7-year-old while playing Kerplunk this past winter holiday. To cope with said bullying, my mind went to the math of the game before me. Ke...Mon, 05 Jan 2026 00:00:00 GMThttps://www.bellabah.com/posts/marxism/https://www.bellabah.com/posts/marxism/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This article is the second installment of my "Musings on x" series with regards to political economy and its attendant philosophy. (COVID-19's made me something of an arm-chair philosopher.) This serves as a first pass on the ...Sat, 09 May 2020 00:00:00 GMThttps://www.bellabah.com/posts/moonlight/https://www.bellabah.com/posts/moonlight/How perfect you looked beneath the moonlight, So I bought the moon and named it after you, Wove the stars into our own constellation, And wrapped your tapestry in the velvety black of night, And in our marble pavilion, gathered fairies to play our song on moonflower trumpets, But, it was a gift...Sun, 12 Nov 2023 00:00:00 GMThttps://www.bellabah.com/posts/may-things-go-the-ideal-way/https://www.bellabah.com/posts/may-things-go-the-ideal-way/I’ve often said May things go the ideal way and so furiously do I urge it on that much like a boy, who in his little sail boat will blow furiously against her sails supremely confident that with his lungs alone and the strength of their combined, forceful, breathy desire and perhaps with the...Fri, 25 Aug 2023 00:00:00 GMThttps://www.bellabah.com/posts/misc-hands/https://www.bellabah.com/posts/misc-hands/A recurring theme of mine is that shortly after reading a book, particularly a biography, I'll pick up a few things from the story's protagonist and try to implement them in my own life. The drawings you'll see are one such case. After reading (and not finishing) Walter Isaacson's biography on Renai...Wed, 22 Jan 2020 00:00:00 GMThttps://www.bellabah.com/posts/of-worlds-becoming/https://www.bellabah.com/posts/of-worlds-becoming/Heavy is the head that wears the crown, Forged of lofty expectations, And sagged are the shoulders, Underneath a world unborn, But heavier still, Are man and his dreams taken together, Sat astride the beast of burden, Unduly saddled, With a load not its own, And yet, the crown gleams, With...Sat, 07 Dec 2024 00:00:00 GMThttps://www.bellabah.com/posts/nozick/https://www.bellabah.com/posts/nozick/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> I'd written this piece for a class on Justice at MIT in response to a prompt--however, as per the professor's request, I will not be sharing the prompt; that said, the article remains readable even without prior knowledge of t...Tue, 24 Nov 2020 00:00:00 GMThttps://www.bellabah.com/posts/on-consciousness/https://www.bellabah.com/posts/on-consciousness/There's a recurring theme in my life's adventures: I'll head out on a backpacking trip with friends, some intriguing question will inevitably surface as we muck about, a lively discussion ensues, and then I find myself compelled to put pen to paper—or fingers to keyboard—once I'm home. This time, t...Wed, 11 Jun 2025 00:00:00 GMThttps://www.bellabah.com/posts/on-open-source-llms-meta/https://www.bellabah.com/posts/on-open-source-llms-meta/**TLDR**: Meta's decision to open-source Llama 3.1 is a calculated bet on the future of content creation and ad campaign creation. By making AI models like Llama widely available, Meta is poised to benefit from the increased demand for curation, personalization, and distribution of AI-generated cont...Thu, 08 Aug 2024 00:00:00 GMThttps://www.bellabah.com/posts/on-the-beginning-of-things/https://www.bellabah.com/posts/on-the-beginning-of-things/I had an interesting discussion this past weekend on the "beginning of things." Someone making their case implied early on that "all things have a beginning". One way or another, I got to thinking: *do **all** things necessarily have a beginning?* For all physical things and processes, we can confi...Mon, 19 May 2025 00:00:00 GMThttps://www.bellabah.com/posts/perhaps-i-should-have-been-a-painter/https://www.bellabah.com/posts/perhaps-i-should-have-been-a-painter/Much to the disappointment of romantics But of no surprise to the sensible Poems are a lousy medium for one’s feelings For already it is clear to me— The sorry amateur I am That I’d sooner run out of words and their arrangement Than exhaust endless, pouring feeling...Fri, 25 Aug 2023 00:00:00 GMThttps://www.bellabah.com/posts/prayer-on-a-bowsprit/https://www.bellabah.com/posts/prayer-on-a-bowsprit/O Lord, Steer me through affairs of the heart, Mine vessel I surrender to thee, Take from me the wheel, Bind me steadfast to the bowsprit, So my weeping, Tears akin to mortal rain, May fall harmlessly into the ocean below, And not flood this ship, Lord, Guide me through matters of the hea...Sat, 16 Sep 2023 00:00:00 GMThttps://www.bellabah.com/posts/psychological-oppression/https://www.bellabah.com/posts/psychological-oppression/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> I've been having a hard time writing: I'll open up my notes app and upon seeing the several, unfinished drafts of essays, I immediately lose motivation and close the app. That said, I think I've identified why I'm having troub...Fri, 08 Jan 2021 00:00:00 GMThttps://www.bellabah.com/posts/rawls/https://www.bellabah.com/posts/rawls/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> I'd written this piece for a class on Justice at MIT in response to a prompt--however, as per the professor's request, I will not be sharing the prompt; that said, the article remains readable even without prior knowledge of t...Tue, 24 Nov 2020 00:00:00 GMThttps://www.bellabah.com/posts/reflections-on-progress-and-poverty-part-1/https://www.bellabah.com/posts/reflections-on-progress-and-poverty-part-1/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This work departs from the traditional essay format. It presents a series of personal annotations and critical reflections inspired by excerpts from Henry George's seminal text, Progress and Poverty. Certain excerpts will be p...Sun, 07 Apr 2024 00:00:00 GMThttps://www.bellabah.com/posts/root-cause-analysis/https://www.bellabah.com/posts/root-cause-analysis/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote title="Executive Summary"> Root Cause Analysis (RCA) has long been the backbone of reliability and safety programs. It works well when a clear failure can be isolated and explained, but can struggle with the messy, adaptive rea...Mon, 25 Aug 2025 00:00:00 GMThttps://www.bellabah.com/posts/saving-for-retirement/https://www.bellabah.com/posts/saving-for-retirement/I'd written this last summer for the Muslim Student Association here at MIT. I am by no means a financial expert, but I want to share with you all the things I've learned about saving for retirement in the United States of 'Murica. If I've made mistakes, let me know and I'll correct them -- I invite...Mon, 20 Jan 2020 00:00:00 GMThttps://www.bellabah.com/posts/seasons-in-all-things/https://www.bellabah.com/posts/seasons-in-all-things/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> A couple of years ago I read ["Big Panda and Tiny Dragon"](https://www.goodreads.com/book/show/55926835-big-panda-tiny-dragon), a picture book that extols some rather Buddhist virtues on patience, calm, and letting go. One pag...Tue, 10 Mar 2026 00:00:00 GMThttps://www.bellabah.com/posts/silence-the-usurper/https://www.bellabah.com/posts/silence-the-usurper/In the hollow of his grand piano, Silence sang, Ecstatic in her soundless melody, For as time passed, a maestro’s fascination with Music’s theory, Eclipsed his desire to play, He starved her of all things: his tender touch, his adoration, his affection— And Music languished in a labyrinthine mi...Sun, 11 Aug 2024 00:00:00 GMThttps://www.bellabah.com/posts/sierraleone-and-her-manufactures/https://www.bellabah.com/posts/sierraleone-and-her-manufactures/I had written this on January 7, 2017 while I was in Freetown, Sierra Leone. I believe this was written shortly after reading "The Wealth and Poverty of Nations" by David Landes for the second time. The essay's content is pretty much what the title states. It's an economic essay on Sierra Leone, h...Tue, 21 Jan 2020 00:00:00 GMThttps://www.bellabah.com/posts/spheres-and-shadows/https://www.bellabah.com/posts/spheres-and-shadows/A good mathematical puzzle often begins not with a question, but with a statement—one so elegant it feels both obvious and impossible. For me, this moment arrived during a commute, watching a 3Blue1Brown video featuring Terence Tao[^1]. At one point, a theorem was presented (somewhat casually): *if ...Mon, 07 Jul 2025 00:00:00 GMThttps://www.bellabah.com/posts/suitors-of-the-sun/https://www.bellabah.com/posts/suitors-of-the-sun/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This poem was inspired by a quote attributed to Napoleon from a book I'd recently finished titled "Mind of Napoleon" compiled by J. Christopher Herold. *"Everybody has loved me and hated me; everybody has taken me up, dropp...Sat, 17 Feb 2024 00:00:00 GMThttps://www.bellabah.com/posts/sum-of-digits-divisible-by-3/https://www.bellabah.com/posts/sum-of-digits-divisible-by-3/## Motivation My friends invited me to lunch at the Google office today (very fortunate for a man who's fending on his own). While eating, we somehow ended up debating the supposed superiority of the dragon over the hare in the Chinese zodiac. As a loyal hare, I came to the defense of hares everywh...Sat, 07 Feb 2026 00:00:00 GMThttps://www.bellabah.com/posts/the-data-quality-objection/https://www.bellabah.com/posts/the-data-quality-objection/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote title="Executive Summary"> A common objection to statistical AI systems in complex industries is "Garbage in, garbage out" (GIGO). The view is that a model whose inputs are noisy can only produce noisy outputs. While this conta...Sun, 11 Jan 2026 00:00:00 GMThttps://www.bellabah.com/posts/the-tortoise-and-the-eagle/https://www.bellabah.com/posts/the-tortoise-and-the-eagle/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> Inspiration taken from Aesop's fable "The Tortoise and The Eagle". Variations of it can be found here https://fablesofaesop.com/the-tortoise-and-the-eagle.html. </AuthorNote> A Tortoise declared to all the small animals aroun...Sun, 22 Oct 2023 00:00:00 GMThttps://www.bellabah.com/posts/tumbleweed/https://www.bellabah.com/posts/tumbleweed/Two lovers Apart Separated by large and empty desert expanse On which the wind gently rocks tumbleweeds to and fro So tangled so as to never unravel Between— Two lovers gazing longingly at the other, Having taken cue from nature *How I wish we’d tumble into tight embr...Fri, 25 Aug 2023 00:00:00 GMThttps://www.bellabah.com/posts/webs/https://www.bellabah.com/posts/webs/Is technology not innate to us as webs are to the patient spider's craft? We weave our networks, ever more complex, both born of instinct, shaped by nature's law. <br/> But here we part from spider's ancient art: our webs, sprung of that same primal need, become the snares that hold us fast— ...Tue, 03 Jun 2025 00:00:00 GMThttps://www.bellabah.com/posts/willful-arrogance/https://www.bellabah.com/posts/willful-arrogance/There is a certain arrogance in man, That has him believe, Despite all, that he will make it happen, But like a deluge wherefor man would fix a dam in prevention, God humbles him, For God intended man prostrate and not dictate the universe. But there are times, When the will of man is so conc...Mon, 25 Dec 2023 00:00:00 GMThttps://www.bellabah.com/posts/workhorse/https://www.bellabah.com/posts/workhorse/What is one to do? with a machine, Which, if left to its own devices, Will gladly go the distance, And unwittingly grind its gears to dust. But so too, Were it restrained and tethered, Will shake itself apart, In protest....Thu, 20 Nov 2025 00:00:00 GMThttps://www.bellabah.com/posts/zion-thinking/https://www.bellabah.com/posts/zion-thinking/import AuthorNote from '../../components/AuthorNote.astro'; <AuthorNote> This article is unstructured, so handle with care as things won't transition or segue as nicely as they could. I didn't bother very hard to change that, it'd have been more work than it's worth to corral everything into greate...Tue, 05 Nov 2024 00:00:00 GMT