Chancellor Ceti's Blog

Orson Welles’ Citizen Kane – An Exploration of Media, Power, and the Meaning of Happiness

Thu, 19 Jun 2025 00:00:00 GMT

Orson Welles’ Citizen Kane – An Exploration of Media, Power, and the Meaning of Happiness

Citizen Kane is widely cited as one of the best American movies, so I figured it was time to check it out. Here are my rambling thoughts on the film. I don’t spoil anything significant, so you may read without fear. Enjoy!

The film begins by showing the grand mansion of Charles Foster Kane: once the most powerful newspaper publisher in America, he recently died alone with his power significantly diminished. From the very beginning, I was struck by the opulence of Kane’s lifestyle; a mansion that was compared to Kublai Khan’s Xanadu, a huge statue collection, and two failed marriages to trophy wives. All this wealth, yet even without seeing the man, I got a sense that he wasn’t really happy when he died. Despite the amount of money poured into its design, Kane’s pleasure palace looks more like a scene out of Dracula than a place for fun.

The visuals are amazing from the very beginning; there’s some kind of overlay of multiple shots that is disorienting and aesthetically pleasing at the same time. We see a variety of scenes superimposed over a shot of Kane’s mansion as the credits roll; for 1941, this is incredible film editing and, even today, one of the more interesting ways a film has grabbed people’s attention during the credits.

After this media tycoon’s death, the writers at his newspaper The New York Inquirer decide to write an obituary for him. However, they are flummoxed by the meaning of his last words – “Rosebud.” To decipher this enigma, the journalists read old diaries, interview Kane’s old friends, and dig into his little-known past.

The story is thus presented through flashbacks, beginning with his early childhood in a middle-class family and showing how the discovery of gold on his family’s property launches him into the upper class. He is raised under a bank’s supervision and grows up without discipline or a strong value system – essentially a playboy millionaire. Lacking any ambition in life, he is uninterested in most of the businesses the bank manages under his name, except for the New York Inquirer newspaper, thinking “it would be fun to run a newspaper.”

The newspaper, however, ends up being more than fun: it brings Charlie tremendous power, allowing him to swing elections and even start wars according to his whims. This part of the film tackles a theme still relevant today: sensationalist reporting and the power of media.

In 1941, this topic was a hot issue because of the recent Spanish-American war. For those unfamiliar with this bit of history, the Spanish-American War was a brief conflict between Spain and the US that resulted in over 50,000 casualties (almost all Spanish) and the ceding of Spain’s last colonies to the United States. The war was provoked by the sinking of a US ship in Havana under suspicious circumstances. To this date, there is no consensus on what caused an explosion onboard the ship, but at the time, sensationalist reporting popularized the theory that the Spanish navy was responsible for the explosion. The sensationalist reporting of the time was given the name “yellow journalism” – its usage is infrequent today, but at the time, it was a well-known term. Yellow journalism played a large part in provoking the Spanish-American War, swaying public opinion in favor of war with very little evidence to back up the newspaper headlines.

Citizen Kane looks at events like this from the perspective of the powerful men running newspapers. What’s remarkable is the nonchalance with which Kane makes decisions that can result in tens of thousands of deaths. The film makes the subject of its critique clear, explicitly referring to the Spanish-American war and the role newspapers played in its start:

Bernstein: There is no war in Cuba. Signed Wheeler. Any answer?

Kane: Dear Wheeler, you provide the prose poems, I’ll provide the war.

The film deserves praise for highlighting, as early as 1941, the dangers of media consolidation and sensationalist reporting. Citizen Kane’s message has only grown more important with time. In Italy, we may look at the example of Berlusconi if we wish to see the continuity of this trend; Berlusconi used his control of the Italian media to cement his power and prevent criticism of his policies from reaching the public. In the United States, we can see a similar situation in the Murdoch family and the poisoning of Republican politics by FOX News.

Charles Foster Kane used sensationalist reporting to provoke public outrage when desired, and when he wished to shut off the public’s mind and keep people passive, he would shift focus to murder cases and gossip. This is the same thing that media outlets do today – e.g. FOX (US), JoongAng (South Korea), or Times of India. Want to create a wave of hatred towards Muslims in India? Sensationalize individual cases of Muslims committing crimes and use violent, hyperbolic rhetoric. Want people to ignore the slow death of democracy in India and continue voting BJP? Push headlines like “housewife murders husband and puts him in freezer” and don’t mention press freedom, economic disparity, or any actual issues in your newspaper. If you don’t talk about it, people will slowly forget it’s an issue.

Citizen Kane is an amazing movie because it brings attention to critical issues in our society: turns out that we haven’t learnt much from our failures pre-1941. The movie creates a dark representation of media consolidation and yellow journalism, with a warning just as effective today as it was in 1941.

It’s doubly interesting because it focuses on the powerful men responsible for this destruction, rather than the destruction itself. Citizen Kane is, in many ways, a psychological film. We’re led to ask the question: “what kind of man knowingly chooses to abuse power on such a scale and with such devastating impact?” Kane’s character is a prototype for all the villains of modern society: Elon Musk, Mark Zuckerberg, and other playboy millionaires whose immaturity puts our future at risk. If you want to understand our current problems and the men responsible for them – Citizen Kane is the movie for you.

Many films have attempted this critique of “the lives of the wealthy and powerful” and examined the playboy millionaire psyche, but very few achieve the balance and impact of Citizen Kane. The film isn’t over-the-top like many satirical films on this topic are. This movie is the most accurate depiction I’ve seen so far of the megalomania and lust for power that drives men like Elon Musk or Silvio Berlusconi.

Kane feels that he deserves the people’s love and exhibits the messiah complex common among today’s politicians and media tycoons. His happiness comes from his sense of power, and this dependence drives him to become increasingly malicious with his news reporting. Exercising power is the only thing that makes him feel alive.

Especially significant is this exchange midway through the film:

Emily: Really, Charles, people will think…

Kane: What I tell them to think.

(The sharp sound of Kane putting down his coffee cup punctuates his comment.)

Leaving aside the depiction of media tycoons specifically, the movie does a fantastic job of criticizing the behavior of the rich and famous men of America. The movie calls out billionaires’ practice of marrying “trophy wives,” long before the term was even in usage. Kane marries famous women who can boost his reputation, but he cares little for them, and both his marriages fail. His wives endure the neglect and disrespect up until their patience expires, leading to conversations such as this one

Kane: Whatever I do, I do because I love you.

Susan: You don’t love me! You want me to love you – sure – I’m Charles Foster Kane. Whatever you want – just name it and it’s yours! But you gotta love me!

The film accurately portrays all the worst aspects of billionaires’ behavior: trophy wives, opulent lifestyles, and a pathological obsession with image.

In search of admiration and status, Kane collects statues, builds a giant mansion, and marries the most “cultured” women he can find – yet he cares little for his statues, his mansion, or his wives. He is plagued by loneliness and lives in denial of his problems. This 1941 critique of wealthy men’s behavior and psychology has stood the test of time: billionaires today act almost the same way Kane did. Orson Welles’ brilliant acting makes you hate the character of Kane as if he were Musk or Zuckerberg right in front of your eyes.

Yet at the same time, the film induces pity for Kane at the end. We briefly see his childhood at the beginning of the film; here, he is innocent, cares little for money or power, and seems to enjoy life. Comparing this happy child to the dark and lonely figure at the film’s end causes us to reflect on how wealth and power can change a man. His descent into madness isn’t rapid, but rather occurs slowly throughout the movie until it suddenly strikes us – “oh wow he’s evil.” The death of happiness, idealism, and morality in Kane is gradual, allowing us to appreciate the scale of the tragedy and view the film as a cautionary tale. Money, power, and influence are great things to have, but on their own, they can’t bring true happiness and, instead, will often make you a worse person.

In addition to the brilliant scriptwriting, acting, and plot that lets Citizen Kane tackle such heavy topics, the editing and cinematography of this film were crucial to its impact. The lighting is used to highlight the dark, murky nature of Kane’s past; as a reporter sits in a hall discussing secret memoirs of Kane’s friends, the only light comes from a small window above him, creating the haunting effect shown below. Lighting is effectively used throughout the film to characterize characters, places, and scenes; Kane is shrouded in secrecy and backdoors politicking, and the film uses lighting to subtly build this atmosphere.

The mark of a good film is that it uses not only dialogue but also visuals to tell a story – Citizen Kane does this spectacularly. Kane casts a long shadow wherever he goes, and he is hopelessly alone in his mansion. The visuals of this movie brilliantly capture this image, making Citizen Kane a top tier film.

I could go on and on about how different camera angles and lighting choices help indirect characterization, but I won’t belabor the point.

Citizen Kane is a film that explores many important themes – media, power, and the meaning of happiness – and its brilliant acting, screenwriting, and cinematography allow it to tackle these topics with great impact. It is a movie that you enjoy but also one that makes you think. At the beginning, we wonder how a man so powerful ended up dying lonely and depressed. However, the puzzle of Kane’s last words is what truly guides the deep thinking of this film. “What does Rosebud mean?” is a question that leads us to explore all these themes through the lens of Kane’s life story. The intelligent representation of such heavy themes is what makes Citizen Kane one of the great American movies.

A Review of Park Chan-wook's film Oldboy

Sat, 14 Jun 2025 00:00:00 GMT

A Review of the film Oldboy

A Review of Park Chan-wook's film Oldboy

For a film inspired by Oedipus Rex, I was expecting this film to be dark, but after watching the movie, I think even Sophocles would've been unable to dream this up. If sex or extreme violence spoils a movie for you, please avoid this film.

Oldboy is a genre film, so I understand it will not appeal to everyone’s taste. However, for fans of action thrillers, this movie is a must-watch. The film follows Oh Dae-su, a violent, chronically drunk man, after he is kidnapped on a rainy night while trying to get home to his family. We see him spend 15 years imprisoned in a room, not knowing the reason or the duration of his punishment, and Choi Min-sik (lead actor) brilliantly captures the psychological impacts of this imprisonment. In one scene, we see him plead with his captors for a bit of conversation, then turn to cursing at them, and finally go back to sobbing, apologizing, and begging to know why he’s been jailed. Choi’s brilliance as an actor makes the anguish and desperation of his character come to life, making the first 30 minutes of this film already horrifying.

The film turns even darker, however, after Oh Dae-su is released. During his confinement, he spent years punching the walls, thinking about how to track down his captors and get his revenge on them. Once out of prison, he immediately starts getting mysterious clues from his captors about how to find them. His search for answers leads him into increasingly dangerous situations, creating intense action sequences and increasing the terror we feel throughout the movie. There is less action here than in films like John Wick, but the action sequences are of incredible quality and add to the gritty nature of the movie.

Choi’s struggle grows more intense after he falls in love with Japanese sushi chef Mi-do – their relationship is marked by Choi’s suspicion of her and his violent, erratic behavior as his desire for revenge consumes him. Eventually, the film approaches its climax as Choi’s former captors threaten to kill Mi-do in 5 days unless he can figure out why he was imprisoned and then released.

The film’s climax lasts around half an hour and is some of the most powerful cinema I’ve seen in my life. Towards the end, you feel like crying, vomiting, knocking yourself out, and screaming at the director all at the same time. There is a horrifying twist, heart-wrenching acting all around, and even more grisly violence to add to the evil of this movie.

The film’s ending allows multiple interpretations, adding confusion to the already powerful emotions of rage, disgust, and horror that I felt. I spent half the movie on the edge of my seat, as desperate as the protagonist to understand why he was jailed for 15 years. By the end, after finding that answer, I was just desperate for Choi and Mi-do’s suffering to be over – their superb acting elicits sympathy and anguish from the audience.

My only complaint with the film would be slightly stretching reality at two points – however, the dramatic value of this outweighed the loss of realism, so it hardly detracts from the film’s quality.

This movie doesn’t have any deep themes or much of a message, but fans of action thrillers must watch Oldboy. Incredible acting, great action sequences, and a horrifying plot – seriously, this movie’s ending goes in my “top 10 most horrifying, disgusting, and depressing endings” list.

A Review of Rohinton Mistry's novel 'A Fine Balance'

Sun, 06 Jul 2025 00:00:00 GMT

A Review of the Rohinton Mistry's novel 'A Fine Balance'

A Review of Rohinton Mistry’s “A Fine Balance”

“You see, you cannot draw lines and compartments, and refuse to budge beyond them. Sometimes you have to use your failures as stepping-stones to success. You have to maintain a fine balance between hope and despair.”

Rohinton Mistry’s 1995 novel “A Fine Balance” owes its title to the idea of balancing hope and despair even in the darkest of times. However, the word “fine” is an understatement – “precarious” is a better word to describe that balance amidst the death and destruction of Mistry’s world.

The book is set during the Emergency in India. For those unfamiliar with Indian history, the Emergency was a period between 1975 and 1977 during which the prime minister Indira Gandhi declared a state of emergency throughout the country to crack down on political opposition and avoid the consequences of the Supreme Court convicting her of electoral fraud. This was a terrifying time in India. Political opponents were jailed and tortured, the poor were subjected to forced sterilizations, and millions were displaced by slum demolitions in the name of “city beautification.”

Mistry’s novel shows the impacts of the Emergency on the lives of ordinary people living in an already cruel world.

The story centers around four characters from different backgrounds who end up living together during the Emergency and developing a powerful friendship: a widow struggling to make rent while still haunted by the loss of her husband years ago; a college student coping with the disappearance of his best friend, an activist who incurred the government’s wrath; and two Dalits fleeing caste violence in their village only to then meet the trials of poverty in the big city.

The book tackles Emergency-era India by taking us beyond the realm of summaries and data tables and into the tents where men underwent forced sterilizations and into the slums that were destroyed by Sanjay Gandhi’s insanity. We see people’s lives, already dire, thrown overnight into even greater turmoil by forces beyond their control. History is shown as an unstoppable beast, destroying everything in its wake and leaving ordinary people to maintain the fine balance between hope and despair, even as the whole world is pitted against them. The book makes the Emergency – resplendent in its injustice, its horrors, and its violence– come to life, doing justice to the story of one of the darkest times in India.

The book goes beyond the evils created by Indira Gandhi. Much of the suffering in the novel isn’t related to the Emergency but rather to the status quo prior to that added bit of hellfire. The squalid conditions of the poor shown in this book existed prior to the Emergency and still exist today. The injustice suffered by Dalits is similarly constant throughout Indian history. Government corruption, at every level, is a constant not just in Indian history but through all modern history. “A Fine Balance” depicts life not only during the Emergency but through all of post-Independence history, portraying problems that have hounded us from 1947 to today.

In addition to the horrifying illustration of Emergency-era India, Mistry’s novel beautifully captures the complexity of human relationships. Mistry shows a father and son tragically drifting apart, each one’s life being destroyed by their inability to reconcile, and a Parsi girl fighting her brother for independence and control of her life after the death of their father. The novel shows how people form friendships in the strangest ways, united only by their shared struggle and by the simplest acts of kindness, and how seemingly unbreakable friendships are broken with the passage of time and the cruelty of the world. The relationships shown in this book are realistic and offer a powerful lesson about how, even in the terror of Indira Gandhi’s Emergency, the connections between us can help maintain the fine balance between hope and despair

Despite the serious topics tackled by this book, Mistry intersperses all this doom and gloom with humor. He takes delight in highlighting the most ridiculous parts of Indian politics and society. There is an entire chapter dedicated to satirizing Indian political rallies. Mistry describes buses rounding people up in a slum and taking them to attend a political rally with the promise of tea and snacks. What follows is a complete circus: ministers demonstrating exaggerated subservience to their higher-ups, attendees hilariously uninterested in the speeches, and grandiose stunts failing in the most ridiculous ways imaginable. An eighty-foot cutout of Indira Gandhi fell on top of the crowd, with security personnel comically struggling to keep it upright and attendees scattering every direction, eliciting the following response from three impassive onlookers

“Nobody wants to be caught in the Prime Minister’s embrace,” said Rajaram.

“But she tries to get on top of everyone,” said Om.

“Shameless boy,” said his uncle.

Mistry takes the insanity of the world and turns it into irresistible comedy.

The book is often reminiscent of “Lazarillo de Tormes” or “The Master and Margarita” in its ridiculous yet macabre comedy. One feels sick for laughing at certain scenes but can not help it, overcome by the absurdity. A funeral procession of beggars – limping and crawling according to their respective disabilities – is accompanied by a police escort, often being left behind by pallbearers unused to the slow pace. The occasion of the funeral is tragic, but the image so absurd that it triggers laughter. In another scene, while squatting over train tracks, a slum dweller philosophizes on the art of open-air defecation, earning him the title “Goo Guru” among his students who are new to the lifestyle. The absence of toilets and the filthiness of the slum is terrible, but Mistry uses humor to maintain the fine balance even in these unpleasant moments. He inserts his unique brand of morguehouse humor everywhere, making us reluctantly smile even as the story gets darker and darker.

The book’s prose is beautiful, making every part of the world come to life. Mistry gives us a sweeping portrait of Emergency-era India, forcing us to see the victims as real people like you or I. The suffering and the terror of the Emergency come to life, leaving a haunting impact on even the bravest reader. Despite the immense pain suffered by characters, Mistry’s novel, true to its name, does show how we can maintain a fine balance, how joy can come out of even the worst places. The novel demonstrates how friendship, a good sense of humor, and well-made chapatis can help people balance hope against despair, even as the world is unimaginably dark and cruel.

Review of William Dalrymple’s 'In Xanadu'

Mon, 15 Jun 2026 00:00:00 GMT

Review of William Dalrymple’s “In Xanadu”

This book is about William Dalrymple, at the age of 21 in 1986, retracing the steps of Marco Polo, traveling over land from Jerusalem to Xanadu in an extraordinary journey traversing Turkey, Iran, Pakistan, and northern China. The events in this book touch on many different cultures, histories, and landscapes, making it an amazing read. It also has just the right mix of humor, immersive descriptions of different places, and honesty about the difficulties of travel as well as the amazing things he saw. A note before continuing – there are some spoilers here for the sake of illustrating what the book is like, but nothing significant I hope.

Map of Dalrymple’s path, pulled from the book

The humor makes this book quite unique in its genre, since Dalrymple did a great job finding mirth in even the most dire circumstances, and he had lots of wild experiences to keep providing joke material. I was originally planning to include half a dozen examples of the funniness, but that would make this review too long, so here’s a sample of the Mr Flying Chicken episode:

Mr Flying Chicken was a gentleman of Singaporean origin who was remarkable chiefly for his kingly girth and his efforts to maintain it by constant feeding. Mr Flying Chicken was, appropriately enough, a seismologist. He was just returning to Peking after several months working on the earthquake problems of Urumchi. His company clearly valued the services of Mr Chicken for they had supplied him with all that was needed to keep him in good spirits for the duration of the journey, namely one very large hamper. This he tucked into with great enthusiasm. Before our eyes, in a matter of minutes, he consumed batteries of boiled eggs, bean curds barely unwrapped from their boxes, half-salamis imported at great cost from Italy, great lumps of dried pickled fish. These he washed down with cans of Chinese beer and inter-course slices of pineapple pie. But it was the poultry that was most dear to him. From a separate compartment in the hamper Mr Chicken produced a whole, cold boiling fowl. He lifted it aloft with the same reverence as a Catholic priest might lift the host at the elevation. He looked at Louisa and me with hungry eyes. ‘Fly Chikky,’ he murmured. After we had made friends with Mr Flying Chicken the journey turned into something of a dorm feast. He shared his poultry with us and in return we offered him a bag of melons we had bought in Turfan. As the afternoon went by we slowly ate our way through Mr Chicken’s hamper, until, sometime towards sunset we reached the bottom. Mr Chicken surveyed the empty hamper with great sadness. ‘No chikky, no agg, no pie-pie,’ he said. He picked at the pile of bones on the floor of the compartment, and looked around for something else to consume. There was nothing, and, as a glance at his watch revealed, it was more than two hours until the dining car opened. A look of infinite melancholy clouded his face.

Even though his journey is challenging at many points, his sense of humor keeps the book always entertaining to read. The above excerpt also indicates another laudable quality of the book: honesty to the point of horrific political incorrectness. I doubt this book could be written today without receiving complaints about racial stereotyping, homophobia, Islamophobia, objectification of women, etc – he at one point tried explaining “the Turks’ easy drift out of heterosexuality” as a result of Turkish women’s noses being too large, chins too prominent, and “baggy wraps concealing pneumatic bodies” (offensive to some? maybe. funny? absolutely yes). Goodreads has denounced this book as a manifestation of the patriarchy and cultural imperialism etc-etc, but I found it to be great humor that was respectful of other cultures’ wonders while also honest about what Dalrymple didn’t find as praise-worthy. If you want a bright young man’s honest assessment of his experiences traveling across the Middle East, Central Asia, and part of China, this is a great read that emphasizes both the positive traits of the people and the beauty of certain places along with the more unpleasant behaviors and uglier sights. Please ignore the nonsense on Goodreads – anyone familiar with Dalrymple’s other writing and his political beliefs should be well-aware that he is the furthest possible thing from a racist or an Islamophobe, and any use of racial stereotypes was solely for the purpose of humor. His brutal honesty draws controversy but in fact is what makes it so insightful about the many places he visited – you’re not just visualizing places and people, but also the thoughts and reactions Dalrymple had as he interacted with them. There is an admirable openness and irreverence in his tone.

I also enjoyed Dalrymple’s insight on history and architecture. He knew exactly which parts of history were most interesting to a lay audience and made centuries-old crusader lore very fun to read about. He gave fascinating context on topics as esoteric as the medieval Order of Assassins, Ilkhan Uljetu’s construction of the city of Sultaniya, its wonders and why it was doomed to fail after his death, and the chaos of the 1271 papal conclave. Dalrymple’s passion for the subject bleeds through the pages and makes the reader as excited as him. It’s fun to see someone so opinionated on Islamic architecture, completely dismissive of some buildings while awe-struck by others. He writes off the ones he dislikes, but when he finds a structure truly inspiring, he writes beautifully about it.

The mausoleum is octagonal, rising to a parapet from which springs a crown of eight minarets and a bee-hive dome. The sides of the octagon are not equal. There is a main front, once the climax of the Mall of Sultaniya. On it a central doorway is flanked by six blind arches, three on each side, once filled with faience-work inlay. The wall of tobacco-brick rises up to an open, arcaded gallery. This, as Byron pointed out, is a façade, a new departure in Islamic architecture. It was built primarily to be looked at. Unlike almost all earlier Islamic buildings which were bounded by walls and faced inwards, the tomb of Uljetu is centred on the dome and looks out. It is a public building, built at the centre of an imperial capital, a concrete expression of the Emperor’s power.

With its city decayed and its empire fallen, there could be something almost pathetic about so proud and vain a monument. Yet the building still retains great dignity and power. This is especially so of the interior. Nothing, except perhaps Hagia Sophia, prepares one for the sheer scale of the vast, unsupported, heavenward-thrusting dome. It encloses an enormous space, far greater than one would expect from the outside. It dwarfs the observer.

Picture of the Soltaniyeh mauseoleum Dalrymple praised, taken from Wikimedia Commons under GNU Free Documentation License

Dalrymple’s extensive knowledge of history and architecture, combined with his passion for both subjects, makes the book both educational and fun to read, packed with descriptions of beautiful mausoleums and castles and the gory history accompanying them.

Although much of this book focuses on the history of Marco Polo’s times, the dramatic political changes of the 20th century forced Dalrymple to also address some more recent issues, and his insight into these topics is equally fascinating. He meets with an Armenian priest in Iran, who complains of the Shah’s destruction of old gardens and merchant’s houses in favor of modern, western-looking high-rise developments, but then emphasizes “at least people used to have fun in the Shah’s days” and complains of Khomeini replacing cinemas with revolutionary lecture theatres and bars with non-alcoholic carrot milk shakes. Dalrymple also personally experiences the hardships of Sharia law, and his female companion Laura was forced to wear a chador throughout their time in Iran and pretend to be Dalrymple’s wife. In Xinjiang, he meets an educated Muslim who tells him about the suppression of the Uighur language and Islam, as well as his personal difficulties of being “over-educated for the taste of most Muslims” but “considered old-fashioned and backward by his contemporaries at university.” In Israel, he describes the tensions between Arabs and Jews through his conversation with an Arab tailor complaining of the dual legal system and discrimination against Arabs, as well as his disturbing conversation with two urbane, seemingly-liberal Jews who then shocked Dalrymple with their full-throated support for illegal occupation of Jordanian territory. Lots of interesting glimpses of what these places were like (many still relevant today), combined with Dalrymple’s own eloquent interpretation of all this history.

For two thousand years Jerusalem has brought out the least attractive qualities in every race that has lived there. The Holy City has had more atrocities committed in it, more consistently, than any other town in the world. Sacred to three religions, the city has witnessed the worst intolerance and self-righteousness of all of them.

Dalrymple’s description of recent history and the state of affairs at the time of his traveling serves as an amazing window into what these parts of the world were like in 1986. Aside from depressing political developments, Dalrymple’s description of landscapes is enchanting. He traveled through deserts, fertile plains, and mountains and captured the beauty of all of them with a writing style that blurred the lines between poetry and prose. Even when he was at his most opinionated and cynical, he did a great job creating a picture of what he was witnessing.

As we drove on the landscape became harsher still. The scrub turned to sand and the shallow line of mountains that formed the horizon to our right dipped lower and lower and then hit the plain. There was a gap, a last craggy outcrop and then nothing. Never has a landscape filled me with such a sense of melancholy. It felt as if some terrible biblical disaster had taken place, that its inhabitants had been caught committing sodomy or castrating Israelites, whereupon fire and brimstone had rained down from the sky, leaving only a few dazed-looking nomads and an awful lot of sand.

Also praise-worthy is the sheer amount of adventure Dalrymple had: multiple run-ins with the police in countries governed by authoritarian regimes, alone and lost on a remote mountain where he stumbles upon a pre-Islamic animistic ceremony and pontificates on the symbolism of standing where Alexander the Great fought his last siege, and accidentally wandering into the the Chinese nuclear testing ground in the desert of Lop. It’s impossible to put down, and I’m simply in awe of how lucky this guy was at surviving his own recklessness. It isn’t all exciting, and there are also long segments where Dalrymple is exhausted, bored, and depressed by the hardships of traveling in the bed of a coal truck while keeping his head down to hide from military patrols (arguably itself an adventure); but even then, his eloquence and humor keep the book interesting.

All in all, 10/10 read. Fantastic descriptions of people, places, history, and architecture. Fun, informative, sometimes hilarious, and never a dull chapter. I highly recommend it if you like travel writing.

Advice from the Heart for the Leadership of the American Left

Fri, 26 Jun 2026 00:00:00 GMT

Advice from the Heart For the Leadership of the American Left

Advice from the Heart for the Leadership of the American Left

To Mr. Mamdani, the Young Turks in the Democratic Party, and other radical leftists in America,

I respect that some of your favored candidates hold views I disagree with, and I’m even willing to tolerate a few congressmen who “are Westerners fighting for the total eradication of Western civilization”, as Democratic candidate for Congress Avila Chevalier has proclaimed herself to be. But for the sake of political viability and not freaking out establishment stooges such as myself, I have a few suggestions for your vetting process and management of social media presence.

First, I suggest any leftists with political aspirations use the MESS test before posting on social media. MESS stands for Monumentally Embarrassing Social Media Statements your candidates posted while “fucking around on the internet”, as Democratic candidate for Senate Graham Platner so eloquently put it. Before you click “post,” ask yourself – “is this a Monumentally Embarrassing Social media Statement?” If the answer is yes, then don’t click post!

This simple strategy will help you avoid significant embarrassment and allow your candidates to keep their racist, anti-Zionist, far-left, and violent views to themselves so that people can at least claim ignorance when voting stupidity into power (which they’re already doing even with full awareness). When I was in preschool, I was taught about everyone needing to have some “inside thoughts”: things you think or feel but that you don’t express out loud because it could cause problems for you or other people. American leftists would do well to start keeping some “inside thoughts” rather than loudly voicing every opinion they have. For example, it’s perfectly fine that Graham Platner thought of himself as a communist five years back, thinks all cops are bastards, and has had a Nazi tattoo since 2007 (although he claims he never bothered to find out what the tattoo was until 2026). It’s just that he’d really do himself and his party a service if he would keep these things to himself rather than loudly advertising these beliefs on a Reddit account very easily linked to his real-life identity, potentially jeopardizing the Democrats’ chances at victory in Maine against a Republican incumbent after these posts were discovered by journalists.

Or take Darializa Avila Chevalier as another example: a democratic socialist endorsed by Zohran Mamdani for a New York congressional election. Defender of the poor, critical of ICE, speaks up for Gaza – all sounds great, until you stumble upon her social media posts from 4-5 years back. These include criticizing Black and Arab men for “fetishizing ugly colonizer women” (wasn’t the GOP the one attacking interracial relationships earlier?), calling Biden a “rapist” and “war criminal,” claiming Israel doesn’t exist, and making some very nuanced and thought-provoking remarks on police reform:

During the nationwide protests in 2020 following the killing of George Floyd, Avila Chevalier responded to a user asking what a better slogan would be than “defund the police,” by posting, “F**k you. We’re gonna defund and abolish. You don’t get to water down our movements.”

Two days later, Avila Chevalier rejected an argument that abolishing police meant ending policing only “as we know it.”
“No. It means ending policing full stop. Period. No more police at all ever,” she replied, adding several clap emojis.

She also reposted a message stating, “In New York they don’t say ‘I love you,’ they say ‘NYPD suck my dick’ and I think that’s beautiful.”

Again, all very valid opinions backed by evidence and logic I’m sure, but maybe it would’ve been good for her political career if she’d kept these opinions to herself.

Or, alternatively, don’t just stop at keeping your radical, poorly thought-out, and offensive views inside your head – maybe don’t adopt these opinions at all! I’m probably being impractical, but is it really too much to ask that the left find candidates who aren’t anti-Zionist, racist, or against such basic things as policing and a prison system?

Oh, and another pointer – if you really must call for the total eradication of Western civilization, try making your argument without extensive use of profanity and ad hominem attacks. It really discredits your argument, makes you look intellectually immature, and causes massive embarrassment a few years later when you run for public office. For example, instead of posting

“We shouldn’t have the eat the pain because you c*nts and Massachusetts couldn’t act like adults. F**k off and die, leave Maine out of your capitalist fantasies.”

Perhaps Mr. Platner could’ve written something along the lines of “respectfully, I agree to disagree because XYZ.” Teenagers can be excused for expletive-laden attacks on online interlocutors when arguing over politics – 37-year-old men looking to enter politics should be more circumspect in their speech. Or, when you lose your head in the moment, at least try to feign remorse later rather than doubling down on ad hominem attacks in CNN interviews.

In another post in 2010, Platner took aim at musician Ted Nugent, a conservative activist. “As a combat veteran, that m*therf**ker makes me want to puke when he spews his warmongering macho bullshit. Suck a d*ck, Ted.”
“To be fair,” Platner told CNN. “I’m not really regretful of that one.”

Avila Chevalier and Platner have shown very little regret for their reprehensible remarks online (and in Chevalier’s case, some of her activism at Columbia University), and the left-wing establishment as a whole has shown too little discomfort with their support for such people.

Finally, a word to the leadership of this new radical faction plagued by candidates with severe runs-mouth-like-loose-cannon syndrome. Before you endorse a candidate and begin campaigning for them, you should ask them a few questions

Any Nazi tattoos or other skeletons in the closet we should know about?
Are any of your ideas dangerous to the country’s future if actually implemented and likely to alienate a majority of Americans?
Have you ever expressed an interest in “the pyromania associated with anarchism” the way Avila Chevalier did in 2020?
Are any of your other statements or posts so vile and/or deranged that we should seriously reconsider endorsing you?

Because it’s embarrassing that left-wing politicians are receiving such little vetting before being endorsed in important elections in the House and Senate. The GOP can afford to nominate people with a history of racist and sexist remarks, since their base is less bothered by it and some of their voters actually appreciate it – the Democratic Party, however, will not survive if its candidates resort to the same level of vulgarity and coarseness as Republicans. Mamdani did not endorse a candidate in every district of New York, he endorsed only three and attested to their stellar character in interviews. Given the selectivity of his endorsements, it is baffling that he (and for that matter, anybody else) didn’t bother to ask his favored candidates about any skeletons in the closet, of which Avila Chevalier has plenty. Mamdani’s response to the Avila Chevalier controversy was:

When it comes to Darializa’s campaign, I had not seen those tweets and what I’ve heard from her and what I know a lot of others in the district that have heard from her is that her views have evolved and that the campaign she is running on is reflective of what she’s going to be fighting for

That’s the kind of apology I might give for my short obsession with Noam Chomsky in 9th grade – on the other hand, woefully inadequate for a prominent Democratic politician explaining his favored congressional candidate’s history of racist, vulgar, and far-left rhetoric. The nominations of Graham Platner and Darializa Avila Chevalier constitute some of the worst vetting of political candidates in the history of the American left. Either Mamdani is lying about these tweets being surprising news to him, in which case it’s messed up that he still endorsed her, or he and other democratic socialists were incredibly negligent in their vetting.

So, again – great job on calling out weaknesses of mainstream Democratic politics, but before you can become a viable alternative, you really should work on getting slightly more sane candidates who are more palatable to the majority of Americans’ political and cultural sensibilities, and also less likely to cause a complete breakdown of law and order and a collapse of the economy.

Regards,

An Establishment Stooge

Interesting Articles, Poetry, Music, etc – April 12

Sun, 12 Apr 2026 00:00:00 GMT

Interesting Articles, Poetry, Music, etc – April 12

Hello everyone, it’s been a while since I last wrote! I’ve encountered lots of interesting things since then, so I’ve here attempted a compilation of them, as well as a summary of what I’ve been up to.

When I last wrote, I was reading Frank Dikotter’s “China After Mao,” which I have now finished. I’ve also finished Ramachandra Guha’s “India After Gandhi,” Roberto Bolaño’s “2666,” Neel Mukherjee’s “The Lives of Others,” Harriet Tytler’s “An Englishwoman in India,” William Dalrymple’s “The Anarchy,” Amitav Ghosh’s “The Shadow Lines,” Upamanyu Chatterjee’s “English, August” and “Mammaries of the Welfare State,” and Declan Walsh’s “The Nine Lives of Pakistan.” I enjoyed all of these books, and I’m in the process of writing reviews for some (all?) of them, so look forward to that. Until I find the motivation to finish book reviews, a google search will hopefully suffice for anyone curious about these books. I’m trying to get better at writing book reviews and not relegating half-finished drafts to my Documents folder, but motivation is a scarcer resource than RAM these days.

Apart from full-length books, I’ve also been reading some essays and short stories. Here are the highlights. Sorry for the link dump, but my last post was ~3 months ago so I’ve read a lot of interesting stuff since then haha. I found these links from a mix of surfing, following a select few news sites, and getting recommendations from people (yes, humans still give better recommendations than algorithms):

This is Nick Wolven’s ‘Caspar D. Luckinbill, What Are You Going to Do?’, an interesting short story that I felt is relevant to our present reality. Lots of food for thought on the role of mass media and tech billionaires in shaping society, and what our own responsibilities are towards humanity and future generations.
This is a fun article on the black market in General Ne Win’s Burma – lots of creative money-making schemes, an interesting story of individuals’ cunning helping them outsmart a poorly managed and overly restrictive socialist economic system. The website this article is from, New Mandala, is actually a very cool site with lots of other interesting articles, and I recommend checking it out if you’re interested in Southeast Asia.
Here’s another New Mandala article, this one about how corruption and a lack of public oversight hinder Indonesia’s efforts at flood prevention. When you hear the idea, it seems almost obvious, but it’s something I hadn’t thought about at all until reading this article. Very informative.
This is an amazing series of articles at theprint.in that talks about interesting parts of medieval history and how they connect to contemporary social and political issues. Two particularly interesting articles are this one about the long history of Afghans in south Asia and this one about the history of Srivijaya and why the government’s new name for Port Blair is absurd.
Tragicomic story of a UP village that started worshipping a dog – this is a story that made me laugh, even though I felt bad for doing so; bizarre case of an Uttar Pradesh village worshipping a dog after he started walking circles around a Hanuman idol, then it turns out he actually had a life-threatening infection messing with his brain. So, making a Yogi nicknamed “Bulldozer Baba” into a chief minister does make your population nuttier… who would’ve thought?
The long, inglorious history of Galgotias University – hilarious story of Galgotias University, which recently made headlines for marketing a Chinese-made robot as if it was their own at an AI fair. Turns out they have a long and inglorious history of similar mess-ups and have gained prestige partly through blind support for the BJP. Very funny – among other stories, one part is about students at a protest against INC who, when questioned by reporters, don’t know why they’re protesting and misread ‘urban naxal’ on one sign as ‘urban Maxwell.’
Here’s an inspiring story about a 14-year-old making well-informed anti-BJP content on social media (at one point there was an FIR against him before cops realized he’s 14). Super cool story, glad people like this exist
Poverty and malnutrition among West Bengal’s tribal communities, and the state government’s complete indifference – yes, in the year 2026, the Bengal government still is unable to fix issues as basic as ensuring their citizens don’t die of hunger. This article tells you all you need to know about the TMC government’s record on improving the lives of Adivasis.
Aaand, another story on West Bengal and how the TMC government avoids fixing its unemployment crisis by just throwing welfare money at people and praying nobody notices that the actual problem remains unchanged. State debt ballooned from 1.9 lakh crore in 2011 to 7 lakh crore today, and yet TMC is funding welfare schemes where the cost is rising 47% year-on-year while cutting spending on actual industrial development. I’m not an economist, but this seems like bad policy to me…
Aaaaaaand, a story on how BJP is similarly indifferent to people’s suffering in Bengal – Amit Shah visited a tribal home in Bengal in 2020, since then the family of six has been surviving on around Rs 300 per day of work (note that as day laborers, they can’t even find work every day) and are struggling to find money to buy their daughter’s insulin, eating plain rice every day because they can’t afford vegetables. They report that they weren’t able to actually talk to Amit Shah for even a minute and have found little support from the BJP, revealing that Amit Shah’s visit was just a photo-op and not the magnanimous outreach effort the BJP advetised it as. Pretty shameful – if Amit Shah was going to drive all the way out there to have his lunch, he could have devoted even 2 minutes to hearing about the family’s lives and understanding their problems. These politicians don’t care about the voters, only about their votes.
Pivoting away from Bengal, Reporters’ Collective reveals probable corruption in Assam electricity contract with Adani Power – well-researched article with disturbing implications. Assam state government is paying Adani Power for 6000 MW of more electricity by 2035 despite the Power Ministry saying only 3483 MW is needed by that time. Assam government also rejected, without explanation, reasonable proposals for getting the electricity at a lower cost, e.g. the idea of not building a new power plant and instead buying non-contractually-bound electricity sold on a kind of spot market at lower prices. Lots of unanswered questions and inconsistencies in the government’s explanation, which makes me inclined to believe this is deliberate corruption rather than simple incompetence. On a related note, also see RK Singh’s accusations that Adani is over-charging the Bihar state government for electricity that could cost the state Rs 62,000 crore over the span of 25 years – his claims have credibility due to his record of integrity and experience as Union Power Minister. It’s even more suspicious because Ananda Bazar Patrika has surreptitiously deleted all their content related to RK Singh’s claims. Claims of corruption, followed by self-censorship by a prominent newspaper, hmm… Neither case has conclusive evidence yet, but given Adani’s past record, there’s reasonable grounds to believe these accusations have merit. We all vaguely know “BJP and Adani are looting,” but I found these concrete examples interesting.
Inspiring story on Bengal Gazette of how a Bangladeshi woman was inspired by her country’s history to become a war zone doctor in Gaza, Yemen, Syria, Sudan, Ukraine, Sierra Leone, and Rohingya refugee camps. Her grandfather was murdered by the Pakistani army during the 1971 Liberation War, when he stayed at his hospital to continue treating patients instead of evacuating. Now the granddaughter, who has followed in his footsteps, reflects on how her family and her country’s history have inspired her to risk her life to deliver life-saving aid in war zones. An amazing story of courage and individuals’ commitment to doing good. I’m grateful that people like this exist.
On the topic of inspiring people, the Wikipedia page for Jacobo Timerman is one of the most inspiring stories I’ve read. Timerman ran newspapers in 1960s and 70s Argentina that reported on both left-wing and right-wing terrorism, despite him facing multiple death threats and assassination attempts for his work. His commitment to reporting the truth resulted in him being arrested and tortured under the Videla dictatorship; after being released and exiled to Israel, he continued to fight for the truth even after his traumatic experience. Timerman was a self-described Zionist for most of his life, but after seeing the atrocities being committed in the 1982 Lebanon War, he wrote a book critical of Israeli policy in Lebanon and Gaza – this is incredible intellectual integrity, the ability to criticize a country you so strongly love, and to risk alienation from your entire community as a result of your views. Timerman also motivated one of his sons to suffer a jail sentence rather than be complicit in Israeli atrocities through military service in Lebanon. He later returned to Argentina and continued to criticize the government’s authoritarianism and refusal to prosecute human rights violations committed during the Dirty War. An incredible human being, I was very inspired by his story.
This is an interesting article by Siddharta Deb about the many struggles he faced in getting from Calcutta to Columbia University, how he slowly became disillusioned with the university’s administration and campus culture, and various reflections on his intellectual journey. Incredible story with lots of interesting thoughts on campus cultures, intellectual freedom, and the allure that distant places can hold in our imagination.

Link-dump finished, hurrah! Outside of the aforementioned books and links, I’ve also been reading “The Disinherited State: A Study of West Bengal 1967-70” by Shankar Ghosh, an amazing book that I’m learning a lot of history from. After getting through ~100 pages, I’m impressed by how badly the first United Front government bungled everything: chaotic coalition politics with lots of defections, a labor minister who let gheraos run wild, and communist parties just barely reining in their zealots who wanted armed revolution. The book offers a very informative and entertaining account of these pivotal years in West Bengal’s history, and I’m enjoying it. I’m impressed by how many obscure details there are that you’d have a hard time discovering online: how the preventive detention of Muslims during the 1965 India-Pakistan War contributed to Congress losing the Muslim vote in 1967, how a gherao by women of the Home Minister Kiran Shankar Roy led to the establishment of the Kolkata women’s police division, and many more interesting factoids. Fascinating book with lots of niche information and powerful analysis of some of the most important years in Bengal’s history.

I’ve also been reading more Bengali poetry by Sukanta Bhattacharya and am greatly enjoying his work. I particularly liked “Ekti Moroger Kahini,” a darkly funny poem about a starving rooster searching for food in a palace who instead ends up as food, and “Kolom,” a poem where even Sukanta’s pen is imagined as a victim of exploitation and he calls on the pen to join all the oppressed in a revolution, where history is written in blood rather than ink. All of Sukanta’s work is amazing – he had so much anger at the world’s injustice, and this despairing vision of death and famine all around, yet at the same time he expressed an incredible amount of hope that these evils can be overcome through courage, class consciousness, and hope for a better world. I’m inspired by the fact that someone can see so much darkness all around the world (even pens and chickens are imagined as sufferers of oppression!) and still believe that humans have the power to fix things. He uses language beautifully, constructing images of deserts, palaces, and revolutions that are vivid in your imagination as you read, and all his poems have a lyrical quality that makes them fun to read out loud.

Pivoting to music, I’ve recently been enjoying the songs of this Indonesian rock group Efek Rumah Kaca (‘greenhouse effect’) – very good instrumentals and vocals, and they have some of the best lyrics I’ve seen in rock. Lots of political and social commentary, which is the type of thing that I love. I really liked their eponymous album Efek Kaca Rumah; I’m going slowly through their music because their songs have a lot of new Indonesian vocabulary, but this one album already has me hooked. Their songs “Di Udara” and “Efek Rumah Kaca” are especially powerful. “Di Udara” is dedicated to Munir Said Thalib, a human rights activist who was assassinated by the Indonesian intelligence agency (very inspiring man, I suggest reading his wikipedia page) – powerful lyrics and a moving song. The name “Di Udara” means “in the air”, a reference to Munir having been poisoned while on an airplane. “Efek Rumah Kaca” (‘greenhouse effect’) is about climate change and the apocalyptic world we’re leaving behind for the next generation, again very good. I love this rock group, hope you guys will like it too.

This is another really good Efek Rumah Kaca song, “Seperti Rahim Ibu” (‘like a mother’s womb’)– it expresses the wish that one’s country could be ‘like a mother’s womb’ and actually nurture and protect its people, rather than being a place of horror and bloodshed. Uplifting song with a lot of hope in it, I liked it. It’s doubly interesting because the lyrics for this one were a joint effort between Cholil Mahmud, the lead singer of the group, and Najwa Shihab, an Indonesian journalist with a reputation for tough interviews and intellectual rigor. Funny story about Najwa Shihab that I found on her wikipedia page– she once interviewed an empty chair during COVID after the country’s health minister did not show up and was ignoring widespread criticism of his handling of the pandemic. The health minister in question was stripped of his medical license in 2022 for employing pseudo-scientific stroke treatments and being, in general, a really stupid guy. Indonesian RFK Jr…

Moving from rock to kpop, the group Fifty Fifty did a cover of Pink Floyd’s “Wish You Were Here”– great vocals re-interpreting one of the best rock songs ever, I liked this version a lot. I’ve recently started liking Fifty Fifty’s live vocals and also enjoyed this live version of their song “Tell Me”, performed by the original group line-up (unfortunately fractured by a messy legal battle with the company, but at least they’re back to making music now, albeit with new members).

I also discovered an awesome Bangla rock/folk/comedy-performance group called Hooligaanism. My introduction to the group was this hilarious, intelligent, and well-performed satirical song about West Bengal politics, “Tumi Mosti Korbe Jani”. It makes fun of Bengal’s most absurd phenomena such as the voter roll SIR and the AI craze, and it also criticizes all the main parties (TMC, CPIM, and BJP) with funny references to their most infamous scandals in Bengal. I also liked that it captured a broader sense of exasperation with the status quo in Bengal: college graduates who can’t get jobs in a broken economy, while our politicians yammer on and on about the Bangladeshi ‘ghuspaithiya’ conspiracy theory and renaming the state (which is sure to create jobs, of course). I liked the energetic feeling of the music and the sense of humor, which is derived not just from clever lyrics but also from the members’ acting abilities and how they perform some of the more conversational parts of the song. The lyrics are impressive for squeezing in so much wit and humor, with references as diverse as the patriotic song “Bolo Bolo Bolo Sobe,” political controversies surrounding three Ghosh’s in three different parties (very funny), the pseudo-archaeology behind the Babri Masjid demolition’s justification, and the Supreme Court’s wishy-washy stance on free speech. A fun song with a powerful message – I’m glad some musicians are discussing people’s real issues with their work rather than only regurgitating the same decades-old clichés of love songs. I also liked this song “Prithibita Bhalo Lokeder Noy”, which laments how the easygoing and carefree lifestyle of youth is sadly snatched away from people by the financial obligations of marriage and simply just growing up – very funny song although the lyrics are a bit sad.

And then, possibly the biggest music-related news I have from the last several months – I went to NMIXX’s concert a few days ago!! It was an awesome night, they played all my favorite songs and performed spectacularly – great vocals and dancing, I was very hyped up the whole time. I had lots of fun, this is probably my best 2026 experience so far. I’m planning to write something a bit longer about the concert in the future, so I won’t ramble too much about it now, but I just wanted to mention it here for the purpose of completeness.

Anyway, that concludes everything I wanted to pack into this post. I hope some of this is interesting – not sure if people like this format of post, since it’s not an original contribution so much as an aggregation of others’ work, but I like the idea of helping people find interesting content through posts like this. Cheers, hope everyone is doing well.

Brainrot Language, and the Decay of Generation Z’s Intellectual Life and Culture

Fri, 12 Jun 2026 00:00:00 GMT

Brainrot Language, and the Decay of Generation Z’s Intellectual Life and Culture

A long time back, I saw a meme on Reddit about how the amount of words a language has for something is indicative of how important that thing is to a culture. The particular case highlighted was the sixteen words the ancient Romans had for “young male prostitute” (more words than Eskimos have for ‘snow’), which indeed correlates with the widespread presence of them in Roman society. Although this joke is a bit vulgar for a semi-formal blog post, and the meme was linguistically inaccurate (among other issues, some of the words were adjectives and not specific to just prostitution), it’s still funny and also a surprisingly good entry point for discussing the English language today. What ideas, concepts, or things are becoming increasingly important in society nowadays, necessitating the creation of more words for them? The first few ideas that come to my mind are the decay of the internet (‘enshittification’) and the worsening of political discourse (‘gaslighting’), but the most obvious winner for “category of word rapidly rising in importance and quantity” is brainrot.

Brainrot is by its very nature meant to not have meaning, which makes it feel counter-intuitive to seek a link between brainrot and a larger trend of certain things gaining importance in society. However, it is precisely this quality of meaninglessness in speech that has been rising, and the increase in brainrot words is symptomatic of that.

Before beginning the actual analysis, a summary is needed of what brainrot even is, for non-Gen Z readers or those who’ve luckily not been exposed to this monstrosity. Merriam-Webster defines it as “shallow or addictive online content,” but this doesn’t quite capture how it works since it focuses on social media content rather than the words and speech patterns derived from it. The process usually looks something like this. In 2025, the rap song “Doot Doot (6 7)” was released and started going viral online because it was used in basketball youtube shorts, especially in videos with tall players like LaMelo Ball who is 6 feet and 7 inches tall (thus ‘6-7’). The meme became part of Gen Z and Gen Alpha culture as a whole, rather than just basketball, after a video of a 12-year-old shouting ‘6-7’ went viral 1. Since then, it’s become (by my estimation) the most famous and widely used slang in Gen Z and Gen Alpha. How do people use it, you ask? Here are some particularly interesting explanations

Aspen Bohlander, 15, estimated that she hears “6-7” around 80 times a day. “It’s more of an ironic thing,” said Bohlander, a sophomore at Oak Park and River Forest High School in Oak Park, Ill. “People are making fun of the fact that it’s not funny.” 1

The ridiculousness and pointlessness of “67” is perhaps why it has succeeded so extravagantly as a meme, breaking out of the classroom to become Word of the Year 2

In summary, you can say ‘6-7’ at any point in a conversation, with zero context to trigger it, and you will be met with a chorus of sycophants screaming ‘6-7’ with you and performing the accompanying hand gesture. It isn’t even meant to be funny, as some people are acknowledging despite still saying it 24/7. Sounds pretty stupid, right? It is, and it’s part of a wider problem of people replacing actual conversation content with meaningless brainrot to obscure the fact that they don’t have anything meaningful to say.

Some people will dismiss ‘6-7’ and similar brainrot (there are many such words out there) as kids being kids, just having fun, a harmless trend. However, there are a few key differences that separate today’s brainrot from earlier generations’ harmless inside jokes. The first is that brainrot just isn’t funny. Every generation has had its own ‘low-brow’ humor, e.g. laughing any time the product ‘23x3’ appears or an opportunity arises to say “that’s what she said,” but these earlier jokes were different because there was at least a certain trigger necessary for the word/phrase to be said, and its meaning was associated with that trigger. Some thought and meaning were tied to “that’s what she said” – sure, a few people would really try to twist words’ meanings to give random sentences a dirtier meaning, but there was at least some thought put into the jokes. Similarly, you’d only laugh if the number ‘69’ actually appeared somewhere – nobody would randomly shout ‘69’ and trigger a bout of laughter among their friend group. Today’s brainrot, on the other hand, requires no thought or meaning, and you can shout ‘6-7’ or ‘sigma’ at any time and trigger laughter. This is the key difference between earlier low-brow humor and today’s brainrot: the lack of thought or meaning in our speech is worse today than ever before.

The other worrying trend is that ‘6-7’ isn’t a supplement to normal intelligent conversation where people act a bit silly in their down-time. It’s become a way of avoiding meaningful conversation entirely, where teenagers’ hangouts don’t involve conversations about books, movies, or even gossip about their own lives, so much as it’s an endless stream of internet brainrot. I’ve heard many conversations where absolutely nothing meaningful is said, not even real-life gossip, and it’s just an exchange of various brainrot words and phrases. Interestingly, there is a strong correlation between not reading long-form content (i.e. anything longer than the text in Youtube Shorts videos) or watching good films (i.e. not “Superman” or “The Minecraft Movie”) and the tendency to use brainrot. People who consume interesting, meaningful media have real content to talk about and don’t have to resort to ‘6-7’ to hide that they have nothing valuable to say. In this way, brainrot is a manifestation of a broader trend of the average person’s media consumption becoming increasingly inane, and human speech correspondingly growing poorer in intellectual content.

Aside from the stupidity of entire conversations where nothing meaningful is said, this is also a worrying amount of control that inane Youtube Shorts trends are having over our lives. I’ve been noticing for a while that teenagers’ hangouts increasingly don’t involve gossiping, gaming, or even vandalizing bathrooms together (at least that had a social aspect), but just 10 people sitting in a circle and watching Youtube Shorts without earphones – does the cacophony of all the videos playing together enhance the experience? – and not even finishing entire Shorts, watching 5 seconds of one video before scrolling to the next. When people are on their own, there isn’t even a contest between bathroom vandalism and Youtube Shorts – every waking moment is spent on one of the three main platforms (Youtube Shorts, Tiktok, Instagram Reels), mindlessly scrolling through the most inane content. And now, even human conversation has been taken over by the culture of meaninglessness that short-form video content promotes. Note that brainrot words are essentially a result of the algorithms pushing certain videos to virality and thus making brainrot words/phrases go mainstream; no longer do people choose their own words associated with individual thoughts and deliberately-chosen meanings – now, even speech is an extension of the control that the algorithms have over our minds. When the algorithms have this much control over our culture, even to the point of controlling how we talk, I refuse to believe the trends are still harmless fun – it’s taken on a distinctly dystopian quality now.

I’ve been talking about these issues for a long time, but my concerns are usually dismissed. People with an interest in linguistics often accuse me of linguistic prescriptivism, and a more common phrasing is ‘elitism.’ The charge of elitism is nonsensical – it isn’t just elites who have an interest in people’s minds being independent from corporate-run algorithms’ control (often elites wish the exact opposite), and human speech retaining intelligence and meaning, these things should be everyone’s concern. However, the accusation of linguistic prescriptivism is a bit more interesting. I certainly am guilty of linguistic prescriptivism – but is that such a bad thing? Many thinkers have criticized the rhetoric of fascism, e.g. the creation of ‘us vs them’ mentality and use of racial/religious/etc slurs, but this is never labeled linguistic prescriptivism or criticized as such. While brainrot isn’t quite as dangerous as fascist rhetoric, I am making a similar argument about the social good derived from people thinking before speaking and attributing meaning to words, which I don’t think is a harmful mode of linguistic prescriptivism. The concept carries a negative connotation because prescriptivism is often employed by cultural chauvinists seeking to standardize the use of a language to exclude words derived from indigenous languages, or slang used by marginalized groups; while this specific form of linguistic prescriptivism is harmful, I think there are plenty of productive and morally correct ways of judging the relative merits of different styles of speech, and how they impact society.

This post isn’t meant to be anti-fun or looking down my nose at people who like Youtube Shorts. Meaningless trends can often be fun, and there’s nothing wrong with that. However, the degree to which short-form videos are shaping our culture and depriving it of intellectual depth is worrying. Brainrot’s omnipresence in Gen Z speech and culture is a symptom of larger issues: corporate algorithms controlling our thoughts and speech, the inane media consumption of the average person, and the increasing rarity of discourse on socially important or intellectually enriching topics. If we want the English language to continue being a vessel for conveying meaningful thoughts, we must acknowledge brainrot speech as a threat to the intellectual life of younger generations.

Sources I quoted from and got background information from:

A Crash Course on Preventive Detention Laws in India

Wed, 10 Jun 2026 00:00:00 GMT

A Crash Course on Preventive Detention Laws in India

Note before starting: this post wasn’t originally written for the blog, it was an email I sent on May 3 amidst the Bengal assembly elections and some chaos over the Election Commission attempting to preventively detain TMC leaders. I’ve very slightly changed the email and reposted it here because I felt it was interesting and educational enough to merit a spot on the blog. Therefore, the style is a bit different from what’s usually on the blog. I don’t think this is really an issue because it’s packed with good content, but I wanted to explain that oddity before starting. Now, onto my lightly-edited email.

After our conversation on the phone a few days ago about preventive detention, I created a small “crash course on preventive detention laws in India” because the topic is interesting, and it’s a bit disturbing how little it’s talked about or even known about in India.

Starting with the most recent incident – here are articles on Election Commission’s attempt at preventive detention of over 1000 people, mostly TMC leaders, including sitting MLAs and TMC candidates. Thankfully stopped by the Calcutta High Court, but still, seriously?

https://thewire.in/government/election-commission-issued-troublemakers-list-tmc-leaders-polling-day-bengal

Don’t get your hopes up though – Calcutta HC stopped preventive detention from happening solely on the basis of this list, but they allowed preventive detention under preexisting laws 1. Which is where you get this – NDTV reports 571 people taken into “preventive custody” in connection with Bengal polls on April 23 2, and by April 28 Rediff puts the number at 2473 according to the EC itself 3.

This is bad and tramples on the idea of due process, but nothing out of the usual. If you’re interested in India’s long and inglorious history of preventive detention, check out the Unlawful Activities Prevention Act (UAPA) and the Jammu and Kashmir Public Safety Act (PSA)

https://en.wikipedia.org/wiki/Unlawful_Activities_(Prevention)_Act,_1967

https://en.wikipedia.org/wiki/Jammu_and_Kashmir_Public_Safety_Act,_1978

Both are being used to jail dissidents, political opponents, and generally anyone who ticks off the ruling party. Kashmir’s PSA will let the government jail someone “with a view to preventing him from acting in any manner prejudicial to the security of the Union territory of Jammu and Kashmir or the maintenance of the public order” 4. Incredibly vague, wonder what could go wrong here?

Interestingly, the first case of J&K’s PSA being used was Sheikh Abdullah jailing a trade union leader in 1978 who campaigned for the Janata Party in the previous election 5. So yeah, rough start, but surely things got better from there? Nope, things only got worse. In 2025, the PSA was used to jail an AAP MLA in Kashmir for criticizing a District Magistrate 6. As usual, the detention had no legal or intellectual basis and was overturned, although it took the J&K High Court eight months to deliver relief just last week, criticizing the detention having “non-application of mind” (court-speak for “what the heck were you guys doing”) 7. So yeahhh, we’ve upgraded from jailing opposition party campaigners to jailing actual sitting MLAs for social media posts… How come more people don’t know about this? Sad case of forgotten history and news not considered important enough for people’s time.

The Unlawful Activities Prevention Act (UAPA) is equally draconian and even more dangerous because of its national scope. It defines “unlawful activity” as an action “which causes or is intended to cause disaffection against India” or “which disclaims, questions, disrupts or is intended to disrupt the sovereignty and territorial integrity of India,” among a bunch of other equally vague thought-crimes 8. As you might expect, this has opened the door to all kinds of abuse of power, where people are jailed for campaigning for marginalized communities’ rights in ways that irritate politicians. In a four-year period 2019-2023, there were over 10,000 UAPA arrests but only 335 convictions 9. From 2016 to 2020, 24,134 people were accused under the UAPA, of whom only 212 were convicted and 386 acquitted – most of the accused spend years languishing in preventive detention before the court says “haha sorry, you can go now” 10. No evidence needed to detain political opponents for years on end, one of the most shameful pieces of legislation that India has passed.

The UAPA has been used to punish leaders of protest movements. Some interesting examples:

Sharjeel Imam was jailed under the UAPA for a speech where he argued for blockading the Siliguri Corridor and cutting off the northeast to protest the Citizenship Amendment Act (CAA), The blockade proposal was not the main point of the speech and, in my opinion after reading+watching it, a mix of hyperbole and the fervor of a young kid who had rapidly and unexpectedly gotten a large audience; there was no credible threat of him actually blockading the Siliguri Corridor and cutting it off. He is still in jail and has cases against him in multiple states, including Manipur and Arunachal Pradesh where he did not even give speeches. He’s accused of having triggered the 2020 Delhi anti-CAA/NRC riots and the resulting violence. Shekhar Gupta’s words here convey my opinion well, so I’ll quote:

“It still doesn’t justify his long incarceration because you can’t jail young people indefinitely for stupidity and bringing disgrace on their IIT education.” 11

Umar Khalid (the more famous case) is also in jail under the UAPA for speeches that incited the 2020 anti-CAA riots, as are multiple other people.
The most ridiculous application of the UAPA is probably the Bhima Koregaon case. The details of this one are messy, but the high-level summary is as follows: every year, thousands of Dalits come to Bhima Koregaon in Pune to celebrate the contributions of Dalit soldiers in an 1818 battle that the British won against the Marathas. However, in 2018, clashes broke out between the Dalits and the Marathas due to disagreements over the history and mutual dislike for reasons I’m sure you can guess (the burning of Ambedkarite flags and desecration of a historically significant Dalit tomb give some clues). The Maharashtra police chose not to investigate RSS organizers accused of instigating the violence (many of whom had a history of rioting, such as Sambhaji Bhide); instead, the police brought charges against people who gave speeches criticizing the oppression of Dalits, arguing that these speeches incited the violence. The argument didn’t make much sense, so the government added masala by claiming that these activists were actually Naxalites hoping to recruit Dalits to the Maoist cause through distortion of history – that’s how the case soon resulted in 16 people being arrested under the UAPA 12. Most of these cases were absurd, here’s a sample:
1. Stan Swamy, an 81-year-old Jesuit priest and activist for tribal rights accused of supporting Maoists and inciting the Bhima Koregaon violence. He died in jail a few years ago after being subjected to multiple indignities, such as being denied for weeks a sipper straw despite having Parkinson’s and struggling to drink water. Since his death, the Washington Post has reported that evidence was planted on his computer by hackers over the span of two years 13, and that he was also a surveillance target for Israeli-supplied spyware that the Pune Police were using 14. The whole case is a mess of fabricated evidence and violations of due process.
2. Varavara Rao, age 78 at the time of being arrested, accused of having Maoist links and giving speeches inciting violence. He was a poet and activist, speaking out about issues like land reform and staged encounters against Naxals. His wikipedia page is very interesting, I recommend reading it – the government’s been out to get him for a loooong time. Arrested several times during the Emergency, released over and over due to lack of evidence that he actually incited violence, then arrested several times post-Emergency as well for inciting violence and attempting to overthrow the government (in one case, acquitted 17 years after the case’s start) 15. However, the Bhima Koregaon incident was where he ran out of his 9 lives. He has gotten bail, but the charges are sticking, mainly because the burden of proof is so low for UAPA arrests. The case against him and similar activists is so bad it’s almost funny:
  1. One lawyer was accused of creating anti-government opinion for Naxalite recruitment through photo exhibitions on mob lynchings (anti-lynching = Maoist – got that?) 16
  2. A fact-finding commission investigating a staged encounter that killed 40 people was accused of plotting to negatively portray the state and promote Naxalite thought 16
  3. Some activists were accused of plotting to assassinate Modi, on the basis of a letter planted on someone’s computer with malware (yes again) 17. This fabricated letter is doubly ridiculous because the dissenting opinion in the Supreme Court correctly identified it as a fake, despite the majority ruling in favor of the prosecution; the dissenter DY Chandrachud (future Chief Justice) noted that in 17 places, the letter used Marathi words in Devanagari despite the letter’s purported author not being a Marathi speaker
  4. Also interesting is that the prosecution used the word “urban naxal” in a formal court prosecution:
    “Possessing Naxalite materials is one aspect, but spreading thoughts of the Naxalites…that is the agenda of urban Naxals,” said Pawar. “They are not innocent. They are intelligent persons. This is a top-level conspiracy to threaten the sovereignty and integrity of India.” 16.

The PSA and the UAPA are the most infamous preventive detention laws because their cases are more high-profile. However, there are many ‘petty’ cases of preventive detention like those of the TMC workers in Bengal.

Section 170 of the BNSS allows preventive detention by a “police officer knowing of a design to commit any cognizable offence” for up to 24 hours without a warrant, a power that is often abused.

There is also the National Security Act (NSA), used recently to arrest Sonam Wangchuk after protests calling for Sixth Schedule constitutional protections turned violent. He was released after 6 months in jail where he was prosecuted using poor evidence, often clips of his speeches taken out of context. The NSA allows detention of people “acting in any manner prejudicial to the defence of India, the relations of India with foreign powers, or the security of India” or “acting in any manner prejudicial to the maintenance of Public order” etc 18. The NSA allows preventive detention without formal conviction for up to 3 months, renewable in 3-month blocks by the state government for up to 12 months without any charges being pressed.

As this email has hopefully demonstrated, preventive detention isn’t some long-gone law used by the British Raj and since abandoned. It is still used today and has been strengthened and expanded by post-1947 governments. Used widely across India to harangue opposition politicians (notably in Kashmir), shut down protests and dissent (Ladakh and Delhi anti-CAA protests), and influence election outcomes (Bengal).

Sources

Source On Calcutta HC allowing preventive detention in accordance with existing statutes: https://www.ndtv.com/india-news/calcutta-high-court-allows-preventive-arrests-for-bengal-elections-as-per-law-11394622 ↩︎
NDTV source On # of people detained in Bengal: https://www.ndtv.com/india-news/west-bengal-election-2026-phase-1-voting-live-updates-trinamool-tmc-bjp-fight-for-152-seats-pm-modi-mamata-banerjee-11395947#544618 ↩︎
rediff on # of people detained: https://www.rediff.com/news/commentary/2026/apr/28/over-2000-in-preventive-custody-ahead-of-bengal-polls/410f2e7deff65a93a0cb7f4a685e69fb ↩︎
full PSA 1978 text here, not very interesting but linking source because it’s so unbelievable https://www.indiacode.nic.in/bitstream/123456789/16496/1/public_safety_act%2C_1978.pdf ↩︎
as usual, great history lesson from Praveen Swami at theprint.in – this one is actually worth reading https://theprint.in/opinion/security-code/restoring-jks-statehood-kashmiris-need-treated-other-indians/2715419/↩︎
on AAP MLA jailed under PSA: https://theprint.in/india/jks-lone-aap-mla-mehraj-malik-booked-under-psa-jail-cant-intimidate-soldier-of-aap-says-kejriwal/2738706/↩︎
on MLA being released last week: https://www.thehindu.com/news/national/jammu-and-kashmir/aap-mla-mehraj-malik-released-from-kathua-jail-after-jk-hc-quashes-his-psa-detention/article70914781.ece ↩︎
UAPA 1967 wording I quoted from: https://www.mha.gov.in/sites/default/files/A1967-37.pdf ↩︎
Source on UAPA low conviction rate: https://thewire.in/government/over-10000-persons-arrests-under-uapa-but-only-335-convictions-between-2019-23 ↩︎
Second source on UAPA low conviction rate: https://thewire.in/government/uapa-case-data-process-punishment-home-ministry-rajya-sabha ↩︎
Shekhar Gupta article with Sharjeel Imam quote: https://theprint.in/opinion/writings-on-the-wall/writings-on-the-wall-bengals-epitaph-for-left-is-i-let-doctrine-become-dogma-ideology-obstacle/2913628/↩︎
Source on # of arrests in Bhima Koregaon case: https://www.amnesty.org/en/petition/indian-authorities-must-release-all-imprisoned-activists-in-the-bk16-case/↩︎
Source on planted evidence against Stan Swamy: archived version at https://web.archive.org/web/20221220055653/https://www.washingtonpost.com/world/2022/12/13/stan-swamy-hacked-bhima-koregaon/ and original at https://www.washingtonpost.com/world/2022/12/13/stan-swamy-hacked-bhima-koregaon/↩︎
Source on Pune police using Israeli spyware against Stan Swamy and others: https://www.washingtonpost.com/world/2022/12/13/stan-swamy-hacked-bhima-koregaon/ (archived at https://web.archive.org/web/20221220071249/https://www.wired.com/story/modified-elephant-planted-evidence-hacking-police/ )↩︎
Source on Varavara Rao’s history: archived at https://web.archive.org/web/20200718032019/https://indianexpress.com/article/explained/varavara-rao-politics-jail-coronavirus-6510434/↩︎
Source on absurd prosecution of Varavara Rao and other ‘urban naxals’: https://scroll.in/article/892464/photo-shows-about-lynchings-seeking-arms-from-nepal-claims-against-activists-arrested-on-tuesday ↩︎
Source on planted evidence about PM assassination: https://web.archive.org/web/20210706104148/https://www.washingtonpost.com/world/2021/07/06/bhima-koregaon-case-india/↩︎
Wording of National Security Act: https://www.mha.gov.in/sites/default/files/2022-08/ISdivII_NSAAct1980_20122018%5B1%5D.pdf ↩︎

Interesting Things I Did in the Week of 30 November

Mon, 08 Dec 2025 00:00:00 GMT

Interesting Things I Did in the Week of 30 November

This is going to be very unstructured and rambling, but I figured my blog is a good place to document my learning/reading journey. 99% of this will probably be uninteresting to readers, but I hope one or two of the links here might pique someone’s curiosity. For people uninterested in Indian politics, skip ahead to where I talk about other stuff (there’s a big horizontal line sectioning it off). Also, fair warning that the stuff on Indonesia is a bit grisly (cannibalism and ethnic conflict). Now, jumping into news stuff I read this week…

On Monday, I read this short article on the surrender of several Naxals in Maharashtra, and the “related links” led me down an interesting path from there.

This is a good article on the problems facing the Communist Party of India (Maoist) today. The author focuses on how the recent encounter deaths of several leaders have led to a split among the remaining leadership between those who wish to continue armed resistance and those who want to surrender and pursue nonviolent means. The article also touches on how some leaders are old or in poor health, and the younger leaders have military expertise but no political talent, making it hard to maintain internal unity and keep recruitment strong. This is a good read for anyone interested in the future of the Naxal movement.

I liked this opinion article that advocated for a ceasefire and a more humane approach to dealing with the Naxal movement. The article argues that Naxals are Indian citizens and should be treated as such, especially in light of the very real grievances that they hold against the state; the author’s proposed solution is a ceasefire with promises of less harsh punishment and rehabilitation for those who surrender, which strikes me as a far better solution than the Home Ministry’s policy of forever waging a brutal war of attrition against poor villagers in Chhattisgarh and Odisha. The writer also makes an interesting point about how Amit Shah’s 31 March 2026 deadline for ending the counterinsurgency operation could increase the number of fake encounters and civilian deaths since it puts pressure on the security forces to move faster than possible when respecting the rules of engagement – I actually had not considered this point until now. On a completely different note, the author of the article, Prakash Singh, is interesting in his own right; he is a retired IPS officer who served in his career as Director General of Police, Chief of the Border Security Force, UP police, and Assam police, and he’s written a few books on counterinsurgency and the Naxal movement. Very cool discovery of an interesting person.

This is a good article by Arun Kumar on problems with the Indian government’s methodology for GDP calculation and why the IMF has downgraded the quality of India’s GDP data to a C. I also read Arun Kumar’s article on the new Labour Codes that makes good points about how the Codes will exacerbate labour’s weaknesses in wage bargaining and how they have the potential to worsen unemployment and hurt aggregate demand.

The Arun Kumar article on Labour Codes led me to this absolutely brilliant article that goes into even greater depth on the subject. It explains what the Codes change and how they will end up hurting workers. This is the most informative article I read this week, and I HIGHLY recommend it to anyone interested in this topic since it explains the procedural illegitimacy of the Codes (not consulting the Indian Labour Conference or allowing debate), their reduction of workers’ bargaining power, and their potential to open the door to privatization of state assets. There are a lot of good points discussed here, but one of the most interesting numbers is that the new Industrial Relations code has exempted companies with under 100 workers (used to be 300) from needing government permission for retrenchment or closure, allowing 90% of India’s companies to arbitrarily lay off workers en masse without needing to coordinate with the government. The Occupational Safety and Health Code similarly redefines ‘factory’ to exempt industrial units with under 20 workers (used to be 10) from many government regulations, encouraging companies to fragment their workforce to escape compliance.

This is a tragic article on the recent murder of Saksham Tate, a 20-year-old Dalit man, in Nanded at the hands of his in-laws who refused to accept their daughter’s intercaste marriage. Saksham Tate was reportedly shot in the chest and then hit on the head with a tile by his wife’s brother; five of her relatives are now in police custody in connection with the case.

This was a really cool article on a new MF Husain museum in Qatar, built exactly how he had asked for it.

This was a good opinion article on Macaulay that argues that he was a force for good in India, reducing emphasis on traditional Sanskrit education that had little value and introducing the country to European literature. Shankar Sharan does a good job of refuting lies about Macaulay, proving that Macaulay didn’t forbid Indians from pursuing Sanskrit education if they so wished but merely removed British promotion of it. The article concedes that Macaulay was misguided in seeing Indian literature as being so worthless but defends the fact that Macaulay truly wanted what was best for education in India and that he did succeed in improving the system. An important read, considering how our politicians are still using the long-dead Macaulay as a bogeyman for the inadequacy of our education system and a half-imagined problem of being over-dependent on the western world. That article on Macaulay’s influence on the education system led me to another good article praising Macaulay’s criticism of the caste system and his vision of a freer India; I learned a lot from this one, especially about Macaulay’s insistence on giving Dalit children equal access to education and his belief that “no native of our Indian empire shall, by reason of his colour, his descent, or his religion, be incapable of holding office.” This quote from Macaulay was also quite powerful

It would be, on the most selfish view of the case, far better for us that the people of India were well governed and independent of us, than ill governed and subject to us; that they were ruled by their own kings, but wearing our broadcloth, and working with our cutlery, than that they were performing their salams to English collectors and English magistrates, but were too ignorant to value, or too poor to buy, English manufactures. To trade with civilised men is infinitely more profitable than to govern savages.

This was another good article by Shankar Sharan that argues MK Gandhi was the origin of Congress’ tradition of ‘backseat driving’ and lack of respect for democratic process within the party (cough cough, dynasty rule and going out of their way to avoid criticism of the party leadership).

Here’s a good article by a TMC MP on why the BJP won’t win Bengal as easily as they won Bihar. The author conveniently structures the article to have five main points: the BJP’s lack of a well-loved leader in Bengal (the “Nitish factor”), the TMC’s popularity among women, fewer problems with law and order, a stronger economy, and a “bhadralok culture” that makes it harder for the BJP’s Hindutva rhetoric to destroy the Bengali tradition of cosmopolitanism. I’m a bit doubtful of the claim about the economy and the last claim since bhadralok culture is sadly fading in Bengal, but the other three are strong arguments.

This is a good article on book banning in Kashmir and how it goes against basic principles of free expression in India. Some of the most interesting points made here are that some of the banned literature consists of books that are almost entirely reproductions of government documents (what secessionist thought are they fighting there?) and that the police are often seizing books that aren’t even on the official list of banned books.

Sanjeev Chopra wrote a good article on the history of India-China relations and the start of how everything went downhill. Further cements my opinion that a lot of trouble would’ve been avoided if Vallabhbhai Patel hadn’t died so early, article shows he was much more clear-eyed than Nehru on the threat from China. This is another good article on that bit of history.

And then the latest episode in the Bihar assembly election saga: even after losing the actual election, the Mahagathbandhan continues to lose haha. This time, it’s the Rashtriya Janata Dal and Congress blaming each other for the loss and making rash statements threatening to end the alliance. The only hope is that Jan Suraaj can take both parties’ vote share rather than the NDA gobbling it up.

Now here’s some good news – Hany Babu has finally been released on bail after 5 years and 4 months without trial in connection with the Bhima Koregaon case. Horrible that it took so long, but at least the court finally realized the insanity of what the NIA was doing. The article on his release mentioned that he’d written some articles from The Wire while in prison, so out of curiosity I opened this article on how the law tackles the topic of undertrial detention. It was an INCREDIBLE read with some of the best legal analysis I’ve seen, I highly recommend it to anyone interested in the subject. Fun fact, a suspect can be kept in undertrial detention (without conviction) for up to half the maximum jail sentence for the crime they’re accused of; for crimes where the punishment can be life imprisonment or the death sentence, there is no such “half ground” limit, creating a system where undertrial prisoners are effectively assumed “guilty until proven innocent.” This is one of the most shameful parts of the Indian legal system and is worth learning about.

Here is some of the first bad news to emerge about the character of the new Chief Justice of India. In a habeas corpus case over the custodial disappearance of five Rohingya illegal immigrants, CJI Surya Kant said

Once these illegal migrants are in India, they claim right to food and shelter and help for their children. We have many poor people in the country. They have a right over the country’s resources, not the illegal migrants.

Would be nice if the CJI was a bit more concerned by the state’s complete disregard for due process in deportations, rather than making non sequiturs trying to justify depriving migrants of food and shelter.

Here’s some interesting data on how Bangladeshis feel about their political system. An International Republican Institue (IRI) survey of 3270 “likely voters” found that 33% would vote for the Bangladesh National Party (BNP) and 29% for Jamaat e Islami. There’s lots more interesting survey results in the full IRI report here. I’m sad that there’s no grassroots opposition movement against both the BNP and Jamaat, since both of them have a very dark past, but it’s too late for any new party to reach their scale between now and February. Let’s see if “the Dark Prince” (who seems likely to come back to power) truly has changed his ways…

Here’s a good article on the status of the Waqf property registration portal; the website is down most of the time, arbitrarily deletes half-entered data, and crashes off and on, but the BJP government still refused to extend the December 5 deadline for registration. Only on December 5, literally the deadline for registration, did the minority affairs minister tell people that there would be no fines or penalties for the next 3 months against people who didn’t register before the deadline. Classic example of BJP’s chaotic and callous governance style.

And then the latest of the BJP government in Arunachal Pradesh. This article summarizes the Supreme Court’s recent findings on the ‘cartelisation’ (words of Justice Vikram Nath) of work contract awards; turns out that companies owned by BJP Chief Minister Pema Khandu and his family are awarded work contracts even when they give a tender just 0.01% less than competing companies’ tenders, and there are concerns over whether competing companies are even allowed to participate in the tender process. Also interesting is this article on remarks recently made by Ojing Tasing, the state’s panchayats and rural development minister. He has threatened to not provide access to government welfare schemes to panchayat seats that don’t elect BJP candidates. His exact words were

I don’t believe in beating around the bush. The panchayat segments where the BJP candidates lose will not get any scheme. As the panchayati raj minister, I mean what I say

Yikes

Moving away from the topic of politics, I have finished Aakar Patel’s “The Price of the Modi Years” (great book) and have now started Richard Lloyd Parry’s “In the Time of Madness.” It’s an amazing book, and I’m learning a lot. I won’t go super in depth (saving that for a proper book review), but I’ll briefly talk about what I’ve been liking so far. Parry writes really well and has some incredible experiences that he talks about in the book. The first section on the West Borneo headhunting wars introduced me to a bit of history I had never even heard about before; the ethnic violence between the Dayaks and Madurese is one of the darkest chapters in human history, and there’s no comparable conflict through which to try understanding it. The Dayaks would kill Madurese, eat their hearts, and then ritually decapitate them and mutilate the head, believing this ritual cannibalism brought them magic powers. Parry’s book is deeply informative and transported me to a world of unimaginable horror, where he forced me to think about the question of:

How poor an existence these people had, that this hairy lump [a severed human head] on an oil drum should be an emblem of morality and hope

Parry also has a talent for good turn of phrase, and it’s almost addictive to read his book. His prose brings the jungles of West Borneo to life and is immensely satisfying to read.

He’s also good at guessing which factoids will be most interesting to readers, presenting a wealth of knowledge on the Dayaks’ beliefs in black magic and the reasons for hatred between the Dayaks and the Madurese. It’s also nice how Parry adds bits of dark humor to make this otherwise depressing book a bit less heavy. The humor is still very dark, but there’s a kind of very sick irony in some parts such as this one

My idea was to take a shot from behind. There would be no doubt what was depicted – the head of a decapitated man on an oil drum – but without the slashed mouth and lidless eyes, and the ribbons of tissue trailing from the neck. I had knelt down and was raising the camera, when the younger of the brothers spotted what I was doing. He raised his hand, ran forward, then picked up the head and turned it round through 180 degrees to face me. I walked round to the other side, and tried again. The same thing happened. The boy was trying to be helpful. He couldn’t understand why I should avoid the face of the dead man. He wanted to give me the very best view of this magical object that was bringing him and his brother so much excitement and delight.

It’s also interesting to see Parry’s more personal reflections on how he was impacted by what he was seeing. He’s incredibly open about his feelings at the time, and that makes the book even more immersive as we’re able to try imagining what was going through his head as he reported on the conflict.

I had never worked in such conditions before, and nor had anyone I knew. The experience produced two contradictory reactions. The first was relief, together with a guilty pride, in finding myself able to confront horror without being overcome by nausea or fear. The second reaction took the form of troubling questions, which nagged me at odd moments. Why was I not more upset by this? What was wrong with me? I don’t know what to call such an emotion, but it is something close to shame.

I finished the first part on the West Borneo ethnic violence and am almost through the section on the Jakarta riots and the fall of Suharto. The second section is somehow even more informative than the first one, and I started writing down some of the things I read because they piqued my curiosity enough to google them later. Parry makes the entire history of Indonesia seem fascinating, creating an organized framework through which to view much of the history while also presenting the chaos of the inexplicable parts. I learned a lot about the Suharto era and its lasting impact on Indonesia, presented both through historical evidence and Parry’s talent for metaphor

During his presidency, every public and private office in Indonesia carried a pair of photographic portraits: the president, twinned with the vice-president of the moment. In the space of a few months, Suharto’s image had been removed to leave only that of Habibie. But all over the country, he survived, and in appropriately ghostly form. In companies, schools, government offices, even in some private homes, telltale picture hooks still protruded where Suharto once hung, above unfaded rectangles of fresh-looking paint.

What really caught my attention about Suharto was how weird he was – I feel like Elias Canetti or Ashis Nandy would’ve had a lot of fun psychoanalyzing him. He held power for over 30 years, yet he didn’t live a very lavish lifestyle, choosing to live in a middle class home rather than a palace, and he didn’t establish a cult of personality either – which begs the question, why did he take power in the first place? He laughed at superstitions when meeting western leaders, yet in Indonesia, he encouraged superstitions about the divine source of his power; some of the more interesting theories are that he derived his power from his marriage to Ibu Tien, who was a descendant of the royal house of Solo, and the belief that he wasn’t killed in the 1965 Gestapu coup because a seer advised him to spend the night “at the confluence of two waters,” which convinced him to go fishing that day. No one is sure if Suharto’s beliefs in Javanese mysticism were genuine or just a political tool to win the approval of a superstitious population. That entire period of history is a fascinating mystery.

The Javanese conception of power was also very cool to read about. Similar to the Chinese Mandate of Heaven, the Javanese believe in the “wahyu,” a divine right to rule that can come in many forms. Parry told many interesting stories of how, even in the 1990s, these beliefs held sway, and protestors would often talk to him about how they had seen the wahyu flying through the sky towards an opposition leader’s house a few days before the start of the Jakarta riots. It’s fascinating how kings, and later on politicians, had to combine their military support with the people’s belief in their divine right to rule, even in the 20th century.

Another nice feature of the book is how it’s structured around some central themes: “Something Close to Shame” is on his complex reaction to seeing the headhunting in west Borneo, and the entire book “In the Time of Madness” is organized around the idea of the “Time of Madness” prophesied in the Prelambang Jayabaya, a 12th century Javanese prophecy, being upon us. It adds an oddly poetic character to the book.

Overall, I was awed by how much history Parry had managed to see, and I’ve learnt a ton about the history and culture of Indonesia because of this book. I 10/10 recommend it, based on the 100-something pages I’ve read so far. Incredible to hear the first-hand account of a British journalist witnessing cannibalism in west Borneo, or wandering the Indonesian parliament building the day that protestors were allowed in to stage a demonstration. He’s a great writer with some fascinating stories to tell.

In the world of film, I’ve seen two movies recently: “The Act of Killing” and “A Death in the Gunj.” Both were really good, but I’m going to write about them later on since it’s past midnight now and I don’t want too much overlap between this post and later film reviews (coming eventually haha).

In the world of music, I’ve recently gotten addicted to A.R. Rahman’s song “Dil Se Re” (really good) and “Mist/Fog” from Park Chan-wook’s “Decision To Leave,” while still being addicted (for about a month now) to “Imi Oneun Sori” from Park Chan-wook’s film “The Handmaiden” – just goes to show how good he is at selecting music for his movies haha. I recommend these songs, very good music.

I haven’t discovered too much new music last week, mainly due to laziness about listening to new albums and instead putting Park Chan-wook film soundtracks on repeat, so I’ll hopefully get some new favorites this week.

Well, that sums up this post. Sorry for the rambling nature of it, but writing a structured post takes an obscene amount of time and I hope this is interesting(?). As always, feel free to message me on discord at floofydoggo or email me at chancellorceti <at> gmail.com to talk about anything you found interesting here.

Thanks for reading !!!!!!!!

Deriving the Dirac Delta Term in the Dipole Electric Field Formula

Sun, 20 Apr 2025 00:00:00 GMT

Deriving the Dirac Delta Term in the Dipole Electric Field Formula

Chancellor Ceti

2025-04-20

Introduction
The Derivation
Conclusion

Introduction

The inspiration for today’s post is J.D. Jackson’s "Classical Electrodynamics", which I have been dutifully plodding through for several months now. I recently started Chapter 4 which covers multipole expansions and their application to the study of dielectrics and electrostatics of macroscopic media.

In section 4.1, Jackson presented an interesting derivation of the formula for the electric field of a dipole

\mathbf{E}(\mathbf{x})=\frac{1}{4\pi\epsilon_0}\left[\frac{3\mathbf{n}(\mathbf{p}\cdot\mathbf{n})-\mathbf{p}}{|\mathbf{x}-\mathbf{x}_0|^3}-\frac{4\pi}{3}\mathbf{p}\delta(\mathbf{x}-\mathbf{x}_0)\right]

The derivation uses some very nice tricks, making it satisfying to read, and will be (according to Jackson) "useful in elucidating the basic difference between electric and magnetic dipoles."

However, in the true Jacksonian style, many important details of the derivation are omitted and considered too trivial for the consideration of the great J.D. I spent a good part of my Saturday morning working out some of these details, and I am now sharing my results with the world. I hope this post will provide some intellectual satisfaction to readers and make this derivation more understandable to anyone struggling through Jackson.

Before beginning, I must warn that this blog post will not be very accessible to people lacking background in electrodynamics and vector calculus. There are many identities and formulas used here, and deriving all of them would not make sense, given that any electrodynamics student should know them.

With those preliminaries covered, let us begin!

The Derivation

Jackson begins by considering a localized charge distribution \rho(\mathbf{x}) that leads to an electric field \mathbf{E}(\mathbf{x}) throughout space. He proposes integrating the electric field over the volume of a sphere of radius R.

We choose the origin as the center of the sphere and begin with

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\int_{r<R}\boldsymbol{\nabla}\Phi\,d^3x

Now we use the following important identity to turn our volume integral into a surface integral

\iiint_{V}\boldsymbol{\nabla} f\,dV=\iint_{\partial V}f \cdot \mathbf{n}\,dS

where \mathbf{n} is the outward unit normal to the boundary of V, \partial V.

For anyone unfamiliar with this identity, it can be easily derived using the divergence theorem – proof left as an exercise for the reader.

Use of this identity yields

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\int_{r=R}\Phi \mathbf{n}\,dA

where n is the outward directed normal to the sphere i.e. \mathbf{n}=\mathbf{x}/R

Now Jackson switched our integral over area elements to an integral over solid angle. The appropriate scale factor is

\,dA=R^2\,d\Omega

For those unfamiliar with solid angle integration, the Wikipedia article gives a decent introduction.

Using this change to solid angle integration, we find

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\int_{r=R}R^2\,d\Omega \Phi(\mathbf{x})\mathbf{n}

Now Jackson brings in the definition of electrostatic potential as a volume integral i.e.

\Phi(\mathbf{x})=\frac{1}{4\pi\epsilon_0}\int_{}\frac{\rho(\mathbf{x'})}{|\mathbf{x}-\mathbf{x'}|}\,d^3x'

Substitution of this formula gives us

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{R^2}{4\pi\epsilon_0} \int_{r=R}\mathbf{n}\,d\Omega \int_{}\frac{\rho(\mathbf{x'})}{|\mathbf{x}-\mathbf{x'}|}\,d^3x'

Jackson interchanges the two integration operators (justified by Fubini’s Theorem I think? I haven’t studied analysis, if anyone has the time I’d love to see how we justify this interchange) now to get

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{R^2}{4\pi\epsilon_0} \int_{}\,d^3x'\rho(\mathbf{x'}) \int_{r=R}\frac{\mathbf{n}}{|\mathbf{x}-\mathbf{x'}|}\,d\Omega

Thus far Jackson has been quite friendly – we’ve been dealing with very basic vector calculus and haven’t met anything outlandish. Here, however, all hell breaks lose.

We focus on the surface integral first.

Recall that the normal vector to the sphere can be expressed as \mathbf{n}=\mathbf{x}/R, allowing us to express the normal vector in spherical coordinates now

\mathbf{n}=\mathbf{i}\sin\theta\cos\phi+\mathbf{j}sin\theta\sin\phi+\mathbf{k}\cos\theta=\sin\theta(\mathbf{i}\cos\phi+\mathbf{j}\sin\phi)+\mathbf{k}\cos\theta

Now Jackson invites us to notice, as any normal person would (sarcasm), that the components of this vector can all be expressed as linear combinations of spherical harmonics with l=1

A quick look at a table of spherical harmonics reveals this to be true. Indeed, we can find quite easily that

\begin{split} \mathbf{n}&=\sqrt{\frac{2\pi}{3}}\biggl([-Y_{1,1}(\theta,\phi)+Y_{1,-1}(\theta,\phi)]\mathbf{i}+i[Y_{1,1}(\theta,\phi)+Y_{1,-1}(\theta,\phi)]\mathbf{j}\biggr) \\ &+\sqrt{\frac{4\pi}{3}}Y_{1,0}(\theta,\phi)\mathbf{k} \end{split}

Now, the central theme of this chapter is using spherical harmonics to find cool series expansions. So the next step is rather obvious.

We recall our expansion for \frac{1}{|\mathbf{x}-\mathbf{x'}|} in terms of spherical harmonics as

\frac{1}{|\mathbf{x}-\mathbf{x'}|}=4\pi\sum_{l=0}^{\infty}\frac{1}{2l+1}\frac{r_<^l}{r_>^{l+1}}\sum_{m=-l}^{l}Y_{lm}^*(\theta',\phi')Y_{lm}(\theta,\phi)

where r_> is the greater of r and r' and r_< is the smaller of the two.

Now we combine these two results to express the solid angle integral as

\int_{r=R}\,d\Omega\frac{\mathbf{n}}{|\mathbf{x}-\mathbf{x'}|}=4\pi\int_{r=R}\,d\Omega \mathbf{n}\sum_{l=0}^{\infty}\frac{1}{2l+1}\frac{r_<^l}{r_>^{l+1}}\sum_{m=-l}^{l}Y_{lm}^*(\theta',\phi')Y_{lm}(\theta,\phi)

Now let’s interchange the summation operators with the integration operator and take terms independent of \Omega outside of the integral.

\int_{r=R}\,d\Omega\frac{\mathbf{n}}{|\mathbf{x}-\mathbf{x'}|}=4\pi\sum_{l=0}^{\infty}\frac{r_<^l}{(2l+1)r_>^{l+1}}\sum_{m=-l}^{l}Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\mathbf{n}\,d\Omega

Now consider just this part of the expression

Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\mathbf{n}\,d\Omega

Recall our expression for \mathbf{n} in terms of spherical harmonics. Ignore the constants in that and consider its general form, giving us

\begin{split} Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\mathbf{n}\,d\Omega=\\ Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi) \left[a(-Y_{1,1}+Y_{1,-1}) \mathbf{i}+b(Y_{1,1}+Y_{1,-1}) \mathbf{j}+cY_{1,0} \mathbf{k}\right]\,d\Omega \end{split}

Now we must recall the orthogonality relation for spherical harmonics

\int_{r=R}Y_{lm}(\theta,\phi)Y_{l'm'}(\theta,\phi)\,d\Omega=\delta_{ll'}\delta_{mm'}

Evidently, the only nonvanishing terms here are the l=1 terms because of our orthogonality relation and the expression for \mathbf{n} in terms of Y_{1m} spherical harmonics.

Thus, we have \int_{r=R}\,d\Omega\frac{\mathbf{n}}{|\mathbf{x}-\mathbf{x'}|}=4\pi\cdot\frac{r_<}{3r_>^2}\sum_{m=-1}^{1}Y_{1m}^*(\theta',\phi')\int_{r=R}Y_{1m}(\theta,\phi)\mathbf{n}\,d\Omega

Quite a simplification! We have even more nice tricks here though.

Again consider

\sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\mathbf{n}\,d\Omega

To make our expression for \mathbf{n} a bit less ugly, I’ll write it in a more abstract form as

\mathbf{n}=\sum_{a=1}^{3}\mathbf{e}_a\sum_{b=-1}^{1}Y_{1b}(\theta,\phi)c_{ab}

where \mathbf{e}_1=\mathbf{i},\mathbf{e}_2=\mathbf{j},\mathbf{e}_3=\mathbf{k}

Comparison with our earlier expression shows that this is essentially the same thing – just let c_{11}=-\sqrt{\frac{2\pi}{3}},c_{30}=\sqrt{\frac{4\pi}{3}} etc

Now let’s look again at \begin{split} &\sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\mathbf{n}\,d\Omega\\ &= \sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\sum_{a=1}^{3}\mathbf{e}_a\sum_{b=-1}^{1}Y_{1b}(\theta,\phi)c_{ab}\,d\Omega\\ &= \sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\sum_{a=1}^{3}\mathbf{e}_a\sum_{b=-1}^{1}c_{ab}\int_{r=R}Y_{lm}(\theta,\phi)Y_{1b}(\theta,\phi)\,d\Omega\\ &=\sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\sum_{a=1}^{3}\mathbf{e}_a\sum_{b=-1}^{1}c_{ab}\delta_{mb}\\ &=\sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\sum_{a=1}^{3}c_{am}\mathbf{e}_a\\ &=\sum_{a=1}^{3}\mathbf{e}_a\sum_{b=-1}^{1}Y_{1b}^*(\theta',\phi')c_{ab} \end{split}

Incredible! This is the exact same thing as our expression for \mathbf{n} except that instead of \theta and \phi we have \theta' and \phi'

If we consider what those angles mean in the definition of \mathbf{n} we will realize that this new expression is another outward unit normal, except to \mathbf{x'} rather than \mathbf{x}

Thus we have

\sum_{m=-1}^{1}Y_{lm}^*(\theta',\phi')\int_{r=R}Y_{lm}(\theta,\phi)\mathbf{n}\,d\Omega=\mathbf{n'}

where \mathbf{n'}=\mathbf{r'}/r'

Now let’s take this result back to our larger expression

\int_{r=R}\,d\Omega\frac{\mathbf{n}}{|\mathbf{x}-\mathbf{x'}|}=4\pi\cdot\frac{r_<}{3r_>^2}\sum_{m=-1}^{1}Y_{1m}^*(\theta',\phi')\int_{r=R}Y_{1m}(\theta,\phi)\mathbf{n}\,d\Omega

=\frac{4\pi r_<}{3r_>^2}\mathbf{n'}

A beautifully simple result, considering where we started. Now let’s plug this expression into the even bigger original expression (yes, we really zoomed in a lot)

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{R^2}{4\pi\epsilon_0} \int_{}\,d^3x'\rho(\mathbf{x'}) \int_{r=R}\frac{\mathbf{n}}{|\mathbf{x}-\mathbf{x'}|}\,d\Omega =-\frac{R^2}{4\pi\epsilon_0} \int_{}\,d^3x'\rho(\mathbf{x'})\frac{4\pi r_<}{3r_>^2}\mathbf{n'} =-\frac{R^2}{3\epsilon_0} \int_{}\,d^3x'\frac{ r_<}{r_>^2}\mathbf{n'}\rho(\mathbf{x'})

This is an incredible simplification of our earlier expressions! However, to go further, we must know which is larger of R and r' so that r_> and r_< have some meaning.

Jackson has us consider two different cases. The first is the case where all the charge is contained within the sphere, the second is where the charge lies external to the sphere (see image below).

Visualizations of the two cases considered – taken from Jackson’s textbook

In the first case, all charge is contained within the sphere, so r'<R. Thus we have r_>=R and r_<=r'

This gives us

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{R^2}{3\epsilon_0} \int_{}\,d^3x'\frac{ r'}{R^2}\mathbf{n'}\rho(\mathbf{x'})=-\frac{1}{3\epsilon_0}\int_{}r'\frac{\mathbf{x'}}{r'}\rho(\mathbf{x'})\,d^3x' =-\frac{1}{3\epsilon_0}\int_{}\mathbf{x'}\rho(\mathbf{x'})\,d^3x' =-\frac{\mathbf{p}}{3\epsilon_0} where \mathbf{p}=\int_{}\mathbf{x'}\rho(\mathbf{x'})\,d^3x' is the electric dipole moment of the charge distribution with respect to the center of the sphere.

In the second case, since the charge is external to the sphere, we have r'>R. Thus we find

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{R^2}{3\epsilon_0} \int_{}\,d^3x'\frac{R}{{r'}^2}\mathbf{n'}\rho(\mathbf{x'})=-\frac{R^3}{3\epsilon_0}\int_{}\,d^3x'\frac{\mathbf{n'}}{{r'}^2}\rho(\mathbf{x'}) =-\frac{R^3}{3\epsilon_0}\int_{}\frac{\mathbf{x'}}{{r'}^3}\rho(\mathbf{x'})\,d^3x'

Now a bit of pattern recognition will prove useful. Notice that this integral is just -4\pi\epsilon_0 times the electric field at the center of the sphere (Coulomb’s Law with \mathbf{x}=\mathbf{0})

Also note that the reason it’s a factor of -4\pi\epsilon_0 and not 4\pi\epsilon_0 is that the integrand here is \frac{\mathbf{x}'-\mathbf{x}}{r^3} instead of \frac{\mathbf{x}-\mathbf{x}'}{r^3} as in Coulomb’s Law.

So we have

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{R^3}{3\epsilon_0}\cdot-4\pi\epsilon_0 \mathbf{E}(0)=\frac{4\pi}{3}R^3 \mathbf{E}(0)

Note the sphere’s volumes is \frac{4\pi R^3}{3}

So we have found that the average value of the electric field over a sphere containing no charge equals the field’s value at the sphere’s center. Nice result!

However, returning to the first case, our result there tells us something important.

The traditional expression for the electric field of a dipole at \mathbf{x}_0 is

\mathbf{E}(\mathbf{x})=\frac{3\mathbf{n}(\mathbf{p}\cdot\mathbf{n})-\mathbf{p}}{4\pi\epsilon_0|\mathbf{x}-\mathbf{x}_0|^3}

However, if we integrate this over the volume of the sphere, the resulting integral equals zero. This stands in direct contradiction with our earlier result

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{\mathbf{p}}{3\epsilon_0}

To resolve this contradiction, we introduce the Dirac delta function into our formula and write

Also note our use of the convention that, when an integral diverges, we consider its limit rather than the nonsensical diverging value. If we didn’t use this convention, the \frac{1}{|\mathbf{x}-\mathbf{x}_0|^3} term would lead to a diverging volume integral.

Now with that convention and the addition of a Dirac delta term, this expression’s volume integral agrees with our previous result.

Thus, through an impressive series of mathematical manipulations, we have found an expression for the dipole’s electric field that removes the contradiction in our earlier expression. And we also found a cool bonus result about the average value of an electric field over a sphere!

Conclusion

This has been a lengthy blog post, so I will briefly summarize our key results.

First, we found a nice bonus result about the average value of an electric field over the surface of a sphere being equal to the field’s value at the sphere’s center.

Then we found our main result. If we integrate the electric field over a sphere containing all charge present in a system, the result will be

\int_{r<R}\mathbf{E}(\mathbf{x})\,d^3x=-\frac{\mathbf{p}}{3\epsilon_0} where \mathbf{p}=\int_{}\mathbf{x'}\rho(\mathbf{x'})\,d^3x' is the electric dipole moment of the charge distribution with respect to the center of the sphere.

We realized that, in order to avoid contradicting this result, we must modify our expression for the electric field casued by a dipole at \mathbf{x}_0

We thus found

A number of interesting techniques were used in this derivation. We exploited the expansion in spherical harmonics of \frac{1}{|\mathbf{x}-\mathbf{x'}|} and then made use of the orthogonality of spherical harmonics. We also made good use of many different formulas from electrodynamics, providing a nice example of how different concepts connect at the most unexpected times.

None of the thinking here is greatly original. I merely filled in some missing details in Jackson’s derivation. To anyone interested in seeing more elegant work like this, I highly recommend reading J.D. Jackson’s "Classical Electrodynamics." The book is sometimes difficult to follow, but when you understand him, it feels magical.

I hope that some of the manipulations shown here proved interesting and gave the reader some intellectual satisfaction. As always, if you have any comments or questions, feel free to contact me by email at chancellorceti@gmail.com or on Discord where my username is floofydoggo.

And to anyone reading Jackson’s book, I hope this more detailed derivation has provided more clarity to section 4.1 haha. I spent a few hours this morning understanding that section, so I suppose this is my "April contribution to humanity", if you will. Perhaps this will aid some long-suffering Jackson student.

With all that said, watch for my next blogpost! It will likely involve some more content from Jackson’s monster of a textbook. If you enjoy my writing, be sure to send it to anyone else you think might like it.

Improvements on Stirling’s Approximation using Taylor Series Expansions

Tue, 11 Mar 2025 00:00:00 GMT

Improvements on Stirling’s Approximation using Taylor Series Expansions

Chancellor Ceti

2025-04-20

Introduction
The First Series Expansion
The Second Series Expansion
Knowing which terms to keep
Conclusion

Introduction

Stirling’s Approximation is a well-known approximation to the factorial. n!\sim \biggl(\frac{n}{e}\biggr)^n\sqrt{2\pi n} This approximation is quite good for sufficiently large n. For n=100, the approximation only has a 0.08 \% error.

However, we must ask – can this approximation be improved upon? Stirling’s Approximation has a convenient expression – simple, not painful to plug into a calculator. But can we find an uglier solution that yields a better approximation? The answer – yes, with special emphasis on the word "uglier"

The First Series Expansion

Let’s start with what we know – how to derive Stirling’s Approximation. The path to an improvement will make itself quite obvious midway through the derivation.

We know that n!=\Gamma(n+1)=\int_{0}^{\infty}x^ne^{-x}\,dx A path towards an approximation makes itself obvious to us. If we want to approximate n! all we have to do is approximate \Gamma(n+1). And if we want to approximate \Gamma(n+1), all we have to do is approximate x^ne^{-x}

Let’s rewrite that integrand as

x^ne^{-x}=e^{n\ln{x}-x}

Let’s play around with introducing a new variable y=x-n

Then we have n\ln{x}-x=n\ln(y+n)-y-n=n\ln\biggl[n\biggl(1+\frac{y}{n}\biggr)\biggr]-y-n n\ln{x}-x=n\ln{n}+n\ln\biggl(1+\frac{y}{n}\biggr)-y-n

Now think about the fraction \frac{y}{n} \frac{y}{n}=\frac{x-n}{n}

Now consider a few things. The graph of x^ne^{-x} has a sharp peak at x=n (proof left as an exercise for the reader, just set the derivative to zero)

Near the peak at x=n, we must have x-n near zero.

Far away from x=n, x^ne^{-x} takes on small, negligible values – the larger n is, the sharper the peak and the more irrelevant are the terms far from the peak.

So if we only consider terms near the peak (valid for large n), then \frac{y}{n}=\frac{x-n}{n}\approx 0

But wait, we have \ln\bigl(1+\frac{y}{n}\bigr)

We know that the Maclaurin series expansion for \ln(1+x) converges for |x|<1 so, given that |\frac{y}{n}|\approx 0, we can use the Maclaurin series expansion for the logarithm!

Also note that, for very small x, we can keep just the first few terms from the \ln(1+x) expansion and have a small error. As x gets larger, the error from the truncated Maclaurin series grows.

Since \frac{y}{n} is very small here, we can use the truncated Maclaurin series with a very small error, the error getting smaller with larger n.

So we then have

n\ln{x}-x=n\ln{n}+n\Biggl[\biggl(\frac{y}{n}\biggr)-\frac{1}{2}\biggl(\frac{y}{n}\biggr)^2+\sum_{k\ge 3}(-1)^{k+1}\frac{y^k}{kn^k}\Biggr]-y-n n\ln{x}-x=n\ln{n}+y-\frac{y^2}{2n}+\Biggl(\sum_{k\ge 3}(-1)^{k+1}\frac{y^k}{kn^{k-1}}\Biggr)-y-n n\ln{x}-x=n\ln{n}-n-\frac{y^2}{2n}+\Biggl(\sum_{k\ge 3}(-1)^{k+1}\frac{y^k}{kn^{k-1}}\Biggr)

Amazing! Now let’s plug all of this back into our integral for the gamma function.

\Gamma(n+1)=\int_{0}^{\infty}e^{n\ln{x}-x}\,dx

Whoops, our expression for n\ln{x}-x is in terms of y and our integral is dealing with x Easily fixed – let y=x-n so that \,dx=\,dy

The bounds of integration change from (0,\infty) to (-n,\infty)

\Gamma(n+1)=\int_{-n}^{\infty}\exp\Biggl(n\ln{n}-n-\frac{y^2}{2n}+\sum_{k\ge 3}(-1)^{k+1}\frac{y^k}{kn^{k-1}}\Biggr)\,dy

Using e^{a+b}=e^ae^b we find

\Gamma(n+1)=\int_{-n}^{\infty}\exp(n\ln{n}-n)\exp\Biggl(-\frac{y^2}{2n}+\sum_{k\ge 3}(-1)^{k+1}\frac{y^k}{kn^{k-1}}\Biggr)\,dy

Note that e^{n\ln{n}-n}=e^{n\ln{n}}e^{-n}=n^ne^{-n}=\bigl(\frac{n}{e}\bigr)^n

\Gamma(n+1)=\biggl(\frac{n}{e}\biggr)^n\int_{-n}^{\infty}\exp\Biggl(-\frac{y^2}{2n}+\sum_{k\ge 3}(-1)^{k+1}\frac{y^k}{kn^{k-1}}\Biggr)\,dy =\biggl(\frac{n}{e}\biggr)^n\int_{-n}^{\infty}\exp\Biggl(-\frac{y^2}{2n}+\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\ldots\Biggr)\,dy

Now recall the earlier argument about a truncated series having low error since \frac{y}{n}\approx 0 near the integrand’s peak. This seems like a good point to use that truncated series – but how many of the terms do we keep?

Let’s set a definite goal. Suppose we want an error that is O(n^{n-3/2}) How many terms should we keep to achieve that? I’ll give the details later, but in this case, we only need to keep the first three terms for our desired accuracy.

\Gamma(n+1)\approx \biggl(\frac{n}{e}\biggr)^n\int_{-n}^{\infty}\exp\Biggl(-\frac{y^2}{2n}+\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\Biggr)\,dy

Let’s pull the first term out to get

\Gamma(n+1)\approx \biggl(\frac{n}{e}\biggr)^n\int_{-n}^{\infty}\exp\Biggl(-\frac{y^2}{2n}\Biggr)\exp\Biggl(\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\Biggr)\,dy

Also, to make our life easier, let’s mess with the bounds of integration a bit here. When working in terms of x, our integrand’s peak was at x=n Now that we are working with y=x-n our integrand’s peak should be at y=-n

For very large n, the peak will be very sharp so terms to the left of the peak will be negligible. Thus, we can change (-n,\infty) to (-\infty,\infty) and incur very little error.

So we have

\Gamma(n+1)\approx \biggl(\frac{n}{e}\biggr)^n\int_{-\infty}^{\infty}\exp\Biggl(-\frac{y^2}{2n}\Biggr)\exp\Biggl(\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\Biggr)\,dy

The attentive reader will realize that this section’s title of "The First Series Expansion" implies that we will use another series expansion – any guesses what we’re gonna use now?

The Second Series Expansion

To anyone who predicted we would now use the Taylor series for e^x – yes, you guessed right.

Let’s expand out

\exp\Biggl(\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\Biggr)=\Biggl(1+\biggl[\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\biggr]+\frac{1}{2}\biggl[\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\biggr]^2+\ldots\Biggr) If we want an error that is O(n^{n-3/2}) , we can drop terms of order y^8 and onwards – I will prove this later. So we find that \exp\Biggl(\frac{y^3}{3n^2}-\frac{y^4}{4n^3}\Biggr)\approx \Biggl(1+\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\frac{y^6}{18n^4}-\frac{y^7}{12n^5}\Biggr)

Then we have

\Gamma(n+1)\approx \biggl(\frac{n}{e}\biggr)^n\int_{-\infty}^{\infty}\exp\Biggl(-\frac{y^2}{2n}\Biggr)\Biggl(1+\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\frac{y^6}{18n^4}-\frac{y^7}{12n^5}\Biggr)\,dy

Let us now introduce

I_k=\int_{-\infty}^{\infty}\exp\biggl(-\frac{x^2}{2n}\biggr)x^k\,dx

If k is odd, the integrand becomes an odd function because \exp\biggl(-\frac{(-(2m+1))^2}{2n}\biggr)(-x)^{2m+1}=-\exp\biggl(-\frac{(2m+1)^2}{2n}\biggr)x^{2m+1}

Since the bounds of integration run from -\infty to \infty the integral must then equal zero when k is odd. So we can consider only the case where k is even i.e.

I_{2m}=\int_{-\infty}^{\infty}\exp\biggl(-\frac{x^2}{2n}\biggr)x^{2m}\,dx

Let u=\frac{x}{\sqrt{2n}} so that \,dx=\sqrt{2n}\,du

Then we have

I_{2m}=\sqrt{2n}\int_{-\infty}^{\infty}e^{-u^2}\left(u\sqrt{2n}\right)^{2m}\,du=(2n)^{m+\frac{1}{2}}\int_{-\infty}^{\infty}e^{-u^2}u^{2m}\,du

Rename u to x and we have

I_{2m}=(2n)^{m+\frac{1}{2}}\int_{-\infty}^{\infty}e^{-x^2}x^{2m}\,dx

Integrate by parts using u=e^{-x^2} and \,dv=x^{2m} \,du=-2xe^{-x^2} v=\frac{x^{2m+1}}{2m+1}

I_{2m}=(2n)^{m+\frac{1}{2}}\left(\left.e^{-x^2}\frac{x^{2m+1}}{2m+1}\right\rvert_{-\infty}^{\infty}+\frac{2}{2m+1}\int_{-\infty}^{\infty}e^{-x^2}x^{2m+2}\,dx\right) =(2n)^{m+\frac{1}{2}}\left(\frac{2}{2m+1}\right)\int_{-\infty}^{\infty}e^{-x^2}x^{2(m+1)}\,dx

Let

Q_{2m}=\int_{-\infty}^{\infty}e^{-x^2}x^{2m}\,dx

Then, from our formula for I_{2m} that we had just before integration by parts,

I_{2m}=(2n)^{m+\frac{1}{2}}Q_{2m}

But we also know that

I_{2m}=(2n)^{m+\frac{1}{2}}\left(\frac{2}{2m+1}\right)Q_{2(m+1)}

This tells us that

Q_{2m}=\left(\frac{2}{2m+1}\right)Q_{2(m+1)}

Q_{2(m+1)}=\left(\frac{2m+1}{2}\right)Q_{2m} Q_{2m}=Q_{2(m-1+1)}=\left(\frac{2(m-1)+1}{2}\right)Q_{2(m-1)}=\left(\frac{2m-1}{2}\right)Q_{2(m-1)}

We know that Q_{0}=\int_{-\infty}^{\infty}e^{-x^2}\,dx=\sqrt{\pi}

So now we can solve for Q_{2m} in the way we would solve any recurrence relation

Q_{2m}=\left(\frac{2m-1}{2}\right)Q_{2(m-1)}=\left(\frac{2m-1}{2}\right)\left(\frac{2m-3}{2}\right)Q_{2(m-2)} =\left(\frac{2m-1}{2}\right)\left(\frac{2m-3}{2}\right)\cdots\left(\frac{1}{2}\right)Q_0 =\frac{1}{2^m}\left(\prod_{i=1}^{m-1}(2i+1)\right)\sqrt{\pi}

Note that

\prod_{i=1}^{m-1}(2i+1)=\frac{1\cdot 2\cdots (2m-1) \cdot 2m}{2\cdot 4 \cdots(2m-2) \cdot 2m}=\frac{(2m)!}{\prod_{i=1}^{m}(2i)}i=\frac{(2m)!}{2^mm!}

Thus we have

Q_{2m}=\frac{1}{2^m}\left(\frac{(2m)!}{2^mm!}\right)\sqrt{\pi}=\frac{(2m)!}{2^m\cdot 2^mm!}\sqrt{\pi}=\frac{(2m)!\sqrt{\pi}}{2^{2m}m!}

I_{2m}=(2n)^{m+\frac{1}{2}}Q_{2m}=(2n)^{m+\frac{1}{2}}\frac{(2m)!\sqrt{\pi}}{2^{2m}m!}=n^{m+\frac{1}{2}}\frac{(2m)!\sqrt{\pi}}{2^{m-\frac{1}{2}}m!}

Now let’s return to our expression for the factorial. Note that we drop all terms of the form I_{2k+1} since they equal zero.

\Gamma(n+1)\approx \biggl(\frac{n}{e}\biggr)^n\int_{-\infty}^{\infty}\exp\Biggl(-\frac{y^2}{2n}\Biggr)\Biggl(1+\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\frac{y^6}{18n^4}-\frac{y^7}{12n^5}\Biggr)\,dy =\biggl(\frac{n}{e}\biggr)^n\Biggl(I_{0}+\frac{I_3}{3n^2}-\frac{I_4}{4n^3}+\frac{I_6}{18n^4}-\frac{I_7}{12n^5}\Biggr) =\biggl(\frac{n}{e}\biggr)^n\Biggl(I_{0}-\frac{I_4}{4n^3}+\frac{I_6}{18n^4}\Biggr) =\biggl(\frac{n}{e}\biggr)^n\Biggl(\sqrt{2\pi n}-\frac{24n^{5/2}\sqrt{2\pi}}{32n^3}+\frac{720n^{7/2}\sqrt{2\pi}}{864n^4}\Biggr) =\biggl(\frac{n}{e}\biggr)^n\sqrt{2\pi n}\Biggl(1+\frac{1}{12n}\Biggr)

Remembering that we chose terms so that we have an error of O(n^{n-3/2}) we can write \Gamma(n+1)=\biggl(\frac{n}{e}\biggr)^n\sqrt{2\pi n}\Biggl(1+\frac{1}{12n}+O\left(\frac{1}{n^2}\right)\Biggr)

Let’s see how much of an improvement this is.

Plots of percent error for the two estimates to n! – the pink graph is the percent error for the standard approximation, the green graph is the percent error for our improved approximation.

Knowing which terms to keep

Earlier I promised to explain why I dropped the terms I dropped – here you go.

Let’s look at the first place where we dropped terms.

\Gamma(n+1)=\biggl(\frac{n}{e}\biggr)^n\int_{-n}^{\infty}\exp\Biggl(-\frac{y^2}{2n}+\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\ldots\Biggr)\,dy =\biggl(\frac{n}{e}\biggr)^n\int_{-n}^{\infty}\exp\Biggl(-\frac{y^2}{2n}\Biggr)\exp\Biggl(\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\ldots\Biggr)\,dy

Suppose we want an error that is O(n^{n-\alpha/2}) Consider the k’th term in the second exponential,

(-1)^{k+1}\frac{y^{k+2}}{(k+2)n^{k+1}}

Now suppose we keep all terms up to the k’th term and Taylor expand. We will get

1+\left[\frac{y^3}{3n^2}+\ldots+\frac{(-1)^{k+1}y^{k+2}}{(k+2)n^{k+1}}\right]+\frac{1}{2}\left[\frac{y^3}{3n^2}+\ldots+\frac{(-1)^{k+1}y^{k+2}}{(k+2)n^{k+1}}\right]^2+\ldots

Suppose we keep all the terms in this expansion up to the j’th term. The j’th term in this second series expansion is \frac{1}{j!}\left[\frac{y^3}{3n^2}+\ldots+\frac{(-1)^{k+1}y^{k+2}}{(k+2)n^{k+1}}\right]^j \sim \left[\frac{y^3}{n^2}+\ldots+\frac{y^{k+2}}{n^{k+1}}\right]^j Remember we wanted an error of O(n^{n-\frac{\alpha}{2}})

Now we want to choose j such that there is AT LEAST one term within the larger j’th term whose contribution to the approximation is of an order greater than n^{n-\frac{\alpha}{2}}

Note that there can be unnecessary terms within that j’th term – those can be dropped. But so long as there is even one necessary term, we want to consider the whole j’th term and then remove specific "sub-terms" as needed.

The term with largest-order contribution in that j’th term is going to be \sim \frac{y^{3j}}{n^{2j}} Using our earlier formula for I_k, we see that the contribution will be of order \sim n^{n-2j+\frac{1+3j}{2}}=n^{n-\frac{j-1}{2}}

We want this order to be greater than n^{n-\frac{\alpha}{2}}

The order increases/decreases in integer increments, so the smallest order greater than n^{n-\frac{\alpha}{2}} is n^{n-\frac{\alpha}{2}+1}=n^{n-\frac{\alpha-2}{2}}

So we want the order of that contribution to be greater than or equal to this MINIMUM order of contribution for the term to be relevant

i.e.

n-\frac{j-1}{2}\ge n-\frac{\alpha-2}{2} j-1\le\alpha-2 j\le\alpha-1

This inequality tells us that, for any j<\alpha+1, there will be AT LEAST one term we want to keep within that larger j’th term. We want to collect all the terms with some relevant contribution, so we take the largest possible j that has a term we want.

j=\alpha-1

Now for k we similarly want to set k to be as high as we can get it without missing any important terms. We need AT LEAST one important term added by setting k to whatever value it is. The term with highest-order contribution corresponding to changes in k comes from the first term in the exp-series expansion (refer back to the start of this section if confused)

\sim \frac{y^{k+2}}{n^{k+1}}

If even just this term is relevant, we have justification for setting k to include this term.

The contribution from this term is of order \sim n^{n-(k+1)+\frac{1+(k+2)}{2}} = n^{n-\frac{k-1}{2}}

We want the order of that contribution to be at least n^{n-\frac{\alpha-2}{2}}

n-\frac{k-1}{2}\ge n-\frac{\alpha-2}{2} k-1\le \alpha -2 k\le \alpha-1

This tells us that for all k\le \alpha-1 we will have AT LEAST one term we need to keep. We take the largest k value permitted by this inequality, giving us all the terms needed as a result.

k=\alpha-1

So if we want an error in our approximation that is O(n^{n-\frac{\alpha}{2}}) then we can drop terms in our series expansions as follows

We let k=\alpha-1 j=\alpha-1

In our integral for the gamma function, we will keep the terms in the second exponential up to the k’th term, i.e. approximate as

\Gamma(n+1) \approx \left(\frac{n}{e}\right)^n\int_{-\infty}^{\infty}\exp\left(-\frac{y^2}{2n}\right)\exp\left(\frac{y^3}{3n^2}-\frac{y^4}{4n^3}+\ldots+\frac{(-1)^{k+1}y^{k+2}}{(k+2)n^{k+1}}\right)\,dy

And then when we Taylor-expand the second exponential in that integral, we truncate the series in this manner 1+\left[\frac{y^3}{3n^2}+\ldots+\frac{(-1)^{k+1}y^{k+2}}{(k+2)n^{k+1}}\right]+\ldots+\frac{1}{j!}\left[\frac{y^3}{3n^2}+\ldots+\frac{(-1)^{k+1}y^{k+2}}{(k+2)n^{k+1}}\right]^j

When we substitute that series expansion back into our integral, we will have an approximation of the form

\Gamma(n+1)\approx \left(\frac{n}{e}\right)^n\sum_{m}\frac{I_{2m}}{n^{s_i}}

Where we have

I_{2m}=n^{m+\frac{1}{2}}\frac{(2m)!\sqrt{\pi}}{2^{m-\frac{1}{2}}m!}

This gives us a way to improve on the Stirling Approximation to any desired accuracy. The result quickly gets ugly for increasing accuracy. However, if you’re willing to tolerate the ugliness, the increased accuracy is quite satisfying to have.

Conclusion

Hopefully you enjoyed this post. I have not written anything in a long time because of a combination of factors – I’ve been busy with lots of different things, I had a bit of anxiety about the quality of my writing, and the reasons go on and on. I’m hoping to write more in the next few months, however, and build this habit again. I have some nice ideas about stuff to write about, so expect some interesting content.

If I made any errors here or if you have any suggestions to make, please contact me at my discord floofydoggo or my email address chancellorceti@gmail.com

I would also like to give credit to Daniel Schroeder’s textbook "An Introduction to Thermal Physics" that showed me this proof of Stirling’s Theorem for the first time and got this question into my head. Amazing textbook, I learnt quite a bit from it.

I hope to return with more interesting stuff soon. Thanks for reading!

Discourse on the Israel-Hamas Conflict: Debates Over Genocide, Low Evidentiary Standards, and the Risk of Getting Bogged Down in Semantics

Thu, 02 Jul 2026 00:00:00 GMT

Why ‘Class Struggle’ Rhetoric is a Bad Idea in Democracies

Discourse on the Israel-Hamas Conflict: Debates Over Genocide, Low Evidentiary Standards, and the Risk of Getting Bogged Down in Semantics

The Israel-Hamas war has become one of the most polarizing topics in America, and as is usual with controversial issues, the quality of discourse has correspondingly degraded. Words are used loosely and with the intent of provoking outrage rather than making factual statements. There are many examples, such as the incorrect equating of anti-Zionism with antisemitism; the replacement of concrete policy objectives with slogans like “Free Palestine,” “Globalize the Intifade,” and “From the River to the Sea”; and, most prominently, the fixation on characterizing Israel’s actions as genocide.

There is growing consensus among commentators who are otherwise level-headed and evidence-driven that the war in Gaza does constitute genocide, but the way the word is being used reflects a lowering of evidentiary standards and a form of ideological purity test that is damaging to the movement for a peaceful end to the conflict.

Low Evidentiary Standards Applied in the Investigations Alleging Genocide

I will begin by addressing my concerns about the low evidentiary standards used when characterizing the IDF’s actions as genocide. The UN defines genocide as follows:

In the present Convention, genocide means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:

Killing members of the group;

Causing serious bodily or mental harm to members of the group;

Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;

Imposing measures intended to prevent births within the group;

Forcibly transferring children of the group to another group.

Since the first day of the conflict, the IDF has been committing several of these acts against the nation of Palestine, so that part of the definition is clearly met. What remains up for debate, however, is the part about “intent to destroy.” Intent is one of the most difficult things to prove in law because it’s something that exists in the mind, rather than a fact easily proved by observation or statistics. Genocidal intent is especially difficult to prove because there is a differentiation between dolus specialis, ‘special intent,’ and dolus generalis, ‘general intent.’ In this context, dolus generalis refers to the intent of committing a specific action in a military conflict (e.g. deliberately striking hospitals, as opposed to a rocket missing its target and hitting one), whereas dolus specialis is the intent of actually aiming to destroy a national, ethnical, racial, or religious group in whole or in part through that action. Dolus generalis is easily proved for most of the acts being characterized as genocide – the IDF has itself admitted to bombing civilian infrastructure in Gaza. However, evidence for dolus specialis is much harder to find, and the UN Human Rights Council’s (UNHRC) case claiming to prove it does not meet these high evidentiary standards.

The UNHRC’s investigation was led by the Independent International Commission of Inquiry on the Occupied Palestinian Territory, chaired by a three-member panel of experts on human rights. The Commission concluded that Israel was committing genocide in Gaza, and their results have since become part of the basis for many people’s use of the word. Despite the UNHRC’s prestige and credibility, some of the evidence they have used is deeply insufficient to prove genocidal intent. They have relied heavily on statements made by Israeli leaders, poorly linked to intent to destroy all or part of the Palestinian nation. For example, this is one of the quotes cited as evidence of genocidal intent.

At a press conference held in the early afternoon of 7 October 2023, Prime Minister Netanyahu vowed to inflict “mighty vengeance” on “all of the places which Hamas is deployed, hiding and operating in, that wicked city, we will turn them into rubble. I say to residents of Gaza: leave now because we will operate forcefully everywhere.” Although Netanyahu’s statement carefully directed the call for vengeance at ‘Hamas locations’, his use of the phrase ‘wicked city’ in the same statement implied that he saw the whole city of Gaza as responsible and a target for vengeance. He told Palestinians in Gaza to ‘leave now because we will operate forcefully everywhere’, making no distinction between combatants and civilians and knowing that Palestinians in Gaza had nowhere to go.

The use of the phrase ‘wicked city’ is far from evidence of genocidal intent. It is equally probable that it is hyperbole catering to a population enraged by the killing of over a thousand people by a terror attack on the same day. This is not an explicit call to specifically target and kill Palestinian civilians – while it does prove significant animosity towards Palestine, it stops at that. By this standard, Donald Trump could also be accused of harboring genocidal intent towards Iran, since he has made equally violent statements such as these:

A whole civilization will die tonight, never to be brought back again. (Quoted from NYT)

We are going to hit them extremely hard over the next two to three weeks, we’re going to bring them back to the stone ages, where they belong. (Quoted from Al Jazeera)

I could go on producing hyperbolic, violent statements made by Trump, or other war-time leaders in world history. The point stands that military conflicts bring out the worst in people, and political leaders often grow more violent and extreme in their speech as a result. Netanyahu’s remarks, like those of Trump, are violent and reprehensible, likely responsible for encouraging military excesses, but don’t prove they truly wanted a whole civilization to die. By the UNHRC commission’s evidentiary standards, any kind of violent wartime hyperbole could be used as evidence for genocide.

Two of the most famous cases of genocide, with the strongest evidence, are the Holocaust and the Rwandan Genocide. Quotes from prominent leaders were also used in these cases to prove genocidal intent, but the evidentiary standards were much higher. Leading radio station RTLM in Rwanda called to “cut down the tall trees,” a euphemism for killing Tutsis, and “exterminate the cockroaches,” speech much more directly linked to systematic extermination of an ethnic group’s civilian population, a link strengthened by the fact that many of the genocide’s perpetrators were following the guidance of these broadcasts and receiving guidance from RTLM on where civilians were hiding and how to kill them. Similarly, the words of German leaders during the Holocaust left no doubt about genocidal intent: Hitler said in a 1942 speech that “the result of this war will be the complete annihilation of the Jews,” Hans Frank (governor of occupied Poland) said in 1941 “one way or another – I will tell you quite openly – we must finish off the Jews,” and the list of damning evidence is seemingly endless. This kind of speech was also easily distinguished from mere hyperbole by the fact that people acted on these orders, rounding up the entire civilian Jewish population across Nazi Germany and doing precisely what Hitler was calling for. There was an abundance of evidence linking Hitler’s words to the Nazis’ actions, proving genocidal intent through the combination.

As much as I abhor what the IDF is doing in Gaza, I don’t think Netanyahu’s speech is strong evidence of genocidal intent, when compared to the evidentiary standards used in the past. And while the Commission wasn’t relying on this quote alone, I invite the reader to read the relevant section of the report and judge for themselves whether all the cited quotes, taken together, are anywhere near as direct a link to genocidal intent as the rhetoric of the Holocaust and Rwandan Genocide were. I thought not, but unfortunately this would be closer to a whitepaper than a blog post if I considered each quote one-by-one, so I will leave that task to the more energetic readers.

The Commission’s report also extensively cites damage to hospitals, schools, and other civilian infrastructure as evidence of genocidal intent. Their logic rests on the assumption that

Mens rea can also be established through indirect evidence based on the “objective probability of these conditions leading to the physical destruction of the group in part.”

By this standard, the Allied forces’ carpet bombing in World War 2, the Soviet-Afghan War, and other conflicts could as easily be used to establish mens rea for genocidal intent. Military forces often show callous disregard for civilian life and target civilian infrastructure to decrease morale, and this occurs even in cases that historically haven’t been considered genocide, as with the cases mentioned. Granted, the Commission isn’t considering the acts alone but also the speech and political climate motivating them; however, the Commission fails to show that the bombing of civilian infrastructure is directly motivated by the kind of ‘annihilation rhetoric’ being pushed by specific sectors of Israeli society, rather than the unfortunately frequent tendency of generals to target civilian infrastructure to hasten the end of a war. As such, the destruction of civilian infrastructure can’t be used as conclusive evidence of genocidal intent in this case, and it is as easily attributable to callousness and/or targeting civilians to accelerate the capitulation of Hamas (one of the stated goals of the IDF’s campaign). By no means are Allied actions in World War 2 or the Soviet-Afghan War shining examples that the IDF should seek to replicate – extensive war crimes were committed, and the targeting of civilians was wrong. I’m not trying to condone their actions by saying “look others have done it!” but rather point out that it’s possible they are doing it as a horrific strategy of ‘total war’ meant to hasten the end of the conflict, rather than genocidal intent of truly destroying the entire nation of Palestine.

The Commission also claims that children were directly targeted by the IDF, citing the fact that out of the 60,199 Palestinians killed (as of 31 July 2025), 18,430 were children. While this is a horrifying statistic, it seems much less like direct targeting when one considers that 47.3% of the population in Gaza is under 18 (in comparison, the UN found 30% of casualties were children), according to the Palestinian Ministry of Health’s own numbers. In this context of warfare in densely-populated urban areas, Hamas staging attacks out of colleges, hospitals, and children’s playgrounds (i.e. Israel can’t attack Hamas without attacking some civilian infrastructure, even if the current campaign is excessive and paying little regard for precision and protection of civilian life), and a large population of children, the high number of children being killed is weak evidence for proving direct targeting. Hamas’ crimes by no means justify the IDF’s own crimes, but it does provide another explanation for why the IDF is attacking so much civilian infrastructure and killing so many children, as opposed to the UNHRC blaming it on genocidal intent. The IDF is guilty of callousness, a lack of respect for civilian life, and insufficient measures to protect civilians, and the Israeli political establishment is guilty of making violent, provocative statements that have likely worsened IDF callousness and incited some soldiers to deliberately target civilians. However, the claim that the Israeli state is directly targeting children does not have enough evidence.

I want to particularly emphasize the historical precedent for scorched-earth tactics and atrocities against civilians often being unlinked to genocidal intent. The British destroyed farmland in their counter-insurgency operations in the Malaysian Emergency (1948-50) and in the Second Boer War, with the intent of denying food to the militant forces, but their actions had an equally devastating impact on the civilian population, many of whom died of starvation. The Allied forces in World War 2 bombed civilian infrastructure and deliberately targeted civilians to try hastening the capitulation of Japan and Germany. When fighting the mujahideen, Soviet forces in Afghanistan committed many massacres against civilians, used bombs that children often mistook for toys, and bombed crops and irrigation systems. None of this excuses the IDF’s actions, but it does show that all of this has been done before without genocidal intent. Counter-insurgency operations lead to demoralized, weary troops who often vent their frustration on the civilian population, a problem exacerbated in this case by Israeli propaganda and the atrocities of Hamas that have caused so much Israeli animosity towards the Palestinian population as a whole. In addition to the issue of undisciplined troops, the deliberate targeting of civilians, on direct orders of military leadership, is often used as a tactic for hastening the capitulation of enemy forces through demoralization, denial of food or humanitarian relief to combatants, and reduction of civilian support for enemy forces. This behavior is wrong in the current conflict and has been wrong throughout history, but it shows that the IDF’s actions could be motivated by inhumane military strategy and not by genocidal intent – there is plenty of historical precedent for this, and the UNHRC has not adequately shown that this alternative explanation is less plausible than their own.

The Commission’s argument doesn’t rely on individual pieces of evidence – it sees the combination of all these facts as sufficient to conclude there is genocidal intent. However, the existence of a cohesive and plausible alternative explanation, even for all of this taken together, undermines the strength of their inference. I’m not contesting that war crimes and atrocities against civilians have been committed, but rather that the sole explanation is genocidal intent, rather than a combination of inhumane military calculations, collective punishment, a lack of accountability for war crimes as well as tacit encouragement, and disregard for civilian life.

The Commission’s full report is 72 pages long and can be found on the UN website. There are many other facts used as evidence of genocidal intent, but I don’t have the time to go through all of their evidence, so I will cut it short here. I will concede that some of the evidence is strong and suggests a high probability of genocidal intent, but much of it is also weak evidence that ignores the many other explanations for high civilian casualties and the historical precedent of targeting of civilians often being unlinked to genocidal intent. I think individuals should be able to opine, with a healthy degree of doubt, that there is genocidal intent with some evidence to back it up – however, there isn’t enough evidence for a court or prominent institution to definitively make that conclusion, and it was wrong for the UNHRC to publish a report that did so, heavily relying on reasoning I find unpersuasive and neglect of the many factors complicating the protection of civilians.

Getting Bogged Down in Semantics

Many of my readers will likely disagree with my above assessment of the UNHRC report, and some will take that as a reason to assume we have polar opposite views on the Israel-Hamas war. This is a mistake – I, and others skeptical of the ‘genocide’ label, have much more in common with the people claiming there is a genocide taking place than those denying the committing of any war crimes at all. Given the specific definition of ‘genocide’ and the high evidentiary standards needed to prove ‘intent to destroy,’ I am unwilling to use that word, but I am outraged, as any sane observer is, at the lack of accountability for IDF soldiers’ war crimes, the Israeli government’s dehumanization of Palestinians, the insufficient effort invested in facilitating aid delivery and protecting civilians, the disregard for civilian life, and all the other horrible things the Israeli state is doing in Palestine. Despite acknowledging all of this, in today’s political climate, many other Israel-critics will ignore all of this overlap of goals and zero in on my discomfort with using the word ‘genocide.’

The critical discourse on the Israel-Palestine conflict has devolved into witch-hunting and ideological purity tests. A large number of Americans are not significantly enough invested in the issue to care what someone else believes in, but among the people critical of Israel’s military actions and closely following the conflict, there is a growing tendency to attack anyone who doesn’t use the same vocabulary and doesn’t believe in certain core markers of being anti-Israel enough. 77% of Democrats believe Israel is committing genocide, according to an August 2025 Quinnipiac University poll, and many of them are quite adamant that the other 23% must also believe Israel is committing genocide, or else they are pro-Israel, or pro-genocide, or just generally a bad person. I have seen many Israel-related conversations, with otherwise usually intelligent people, decay into ideological purity tests once doubt is expressed about the genocide claim or support is expressed for Zionism defined purely as ‘Israel’s right to exist.’ While I can’t find statistics on the frequency of such interactions, my personal experience and related statistics on political polarization (e.g. attitudes towards children marrying people supporting a different party) make me suspect this is a large but insufficiently reported issue.

The ideological purity test is generally a sign of bad-faith debating, a left-wing counterpart to the “owning the libs” mentality as opposed to genuine interest in finding common ground between people who really do agree on a lot of things. But it is especially damaging in the context of discourse on the Israel-Palestine conflict because the forces that reason and basic humanity face are so powerful, and this kind of ideological purity testing alienates a lot of people who are currently essential to promoting better discourse and pushing for an end to the violence in Gaza. Campus protests with slogans like “globalize the intifada” and “from the river to the sea” alienate many people who abhor the IDF’s actions in Gaza but believe that Israel should still exist, and the animosity towards genocide skeptics has the same effect.

That is why I urge that we don’t get bogged down in semantics. It should not matter so much what words we use to denounce the violence, be it ‘genocide’ or just ‘war crimes,’ as the fact that we agree that something terrible is happening and we should act to stop it 1. I believe in precision with the use of words, which is why I hesitate to call this a genocide, but I also believe that a shared goal of ending violence is more important than endless flame wars over what specific words we are using to pursue that goal. I will gladly work with someone who calls this a genocide but otherwise has views largely compatible with my own (read: does not believe in ‘from the river to the sea’ and/or condone Hamas) – I hope others will show a similar willingness to work with people sharing their support for human rights, regardless of minute disagreements. This is a time for unity among sane observers, not further infighting and purity testing.

While doing research for this post, I came across this great Politico article that makes almost the same point about the importance of not getting overly absorbed in fighting over the use of specific words. I recommend reading it.↩︎

Solving an Epic Boundary Value Problem from J.D. Jackson’s 'Classical Electrodynamics' – Laplace’s Equation in Polar Coordinates!

Sun, 20 Jul 2025 00:00:00 GMT

Solving an Epic Boundary Value Problem from J.D. Jackson’s "Classical Electrodynamics" – Laplace’s Equation in Polar Coordinates!

Chancellor Ceti

2025-07-20

Introduction
Laplace’s Equation in Polar Coordinates
Applying boundary conditions to determine the coefficients
Finding a closed form – wizardry with complex numbers
Conclusion

Introduction

Today I present the solution to one of my favorite problems from J.D. Jackson’s "Classical Electrodynamics." The problem reads as follows

Two conducting planes at zero potential meet along the z axis, making an angle \beta between them, as in Fig. 2.14. A unit line charge parallel to the z axis is located between the planes at position (\rho',\phi').

Show that (4\pi\epsilon_0) times the potential in the space between the planes, that is, the Dirichlet Green function G(\rho,\phi;\rho',\phi'), is given by the infinite series

G(\rho,\phi;\rho',\phi')=4\sum_{m=1}^{\infty}\frac{1}{m}\rho_{<}^{m\pi/\beta}\rho_{>}^{-m\pi/\beta}\sin(m\pi\phi/\beta)\sin(m\pi\phi'/\beta)

By means of complex-variable techniques or other means, show that the series can be summed to give a closed form

G(\rho,\phi;\rho',\phi')=\ln(\frac{(\rho)^{2\pi/\beta}+(\rho')^{2\pi/\beta}-2(\rho\rho')^{\pi/\beta}\cos\left[\pi(\phi+\phi')/\beta\right]}{(\rho)^{2\pi/\beta}+(\rho')^{2\pi/\beta}-2(\rho\rho')^{\pi/\beta}\cos\left[\pi(\phi-\phi')/\beta\right]})

While this problem seems intimidating, it can be very elegantly reduced to basic mathematical operations. The solution employs many of my favorite tricks, so I was very pleased to encounter this problem. I hope the reader will find the solution as entertaining. If you want to attempt the problem on your own, please do so now – the next section will contain spoilers :)

Laplace’s Equation in Polar Coordinates

Given the problem description, it is obvious we are solving Laplace’s Equation. The differential form of Gauss’ Law tells us \nabla \cdot \mathbf{E}=\frac{\rho}{\epsilon_0}

But we also know that \mathbf{E}=-\nabla \Phi. Therefore, \nabla \cdot \mathbf{E}=-\nabla \cdot (\nabla \Phi)=-\nabla^2{\Phi}

In regions free of charge (such as the region described in this problem), \rho=0 so Gauss’ law tells us \nabla \cdot \mathbf{E}=0

Therefore,

\nabla^2{\Phi}=0

This is the famed Laplace’s Equation that Jackson readers must worship. In two dimensions, the Laplacian takes the simple form \nabla^2=\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}

The geometry of this problem makes it convenient to use polar coordinates. Through a lengthy derivation, it can be found that in polar coordinates, Laplace’s equation is

\nabla^2{\Phi}=\frac{1}{\rho}\frac{\partial }{\partial \rho}\left(\rho\frac{\partial \Phi}{\partial \rho}\right)+\frac{1}{\rho^2}\frac{\partial^2\Phi}{\partial\phi^2}

The proof is left as an exercise for the morbidly curious reader. If you do it during English class and send proof that you got in trouble for it, I’ll nominate you for the Nobel Prize if I ever get on the committee.

We can use separation of variables to easily solve this differential equation. Assume the solution is of the form \Phi(\rho,\phi)=R(\rho)Q(\phi)

Then

\nabla^2{\Phi}=\frac{Q(\phi)}{\rho}\frac{\partial }{\partial \rho}\left(\rho\frac{dR}{d\rho}\right)+\frac{R(\rho)}{\rho^2}\frac{d^2Q}{d\phi^2}=0

Note that, since \nabla^2{\Phi}=0, we also know that

\nabla^2{\Phi}\left(\frac{\rho^2}{\Phi}\right)=0

We can thus multiply by \frac{\rho^2}{\Phi} on both sides to obtain

\nabla^2{\Phi}=\frac{\rho}{R(\rho)}\frac{\partial }{\partial \rho}\left(\rho\frac{dR}{d\rho}\right)+\frac{1}{Q(\phi)}\frac{d^2Q}{d\phi^2}=0

This has separated the radial and angular dependence of the equation. We can set both equal to a constant and solve the differential equations separately now. Let

\frac{1}{Q(\phi)}\frac{d^2Q}{d\phi^2}=-v^2

Start with the case where v>0

There are two linearly independent solutions to this differential equation, so by superposition, the general solution must be

Q(\phi)=A_ve^{iv\phi}+B_ve^{-iv\phi}

The radial equation is a bit more complicated, but it has the familiar form of an Euler-Cauchy differential equation once we expand the partial derivative.

\frac{\rho}{R(\rho)}\frac{\partial }{\partial \rho}\left(\rho\frac{dR}{d\rho}\right)=\frac{\rho}{R(\rho)}\left(\frac{dR}{d\rho}+\rho\frac{d^2R}{d\rho^2}\right)

We set this equal to the constant v^2 to obtain

\frac{\rho}{R(\rho)}\left(\frac{dR}{d\rho}+\rho\frac{d^2R}{d\rho^2}\right)=v^2

\rho^2\frac{d^2R}{d\rho^2}+\rho\frac{dR}{d\rho}=v^2R(\rho)

Now use the ansatz R(\rho)=C\rho^n

This yields

C\left(\rho^2n(n-1)\rho^{n-2}+\rho n\rho^{n-1}\right)=v^2C\rho^n

n(n-1)\rho^n+n\rho^n=v^2\rho^n

(n(n-1)+n)\rho^n=v^2\rho^n n^2=v^2 n=\pm v

Thus, we find

R(\rho)=a_v\rho^v+b_v\rho^{-v}

For the case where v=0, we find

\frac{d^2Q}{d\rho^2}=0

which means

Q_{v=0}(\phi)=A_0+B_0\phi

And we then find that the radial equation becomes

\rho\frac{d^2R}{d\rho^2}+\frac{dR}{d\rho}=0

The first solution to this is the trivial R_1(\rho)=a_0

If we let u=\frac{dR}{d\rho} and assume u=Cx^n, we can find the second solution

\frac{nu}{x}=-\frac{u}{x} n=-1 \frac{dR}{d\rho}=\frac{C}{x} R_2(\rho)=b_0\ln(\rho)

The complete solution is the superposition of these two,

R_{v=0}(\rho)=a_0+b_0\ln(\rho)

Now remember our solution is of the form \Phi(\rho,\phi)=R(\rho)Q(\phi). We have found infinitely many solutions corresponding to different values of v, so the complete solution must be their linear superposition

\Phi(\rho,\phi)=\sum_{v=0}^{\infty}R_v(\rho)Q_v(\phi) =(a_0+b_0\ln(\rho))(A_0+B_0\phi)+\sum_{v>0}(a_v\rho^v+b_v\rho^{-v})(A_ve^{iv\phi}+B_v^{-iv\phi})

Now we can successively apply boundary conditions to find the coefficients.

Applying boundary conditions to determine the coefficients

The potential must equal zero on the surface of both planes, so we can start with the bottom plane (\phi=0) and find

\Phi(\rho,\phi=0)=0

A_0(a_0+b_0\ln(\rho))+\sum_{v>0}(a_v\rho^v+b_v\rho^{-v})(A_v+B_v)=0

For the first term to equal zero regardless of \rho, it is necessary that A_0=0

For the terms with v>0 to equal zero, we need

A_v+B_v=0

A_v=-B_v

We can now absorb the A_v into the a_v and b_v since (a_v\rho^v+b_v\rho^{-v})(A_ve^{iv\phi}-A_ve^{-iv\phi})=(A_va_v\rho^v+A_vb_v\rho^{-v})(e^{iv\phi}-e^{-iv\phi})

A_va_v and A_vb_v is just another series of constants dependent only on v, so we can make the change a_v\rightarrow A_va_v and b_v\rightarrow A_vb_v

Also note that e^{iv\phi}-e^{-iv\phi}=C\sin(v\phi) – so we can rewrite that part of the equation and ignore the C by again absorbing it into the a_v and b_v constants.

Thus, from using \Phi(\rho,\phi=0)=0, we have found

\Phi(\rho,\phi)=(a_0+b_0\ln(\rho))(B_0\phi)+\sum_{v>0}(a_v\rho^v+b_v\rho^{-v})\sin(v\phi)

Again note that B_0 can be absorbed into a_0 and b_0 to give the slightly simpler form

\Phi(\rho,\phi)=(a_0+b_0\ln(\rho))\phi+\sum_{v>0}(a_v\rho^v+b_v\rho^{-v})\sin(v\phi)

Now we apply the next boundary condition, that \Phi=0 on the top plane. The top plane is defined by \phi=\beta, so we have \Phi(\rho,\phi=\beta)=0

(a_0+b_0\ln(\rho))\beta+\sum_{v>0}(a_v\rho^v+b_v\rho^{-v})\sin(v\beta)=0

For a_0+b_0\ln(\rho)=0 to be true regardless of \rho, we need a_0=b_0=0 since the constants can’t vary with \rho

Similarly, we need \sin(v\beta)=0 for v>0

For this to hold true, it is necessary that

v\beta=m\pi v=\frac{m\pi}{\beta} \text{ for } m=1,2,\ldots

Now we find

\Phi(\rho,\phi)=\sum_{m>0}\left(a_m\rho^{\frac{m\pi}{\beta}}+b_m\rho^{-\frac{m\pi}{\beta}}\right)\sin(\frac{m\pi\phi}{\beta})

Now we employ some mathematically shady trickery. We can arbitrarily divide the region into two subregions with different functions for \Phi. Let us define \Phi_1 for \rho<\rho' and \Phi_2 for \rho>\rho'

When \rho<\rho', we are close to the origin – to have a well-defined solution near \rho=0, we must avoid the undefined behavior of \rho^{-\frac{m\pi}{\beta}}. Therefore, we set b_m=0 for all m>0 in \Phi_1

Similarly, \Phi_2 is defined for arbitrarily large \rho>\rho'. \rho^{\frac{m\pi}{\beta}} will go to infinity as \rho grows, so to avoid undefined behavior, we must have a_m=0 for m>0 in \Phi_2

Thus, we find

\Phi_1(\rho,\phi)=\sum_{m>0}a_m\rho^{\frac{m\pi}{\beta}}\sin(\frac{m\pi\phi}{\beta})

\Phi_2(\rho,\phi)=\sum_{m>0}b_m\rho^{-\frac{m\pi}{\beta}}\sin(\frac{m\pi\phi}{\beta})

For the next boundary condition, we use the formula for the discontinuity of the electric field’s normal component across a boundary

(\mathbf{E}_2-\mathbf{E}_1)\cdot\mathbf{\hat{n}}=\frac{\sigma}{\epsilon_0}

where \sigma is the charge density.

For the uninitiated, this formula can easily be derived by applying Gauss’ Law to an infinitesimally small Gaussian pillbox straddling a boundary.

Note that \mathbf{E}=-\nabla \Phi so

\mathbf{E}\cdot\mathbf{\hat{n}}=-(\nabla \Phi)\cdot\mathbf{\hat{n}}=-\frac{\partial \Phi}{\partial \mathbf{\hat{n}}}

At the boundary defined by \rho=\rho', the unit outward normal is the unit vector in the radial direction, so

\frac{\partial \Phi}{\partial \mathbf{\hat{n}}}\Big|_{\rho=\rho'}=\frac{\partial \Phi}{\partial \rho}\Big|_{\rho=\rho'}

Therefore, we find that

\left(-\frac{\partial \Phi_2}{\partial \rho}+\frac{\partial \Phi_1}{\partial \rho}\right)\Big|_{\rho=\rho'}=\frac{\sigma}{\epsilon_0}

The charge density at \rho=\rho' is

\sigma=\frac{\lambda\delta(\phi-\phi')}{\rho'}

where \lambda is the total charge contained in the line charge. Note that the factor of \frac{1}{\rho'} appears because

\delta(\mathbf{x}-\mathbf{x}')=\frac{1}{\rho'}\delta(\rho-\rho')\delta(\phi-\phi')

This formula arises from the necessity that \int_{\mathbb{R}^2}\delta(\mathbf{x}-\mathbf{x'})\,d\mathbf{x}=1

We can combine all these formulas and evaluate the partial derivatives to find

\sum_{m>0}\left(\frac{a_mm\pi}{\beta}(\rho')^{\frac{m\pi}{\beta}-1}+\frac{b_mm\pi}{\beta}(\rho')^{-\frac{m\pi}{\beta}-1}\right)\sin(\frac{m\pi\phi}{\beta})=\frac{\lambda\delta(\phi-\phi')}{\rho'\epsilon_0}

We can multiply by \frac{\rho'\beta}{\pi} on both sides to get

\sum_{m>0}\left(a_mm(\rho')^{\frac{m\pi}{\beta}}+b_mm(\rho')^{-\frac{m\pi}{\beta}}\right)\sin(\frac{m\pi\phi}{\beta})=\frac{\beta\lambda\delta(\phi-\phi')}{\pi\epsilon_0}

The presence of \delta(\phi-\phi') on the right hand side suggests multiplying by \sin(\frac{n\pi\phi}{\beta}) on both sides and integrating over \phi.

How do we know to do this? Frankly speaking, because I’ve seen this trick used several times in other boundary value problems. It isn’t immediately obvious to a newbie, but if you’ve done enough problems, the idea just naturally pops into your head when it is applicable. This is also one of my favorite tricks in boundary value problems, so that’s probably another reason why it comes to me so quickly.

The integral on the right side is

\frac{\beta\lambda}{\pi\epsilon_0}\int_{0}^{\beta}\sin(\frac{n\pi\phi}{\lambda})\delta(\phi-\phi')\,d\phi=\frac{\beta\lambda}{\pi\epsilon_0}\sin(\frac{n\pi\phi'}{\lambda})

The integral on the left side is

\sum_{m>0}m\left(a_m(\rho')^{\frac{m\pi}{\beta}}+b_m(\rho')^{-\frac{m\pi}{\beta}}\right)\int_{0}^{\beta}\sin(\frac{m\pi\phi}{\beta})\sin(\frac{n\pi\phi}{\beta})\,d\phi

The observant reader will immediately see this integral can be solved by recalling the orthogonality of sine functions. For readers who don’t know what that means, try solving the integral on your own and isolating the cases where n=m and n\ne m – the orthogonality is easily derived.

I omit the calculation because it’s a standard result. We find that the result is

\sum_{m>0}\frac{m\beta}{2}\left(a_m(\rho')^{\frac{m\pi}{\beta}}+b_m(\rho')^{-\frac{m\pi}{\beta}}\right)\delta_{mn}=\frac{n\beta}{2}\left(a_n(\rho')^{\frac{n\pi}{\beta}}+b_n(\rho')^{-\frac{n\pi}{\beta}}\right)

Thus, equating the left and right sides again,

\left(a_n(\rho')^{\frac{n\pi}{\beta}}+b_n(\rho')^{-\frac{n\pi}{\beta}}\right)=\frac{2\lambda}{n\pi\epsilon_0}\sin(\frac{n\pi\phi'}{\beta})

We can change n to m to make this result mesh better with the rest of our solution.

\left(a_m(\rho')^{\frac{m\pi}{\beta}}+b_m(\rho')^{-\frac{m\pi}{\beta}}\right)=\frac{2\lambda}{m\pi\epsilon_0}\sin(\frac{m\pi\phi'}{\beta})

This result seems useless, but it becomes incredibly powerful when combined with the result of applying another boundary condition. We next consider the continuity of the tangential component of the electric field across a boundary, i.e.

\mathbf{E}_2\times\mathbf{\hat{n}}=\mathbf{E}_2\times\mathbf{\hat{n}}

Again, this is a standard result of electrodynamics. For the uninitiated, this result can be derived by considering the integral form of Faraday’s Law applied to an infinitesimally small rectangular loop around a boundary.

Using properties of the cross product or a simple geometric argument (the details are omitted because it can be done mentally), it can be seen that the above formula is equivalent to

\frac{\partial \Phi_1}{\partial \phi}\Big|_{\rho=\rho'}=\frac{\partial \Phi_2}{\partial \phi}\Big|_{\rho=\rho'}

Evaluating these partial derivatives yields

\sum_{m>0}\frac{a_mm\pi}{\beta}(\rho')^{\frac{m\pi}{\beta}}\cos(\frac{m\pi\phi}{\beta})=\sum_{m>0}\frac{b_mm\pi}{\beta}(\rho')^{-\frac{m\pi}{\beta}}\cos(\frac{m\pi\phi}{\beta})

For these series to equal each other independent of \phi, we need

a_m(\rho')^{\frac{m\pi}{\beta}}=b_m(\rho')^{-\frac{m\pi}{\beta}}

b_m=a_m(\rho')^{\frac{2m\pi}{\beta}}

Incredible progress! Now go back to our result from the earlier boundary condition and plug this new result in:

\left(a_m(\rho')^{\frac{m\pi}{\beta}}+b_m(\rho')^{-\frac{m\pi}{\beta}}\right)=\frac{2\lambda}{m\pi\epsilon_0}\sin(\frac{m\pi\phi'}{\beta})

2a_m(\rho')^{\frac{m\pi}{\beta}}=\frac{2\lambda}{m\pi\epsilon_0}\sin(\frac{m\pi\phi'}{\beta})

a_m=(\rho')^{-\frac{m\pi}{\beta}}\frac{\lambda}{m\pi\epsilon_0}\sin(\frac{m\pi\phi'}{\beta})

This gives us formulas for a_m and b_m! Now we can plug them into our formula for \Phi and find \begin{aligned} & \Phi(\rho,\phi;\rho',\phi') =\\ &\frac{\lambda}{\pi\epsilon_0}\sum_{m>0}\frac{1}{m}\sin(\frac{m\pi\phi'}{\beta})\sin(\frac{m\pi\phi}{\beta})\cdot\begin{cases} (\rho')^{-\frac{m\pi}{\beta}}\rho^{\frac{m\pi}{\beta}} & \text{ for } \rho<\rho' \\ (\rho')^{\frac{m\pi}{\beta}}\rho^{-\frac{m\pi}{\beta}} & \text{ for } \rho>\rho' \end{cases} \end{aligned}

Now if we let \rho_{<}=\text{min}(\rho,\rho') and \rho_{>}=\text{max}(\rho,\rho'), we have

\Phi(\rho,\phi;\rho',\phi') = \frac{\lambda}{\pi\epsilon_0}\sum_{m>0}\frac{1}{m} \rho_{<}^{\frac{m\pi}{\beta}}\rho_{>}^{-\frac{m\pi}{\beta}}\sin(\frac{m\pi\phi'}{\beta})\sin(\frac{m\pi\phi}{\beta})

Now if we let \lambda=1 (the total charge in the line charge) and multiply by 4\pi\epsilon_0, we get the Green function for this problem

G(\rho,\phi;\rho',\phi')=4\sum_{m=1}^{\infty}\frac{1}{m}\rho_{<}^{m\pi/\beta}\rho_{>}^{-m\pi/\beta}\sin(m\pi\phi/\beta)\sin(m\pi\phi'/\beta)

Voila, part a of the problem is solved! I found this solution incredible, and I hope you do too. We used a staggering amount of techniques to reduce a complicated problem to an elegant series solution – that, to my mind, is the beauty of boundary value problems.

Now we solve part b of the problem and find a closed form through even more elegant manipulations!

Finding a closed form – wizardry with complex numbers

Let’s start by rewriting the sine product as a sum of cosines, i.e.

\sin(\frac{m\pi\phi'}{\beta})\sin(\frac{m\pi\phi}{\beta})=\frac{1}{2}\left(\cos(\frac{m\pi}{\beta}(\phi-\phi'))-\cos(\frac{m\pi}{\beta}(\phi+\phi'))\right)

=\frac{1}{2}\left(\Re(e^{\frac{im\pi}{\beta}(\phi-\phi')})-\Re(e^{\frac{im\pi}{\beta}(\phi+\phi')})\right)

G=2\Re\left(\sum_{m=1}^{\infty}\frac{1}{m}\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{m\pi}{\beta}}e^{\frac{im\pi}{\beta}(\phi-\phi')}-\sum_{m=1}^{\infty}\frac{1}{m}\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{m\pi}{\beta}}e^{\frac{im\pi}{\beta}(\phi+\phi')}\right)

Now define

z_1=\left(e^{i(\phi-\phi')}\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{\pi}{\beta}}

z_2=\left(e^{i(\phi+\phi')}\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{\pi}{\beta}}

This allows us to rewrite the series in the cleaner form

G=2\Re\left(\sum_{m=1}^{\infty}\frac{z_1^m}{m}-\sum_{m=1}^{\infty}\frac{z_2^m}{m}\right)

This is another point where a good memory will help solve the problem. Recall the Taylor series expansion for \ln(1+x)

\ln(1+x)=\sum_{m>0}(-1)^{m+1}\frac{x^m}{m}=x-\frac{x^2}{2}+\frac{x^3}{3}-\cdots

Plugging in -x gives

\ln(1-x)=-\sum_{m>0}\frac{x^m}{m}=-x-\frac{x^2}{2}-\frac{x^3}{3}-\cdots

Now it becomes clear that

-\ln(1-x)=\sum_{m>0}\frac{x^m}{m}

Thus,

G=2\Re\left(-\ln(1-z_1)+\ln(1-z_2)\right)=2\Re\left(\ln(\frac{1-z_2}{1-z_1})\right)

Excellent! We are close to the structure desired by the problem’s description. We have the logarithm of a quotient, but the tricky part is taking the real part.

Consider the real part of such a logarithm:

\Re(\ln(1-z))=\Re\biggl[\ln(|1-z|)+i\mathop{\mathrm{Arg}}(1-z)\biggr] =\ln(|1-z|)=\ln(\sqrt{(\Re(1-z))^2+(\Im(1-z))^2}) =\frac{1}{2}\ln\left[\left(1-|z|\cos(\mathop{\mathrm{Arg}}z)\right)^2+\left(|z|\sin(\mathop{\mathrm{Arg}}z)\right)^2\right] =\frac{1}{2}\ln\left[1+|z|^2-2\Re(z)\right]

Great, this is a clean way of expanding the real part of our logarithm!

Note that

|z_1|=\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{\pi}{\beta}}

|z_2|=\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{\pi}{\beta}}

\Re(z_1)=\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{\pi}{\beta}}\cos(\frac{\pi}{\beta}(\phi-\phi'))

\Re(z_2)=\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\frac{\pi}{\beta}}\cos(\frac{\pi}{\beta}(\phi+\phi'))

Then we have

G=\ln\left(\frac{1+|z_2|^2-2\Re(z_2)}{1+|z_1|^2-2\Re(z_1)}\right) =\ln\left(\frac{1+\left(\frac{\rho_{<}}{\rho_{>}}\right)^{2\pi/\beta}-2\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\pi/\beta}\cos\left(\frac{\pi}{\beta}(\phi+\phi')\right)}{ 1+\left(\frac{\rho_{<}}{\rho_{>}}\right)^{2\pi/\beta}-2\left(\frac{\rho_{<}}{\rho_{>}}\right)^{\pi/\beta}\cos\left(\frac{\pi}{\beta}(\phi-\phi')\right) }\right) =\ln\left(\frac{(\rho_{>})^{2\pi/\beta}+\left(\rho_{<}\right)^{2\pi/\beta}-2\left(\rho_{<}\rho_{>}\right)^{\pi/\beta}\cos\left(\frac{\pi}{\beta}(\phi+\phi')\right)}{ (\rho_{>})^{2\pi/\beta}+\left(\rho_{<}\right)^{2\pi/\beta}-2\left(\rho_{<}\rho_{>}\right)^{\pi/\beta}\cos\left(\frac{\pi}{\beta}(\phi-\phi')\right) }\right)

Now note that, since \rho_{>} and \rho_{<} have the same exponent everywhere, we can just replace them with \rho and \rho'.

G(\rho,\phi;\rho',\phi')=\ln\left(\frac{(\rho)^{2\pi/\beta}+\left(\rho'\right)^{2\pi/\beta}-2\left(\rho\rho'\right)^{\pi/\beta}\cos\left(\frac{\pi}{\beta}(\phi+\phi')\right)}{ (\rho)^{2\pi/\beta}+\left(\rho'\right)^{2\pi/\beta}-2\left(\rho\rho'\right)^{\pi/\beta}\cos\left(\frac{\pi}{\beta}(\phi-\phi')\right) }\right)

Behold! The epic closed form solution to the problem. My mind was blown away by how such a complicated series could be reduced to a closed form. The final solution looks cool – which, let’s be honest, is all we care about – but is also surprisingly well-behaved. There’s a singularity at (\rho',\phi') but, other than that, the function is everywhere finite and continuous for 0\le\phi\le\beta and 0\le\rho<\infty

What is especially surprising is continuity, since our series solution was a piecewise function. It’s incredible that such a gnarly series produced such an elegant closed form.

Visualization of the electric potential for \beta=\frac{\pi}{3}, (\rho',\phi')=(0.8,\frac{pi}{8})

Conclusion

I hope the reader has found this problem as entertaining as I did. As always, if you have any questions or thoughts about this post, feel free to contact me on Discord or via email. I have a few other Jackson-related posts I plan to write soon, but it takes a long time to write LaTeX, so the post schedule is chaotic.

I tried to be thorough with my explanations at the start of this post, but after a few hours of writing, my patience likely wore out. Apologies if some parts of this post are less understandable than others :) Please message me to ask about anything that’s unclear or confusing.

Also, if there are any other people reading Jackson or people who would want to talk about the book with me – please contact me!! I’m tired of getting stuck on one equation for an hour, only to realize there’s a typo or something similarly stupid. It’s easier to read this book in a group than to read it alone, and I’d love to work with another devotee to the holy church of Jackson. If I was doing this in college, I’d have Jackson buddies, but instead I’m hoping someone on the internet reads this haha.

Thanks for reading, please contact me if this is interesting (I’m lonely) !!!

Life Update For January 2026

Tue, 20 Jan 2026 00:00:00 GMT

Life Update For January 2026 | Chancellor Ceti

Life Update For January 2026

Hello! After the last two ‘serious posts,’ I figured it was time to give a personal update again. A lot has happened over the last ~two months, so as usual, this will be a rambling and poorly structured post. I’ll start by griping about school and then transition to more interesting content – sorry for the negative rant, but school is 31% of my awake hours, so it takes up a proportionate share of my update.

The first major development is that I am now in the second semester of my senior year (12th grade) of high school, which is great news because I have no obligations or stress during this time. Colleges don’t consider second semester grades for admission, and they don’t rescind an admissions offer unless you’re failing half your classes or get suspended for trying to set a toilet on fire. You can easily figure out a class is populated by 12th graders by counting how many are asleep, playing video games, or watching Youtube. As a result, I’ve got a bit more free time during school hours now, which I’m devoting to reading and studying languages.

However, I’m a ‘quasi-senior’ because I’m early graduating; half my courses are full of 12th graders, the other half full of 11th graders. While 12th graders have finished college applications and are now sleeping through classes, 11th graders are doing the exact opposite, averaging 4 hours of sleep every night because they’re just about to start college applications. Given that I exist between these worlds, I see a morbidly funny dichotomy between apathy and over-work, alternating every 90 minutes as I change classes. I’m getting a kind of ‘half-senior, half-junior (11th grade)’ experience where I spend half the day relaxing in senior-majority classes and the other half enduring a barrage of tests in junior-majority classes. While it is better than the fully stressful junior experience sans early graduation, it still is a bit frustrating to be deprived of the full luxury experience.

The lack of stress is also something that I’m paradoxically conflicted about. While it is nice to enjoy my own books at school, all this free time exacerbates my previous irritation with having to attend high school; if I’m going to spend these 8 hours reading my own stuff, why did I have to show up here at all? I spend half the day reading “China After Mao” and studying Indonesian, and I spend the other half trying to tune out lectures and race through tests that no longer matter because I’m in the second semester. The sheer pointlessness of the second semester is a bit infuriating, like a kind of spiritual prison. My life is put on pause, and I’m unable to advance in my main career progression through college courses that will actually serve a purpose in my life; instead, I’m just killing time, waiting to leave 12th grade and enter college where my courses (and the 8 hours they occupy) actually contribute to my life. Something feels wrong about condemning kids to 8 hours of school when the courses and exams no longer matter, and the only reason for showing up is to get marked on the attendance sheet and keep grades above a 70 to prevent admissions offers being rescinded.

School is doubly frustrating for me because I’ve really started to dislike the culture here. A lot of people enjoy senior year because it’s more time to hang out with their friends, but I have no strong friendships at school. I occasionally had good conversations with other juniors last year, but since they’re all busy prepping for college applications, I’m increasingly deprived of even these chance encounters. Leaving aside those rare kids who are fun to talk to, most of the conversations at school consist of inane brainrot (67 and skibidi toilet), exchanging information about tests (technically not allowed but academic integrity is a joke), or gossiping. Since none of these interest me much, I’ve been left without much of a social life.

There’s a lot of other stuff I dislike about the school, the classes, and the kids here, but I’m omitting it to avoid the risk of sounding like a misanthropic crybaby. The social life problems are probably my fault to some extent, so I don’t want to sound completely insane by rambling on about that for several paragraphs. I’ll summarize all of that ranting with a quick “I hate this place and can’t wait to get out of here.”

With that update on school out of the way, onto more interesting things!

Outside of loneliness and frustration with school’s pointlessness, my life has been going pretty well. I’ve finished three amazing books this month, thanks in part due to the extra reading time at school. They are “The Jakarta Method” by Vincent Bevins, “We Do Not Part” by Han Kang, and “From Heaven Lake” by Vikram Seth. I hope to finish book reviews for all of them in the next few days and post them on my blog, so I’ll abstain from yapping about them here and save my thoughts for those posts.

I’ve now started Frank Dikötter’s “China After Mao,” which I’m already loving. This book is a history of China after Mao (surprise) from 1976 to 2012, focusing on political and economic transformations. I’ve been drawn in by the level of detail and the complexity of the narrative he presents; rather than framing it as a well-calculated rise to being a superpower, Dikötter portrays China’s rise as being chaotic, prone to frequent halts, and plagued by a failure to bring about true political or economic liberalization. After finishing just the first chapter, I feel delightfully overwhelmed by information; the political machinations of the Politburo members and the disastrous pendulum of economic policy create reading that’s both informative and entertaining.

If you want a month-by-month replay of the events leading up to and following Deng Xiaoping’s rehabilitation in 1977, this is the book for you. If you want a riveting story of seesawing between centralized control of the economy and devolution of planning powers, with the chaos that it created, this is the book for you. If you want to learn about how flattery of American diplomats, vying for ‘Most Favoured Nation’ status with the US, and other diplomatic intrigue shaped our world today, this is the book for you. If you just want to learn a ton about post-Mao China and engage with interesting ideas, this is the book for you.

I’ve also been working on learning more Indonesian, Spanish, and Bengali, and I’ve started again trying to learn Mandarin. The juggling of so many projects likely limits my progress in each of them, but I don’t really care since I’m doing this for fun and am enjoying myself a lot. I also have enough time that multitasking hasn’t significantly limited me, so I’m satisfied with my current pace of progress.

In Indonesian and Mandarin, I’m learning from the ground up and just starting to form basic sentences, but I’m able to consume more interesting content in Spanish and Bengali due to my higher degree of fluency. I’m technically already ‘fluent’ in Bengali, but I can only speak in an informal register and I lapse into English when discussing complex topics. I’ve therefore started pushing myself to learn the more formal vocabulary and am now reading Bengali newspapers like Prothom Alo that use complex language: great for learning Bangla and also for following the news. In addition to formal vocabulary, my reading of Prothom Alo and Kazi Nazrul Islam’s poetry is letting me learn vocabulary that’s rarely used in West Bengal but ubiquitous in Bangladesh. I’ve learned a lot over the last few weeks, and it’s been very satisfying.

To further my learning of Spanish, I’ve begun reading El País and 2666 (amazing book) with a lot more vigor. I want to highlight this article as an especially interesting El País story based on a series of interviews with Gabriel Boric. Boric is, to my mind, one of the most inspiring politicians of our times (coherent and logical when speaking, as president he crushed inflation while also raising minimum wage, introducing 40 hour work-week, and reforming pension system), and I liked reading his reflections on politics and also learning about his various niche interests – turns out the president of Chile is a fan of both Radiohead and K-pop, in addition to a bunch of other things you wouldn’t typically associate with a president. That article has lots of fun Boric trivia while also presenting interesting ideas on the future of the left and how it can fight the rising tide of far-right politics.

I’ve also finished Part 2 (the part about Amalfitano) of 2666 and am really enjoying Part 3! Bolaño writes really well and, more than directly saying anything, his book is good at creating a feeling of dread and horror around a place, and conveying the book’s themes through that characterization. Another super interesting bit of Spanish media is the 3-part documentary “La Batalla de Chile (The Battle of Chile) directed by Patricio Guzmán. The movie covers the events leading up to the 1973 military coup in Chile and the battle between”Poder Popular” (people’s power) and fascism. It’s a devastating film showing how collusion between wealthy businessmen, the Chilean military, and the CIA led to a bloody coup and the destruction of a country’s collective dreams. More full review coming in a blog post soon (maybe?).

For those curious about my STEM pursuits, I’ve taken a small hiatus, in part due to burnout; turns out it eventually gets a bit tiring to spend three-ish years studying college-level math, physics, and computer science without support from anyone around you! I still love these subjects, but they require perseverance and energy that I just can’t muster right now. So for the next few months at least, I will not be studying physics or math with the same vigor I used to. That shouldn’t decrease the amount of content on my blog though, since I’m still engaging with plenty of interesting ideas in other fields. Speaking of the blog, this ‘second semester free time boost’ will hopefully also let me write here more often; look forward to that!

That mostly sums up recent happenings. If the meteorological gods are reading this, thanks for the snow; missing four days of school is the best thing to have happened in a while. As always, feel free to contact me if you have anything interesting to say (about page has email+Discord). Farewell until the next post!

June 5 Curated Media Diet: News, Politics, And K-pop Music

Fri, 05 Jun 2026 00:00:00 GMT

June 5 Curated Media Diet: News, Politics, And K-pop Music

Hello again to readers, here’s another post compiling some of the most interesting content I’ve seen online recently. I’ve realized I like this style of post, so I’ll likely keep doing it in the future. Warning in advance, these posts won’t have as much attention to grammar or writing quality as my more focused essays – these focus on dumping interesting content with enough commentary to summarize what’s in the articles and why they’re interesting, so eloquence and formality aren’t as big of a priority. Honestly I think I do a better-than-average job on this kind of writing, because other link dump-style posts I’ve seen online don’t even bother with these semi-descriptive summaries and reactions to articles and instead just give 5-10 word summaries for each one. Anyway, back to the actual content of this post.

Starting with stuff related to current events:

This is one of the best articles I’ve found so far on the ebola outbreak in the Democratic Republic of Congo (DRC) and the absolute hell that it is, worth reading. A terrifying read on how USAID cuts and western apathy have produced chaos in a small mining town in the DRC (for details on impact of the USAID cuts, rather than a solely objective look at “what’s happening,” Kristof wrote a decent article in NYT). On a side-note, I was rather pleased to see Declan Walsh is now NYT’s chief Africa correspondent – aside from having enjoyed his book “9 Lives of Pakistan,” he has an impressive history in journalism, and I recommend checking out his Wikipedia page if you haven’t already. If Pakistan kicked him out of the country, Egypt tried arresting him, and he then got a Pulitzer for reporting on the Sudanese Civil War, he’s clearly doing something right haha.

Here is some very interesting theorizing on Saudi Arabia’s refusal to share airspace with the US

I’m not sure if House of Saud has found the correct explanation, but this is certainly an interesting theory. Tldr, Saudis have a huge fiscal crisis, and the White House’s peace plan would’ve gotten rid of the conflict premium on oil prices and pushed it well below Saudis’ fiscal breakeven price => war is cheaper than peace for the Saudis. Also, the US-Saudi negotiations are being brokered by Jared Kushner, who’s growing fat on Saudi money, i.e. the guy running those talks is simultaneously being paid by the party that benefits most from the war. Conflict of interests much?

On a side-note, House of Saud is a really interesting site, and if you’re interested in the Middle East and geopolitics stuff, I recommend adding it to your media diet if it isn’t there already.

Pivoting to Latin America – if you want some fun political chaos to follow, keep an eye on the runoff elections in Peru and Colombia this month. Two nutty far-right candidates with a decent chance of winning, let’s see how it goes. Colombia’s far-right candidate Abelardo de la Espriella is truly fascinating, here are some things that stuck with me from my reading.

He admitted on TV to tying cats to firecrackers and watching them explode as a kid – I’m curious if there’s some kind of psychological link between fascist sympathies and a proclivity towards animal abuse, since in addition to de Espriella, Trump’s former DHS Secretary Kristi Noem shot a dog, the NRA president Doug Hamlin burned and dismembered a cat for not using a litterbox, and the Heritage Foundation president and key architect of Project 2025, Kevin Roberts, also told stories of beating the neighbor’s dog to death with a shovel for barking too much. Also, no I didn’t know all these stories just randomly, I read the cats-and-firecrackers thing, then I remembered the Kristi Noem story, and decided to see which other nutcases were also animal abusers and found this https://archive.is/afMvw – quite the rabbit hole… Seriously, what is wrong with some of these far-right politicians??
Returning to the story of Colombia’s far-right candidate – he made a career as a lawyer defending politicians accused of illegal collusion with far-right paramilitaries for election-rigging, as well as defending Maduro’s money launderer. He testifies to the strong moral character of all his clients and sees the paramilitary leaders as productive political forces rather than narcoterrorists, despite all evidence to the contrary. This wikipedia page is worth reading for a quick overview, the parapolitics scandal is fascinating and lies at the crux of why Colombia’s far-right is so dangerous – multiple congressmen and governors indicted, including the president’s own cousin. Maybe not a good sign that de Espriella supports these characters?
He’s also been accused by several clients of demanding massive sums of money for influencing judges and congressmen to swing cases in their favor, and then promptly abandoning them to the legal system once he’d made enough money.
+ the usual far-right obsessions – suing reporters for negative coverage, opposing rights of homosexuals and transgender people that they’ve already been legally granted, opposition to abortion, ‘mano dura’ (Latin American version of ‘tough on crime’) politics and replacing negotiations with insurgent groups with the “boomboom everyone dead” strategy (because that worked so well for the last few decades of course)

The above details mostly come from this El País article

Not going to blabber as much about Peru’s far-right candidate Keiko Fujimori – she’s pretty much a carbon copy of her father, so there isn’t much “new” over there, unlike Espriella who represents a complete break with the traditional right-wing and a shift to more colorful populism. But of course, I wouldn’t have mentioned her unless I had an interesting story about Peru also. Here it is:

If you don’t know about the controversy around Alberto Fujimori’s wife, it’s a must-read. She publicly denounced her husband’s government for corruption and authoritarianism and was then thrown out of her position as First Lady. She later claimed that Fujimori’s intelligence services tortured her and she showed scars to prove it (Fujimori claims it was some strange Japanese medical treatment that caused them) – although Fujimori’s rebuttal lost credibility after a former intelligence agent testified to having seen her “naked and cowering in a basement cell at army intelligence headquarters in 1995” (from a 2002 AP article).

And now the daughter’s aligned with daddy dearest and campaigning for another season of corrupt authoritarian dystopia – what a family…

For less depressing news from Latin America, I recommend this El País article on Iván Cepeda, the left-wing candidate in Colombia’s upcoming runoff election who will face off against cat-killer. It doesn’t talk much about his policy proposals but provides a very interesting biography of his life; although it’s a visibly biased endorsement piece, it’s worth reading because Cepeda has an inspiring life story of resilience (his father was assassinated for his left-wing politics) and fighting for justice (prominent advocate for the victims of right-wing paramilitary violence). I don’t know enough about his policies to say for sure whether they will be good for Colombia, and his refusal to distance himself from Petro’s failures isn’t promising; but speaking solely from the perspective of morals and who seems to be a better human being, Cepeda would have my vote over Espriella any day if I was a Colombian.

Moving over to the US now, there’s even more entertaining+interesting insanity here.

Samurai vs squatters! Sounds like the title of a bad cyberpunk video game, yet somehow this is real. Extreme tenants’ rights legislation has made it nearly impossible for landlords to evict squatters in parts of California, leading to some people now employing these samurai-wielding squatter removal services. This is a very interesting read, as well as a morbidly entertaining one. In the absence of viable legal solutions to problems, shady extrajudicial solutions usually fill the gap, as this article painfully demonstrates. Yet another example of California’s regulatory mess, purportedly in defense of the poor and marginalized, actually working more towards the detriment of property-owners and society as a whole (which benefits from property-owners’ productive use of capital) rather than towards the benefit of poor people. If anyone has gained from this type of bureaucracy-increasing legislation, it’s the criminals and miscreants who are most inclined and best-equipped to take advantage of the legal loopholes created.

Staying on the topic of California, here’s a similar case of bureaucratic insanity – California’s Environmental Quality Act (CEQA). I was introduced to this monstrosity through a Reason.com article on how the CASE union representing state-employed legal workers is threatening to sue Gavin Newsom under CEQA, because his demand for state-employed workers to show up in-person four days a week hasn’t been accompanied by an environmental study investigating the effect that this additional commute will have on CO2 emissions. A law that allows employees to sue the state’s governor over being asked to show up to work – what a great idea!

More specifically, CEQA requires government agencies to study the environmental impacts of any ‘projects’ they begin, with citizens being enabled to sue the government if they feel that obligation is not being adequately met. I’ve put ‘projects’ in quotation marks because of its dangerously vague definition under CEQA, which encompasses government construction but also personnel policies (as in this case), projects started by private corporations that just so happen to be obtaining government approval at some stage, and all other kinds of sketchy extensions of the definition.

My initial reaction to the article was “wait, wouldn’t this let anybody stall any government or corporate action for as long as they want using the flimsiest justification loosely related to environmental concerns?” Aaaand, yep, that’s exactly what it does. I got curious and opened a bunch of links from the original article, and WOW what a mess.

Here’s another story on CEQA (from 2024) and how it allows property developers’ competitors to ‘greenmail’ them with CEQA lawsuits, indefinitely stalling new projects by demanding studies of environmental impacts until they get paid off (euphemistically known as ‘out-of-court settlement’). The low threshold for filing a CEQA lawsuit (some of these lawsuits’ objections are truly absurd), combined with the months-long litigation process, has made the law ripe for abuse – developers often find it cheaper to just pay off the plaintiff rather than fight their case and waste time in court and then even more time awaiting the results of their further environmental studies. In one case, a greenmailer explicitly said “You know the drill. It’s going to take a check to make this go away.” Isn’t this just… extortion?

Since then, there have been some attempts at reform, such as eliminating the requirement of noise pollution studies (a recipe for abuse, since any building project generates noise), but much remains to be done because reforms are having to block specific provisions case-by-case, while miscreants are coming up with new legal loopholes faster than legislation can be passed. Maybe… maybe this just wasn’t a good idea?

And another equally illuminating story on CEQA greenmailing from 2019, this one on how unions abuse the law to force companies to use their labor, something developers try to avoid because of the overly bureaucratic workplace rules and higher labor costs.

This article is especially interesting because towards the end, it highlights how CEQA greenmailing is also worsening California’s housing crisis by delaying the construction of new housing with frivolous lawsuits and increasing projects’ costs by forcing developers to use more expensive union labor. Another example of how housing affordability issues are fundamentally a supply-side problem rather than a case of evil landlords extorting their tenants.

Finally, here’s a 2023 story on how NIMBYs abused CEQA to block UC Berkeley from building additional student housing due to a lack of studies on how it would affect noise pollution.

Shifting to the other end of the US now, New York City: Zohran Mamdani’s democratic socialism has gotten a lot of people’s hopes up, but let’s see what’s actually happening behind all the grandstanding.

Here’s a good NYT article on Mamdani’s handling of the Economic Development Corporation (EDC). Five months into his tenure, he has still not appointed an EDC head due to administrative paralysis over what the EDC’s goal should even be in this new democratic socialist paradise; although the EDC has traditionally been used to spur economic growth by supporting select projects with city real estate and tax breaks, Mamdani and his supporters want the EDC to now focus more on social justice programs such as city-run grocery stores. This broader shift in focus from economic development to social justice and economic regulation is sparking justified concern among many experts, as explained in the NYT article. My view is that, while both economic growth and social justice are important, Mamdani’s handling of the EDC suggests that he isn’t broadening the administration’s scope so much as completely shifting it, sacrificing economic development for his politics of always backing the little guy against large corporations. What this approach neglects is that economic development and social justice are interconnected rather than mutually exclusive: welfare spending and state ownership of essential services is good, but inadequate if unaccompanied by government support for entrepreneurship and job creation. The EDC turmoil, combined with similar anti-business policies such as tax hikes and demonizing the rich on social media, might prove problematic for both rich people and poor people, as much as Mamdani might like to pretend that only the rich benefit from economic growth right now.

And another NYT article on how Mamdani is collaborating with Governor Kathy Hochul to solve the budget crisis. The article somewhat discredits his claim that the budget balancing was “democratic socialism” and “government that delivers for the people who make this city run”; despite Mamdani’s boasting about some savings being obtained through a new tax on luxury second homes and slashing of unnecessary spending, most of the $12 billion came from the governor providing a massive infusion of cash from state tax revenue, as well as delaying several programs promised by Mamdani in his campaign such as reducing class sizes in schools and delaying payments to pension funds (risky much?). Seems like a classic case of kicking the can down the road rather than actually solving the budget deficit issue…

Moving on to music – I haven’t been exploring too much new stuff lately, but I have two nice new kpop discoveries to share.

First is ITZY’s new mini-album Motto. The title track is really good, and for me, it was the highlight of the new release. Worth listening to if you enjoy kpop. Good instrumentals, catchy tune, just fun to listen to.

The other awesome discovery is NMIXX’s performance at the Festival de la Canción de Viña del Mar in Chile (Latin America’s oldest and largest music festival) in March. I had seen this on Youtube a while ago and watchlisted it, but my laziness kept me from watching it until recently. It’s an incredible performance with lots of energy, great vocals and dancing, and really cool stage/visual effects. You have to skip around the talking segments a bit since it’s a video of the full performance, but this is otherwise worth watching in full. However, I do have to note that I did watch the talk segments the first time I saw it, just because it’s such a cool sight to see a Korean group speaking Spanish to an entirely Chilean audience with very little preparation. The whole performance is a great achievement of capitalism and the globalization of culture – yes, yes, environmental degradation, neocolonialism, and the marginalization of indigenous voices, BUT it also gave us a Korean group singing a song with a mix of Portuguese and English lyrics to an entirely Chilean, Spanish-speaking audience! Quite the achievement, in my opinion. Maybe Marx would’ve been a kpop fan if he lived in our century.

On a side-note, NMIXX is my favorite kpop group at the moment, and if you haven’t listened to their full discography yet, I highly recommend it. At least half their tracks rank among my “top-tier kpop songs” mental list.

That concludes today’s post. Hopefully some of this is interesting, look forward to a more regular posting schedule over the next few weeks thanks to my summer vacation.

Lattice Points Visible from the Origin using Euler Product Formula and Evaluation of Zeta Function

Fri, 21 Oct 2022 00:00:00 GMT

Lattice Points Visible from the Origin using Euler Product Formula and Evaluation of Zeta Function

Lattice Points Visible from the Origin using Euler Product Formula and Evaluation of $\zeta(2)$

Chancellor Ceti

October 2023

Introduction
Expressing the problem mathematically
Turning our ratio into an infinite product
Euler’s Product Formula
A cool conclusion to our problem– Apostol’s Solution to the Basel Problem

Introduction

This is a fascinating result I encountered some time back in Tom Apostol’s Introduction to Analytic Number Theory that counted the density of lattice points visible from the origin. For readers who are unfamiliar with that terminology, a lattice point is a point in the plane with integer-valued coordinates, and a lattice point is visible from the origin if a line can be drawn to it from the origin containing no other lattice points. And by density, all we mean is the ratio of lattice points visible from the origin to the total amount of lattice points as we let the amount of lattice points approach infinity.
Apostol showed that the answer to this problem is intimately tied with number theory and especially the Riemann Zeta function, one of the most celebrated topics in mathematics. I have followed a slightly different approach from Apostol, inspired by my knowledge of the Euler Product Formula and Zeta function, but it yields the same result and somewhat more elegantly. This solution has many parts and hopefully the reader will learn many different things from this one post. So without further ado, let’s jump into the problem.

Expressing the problem mathematically

Before anything else, let’s define lattice points and visibility a bit more concretely. As said earlier, attice points are simple– points on a 2d grid with integer-valued coordinates. And a lattice point $p$ with coordinates $(a,b)$ is said to be visible from the origin if there are no lattice points between $p$ and the origin on the line joining $p$ to the origin apart from $p$ and $(0,0)$. Defining this mathematically is now simple.
Suppose there is a lattice point $q$ that is between $p$ and the origin on the line joining the point $p$ with coordinates $(a,b)$ to the origin at $(0,0)$. So if such a point $q$ exists, then it has the coordinates $(ka,kb)$ for some $0<k<1$. This is easily explained by the following logic. If $q$ has coordinates $(c,d)$, then $d=\frac{b}{a}c$ for some $0<c<a$ since that is the equation of the line connecting $p$ to the origin, and the constraints on $c$ are because $d$ is between $b$ and $0$. So $0<d<b$, and $kb$ with $0<k<1$ satisifies these constraints. The definition of $c$ is already justified by the previous argument that $0<c<a$ and the fact that $c=ka$ with $0<k<1$ satisfies that constraint.
So $(a,b)$ is visible from the origin if there are no lattice points $(ka,kb)$ with $0<k<1$. Since $(ka,kb)$ is a lattice point, it must have integer-valued coordinates. So $k$ must be rational and can be expressed as $\frac{m}{n}$ where $n|a$ and $n|b$, else the coordinates would not be integral. Also note that $n$ can not equal $1$ or $q$ would not be between $p$ and the origin.
So our problem is now reduced to this: what is the ratio of integer-valued pairs $(x,y)$ not possessing a common divisor $k>1$ to the total number of integer-valued $(x,y)$ pairs? How might we go about tackling this problems? Enter the world of number theory.

Turning our ratio into an infinite product

We seek the ratio of coprime $(x,y)$ pairs to the total number of such pairs.
When there are infinitely many integer choices of $x$ and $y$, we can see this ratio as a probability of two random integers being coprime. For two numbers to be coprime, there must be no prime $p$ that divides both numbers. To show this fact, we first introduce the notation \[gcd(a,b)=c\] to mean the greatest common divisor of $a$ and $b$ is $c$ (this makes our lives much easier).
And we additionally introduce the notation $p|n$ for $p$ divides $n$, mathematically $n=px$ for some integer $x$. Then, by the fundamental theorem of arithmetic, if $gcd(x,y)>1$, then letting $d$ be the gcd, we have \[d=\prod_{i=1}^{r}p_i^{a_i}\] So if $gcd(x,y)=d$, then $d|x$ and $d|y$ implying $p_i | x$ and $p_i | y$ for all $i$, since if $d|x$, then $x=dk$ for some integer $k$, and then since $p_i | d$, $d= p_ij$ for some $j$ implying $x = p_ijk$, which means $p_i|x$. So in order for $gcd(x,y)=1$ to be true, there must be no prime $p$ that divides both $x$ and $y$.
It is obvious that the events $p|n_1$ and $p|n_2$ are independent since one can occur with no effect on the probability of the other, so their compound probability is the product of the individual probabilities. Now consider the probability of a prime $p$ dividing a random integer $n$. By studying the multiples of $p$, it becomes obvious that every $p$’th integer is divisible by $p$. So if we consider the set of all integers, intuitively, the probability of a random integer $n$ being divisible by $p$ is $\frac{1}{p}$.
Now we introduce the notation $p\nmid n$ for $p$ does NOT divide $n$ or, otherwise put, $n$ is not an integer multiple of $p$. For $n_1$ and $n_2$ to be coprime, there must be no $p$ such that $p|n_1$ and $p|n_2$. Since the events $p|n_1$ and $p|n_2$ are independent, the events $p\nmid n_1$ and $p\nmid n_2$ are likewise indepdent.
Because the probability of $p$ NOT dividing $n$ is the complement of the probability of $p$ dividing $n$, \[P(p\nmid n)=1-\frac{1}{p}\] where $n$ is a random integer. Then the probability that $p$ divides neither $n_1$ nor $n_2$ is the complement of their compound probability, \[P((p\nmid n_1)\cap (p\nmid n_2))=1-\frac{1}{p^2}\] where $n_1$ and $n_2$ are again random integers.
So this is the probability that a prime $p$ does not divide both $n_1$ and $n_2$. But for $n_1$ and $n_2$ to be coprime, there must be NO prime dividing both integers. Since the events $(p_1\nmid n_1\cap p_1\nmid n_2)$ and $(p_2\nmid n_1\cap p_2\nmid n_2)$ are independent(this is obvious since the divisibility of an integer by one prime has no impact on its divisibility by another), we have the probability of $n_1$ and $n_2$ being coprime as the product of the probabilities \[P((p_i\nmid n_1)\cap (p_i\nmid n_2))=1-\frac{1}{p_i^2}\] over all primes $p_i$. Thus, \[P((gcd(x,y)=1))=\prod_{p}1-\frac{1}{p_i^2}\] and since $P((gcd(x,y)=1))$ is the ratio of coprime pairs of integers to total pairs of integers, this infinite product is our answer. So now our problem is reduced to evaluating this product, which many of you are probably doubting is even possible right now.
Luckily, we have a tool that lets us simplify this menacing product into a menacing sum(crazy, I know)– Euler’s Product Formula.

Euler’s Product Formula

We start with the formula \[\label{eq:powseries1} \frac{1}{1-x}=\sum_{n\ge 0}x^n\] This is easily proved by letting \[S=\sum_{n\ge 0}x^n\] and noting that \[S=1+x+x^2+\cdots\] while \[Sx=x+x^2+x^3+\cdots\] so that \[S-Sx=1\] Then \[S(1-x)=1\] so \[S=\frac{1}{1-x}\] It can further be shown that this series is convergent, in the traditional high school calculus sense, no real analysis :) , for $|x|<1$. With that in mind, let’s consider the infinite product \[\prod_{p}\frac{1}{(1-\frac{1}{p^s})}\] Since $|\frac{1}{p^s}|<1$, we can use our previous identity to see that \[\prod_{p}\frac{1}{(1-\frac{1}{p^s})}=\prod_{p}\sum_{n\ge0}\frac{1}{p^{ns}}\] Expanding this product, we see that \[\prod_{p}\sum_{n\ge0}\frac{1}{p^{ns}}=(1+\frac{1}{2^s}+\frac{1}{4^s}+\cdots)(1+\frac{1}{3^s}+\frac{1}{9^s}+\cdots)\cdots\] By the fundamental theorem of arithmetic, all integers greater than $1$ are the product of a finite number of primes raised to integer powers. Now if we multiply together any terms in this product, we get either $1$ if all terms are $1$ or something of the form \[\frac{1}{\prod_{i=1}^{r}p_i^{a_is}}\] which is by the fundamental theorem of arithmetic equal to \[\frac{1}{n^s}\] for some integer $n>1$ So really, \[\prod_{p}\frac{1}{(1-\frac{1}{p^s})}=\sum_{n\ge1}\frac{1}{n^s}\] But now we have transformed our product into a sum that has been extensively studied and is a function in itself: \[\zeta(s)=\sum_{n\ge1}\frac{1}{n^s}\] Behold, the Riemann Zeta Function!! But returning to the previous section where we were trying to evaluate \[\prod_{p}1-\frac{1}{p_i^2}\] we see that this is equal to \[\prod_{p}\Biggl(\frac{1}{1-\frac{1}{p_i^2}}\Biggl)^{-1}=\Biggl(\prod_{p}\frac{1}{1-\frac{1}{p_i^2}}\Biggl)^{-1}=\Biggl(\sum_{n\ge0}\frac{1}{n^2}\Biggr)^{-1}=\frac{1}{\zeta(2)}\] So now we just need to evaluate the crazy expression \[\frac{1}{\zeta(2)}\] This is actually a rather famous problem in mathematics known as the Basel Problem that has been solved in many ways. In the next section, we look at a cool solution by Tom Apostol to the Basel Problem to get the final numerical answer to our problem.

A cool conclusion to our problem– Apostol’s Solution to the Basel Problem

Quick note before showing Apostol’s Solution. There are MANY approaches to the Basel Problem, all thought up by brilliant mathematicians. I chose to demonstrate this one because it uses nothing but elementary calculus and the simplification process is something I can imagine a normal human being doing. For people who have seen other solutions, Euler’s is much simpler, but it would require almost prophetic foresight to see the link between Taylor Polynomials and the Basel function (prophetic foresight that Euler somehow had). Then there’s the very simple Fourier Series solution, but that’s not taught in high schools and I don’t want to exclude half of this post’s potential readers. So we’re gonna be looking at a double integral solution :) Apostol starts by considering the integral \[\int_{0}^{1}\int_{0}^{1}\frac{1}{1-xy}\,dx\, dy\] He shows that this is equivalent to $\zeta(2)$ because, due to our earlier power series identity, \[\begin{aligned} &\int_{0}^{1}\int_{0}^{1}\frac{1}{1-xy}\,dx\,dy=\int_{0}^{1}\int_{0}^{1}\sum_{n\ge0}(xy)^n\,dx\,dy=\sum_{n\ge0}\int_{0}^{1}x^n\int_{0}^{1}y^n\,dy\,dx\\ &=\sum_{n\ge0}\frac{1}{n+1}\int_{0}^{1}x^n\,dy=\sum_{n\ge0}\frac{1}{(n+1)^2}=\zeta(2) \end{aligned}\] Now Apostol shows an alternative way of evaluating this integral. He begins by making the change of variables \[x=\frac{u-v}{\sqrt{2}}\] \[y=\frac{u+v}{\sqrt{2}}\] so that we can now write \[1-xy=1-\frac{u-v}{\sqrt{2}}\frac{u+v}{\sqrt{2}}=1-\frac{u^2-v^2}{2}=\frac{2-u^2+v^2}{2}\] The reason for this change of variables now quickly becomes apparent, as Apostol continues by considering the region of integration in the u-v plane. Writing $u$ and $v$ in terms of $x$ and $y$, we obtain \[u=\frac{\sqrt{2}}{2}(x+y)\] and \[u=\frac{\sqrt{2}}{2}(y-x)\] So that the following $x,y$ points correspond to these $u,v$ points \[(x,y)=(0,0)=>(u,v)=(0,0)\] \[(x,y)=(0,1)=>(u,v)=\biggl(\frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\biggr)\] \[(x,y)=(1,1)=>(u,v)=(\sqrt{2},0)\] \[(x,y)=(1,0)=>(u,v)=\biggl(\frac{\sqrt{2}}{2},\frac{-\sqrt{2}}{2}\biggr)\] Now with these points in mind, we can draw the region of integration as a square in the u-v plane, allowing us to observe some interesting properties.

Notice that this square is symmetric about the u-axis. This is a consequence of the fact that $u^2=(-u)^2$. We can exploit this symmetry to now separate the top half into 2 parts– the part with $u<\frac{\sqrt{2}}{2}$ and the part with $u>\frac{\sqrt{2}}{2}$– and multiply that by two to get the entire integral. Using our expression for 1-xy, we have \[\begin{aligned} &\int_{0}^{1}\int_{0}^{1}\frac{1}{1-xy}\,dx\,dy=2\int_{0}^{\frac{\sqrt{2}}{2}}\int_{0}^{u}\frac{2\,dv}{2-u^2+v^2}\,du+2\int_{\frac{\sqrt{2}}{2}}^{\sqrt{2}}\int_{0}^{\sqrt{2}-u}\frac{2\,dv}{2-u^2+v^2}\,du\\ &=4\int_{0}^{\frac{\sqrt{2}}{2}}\int_{0}^{u}\frac{\,dv}{2-u^2+v^2}\,du+4\int_{\frac{\sqrt{2}}{2}}^{\sqrt{2}}\int_{0}^{\sqrt{2}-u}\frac{\,dv}{2-u^2+v^2}\,du \end{aligned}\] Aha, now these are integrals that we know how to evaluate (at least kind of). For the sake of not making this 10 pages, I’m going to assume knowledge of the fact that \[\frac{d}{\,dx}\arctan (x)=\frac{1}{x^2+1}\] and let the reader prove for themselves that \[\label{eq:int1} \int_{0}^{x}\frac{dt}{a^2+t^2}=\frac{1}{a}\arctan\biggl(\frac{x}{a}\biggr)\] by using integration by parts. This allows us to eliminate the inner integral \[\begin{aligned} & 4\int_{0}^{\frac{\sqrt{2}}{2}}\int_{0}^{u}\frac{\,dv}{2-u^2+v^2}\,du+4\int_{\frac{\sqrt{2}}{2}}^{\sqrt{2}}\int_{0}^{\sqrt{2}-u}\frac{\,dv}{2-u^2+v^2}\,du \\&=4\int_{0}^{\frac{\sqrt{2}}{2}}\frac{1}{\sqrt{2-u^2}}\arctan\Biggl(\frac{u}{\sqrt{2-u^2}}\Biggr)\,du+4\int_{\frac{\sqrt{2}}{2}}^{\sqrt{2}}\frac{1}{\sqrt{2-u^2}}\arctan\Biggl(\frac{\sqrt{2}-u}{\sqrt{2-u^2}}\Biggr)\,du\\&=I_1+I_2 \end{aligned}\] where $I_1$ and $I_2$ are defined as a normal human being defines them. Now Apostol makes another masterful u-substitution, writing $u=\sqrt{2}\sin{\theta}$ in $I_1$, so that \[du=\sqrt{2}\cos{\theta}\,d\theta=\sqrt{2-u^2}\,d\theta\] because \[\sqrt{2-u^2}=\sqrt{2-2\sin^2{\theta}}=\sqrt{2(1-\sin^2{\theta})}=\sqrt{2\cos^2{\theta}}=\sqrt{2}\cos{\theta}\] by the Pythagorean Identity for trig functions. The usefulness of this becomes obvious when we see that \[\frac{\,du}{\sqrt{2-u^2}}=\,d\theta\] And additionally, \[\tan{\theta}=\frac{\sin{\theta}}{\cos{\theta}}=\frac{\sqrt{2}\sin{\theta}}{\sqrt{2}\cos{\theta}}=\frac{u}{\sqrt{2-u^2}}\] The bounds of integration remain simple as well. Solving $\sqrt{2}\sin{\theta}=\frac{\sqrt{2}}{2}$ for $\theta$, we find $\theta=\arcsin\bigl(\frac{1}{2}\bigr)=\frac{\pi}{6}$ And of course, if $\sqrt{2}\sin{\theta}=0$, then $\theta=0$ Wow, quite a substitution! Evaluating the first half of this integral is trivial now. \[\begin{aligned} &I_1=4\int_{0}^{\frac{\sqrt{2}}{2}}\frac{\,du}{\sqrt{2-u^2}}\arctan\Biggl(\frac{u}{\sqrt{2-u^2}}\Biggr)=4\int_{0}^{\frac{\pi}{6}}\arctan(\tan(\theta))\,d\theta=4\int_{0}^{\frac{\pi}{6}}\theta\,d\theta\\ &=4\Biggl(\frac{\pi}{6}\Biggr)^2\frac{1}{2}=\frac{\pi^2}{18} \ \end{aligned}\] $I_2$ is evaluated in a similar fashion, letting $u=\sqrt{2}\cos{2\theta}$ so that \[\begin{aligned} &du=-2\sqrt{2}\sin{2\theta}\,d\theta=-2\sqrt{2}\sqrt{1-\cos^2{2\theta}}\,d\theta=-2\sqrt{2}\sqrt{1-\frac{1}{2}\bigl(\sqrt{2}\cos{2\theta}\bigr)^2}\,d\theta\\ &=-2\sqrt{2}\sqrt{1-\frac{u^2}{2}}\,d\theta=-2\sqrt{2-u^2}\,d\theta \end{aligned}\] This substitution also lets us simplify the expression inside the $\arctan$ quite a bit since \[\begin{aligned} \frac{\sqrt{2}-u}{\sqrt{2-u^2}}=\frac{\sqrt{2}(1-\cos{2\theta})}{\sqrt{2-2\cos^2{2\theta}}}=\sqrt{2}\frac{1-\cos{2\theta}}{\sqrt{2(1-\cos^2{2\theta)}}}=\frac{1-\cos{2\theta}}{\sqrt{1-\cos^2{2\theta}}}=\frac{1-\cos{2\theta}}{\sin{2\theta}}=\tan{\theta} \end{aligned}\] where the last simplification follows from some simple trigonometry left as an exercise for the reader. We can also rewrite the bounds of integration similarly to last time since $\cos{0}=1$, so when $u=\sqrt{2}$, $\theta=0$. Similarly, if $u=\frac{\sqrt{2}}{2}$, $\theta=\frac{\pi}{6}$ Before plunging into the integral, let us also note that \[\frac{du}{\sqrt{2-u^2}}=-2\,d\theta\] Then \[\begin{aligned} I_2=4\int_{\frac{\sqrt{2}}{2}}^{\sqrt{2}}\frac{\,du}{\sqrt{2-u^2}}\arctan\Biggl(\frac{\sqrt{2}-u}{\sqrt{2-u^2}}\Biggr)=4\int_{\frac{\pi}{6}}^{0}-2\arctan(\tan(\theta))\,d\theta=8\int_{0}^{\frac{\pi}{6}}\theta\,d\theta=4\biggl(\frac{\pi}{6}\biggr)^2=\frac{\pi^2}{9} \end{aligned}\] If you’re confused about how the order of integration flips, try proving that \[\int_{a}^{b}f(x)\,dx=-\int_{b}^{a}f(x)\,dx\] But then \[\zeta(2)=I_1+I_2=\frac{\pi^2}{18}+\frac{\pi^2}{9}=\frac{3\pi^2}{18}=\frac{\pi^2}{6}\] And thus, going back several sections to our original problem,we see that the density of lattice points visible from the origin is \[\frac{1}{\zeta(2)}=\frac{6}{\pi^2}\]

Matrix Exponentiation for n'th term of Linear recurrence

Mon, 13 Jun 2022 00:00:00 GMT

Matrix Exponentiation for n’th Term of Linear Recurrence

Chancellor Ceti

June 2023

Introduction
Matrix Logic
How to raise matrices to powers FAST
Code and Closing Thoughts

Introduction

A problem that often rises in the domain of competitive programming is, given an integer n, a sequence of numbers $f_0,f_1..,f_{k-1}$, and a sequence of numbers $c_i$ that satisfy \[\sum_{i=1}^{k}c_if_{n-i}=f_n\] finding $f_n$ efficiently. A naive approach to this would be starting at $f_k$ and using the recurrence relation to successively compute all $f_i$ up to $f_n$. This approach clearly runs in linear time, $O(n)$. While this is an acceptable starting point, as $n$ grows, this calculation takes more and more time– we can do better than this. Rest assured, the solution I outline here will run in logarithmic time, $O(k^3\cdot \log_2n)$, by making use of the idea of binary exponentiation. I’ll start by explaining why we need matrices here in Section 2, and then in Section 3, I’ll show how we can make this run in logarithmic time using binary exponentiation. Finally, I’ll show my personal Rust implementation and offer some closing thoughts on this whole process. With that out of the way, let’s start by talking about the matrix part of matrix exponentiation.

Matrix Logic

Note– you need to know what a matrix is and how to multiply two matrices together in order to understand this. If that sounds unfamiliar to you, you should probably brush up on that. If you were awake in your linear algebra class, this should be a walk in the park. We have \[\sum_{i=1}^{k}c_if_{n-i}=f_n\] and are given $f_0,f_1,..,f_{k-1}$. Let’s put the values of $f_i$ that we have into a column vector $F$ such that \[F=\begin{pmatrix}f_0\\f_1\\.\\.\\.\\f_{k-1}\end{pmatrix}\] Now the question is, what can we do to $F$ that would produce \[F'=\begin{pmatrix}f_1\\f_2\\.\\.\\.\\f_k\end{pmatrix}\] Now we introduce the matrix \[T=\begin{pmatrix}0 & 1 & 0 & 0 & . & .\\ 0 & 0 & 1 & 0 & . & .\\ 0 & 0 & 0 & 1 & . & .\\ . & . & . & . & . & .\\ c_k & c_{k-1} & c_{k-2} & . & . & c_1 \end{pmatrix}\] An elementary calculation will confirm that \[T * F = F'= \begin{pmatrix}f_1 \\ f_2 \\ .\\ . \\f_k\end{pmatrix}\] Clearly $T$ bears some relevance to this problem. Upon some further experimentation, we see that, in general, \[T^n*F=F^{(n)}\] where \[F^{(n)}=\begin{pmatrix}f_n\\f_{n+1}\\.\\.\\f_{n+k-1}\end{pmatrix}\] and $T^n$ denotes the multiplication of $T$ with itself $n$ times. The induction proof is here for those who enjoy rigor. If you don’t like strange matrix manipulation, then you can skip ahead to Section 3.

Let’s start with the base case, $n=1$. \[T*F=\begin{pmatrix}1*f_1\\1*f_2\\.\\.\\c_kf_0+c_{k-1}f_1+\cdots+c_1f_{k-1}\end{pmatrix}=\begin{pmatrix}f_1\\f_2\\.\\.\\f_k \end{pmatrix}\] due to the definition of matrix multiplication and the recurrence definition of $f_k$. So the base case is clearly true, showing $T^1*F=F'$. Now assume that $T^n*F=F^{(n)}$ for any n. Then \[T^{n+1}*F=\begin{pmatrix}f_n\\f_{n+1}\\.\\.\\f_{n+k-1}\end{pmatrix}*\begin{pmatrix}0 & 1 & 0 & 0 & . & .\\ 0 & 0 & 1 & 0 & . & .\\ 0 & 0 & 0 & 1 & . & .\\ . & . & . & . & . & .\\ c_k & c_{k-1} & c_{k-2} & . & . & c_1 \end{pmatrix}=\begin{pmatrix}f_{n+1}\\f_{n+2}\\.\\.\\f_{n+k}\end{pmatrix}\] by the same definitions as before. So clearly the hypothesis is true, and $T^n*F=F^{(n)}$.

Great, we now know that $f_n$ is just the first entry in the vector $F^{(n)}=T^n*F$. Now we come to the question of how to compute this in logarithmic time– enter binary exponentiation!

How to raise matrices to powers FAST

Binary exponentiation, as the name suggests, utilizes the binary representation of the exponent you are raising a base to. Naive exponentiation, running in linear time, would utilize the fact that \[T^n=\prod_{i=1}^{n}T\] and multiply $T$ by itself $n$ times for $O(n)$ running time(note: the empty product is equal to $1$). This, however, is not optimal. The following definition of $T^n$ can be verified by simple arithmetic. \[T^n=\begin{cases} 1 &\text{if } n==0\\ (T^{\frac{n}{2}})^2 &\text{if } n>0 \text{ and } n \text{ even} \\ (T^{\frac{n-1}{2}})^2*T &\text{if } n>0 \text{ and }n \text{ odd} \end{cases}\] This suggests an algorithm of the form

function pow(t:matrix, n:int)->matrix
    if n==0
        return I
    res = pow(t,floor(n/2))
    if n%2==0
        return res*res
    else
        return res*res*t

where I is the identity matrix. We can do away with the messy recursion by writing the equivalent

function pow(t:int,n:int)
    res = I
    while n>0
        if n%2==1
            res = res*t
        t = t*t
        n/=2
    return res

since $I*T=T$. This is $O(\log_2n)$ time complexity since it has as many iterations as it takes to reduce $n$ to $1$ by dividing by $2$, which is the nature of a logarithmic function. So, armed, with binary exponentiation, let’s see what a proper implementation of this looks like!

Code and Closing Thoughts

A decent implementation of the algorithm described below is given here, written in Rust. The modulo parameter in my functions is a trivial extension to the original concept designed to meet certain problem constraints. All in all, this runs in $O(k^3*\log_2n)$ time because matrix multiplication is not a constant time operation– there’s three nested loops, with time dependent on $k$, in the

matrix_mult

function. This can definitely be optimized further, but for almost all purposes, this will be perfectly fine performance. If anyone finds a mistake in any of this or a cool optimization, please contact me on Discord at

floofydoggo

or email me at chancellorceti@gmail.com And now, finally the long-awaited code!

fn matrix_mult(
    a: Vec<Vec<i128>>,
    b: Vec<Vec<i128>>,
    modulo: i128
    )-> Vec<Vec<i128>> {
    let mut res: Vec<Vec<i128>> = vec![vec![0; b[0].len()];
    a.len()];
    for i in 0..a.len() {
        for j in 0..b[0].len() {
            for k in 0..a.len() {
                res[i][j] += a[i][k] * b[k][j];
            }
            res[i][j] %= modulo;
        }
    }
    res
}
fn matrix_pow(
    m: Vec<Vec<i128>>,
    n: i128,
    modulo: i128
)-> Vec<Vec<i128>> {
    let mut base = m.clone();
    let mut res: Vec<Vec<i128>> = vec![vec![];m.len()];
    for i in 0..res.len(){
        let mut row:Vec<i128> = vec![0;res.len()];
        row[i]=1;
        res[i]=row;
    }
    let mut nc = n.clone();
    while nc > 0 {
        if nc % 2 == 1 {
            res = matrix_mult(
                res,
                base.clone(),
                modulo.clone()
            );
            nc -= 1;
        }
        base = matrix_mult(
            base.clone(),
            base.clone(),
            modulo
        );
        nc /= 2;
    }
    res
}
pub fn nth_term(
    coeffs: Vec<i128>,
    init: Vec<i128>,
    n: i128,
    modulo: i128
    ) -> i128 {
    let k = coeffs.len();
    let mut t: Vec<Vec<i128>> = vec![vec![]; k];
    for i in 0..k - 1 {
        let mut row: Vec<i128> = vec![0; k];
        row[i + 1] = 1;
        t[i] = row;
    }
    t[k - 1] = coeffs.into_iter().rev().collect();
    let t_pow = matrix_pow(t, n, modulo);
    let mut init_matrix: Vec<Vec<i128>> =
        vec![vec![]; init.len()];
    for i in 0..init.len() {
        init_matrix[i] = vec![init[i]];
    }
    let res_matrix = matrix_mult(
        t_pow,
        init_matrix,
        modulo
        );
    res_matrix[0][0]
}

Some Moral Quandaries on What Constitutes Justified and Productive Forms of Protest

Thu, 11 Jun 2026 00:00:00 GMT

Some Moral Quandaries on What Constitutes Justified and Productive Forms of Protest

Note before starting – as with my ‘crash course on preventive detention in India,’ this post wasn’t originally written for the blog. Rather, it was a series of messages I sent over Discord when monologuing late at night three months back and nobody was responding, allowing me to start entering a great rambling flow state. I’ve pasted my Discord rambling over here with almost zero editing because a) editing would take a lot of effort b) it’s readable and interesting as is. Also, for this kind of writing, I like the current format more than a structured essay style, since I’m not presenting a cohesive argument and am instead creating a list of questions and leaving the reader to mull over the answers. Hopefully some of these questions will seem to you as interesting as I found them.

Also, disclaimer, posing a question about a form of protest does not constitute an endorsement of it – this is purely philosophical (read: not glorifying or endorsing self-harm as a form of protest). I wish this disclaimer wasn’t necessary, but nowadays you have to be very careful when talking about mental health-related topics or else you’ll get crucified online…

Now on with the actual post.

Odd question

what do you guys think of self-harm as a form of political protest?

at the moment I am against in all but the most extreme cases It’s a horrible thing for political activism to take lives in such brutal ways, but at the same time, one can’t deny its success; and in cases where the self-harm is in protest of something taking even more lives, I can’t help but wonder if there’s net good being done

Also, are such acts a sign of mental illness?

The self-immolations protesting Mandal Commission implementation strike me as having been excessive, as do the suicides in protest of attempts at imposing Hindi in southern India. But self-immolations of Tibetans protesting Chinese rule, or the famous Cambodian buddhist self-immolation that actually ended up influencing JFK’s decision to stop backing Ngo Dinh Diem – in cases of such desperation, with so many lives at stake, did these suicides make sense?

It’s an interesting question

Self-immolation has played a large part in shaping our world today and will likely continue to stay relevant

I suppose this is also related to the larger debate about the right to die

possibly one of those questions we’ll never have a satisfactory answer to

self-immolation is such a tragic thing, I feel really depressed thinking about how common it has been as a form of protest

why did the world have to be so dark that people felt driven towards it?

the people who survive self-immolation attempts lead a shell of a life afterwards

sorry

this was likely too dark of a question

the whole topic is interesting though – what constitutes an effective, moral (does such a thing exist?) act of protest

The gherao in India is especially controversial because it blurs the line between constructive civil disobedience and just harassment & coercion

and then the whole ‘self-harm as protest’ is a disturbingly common thing in India

Gandhi literally helped create the nation with it – hunger strikes are self-harm, even though many Indians don’t like thinking in those terms

then there’s the industrialists’ strikes in 1970s Chile – this is interesting because

you might disagree with their reason for striking (opposition to Allende govt), but in a democratic society, they have the right to strike, just as much as any worker
but there’s also an argument that it shouldn’t have been allowed, considering the damage this did to the economy and the destabilization of Allende’s government +the potential catastrophe (thankfully averted) resulting from halting the distribution of food, medicine, etc

Strikes, in general, raise a lot of questions about morality imo

The 1970s Chilean strikes are doubly interesting because of the additional question of “does the right to strike apply to employers as well as employees, if employers somehow end up feeling like the wronged party?”

the 1970s Chilean strikes trigger an instinctive reaction of disgust since they undermined a democratically elected regime and aided the eventual military coup, but speaking in terms of ‘right to strike,’ it’s an interesting conundrum

Then there’s the question of whether it’s justified to force a state assembly to dissolve using mass protest – this was done in Gujarat during the Navnirman Andolan and then attempted in Bihar during the JP movement

They were fighting corruption and misrule, but even with noble intentions, is it okay to bypass democratic processes and coerce democratically elected representatives into resigning?

Then there’s the issue of “how much disruption of day-to-day life is too much?” – blocking roads puts pressure on corrupt and/or authoritarian governments but also disrupts day-to-day life, the economy, and essential services like ambulances and fire trucks

then there’s the issue of ‘what level of corruption of democracy is enough to justify armed rebellion?’ – many people agree that armed rebellion is acceptable against a dictatorship without elections, but if there’s a democracy in name but that doesn’t really function bc of voter coercion and arresting opposition leaders, is armed rebellion justified?

This ‘armed rebellion in a deeply flawed democracy’ route was pursued by JKLF in J&K after 1987 rigged state assembly elections – JKLF and the Kashmir militancy turned into a senseless slaughter of civilians after the whole thing turned into another war of jihad, but in an alternate history where Kashmiris opted for resistance targeting military sites instead of civilians and focused on democratic reform rather than jihad, would that alternate approach have been justified?

I am inclined to say “no, it isnt justified” to this one, primarily because a “yes” would imply that it’d be fine for around half the world to erupt into civil war 💀

but what degree of electoral malpractice and suppression of dissent is enough to justify armed rebellion?

the US gave up on peaceful resistance pretty quickly – Indians were willing to take more bullets when fighting the British, without abandoning non-violence. Would India have been justified in picking up guns against the British, given the violence employed against Indian civilians?

Far less people died in America as a result of British suppression of dissent than did in India, which makes this an even more interesting question

anyway

mull those over if you want ig

i love how nowadays we’re somehow stuck debating stuff that i wish we could all agree on; somehow we disagree on “should we vaccinate our kids against deadly diseases” and “should we impose 200% tariffs on other countries b/c of trade deficits,” and we have to debate that instead of turning to topics with just a tad bit more complexity 💀

also in the realm of protests – we’re somehow divided over the question ‘should we vandalize paintings with soup to protest climate change?’ as if this is somehow a meaningful or constructive way of changing the status quo

if we can’t reach a sensible conclusion on these issues that are, in my opinion, pretty black-and-white, i wonder if we’ll ever get to debating these more grey-area issues 💀

also, does anyone else find it bizarre that in 12 years of education we’re never asked to consider these ^ questions?

ah well

time to sleep

How Park Chan-wook’s 'No Other Choice' Creates a Devastating Picture of Korean Capitalism and Its Brutality

Tue, 20 Jan 2026 00:00:00 GMT

How Park Chan-wook’s “No Other Choice” Creates a Devastating Picture of Korean Capitalism and Its Brutality

Warning in advance: this review has spoilers for every part of the movie. It’s also a rambling, unstructured dump of my thoughts on the film, rather than a coherent film review or academic paper analyzing the movie. Thou hast been forewarned!

To begin, a sampler of the movie’s paper humor, because Park Chan-wook somehow made paper the funniest thing in the world.

“Remember what you said? A-ra, your lips are softer than the highest quality Okamoto tracing paper.”

“Akimoto. Okamoto is a condom brand.”

“A-ra, your lips are softer than the highest quality Akimoto tracing paper.”

I never thought this many paper jokes could be made until I saw this movie – quite impressive.

But paper humor aside, “No Other Choice” is an incredible synthesis of probing the darkest depths of the human soul, criticizing capitalism on many fronts, and blending all this darkness with an abundance of paper jokes. As with all of Park Chan-wook’s films, this one is layered and full of symbolism, making it a delight to think about long after having watched it – which is why I’ve written this post to lay out some of my main thoughts on it.

I think this film is especially remarkable because it takes the ‘capitalism critique’ genre further than Parasite or similar movies have. “No Other Choice” explores the illusory nature of job security, the dehumanization of human beings in the age of acquisitions and automation, and the desperation of people on the losing end of this economic system.

The Transformation of Man-su

The start of the film created an idyllic imagination of a middle-class Korean family: happy marriage, two kids, two adorable dogs, beautiful house, and a weekend barbecue on a gorgeous summer day. Even as I was watching this, I was predicting it wouldn’t last long – Park Chan-wook’s imagination is too dark for anything so cheerful to last. And I was soon proven right. Shortly after this opening scene, Man-su’s employer, Solar Paper, is bought by an American company, leading to the layoff of Man-su and many of his colleagues.

Man-su’s idyllic life quickly collapses after this. His confidence is wiped out after he realizes that 25 years of service to one company has earned him no kind of job security, and he begins to fail job interviews with comical awkwardness. Man-su’s family is forced to cut back on expenses, downgrading to a cheaper car, sending their two dogs away to Man-su’s in-laws, and putting their house up for sale.

These material losses are accompanied by a breakdown of the warm familial ties seen at the start. Man-su’s daughter Ri-one, who was already antisocial, withdrew even further after the loss of the dogs because of her deep attachment to them. Man-su senses his wife’s growing disappointment with his unemployment and begins suspecting her of infidelity as a result of the growing divide between them. And his son, Si-one, is eventually drawn into crime, thinking that stealing iPhones might bring some more money to his desperate family.

All these factors drive Man-su to the desperation that makes him decide he has “no other choice” but to kill his top job competition. However, the depth of this movie lies exactly in its title – did Man-su really have no other choice? The movie reflects the sinister way in which Korean capitalism drives people against each other, forcing the working class to claw at each other rather than uniting against the bourgeoisie who are the true source of their problems. Man-su had plenty of other choices. He could’ve continued struggling to get a job without resorting to murder, as most sane people would do; he had the choice of leaving the paper industry and trying his luck elsewhere; when carrying out the final murder, he could’ve trusted that Seon-chul would recommend that Moon Paper hire Man-su as a second manager, rather than murdering Seon-chul to take his place. Instead, the desperation caused by unemployment made Man-su feel like he was cornered and had ‘no other choice’ than carrying out these murders. The film brilliantly portrays how the competitive nature of capitalism pits people against each other, even if they should be logically united by a common struggle.

Man-su’s character starts out with a belief in camaraderie among paper men, saying “even a sheet of paper is better lifted together.” Before being laid off, he tried talking to one of the new American owners to plead for his coworkers’ jobs, never suspecting that his own job was at risk as well. However, once Man-su is the one without a job, this humanity evaporates, and he’s suddenly willing to kill his fellow paper men for a better chance at feeding his own family. This transformation is one of the most powerful themes of the movie: how capitalism causes camaraderie and basic humanity to evaporate into a ruthless dog-eat-dog world.

Of course, this is a concept most people are already familiar with; the power of Park Chan-wook’s movie is that he makes it sink in at an emotional level. Man-su’s character visibly changes throughout the film, starting out clumsy and indecisive with the murders and slowly becoming more comfortable with killing. His first abortive murder attempt with the flowering pots turns comical when he can’t decide which pot to use, struggles to lift them, and is then seen by the lady who owns the pots. When he then gets serious and sets out to kill Beom-mo with a gun, his first attempt there is foiled by a snakebite, unfolding into even more comedy as Beom-mo’s wife then starts trying to suck the poison out of the wound while Man-su struggles to video-call his wife without her seeing what’s happening. His second attempt on Beom-mo’s life is even funnier and is one of the most memorable scenes from the film (not summarizing because it’s just too much funniness).

The second and third killings, in contrast, have a more sinister quality to them. The second killing is less drawn out and feels more abrupt, with none of the comedic effects inserted anymore. The camera shot also creates a darker mood during it, with the turbulent waves crashing onto the rocky shore on one side of the shot, and the murder scene on the other side, the two separated by the jagged cliffs in between – again, Park Chan-wook’s filmmaking genius at its peak. This marks a turning point; while Man-su was still clumsy, this killing was nowhere near as chaotic as the first, and marked Man-su’s growing comfort with murder as a means of gaining employment.

The final killing is the most brutal, as Man-su sees that he actually does have other choices; at one point, he tries getting Seon-chul to recommend him as a second manager rather than killing him and taking his place. However, Man-su is now too far in, remarking that stopping here would make the deaths of the first two meaningless. This, however, is a poor rationalization for the third killing; the Man-su shown at the start of the film would have trusted his fellow paper man’s promise of a recommendation and immediately dropped the idea of murder. The new Man-su, however, has been turned into a monster by the competitive nature of capitalism, and he no longer trusts his fellow workers, seeing Seon-chul’s death as the only surefire way of getting a job. The loss of Man-su’s morality is terrifyingly captured by this ability to crudely rationalize murder as ‘necessary’ despite the true motive being self-interest. The inhuman way Man-su kills Seon-chul (wrapping him in plastic, burying him, and then choking him on his own vomit) completes this characterization of Man-su as a much crueler man than the version shown at the start.

The conclusion of the film is when Man-su’s murders finally make him the most qualified candidate by a literal ‘process of elimination.’ It’s frightening to see how much Man-su has changed by this point. I was especially moved by the following exchange between Man-su and his new employers at Moon Paper.

Man-su: When you say fully automated, the workers… will have to be reduced, right?

Moon Paper: That’s the whole point of the system. No other choice. Do you have any objection? If you don’t like it, you can say no.

Man-su: Not at all. How can you go against the times? But at any rate, you need one person to watch over it all, right?

At the beginning of the film, Man-su risks his own career to campaign against Solar Paper’s mass layoffs. At the end, however, he sees mass layoffs as another situation in which there is ‘no other choice,’ and he crudely rationalizes this cruelty with the argument of “how can you go against the times?” The things that originally made Man-su’s character endearing have all disappeared; the coldness of the capitalist system has turned Man-su into a killer, who sees the corporate layoffs in the same way he views his murders – “no other choice.” Rather than question the inhumanity of the system governing his life, he allows it to completely transform him into this perverse idea of the ‘perfect employee’: subservient to his bosses, ready to do anything to be ‘King Rat’ in the capitalist world, unquestioning of the cruelty he lives in and actively aids.

This steady progression of Man-su’s character builds a powerful portrayal of how capitalism has built a dog-eat-dog world in which good-hearted men turn cruel, in hopes of beating their co-sufferers in the giant rat race that we call the job market. The film goes beyond describing the system as cruel, however, and also highlights the pointlessness of it. “No Other Choice” brilliantly portrays how even the putative winners in the capitalist system are not truly happy.

The pointlessness of this rat race is conveyed through the final scenes of the film. Man-su gets his dogs back, making his daughter happy enough to begin playing the cello for her family again. However, this beautiful, human moment of family connection is lost on Man-su; he’s stuck in a traffic jam, on his way to the job he killed three people to get. The viewer is left wondering what kind of amazing work experience might be worth such a path of violence – turns out, three people’s lives weren’t worth too much for Man-su. The new paper factory is fully automated, leaving Man-su to mindlessly watch over a bunch of machines, completely alone in a massive factory where humans are no longer needed except for “one person to watch over it all.” All the things he mentioned loving about his work– drinks with colleagues, the feeling of touching paper, the sense of accomplishment– have been erased by the power of automation. Man-su is given a pyrrhic victory where he doesn’t really even win, becoming “King of Turd Island” where he gets a salary but is deprived of all the human aspects that made his job fun. To my mind, the worst part of Man-su’s transformation isn’t even the readiness to kill, but rather the fact that he sees this outcome as a victory. The old Man-su would’ve hated this new paper factory, but this transformed version sees the soulless factory as a good reason for having killed three people.

The satisfaction of his work life has vanished, but his family life is also different now. His wife is colder towards him now, accepting the murders to keep their family together but no longer able to see Man-su as the same man. She counts down when they hug and no longer presents the same warmth towards him. The loss of Man-su’s humanity has driven a wedge between him and his family – he’s no longer the same man they loved at the movie’s start. While the family stays together, there’s now more emotional distance.

Symbolism and Motifs

The representation of these complex themes is aided by Park Chan-wook’s talent for symbolism and motifs. I’m terrible at this kind of analysis, but I think I did pick up on a few intentionally placed motifs. Man-su is plagued by a toothache throughout the movie, particularly flaring up when he’s plotting his murders, and he finally removes this troublesome tooth when he gets drunk to prepare himself for the final murder. This rotten tooth is symbolic of Man-su’s corrupted morality; it troubles him throughout the film as he executes the murders, but when he finally drowns what’s left of his moral compass in alcohol, this rotting morality is violently removed with a pair of pliers. The rotting tooth is a powerful symbol of Man-su’s moral decay and how he eventually resorted to violently ripping out what was left of his moral compass in order to continue his quest to be ‘King Rat’ in the capitalist world.

Also interesting is the symbolism of Man-su’s love for plants. He dedicates himself to caring for plants in his greenhouse at the start of the film, but he slowly stops using the greenhouse for gardening and converts it into a place to plot murders. After failing a job interview, he vented his frustration on a bonsai tree he used to love, cruelly breaking its branches with thick wires; his love has been replaced by violence and anger. This motif is continued when Man-su tries killing Seon-chul by dropping a potted plant on his head – again, his love for plants is transformed into a drive to kill. I speculate that the plants in this film are yet another symbol of Man-su’s original kindness, slowly being replaced with cruelty as Man-su loses his moral grounding. This interpretation is further supported by Man-su hiding a dead body by planting an apple tree over it; a superficial kindness now conceals a dark and violent soul.

Subtle details in the film tie together to enhance Park Chan-wook’s critique of capitalism and the culture it has created. When Man-su is planning the first murder, he sadly notices that Beom-mo’s pear tree is being eaten by bugs; at the end of the film, Man-su’s apple tree is just as neglected and being eaten by bugs, and his daughter Ri-one is the only person who notices it. Ri-one symbolizes the goodness and morality of children, their humanity still uncorrupted by the ravages of capitalism and the dog-eat-dog world; just as her cello music is the only human thing left at the end of the film, so too is she the only one to notice the apple tree’s plight.

This motif is taken even further during the credits where automated deforestation takes place in the service of the paper factories. It’s a contradiction of enormous proportions for Man-su, a plant lover, to work in a paper factory whose entire existence relies on the destruction of forests. Man-su’s ability to ignore this contradiction reflects how he, and everyone else living in the capitalist world, is forced to turn off certain parts of their morality in order to cope with the violence of the system they serve. If you pay too much attention to the contradictions within the system and the cruelty of it, the realization would destroy you.

The Culture Surrounding Korean Capitalism

Ri-one’s character is also interesting; almost all her lines are mimicry of the adults and the harshest things they’ve said or done. She is a foil to the adults’ inhumanity, representing the innate goodness of children before their corruption by the dog-eat-dog world’s pressure. Ri-one parrots her mother’s angry outbursts to Man-su, giving a look into their collapsing marriage, and throughout the movie also repeats her parents’ heartbreaking announcement that the dogs will be sent away, “in these circumstances, we can’t afford to feed so many mouths.” Ri-one’s character offers a look into the chaos and violence of the adults’ lives but contrasts it with her own innocence and goodness; her cello music at the end of the film is the only positive aspect of the scene Man-su has created, standing in stark contrast to his Kafkaesque shuffling between the traffic jam and the automated factory. As noted before, she was also the only person in the family to notice the bugs eating Man-su’s apple tree, marking how she still retains the humanity that Man-su has lost.

The cello music itself reveals another contrast between Ri-one and her parents. While Ri-one loves the music for its beauty, her parents view it in a utilitarian manner, repeatedly remarking how “without music she’ll never be independent.” While her parents also appreciate the music’s beauty at some level, this human motive is subsumed by their desire for Ri-one to be successful within the capitalist world.

These many contrasts between Ri-one and her parents highlight the way that the adults have been transformed by their experience living under capitalism. They no longer have the innocence to spend their whole day appreciating the beauty of music; financial hardship and the pressure of the dog-eat-dog world force Man-su and his wife Mi-ri to always be thinking about how music can help their daughter succeed in this nightmarish system. Ri-one’s kindness toward the tree and her gentle nature reflect what Man-su used to be before desperation drove him to bury his conscience. The writing of this character contributes significantly to Park Chan-wook’s critique of capitalism and how it drives people to lose the kindness and innocence that children are born with.

This idea of innocence being robbed by societal pressure is expanded upon throughout the movie. When Man-su goes to kill Beom-mo, the long comedic sequence has a flashback that shows Beom-mo and his wife A-ra when they were young and first fell in love. These are completely different people from the sad couple shown in the present day; they were young, excited by their work, and in love with each other. In the present day where Man-su is about to kill Beom-mo, Beom-mo has turned into an alcoholic after being laid off, A-ra is cheating on him, and both have lost whatever idealism and romance once brought them together, ultimately culminating in A-ra shooting Beom-mo in a fit of rage over the disappointment of their marriage. The flashback highlights this contrast and shows how Korean capitalism extinguishes the flame of idealism and romance that exists within young people; in Beom-mo’s life, hope and love are destroyed by layoffs and the devastation that follows them.

The central theme of this movie, ‘no other choice,’ also offers an interesting perspective on how capitalism is shaping South Korean culture. Man-su repeatedly justifies his cruelty by claiming he has ‘no other choice,’ but the very title of the movie drives viewers to question whether that is true. There’s a cognitive dissonance between Man-su’s justification of his actions and the actual multitude of ‘choices’ he has to rescue himself without resorting to murder. His wife suggested selling the house and moving to a small apartment to cut costs, but he is appalled by this proposition. Every cost-cutting maneuver is felt by Man-su’s family as a punishment; when listing in order of importance the sacrifices he’s made because of unemployment, Man-su sees Netflix coming right after putting up their house for sale

Listen, please. My wife is doing part time work, we put our home up for sale, canceled Netflix…

What?

Attachment to one’s ancestral home is human, but Man-su and his family also exhibit an attachment to luxuries like Netflix, tennis lessons, $50,000 cellos, and fancy cars. The loss of these luxuries corresponds to a loss of social status for Man-su; he feels like less of a man because he can not afford these things, and in his mind, this creates a heightened sense of catastrophe and desperation. While in therapy for unemployed people, Man-su chants “I’m a man, I’m a good person” as if he needs help believing it. Korean capitalism has turned fancy cars and big homes into status symbols that determine how much of a man someone is; Man-su’s unemployment doesn’t just worsen his material condition but also constitutes a kind of emasculation for him, creating a sense of desperation that wouldn’t otherwise exist.

This sense of emasculation is exacerbated by the fact his wife is now the primary earner in the family. This is frequently a cause of embarrassment for men with a macho complex, and it’s shown throughout the movie that Man-su resents this reversal of roles. He shows hostility towards Mi-ri’s boss, suspecting him of trying to seduce Mi-ri, and seeks any excuse available to think poorly of his wife’s job. When his car stalls in front of Mi-ri’s boss, he grumbles under his breath about how embarrassing it is. While psychoanalysis is always a sketchy field, there’s reasonable evidence to think that Mi-ri becoming the primary bread-winner added to Man-su’s sense of emasculation.

Another factor contributing to Man-su’s sense of being less ‘manly’ is that Man-su can only find part-time, degrading work. When working in the grocery store, after finishing his shift, his work clothes are taken away, leaving him in only his underwear, a stark contrast to the dignified uniform he always wore at Solar Paper; the loss of his cushy job forced Man-su to take up work that treated him with less dignity and made him feel even less like a man. In this scene where Man-su is left in his underwear, he trudges off to change with a gait that indicates a sense of humiliation and shame. Man-su’s obsession with needing to confirm “I’m a man, I’m a good person” reflects how his desperation didn’t result so much from material circumstances as it did from a sense of emasculation and personal failure, driven by absurd societal standards and an unhealthy conception of masculinity. Unemployed people don’t naturally tend to start murdering people; Man-su is driven by a deeper problem of feeling that he is less of a man because of his unemployment and loss of social status.

“No Other Choice” is also effective at highlighting the issue of dog-eat-dog culture. As I discussed earlier in this post, Man-su gradually transitioned from seeing other paper men as comrades, to seeing them as obstacles to securing employment in a competitive job market, providing an effective critique of dog-eat-dog culture. However, the film also portrays this issue by highlighting the similarities between Man-su and his victims; Man-su has an especially difficult time killing them because they’re people he would ordinarily have regarded as fellow paper men, and as he carries out the murders, he is painfully aware of all the things he has in common with his victims. When killing Beom-mo, he bonds with him over their shared love for paper and their common struggle with unemployment, highlighting the cruelty of a system that pushes people who would ordinarily be friends to instead fight against each other. In Man-su and Beom-mo’s dramatic confrontation, Man-su exasperatedly asks Beom-mo why he didn’t listen to his wife and sell their home or seek work outside of the paper industry – ironically, Man-su received the same suggestions from his wife and ignored them as well, with the same motives as Beom-mo. The similarities between Man-su and Beom-mo make it obvious the two would’ve been friends if not for the dog-eat-dog nature of capitalism and the cruelty to which it drove Man-su, and this tragedy highlights a systemic issue of the capitalist system as it exists today.

Similar scenes take place when Man-su goes to kill Si-jo and Seon-chul. He briefly bonds with Si-jo, literally calling him an “unemployed comrade” and connecting again over their shared struggle, only to use this connection and the corresponding trust as a way to deceive Si-jo and eliminate him – just another tragic consequence of the dog-eat-dog world and the drive to out-compete one’s own friends. All of Man-su’s victims are people he would’ve ordinarily been good friends with; it is only because of dog-eat-dog capitalism that Man-su is forced to treat these people as his enemies and ruthlessly kill them. The highlighting of similarities between Man-su and his victims is a clever way Park Chan-wook criticizes the culture surrounding capitalism, a culture that divides people who would otherwise be driven to unite around common psychographics and a shared struggle.

“No Other Choice” also does a great job of highlighting the insanity of workers showing love and respect towards companies that barely see them as people. The most extreme example is Beom-mo, who shows a hilarious attachment to the paper industry; he doesn’t just thank it for the money he earns but rather credits it with the existence of money itself. Beom-mo has become so obsessed with the paper industry that he sees it as his very identity and believes it truly is the most important thing in the world.

Beom-mo: Paper has fed me for 25 years, honey. It’s how I’m meant to be, I’ve no other choice. You’ve been fed by the money I earned from paper, too. That money was printed on paper I made, and the cigarette filter you smoke is paper, too. If we don’t use paper, who will?

A-ra: What?

This attachment to the paper industry seems ridiculous in light of the brusque way Beom-mo was laid off, and this is precisely what “No Other Choice” tries to highlight. All of these ‘paper men’ have lives that revolve around their employers and how amazing they are, to the point that the very word ‘man’ becomes hyphenated to ‘paper,’ yet their employers barely view them as human beings. This film reflects a global issue of how our work defines our very identity, and how we are expected to love and respect our employers without expecting even a fraction of that respect from the employers themselves.

Finally, I’d like to consider how the title “No Other Choice” sets up the core theme of the movie: how cruelty is rationalized under capitalism with this idea of there being ‘no other choice’, even when there is. Man-su slowly becomes just like his cruel employers at Solar Paper with his use of the ‘no other choice’ line. The employers have a choice to sacrifice some of their profits to show a bit more kindness towards their workers, but since the nature of capitalism disincentivizes such basic humanity, they tell themselves there’s ‘no other choice’ when there is. Man-su had a choice to try cutting back on expenses or seeking a less cushy job, rather than killing people; but again, the desperation of unemployment drives Man-su to justify murder by saying he had ‘no other choice.’ The justification of ‘no other choice’ reflects the drive to turn off one’s brain and ignore the cruelty of capitalism, choosing the easy route of becoming part of the problem rather than taking up the insurmountable task of fighting against it. There are always other choices than cruelty, but saying ‘no other choice’ makes one’s own life easier at the expense of others; in this film, that idea is portrayed as the driving force of Korean capitalism and its brutality.

The movie’s ending depicts an apocalyptic vision of Korean capitalism. Men’s morality is destroyed by the need to compete for jobs, while jobs themselves turn into loneliness and monotony, providing little satisfaction beyond a paycheck; the economy is driven partly by these amoral worker bees, but mostly by automation that removes the human and personal quality of production. Production is contingent on cruelty towards people as well as cruelty towards the planet itself, with a terrifying scene of mechanized deforestation playing out in the final minutes of the film. This is the true face of today’s capitalism.

Concluding Thoughts

I could go on talking about this film for a lot longer. This post mainly focused on analysis, since that provides more scope for content than just fangirling over Park Chan-wook (which I spend a lot of time doing outside my blog), but I also want to appreciate the brilliant execution of this film. The movie had an incredible soundtrack, and I’m now addicted to Red Dragonfly, the song that was playing during the first killing; all of the songs fit well with the moment in the movie at which they were playing, really adding to the experience. The cinematography and editing were beautiful, and I’m especially fond of some of the shots that faded into other shots. The movie did a great job showing the cruelty of mass layoffs; it acknowledges that unemployment is more than just having to look for another job, but that it also leads to a loss of confidence, family trouble, and utter desperation as month after month can go by without new employment being found – as the movie said, ‘to be fired is to be axed.’ The acting was superb, and the script was brilliant – hats off to whoever spent this long coming up with paper jokes, I was laughing for a great part of the movie. Out of sheer admiration for the creativity, here’s another paper joke:

I’m like one of your precious paper machines. Neglect me, and I’ll break! Hurry up and smother me in that lube oil! Or I’ll rip you to pieces, like tracing paper!

The entire movie was brilliant, one of the best I’ve ever seen. Park Chan-wook has created a nightmarish vision of Korean capitalism, one which will be haunting my dreams for many years to come.

An Update on My Life -- Venting, Reading, Films, and Music Dump

Tue, 25 Nov 2025 00:00:00 GMT

An Update on My Life -- Venting, Reading, Films, and Music Dump

An Update on My Life – Venting, Reading, Films, and Music Dump

Since writing math and physics content takes an obscene amount of time and inspiration that I currently lack, I thought I’d write a less serious post for once – this will hopefully also satisfy the people who tell me blog posts shouldn’t take half an hour to read.

So, recent developments – I am almost done with my college applications! The bulk of the writing was in my first wave of applications due December 1st, and I am on the verge of submitting those, so I’m close to the end of my suffering. I’ll likely write something at greater length about the process later on, but I’ll briefly describe my most important complaints.

The writing style that colleges expect is sappy and cringe-inducing. Most of the “exemplar” essays are atrocious, and I would vomit if I ever wrote anything like them. The recommended format makes it impossible to avoid this, since it’s asking kids to write essays of the form “Object X symbolizes my life because launch into overly metaphorical cringe-inducing story of how beautiful your soul is.” Why are we encouraging kids on the cusp of adulthood to write about how their stuffed animals represent different aspects of their personality?? The exemplar essays are overly descriptive of irrelevant details, packed with malfunctioning metaphors, and always cliché, which brings me to point 2….
It’s impossible to avoid being cliché when your essay is one of 1000 that the admissions officer will see, and you’ve received the same advice as the other 999 kids. We’re asked to “find our voice,” but none of us are developed enough as writers that we have a distinctive writing style the way Hemingway or V.S. Naipaul would. Which brings me to point 3…
The last 3 years of high school English classes have done nothing to prepare us for this kind of writing. We have only worked on literary analysis and rhetorical analysis, writing about how authors use metaphors and similes to develop a theme, but we’ve never worked on writing personal statements. This feels like a failure of the high school curriculum that goes beyond college applications, since only 0.1% of students will go into literary analysis… maybe some of this time would’ve been better spent helping kids develop more basic but widely applicable skills?
There’s also the issue of how repetitive the prompts are. There’s a massive amount of overlap between different universities’ prompts, but there’s always just slightly different enough that you can’t copy-paste essays from other prompts. It feels like a huge waste of our time.
The emphasis on extracurricular activities leads to the issue of Linkedin resumé padding. A lot of things sound more impressive on paper than they actually are. A few examples:
- Orchestra social media manager = posted a low-quality Tiktok once every 3 months
- Member of National Honor Society (NHS) = logged 10 hours of volunteering every semester, often through a mix of fudging numbers and forcing oneself to work just to put the “NHS” label on college applications (as admitted by many people I personally know)
- District champion at Python programming UIL = was the fastest at translating pseudocode into Python code when competing against an army of skids (yes this is what the Python programming UIL finals actually were, feel free to laugh)
The use of GPA as a criterion for auto-admission in Texas schools rewards cheating, grade inflation (in AP Physics C, a 40% turns into a 90% through “grade-banding”), and teachers’ favoritism. A large amount of kids with top 6% GPA at my school are cheating on tests, by their own admission. Even if GPA isn’t the deciding factor in admissions, it’s further contributing to the current disaster.
SAT and ACT don’t reflect any kind of intelligence or even competence in math and reading comprehension. The SAT now lets students use Desmos, which allows them to find the solutions to equations without actually doing any math. There can be a debate over whether a test of 7th grade algebra should factor into college admissions, but now the SAT isn’t even testing kids’ knowledge of elementary algebra, let alone more advanced topics.

Well, that’s that. As stressful as exams are, I now feel like a board exam (JEE!!) would lead to a more meritocratic and efficient admissions system than the current quagmire I’m wading through.

Apart from college applications, I’ve been suffering a great deal at school lately, but that’s a separate story for another blog post; I feel I have already dumped enough negativity here regarding college applications.

On to the positive developments. My Thanksgiving break has started, and I’m already down sick! Thankfully it isn’t anything too severe, but I still find it irritating. I’ve mostly recovered and am now splitting my time between a few activities. I’ve been feverishly reading Aakar Patel’s “The Price of the Modi Years” and am learning about the last ten years of disastrous governance under Modi. I’ll soon write a more detailed post, but until then, did you know that former Chief Justice Ranjan Gogoi once served on a bench investigating a sexual-harassment case against himself? Or how about the fact that, in 2021, a RTI request found that the Supreme Court had 54 pending habeas corpus petitions, with the oldest dating back to 16 years before. Even more interestingly, did you know that Justice Arun Mishra was on the bench judging the Rubabbuddin Sheikh vs State Of Gujarat & Ors case (where “ors” included current home minister Amit Shah), despite having earlier recused himself from the case? Many interesting things can be learnt from Aakar Patel’s book…

I’ve also been slowly making progress through Syed Mujtaba Ali’s “Deshe Bideshe” in the original bangla! My reading/writing skills in bangla are nonexistent, so I’m very excited to be developing them. The book is interesting, telling the story of his stay in Afghanistan with some very beautiful language. He has a good sense of humor and a talent for poetry, so I’m enjoying the book a lot even though it’s a difficult read.

I’ve also begun reading Kazi Nazrul Islam’s poem “Bidrohi” and some more of Sukanta Bhattacharya’s poetry. “Bidrohi” is an INCREDIBLE poem, blending Hindu and Muslim religious imagery with terrifying metaphor to create an exaltation of the pre-Independence rebel. There is an especially good recitation here for anyone who is interested https://www.youtube.com/watch?v=29X1GFso6y0 I reread Sukanta Bhattacharya’s poem “Ae Mahajibhon” (amazing poem), which I had read with an English transliteration before but never in the Bangla script until now, so that was also quite satisfying.

Today I started watching Sanjay Kak’s documentary “Jashn-e-Azadi.” I’ve only watched Part 1 so far, but I’m already impressed by the film. It opens by following a father as he looks for his son’s grave in the “martyrs’ graveyard,” setting the tone for this sobering work of cinema, and continues by exploring the violence and repression that rules Kashmir. The phrase “cordon and search,” distant and intangible in a book, becomes more real as the true violence of such operations is revealed: burnt homes, civilians caught in the crossfire, extrajudicial killings, and grieving families. Sanjay Kak takes a very lyrical approach to documentary filmmaking and weaves poetry into his film, just as he did in “Mati ke Laal.” The choice of ghazals beautifully reflects Kashmiris’ own reflections on the nature of freedom and the horrors they have witnessed. The film is titled “Jashn-e-Azadi,” meaning “celebration of freedom,” and it is quite successful in exploring that topic – what does freedom really mean in a state under martial law, where the Indian constitution is slowly being forced upon them at the cost of tens of thousands of lives? The end of Part 1 shows Srinagar on Independence Day, where the only people celebrating in the streets are the soldiers, guarded by a labyrinth of barbed wire and rooftops manned by snipers – a powerful message about what kind of “freedom” is really being brought to Kashmir.

I’m also hoping to read some of Roberto Bolaño’s “2666” and make progress on learning Indonesian over the break, but I’m not sure how much time will permit. Another goal was writing more over this break, and this post has already made some progress towards that goal, so hooray!

Switching tracks again – on a long drive I started listening to some music I recently downloaded but hadn’t had the chance to listen to until then, and I realized a lot of it was really good.

In the kpop world, I liked Nmixx’s album “Blue Valentine” and TripleS’s album <ASSEMBLE24>. Not all the songs are amazing, but there’s a decent number of good songs in both albums.

In the Hindi music world, I have fallen in love with the Gangs of Wasseypur soundtrack (more on the film later). All of the songs worked well in the context of the film – the goofy songs (e.g. “Tain Tain To To”) worked when paired with specific parts of the film, creating comedic effect and irony where necessary. However, some songs are amazing even outside of the film’s context. In particular, I recommend “Teri Keh Ke Lunga,” which has some incredible singing by Amit Trivedi and a very dark, foreboding feeling; “Jiya Tu” which provides a good laugh and a burst of energy; “Taar Bijli,” a mournful song with beautiful vocals and some subtle political commentary embedded into the lyrics; and “Loonga Loonga,” a song with good energy that also has some good lyrics (“ae jawanon, garibi tod deti hai jo riske khaas hote hain! aur paraye apne hote hai jab paise paas hote hain!”).

I watched a number of good films in the last week or two, and I hope to write reviews for the following: “Gangs of Wasseypur”, “The Handmaiden”, and “Jukti Takko Aar Gappo.” I also want to write a review for V.S. Naipaul’s “A House For Mr. Biswas” because I finished reading it very recently.

That’s about it for now. I will likely do more random brain dumps of this sort in the future, since this kind of writing is very stress-free and lets me get out a lot of thoughts and recent events in a very easy format. Apologies to my readership of 3.28 people who might have found this boring or too chaotic. If you did somehow end up liking one of the films, poems, or songs mentioned here or something similar, feel free to talk to me about it (contact info on the about page of my blog).

Of -ist's and -ism's

Fri, 05 Jun 2026 00:00:00 GMT

Of -ist's and -ism's

Of -ist’s and -ism’s

There is an increasing tendency in politics for people to identify as an ‘-ist’ following a particular ‘-ism’ without doing significant research into what that ideology stands for and what the merits are of its values and ideas. This is partly a product of increased political polarization: when your relationships and popularity would be threatened by not explicitly identifying yourself with a certain movement, it’s natural to signal which camp you’re in. Despite the instinctive nature of such self-classification, this behavior is damaging to intelligent political discourse and, by corollary, democracy across the world.

The first issue is that this trend has contributed to increased dogmatic thinking and refusal to question one’s ideas. When someone is comfortably within a certain camp, they become less inclined to seek answers to questions independently and in an unbiased manner, and more likely to search for what adherents to their chosen ideology typically believe in. Less people search for opinions of multiple sources, empirical evidence, and a theoretical basis when trying to understand a complex issue – many of the ’-ist’s tend to look for what their favorite columnist or theoretician has said, and then place blind faith in their opinion without trying to form their own assessment of the issue. This type of andhbhakt thinking is scarcely better than that of religious fanatics who go running to a cleric any time they have a doubt over a social or political issue, e.g. the place of women in society: neither the political nor the religious andhbhakt approaches social and political issues with an unbiased mind, neither bothers to think about their opinions, and both have a negative impact on the quality of political discourse.

Continuing on this theme of poor thinking, there is also a mindset that if you agree with propositions X,Y, and Z, then you should be classified as a something-ist, and therefore you also agree with propositions A,B, and C. Both sides of the political spectrum are guilty of this. For example, the news site Reason.com identifies itself as fully libertarian, which often leads to problematic video titles such as “Debate: Should libertarians Love or Hate Pope Leo’s AI Letter?” – despite calling itself a debate, the video’s title implies a certain degree of groupthink through its presumption that all libertarians should either love or hate the Pope’s stance on AI; rather than accommodating a multiplicity of viewpoints among libertarians, videos like this seek to prescribe what libertarianism is about and what libertarians should believe in. The very idea that you should support something solely because of what “-ism” you believe in discourages independent thinking and arguments grounded in reason, despite the website’s title and professed goal of “free minds, free markets.” While this title might itself be indicative of bad wording rather than mal-intent, the general style of reporting on the site indicates a larger problem. By identifying themselves with the ideology of libertarianism and rigidly defining it as unconditional love for the market and opposition to any kind of regulation, the authors at that site, along with many other self-identifying libertarians, weaken their ability to adopt nuanced viewpoints that integrate elements of different ideologies, e.g. the ability to both support free markets and the need to control rent-seeking behavior and negative externalities created by large corporations.

A possible objection to the above analysis is that the video title refers to a hypothetical set of axioms (read: ideology) rather than a prescriptive approach to political discourse, i.e. that it supposes if a person supported X,Y,Z values fully, then they should take a certain stance, but without explicitly advocating for people fully supporting those values; however, these videos don’t specifically list the axioms assumed and instead directly link their policy prescription with adherence to an ideology that is presented as the only correct one. My detailed analysis of that video title doesn’t stem from a particularly strong hate for one video, but rather because it’s an illustrative example of the broader problem and a neat way of discussing my working theory of ideologies. I used the word “axiom” above to describe differences between two ways of treating political ideologies; although this term isn’t frequently used to discuss ideologies, it is an apt description for the process at work.

An ideology is a belief system like any other: you begin with a set of core values and propositions you assume to be true, and you arrive at a set of policy proposals based on them. Just as religious belief systems depend on assuming the absolute truth of a religious text (or multiple), so too does complete adherence to political belief systems depend on the absolute truth of certain propositions. Doctrinaire Marxists have an unshakeable faith in the truth of what is written by Marx, while doctrinaire Marxist-Leninists add State and Revolution to the holy scriptures, and these tribes justify most of their beliefs solely through quoting their scriptures; on the other side of intellectual laziness, the most dogmatic of libertarians have a fervent belief in the virtue of free markets and the evil of government regulation, and this is the basis for all their opinions. I repeatedly used qualifiers like “complete adherence” and “doctrinaire” here to emphasize that this article, and the behavior it criticizes, is not talking about the ’-ist’s who have the intellectual integrity to challenge core tenets of their ideology and arrive at their own conclusions – I am referring to those who blindly treat certain values, ideas, or texts as solemn truth without clearly defining or understanding what these assumptions even are.

Political ideologies are useful as a set of axioms, where you treat it as a hypothetical that X,Y, and Z axioms are true, and you see where that takes you. The problem is that we have stopped treating these axioms as hypothetically true and are instead taking them for granted, and even ceasing to explicitly define what axioms we are using. People declare themselves as a “socialist” without defining what specific values that entails beyond “social ownership of the means of production,” or a “libertarian” with only the vaguest idea of being in favor of “free minds and free markets.” Declaring oneself as an ‘-ist’ is nowadays often a euphemism for letting an established community and body of work do your thinking for you, and thus avoiding the productive thinking that used to be more compatible with subscribing to an ideology.

Compare this to where political ideologies took root, and the level of rigor present in those foundational texts. Marx’s Das Kapital clearly defined the most foundational concepts he utilized, starting with the different kinds of value and building up to a complex theory of labor exploitation as a result of capitalists keeping surplus value as profit. Marx did not start with broad generalizations as his axioms, he began with atomic, fundamental concepts as axioms, justified with independent thinking and extensive knowledge of existing literature on political economy. He was completely aware of what axioms (e.g. the labor theory of value 1) were necessary to arrive at some of his conclusions and willing to engage in debate on the factuality of them. How many of his self-proclaimed followers today can claim the same level of intellectual rigor? Very few people have read Das Kapital, let alone attempted to seriously think about the prior assumptions upon which their own ideology rests. The same goes for most of today’s enthusiastic ‘-ists’ when compared to the foundational thinkers of their ideologies. Ideologies like Marxism, libertarianism, or democratic socialism were meant to be schools of thought centered around an initial set of thinkers’ ideas, aimed at promoting constructive political discourse, rather than the echo chambers and breeding grounds for lazy thinking that they have become today.

The above analysis proved two dangers of over-eagerness to adopt an “-ism”: a tendency to prescribe what positions a person should support based on their chosen ideology, rather than encouraging unbiased searches for answers, and a failure to clearly define or debate the axioms upon which the validity of an ideology rests, leading to muddled thinking.

Another serious danger of this rise in self-identifying ‘-ist’s is that people are committing themselves to a political camp, with a loyalty similar to those of sports teams’ fans, at an increasingly young age. By their middle age, most people are firmly committed to some set of values, which is a natural consequence of having spent more time thinking on political issues and having a stronger idea of what one believes in; however, it’s worrying that many kids in high school and even middle school have begun to identify as ‘-ist’s before they’ve even taken the time to explore what their’-ism’ stands for and be introduced to different ideologies. This premature identification with an ideology is harmful to the type of dynamic thinking that is enabled by youth and essential to proper intellectual development. Although the young have always been a bit more brash in believing the rightness of their beliefs, the blind faith in an ‘ism’ is much stronger than the ‘arrogance of youth’ because the existence of a large community around one’s dogma and the support of reputed scholars help people justify it to themselves in a way they otherwise couldn’t.

People doing intellectually rigorous studies of political questions were always a minority of the population – most of us just don’t have the time or motivation; however, the increased early adoption of ’-ism’s has further shrunk the number of people giving themselves a solid education in different ideologies and views on politics in their youth. People declaring themselves staunch socialists at the age of 15 are unlikely to ever interact with libertarian ideas and introduce necessary nuance and depth to their belief system, and this is the core issue. At the age of 40, if someone has already interacted with lots of different ideas, there is less harm in announcing that, after all that reflection, one feels the closest affinity towards one particular ideology – young people, however, are sabotaging their intellectual development through this kind of thinking.

People’s ideas should be dynamic and always subject to scrutiny, revision, and internal cringe a few months later when they’ve completely recanted. I remember being a fervent libertarian in 8th grade while reading Ayn Rand, and then within a few months almost feeling embarrassment at some of the ridiculously naive ideas I’d held; then at the start of 9th grade, I swung in the completely opposite direction of naivety and started dreaming of a wealth cap and redistribution of all wealth people held in excess of a billion dollars, with Noam Chomsky being a key intellectual influence. After spending time on both extremes of the political spectrum, I slowly arrived at what I hope is today a somewhat more balanced, rational approach to politics and understanding the world. However, even now, nothing I think, say, or write is with complete confidence, and I might find even this blog post a product of shoddy thinking five years down the line.

Self-doubt, and skepticism in general, are necessary to avoid dogmatic thinking and becoming overly comfortable with one’s preexisting beliefs. The habit of young people to fully subscribe to an ideology, without accommodating for doubt or the need to study other belief systems, undermines their capacity for intellectual rigor and productive political discourse.

There’s also the well-known tendency to only talk to or read the writings of people sharing your ideology, yet another danger of subscribing to an ‘-ism’ with too little self-doubt. As with all the problems listed above, this tendency worsens people’s thinking by reducing their exposure to conflicting ideas and removing the possibility for depth or nuance in their belief system.

And, leaving aside all the practical problems resulting from ‘-ist’s and’-ism’s, the idea itself is a bit ridiculous. Most people’s belief systems are far too complicated to be summarized by a single word. Granted, these classifications are useful for a quick summary and first-glance evaluation of where someone lies on the political spectrum, but associating these labels with anything deeper is often counter-productive. The Political Compass test tells me I am far down in the bottom-left corner, even though I am at odds with many of the policies backed by other people in that part of the Compass; shared values and morals, a large part of what the test assesses, do not imply complete agreement on all matters of policy, but many people treat ideological classifications as if they truly were the end-all-be-all of what one believes in. A simple ‘socialist-or-libertarian’ classification would have a hard time accommodating for many people’s belief systems, including mine, especially when they incorporate an appropriate degree of self-doubt and constantly changing ideas.

This isn’t a vendetta against thinking about politics in terms of ideologies: they’re a useful shorthand and thinking framework, and don’t deserve to be entirely scrapped. However, we do need to seriously reconsider how we are using them and what impact they are having on our thinking. To promote better political discourse and strengthen democracy, we need to fight harder against ‘-ist’s and’-ism’s being used as a path towards dogmatic thinking and intellectual laziness.

The treatment of the labor theory of value as an axiom rather than a provable matter of fact will draw the ire of many, but I think it is the most reasonable interpretation. Marx’s justification of the labor theory of value is exactly that: more of a justification than a full proof. Chapter 13 of Amartya Sen’s memoir “Home In The World” provides an especially interesting perspective on how to view the labor theory of value, and I’ll quote from it a bit for the curious reader: > Production can thus be described in many different ways. Concentrating on the labour involved is certainly one legitimate way, and it can be seen as appropriate depending on the purpose and context of the description. In presenting his characterization of feudalism, Marc Bloch did not have to apologize, or confess to some error, when he chose a particular aspect on which to focus – to wit, hard labour – the fact that feudal lords ‘lived on labour of other men’. Marx did not have to confess to any blunder – nor did Dobb. The relevance of the labour theory of value depends on which perspective we are trying to highlight

Sen drew on Maurice Dobbs’s interpretation of the labor theory of value and summarized the core conclusion as follows:

Dobb argued that the labour theory is ‘a factual description of a socio-economic relationship’. The fact that this description focuses on human labour in particular does not make it false: it reflects a particular – and important – perspective in which to see the relation between different social agents – workers, capitalists and so on.

Sen’s view aligns well with my own, so I relegated the task of explaining to him. Returning to my own viewpoint – I don’t think any serious thinker should view the labor theory of value as a proveable statement of reality. Rather, it is an axiom that provides a perspective through which to view the world when you ask “what conclusions could one draw if this axiom were assumed to be true?”↩︎

On Western Companies’ Links to Child Labor

Sun, 28 Jun 2026 00:00:00 GMT

On Western Companies’ Links to Child Labor

Most people living in the western world agree that child labor is a violation of human rights and horrific form of exploitation. The seemingly natural corollary is that Western companies, therefore, should stop purchasing products produced by harmful child labor, and their refusal to do so is reprehensible. However, this perspective has several issues that are rarely thought about, yet essential to formulating a practical solution to the issue.

Suppose, hypothetically, that Western companies completely quit purchasing all goods whose production involved harmful child labor. Such a move, undertaken without other poverty-alleviating measures, would be unlikely to improve the living standards or economic opportunities for children suffering under child labor. Harmful child labor occurs primarily in one of two situations: the first is forced labor in which children are kept as laborers under duress and without themselves choosing 1 to work, and the second is voluntary child labor that occurs as a result of economic hardship pushing a family to make the choice rather than overt force from kidnappers or an armed group. I will analyze the potential impacts of Western disengagement from child labor in supply chains in both situations.

In the first situation of forced labor, Western companies ending trade with the culpable producers would not free the children from forced labor and could result in human traffickers merely selling captured children to employers unimpacted by the de facto western embargo, e.g. selling them to mines or factories primarily serving a domestic market, or sectors isolated from western markets, such as prostitution. This is not an improvement to the children’s quality of life and does not make significant progress towards ending child labor.

I agree that, even if child labor would still continue with a de facto Western embargo, such a move would decrease the moral repugnance of the status quo in which technology companies are linked to some of the worst human rights abuses of the 21st century. Even if the problem isn’t solved by Western disengagement, there is still value to eliminating some of the market and making it a bit harder for child traffickers to find profit through their atrocities. However, a lasting, comprehensive solution to child labor will necessarily involve action taken by the governments of countries with a high prevalence of child labor, not Western companies taking actions that can only partly mitigate the issue.

A similar dilemma would occur in the second situation of voluntary child labor as a result of economic hardship rather than overt coercion. If Western tech companies stop sourcing minerals from mines employing child labor, poor children could just be displaced into other low-wage sectors supplying the domestic market instead (as before, the exact impact depends on the size of the domestic market as compared to export volume). If anything, the decreased demand for minerals might hurt the mining industry and harm the wage growth that is likely already negligible, further punishing the families who send their kids to work due to abject poverty. As repulsive as it sounds, demand from Western companies, while using an exploitative form of labor, might actually be helping raise household income for some of the poorest families in the world who would otherwise be struggling even more to afford food.

The natural objection to this argument is that, thinking beyond short-term income gains, K-12 education is more useful for increasing household income because it enables children to later find higher-paying jobs as adults rather than remaining miners their whole lives. In a world where Ethiopia and South Sudan had functioning K-12 schools, I would vastly prefer children attend those schools rather than work in coal mines that are damaging to their health and their future. Unfortunately, this is not the case in most countries with high prevalence of voluntary child labor: for example, the Democratic Republic of the Congo (DRC) has a poorly-funded education system with huge disparities in access to education, making it impossible for many children to attend schools. The DRC’s government has historically been unable to pay teachers their salaries, and in many rural areas, parents have to cover part or all of teachers’ salaries as a part of school fees, making it impossible for poor families to pay for their kids’ enrollment. Large parts of the country do not even have schools, forcing children to travel impractically long distances to receive a sub-par education that likely won’t even provide access to better-paying jobs 2. However, it is impractical for kids from destitute families to sit at home, unable to attend school, while their families struggle to put food on the table. Western companies’ connection to child labor is, in this case, a vital means of poverty alleviation so long as education remains inaccessible and families are so poor that they can’t afford to leave any income source (even their own children) untapped 3.

It is this second situation, of voluntary child labor caused by family poverty, that makes me reluctant to support a complete abstention by Western companies from supply chains using child labor. I find the situation as horrifying as anyone else and would support Western withdrawal from child labor if there were a functioning education system to serve as an alternative to child labor; however, in the absence of such circumstances, it’s possible that Western withdrawal could cause more harm than good, as demonstrated above. The case of forced child labor is less complex, in that the workers are not paid and therefore there is no poverty alleviation taking place; but even then, Western disengagement does not solve the issue, and forced child labor, which takes place only in conflict zones under specific circumstances, is likely a less significant share of total child labor when compared to the voluntary case.

This post ends with an unsatisfying answer – I don’t know exactly where I stand on this issue. I feel repulsed by the idea of Western tech companies profiting off child labor in Africa, but at the same time, Western disengagement would not solve the issue of child labor and could actually worsen poverty in many parts of the world. As such, I can not confidently support complete elimination of child labor from Western companies’ supply chains. If such a move were accompanied by the establishment of strong education systems and broader poverty alleviation measures in countries with high child labor prevalence, I would see it as a necessary and beneficial move – but given the current state of governance in the DRC, South Sudan, etc, such wide-sweeping reforms are unlikely, and I am not sure Western disengagement alone will lead to a positive outcome. This post is not a rigorous economic analysis that provides a conclusive answer to the question, which is why I am ending with a strong note of uncertainty. However, I do hope that this has introduced new facets of the problem to some readers and helped deepen people’s understanding of child labor.

Footnotes

When I refer to children ‘choosing’ to work, I’m not implying children can provide informed consent to an employer-employee contract. I’m talking about choosing to take on a job, even if that consent is a result of family pressure to work due to economic hardship. The same nuance applies to the use of the word ‘voluntary’ and similar phrasing. Perhaps not the most precise use of language, but it is simpler than adding this in parentheses a dozen times. I added this endnote out of an abundance of caution, wary that some readers would not apply the principle of charity when reading this.↩︎
See https://doi.org/10.1016/j.heliyon.2024.e30771 “Does the education system matter? Exploring in-depth joint school attendance, hazardous and non-hazardous activities in artisanal and small-scale mining in the Democratic Republic of the Congo” published in Heliyon↩︎
Empirical evidence has consistently supported the conclusion that family poverty is the primary driver of harmful child labor. See “Revisiting the Link between Poverty and Child Labor : The Ghanaian Experience” and “Child Labor, Poverty and School Attendance: Evidences from the Philippines by Region”↩︎

Reflections on My US History Education: Bias, Dogmatic Thinking, and Other Failings – and How to Do Better

Wed, 03 Jun 2026 00:00:00 GMT

Reflections on My US History Education: Bias, Dogmatic Thinking, and Other Failings – and How to Do Better

Before starting my actual thoughts on this subject, two author’s notes.

1) I’m not an expert on K-12 education across America, and I won’t pretend to be one. This essay therefore focuses more on my personal experience and anecdotal evidence than on statistics or features common to the Common Core or Texas Education Agency as a whole. If you’re looking for a data-backed argument applicable to the entire US, skip this article. This is entirely informed by my own experiences.

2) This isn’t intended as a personal attack or insult towards anyone. If I criticize a teacher, author, or course, it’s a commentary on their ideas and intellectual rigor rather than an attack on them as a person. Didn’t think this would be necessary, but we live in an era of increased sensitivity to criticism…

With that out of the way, on with the actual post.

Social studies differs from other school subjects in that it serves no purpose for students’ career advancement and is instead taught for nobler causes like the enrichment of the mind and the improvement of society. I will focus here on the goal of improving society. To my mind, the logic behind US history education being good for American society is as follows. Students learn about the past and the good things, as well as bad things, that have been done so that they can ‘learn from the past:’ a broad-strokes economic history so students learn the dangers of both laissez-faire capitalism and doctrinaire socialism, an understanding of how social prejudices have shaped some of the most inhumane government policies in America, how US foreign policy has both harmed and helped the world depending on its objectives, etc. Then students should be taught a sense of responsibility and love towards the country so they are determined to apply this knowledge and invest themselves in the slow forwards march of human progress.

This strategy has failed on two fronts, simultaneously being inadequate in imparting lessons from the past and failing to instill a sense of civic responsibility.

The inadequacy in teaching content stems from several factors, but most prominent in my experience is the biases of teachers and their tendency to give undue emphasis to certain topics. The strongest example of this is the poor teaching of economic history. In my 250+ hours spent in an AP US History (APUSH) class, I can’t recall a single instance in which socialist economic ideas received scrutiny, criticism, or any thought beyond blind praise. In contrast, laissez-faire capitalism was the subject of many hours of denigration and moralizing from my teacher. We received countless lectures on the dangers of monopolies and labor exploitation, contrasted with the virtues of unions, price controls, and trust-busting; never, however, did we hear about the ties the Teamsters had to Mafia bosses, how Standard Oil and other ‘evil’ monopolies brought reductions to oil prices and economic growth, or how Wisconsin’s Potter Law imposed price controls on rail fares so stringent that it wiped out railroad companies’ profits and brought railroad expansion to a halt in the state (this law was actually praised by our teacher).

The framings of economic issues were simplistic and closer to propaganda than pedagogy. We were shown countless examples of corruption involving large monopolies, with nothing said of their contributions to affordability and creating jobs, and then asked whether we felt Rockefeller, Carnegie, etc. were “robber baron or captain of industry.” The entire class, barring myself, answered “robber baron,” and the teacher then gave a cryptic smile and moved on, satisfied that her flock was sufficiently in line with her own beliefs. There is a strong argument that these men were “robber barons,” but they also did many great things for the world, and it’s poor teaching to only highlight one side of that story and promote a simplistic “eat the rich” narrative. Incidents like this show a tendency towards ideological conformity and dogmatic thinking that is often encouraged by APUSH teachers, contributing to a weaker understanding of economic history.

Granted, laissez-faire capitalism has historically been harmful to large segments of the American population, quite possibly more so than the excesses of socialism. However, the emphasis on this topic is disproportionately high compared to the complete neglect of socialist excesses. Students graduating from my school, and likely countless others across the US, are receiving a warped worldview in which economic ideologies exist in a Manichaean split between socialism and laissez-faire capitalism – no middle ground is presented as a possibility in high school. There are no lessons on the importance of curbing regulatory bodies and unions, only lessons on curbing monopolies and billionaires. The consequence of this is an uninformed electorate with a poor understanding of economic history and how it can inform decision-making today. No single course can be blamed for the dismal state of American education as a whole, but the poor teaching of US history certainly has played a role in many students graduating high school with little understanding of economics beyond a militant “eat the rich” mentality.

The negative impact of instructors’ biases on the quality of US history education goes far beyond economic history. The oppression of African Americans is a consistent theme throughout the APUSH curriculum, and the reform movements aimed at correcting this are glorified. While there is deserved praise for the nonviolent Civil Rights Movement, there are also some gaping blind spots in the curriculum. The Black Panthers were never mentioned in class and only once in the AMSCO textbook, and the only race riots ever mentioned in class were those in which white people could easily be blamed for the violence, such as the Tulsa race massacre – never did we learn about the 1965 Watts riots or the 1992 orgy of violence and looting that followed the killing of Rodney King. Similarly, our course criticized the Palmer raids and federal government surveillance of leftist activists, but never were we taught about the bouts of anarchist violence that motivated the government’s paranoia – two things can be true at the same time, but our history education did a poor job of acknowledging that fact. The isolated instances of anarchist violence or African American-led race riots don’t justify or erase the wrongs done by the federal government, but it is important to acknowledge both of these processes to have a complete understanding of American history. Beyond purely pedagogical concerns, it’s just irresponsible and morally repugnant to gloss over the wrongs committed by certain communities while bashing others, and then providing justifications along the lines of “natural reaction to oppression” for violence committed by groups one personally supports.

My APUSH teacher went so far as to suggest that the bomb thrown in the Haymarket Affair might not have actually been thrown by a supporter of the labor protest; to this day, I’m unsure if she was making the extraordinary suggestion that the police threw a bomb at their own men to get a reason to shoot protesters. Incidents like this exhibit the amount of mental gymnastics often done in US history courses to glorify all protest movements and avoid discussing the violence or refusal to compromise often exhibited by them. Many young Democrats’ refusal to acknowledge the excesses of the Black Lives Matter movement (commended in class by my teacher despite their purported neutrality) is a prominent manifestation of this failure in education; after being taught that the violence of the proletariat is a myth, and that when it does exist it is justified by years of oppression, it’s no wonder that kids can’t come to terms with how a well-meaning movement can often be hijacked and turned destructive, to the detriment of the movement and the US as a whole. Even more disturbing is the large contingent of Luigi Mangione fans present at my school and among Gen Z as a whole – 250+ hours of US history education, and all they’ve learnt is that shooting CEOs is a productive way of effecting social change. Perhaps there were some blind spots in the curriculum after all…

The instinctive explanation for these shortcomings is that a two-semester course can only fit so much into its time, and that these blind spots are the result of limited time rather than biases or mal-intent. However, this does not compute with my experience dealing with lectures on all manner of esoteric topics chosen at the whim of the teacher rather than integrality to passing the AP exam. We spent a considerable portion of class time on rhetorical and visual analysis, where we interpreted two stray dogs in the corner of a painting as symbols for class struggle or Reagan’s every ‘um’ and ‘ah’ as a rhetorical appeal to Christian values, and we listened to lectures on cults (all right-wing of course), Appalachian culture (hours spent staring at quilts my grandmother could produce with a youtube tutorial), and the teacher’s various other hobby horses. The undue emphasis on certain topics isn’t because of time constraints, but rather because of teachers and curriculum makers’ own ideological leanings and ulterior motives.

The biased teaching of economic history and protest movements has been damaging to many students’ understanding of US history and, by corollary, their ability to make informed decisions about contemporary issues in politics. If one of the goals of history education was producing a more informed electorate, this model is certainly a failure. On one side of the spectrum is Alabama, where students learn that white people colonized a completely empty land without killing anyone and that everyone has always had a good time in America thanks to the benevolence of Jesus and the American government; on the other side is the circus I have just described, in which left-leaning teachers and textbook authors have created a generation of kids following another dogmatic and distorted version of history. If I had to choose, I’d much prefer this slightly-left-leaning mess over Alabama’s dystopian factory of ignorance, but the incompetence of one system doesn’t excuse that of another.

The second major shortcoming of US history courses is the failure to instill a sense of patriotism and civic responsibility in students. There is curently heated debate over this topic, and many political commentators argue this isn’t the duty of the education system to teach these things. However, I see little value in a thorough understanding of history if it is unaccompanied by a love for one’s country and a sense of obligation to apply this knowledge towards its improvement. The education system today receives more funding and expert advice than ever before in US history, yet voter apathy is at a peak and many of America’s bright young scholars show zero interest in voting, discussing politics, or doing anything remotely useful with their social studies education, seen as a distraction from the vastly more important STEM education that leads to a six-figure salary. This can’t be blamed on history courses alone, but they certainly carry a part of the blame. If teaching facts and ‘history’ was the sole purpose of US history education, then the subject would be completely segregated from a larger goal of improving society and strengthening democracy. Therefore, the teaching of patriotic values and civic responsibility is as necessary to US history courses as teaching history itself.

On this front also, high school US history courses have failed, even more spectacularly than in the dimension of actual course content. Most of my APUSH course’s lecture time was spent listing out all the horrible things America has done to African Americans, Native Americans, immigrants, and women; when positive steps forward like the 15th Amendment or Civil Rights Act were discussed, it was almost in passing and always with a mountain of caveats added on to remind students that, even when America does something good, it’s never good enough to merit praise. Granted, civil rights legislation has never been perfect and gaps in enforcement are an issue, but there were achievements nonetheless – listening to my APUSH teacher, it would feel like America is still in the same place today that it was 250 years ago. This negative attitude teaches students pessimism and apathy, rather than inspiring them to follow in the footsteps of the social reformers of history and try to make their own positive impact.

It’s hard to list specific incidents in the course as evidence for this problem because this is more a matter of tone and relative emphasis on different topics than of easily-quotable parts of lectures. However, based on my assessment, this was a significant problem in my APUSH course. I entered the year already a bit pessimistic about the future of the country, due to previous knowledge of the government’s misdeeds, the disappointment of recent political developments, and negative personal experiences; rather than working as a source of inspiration to believe in change and work for it, this course further demotivated me and almost turned my pessimism into hate for the country as a whole. Despite the multitude of inspiring people and movements in history, there was a general attitude of indifference among students throughout the year; although part of this can be blamed on low attention spans and preexisting apathy towards the social sciences, this also reflects a failing on the part of the education system to make history education inspiring. By trivializing the achievements of reform movements and constantly bashing the American government, teachers risk killing students’ belief in the possibility of change and the importance of fighting for it.

I suspect part of the issue is that the pendulum has swung too far in the clash between two narratives of US history. Leftist historians such as Howard Zinn gained enormous popularity at one point of time because they countered a misleading narrative of American exceptionalism similar to Alabama schools’ story of all minorities having a jolly time in America. However, in countering one genre of biased historical narratives, Zinn and his ilk have created yet another genre in which American history is a never-ending saga of class struggle and tragedy, where every reform movement was insufficient and there is nothing to celebrate in the 250 years of independent America. The overly negative US history education I received is part of a larger problem of left-leaning historians and teachers swinging too far in the opposite direction when challenging the dominant narrative of America being the land of milk and honey; while this country has never been perfect and its government has done many horrible things in the last 250 years, that doesn’t justify teachers transferring their personal pessimism and hatred for the government to students.

Traditionally, teachers have tried to motivate and inspire students with the example of great leaders in history: George Washington and Abraham Lincoln used to be in vogue, but now their thoughts on African Americans are too controversial among many leftists for their achievements to deserve recognition, so more recent favorites include Martin Luther King Jr. and Elizabeth Cady Stanton. However, this emphasis on inspiring figures was almost completely missing in my APUSH course, in line with the generally pessimistic and negative attitude. Although MLK and Stanton were treated as positive forces in history, the significantly larger emphasis given to negative historical developments diminished whatever inspirational value they might have had. I am not a proponent of role models or hero-worshipping, since most historical figures have had some personal flaws or prejudices; however, I believe there is value in recognizing some people as inspiring, even if ‘with warts and all,’ and a failure to do so results in increasingly apathetic, demotivated youth.

While it’s hard to quantify the impact of this attitude on students, some educated guesses can be made. A large number of young Americans are uninterested in politics and don’t think it can do anything positive for the country – schools with the left-leaning pessimism described above are likely contributing to this issue and hurting kids’ will to engage with democracy and do good with what they’ve learned in class. There is little value to having a deep understanding of US history if the last time you apply it in your life is the AP exam at the end of 11th grade – on this issue rests the crux of why instilling patriotic values and a sense of civic responsibility is essential to US history education, an element that is painfully absent at the moment.

These problems aren’t universal to schools in America; red states have a diametrically opposite version of this mess, with the same issues except from the opposite end of the political spectrum, and in blue states, I’ve heard much more positive reviews of the APUSH course from some students who had better, or perhaps less biased, teachers. However, I do think these problems exist in a sizable number of US history classes, even if not a majority. The AMSCO textbook commonly used in APUSH courses suffers from the ideological biases and blind spots I outlined above with respect to economic history, race relations, and the violence of many leftist political movements. Even more worrying is that a number of schools are using Howard Zinn’s “A People’s History of the United States” as their US history textbook, despite the academic consensus that it suffers heavily from Zinn’s own confirmation bias, i.e. his desire to morph history to fit a leftist narrative rather than present an objective portrayal of events. If Zinn’s biased narrative was accompanied by an incredibly talented teacher determined to fight dogmatic thinking, it wouldn’t be cause for concern; however, given the average quality of high school teachers in America, it’s risky to give students their first introduction to US history from a textbook well-known for sketchy methodology and poor intellectual rigor. Leaving aside textbooks, the ambiguity of rules on teacher impartiality and the human tendency to preach one’s own beliefs makes me inclined to think my teacher is not alone in committing some of the errors described above.

My time in an AP US History course convinced me that the use of biased textbooks, combined with left-leaning teachers who often can’t separate their teaching from their own beliefs, is dangerous to US history education. I’m reminded of Nietzsche’s famous words from “Beyond Good and Evil”:

“Whoever fights monsters should see to it that in the process he does not become a monster. And if you gaze long enough into an abyss, the abyss will gaze back into you.”

In seeking to counter biased right-wing historical narratives, many left-leaning teachers and curriculum-makers have committed the same sin of polluting education with their own ideological leanings rather than promoting intellectual freedom and an objective treatment of history. The dogmatic thinking and poor teaching on both sides of the political spectrum must be acknowledged and rectified in order to redeem US history education and help develop a better society.

Review of Erika Fatland’s 'Sovietistan'

Thu, 02 Jul 2026 00:00:00 GMT

Review of Erika Fatland’s 'Sovietistan'

Review of Erika Fatland’s “Sovietistan”

Divorce by text message, boiling people alive, and renaming the days of the week after the supreme leader’s family members – just a sample of the terrifying yet fascinating things going on in the former Soviet states of Central Asia, brilliantly described in Erika Fatland’s travel memoir “Sovietistan” (translated from the original Norwegian by Kari Dickson). Readers of my blog will be familiar with my interest in morbid history mixed with complex political issues and gripping narration, and this book perfectly fit into my obsession with that genre.

“Sovietistan” is about the time Fatland spent traveling in Turkmenistan, Kazakhstan, Tajikistan, Kyrgyzstan, and Uzbekistan. Despite the title’s seemingly dismissive treatment of the region, the actual content is far from the usual generalizations about “the Stans” that have shaped most people’s understanding of the region. Fatland goes deep into the unique history, politics, and culture of each country, and I am very satisfied with the depth of knowledge this book has given me. She excels in explaining Soviet policies in each country and how they have shaped their demographics, economies, and cultures to this day. I was particularly fascinated by how Kazakhstan’s ethnic diversity is a result of Stalin-era deportations of people opposed to collectivization and state-enforced atheism, how the retreat of the Aral Sea was a result of Soviet obsession with cotton exports in Uzbekistan (continued to this day by the current government), and how the Soviet regime brutally cracked down on individual identities and cultural heterogeneity. These history lessons were taught through a combination of quoting some fascinating historical sources and drawing on Fatland’s own experiences, entertainingly and powerfully narrated. Her description of the Yaghnobis– an ethnic group who were isolated from other communities until the 1970s, whose language is the last connection to the ancient Sogdian language, and who preserved some of the region’s pre-Islamic, Zoroastrian traditions– was haunting and left a deep imprint on my mind. When Fatland visited, she was unable to find anyone willing to admit cultural differences between Yaghnobis and Tajiks, as their individuality and pride as a people had been beaten out of them by Soviet repression.

“When my son was born, I asked the nurse to write Yaghnobi under nationality,” said one of the men who had not spoken until now. “She didn’t listen to me, and wrote Tajik, and I’m very glad of it now. If she had done what I said, my son would probably have faced countless unnecessary problems.”

These rare people, of whom there are only a few thousand left in the world, whose language is modern day scholars’ only link to the extinct Sogdian language, insist that they are just like the Tajiks. Perhaps the lack of pride and confidence in their own people can be traced to the Soviet Union’s policy on minorities: there were not enough Yaghnobis for them to be given the status of separate nationality. Following the deportations in 1970, the Soviet authorities went as far as to delete Yaghnobi as a separate ethnicity from all registers. They simply decided that the Yaghnobi people no longer existed. All Yaghnobis were instead registered as Tajiks.

The tragedy of Soviet totalitarianism is powerfully highlighted through the stories of people Fatland met. One memorable example was her conversation with an elderly Yaghnobi man who had just finished building a house in 1970 when the government forced him to relocate to a collective farm, where three of his four children died in the first week since their isolation in the Yaghnob valley had prevented the development of immunity to lowlands diseases; by the time he returned to the Yaghnob Valley, after 11 years on the collective farm, his home had been destroyed by the elements and he had to rebuild it and start from scratch, emotionally broken by the loss of three children.

“When I left, my beard was black,” Mirzonazar said. “When I came back, it was white.”

“Now I only go back to Zafarabad to visit the children’s graves,” he said. “Sohibnazar was very special. He was an intelligent boy and did well at school. When he came to ask for ten roubles to buy a notebook and pen, I always gave him twenty, I was so fond of him. Buy yourself some biscuits or pierogi with the extra ten roubles, I told him.”

Fatland’s book is full of these heartbreaking stories of the atrocities resulting from Soviet totalitarianism. She does an excellent job explaining the Soviet-era history both at an intellectual level and also making readers feel the impact in their hearts through stories like this one. Many issues from the Soviet era are discussed, including the deportations of ethnic minorities, collectivization, dekulakization, environmental destruction, and nuclear weapons tests. She also effectively shows how the Soviet-era atrocities and mismanagement, and the resulting consequences in society, politics, and the environment, continue to shape the history of the region today.

This book did a great job revealing the tragedy of the region’s post-Soviet history as well. Fatland gave a dark but often amusing description of Turkmenistan’s cult of personality under its first two presidents – although totalitarianism is a heavy topic, there is also plenty of room for laughter because of dictators’ megalomania and general insanity, e.g. Turkmenistan launching a copy of their president’s ideological manifesto, the Ruhnama, into space in 2005, or the time their president fell off a horse in a race (Fatland was lucky enough to personally witness this) and the security services scrambled to scrub any footage from observers’ cameras (they failed and the world saw the video). She highlights the political environment of fear and terror, and the lack of freedom, but also these more amusing aspects of the dictatorship. She covers the history of the totalitarian regimes, human rights abuses, government corruption, failing economies and healthcare systems, ethnic violence between Uzbeks and Tajiks, the Tajik Civil War, bride abduction in Kyrgyzstan, suppression of religious expression, and the survival of somewhat democratic politics in Kyrgyzstan (now dying again unfortunately) and the bloody history that allowed it to happen. A book with tremendous scope that you will learn a lot from.

There are many interesting personal accounts of how this history has shaped people’s lives, and how people respond to forces of history too powerful for them to individually stop. Fatland describes conversations with one of her drivers, who has the courage to criticize the regime but always in a hushed tone, even in the middle of a desert miles away from civilization, and how he hopes the next generation will change things in Turkmenistan. But she also described some things that show just how dark the world can be, and how abject poverty and societal dysfunction can have devastating consequences. Some of her experiences in Tajikistan left me especially shaken:

A boy came over and sat down beside us.

“This is Rajabal, my second oldest,” Umrimoh smiled. “He’s fourteen.”

He was so small and thin that he did not look a day over eight.

“And what do you want to do when you grow up?” I asked. “Do you want to be a doctor, or a teacher, or maybe a football player?”

“I want to get married in two years’ time,” he said, without a flicker of a smile.

“I want him to study, but all he cares about is getting a wife and some cows,” his mother complained.

“Have you found a wife?”

“No, not yet,” the boy said, just as seriously. “But I’m keeping an eye out. I want a clean wife, the best. Maybe from Zafarabad or Dushanbe.”

“Whenever relatives come to visit from town, he studies the girls carefully,” his mother teased. “She has to be so pure, so clean, not like the girls from the village, who have cow dung under their nails!”

Umrimoh and her friend laughed heartily, but the boy did not bat an eyelid.

However, it is not all doom and gloom. Fatland also highlights the more humorous aspects of totalitarian regimes, the beauty of old Islamic architecture, the mysteries of Bronze Age archaeological finds at Gonur Depe, the story of the Russian artist and collector Igor Savitsky and his art museum in an Uzbek desert (this was one of my favorite parts of the book, Savitsky was an extraordinary person, and it was very inspiring to read how his project succeeded against all odds because of his tenacity), and some of the great achievements of Samarkand and Khiva in medieval times. There is a lot of diversity in subject matter that keeps the book constantly interesting.

This book also excels in immersion and helping visualize what Fatland was actually seeing. Massive kudos to Fatland’s Norwegian prose, as well as the talent of her translator Kari Dickson in losing none of its vibrance.

Here is an excerpt from the beginning of the book about her visit to the Darvaza Gas Crater.

I am lost. The flames in the crater have erased the stars and then drained all the shadows of light. The fiery tongues hiss and spit; there are thousands of them. Some are as big as a horse, others no bigger than raindrops. A gentle heat strokes my cheeks; there is a sweet, sickly odour. Stones loosen from the edge and tumble into the flames without a sound. I step back onto firmer ground. The desert night is cold, without fragrance.

And here is her description of the Karakum desert.

I had never imagined the desert could be like this. The Sahara is a sea of brown, umoving waves, enormous and timeless, but the Karakum Desert is full of colours. The sandy ground is covered in a delicate layer of grass. Scrubby bushes and small, twisted trees grow up the sandy hills; in their shadows, white and yellow flowers bloom. In the middle of the day, the sun in the cloudless sky is warm, but the evenings are cool and the nights just above freezing. No matter how many of the travel agency’s dirty military sleeping bags Murat gives me, I am still cold and lie in the tent longing for the camels’ morning bellow.

Overall, this was a very fun and informative book that had a deep impact on me emotionally. Fatland highlighted the diverse experiences of people in former Soviet Central Asian states, all the suffering they endured because of governmental and societal injustices, but also the strength and courage of individuals even when confronting the power of a totalitarian state. Beautiful writing, great content – 10/10, I would recommend you read this book.

Rs 370 Biryani Guy Is A Victim of Thought Policing and Virtue Signaling, Deserves Justice

Sat, 13 Jun 2026 00:00:00 GMT

Rs 370 Biryani Guy is A Victim of Thought Policing and Virtue Signaling, Deserves Justice

Rs 370 Biryani Guy Is A Victim of Thought Policing and Virtue Signaling, Deserves Justice

Note before starting: this post addresses a controversy involving vulgar language and sexually explicit humor. Perhaps not wise to read in a work or school setting, or to share with young children. Now on with the post.

A Party member lives from birth to death under the eye of the Thought Police. Even when he is alone he can never be sure that he is alone. Wherever he may be, asleep or awake, working or resting, in his bath or in bed, he can be inspected without warning and without knowing that he is being inspected. Nothing that he does is indifferent. His friendships, his relaxations, his behaviour towards his wife and children, the expression of his face when he is alone, the words he mutters in sleep, even the characteristic movements of his body, are all jealously scrutinized. Not only any actual misdemeanour, but any eccentricity, however small, any change of habits, any nervous mannerism that could possibly be the symptom of an inner struggle, is certain to be detected. He has no freedom of choice in any direction whatever. On the other hand his actions are not regulated by law or by any clearly formulated code of behaviour.

In 1984, George Orwell imagined the Thought Police as a representation of 20th century communist governments’ constant policing of citizens’ thoughts and speech, punishing people for so much as thinking bad things about the regime even if they did not actually act on those thoughts. Today, 1984 is frequently used to draw comparisons between authoritarian politicians and the dystopian police state Orwell had imagined, but much rarer is the comparison between 1984 and the thought policing done by many radical feminists, LGBTQ+ activists, and others who claim to be defending the dignity of minorities against offensive remarks. Sexist and otherwise derogatory comments are a real issue in society, but this does not justify violating people’s fundamental rights in order to punish offensive speech. Nonetheless, many left-wing activists show a disturbing willingness to infringe on the right to free speech with the goal of penalizing sexist, racist, etc remarks or thoughts.

I refer, of course, to the now-infamous Rs 370 biryani guy. What a shame – he probably had a life, career aspirations, dreams, and now he shall forever be known as “Rs 370 biryani guy,” his entire life reduced to the fallout of a 2-3 minute joke told at a stand-up act. For those not in the loop, “Rs 370 biryani guy” is Himanshu Jangra, a 23-year-old man who recently went viral for a humorous story he told at a Pranit More comedy show. The story consisted of his repeated attempts at convincing his girlfriend to have sex with him, only to be repeatedly hindered by various circumstances: the girlfriend having to go to the mall, not having condoms, her not being in the mood, and finally her being hungry. The climax to the story was when he solved the hunger issue by taking her to eat Rs 370 biryani, after which she asked to be dropped home, leading to Jhangra joking “maine kaha ki Rs 370 lage hain to use to wasool to karunga hi b*h*nc**de (I said, I’ve spent Rs 370, so I’ll get my money’s worth I’m not translating that)” 1.

This joke has been widely denounced as sexist, implying consent can be bought with Rs 370, objectifying women, promoting rape, etc. A social media pressure campaign resulted in Jangra (a web developer) being fired, although now his boss is also drawing flak because the firing happened due to social media pressure rather than feeling moral obligation to fire an allegedly sexist employee. Then the National Commission for Women (NCW) took suo motu cognizance of the Rs 370 biryani case, issued summonses to the comedian Pranit More and the Rs 370 biryani guy, and sought police action 2. Maharashtra’s cyber police eagerly answered to the call and registered a case against More and Jangra for “obscene and objectionable content” online 3. This encouraged everyone to come get their pound of flesh. Maharashtra’s chief minister Devendra Fadnavis (a staunch feminist of course) denounced the joke and the involvement of everyone at the show, arguing that such jokes “violate societal boundaries” and “the limits of dignity.” Arnab Goswami, eager as always to make money off manufactured outrage, has created a full episode of “Debate with Arnab” inveighing against Jangra 4, and social media has had a field day with Rs 370 biryani memes.

There are some legitimate concerns about male entitlement, sexism, and how cultural factors contribute to the prevalence of rape and sexual harassment in India; however, this joke’s danger to society is being blown out of proportion, and the discussion around these issues is rapidly turning into a witch hunt, an opportunity for everyone to pile on to strengthen their pro-women credentials. My view is that this joke was exactly that – a joke, and not a serious suggestion that Rs 370 biryani can buy sexual consent. Stand-up comedy frequently runs on shock jock humor and exaggeration, and people often say things they don’t seriously mean at stand-up comedy shows. If anyone was seriously drawing life advice from clips of the Rs 370 biryani story, the fault lies more with the viewers than the person making the joke. My own assessment of Jangra’s tone, seriousness and the rest of the story make it seem very unlikely he was seriously equating Rs 370 with sexual consent. In fact, the media’s constant focus on the “wasool to karunga hi” line omits several key details: Jangra was not forcing himself on some girl he’d just met, and in the story, his girlfriend had actually agreed to have sex once before but called off the plan after realizing there were no condoms. Jangra comes across as a bit too obsessed with sex, perhaps a bit too insistent on having it, but he certainly wasn’t suggesting consent could be bought. He was telling a humorous story about his plans for sex being repeatedly foiled and light-heartedly complaining about his girlfriend’s hesitancy irritating him (although he was respectful of it, something his critics conveniently ignore) – this was not some sinister plot to promote rape in India.

The focus on the “wasool to karunga hi” line, being quoted in journalistic-style writing, also ignores another key aspect of the incident – the joke was actually funny. I’d recommend watching the video of the joke, available in chunks here and here (the original video on Pranit More’s channel is now deleted). A typed transcript of any comedy show would result in the comedian coming across as boring and very obscene, since humor isn’t just about a string of words but also the delivery of jokes. Jangra was a master storyteller and had the entire crowd rolling on the floor with laughter; I will admit, even I found it quite funny. Obscene? Yes. Very offensive, risking coming across as sexist? Yes. But unfunny? This joke had me laughing harder than I have in several days – the accusation of the joke being ‘100% sexism, 0% humor’ is unfair and derived from specific parts of the joke being taken out of context and separated from the verbal delivery that made it funny.

Dark humor and slightly offensive jokes are a staple of comedy. American shows like Family Guy and South Park frequently use stereotypes based on race or religion for comedic effect, and nobody is offended because everything is clearly in jest and deliberately testing the audience’s boundaries. Stand-up acts have always been full of edgy humor, lots of swearing, and jokes meant to test people’s boundaries. It’s ridiculous to demand family-friendly stand-up comedy, for this defeats the very purpose of stand-up. CM Fadnavis’ remarks are implying that stand-up comedy should respect ‘societal boundaries’, and the NCW is saying comedians should avoid ‘obscene and objectionable content.’ This would kill most comedy shows overnight. Who gets to decide what jokes are too obscene, versus which ones are just barely respectful enough of societal boundaries to be allowed? This kind of thought policing is a slippery slope that will lead to people being scared of making the kind of edgy jokes that have been key to stand-up comedy’s success.

The Indian legal system has always been too iffy on fundamental rights, struggling to maintain the balance between freedom and maintaining the rule of law. We have ambiguously-worded, oft-abused restrictions on content disruptive of ‘the sovereignty and territorial integrity of India’, laws against ‘outraging the modesty of a woman’ that are vague and once let a lawyer sue Aryan Khan for showing the middle finger in the presence of women, and strict obscenity laws. Policing stand-up comedy is just the latest in India’s long and inglorious history of trampling on freedom of speech, especially in the cases where it is least necessary. Even beyond killing stand-up comedy, it is dangerous to suggest that the state should punish certain kinds of speech that violate arbitrarily decided standards of modesty. There is no objective standard of obscenity, modesty, or acts prejudicial to the maintenance of public order, which is why laws using this kind of language are fraught for abuse, e.g. punishing political opponents, silencing dissent, and using the law to enforce personal beliefs on morality that have no relation to constitutional obligations or the public interest. The critics of ‘Rs 370 biryani guy’ want to add even more vague language to further trample on freedom of speech in India – let’s throw ‘societal boundaries’ and ‘objectionable’ into the mix of legally vague terms, why not! Once you give the government power to police certain kinds of speech, you can’t control how they will interpret those powers and extend them.

I don’t think Jangra’s joke was harmful or a negative influence on the youth, but that isn’t even relevant to the bigger issue of free speech. Suppose, for argument’s sake, that Jangra’s joke actually was promoting rape. Is it the government’s job to punish speech that promotes rape, or for that matter, any kind of dangerous behavior? While saying ‘no’ might seem morally repugnant, the practical implications of answering ‘yes’ are terrifying. Who gets to decide what kind of speech is dangerous or at odds with Indian values? Free speech should be a fundamental right, with as few limits as possible, because limiting it leads to a slippery slope where airtight laws with little scope for abuse are nearly impossible to create. Jangra’s critics argue that his joke promoted rape, but the feminists on social media, the NCW, and Maharashtra cyber police are also promoting a kind of dangerous behavior: punishing people for speech by using massive government overreach. Rhetoric glorifying rape, violence, etc should be combated, but through criticism in the media and education that counters these negative influences, not through use of government power that tramples over the right to free speech. People’s support for the prosecution of Jangra and More is tacit support for abuse of vaguely-worded laws and thought policing.

Some might object to the phrase ‘thought policing,’ since this case involves offensive speech rather than thoughts. However, the issue of thought policing emerges from the fact that Jangra is not the only one named in the case, and the comedian Pranit More is also being investigated. Even supposing that the Rs 370 biryani joke actually was dangerous to society, More was not the one who made the joke, and his only crime is having found it funny and not criticizing it. This controversy goes beyond cracking down on free speech and sets a precedent for policing thought itself. Social media is clamoring for the public shaming and legal punishment of anybody who laughed at the joke and didn’t think it needed criticism. Where does this end? By this logic, you can be a bad person just for having a certain sense of humor, and it is the duty of employers to fire such people, and for the legal system to punish people laughing at jokes that are deemed ‘objectionable’ or ‘violating societal boundaries.’ Should everyone present at the comedy show face charges? Should I face charges for having laughed at it from 13500 kilometers away? Again, a slippery slope that goes beyond demolishing the freedom of speech and threatens the freedom of thought itself.

This post’s title also mentioned virtue signaling, and that’s another important issue I want to address. How much of this outrage is real, rather than people seeking to strengthen their credentials as feminists? It’s unusual for a state’s chief minister to comment on an internet controversy about a stand-up comedy show – how much of CM Fadnavis’ outrage stems from genuine concern about rape culture, and how much is political opportunism and trying to strengthen his popularity among women voters? His feminism was considerably more muted when his own party’s (BJP) Maharashtra chief, Chandrakant Patil, came under fire for sexist remarks directed at Supriya Sule, an MP from the rival NCP:

“Why are you even in politics? Just go home and cook. Go to Delhi or to a cemetery, but get us the OBC quota. Despite being a Lok Sabha member, how come you don’t know how to get an appointment with a Chief Minister?”

Facing a backlash, Mr Patil attempted damage control today saying he meant Ms Sule should “go to the villages and try to understand them” in politics.

“It is in my nature to respect women. What I meant was she should learn to live in rural areas where there are sayings like this. I respect Supriya-tai and we talk often,” the BJP leader said. 5

CM Fadnavis did not call for Patil’s resignation and felt an apology sufficed – even though this apology doesn’t seem quite genuine, since it came only after his laughable attempt at clarifying his insult as encouragement for Ms. Sule to experience village life. Today, Patil is a cabinet minister in Fadnavis’ government. Why is Jangra, a 23-year-old attending a stand-up comedy show, held to a higher standard than the state’s BJP chief? One was forced out of his job and hit with a police case, the other received a promotion. CM Fadnavis’ concern for women’s dignity seems to only be triggered when it is politically convenient – ‘rules for thee, but not for me’. The Rs 370 biryani controversy has received much genuine outrage, but CM Fadnavis’ hypocrisy suggests there’s also a large amount of virtue signaling, i.e. people inveighing against Jangra to give the appearance of being pro-women even if their past actions suggest a not-so-firm commitment to combating sexism.

It is sad that Jangra’s comments are not receiving a fair and impartial assessment from the public. Rather, his case has become an opportunity for everyone to prove how robust their support for feminism is, and for selective prosecution on the basis of social media virality rather than actual gravity of an offense. I wish Jangra, More, and whoever else is dragged into this controversy 6 the best of luck in receiving a fair trial (difficult given the virality and fervor surrounding the case) and getting their lives back. No one deserves to be crucified for one slightly offensive joke at a stand-up comedy show, when politicians and powerful men get away with far worse. This controversy does nothing to fight rape culture or sexism – it is a witch hunt, and nothing more.

Sources quoted from and footnotes:

https://theprint.in/feature/gurugram-co-sacks-man-for-rs-370-biryani-paisa-vasool-date-story-boss-got-online-flak-too/2955138/↩︎
https://indianexpress.com/article/entertainment/rs-370-biryani-row-ncw-summons-pranit-more-himanshu-jangra-seeks-police-action-10735109/lite/↩︎
https://www.hindustantimes.com/india-news/maharashtra-cyber-police-register-case-against-stand-up-comedian-pranit-more-over-370-biryani-remark-101781184148379.html ↩︎
Arnab Goswami’s debate is here – I do not recommend watching this, or anything else from his show, if you value your time and sanity. However, sometimes Mr. Goswami does offer good comedic value because his average decibel level of “ear-splitting shrieks” is quite funny. I would actually recommend this compilation video of him yelling if your sense of humor is as broken as mine, as well as this video of him repeatedly saying “how dare you say I take money.”↩︎
https://www.ndtv.com/india-news/maharashtra-bjp-chief-chandrakant-patil-says-in-sexist-jab-at-supriya-sule-go-home-and-cook-3010589 ↩︎
“Additionally, the NCW has requested details regarding action taken against those involved, the authentication and examination of the viral video evidence, and the role played by the organisers, performers and venue management” reported by Hindustan Times here. Let’s hope they don’t go after the security at the venue who chuckled a bit at the joke… Social media is also digging up earlier controversial jokes made on Pranit More shows, such as this female doctor who made a joke about comparing the sizes of male different cadavers’ genitalia. There’s now a social media campaign against her as well.↩︎

Solving the Coolest Integral Ever – Fourier Series, Gamma Functions, and the Riemann Zeta Function

Sat, 18 Oct 2025 00:00:00 GMT

Solving the Coolest Integral Ever – Fourier Series, Gamma Functions, and the Riemann Zeta Function

Chancellor Ceti

2025-10-18

Introduction
Bringing in the gamma function – an observation about the integrand’s structure
Finding the Fourier Series for s(1-s)
A Brief Analysis Interlude for the Depraved
Finding a recurrence relation and turning the integral into a more tractable series
A moderately gnarly series
A very gnarly series made easier by our having solved a moderately gnarly one
Wrapping up and solving the integral

Introduction

A few days ago, I was feeling a bit low, so like any normal person, I lay in bed for several hours solving integrals I found on Youtube. I would open a video, pause it at the start, solve the problem, and then see how the uploader had done it. This went on for a long time until I found one Maths505 video that changed the course of my Sunday afternoon. The problem in the video was itself fairly normal, but in the comments section, a certain gentleman by the name of "TiFn4G" suggested an integral for Maths505 to do:

I=\int_{0}^{1}\frac{x-\frac{1}{2}}{\ln(\frac{x}{1-x})}\,dx

Through a lucky find in the comments section, I encountered the love of my life: this integral is the most elegant one I have ever seen. Since I loved the problem so much, I thought I would share the solution with other underemployed people on the internet. I encourage readers to attempt this problem on their own before going to the next section; it’s rare to find a problem this fun, so don’t spoil it by checking the solution before you’ve completely exhausted yourself!

With that out of the way, let’s jump into the actual solution.

Plot of the integrand from 0 to 1

Bringing in the gamma function – an observation about the integrand’s structure

The integrand is very gnarly, and the problem presents a definite integral, which led me to believe that no elementary antiderivative exists here. Given this hunch, we already have some clues about what kind of tactics need to be employed here. The first thing that jumped out at me was that the integrand was very similar to \frac{x-1}{\ln x}, which has the convenient integral representation

\int_{0}^{1}x^s\,ds=\frac{x-1}{\ln x}

The function x^s, when multiplied by other terms resulting from our algebraic manipulation, seemed likely to yield some useful properties. So I decided to try breaking up the integrand in a way that would let me use this integral representation.

The logarithm in the denominator is tricky to rearrange, so I decided to instead focus on the numerator and try isolating a term of \frac{x}{1-x} over there.

If we let u=\frac{x}{1-x}, we can find

u-ux=x

x=\frac{u}{u+1}=\frac{u+1-1}{u+1}=1-\frac{1}{u+1}

This yields

x-\frac{1}{2}=\frac{1}{2}-\frac{1}{u+1}=\frac{u+1}{2(u+1)}-\frac{2}{2(u+1)}=\frac{u-1}{2(u+1)}

Note u+1=\frac{x}{1-x}+\frac{1-x}{1-x}=\frac{1}{1-x}

x-\frac{1}{2}=\frac{\frac{x}{1-x}-1}{2/(1-x)}

Therefore,

\frac{x-\frac{1}{2}}{\ln(\frac{x}{1-x})}=(1-x)\frac{\frac{x}{1-x}-1}{2\ln(\frac{x}{1-x})}

I=\int_{0}^{1}\frac{x-\frac{1}{2}}{\ln(\frac{x}{1-x})}=\frac{1}{2}\int_{0}^{1}(1-x)\frac{\frac{x}{1-x}-1}{\ln(\frac{x}{1-x})}

Excellent! Now it becomes clear how we can use the aforementioned integral representation.

I=\frac{1}{2}\int_{0}^{1}(1-x)\left(\int_{0}^{1}\left(\frac{x}{1-x}\right)^s\,ds\right)\,dx=\frac{1}{2}\int_{0}^{1}\left(\int_{0}^{1}x^s(1-x)^{1-s}\,ds\right)\,dx

Since the integrand is measurable and nonnegative for all the values of x and s within the region of integration, Tonelli’s Theorem lets us exchange the order of integration to find

I=\frac{1}{2}\int_{0}^{1}\left(\int_{0}^{1}x^s(1-x)^{1-s}\,dx\right)\,ds

As we had hoped, the integral representation involving x^s did indeed yield a convenient expression. We know that

B(m,n)=\frac{\Gamma(m)\Gamma(n)}{\Gamma(m+n)}=\int_{0}^{1}x^{m-1}(1-x)^{n-1}\,dx

Note that s=(s+1)-1 and (1-s)=(2-s)-1, so that

So our integral now becomes

I=\frac{1}{2}\int_{0}^{1}B(s+1,2-s)\,dx=\frac{1}{2}\int_{0}^{1}\frac{\Gamma(s+1)\Gamma(2-s)}{\Gamma(3)}\,ds

I=\frac{1}{4}\int_{0}^{1}\Gamma(s+1)\Gamma(2-s)\,ds

Again, we’re forced to marvel at the ingenuity of this problem and how nicely everything simplifies. The integrand’s structure now makes the next step obvious: rearranging to utilize the reflection property i.e.

\Gamma(s)\Gamma(1-s)=\frac{\pi}{\sin(\pi s)}

Note that

\Gamma(s+1)\Gamma(2-s)=\biggl(s\Gamma(s)\biggr)\biggl((1-s)\Gamma(1-s)\biggr)=s(1-s)\cdot \Gamma(s)\Gamma(1-s)

So we find that

I=\frac{1}{4}\int_{0}^{1}s(1-s)\cdot \frac{\pi}{\sin(\pi s)}\,ds=\frac{\pi}{4}\int_{0}^{1}\frac{s(1-s)}{\sin(\pi s)}\,ds

There are a few approaches to this. My instinct told me that a contour integral approach could likely work, but a solution using Fourier series seemed more tractable. \frac{\cos(2\pi ns)}{\sin(\pi s)} presents a world of useful properties and recurrence relations. Thus, we arrive at the next chapter of our journey.

Plot of the integrand s(1-s)/sin(pi s)from 0 to 1

Finding the Fourier Series for s(1-s)

This part involves fairly standard calculations, but for completeness and the benefit of less experienced calculus students, I have included all the steps.

We seek a series representation of the form

s(1-s)=\sum_{k=0}^{\infty}a_k\cos(2\pi ks)

By multiplying both sides by \cos(2\pi js) and integrating from 0 to 1, it is easily found that

a_0=\int_{0}^{1}s(1-s)\,ds=\frac{1}{6}

a_k=2 \int_{0}^{1}s(1-s)\cos(2\pi ks)\,ds

This second integral is easily evaluated using integration by parts (details omitted because anyone who’s gotten this far knows how to do it):

a_k=\frac{-u\cos u}{2(\pi k)^3}\Bigg|_{0}^{2\pi k}=\frac{-1}{\pi^2 k^2}

Thus,

s(1-s)=\frac{1}{6}-\frac{1}{\pi^2}\sum_{k=1}^{\infty}\frac{\cos(2\pi ks)}{k^2}

We can substitute this back into our integral to find

I=\frac{\pi}{4}\int_{0}^{1}\csc(\pi s)\left(\frac{1}{6}-\frac{1}{\pi^2}\sum_{k=1}^{\infty}\frac{\cos(2\pi ks)}{k^2}\right)\,ds

I=\frac{\pi}{24}\int_{0}^{1}\csc(\pi s)\,ds-\frac{1}{4\pi}\int_{0}^{1}\left(\sum_{k=1}^{\infty}\frac{\cos(2\pi ks)}{\sin(\pi s)\cdot k^2}\right)\,ds

This looks intimidating, but the magic potato energy of the universe makes it possible to go further.

A Brief Analysis Interlude for the Depraved

The first thing most readers will notice is that \csc(\pi s) has a singularity at s=0, making everything here diverge if we naively go about this. To avoid that problem, truncate the bounds of integration to be [\epsilon,1-\epsilon] where \epsilon \to 0. Once the limit is taken, the integrals will be the same on the truncated bounds as they are on [0,1].

Now, it becomes clear that, at some point, the ability to interchange summation and integration in the right-hand term will be useful. However, the presence of \sin(\pi s) makes it dubious whether that is possible due to issues of divergence. We can demonstrate uniform convergence to prove the validity of interchanging these operators.

Define

S_N(s)=\sum_{k=1}^{N}\frac{\cos(2\pi ks)}{k^2}=\sum_{k=1}^{N}g_k(s)

S(s)=\lim_{N\to \infty}S_N(s)

We find that

\left|g_k(s)\right|=\left|\frac{\cos(2\pi ks)}{k^2}\right|\le\frac{\left|\cos(2\pi ks)\right|}{k^2}\le \frac{1}{k^2}

Now, if we let M_k=\frac{1}{k^2}, we can use the Weierstrass M-test to find

\left|g_k(s)\right|\le M_k

And we see that \sum_{k=1}^{N}M_k converges

\lim_{N\to\infty}\sum_{k=1}^{N}M_k=\sum_{k=1}^{\infty}\frac{1}{k^2}=\zeta(2)=\frac{\pi^2}{6}

Therefore, S_N(s)=\sum_{k=1}^{N}g_k(s) converges absolutely and uniformly i.e.

\lim_{N\to\infty} \sup_{s \in [0,1]}\left|S_N(s)-S(s)\right|=0

Now, our integrand is \csc(\pi s)S_N(s)

Recall that we truncated the bounds of integration to be [\epsilon,1-\epsilon] where \epsilon\to 0. So we seek to prove uniform convergence on that interval.

We find

\left|\csc(\pi s)S_N(s)-\csc(\pi s)S(s)\right| =\csc(\pi s)\left|S_N(s)-S(s)\right|\le\csc(\pi s)\sup_{s \in [\epsilon,1-\epsilon]}\left|S_N(s)-S(s)\right|

As N\to\infty, that final expression goes to zero due to the uniform convergence of S_N(s) – note that [\epsilon,1-\epsilon] is a subset of [0,1], so the uniform convergence of S_N on [0,1] applies on the truncated interval as well.

This yields

\lim_{N\to\infty}\sup_{s\in [\epsilon,1-\epsilon]}\left|\csc(\pi s)S_N(s)-\csc(\pi s)S(s)\right|=0

Therefore, the integrand \sum_{k=1}^{N}\frac{\cos(2\pi ks)}{\sin(\pi s)\cdot k^2} converges uniformly, so we can interchange summation and integration!

Finding a recurrence relation and turning the integral into a more tractable series

With that brief foray into analysis completed, let us return to our problem

I=\frac{\pi}{24}\int_{0}^{1}\csc(\pi s)\,ds-\frac{1}{4\pi}\int_{0}^{1}\left(\sum_{k=1}^{\infty}\frac{\cos(2\pi ks)}{\sin(\pi s)\cdot k^2}\right)\,ds

Having just proved uniform convergence of the sum being integrated, we can interchange summation and integration to get

I=\lim_{\epsilon\to0}\left(\frac{\pi}{24}\int_{\epsilon}^{1-\epsilon}\csc(\pi s)\,ds-\frac{1}{4\pi}\sum_{k=1}^{\infty}\frac{1}{k^2}\left(\int_{\epsilon}^{1-\epsilon}\frac{\cos(2\pi ks)}{\sin(\pi s)}\,ds\right)\right)

Note that we also moved \frac{1}{k^2} out of the integral since it is a constant with respect to s.

This most recent form of the integral suggests a search for a recurrence relation as the most reasonable next step. We know that \cos(2\pi ks)-\cos(2\pi(k-1)s) has a useful formula in terms of sines, so it seems probable that a recurrence relation of some sort can be found for \int_{0}^{1}\frac{\cos(2\pi ks)}{\sin(\pi s)}\,ds.

This approach has the added benefit of offering the possibility of cancelling out the first cosecant integral that diverges.

Before doing that, though, introduce the substitution u=\pi s and get

I=\lim_{\epsilon\to0}\left(\frac{1}{24}\int_{\epsilon}^{\pi(1-\epsilon)}\csc(u)\,du-\frac{1}{4\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\left(\int_{\epsilon}^{\pi(1-\epsilon)}\frac{\cos(2nu)}{\sin(u)}\,du\right)\right)

With that done, we’re ready to look for our recurrence relation. Define

L_n(\epsilon)=\int_{\epsilon}^{\pi(1-\epsilon)}\frac{\cos(2nu)}{\sin(u)}\,du

Now recall the trigonometric identity

\cos\alpha-\cos\beta=-2\sin\left(\frac{\alpha+\beta}{2}\right)\sin\left(\frac{\alpha-\beta}{2}\right)

Using this, we find that

L_{n-1}(\epsilon)-L_n(\epsilon)=-2 \int_{\epsilon}^{\pi(1-\epsilon)}\frac{\sin((2n-1)x)\sin(-x)}{\sin x}\,dx =2 \int_{\epsilon}^{\pi(1-\epsilon)}\sin((2n-1)x)\,dx

Note that this integral no longer has any singularities, so we can safely take the limit

\lim_{\epsilon\to0}\left(L_{n-1}(\epsilon)-L_n(\epsilon)\right)=2 \int_{0}^{\pi}\sin((2n-1)x)\,dx

\lim_{\epsilon\to0}\left(L_{n-1}(\epsilon)-L_n(\epsilon)\right)=\frac{-2}{2n-1}\cos x\Big|_{0}^{2\pi n-\pi}=\frac{4}{2n-1}

We can sum over this relation from 1 to n to find

\lim_{\epsilon\to0}\left(\sum_{k=1}^{n}\left(L_{k-1}(\epsilon)-L_k(\epsilon)\right)\right)=\sum_{k=1}^{n}\frac{4}{2k-1}

Alo notice that this sum telescopes, i.e.

\lim_{\epsilon\to0}\left(\sum_{k=1}^{n}(L_{k-1}(\epsilon)-L_k(\epsilon))\right)=\lim_{\epsilon\to0}\left(-L_n(\epsilon)+L_0(\epsilon)\right)

Therefore,

\lim_{\epsilon\to0}\left(L_0(\epsilon)-L_n(\epsilon)\right)=\sum_{k=1}^{n}\frac{4}{2k-1}

\lim_{\epsilon\to0}L_n(\epsilon)=\lim_{\epsilon\to0}\left(L_0(\epsilon)-\sum_{k=1}^{n}\frac{4}{2k-1}\right)=\lim_{\epsilon\to0}\left(L_0-\sum_{k=0}^{n-1}\frac{4}{2k+1}\right)

Now recall that, with our limiting procedure involving \epsilon,

I=\lim_{\epsilon\to0}\left(\frac{1}{24}\int_{\epsilon}^{\pi(1-\epsilon)}\csc(u)\,du-\frac{1}{4\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\left(\int_{\epsilon}^{\epsilon(1-\pi)}\frac{\cos(2nu)}{\sin(u)}\,du\right)\right)

=\lim_{\epsilon\to0}\left(\frac{1}{24}\int_{\epsilon}^{\pi(1-\epsilon)}\csc(u)\,du-\frac{1}{4\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}L_n(\epsilon)\right)

=\lim_{\epsilon\to0}\left(\frac{1}{24}\int_{\epsilon}^{\pi(1-\epsilon)}\csc(u)\,du-\frac{1}{4\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\left(L_0(\epsilon)-\sum_{k=0}^{n-1}\frac{4}{2k+1}\right)\right)

=\lim_{\epsilon\to0}\left(\frac{1}{24}\int_{\epsilon}^{\pi(1-\epsilon)}\csc(u)\,du-\frac{1}{4\pi^2}L_0(\epsilon)\zeta(2)+\frac{1}{\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=0}^{n-1}\frac{1}{2k+1}\right)

Now, the observant reader will notice that

\lim_{\epsilon\to0}\int_{\epsilon}^{\pi(1-\epsilon)}\csc u\,du=\lim_{\epsilon\to 0}\int_{\epsilon}^{\pi(1-\epsilon)}\frac{\cos(2u\cdot 0)}{\sin u}\,du=\lim_{\epsilon\to0}L_0(\epsilon)

Therefore,

\lim_{\epsilon\to0}\left(\frac{1}{24}\int_{\epsilon}^{\pi(1-\epsilon)}\csc(u)\,du-\frac{1}{4\pi^2}L_0(\epsilon)\zeta(2)\right) =\lim_{\epsilon\to0}\left(\frac{L_0(\epsilon)}{24}-L_0(\epsilon)\cdot\left(\frac{1}{4\pi^2}\right)\left(\frac{\pi^2}{6}\right)\right) =\lim_{\epsilon\to0}L_0(\epsilon)\left(\frac{1}{24}-\frac{1}{24}\right)=0

Excellent cancellation of the divergent terms! We are left with

I=\lim_{\epsilon\to0}\left(\frac{1}{\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=0}^{n-1}\frac{1}{2k+1}\right)

Note that no terms involving \epsilon are left, so we can remove the limit and get

I=\frac{1}{\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=0}^{n-1}\frac{1}{2k+1}

Now notice that

\sum_{k=0}^{n-1}\frac{1}{2k+1}=1+\frac{1}{3}+\ldots+\frac{1}{2n-1}=H_{2n}-\sum_{k=1}^{n}\frac{1}{2n}=H_{2n}-\frac{H_n}{2}

where H_n is the n’th harmonic number.

This lets us simplify our series into

I=\frac{1}{\pi^2}\sum_{n=1}^{\infty}\frac{1}{n^2}\left(H_{2n}-\frac{H_n}{2}\right)

We must now evaluate these two sums separately

I=\frac{1}{\pi^2}S_1-\frac{1}{2\pi^2}S_2

S_1=\sum_{n=1}^{\infty}\frac{H_{2n}}{n^2}

S_2=\sum_{n=1}^{\infty}\frac{H_n}{n^2}

Let us begin with the second sum, which has a simpler H_n rather than H_{2n}

Plot of S_1=\sum_{n=1}^{N}\frac{H_{2n}}{n^2} in green and S_2=\sum_{n=1}^{N}\frac{H_n}{n^2} in white with N \in [0,1000], showing visually how these series converge

A moderately gnarly series

We are considering

S_2=\sum_{n=1}^{\infty}\frac{H_n}{n^2}

The first trick we employ is introducing an integral representation for the harmonic numbers,

H_n=\int_{0}^{1}\frac{1-x^n}{1-x}\,dx

Plugging this in yields

S_2=\sum_{n=1}^{\infty}\frac{1}{n^2}\left(\int_{0}^{1}\frac{1-x^n}{1-x}\,dx\right)=\int_{0}^{1}\frac{1}{1-x}\left(\sum_{n=1}^{\infty}\frac{1-x^n}{n^2}\right)\,dx

The interchange of integration and summation can be justified by Tonelli’s theorem, since \frac{1-x^n}{n^2(1-x)} is measurable and nonnegative for x\in (0,1).

We can use use the definition of the polylogarithm to turn this into a friendlier expression

\mathrm{Li}_n(x)=\sum_{k=1}^{\infty}\frac{x^k}{k^n}

S_2=\int_{0}^{1}\frac{\zeta(2)-\mathrm{Li}_2(x)}{1-x}

Now we must find the integral of \frac{\mathrm{Li}_2(x)}{1-x}.

Apply integration by parts with u=\mathrm{Li}_2(x) and \,dv=\frac{1}{1-x}. We easily find that v=-\ln(1-x)

From the definition of the polylogarithm, we find

\frac{\,d}{\,dx}\mathrm{Li}_n(x)=\sum_{k=1}^{\infty}\frac{kx^{k-1}}{k^n}=\frac{1}{x}\sum_{k=1}^{\infty}\frac{x^k}{k^{n-1}}=\frac{\mathrm{Li}_{n-1}(x)}{x}

So \,du=\frac{\mathrm{Li}_1(x)}{x}

However, note that

\mathrm{Li}_1(x)=\sum_{k=1}^{\infty}\frac{x^k}{k}=-\ln(1-x)

Therefore, \,du=\frac{-\ln(1-x)}{x}

Thus,

\int \frac{\mathrm{Li}_2(x)}{1-x}\,dx=-\ln(1-x)\mathrm{Li}_2(x)-\int \frac{\ln^2(1-x)}{x}\,dx

This new integral can be solved with the substitution t=1-x, yielding

\int \frac{\ln^2(1-x)}{x}\,dx=-\int \frac{ln^2(t)}{1-t}\,dt

Again apply integration by parts with u=\ln^2(t), \,dv=\frac{1}{1-t}, \,du=\frac{2\ln(t)}{t}, v=-\ln(1-t) and find

\int \frac{ln^2(t)}{1-t}\,dt=-\ln^2(t)\ln(1-t)+2\int \frac{\ln(t)\ln(1-t)}{t}\,dt

Finally, apply integration by parts just once more with u=\ln(t) and \,dv=\frac{\ln(1-t)}{t}. Remember the formula for the derivative of \mathrm{Li}_2(x)=\frac{-\ln(1-x)}{x} so v=-\mathrm{Li}_2(t). Thus,

\int \frac{\ln(t)\ln(1-t)}{t}\,dt=-\ln(t)\mathrm{Li}_2(t)+\int \frac{\mathrm{Li}_2(t)}{t}\,dt=-\ln(t)\mathrm{Li}_2(t)+\mathrm{Li}_3(t)

Now go back to our original integral and remember to change t to 1-x everywhere, in accordance with our substitution

\int \frac{\mathrm{Li}_2(x)}{1-x}\,dx=-\ln(1-x)\mathrm{Li}_2(x)-\int \frac{\ln^2(1-x)}{x}\,dx

=-\ln(1-x)\mathrm{Li}_2(x)+\int \frac{\ln^2(t)}{1-t}\,dx

=-\ln(1-x)\mathrm{Li}_2(x)-\ln^2(1-x)\ln(x)-2\ln(1-x)\mathrm{Li}_2(1-x)+2\mathrm{Li}_3(1-x)

Excellent!

Now let’s go back to our earlier expression

S_2=\int_{0}^{1}\frac{\zeta(2)-\mathrm{Li}_2(x)}{1-x}

\begin{gathered} S_2 = \biggl(-\zeta(2)\ln(1-x)+\ln(1-x)\mathrm{Li}_2(x)+\ln^2(1-x)\ln x\\ \qquad+2\ln(1-x)\mathrm{Li}_2(1-x)-2\mathrm{Li}_3(1-x)\biggr)\Big|_{0}^{1} \end{gathered}

Note that \mathrm{Li}_n(0)=0, \mathrm{Li}_n(1)=\sum_{k=1}^{\infty}\frac{1}{k^n}=\zeta(n), and \ln(1)=0. This makes most of the terms go to zero and yields

\sum_{n=1}^{\infty}\frac{H_n}{n^2}=-\zeta(2)ln(0)+\ln(0)\zeta(2)+2\zeta(3)=2\zeta(3)

What an incredible simplification! Now let’s see how to go about the more complicated sum S_1.

A very gnarly series made easier by our having solved a moderately gnarly one

Now for the most intimidating series yet,

S_1=\sum_{n=1}^{\infty}\frac{H_{2n}}{n^2}

Begin by noting that

H_{2n}=\sum_{k=1}^{n}\frac{1}{k}+\sum_{k=n+1}^{2n}\frac{1}{k}=H_n+\sum_{k=1}^{n}\frac{1}{n+k}

Therefore,

S_1=\sum_{n=1}^{\infty}\frac{H_{2n}}{n^2}=\sum_{n=1}^{\infty}\frac{H_n}{n^2}+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{n^2(n+k)}

S_1=2\zeta(3)+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{n^2(n+k)}

This double summation looks intimidating but actually becomes amazingly simple once a partial fraction decomposition is introduced that leads to a telescoping property. We use

\frac{1}{n^2(n+k)}=\frac{1}{n^2k}+\frac{1}{k^2}\left(\frac{1}{n+k}-\frac{1}{n}\right)

This leads to

\begin{aligned} \sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{n^2(n+k)}&=\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=1}^{n}\frac{1}{k}+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{k^2}\left(\frac{1}{n+k}-\frac{1}{n}\right)\\ &=\sum_{n=1}^{\infty}\frac{H_n}{n^2}+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{k^2}\left(\frac{1}{n+k}-\frac{1}{n}\right)\\ &=2\zeta(3)+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{k^2}\left(\frac{1}{n+k}-\frac{1}{n}\right) \end{aligned}

Now we make a series of maneuvers to try to find a telescoping relation. First notice that we would infinitely prefer to have \frac{1}{n^2} rather than \frac{1}{k^2} so that we can get nice relations to the Riemann zeta function. Therefore, we need to try re-indexing to get that term.

We can re-index using the following argument. Suppose f(k)=\frac{1}{k^2} and g(n,k)=\frac{1}{n+k}-\frac{1}{n}

Then we have a double sum of the form

\begin{aligned} \sum_{n=1}^{\infty}\sum_{k=1}^{n} f(k)g(n,k) &= f(1)g(1,1) \\ &\quad + \bigl[f(1)g(2,1) + f(2)g(2,2)\bigr] \\ &\quad + \bigl[f(1)g(3,1) + f(2)g(3,2) + f(3)g(3,3)\bigr] + \cdots \\ \\ &=f(1)g(1,1)+f(2)\biggl(g(2,2)+g(3,2)+\cdots\biggr) \\ &\quad + f(3)\biggl(g(3,3)+g(4,3)+\cdots\biggr)+\cdots \\ \\ &=\sum_{n=1}^{\infty}f(n)\sum_{k=n}^{\infty}g(k,n) \end{aligned}

So, with our choice of f(k) and g(n,k), we find

\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{k^2}\left(\frac{1}{n+k}-\frac{1}{n}\right)=\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=n}^{\infty}\left(\frac{1}{n+k}-\frac{1}{k}\right)

Great, we’ve gotten that \frac{1}{n^2} that leads to zeta function terms, and we also have an inner sum that easily yields a telescoping relation.

Let’s consider the inner sum on its own \begin{split} & \lim_{N\to\infty}\sum_{k=n}^{N}\left(\frac{1}{n+k}-\frac{1}{k}\right) \\ & =\lim_{N\to\infty}\left(\sum_{k=n}^{N-n}\frac{1}{n+k}+\sum_{k=N-n+1}^{N}\frac{1}{n+k}-\sum_{k=n}^{2n-1}\frac{1}{k}-\sum_{k=2n}^{N}\frac{1}{k}\right) \\ & = \lim_{N\to\infty}\left(\sum_{k=n}^{N-n}\frac{1}{n+k}+\sum_{k=N-n+1}^{N}\frac{1}{n+k}-\sum_{k=n}^{2n-1}\frac{1}{k}-\sum_{k=n}^{N-n}\frac{1}{n+k}\right)\\ & = \lim_{N\to\infty}\left(\sum_{k=N-n+1}^{N}\frac{1}{n+k}-\sum_{k=n}^{2n-1}\frac{1}{k}\right)\\ &=-\sum_{k=n}^{2n-1}\frac{1}{k}=-(H_{2n-1}-H_{n-1})=H_{n-1}-H_{2n-1}\\ &=H_n-\frac{1}{n}-\left(H_{2n}-\frac{1}{2n}\right)=H_n-H_{2n}-\frac{1}{2n} \end{split}

Therefore,

\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=n}^{\infty}\left(\frac{1}{n+k}-\frac{1}{k}\right)=\sum_{n=1}^{\infty}\frac{H_n}{n^2}-\sum_{n=1}^{\infty}\frac{H_{2n}}{n^2}-\frac{1}{2}\sum_{n=1}^{\infty}\frac{1}{n^3} =2\zeta(3)-S_1-\frac{\zeta(3)}{2} =\frac{3\zeta(3)}{2}-S_1

Now combine our last few major results to find

\begin{split} S_1 &=2\zeta(3)+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{n^2(n+k)}\\ &=2\zeta(3)+\left(2\zeta(3)+\sum_{n=1}^{\infty}\sum_{k=1}^{n}\frac{1}{k^2}\left(\frac{1}{n+k}-\frac{1}{n}\right)\right)\\ &=4\zeta(3)+\sum_{n=1}^{\infty}\frac{1}{n^2}\sum_{k=n}^{\infty}\left(\frac{1}{n+k}-\frac{1}{n}\right)\\ &=4\zeta(3)+\left(\frac{3\zeta(3)}{2}-S_1\right) \end{split}

And finally, we arrive at

S_1=\sum_{n=1}^{\infty}\frac{H_{2n}}{n^2}=\frac{11\zeta(3)}{4}

Yet another mind-blowing simplification. Now let’s plug our values for S_1 and S_2 into our expression for I to actually solve the integral.

Wrapping up and solving the integral

Our last expression for I was

I=\int_{0}^{1}\frac{x-\frac{1}{2}}{\ln\left(\frac{x}{1-x}\right)}\,dx=\frac{1}{\pi^2}S_1-\frac{1}{2\pi^2}S_2

We found that S_1=\frac{11\zeta(3)}{4} and S_2=2\zeta(3)

Therefore,

\int_{0}^{1}\frac{x-\frac{1}{2}}{\ln\left(\frac{x}{1-x}\right)}\,dx=\frac{11\zeta(3)}{4\pi^2}-\frac{4\zeta(3)}{4\pi^2}=\frac{7\zeta(3)}{4\pi^2}

What an incredible result! We’ve managed to get an answer involving both \pi^2 and \zeta(3), which is really cool.

After having done so much work, it’s easy to lose sight of just how convoluted this process was and how many times the integral proved to have really nice properties that made life easier. Divergent terms appeared several times, such as \int_{0}^{1}\csc(\pi s)\,ds and \lim_{x\to0}\ln(x)\zeta(2), but always in such a manner that they cancelled out and didn’t cause problems, which strikes me as incredible. In the sums, we found lots of recurrence relations and telescoping relations that led to crazy simplifications where almost all the terms disappeared. And we got to introduce all kinds of exotic functions with amazing properties, which further added to the fun – \zeta(s),\Gamma(s), and \mathrm{ Li}_n(x). The vast array of techniques used and the elegance of the solution have made this made my favorite integral and hopefully at least top 10 for my readers as well.

Today we have learnt that the Maths505 comments section may or may not contain the key to enlightenment in the form of indefinite integrals. Hopefully the reader has enjoyed this mathematical nirvana as much as I have. If you have comments, corrections, or random thoughts, feel free to message me on Discord or email me (contact info in the About section of this site). Thanks for reading!

My Review of ‘The Disinherited State: A Study of West Bengal 1967-70’ by Sankar Ghosh

Fri, 05 Jun 2026 00:00:00 GMT

My Review of ‘The Disinherited State: A Study of West Bengal 1967-70’ by Sankar Ghosh

This is one of the best history books I’ve read; tons of evidence paired with strong analysis that provides a great framework for understanding West Bengal’s United Front (UF) government, and it’s also just really fun to read. I was initially skeptical of a 300 page book on a time span of just three years, but this book proved that the UF government witnessed enough chaos for its story to fill well over 300 pages. The strongest point of this book is its immense educational value. Before reading this book, I was only dimly aware of the UF as a shaky coalition between the Bangla Congress, CPIM, and other left parties, plagued by the wave of violence sparked by Naxalbari, CPIM’s own political violence, and the UF giving workers an implicit invitation to gherao factory managers. Ghosh’s book strengthened my understanding of these key issues and introduced me to many others I was unaware of: Jyoti Basu’s misuse of the police for political purposes, the infighting and chaotic deal-making between UF constituents, the UF’s support for extrajudicial occupation of benami land, and more. Apart from highlighting the key issues of the UF government, it’s also useful as a chronological, blow-by-blow account of how the UF both rose and fell (twice) as a result of its infighting and poor governance. Anyone seeking to understand West Bengal’s history or the roots of its current problems would benefit from reading this book, as well as people just interested in a fascinating story with lots of food for thought.

I was impressed by the large amount of evidence presented by Ghosh, much of which would be difficult to find today through Google searches or even searching archived newspapers or government records (often poorly kept). He frequently cited incidents of violence or political controversy of which little record exists online apart from brief mentions in archived minutes of Rajya Sabha debates, making the book a brilliant feat of documenting history that would otherwise disappear from public record and memory. The incidents he cited were also just fascinating to read about, often reading more like narrative fiction than the dense history book this appears to be: stories of comical blunders committed by long-gone parties like the Bolshevik Party and Revolutionary Communist Party of India (RCPI), leading to more party splits and political chaos; cases of rioting and violence that reveal the complete collapse of law and order under the UF, while also told in such a gripping way that it’s addictive to read; and a talent for guessing which stories will best prove his argument while also entertaining readers, such as an incident in which the first UF Labor Minister Subodh Banerjee (the progenitor of the gherao) was himself gherao’ed. Ghosh makes great use of these 300 pages to introduce all the key events on the timeline of UF rule and also highlight lesser-known incidents that are demonstrative of larger problems. By the end of the book, you have a much clearer picture of what life was like amidst the violence and disorder of these 3 years. Even beyond its other intellectual merits, this book is commendable as an aid to immersion in a particular time and place.

Apart from the narrative-style evidence consisting of reports on events and happenings, Ghosh also makes excellent use of tables and numbers that highlight the economic problems of Bengal under the UF, e.g. a table showing the number of work stoppages, men involved, and man-days lost in Bengal every year from 1960 to 1969, or a comparison of what percent of ICICI and IFC assistance went to Bengal versus different states, or a table showing per capita central government assistance to different states under the economic plans dating from 1956 to 1968. In other words, it’s an economics-enthusiast’s paradise. Many of these numbers would be hard to find anywhere else without being a professional historian who would get paid to spend hours searching through ancient government records.

The wealth of narrative-style evidence and numerical evidence lends a high degree of credibility to Ghosh’s arguments. His strong analytical skills further strengthen the book: clear thinking and an ability to synthesize dozens of events and tables into an overarching narrative of how structural faults in the UF made it dead on arrival. He identifies trends and fundamental problems that help understand why the UF government was such a disaster. Particularly interesting is his analysis of the left parties’ motives for allying with the Bangla Congress and forming the ruling coalition.

The main reason for the clashes between the UF parties was that though they had decided to co-exist in the Government, they were against co-existence on the organisational level. They wanted not merely to grow, but to grow at the expense of their colleagues in the Front. As the most powerful constituent with control over all departments dealing with mass organisations, the CPI(M) was in a much better position than the other parties to carry out this programme. It could dole out privileges to the mass organisations through the departments concerned to prepare the ground for a take-over; it could restrain the police or, if necessary, use them to its own end at the time of the takeover.

Ghosh provides a number of interesting explanations for the UF government’s dysfunction, most ultimately stemming from deeper issues with the constituent parties’ motives and their constant clash with each other. For example, the Socialist Unity Centre’s (SUC) Subodh Banerjee was the Labor Minister in the first UF government, and his lasting ‘contribution’ to Bengal was the introduction of the gherao, a form of labor protest that did irreparable damage to the state’s economy. Ghosh cited an interesting and rather convincing explanation (initially voiced by other left parties opposed to the SUC) for Subodh Banerjee introducing a measure so damaging to his own government’s reputation:

Other left parties have alleged that the SUC encouraged gheraos because of its weakness in the labour front. It did not control big unions capable of organising strikes; in many units it was altogether non-existent. The party had to seek, therefore, a quick and easy way to spread its influence taking advantage of Banerjee’s ministership; it chose gherao as that did not require much organisation. A handful of workers claiming allegiance to the SUC could stage a gherao and through the intervention of the minister wrest some benefits from the employers. The workers, who are primarily interested in immediate benefits, would naturally be attracted towards unions capable of bringing them such easy and quick relief; they would desert their old unions for the small benefits that gheraos might bring. It is stated that the number of SUC unions went up considerably during the nine months of the first UF regime while many old established unions lost heavily in membership. With the multiplicity of unions, inter-union rivalries sharpened, and the labour movement was, on the whole, weakened by gheraos.

This book offers fantastic analysis of how greed and political rivalry created some of the UF’s worst problems, as shown above. There are also good explanations of the impact all this chaos had on law and order and the state’s economy. For example, here’s Ghosh citing the results of a study on gheraos’ effect, set up by the National Commission on Labor:

Discussing the effects of gheraos the study group reported that in most cases gheraos had left a trail of indiscipline, go-slow, or work-to-rule by workers while in others the tempo ’sought to be created as a prelude to gheraos had similar effects. Quality and quantity of products suffered; in some cases factories lost orders as they could not adhere to the production schedule or deliver goods in time. Supervisors could not discharge their normal functions. The normal industrial relations machinery of the State became ineffective. In a number of cases the Labour Minister himself intervened, but there were instances where workers refused to accept his advice and persisted in their coercive tactics. There were cases where the management staff were subjected to harassments, gheraos, and even assault while coming out of conciliation meetings. In some places workers were able to extract concessions from the management. But gheraos led to closure of a number of small establishments and lockouts rendering a large number of workers unemployed. It was estimated that the number of persons rendered unemployed went up approximately to 80,000 by the end of September; however, in the beginning of October some mills resumed working. Gheraos resorted to by workers in some places also stiffened the attitude of the management who might have otherwise settled the disputes on a reasonable basis.

I’m quoting extensively from the book because I think these excerpts offer a good glimpse of the kind of powerful analysis it offers. If you want to learn about the UF government, this is a top-tier book: entertaining, informative, and well-written.

In addition to being a good history book, “The Disinherited State” is useful in its capacity to help us make better decisions in the present. There’s a lot of wisdom to be gained from this book, and many of the forces described in the UF government are still present today. In particular, I feel it’s important for policymakers and voters to keep in mind the continuing issue of unions’ behavior often toeing a line between legitimate protest and extortion, the tendency of the ruling party/parties to use government resources (e.g. police misuse or running patronage networks with government funds and jobs) to strengthen their political front, the issue of political defections stemming from opportunism and backdoors conniving, and the prevalence of political violence. If this book is read closely, a lot can be learnt both about the past and the present.

Closing note -- no, I didn't misspell Mr. Ghosh's first name, I have no idea why there is so little consistency in the English transliterations of Bengali names.

My Thoughts on Melita Maschmann’s 'Account Rendered: A Dossier On My Former Self'

Sun, 11 Jan 2026 00:00:00 GMT

My Thoughts on Melita Maschmann's "Account Rendered: A Dossier On My Former Self"

My Thoughts on Melita Maschmann’s “Account Rendered: A Dossier On My Former Self”

I’m going to preface this book review by saying that I do draw some connections here between Nazi Germany and current-day political movements. I am at no point trying to trivialize the atrocities committed by Nazi Germany or compare their magnitude to anything being done today, but it is important to notice that there are similarities in how Nazism took root in Germany and how similar extremist ideologies gain support today. I am attempting to draw lessons from the past here, and I am not trying to equate the atrocities of Nazi Germany with anything being done today. This is a common accusation leveled against articles on this topic, so I thought I should include this explanation; apologies for the length. With that out of the way, onwards with the actual book review.

“Account Rendered” was written by Melita Maschmann, a former Nazi who became one of the rare success stories of denazification; this book is the story of her ideological and personal development, starting from her early childhood and ending in the aftermath of World War 2 as she finally realizes the inhumanity of National Socialism and recants her beliefs. Maschmann gives an incredible analysis of National Socialism and the cultural factors that helped supplant it in the minds of so many of the German people, including herself, while also helping us understand the mechanisms through which complete indoctrination can slowly be fought against.

The most interesting aspect of her story is how ‘normal’ she was; she was born into a slightly conservative middle-class family, and, throughout the book, she demonstrates the capacity for critical judgement of authorities, appreciation for literature, and compassion towards others. None of these would make her mind seem like fertile ground for the seeds of Nazism, and yet she did become infatuated with the racist and antisemitic ideology of Hitler. This book is a fascinating read because it reveals how ordinary, middle-class people can fall prey to political radicalization with devastating consequences.

I don’t want to spoil the entire book, but I will list some of the more interesting factors in her radicalization to give an idea of what the book is about.

The first factor she mentioned was her view of National Socialism as a foil to her parents’ bourgeois values; she cites “a rebelliousness that went beyond the purely personal rebellion of adolescence and was directed against the bourgeois values which my parents represented.” Having grown up under strict parenting, she spent her teenage years looking for ways to rebel and assert her own identity, distinct from that of her parents; National Socialism, which exalted the German peasantry and spoke of a “National Community” of all Germans, seemed the perfect route through which to satiate this teenage thirst to be different from one’s parents.

This idea is interesting for two reasons.

Firstly, the teenage tendency towards rebellion is a universal phenomenon, and I was struck by how Maschmann’s story demonstrates the susceptibility of anyone, regardless of their background or education, to political radicalization. She was driven towards Hitler by factors that could affect anybody, regardless of time or place.

Secondly, this factor is interesting because it reveals the broader theme of how National Socialism gained popularity among many of the more rational Germans by downplaying the antisemitic aspects and emphasizing the desire to rebuild Germany and improve the lives of the poor. This is a constant theme throughout the text; the very name “National Socialism” shows how Nazism succeeded by merging its nationalism and antisemitism with just enough of a socialist veneer to appeal to left-leaning members of the middle class, who would otherwise find Hitler’s fanaticism absurd. Maschmann comments throughout the book on how she found the education on scientific racism comical and poorly thought-out; Nazism gained popularity among putatively more rational parts of the middle class because it hid its ugliest characteristics under the guise of serving the ‘National Community.’

Maschmann herself avoided the most violent and sinister parts of Nazi Germany’s state apparatus, working mainly in the propaganda division and the labor service. Maschmann’s work in the labor service was another factor in her support for Hitler that again ties into this theme of obscuring violent fanaticism beneath a guise of community service and patriotism. She spent a long time in the labor service and reflected throughout the book on how it shaped her opinion of National Socialism. Her work required her to help poor German farmers settle newly annexed Polish land, assisting with agricultural work but also taking care of sick children, helping pregnant women prepare for childbirth, and organizing funerals. Maschmann’s work in the labor service bolstered her belief that National Socialism focused on the benefit of the German poor and that antisemitism and racism were just peripheral components of the ideology.

Despite the labor service showing the community service aspect of National Socialism, she still encountered evidence of Nazism’s inhumanity with increasing frequency – so how did she avoid confronting that evidence and recognizing Nazism for what it was? She constantly emphasizes that the reason her support for Hitler lasted so long was because she trained herself to just not question the most evil things she was witnessing; a big part of the book focuses on how it’s possible for people to so completely shut down some parts of their mind

A person who has never lived under the tutelage of an ‘ideology’ will find it hard to understand how it is possible for such pressing questions not to be asked.

She found a few explanations for her indifference to the atrocities she witnessed and her unquestioning obeisance to National Socialism. She rationalized to herself the cruelty towards the Poles by thinking of the violence unleashed by the Polish partisans and convincing herself that different standards apply during a war.

The war had started. Since I had seen the sufferings of the German community, some of whom had been killed by the Poles, I believed I had learned that one must harden oneself against the sight of human suffering.

After the Kristallnacht, she justified the pogrom by remembering her ideological training that taught her that Jews were the enemies of Germany. This rationalization is interesting because Maschmann herself admitted that the antisemitic and racist components of the ideological training seemed the most ridiculous; she did not see the vilification of Jews as a vital component of National Socialism that she should wholeheartedly support, but rather as a convenient way of avoiding intellectual confrontation with the insane inhumanity staring her in the face. Maschmann’s support of Hitler, throughout the book, has very little to do with the parts of his agenda focusing on the persecution of Jews, homosexuals, or disabled people; she supported Hitler because she believed he was avenging the injustice done to Germany by the Treaty of Versailles, restoring Germany to its ‘rightful place,’ and improving the lot of the poor. She avoided the facts of the regime’s evil through the crude justifications discussed here.

The true horror of this book isn’t that Maschmann was herself cruel or violent, it is that she so completely closed off her mind to confronting the reality around her and found so many ways of rationalizing to herself the cruelty of the Nazis. Even though this wilful ignorance is disturbing to read about, it is important to read this book and see how it came about. Maschmann had Jewish friends even during her early days in the Hitler Youth and saw them as good people; it was Hitler’s dehumanization of Jews in his rhetoric and his framing of them as an evil ‘other,’ separate from the Jews that Maschmann actually saw day-to-day, that allowed Maschmann and countless others to reconcile antisemitism with their own positive relations with Jewish friends and neighbors. She finally cut ties with her Jewish friends not out of hatred for them but rather seeing it as a slightly unfortunate but necessary step to complete her full entry into the sphere of National Socialism.

There was only one thing that made me glad to leave Berlin. In this way I could allow my friendship with you [addressed to one of her Jewish friends] and your family to fade away. I wanted to avoid the open breach, which — after years of evading the conflict — I nevertheless felt to be my duty, because one could only do one of two things: either have Jewish friends or be a National Socialist.

In preaching that all the misery of the nations was due to the Jews or that the Jewish spirit was seditious and Jewish blood was corrupting, I was not compelled to think of you or old Herr Lewy or Rosel Cohn: I thought only of the bogey- man, ‘the Jew’. And when I heard that the Jews were being driven from their professions and homes and imprisoned in ghettos, the points switched automatically in my mind to steer me round the thought that such a fate could also overtake you or old Lewy. It was only the Jew who was being persecuted and ‘made harmless’.

Taken as a whole, Maschmann’s account presents many powerful lessons on how fascist ideologies take root within a population; in her case, it seems to be, among other things, a combination of something new and different appealing to teenage rebelliousness, a veneer of patriotism and community service concealing the violent racism, and rhetoric that treated Jews as a monolithic evil separate from individual people, as well as the idea that the standards of basic humanity change during a war.

This book has special relevance today as the politics of hate again becomes mainstream in many corners of the world. Maschmann’s experience proves that nobody is completely immune to propaganda and radicalization; already, we are seeing rational human beings lend their support to authoritarian regimes with vague promises to “Make America Great Again” or bring “Acche Din” (good days) to India. Maschmann’s book serves as a way of better understanding the current times and also remaining vigilant so that we ourselves do not fall prey to such radicalization, better aware of the mechanisms by which such poisonous ideas enter our minds. It is an essential read for anyone hoping to avoid repeating the mistakes of the past and save the 21st century from a resurgence of politics rooted in hate and fear.

That is what I should like to say to every good person. Not with the implication: ‘Your goodness has feet of clay just as much as mine had’, but rather to implore him: ‘Be on your guard.’ Take warning. There is nowhere any good thing — however worthy of respect it may seem — which one may serve with the means of evil (that is of lovelessness).

However, Maschmann does not just end with an ominous warning. She also describes her slow disillusionment and eventual abandonment of National Socialism. Many of the key steps come from the gradual destruction of Germany and the dream she believed she was fighting for: crawling out of a cellar, the only person alive after thirty people including her parents suffocated or burned to death during a bombing raid; hearing the leader of the Hitler Youth confess to having sent children to fight and die in the defense of Berlin; and finally coming to terms with the defeat of Germany in World War 2, the slaughter of six million Jews, and the inhumanity of the regime she had spent years supporting.

The pessimistic interpretation of her story is that the only way to combat political radicalization is waiting for it to run its course and inevitably end in tragedy. However, Maschmann also highlights cases where, even at the peak of Hitler’s power and the persecution of his political opponents, some incredibly brave and clear-eyed individuals tried to convince her that National Socialism was the wrong path for Germany. While she did not heed their warnings at the time, she remembered their words years later and then began to think about the contradictions they had highlighted in the ideology of National Socialism. After the end of World War 2 and Maschmann’s release from an Allied Forces prison, her denazification was accelerated by honest conversations about National Socialism, Christianity, and the last few years of chaos and violence; she repeatedly noted that the people guiding her away from Nazism had greater integrity and decency than the leaders she had dealt with in the Nazi Party. Maschmann’s story teaches us that open debate and challenging dogmatic thinking can play a crucial role in combating political radicalization and blind faith in extremist ideologies.

Maschmann also became more disillusioned with Nazism as she began to read about the Holocaust, finally being forced to confront the evil of the regime she had supported, and also as she thought critically about how the works of classical German poets such as Hölderlin had been crudely reinterpreted as support for Nazism. The final pages of Maschmann’s book demonstrate the cruciality, even today, of encouraging people to think carefully about everything they read or see and to be aware of everything that goes on in the world, being aware of the atrocities committed in the name of one’s preferred ideology. As we again encounter the issue of political radicalization in the 21st century, many valuable lessons can be drawn from “Account Rendered.”

Maschmann’s book offers a window into an important period of history with many lessons to help us make a better world today; her clear prose and remarkable capacity for self-reflection make this one of the most important books for anyone looking to better understand the rise of Hitler, the process of denazification, and the mechanisms by which political radicalization takes place and can also be combated.

Thoughts on the Cockroach Janta Party

Wed, 10 Jun 2026 00:00:00 GMT

Thoughts on the Cockroach Janata Party

Thoughts on the Cockroach Janta Party

The Cockroach Janta Party (CJP) is useful as a demonstration of public anger and an impetus for the government to do better in the administration of standardized tests, but its current form will not permit it to fulfill any more meaningful role. The party’s rhetoric is designed for a social media movement, and their website explicitly defines them as “a party for the young people who keep getting called lazy, chronically online, and — most recently — cockroaches”; this social media orientation bars them from introducing the depth and nuance necessary in more productive political movements, since they’re marketing themselves on Twitter and Instagram to an audience that likes sound bites and short videos more than complex, long-form communication. This is most clearly reflected in their five-point manifesto. The sentiment behind each of their goals is laudable, but the reductive language and refusal to address more divisive issues is problematic and reflects the broader problem of trying to harness youth anger rather than well-thought-out political ideas. I will review the points in their manifesto one by one and explain my thoughts.

If the CJP comes in power, no Chief Justice shall be granted a Rajya Sabha seat as a post-retirement reward.

The first point about sinecures for retired Chief Justices leverages a public perception of corruption within the institutions of democracy, especially the judicial system, and the Indian public’s instinctive outrage towards any corruption scandal; however, the CJP’s manifesto is only an effective social media campaign playing off that anger, and fails to propose any meaningful path forward. The Chief Justice of India is only one part of the judicial system that has historically suffered from corruption and conflict of interests, and a proper overhaul of the system would seek to reform all the other broken components: executive overreach in judicial matters, the excessive centralization of power within the Supreme Court rather than sharing power with the High Courts, politically motivated transfers of judges, etc. The CJP’s manifesto neglects all of these points and reduces the issue of judicial corruption to the whopping number of two Chief Justices who received Rajya Sabha seats after retirement: a useful promise to make if your goal is mobilizing chronically online reels-junkies, but unhelpful towards actually productive discourse or reform.

If any legit vote is deleted, whether in a CJP or opposition-ruled state, the CEC shall be arrested under UAPA, as taking away voting rights of citizens is no less than terrorism.

The second point about the Chief Election Commissioner (CEC) and vote chori is similarly reductive and symptomatic of social media’s focus on soundbites and knee-jerk reactions rather than well-thought-out solutions to problems. Throwing morally compromised CECs in jail is an emotionally satisfying proposal for angry youths, but this on its own fails to install the more complex institutional safeguards that would actually solve the issue of vote chori and prevent future voter roll revisions from being as poorly managed as the current one. Doubly concerning is that the CJP plans to arrest corrupt CECs under the UAPA rather than under anti-corruption laws, since the UAPA uses vague language to define ‘terrorism’ and has historically been used to punish political opponents and dissidents; this tacit approval of the UAPA is disappointing to see. Equally concerning is the equating of vote chori with terrorism, symptomatic of the CJP’s emotionally charged rhetoric that eschews nuance in favor of anger and knee-jerk reactions – great for street protests and triggering resignations, detrimental to actual statecraft and governance. In this sense, the CJP is no better than the BJP: both parties call their opponents “terrorists” and aim to prosecute them under laws that violate due process, rather than seeking legally sound solutions to complex problems.

Women shall receive 50% reservation, not 33%, without increasing the strength of Parliament. Additionally, 50% of all Cabinet positions shall be reserved for women.

The third point about women’s reservations in the Lok Sabha is a good idea, but the outright refusal to consider delimitation is possibly a mistake. Introducing a 50% reservation for women in Parliament without increasing the number of seats would result in around 36% of all MPs losing their seats (50% reservation minus 14% already women), not because of mistakes on their part that caused the electorate to lose faith in them, but because they’re barred from running in constituencies reserved for women. This would be unfair to the many male legislators who have done good for their constituency and are disqualified from running simply because a compromise couldn’t be worked out over delimitation. The specifics of delimitation are up for debate, e.g. whether the relative strength of different states should stay static or reflect changes in population, but a blanket ban on delimitation is a bad idea. While there are some proposals for how to mitigate the issue of male MPs arbitrarily losing seats (such as rotating which constituencies are women-reserved), this introduces problems with continuity in governance and many promising politicians still having to change constituencies every five years, preventing them from building long-term relationships with constituents and developing the reputations necessary to achieving greater prominence and influence in politics in accordance with their ability. I am myself undecided on how/whether delimitation should be done, which is why I’ve called this ‘possibly’ a mistake – there’s a strong argument to be made that men should be willing to make political sacrifices for the sake of women’s representation, and it’s also difficult to find the correct middle-point between the “one person, one vote” principle and the obligation to balance different states’ interests regardless of population. The optimal solution to this problem will be complex, but the CJP’s outright refusal to consider delimitation seems a knee-jerk reaction to the recent controversy over it, symptomatic of lazy thinking and ignoring potential negative consequences, and unamenable to the compromise necessary to working out a solution in Parliament.

All media houses owned by Ambani and Adani shall have their licences cancelled to make way for truly independent media. Bank accounts of Godi media anchors shall be investigated.

Shifting away from the third point’s partly-reasonable-but-somewhat-flawed idea, the fourth point returns to being completely reductive. The constitutional protection of freedom of speech and press make it illegal to cancel Adani- and Ambani-owned media houses’ licenses just because the CJP dislikes their style of reporting. I’m curious how this would be implemented – perhaps News18 will be deemed disruptive of the “sovereignty and territorial integrity of India” and prosecuted under the UAPA, as they intend to do with the CEC? The Godi media is biased in favor of the BJP, spreads disinformation, and is harmful to Indian society, but the Indian Constitution very wisely protects free speech, meaning that Adani- and Ambani-owned media houses have a right to exist, even if they’re a stain on democracy. A legally sound solution respecting democratic values should combat the issue of biased media through media literacy education in schools and stricter rules on government support to media houses, rather than arbitrarily banning media houses and violating the right to freedom of speech and press. The CJP’s manifesto neglects those more effective solutions in favor of this ban because they are a social-media movement rather than a mature political party: solutions involving arresting people, cancelling licenses, and other extreme, vindictive actions are emotionally satisfying to read about and effective with the CJP’s audience of Twitter doomscrollers, even though these are bad ideas in reality. This point in their manifesto again reflects the core limitation of the CJP.

Any MLA or MP who defects from one party to another shall be barred from contesting elections — and from holding any public office — for a period of 20 years.

Again, back to these reductive-but-popular solutions involving blanket bans and zero nuance. What happens if there is actually good reason for a political defection? Consider the 1969 split of the Indian National Congress, triggered by Indira Gandhi’s development of a cult of personality, support for radical economic policies that discomfited many INC politicians, and her backing of an independent candidate for president over the Congress’ official candidate. This is a clear case of politicians jumping ship because of legitimate concerns with preserving the values for which they joined a party, men of integrity unwilling to place party above morals. Would the CJP have disqualified the INC(O) lawmakers from holding public office? Or, in the 1977 elections, would the CJP have barred Jagjivan Ram from leaving Indira Gandhi’s Congress and joining the Janata Party to defend India against her authoritarianism? This is a clear case of defection, so shouldn’t Jagjivan Ram have been denounced as a political opportunist and barred from politics until 1997? Again, CJP’s proclivity for simplistic blanket-ban solutions reveals serious dangers for the country if treated as serious policy proposals. Political defections motivated by opportunism are a serious issue and need to be more strictly regulated to prevent Aaya Ram Gaya Ram politics, but a blanket ban on defections is throwing the baby out with the bathwater, punishing both the opportunists and the people defecting for legitimate reasons.

The above analysis demonstrates the intellectual poverty of the CJP, leaning on knee-jerk reactions to raise popularity rather than providing serious ideas on how to improve the country. Perhaps this manifesto was meant as satire, in which case I’ve just provided an overly serious analysis and missed the joke; however, the massive attention given to the CJP recently suggests some people are seeing a more profound meaning in these demands and a serious future in the CJP, making this analysis necessary. The CJP provides no path towards comprehensive reform and lacks the intellectual maturity to be a productive political party. Anyone entertaining those delusions should realign their expectations accordingly. They’ve also focused exclusively on issues where there’s a universal consensus like “corruption bad” and “women’s representation good,” while remaining silent on more polarizing but equally pressing issues like foreign policy, economic development, and the dangers of communalism, since any stance on these issues would naturally alienate some people and reduce their popularity; as highlighted throughout this article, the CJP’s fundamental limitation is their focus on popularity over intellectual rigor. This refusal to address more polarizing ideas further reduces their viability as a path towards more comprehensive change in the form of a new political party or long-term movement.

Adding to the mountain of problems facing the CJP is their leadership structure, and the lack thereof. The CJP is a decentralized mass of angry youths following the diktats promulgated over social media by their “founder and convenor” Abhijit Dipke. There is no democratic decision-making body incorporating a diversity of ideological influences and shaping mature, nuanced stances on politics: there is Dipke, and then there are the masses at his beck and call. This makes the CJP’s maturity completely dependent on that of Dipke, who possesses few qualifications beyond competent online shitposting, an undergraduate degree in journalism and a master’s in public relations (neither related to core areas of government policy), and some volunteering for the Aam Aadmi Party. In addition to Dipke’s lack of experience and relevant qualifications for intelligent political thought, the CJP’s simplistic manifesto and focus on populism over intellectual rigor, as highlighted above, reflect poorly on his capacity to shape a more productive movement. Given the lack of a larger decision-making body, there is no self-correction mechanism to add much-needed depth and nuance to the marketing appeal brought by Dipke. The CJP possesses popularity and a few legitimate concerns about corruption and government incompetence, but none of the intellectual or organizational maturity needed to give them a role bigger than ‘social media movement’ or provide practical solutions for governance.

However, the CJP does have some value which I will now address.

Although the two are very different, I find the CJP similar to Karl Marx in some ways. Marx identified grave problems within capitalism and pointed out a need to change things; however, even though he was effective in identifying problems, his proposed solutions were seriously flawed and lacked the intellectual rigor of the rest of his work. The CJP suffers from the same issue: great at identifying some problems in the system, terrible at providing viable solutions. The CJP’s usefulness in today’s India will be similar to the usefulness Marx has historically had among the masses: providing a structure to public anger that puts pressure on the government to do better, even if the CJP itself is unable to itself articulate the details of reforms. Their campaign for the resignation of the Education Minister might not succeed in triggering his resignation, and it certainly isn’t providing any concrete ideas for reform, but it’s valuable because it pressures the government to take accountability for its failure in exam administration and to improve the system.

Despite all the CJP’s problems, I am glad it exists in India today. Unlike Anna Hazare’s “India Against Corruption,” it seems (at least currently) a genuine, groundroots campaign for the government to do better, rather than a group of morally compromised opportunists seeking to gain a foothold in politics by exploiting public anger. If Dipke retains his talent for viral marketing and the movement keeps gaining momentum, the CJP can play an essential role in keeping the government accountable for its actions and providing an impetus for much-needed reforms. The campaign against the Education Minister is already having an impact: it’s prevented the BJP from sweeping the issue under the rug and forced them to acknowledge a failure and work towards a solution. Nobody can say how effective the CJP will be on the exam administration issue, whether the government will actually create a viable solution as a result of this pressure or just implement half-measures and wait for public anger to die down; however, regardless of final outcomes, the CJP has substantially increased the probability of improvements in this area, and for that, we should appreciate them.

How The Trump Administration Controls Venezuela, and Potential Consequences of That Power

Wed, 24 Jun 2026 00:00:00 GMT

How The Trump Administration Controls Venezuela, and Potential Consequences of That Power

Los Estados Unidos son potentes y grandes.
Cuando ellos se estremecen hay un hondo temblor
que pasa por las vértebras enormes de los Andes.
Si clamáis, se oye como el rugir del león.

The United States is strong and big.
When it shakes there is a deep tremor
through the enormous vertebrae of the Andes.
If you clamor, you hear the roar of the lion.

‘A Roosevelt’ by Rubén Dario

Written in 1904, these bitter lines still hold truth over a century later. Rubén Dario’s poetry was inspired by his revulsion at US interventionism in Panama under Theodore Roosevelt, but over a century later, the same history is playing out but in Venezuela and Cuba this time (although it seems Panama might also be on the cards). The Trump administration’s actions in these countries are changing the futures of millions of people and shaping a new geopolitical order. However, even if we are living through a historic moment, most Americans are oblivious to it.

The US intervention in Venezuela received minute-by-minute coverage during the overnight operation to capture Maduro, but since then, the aftermath of “Operation Absolute Resolve” has received less attention from American media. Many Americans are vaguely aware of American “neocolonialism” and “exploitation” taking place in Venezuela right now, but there is less knowledge of the specific mechanisms and processes by which this is taking place. This blog post aims to rectify that information deficit and provide a summary of what has been going on recently, as well as my own thoughts on the crisis.

Following the January 2-3 capture of Nicolás Maduro and his wife Cilia Flores, the United States has established control over the Venezuelan government’s finances, by corollary giving them leverage over government policy. Executive Order 14373, signed on January 9, decreed that revenues earned from the state-owned oil company PDVSA be put in US-controlled accounts, protected from attachment processes being initiated by Venezuela’s creditors, and only released to the Venezuelan government for uses deemed appropriate by the Trump administration. Per the White House’s version of events, this order serves to prevent the money being seized by foreign creditors, somehow protect the western hemisphere against Iranian influence, and help with “stemming the influx of illegal aliens”. The first justification regarding the risk of Venezuelan oil revenues being attached by foreign creditors is possibly a valid reason for some US involvement in Venezuelan affairs 1, while the dangers involving Iran and “illegal aliens” are poor justifications. However, the US’ motives in Venezuela are not so altruistic as to consist solely of protecting their oil revenue from foreign creditors.

The more significant consequence of this executive order is the leverage it gives the White House over the Venezuelan government, creating a situation so dire that Spanish-language press is now referring to them as “los tutelados,” or “the tutelaged ones.” It is illustrative to note that the most direct precedent for EO 14373 is the Development Fund for Iraq (DFI), which similarly prohibited attachment proceedings against Iraqi oil revenues and repatriated funds captured in the Iraq War – notably, the DFI and the executive orders protecting it occurred at a time when the US effectively controlled the Iraqi government following a ground invasion. While these two situations are very different, the comparison is useful for understanding how US control over Venezuelan finances could lead to a 2003 Iraq-like situation today. The last time the US held control over another country’s government revenues, the American government effectively controlled that government, and there’s little reason to expect anything different this time around. Any government policy or action requires money, so by seizing the government purse, the US has the Venezuelan government subordinated to its will, just as it did Iraq.

While the Venezuelan government does have some non-oil revenue, there isn’t enough diversity of revenue sources for this to weaken the US’ control. In 2024, Reuters reported that income from PDVSA accounted for 53% of the government’s budget. For a government so dependent on oil revenue, the US’ control over PDVSA income translates into near-total control of the government’s finances.

While not wishing to belabor the point, I think it’s valuable to highlight another dimension of US leverage over Venezuela: the control over the volume of oil purchases and investment in oil infrastructure, and not just the revenues resulting from them. American companies needed the White House’s approval to begin purchasing Venezuelan oil, and since that permission can be revoked at any time, the Venezuelan government, dependent on oil export revenues, has yet another reason to stay in Trump’s favor. The development of oilfields, also essential to economic growth and increased government revenue, is similarly contingent on US approval, since companies like Chevron, British Petroleum, and Shell are only able to invest in Venezuelan oilfields because of licenses granted by the Treasury Department in February. Therefore, even as the Venezuelan government’s revenue grows as a result of increased oil exports, the US will continue holding a sword over them, forcing the Venezuelan government to comply with the wishes of the Trump administration and eliminating their political autonomy.

After understanding the incredible leverage the US has over the Venezuelan government, the next step is understanding what they wish to do with that power. First, let’s note the title of EO 14373: “Safeguarding Venezuelan Oil Revenue for the Good of the American and Venezuelan People” (emphasis mine). If this doesn’t start to give you an idea of Trump’s intentions, he makes it even clearer when speaking:

“We’re going to be taking out a tremendous amount of wealth out of the ground, and that wealth is going to the people of Venezuela, and people from outside of Venezuela that used to be in Venezuela, and it goes also to the United States of America in the form of reimbursement for the damages caused us by that country” 2

The White House’s rhetoric on Venezuela revolves around masquerading as saviors of the Venezuelan people while also revealing a bit of their ulterior motive of extracting benefits for the US itself (motives made clear thanks to Trump’s runs-mouth-like-loose-cannon syndrome). Everything we know about Trump suggests his concern for Venezuelans’ wellbeing is mainly meant to bring some credibility to his extrajudicial military maneuver in Venezuela, so the true motive for US involvement in Venezuela likely lies in the part about ‘the Good of the American people’ and ‘reimbursement to the United States of America.’

The intersection of US foreign policy and ‘the Good of the American people’ has traditionally meant low, stable oil prices and high profits for American oil companies, and this situation is no different. Venezuela has the world’s largest proven oil reserves (with some important caveats 3), and US control over the Venezuelan government creates a safe environment for American oil companies to take advantage of that opportunity. Freed from the fear of arbitrary nationalization of oilfields and the nuisance of dealing with rampant government corruption, US oil companies can again begin investing in the region and enjoying massive profits. Expanded oil supply will also help reduce oil prices long-term, and strong control over the Venezuelan government will create the stability necessary to prevent the wild price fluctuations that have resulted from historic dependence on Middle Eastern oil.

In addition to oil, the Trump administration is also likely motivated by mining opportunities. Venezuela has the world’s fifth largest gold reserves, mostly undeveloped and providing huge opportunities to future American investors, in addition to coltan and bauxite deposits whose magnitude is still unknown but potentially promising based on numbers from specific regions. But hey, don’t take it from me, let’s ask the president himself!

Q. President Trump, are there going to be any more—you said the oil companies are going to go in there. Are there any other companies that you’ve talked to about dealing with Venezuela? Maybe Mr. Lutnick could talk about that. Are there any other corporations, entities, outside of oil?

The President. Many, outside of the oil business.

Q. Like who?

The President. Well, the oil business, yes. But outside, yes. Howard, do you want to take that?

Secretary of Commerce Howard W. Lutnick. So you have steel. You have minerals, right? All the critical minerals. They have a great mining history that’s gone rusty.
So steel, aluminum, minerals. I mean, this is all—it’s a rich—it was, once upon a time, one of the great economies and cultures of the world, and it was destroyed. And now, President Trump is going to fix it and bring it back for the Venezuelans.

The Trump administration’s statements, combined with common-sense understanding of US foreign policy interests, suggests that the US will likely use its control of the Venezuelan government to gain access to these massive oil and mineral reserves; but while trade and investment themselves are actually beneficial, the lack of regulatory oversight and transparency could have terrifying implications for human rights and environmental degradation. Fair labor practices and environmental considerations tend to hurt companies’ short-term profit margins, and since the Venezuelan government’s regulatory powers are effectively nil under US tutelage, there is a high risk of American companies trampling over human rights and environmental sustainability when pursuing profit in Venezuelan oilfields and mines. There is plenty of historical precedent for this, and the Trump administration, which has already shown itself at ease with killing and destruction in other countries when beneficial to US interests, might enable some of the worst abuses in modern history.

The Venezuelan government currently has little power to regulate foreign corporations, as amply demonstrated above. Neither is there scope for forces within the US to curb Trump’s power: the release of funds to the Venezuelan government and approval of licenses for oil companies is being managed entirely by the White House, a circumstance that will not change unless Congress steps in to reclaim control, an unlikely event given their previous refusal to curb Trump’s war powers in Iran and Venezuela. If Congress won’t curb the president’s power to bomb other countries, it’s unlikely they will curb his use of more subtle means of control.

The lack of transparency and a clear set of rules around US involvement is also detrimental to the creation of a healthy business environment. International capital fled Venezuela under Hugo Chávez’s regime because he made Venezuela a terrible business environment: oilfields held by a company for many years could arbitrarily be seized by the state, and the decay of the rule of law discouraged investment in the country. Today, the White House is encouraging US companies to do business in Venezuela by loosening sanctions and creating an implicit promise of carte blanche, but this is not enough to promote stable, long-term investment. In the absence of clearly defined rules about how the US can involve itself in Venezuelan affairs, what criteria the White House uses to approve the release of funds to the Venezuelan government, and what the long-term plan is for reconstruction of the country (if there is any), investors will always be unsure about the future of any money they have invested there – fearful that corruption may begin to set in again, or that the US might increase their military presence again, etc. This fly-by-night style of managing a country is detrimental to the rule of law necessary for a healthy business environment conducive to foreign investment.

Even aside from the practical considerations regarding pollution, inhumane working conditions, and uncertainty about the country’s future, there is the issue of the undemocratic way in which Venezuela is currently being governed. The ousting of Nicolás Maduro has not been followed up by a dismantling of his authoritarian power structure, and there is still no roadmap for democratic elections and restoration of government institutions’ independence from Maduro’s party. Venezuela is being run by a government without an electoral mandate, which is in turn subordinated to a foreign government, an arrangement that goes against all principles of democracy as well as national sovereignty.

Endnotes

I recommend this LawFare article for more background on Executive Order 14373, the risk of attachment of Venezuelan assets in US courts, and the legal minutiae surrounding this mess.↩︎
Quote from NPR ↩︎
The classification of ‘world’s largest proven oil reserves’ ignores that lots of the oil in Venezuela is difficult to extract and refine and is less accessible than sources like Texan shale oil. This Forbes article provides interesting context on this issue. However, even with lower accessibility taken into consideration, Venezuela still has large economically viable oil reserves, and even their less accessible oil can be extracted with sufficient US investment (something that is already beginning to manifest).↩︎

Why ‘Class Struggle’ Rhetoric is a Bad Idea in Democracies

Thu, 11 Jun 2026 00:00:00 GMT

Why ‘Class Struggle’ Rhetoric is a Bad Idea in Democracies

Note before starting – again, this post is just a copy-pasted Discord rant I wrote back in February. This Discord rambling was closer to a full-length blog post than a normal series of messages in an internet chatroom, so I decided I should just post it here. Again, no editing, so this uses my peculiar blend of internet-speak and formal language that makes me unable to communicate with anybody. The idea here seemed interesting to me, so I went ahead and posted this.

had a thought

‘Class struggle’ rhetoric is a bad idea in democracies because Marx’s idea of utilizing such language to mobilize the masses was built specifically for scenarios where Marxists were ready to massacre capitalists and then create a dictatorship.

The whole point of the massacres and dictatorship in Marxist theory was to prevent the bourgeoisie from rebelling against their property being expropriated; if you center your entire ideology around treating one social class as your enemy, of course they’ll fight back. However, if you try this ‘class struggle’ rhetoric in a democracy, you will meet the same opposition from the bourgeoisie but without the state violence needed to suppress it. The result is that, even if elected on a wave of support from the working class, you’re unable to do anything with your power; the bourgeoisie control much of the economy and the political system, and their opposition to your agenda will cripple you.

Examples? Salvador Allende in Chile – this is usually presented as a tale of “evil capitalists destroy the socialist dream,” but an equally important factor was that Allende literally campaigned by promising to destroy the bourgeoisie’s dominance and then had no tools to counter the inevitable opposition he met from the industrialists. Allende promised socialist policies that would weaken the upper class, but unlike Stalin or Mao, he lacked the state violence needed to force these policies on this now-infuriated upper class. When met with strikes sponsored by the industrialists and constant harassment from an upper class-dominated Parliament, he couldn’t just massacre the strikers and close the Parliament as Marx envisioned, instead he was forced to watch the economy grind to a halt and half his ministers get impeached. Eventually Allende was forced to moderate his stance and start negotiating with the Christian Democrats, but by then, the upper class had already gotten on the path of a military coup. While the evil of the coup can not be excused, it’s also necessary to understand how Allende’s “rich vs poor” rhetoric directly led to attempts at destabilizing his regime, and how Allende was woefully unprepared to deal with these problems that were the obvious consequence of promising to weaken the industrialists’ power.

Modern example that makes this idea relevant? Zohran Mamdani – as NYC mayor, he individually doesn’t have even half the power needed to pursue the huge reforms he wants. To achieve his economic goals, he will need the cooperation of the governor, the state legislature, the MTA, business owners, city council, and countless other groups to effectively enact such huge changes. Many of these people have already just said “no” (notably the CEO of the MTA), making it unlikely Mamdani that will make substantial progress on economic policy if he continues to yell into the void about the capitalists being the real enemies. Whether or not you like it, the upper class controls the apparatus needed to bring reforms; if you can’t find a way to work with them, you won’t get much done. If Mamdani had become president of the newly-formed USSR rather than democratic NYC, he’d be able to just execute the CEO of the MTA and do whatever he wanted with the unchecked powers given to him by the moral supremacy of the proletariat. But here, his demonization of the upper class has just ended up making his government impotent.

Whether class struggle is the correct theory is irrelevant, if we’re speaking in terms of real consequences. What matters is whether screaming ‘class struggle’ helps or hurts – in my opinion, it’s only hurting our ability to create change.

Politicians need to find a way of mobilizing common people while at the same time not alienating the upper class, whose support is needed to actually govern.

hmm

some edited version of this is going on my blog I think

this is actually an interesting idea

similar thing happened with Mandal Commission

“lower castes = friend, upper castes = oppressor” rhetoric reached its climax with the Mandal Commission, which was finally too much for Brahmins etc to bear – result was college kids self-immolating (very effective symbol that riled people up), mass support for the BJP and literally anyone else who would oppose Mandal, and finally the collapse of the United Front.

V.P. Singh needed to find a way of helping the OBCs without so completely alienating Brahmins that they started committing suicide to protest his government

Moral superiority will only take you so far

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