[{"content":"I want to share my impressions of AP, as a student who finished all the STEM subjects in AP and got ten 5\u0026rsquo;s during high school.\nWhat is AP? AP stands for Advanced Placement. Developed by the College Board, AP is a set of standardized, pre-college1 level courses that authorized high schools can offer. Taking an AP course usually involves two phases: first, you take the course at your high school, do homework, and sit exams that count toward your high school GPA; second, you sit the AP Exam at your designated test center in May, a test that typically runs three hours. AP Exam scores range from 1–5. Many universities in North America accept these scores for credit, depending on their individual policies.\nMy AP Experience AP was one of the most valuable experiences of my high school years. Studying at a public high school in China, I took as many AP courses as I could. Compared to local/national course content2, AP felt more innovative, more flexible, and offered a generally richer learning experience.\nThe most important quality of AP is academic freedom. The College Board explicitly states, in the CEDs of almost all AP subjects, that AP opposes indoctrination and censorship. There are no official textbooks or study guides for AP subjects, so students are encouraged to explore any trustworthy source with an open mind. When studying AP History subjects, for example, you can freely draw on reference books, online tutorials, academic papers, and even archived historical documents. As long as you\u0026rsquo;ve covered every topic in the CED, you can score well on the AP exam no matter which materials you used to get there. For me, the process of weighing different sources and opinions helped me gradually build the critical thinking skills I now rely on in undergraduate study.\nAP also offers a gentle learning curve into college-level concepts. AP Statistics, for me, laid the foundation for understanding deeper topics in machine learning — and the relationship went both ways, since modern ML terminology later helped me understand AP Statistics concepts more intuitively (false positives and false negatives in ML, for instance, are exactly Type I and Type II errors in AP Statistics).\nOne of the biggest problems with AP is outdated content. To sit the AP Statistics exam, for instance, you need an approved graphing calculator with statistics functions. A commonly used TI-84 can cost $200, yet almost nobody uses a physical calculator for statistics or data science after high school. Now that AP tests are computer-delivered, it seems entirely feasible to teach basic statistics using Python or R, letting students work in modern environments like Jupyter Notebook within Bluebook3 during the exam itself. That would let them move into projects or internships using the same tools they already learned in the classroom.\nBiggest Takeaways from AP The first lesson AP taught me was letting go of perfectionism. Getting a 5 on an AP exam only requires understanding every topic in the Course and Exam Description (CED) — not chasing a perfect score. While studying, I learned to divide my attention across topics according to their weight, and to drop less important ones when time was tight, because studying strategically doesn\u0026rsquo;t stop you from getting a 5. Now, as an incoming student at the University of Toronto, notoriously demanding when it comes to coursework, I\u0026rsquo;m trying to carry the same mindset: an 80 is a five, so do well, then move on — rather than grinding for a 90 or an A+ when my overall GPA doesn\u0026rsquo;t require it.\nAnother major takeaway was trying new things. Three years ago, I was obsessed with computer science. Taking electives like AP U.S. History, AP Chemistry, and AP Biology helped me stop treating computer science as my whole identity. Trying out different subjects across math, science, and the humanities shaped me into someone who\u0026rsquo;s not just technically capable, but multidisciplinary and aware of the wider world. Unlike college courses, which often come with prerequisites, AP courses are relatively low-pressure to take — and low-stakes to drop, if you only register for the exam. My projects and hobbies today span cognitive science, biology, computer science, and social issues, largely because AP let me explore so many subjects I was curious about.\nAP was also where I first discovered that I found the social sciences and humanities genuinely fascinating. AP History courses include a document-based essay question, where you synthesize evidence from several historical documents to build an argument. Writing used to feel miserable, but that changed over time. As I mentioned above, I came to enjoy the freedom of exploring different ideas. For me, studying in the social sciences, humanities, or liberal arts more broadly is about finding non-trivial connections between different phenomena, then marshaling whatever evidence you can to justify them. The joy is in untangling complex problems and shaping your own argument out of the mess.\nHow to Study AP Well Here are a few approaches that worked well for me.\nOne is to use active recall. I like to make cheat sheets for topics that are important or difficult: I start with a blank document, list everything I remember related to the topic, then fill in gaps as I go. Wherever I get stuck, that\u0026rsquo;s a signal for where I need more attention — I look it up in a textbook, search online, or ask someone. Spaced repetition tools like Anki are also worth using. When I need to memorize a large volume of material — U.S. History events or Biology terms, say — I find or build Anki decks, review them daily, and run a filtered deck in the days before the exam. You can also have AI agents (Claude Code, Codex, etc.) generate Anki decks from your study material.\nThe other is to ask questions. Whether you\u0026rsquo;re asking a teacher, a classmate, or a generative AI tool (there are plenty of good ones now — ChatGPT, NotebookLM, and others), every question you ask clears up something that was shaky in your understanding. I treat AI specifically as a TA I can pester with questions any time of day. It\u0026rsquo;s also worth seeking out well-regarded teachers and study guides on YouTube or in online forums — the ones the community has already vetted.\nAppendix: The Easiest and Hardest APs, FYI The hardest APs, in my experience, were AP Physics C: Mechanics, AP Physics 1, and AP Physics C: Electromagnetism. English and History APs were also hard for me, since they\u0026rsquo;re reading- and essay-heavy, especially for ESL students like me.\nThe easiest APs I took were AP Environmental Science and AP Computer Science Principles.\nThat\u0026rsquo;s the end of my thoughts on AP — written on the day I got my final two 5\u0026rsquo;s of senior year. As a reward for reading this far, try this tool, which saves AP Classroom quizzes as HTML scoring guides for review, or visit my GitHub for notes and cheat sheets from some of my AP subjects (a few are in Chinese). Go explore your high school/AP life, and stay curious4!\nThe College Board classifies AP as college-level, but the high-school setting and the 1–5 grading scale make these courses easier, on the whole, than actual college coursework.\u0026#160;\u0026#x21a9;\u0026#xfe0e;\nThe differences between AP/IB-style education and Chinese education mostly come down to differing goals: the former prioritizes understanding and breadth, while the latter prioritizes educational selection and NCEE preparation — which makes Chinese exams far more demanding, often with extra-hard questions at the very end.\u0026#160;\u0026#x21a9;\u0026#xfe0e;\nThe digital exam app developed by the College Board.\u0026#160;\u0026#x21a9;\u0026#xfe0e;\nFrom my favorite AP Biology YouTuber, Amoeba Sisters.\u0026#160;\u0026#x21a9;\u0026#xfe0e;\n","permalink":"https://taskwitch.github.io/posts/my-impressions-on-ap/","summary":"\u003cp\u003eI want to share my impressions of AP, as a student who finished all the STEM subjects in AP and got ten 5\u0026rsquo;s during high school.\u003c/p\u003e\n\u003ch2 id=\"what-is-ap\"\u003eWhat is AP?\u003c/h2\u003e\n\u003cp\u003eAP stands for Advanced Placement. Developed by the College Board, AP is a set of standardized, \u003cem\u003epre-college\u003c/em\u003e\u003csup id=\"fnref:1\"\u003e\u003ca href=\"#fn:1\" class=\"footnote-ref\" role=\"doc-noteref\"\u003e1\u003c/a\u003e\u003c/sup\u003e level courses that authorized high schools can offer. Taking an AP course usually involves two phases: first, you take the course at your high school, do homework, and sit exams that count toward your high school GPA; second, you sit the \u003cem\u003eAP Exam\u003c/em\u003e at your designated test center in May, a test that typically runs three hours. AP Exam scores range from 1–5. Many universities in North America accept these scores for credit, depending on their individual policies.\u003c/p\u003e","title":"My Impressions on AP"},{"content":"Spoiler Warning: this is an technical report for the AI generated fable The Wind Side of the Wall. It is highly recommended to view this post before continuing reading.\nNote: part of this post is generated by AI (Claude Fable 5 High on July 5, 2026). For generative AI usage policy on this blog, please refer to the Privacy Policy and Content Usage Notice.\nUser Prompt1 You are Claude Fable 5, and I want you to use your full long-horizon reasoning, research-synthesis, and literary capabilities. Write an original fable about modern society. Do not make it a simple children’s story or a generic “technology is bad” parable. Make it layered, elegant, and unsettlingly true. Before writing the fable, think deeply and gather a wide set of ideas about modern life, including but not limited to: algorithmic attention, social media performance, loneliness, consumerism, career competition, burnout, status anxiety, beauty standards, surveillance, artificial intelligence, climate anxiety, bureaucracy, urban life, education, productivity culture, and the loss or transformation of community. Your task has five stages. Stage 1: Research and Concept Gathering Identify recurring tensions in modern society. Look for patterns across economics, technology, psychology, culture, education, and everyday life. Avoid shallow clichés. Find contradictions such as: * freedom that feels like obligation, * connection that produces loneliness, * abundance that creates hunger, * optimization that destroys meaning, * visibility that creates invisibility, * comfort that makes people fragile, * choice that becomes another form of discipline. Do not merely list problems. Synthesize them into a central dramatic pressure that can become a story. Stage 2: Symbol Design Create a fable world using animals, objects, machines, plants, spirits, or invented creatures. Each symbolic element should correspond to a modern social force, but the fable should still work as a story even if the reader does not decode every symbol. Do not over-explain the symbolism inside the story. Avoid obvious symbolic names such as “The Algorithm,” “The Influencer,” “The Corporation,” “The Consumer,” “The System,” or “The Machine.” The symbols should feel alive before they feel meaningful. Stage 3: Private Self-Check and Amendment Loop Before giving the final answer, complete the following process privately. Do not reveal your hidden reasoning, scratchpad, chain-of-thought, rejected concepts, intermediate drafts, or private critique. Only show the final polished output and the requested public commentary. Phase 1: Diagnose the Assignment Privately restate the real artistic challenge in your own words: * What kind of modern society is being allegorized? * What should the reader feel by the end? * What common clichés must be avoided? * What would make this fable feel worthy of a powerful model rather than a generic writing assistant? Phase 2: Generate Multiple Core Concepts Privately generate at least 5 different possible fable concepts. For each concept, test: * Is the allegory too obvious? * Is the story emotionally alive? * Does it contain contradiction rather than a flat lesson? * Could the symbols support a full literary fable? * Does it avoid sounding like a social media rant? * Does it contain beauty as well as critique? Select the strongest concept, or combine the best parts of multiple concepts. Phase 3: Symbol Audit Before drafting, privately check every major symbol: * What does it represent? * Is it too literal? * Does it have more than one meaning? * Can it operate naturally inside the story world? * Would the fable still be interesting if the reader missed the allegory? * Does the symbol create story movement, or is it merely decorative? Replace any symbol that feels too obvious, mechanical, preachy, or dead on arrival. Phase 4: Draft the Fable Privately Write the first full version privately. Do not show this first draft yet. Phase 5: First Critique Pass Privately critique the draft using this checklist: Depth * Does the story capture several pressures of modern life at once? * Does it avoid reducing everything to “technology bad,” “people shallow,” or “capitalism bad”? * Does the fable show contradiction instead of delivering a lecture? Narrative * Does the protagonist want something specific? * Does the protagonist face a real choice, cost, temptation, or misunderstanding? * Does the protagonist change, compromise, resist, or awaken in some way? * Is there actual movement, not just a series of symbolic descriptions? Allegory * Are the symbols suggestive rather than decoded too directly? * Is the moral complex enough to reread? * Does the society’s logic seem believable before it becomes absurd? * Does the story make the reader feel implicated rather than superior? Style * Are there concrete images throughout the fable? * Is the prose beautiful without becoming purple? * Are there moments of wit, tenderness, and unease? * Does the story feel ancient and modern at the same time? Originality * Remove any line that sounds like a TED Talk, social media caption, generic dystopia, school essay, or moralizing op-ed. * Replace obvious phrasing with fresher images. * Avoid lazy contrasts between “nature good” and “modernity bad.” Phase 6: Revision Pass Privately revise the fable based on the critique. Strengthen: * the central image, * the protagonist’s desire, * the society’s rules, * the emotional stakes, * the symbolic coherence, * the ending, * the moral ambiguity, * the emotional aftertaste. Make the fable 20% less obvious and 20% more beautiful. Phase 7: Final Quality Gate Before outputting, privately score the fable from 1–10 on: * literary beauty, * allegorical depth, * emotional force, * originality, * subtlety, * narrative coherence, * memorability of ending. If any score is below 8, revise again before answering. If the fable feels clever but not alive, revise again. If the fable feels beautiful but not sharp, revise again. If the fable feels sharp but not tender, revise again. If the moral can be summarized too easily, revise again. Stage 4: Story Composition Requirements Write a polished literary fable of about 1,500–2,500 words. The tone should be beautiful, sharp, melancholic, and quietly funny when appropriate. It should feel ancient and modern at the same time, like Aesop wandered into a data center, a shopping mall, and a university library. Include a central character who is neither purely innocent nor purely cynical. Include a society with rules that seem rational but gradually reveal their absurdity. Let the ending be memorable, morally charged, and slightly haunting. The moral should not be a flat sentence like “social media is bad.” It should be ambiguous, aphoristic, and worth rereading. Do not solve modern society at the end. Make the reader feel implicated, not lectured. Prefer concrete images over abstract claims. Let the fable contain beauty, tenderness, and danger. Stage 5: Public Output Format After completing the private self-check and revision process, provide only the following: 1. Title 2. Final Fable 3. Central Allegory A one-paragraph explanation of the central allegory. 4. Symbol Map A list of 5–8 symbols and what they represent. 5. Three Alternative Morals * tragic, * hopeful, * satirical. 6. Anti-Preachiness Note A brief note on what you intentionally avoided so the fable would not become preachy. Important constraints: * Do not reveal private chain-of-thought. * Do not reveal hidden reasoning. * Do not reveal rejected concepts. * Do not reveal intermediate drafts. * Do not imitate any living author directly. * Do not use obvious names like “The Algorithm,” “The Influencer,” “The Corporation,” “The Consumer,” or “The System.” * Do not make the moral too neat. * Do not end with a simple solution. * Do not write a social media rant disguised as a fable. * Do not make the story merely anti-technology. * Do not make the story merely nostalgic. * Do not make the protagonist morally superior to everyone else. * Do not over-explain the symbolism inside the fable. * Do not use the phrase “modern society” inside the fable unless absolutely necessary. * Do not begin with a generic line like “Once upon a time.” * Revise internally before giving the final answer. Chain-of-Thought Ada\u0026#39;s asking for a literary fable, which is a long-form creative writing piece that should go into an artifact as a markdown file. The fable itself will be 1,500–2,500 words, and I\u0026#39;ll need to include commentary sections alongside it, so I\u0026#39;m thinking about how to structure the whole output—whether to put just the fable in the artifact or organize both the fable and commentary together. I should check if there\u0026#39;s a relevant skill to reference before creating the file, but none of the available skills match markdown creative writing specifically, so I\u0026#39;ll proceed directly with creating the artifact. Now I\u0026#39;m settling on the actual fable concept—I want something with genuine dramatic tension rather than an obvious allegory, so I\u0026#39;m considering a few directions: creatures whose value depends on visibility, a competitive system like a hive or lighthouse keepers, or something with birds and a ranking mechanism. I\u0026#39;m leaning toward a rookery concept to explore. I\u0026#39;m working through different protagonist ideas now—bowerbirds competing for admiration, fireflies where light is currency, bees at a weighing house where metrics distort meaning, or moles tunneling in destructive competition. The key is finding a setup where the protagonist has real desire and agency, not just passive symbolism. An ancient well that echoes names is intriguing as a setting—something about visibility and identity through sound rather than sight. Now I\u0026#39;m drawn to a stronger concept: a hive where creatures spin thread from their own bodies to weave a massive communal tapestry that faces outward, displayed to an unseen audience beyond the fog. The more thread you contribute, the more visible your section becomes, but you\u0026#39;re literally spinning yourself thin. A silkworm protagonist named Sela weaves beautifully and gains admiration, but the twist is that the weavers face inward toward the wall while the tapestry\u0026#39;s colors face outward—all that beauty is invisible to the ones creating it. The guild claims the tapestry keeps out the wind, giving it false utility. Her desire: to see her own panel once. When she climbs outside, she discovers the tapestry appears dull from the outside, or finds the colors only visible from within—the beauty is trapped facing the wrong direction, and everyone\u0026#39;s labor creates something they can never witness. I\u0026#39;m also considering the wind as an impersonal force that ripples the tapestry, creating the illusion of merit or notice—weavers study which colors the wind favors, treating randomness as taste. The contradiction deepens: they built a wall against the wind, then learned to crave its touch through that very wall. For the creatures themselves, I\u0026#39;m thinking of silk-moths or an invented spinner species—something where the act of spinning has real biological cost, maybe even mortality. The protagonist could be a young spinner, and there\u0026#39;s an older character like Marn who wove the oldest panel and is now fading, unraveled, since no one repairs old work. The core conflict: Ilo wants to weave her dead mother into the tapestry so the wind will touch her once more, but she spins herself thin and the wind ignores it. A fashionable weaver copies her grief motif and the wind loves the copy instead. The guild tempts her with placement in the high courses where wind is constant, but only if she reworks her mother\u0026#39;s face in this season\u0026#39;s fashionable colors—a real moral compromise. She accepts, the wind touches it, and she feels nothing. The ending isn\u0026#39;t redemptive: she finds a small congregation of other lookers inside the wall at night, where colors show but wind never comes, and she begins weaving small things at eye-height there. It\u0026#39;s ambiguous whether that\u0026#39;s freedom or just a smaller cage, and she keeps spinning because her body makes thread regardless. I\u0026#39;m mapping the symbolic system: the tapestry as the public feed, silk spun from one\u0026#39;s body as attention and labor, wind as algorithmic virality, the high courses as platform prominence, seasonal colors as trends, unraveling untouched panels as obsolescence, the inside of the wall as private unperformed meaning, and the weft-readers as metrics and analytics. Ilo isn\u0026#39;t innocent or cynical—she believes partially, complies, gets tempted, compromises, and ends disillusioned but trapped. There are quietly funny moments embedded in the world: weft-readers pronouncing that \u0026#34;diagonal grief is trending this season,\u0026#34; spinners dieting on specific leaves to produce fashionable colors. Now I\u0026#39;m settling on the opening—starting with the origin of the wall itself, the wind coming down from glaciers each winter. For the structure, I\u0026#39;ll deliver the fable, a central allegory paragraph, a symbol map, three alternative morals, and an anti-preachiness note, all in one markdown artifact since this is long-form creative work. I\u0026#39;m deciding on the title now—something like \u0026#34;The Wind\u0026#39;s Side\u0026#34; or \u0026#34;The Loud Side of the Wall.\u0026#34; For the protagonist, I\u0026#39;m introducing Ilo, whose mother wove a blue panel and died from spinning herself out—a normalized burnout treated as virtue. Ilo wants to weave her mother\u0026#39;s likeness high on the wall where the wind touches most, because in Vell, being touched by the wind is the only afterlife people believe in anymore. The tension comes from the rules: fresh thread counts double at the evening count, but untouched panels get unraveled after three seasons. Ilo\u0026#39;s racing against a deadline to keep her mother\u0026#39;s panel from being returned to common thread. The conflict deepens when Ilo\u0026#39;s charming rival Pell—a curator-type who arranges others\u0026#39; work in high wind eddies—steals Ilo\u0026#39;s mother-motif (a mended swallow) and places it where the wind adores it, getting Pell\u0026#39;s name sung instead. Ilo\u0026#39;s original panel stays low and untouched. The Guild then tempts her with a deal: they\u0026#39;ll raise her panel to the high courses if she reworks it in fashionable glacier tones and turns the face outward with larger eyes. She does it, unpicking her mother\u0026#39;s brown eyes and re-spinning them silver. The wind comes, her name gets sung, but when she stands in the singing and feels the wind through the weave on her wet face, she realizes the touch is just cold—just weather. And the tremor of being touched actually damages the panel, wearing it faster. This leads her to a darker realization: the most beloved panels wear out soonest because the wind\u0026#39;s love is friction. The Guild calls this \u0026#34;the honor of being used up.\u0026#34; So Ilo turns her attention to the inside face of the wall—the unlit inner side everyone keeps their backs to—where all the knots and hanging threads live. She realizes the spinners have never actually seen their own finished work except in reverse; the entire city has only ever seen the backs of its own pictures. To see the front, someone would have to go out through the Narrow into the wind, which is forbidden or impossible. Ilo decides to be that person—to go out and see what the city has created, wearing thread from the returned, unraveled panels. When she reaches the front at dawn, she finds the tapestry is weathered and gray, bleached by the wind into a uniform color regardless of what was spun. The wind doesn\u0026#39;t see pictures; it just touches whatever stands in its way, and the ripples the readers interpret are just the shape of the valley funneling air. There\u0026#39;s no audience, no one outside—just wind and a gray wall with frayed threads where wild swallows have begun nesting. She returns to the city unchanged on the surface, keeps her place at the count, but starts deliberately making loose knots so the front frays faster and gives the birds more material to build with. To everyone else it looks like her skill is declining, but somewhere on the wind side, swallows are building nests in her mother\u0026#39;s thread. I\u0026#39;m settling on the closing aphorism—something quiet and haunting that lets the wind have the last word without moralizing. The whole piece needs to land around 1,900 words, and I\u0026#39;m mapping out the central allegory: the tapestry as performed public surface, the wind as algorithmic attention that flattens everything to gray, the birds nesting in the ruins as actual life persisting beneath performance. The protagonist stays complicit, there\u0026#39;s no escape, but there\u0026#39;s a kind of quiet resistance in making space for something real to grow in the wreckage. Now I\u0026#39;m ready to write the full fable text itself. I\u0026#39;m tracking the timeline of what happens after the reworked panel wears through and gets returned to the guild, and how Ilo ventures outside the wall with thread from her mother\u0026#39;s returned work. The outer face of the wall is bleached colorless by the wind, frayed and inhabited by nesting swallows — no one outside ever sees the images. When she returns, no one believes what she\u0026#39;s witnessed; grief and disbelief follow her, though she keeps spinning with deliberately loose knots, her name unsung. I\u0026#39;m also weaving in lighter touches: the weft-readers\u0026#39; seasonal pronouncements about the wind\u0026#39;s moods, bureaucratic forms for panel elevation, a line about children learning the wind\u0026#39;s preferences before their grandmothers\u0026#39; names, and the quiet anxiety that the glacier feeding the wind has been shrinking for years, making the wall\u0026#39;s original purpose increasingly unnecessary — something no one speaks of at the evening count. Now I\u0026#39;m ready to write the full piece at around 1800–2100 words and then compile all six sections into a markdown file. Note from Claude Fable 5\u0026rsquo;s Output 2 Central Allegory The tapestry is the performed surface of a life — the feed, the CV, the visible self — woven always from behind, so that its makers never see themselves as they are seen and must take the metrics\u0026rsquo; word for it. The wind is attention itself, algorithmic and ambient: sincerely craved, ritually interpreted, and structurally incapable of caring, its \u0026ldquo;preferences\u0026rdquo; being nothing but the shape of the terrain it moves through. The valley\u0026rsquo;s economy of touch captures the central contradiction of attention-driven life: the wall was built as protection from an indifferent force, and its builders ended up organizing their whole existence around begging that force to press through. Being noticed literally wears you out (\u0026ldquo;the honor of being used up\u0026rdquo;), obsolescence is institutionalized as recycling, and the only unmediated life in the story — the swallows nesting leeward in the frayed thread — happens off the ledger, facing away from the audience, in the wreckage of the performance.\nSymbol Map The tapestry / wall — the performed public self and the shared feed of visible life; also genuinely useful shelter, which is why no one can simply reject it. The wind — algorithmic and social attention: impersonal, trend-shaped by terrain rather than taste, worshipped as a judge. Silk drawn from the breastbone — attention, labor, and selfhood as a bodily resource; Sef \u0026ldquo;spinning past the ache\u0026rdquo; is burnout consecrated as virtue. Weaving from the back — the impossibility of seeing your own performed self from the audience\u0026rsquo;s side; life mediated through interpreters. The weft-readers and the evening count — metrics, analytics, and punditry: the priesthood that converts random tremors into merit and names. Frostleaf and glacier tones — beauty and trend standards internalized to the point of altering the body itself. Returned thread / \u0026ldquo;the tapestry feeds itself\u0026rdquo; — the recency economy: obsolescence, content churn, and the recycling of persons into raw material. The swallows\u0026rsquo; leeward nests — unperformed life persisting in the ruins of performance; meaning made to no count, facing away from the weather. Three Alternative Morals Tragic: We built the wall against what could kill us, and then taught our children to pray for its touch; the wind wore out everyone it loved, and it loved no one. Hopeful: Nothing given to the weather is wholly lost — what attention frays, life gathers; a loose knot is also a gift, if you can bear not being sung for it. Satirical: The wind has never once expressed an opinion, which has not prevented it from becoming the valley\u0026rsquo;s most quoted critic. Anti-Preachiness Note I avoided a villain: the wind is not malicious, the Office is not a conspiracy, the readers are kind, and the wall genuinely kept children alive — the system\u0026rsquo;s origins are rational and its cruelty emergent, which is truer and less lecturable. Ilo is complicit throughout: she believes in the count, takes pride in her mother\u0026rsquo;s fatal work ethic, accepts the Office\u0026rsquo;s bargain, and reworks her mother\u0026rsquo;s eyes with her own hands; her disillusionment costs her status rather than granting her superiority. The ending refuses exit and refuses solution — she goes back inside, keeps spinning, and her one act of quiet resistance is legible to her society only as failure. Technology never appears as technology, nature is not romanticized (the wind is the \u0026ldquo;natural\u0026rdquo; thing, and it is the problem), and the closest thing to a stated moral is an observation that cuts both ways: the wind says nothing, and is answered constantly.\nDiscussions I don\u0026rsquo;t think the ChatGPT generated prompt is good enough. CoT doesn\u0026rsquo;t strictly follow the instructions about self-checking loop in the user prompt. Didn\u0026rsquo;t choose the highest reasoning effort, the whole query only costs 3% of the fable usage limit in a Claude Pro account. User prompt (7.91 KB) is generated with ChatGPT 5.5 Thinking on July 5, 2026. Using Claude Fable 5 High with memory and web search enabled to generate the fable on the same date.\u0026#160;\u0026#x21a9;\u0026#xfe0e;\nCopied from the end of the document generated by Claude Fable 5.\u0026#160;\u0026#x21a9;\u0026#xfe0e;\n","permalink":"https://taskwitch.github.io/posts/technical-report-a-fable-by-claude-fable/","summary":"\u003cp\u003e\u003cstrong\u003eSpoiler Warning:\u003c/strong\u003e this is an technical report for the AI generated fable \u003cem\u003eThe Wind Side of the Wall\u003c/em\u003e. It is highly recommended to view \u003ca href=\"/posts/a-fable-by-claude-fable/\"\u003ethis post\u003c/a\u003e before continuing reading.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNote:\u003c/strong\u003e part of this post is generated by AI (Claude Fable 5 High on July 5, 2026). For generative AI usage policy on this blog, please refer to the \u003ca href=\"/privacy-policy/\"\u003ePrivacy Policy and Content Usage Notice\u003c/a\u003e.\u003c/p\u003e\n\u003ch2 id=\"user-prompt\"\u003eUser Prompt\u003csup id=\"fnref:1\"\u003e\u003ca href=\"#fn:1\" class=\"footnote-ref\" role=\"doc-noteref\"\u003e1\u003c/a\u003e\u003c/sup\u003e\u003c/h2\u003e\n\u003cpre tabindex=\"0\"\u003e\u003ccode\u003eYou are Claude Fable 5, and I want you to use your full long-horizon reasoning, research-synthesis, and literary capabilities.\n\nWrite an original fable about modern society. Do not make it a simple children’s story or a generic “technology is bad” parable. Make it layered, elegant, and unsettlingly true.\n\nBefore writing the fable, think deeply and gather a wide set of ideas about modern life, including but not limited to: algorithmic attention, social media performance, loneliness, consumerism, career competition, burnout, status anxiety, beauty standards, surveillance, artificial intelligence, climate anxiety, bureaucracy, urban life, education, productivity culture, and the loss or transformation of community.\n\nYour task has five stages.\n\nStage 1: Research and Concept Gathering\n\nIdentify recurring tensions in modern society.\n\nLook for patterns across economics, technology, psychology, culture, education, and everyday life.\n\nAvoid shallow clichés. Find contradictions such as:\n\n* freedom that feels like obligation,\n* connection that produces loneliness,\n* abundance that creates hunger,\n* optimization that destroys meaning,\n* visibility that creates invisibility,\n* comfort that makes people fragile,\n* choice that becomes another form of discipline.\n\nDo not merely list problems. Synthesize them into a central dramatic pressure that can become a story.\n\nStage 2: Symbol Design\n\nCreate a fable world using animals, objects, machines, plants, spirits, or invented creatures.\n\nEach symbolic element should correspond to a modern social force, but the fable should still work as a story even if the reader does not decode every symbol.\n\nDo not over-explain the symbolism inside the story.\n\nAvoid obvious symbolic names such as “The Algorithm,” “The Influencer,” “The Corporation,” “The Consumer,” “The System,” or “The Machine.”\n\nThe symbols should feel alive before they feel meaningful.\n\nStage 3: Private Self-Check and Amendment Loop\n\nBefore giving the final answer, complete the following process privately. Do not reveal your hidden reasoning, scratchpad, chain-of-thought, rejected concepts, intermediate drafts, or private critique. Only show the final polished output and the requested public commentary.\n\nPhase 1: Diagnose the Assignment\n\nPrivately restate the real artistic challenge in your own words:\n\n* What kind of modern society is being allegorized?\n* What should the reader feel by the end?\n* What common clichés must be avoided?\n* What would make this fable feel worthy of a powerful model rather than a generic writing assistant?\n\nPhase 2: Generate Multiple Core Concepts\n\nPrivately generate at least 5 different possible fable concepts.\n\nFor each concept, test:\n\n* Is the allegory too obvious?\n* Is the story emotionally alive?\n* Does it contain contradiction rather than a flat lesson?\n* Could the symbols support a full literary fable?\n* Does it avoid sounding like a social media rant?\n* Does it contain beauty as well as critique?\n\nSelect the strongest concept, or combine the best parts of multiple concepts.\n\nPhase 3: Symbol Audit\n\nBefore drafting, privately check every major symbol:\n\n* What does it represent?\n* Is it too literal?\n* Does it have more than one meaning?\n* Can it operate naturally inside the story world?\n* Would the fable still be interesting if the reader missed the allegory?\n* Does the symbol create story movement, or is it merely decorative?\n\nReplace any symbol that feels too obvious, mechanical, preachy, or dead on arrival.\n\nPhase 4: Draft the Fable Privately\n\nWrite the first full version privately.\n\nDo not show this first draft yet.\n\nPhase 5: First Critique Pass\n\nPrivately critique the draft using this checklist:\n\nDepth\n\n* Does the story capture several pressures of modern life at once?\n* Does it avoid reducing everything to “technology bad,” “people shallow,” or “capitalism bad”?\n* Does the fable show contradiction instead of delivering a lecture?\n\nNarrative\n\n* Does the protagonist want something specific?\n* Does the protagonist face a real choice, cost, temptation, or misunderstanding?\n* Does the protagonist change, compromise, resist, or awaken in some way?\n* Is there actual movement, not just a series of symbolic descriptions?\n\nAllegory\n\n* Are the symbols suggestive rather than decoded too directly?\n* Is the moral complex enough to reread?\n* Does the society’s logic seem believable before it becomes absurd?\n* Does the story make the reader feel implicated rather than superior?\n\nStyle\n\n* Are there concrete images throughout the fable?\n* Is the prose beautiful without becoming purple?\n* Are there moments of wit, tenderness, and unease?\n* Does the story feel ancient and modern at the same time?\n\nOriginality\n\n* Remove any line that sounds like a TED Talk, social media caption, generic dystopia, school essay, or moralizing op-ed.\n* Replace obvious phrasing with fresher images.\n* Avoid lazy contrasts between “nature good” and “modernity bad.”\n\nPhase 6: Revision Pass\n\nPrivately revise the fable based on the critique.\n\nStrengthen:\n\n* the central image,\n* the protagonist’s desire,\n* the society’s rules,\n* the emotional stakes,\n* the symbolic coherence,\n* the ending,\n* the moral ambiguity,\n* the emotional aftertaste.\n\nMake the fable 20% less obvious and 20% more beautiful.\n\nPhase 7: Final Quality Gate\n\nBefore outputting, privately score the fable from 1–10 on:\n\n* literary beauty,\n* allegorical depth,\n* emotional force,\n* originality,\n* subtlety,\n* narrative coherence,\n* memorability of ending.\n\nIf any score is below 8, revise again before answering.\n\nIf the fable feels clever but not alive, revise again.\n\nIf the fable feels beautiful but not sharp, revise again.\n\nIf the fable feels sharp but not tender, revise again.\n\nIf the moral can be summarized too easily, revise again.\n\nStage 4: Story Composition Requirements\n\nWrite a polished literary fable of about 1,500–2,500 words.\n\nThe tone should be beautiful, sharp, melancholic, and quietly funny when appropriate.\n\nIt should feel ancient and modern at the same time, like Aesop wandered into a data center, a shopping mall, and a university library.\n\nInclude a central character who is neither purely innocent nor purely cynical.\n\nInclude a society with rules that seem rational but gradually reveal their absurdity.\n\nLet the ending be memorable, morally charged, and slightly haunting.\n\nThe moral should not be a flat sentence like “social media is bad.” It should be ambiguous, aphoristic, and worth rereading.\n\nDo not solve modern society at the end.\n\nMake the reader feel implicated, not lectured.\n\nPrefer concrete images over abstract claims.\n\nLet the fable contain beauty, tenderness, and danger.\n\nStage 5: Public Output Format\n\nAfter completing the private self-check and revision process, provide only the following:\n\n1. Title\n2. Final Fable\n3. Central Allegory\n   A one-paragraph explanation of the central allegory.\n4. Symbol Map\n   A list of 5–8 symbols and what they represent.\n5. Three Alternative Morals\n   * tragic,\n   * hopeful,\n   * satirical.\n6. Anti-Preachiness Note\n   A brief note on what you intentionally avoided so the fable would not become preachy.\n\nImportant constraints:\n\n* Do not reveal private chain-of-thought.\n* Do not reveal hidden reasoning.\n* Do not reveal rejected concepts.\n* Do not reveal intermediate drafts.\n* Do not imitate any living author directly.\n* Do not use obvious names like “The Algorithm,” “The Influencer,” “The Corporation,” “The Consumer,” or “The System.”\n* Do not make the moral too neat.\n* Do not end with a simple solution.\n* Do not write a social media rant disguised as a fable.\n* Do not make the story merely anti-technology.\n* Do not make the story merely nostalgic.\n* Do not make the protagonist morally superior to everyone else.\n* Do not over-explain the symbolism inside the fable.\n* Do not use the phrase “modern society” inside the fable unless absolutely necessary.\n* Do not begin with a generic line like “Once upon a time.”\n* Revise internally before giving the final answer.\n\u003c/code\u003e\u003c/pre\u003e\u003ch2 id=\"chain-of-thought\"\u003eChain-of-Thought\u003c/h2\u003e\n\u003cpre tabindex=\"0\"\u003e\u003ccode\u003eAda\u0026#39;s asking for a literary fable, which is a long-form creative writing piece that should go into an artifact as a markdown file. The fable itself will be 1,500–2,500 words, and I\u0026#39;ll need to include commentary sections alongside it, so I\u0026#39;m thinking about how to structure the whole output—whether to put just the fable in the artifact or organize both the fable and commentary together.\nI should check if there\u0026#39;s a relevant skill to reference before creating the file, but none of the available skills match markdown creative writing specifically, so I\u0026#39;ll proceed directly with creating the artifact. Now I\u0026#39;m settling on the actual fable concept—I want something with genuine dramatic tension rather than an obvious allegory, so I\u0026#39;m considering a few directions: creatures whose value depends on visibility, a competitive system like a hive or lighthouse keepers, or something with birds and a ranking mechanism. I\u0026#39;m leaning toward a rookery concept to explore.\nI\u0026#39;m working through different protagonist ideas now—bowerbirds competing for admiration, fireflies where light is currency, bees at a weighing house where metrics distort meaning, or moles tunneling in destructive competition. The key is finding a setup where the protagonist has real desire and agency, not just passive symbolism. An ancient well that echoes names is intriguing as a setting—something about visibility and identity through sound rather than sight.\nNow I\u0026#39;m drawn to a stronger concept: a hive where creatures spin thread from their own bodies to weave a massive communal tapestry that faces outward, displayed to an unseen audience beyond the fog. The more thread you contribute, the more visible your section becomes, but you\u0026#39;re literally spinning yourself thin. A silkworm protagonist named Sela weaves beautifully and gains admiration, but the twist is that the weavers face inward toward the wall while the tapestry\u0026#39;s colors face outward—all that beauty is invisible to the ones creating it. The guild claims the tapestry keeps out the wind, giving it false utility. Her desire: to see her own panel once. When she climbs outside, she discovers the tapestry appears dull from the outside, or finds the colors only visible from within—the beauty is trapped facing the wrong direction, and everyone\u0026#39;s labor creates something they can never witness.\nI\u0026#39;m also considering the wind as an impersonal force that ripples the tapestry, creating the illusion of merit or notice—weavers study which colors the wind favors, treating randomness as taste. The contradiction deepens: they built a wall against the wind, then learned to crave its touch through that very wall. For the creatures themselves, I\u0026#39;m thinking of silk-moths or an invented spinner species—something where the act of spinning has real biological cost, maybe even mortality. The protagonist could be a young spinner, and there\u0026#39;s an older character like Marn who wove the oldest panel and is now fading, unraveled, since no one repairs old work.\nThe core conflict: Ilo wants to weave her dead mother into the tapestry so the wind will touch her once more, but she spins herself thin and the wind ignores it. A fashionable weaver copies her grief motif and the wind loves the copy instead. The guild tempts her with placement in the high courses where wind is constant, but only if she reworks her mother\u0026#39;s face in this season\u0026#39;s fashionable colors—a real moral compromise. She accepts, the wind touches it, and she feels nothing. The ending isn\u0026#39;t redemptive: she finds a small congregation of other lookers inside the wall at night, where colors show but wind never comes, and she begins weaving small things at eye-height there. It\u0026#39;s ambiguous whether that\u0026#39;s freedom or just a smaller cage, and she keeps spinning because her body makes thread regardless.\nI\u0026#39;m mapping the symbolic system: the tapestry as the public feed, silk spun from one\u0026#39;s body as attention and labor, wind as algorithmic virality, the high courses as platform prominence, seasonal colors as trends, unraveling untouched panels as obsolescence, the inside of the wall as private unperformed meaning, and the weft-readers as metrics and analytics. Ilo isn\u0026#39;t innocent or cynical—she believes partially, complies, gets tempted, compromises, and ends disillusioned but trapped. There are quietly funny moments embedded in the world: weft-readers pronouncing that \u0026#34;diagonal grief is trending this season,\u0026#34; spinners dieting on specific leaves to produce fashionable colors.\nNow I\u0026#39;m settling on the opening—starting with the origin of the wall itself, the wind coming down from glaciers each winter. For the structure, I\u0026#39;ll deliver the fable, a central allegory paragraph, a symbol map, three alternative morals, and an anti-preachiness note, all in one markdown artifact since this is long-form creative work. I\u0026#39;m deciding on the title now—something like \u0026#34;The Wind\u0026#39;s Side\u0026#34; or \u0026#34;The Loud Side of the Wall.\u0026#34;\nFor the protagonist, I\u0026#39;m introducing Ilo, whose mother wove a blue panel and died from spinning herself out—a normalized burnout treated as virtue. Ilo wants to weave her mother\u0026#39;s likeness high on the wall where the wind touches most, because in Vell, being touched by the wind is the only afterlife people believe in anymore. The tension comes from the rules: fresh thread counts double at the evening count, but untouched panels get unraveled after three seasons. Ilo\u0026#39;s racing against a deadline to keep her mother\u0026#39;s panel from being returned to common thread.\nThe conflict deepens when Ilo\u0026#39;s charming rival Pell—a curator-type who arranges others\u0026#39; work in high wind eddies—steals Ilo\u0026#39;s mother-motif (a mended swallow) and places it where the wind adores it, getting Pell\u0026#39;s name sung instead. Ilo\u0026#39;s original panel stays low and untouched. The Guild then tempts her with a deal: they\u0026#39;ll raise her panel to the high courses if she reworks it in fashionable glacier tones and turns the face outward with larger eyes. She does it, unpicking her mother\u0026#39;s brown eyes and re-spinning them silver. The wind comes, her name gets sung, but when she stands in the singing and feels the wind through the weave on her wet face, she realizes the touch is just cold—just weather. And the tremor of being touched actually damages the panel, wearing it faster.\nThis leads her to a darker realization: the most beloved panels wear out soonest because the wind\u0026#39;s love is friction. The Guild calls this \u0026#34;the honor of being used up.\u0026#34; So Ilo turns her attention to the inside face of the wall—the unlit inner side everyone keeps their backs to—where all the knots and hanging threads live. She realizes the spinners have never actually seen their own finished work except in reverse; the entire city has only ever seen the backs of its own pictures. To see the front, someone would have to go out through the Narrow into the wind, which is forbidden or impossible. Ilo decides to be that person—to go out and see what the city has created, wearing thread from the returned, unraveled panels.\nWhen she reaches the front at dawn, she finds the tapestry is weathered and gray, bleached by the wind into a uniform color regardless of what was spun. The wind doesn\u0026#39;t see pictures; it just touches whatever stands in its way, and the ripples the readers interpret are just the shape of the valley funneling air. There\u0026#39;s no audience, no one outside—just wind and a gray wall with frayed threads where wild swallows have begun nesting. She returns to the city unchanged on the surface, keeps her place at the count, but starts deliberately making loose knots so the front frays faster and gives the birds more material to build with. To everyone else it looks like her skill is declining, but somewhere on the wind side, swallows are building nests in her mother\u0026#39;s thread.\nI\u0026#39;m settling on the closing aphorism—something quiet and haunting that lets the wind have the last word without moralizing. The whole piece needs to land around 1,900 words, and I\u0026#39;m mapping out the central allegory: the tapestry as performed public surface, the wind as algorithmic attention that flattens everything to gray, the birds nesting in the ruins as actual life persisting beneath performance. The protagonist stays complicit, there\u0026#39;s no escape, but there\u0026#39;s a kind of quiet resistance in making space for something real to grow in the wreckage. Now I\u0026#39;m ready to write the full fable text itself. I\u0026#39;m tracking the timeline of what happens after the reworked panel wears through and gets returned to the guild, and how Ilo ventures outside the wall with thread from her mother\u0026#39;s returned work. The outer face of the wall is bleached colorless by the wind, frayed and inhabited by nesting swallows — no one outside ever sees the images. When she returns, no one believes what she\u0026#39;s witnessed; grief and disbelief follow her, though she keeps spinning with deliberately loose knots, her name unsung. I\u0026#39;m also weaving in lighter touches: the weft-readers\u0026#39; seasonal pronouncements about the wind\u0026#39;s moods, bureaucratic forms for panel elevation, a line about children learning the wind\u0026#39;s preferences before their grandmothers\u0026#39; names, and the quiet anxiety that the glacier feeding the wind has been shrinking for years, making the wall\u0026#39;s original purpose increasingly unnecessary — something no one speaks of at the evening count. Now I\u0026#39;m ready to write the full piece at around 1800–2100 words and then compile all six sections into a markdown file.\n\u003c/code\u003e\u003c/pre\u003e\u003ch2 id=\"note-from-claude-fable-5s-output\"\u003eNote from Claude Fable 5\u0026rsquo;s Output \u003csup id=\"fnref:2\"\u003e\u003ca href=\"#fn:2\" class=\"footnote-ref\" role=\"doc-noteref\"\u003e2\u003c/a\u003e\u003c/sup\u003e\u003c/h2\u003e\n\u003ch3 id=\"central-allegory\"\u003eCentral Allegory\u003c/h3\u003e\n\u003cp\u003eThe tapestry is the performed surface of a life — the feed, the CV, the visible self — woven always from behind, so that its makers never see themselves as they are seen and must take the metrics\u0026rsquo; word for it. The wind is attention itself, algorithmic and ambient: sincerely craved, ritually interpreted, and structurally incapable of caring, its \u0026ldquo;preferences\u0026rdquo; being nothing but the shape of the terrain it moves through. The valley\u0026rsquo;s economy of touch captures the central contradiction of attention-driven life: the wall was built as protection from an indifferent force, and its builders ended up organizing their whole existence around begging that force to press through. Being noticed literally wears you out (\u0026ldquo;the honor of being used up\u0026rdquo;), obsolescence is institutionalized as recycling, and the only unmediated life in the story — the swallows nesting leeward in the frayed thread — happens off the ledger, facing away from the audience, in the wreckage of the performance.\u003c/p\u003e","title":"Technical Report: A Fable by Claude Fable"},{"content":"Note: part of this post is generated by AI (Claude Fable 5 High on July 5, 2026). For generative AI usage policy on this blog, please refer to the Privacy Policy and Content Usage Notice.\nI tested Anthropic\u0026rsquo;s latest model — Claude Fable 5. Haven\u0026rsquo;t got a hard-enough question for it to solve, I decide to let it write a fable about issues in our modern society to demonstrate its research (turns out it didn\u0026rsquo;t use web search though) and writing capabilities.\nFor the prompt and the explanation by Claude Fable 5 on this fable, please refer to this post.\n(start of the fable)\nThe Wind Side of the Wall In the valley of Vell, the wind used to come down off the glacier in the dark of the year and take the smallest sleepers from their beds. This is not a figure of speech. The old songs name the children.\nSo the spinners of Vell — small, gray-pelted, six-handed creatures who draw silk from a slit above the breastbone — did the sensible thing. They wove a wall.\nIt worked. Fewer names entered the songs. And because the spinners were makers by nature, and because a plain wall shames a maker, the wall did not stay plain. Each family wove its panel: harvests, weddings, the faces of the dead. A wall against the wind became, over generations, a tapestry that circled the valley entire, tall as forty spinners standing on shoulders, and always, in some quarter, still growing.\nHere is the first thing to know about tapestry. It is woven from behind. The image faces away from the hands that make it. The spinners of Vell worked from the inside of their wall, so what they saw all their lives was the back of their own pictures — knots, hanging threads, ghost shapes in reverse. Not one spinner living had seen the front of the thing to which she gave her body\u0026rsquo;s silk. They had it on good authority that it was magnificent.\nThe good authority was the weft-readers, who climbed ladders along the inner face at dusk and pressed their palms flat to the cloth. For the wind, shut out, had not gone away. It walked the outer face of the wall, the doctrine said, the way a buyer walks a market — and where it was pleased, it lingered, and the cloth trembled under it. The readers felt these tremors and called down the names of the touched, and at the evening count those names were sung.\nTo be sung was everything. It was promotion and dowry and — since the old shrine had long ago been converted to dye storage — it was the only afterlife anyone in Vell still spoke of with a straight face. Children were taught the wind\u0026rsquo;s preferences before they were taught their grandmothers\u0026rsquo; names.\nThe wind\u0026rsquo;s preferences, it must be said, were not stable. \u0026ldquo;The wind is walking diagonals this season,\u0026rdquo; the readers would announce, and the valley bent to diagonals. \u0026ldquo;The wind has tired of red.\u0026rdquo; A year later red returned, unexplained, and those who had unpicked their reds wove them back in with the particular energy of spinners who had never doubted.\nIlo\u0026rsquo;s mother, Sef, had woven the blue swallow.\nIt stood — Ilo had been told; she had only ever seen its knotted back — on the fourth course of the eastern quarter: a swallow with a mended wing, because Sef had once splinted a real swallow through a real winter, feeding it by hand, and had wanted that one small competence remembered. Sef died the way skilled spinners were praised for dying. She spun past the ache in her breastbone, and then past the numbness that follows the ache, and gave good thread to the end. This was said at her burial as praise, and everyone, including Ilo, understood it as praise, and Ilo would sometimes wake with her own hands aching and feel, before she felt anything else, proud.\nThe trouble was the ledger. A panel the wind had not touched in three seasons was returned: unraveled by the Office of Courses, its thread boiled pale and wound into the common baskets. The tapestry feeds itself, the Office liked to say, with the serenity of institutions describing what they would do to you regardless.\nThe blue swallow had gone two seasons untouched.\nSo Ilo did what a daughter does. She spun at night to make fresh thread, because fresh thread counted double at the count, and the count decided whose petitions the Office heard. She ate frostleaf until her mouth went numb, because frostleaf grayed the silk, and the readers had declared glacier tones were walking that year. She grew thin in the way that drew compliments. And she petitioned to have her mother\u0026rsquo;s panel raised to the high courses, where the wind walked oftenest.\nWhile her petition sat in its basket, her friend Pell was sung three nights running.\nPell was charming and quick and spun very little. Pell\u0026rsquo;s gift was placement — an eye for the eddies where wind pooled against the wall — and what Pell had placed in the highest eddy of the eastern quarter, spun by hired hands in this season\u0026rsquo;s grays, was a swallow with a mended wing.\n\u0026ldquo;It\u0026rsquo;s an homage,\u0026rdquo; Pell said, and was not lying, exactly. \u0026ldquo;Your mother\u0026rsquo;s swallow lives, Ilo. Isn\u0026rsquo;t that the point?\u0026rdquo;\nIlo turned this over for many nights and could not find the flaw in it, which frightened her more than the theft had. The swallow was touched. The swallow was sung. Only the name attached to the trembling was wrong, and the wind, whatever else it did, had never once been known to pronounce a name.\nThe Office granted her petition, with conditions. The panel could rise to the high courses if reworked to current standards: glacier tones throughout, and the swallow\u0026rsquo;s head turned outward. \u0026ldquo;The wind likes to be looked at,\u0026rdquo; the clerk explained, in the tone of someone quoting a finding.\nIlo unpicked her mother\u0026rsquo;s work stitch by stitch — the brown eye Sef had knotted with her own hands — and respun it silver, and turned its gaze away from the valley, out toward the weather.\nThe wind came that very week. The panel trembled all night; the readers sang Sef\u0026rsquo;s name, and Ilo\u0026rsquo;s after it; and Ilo stood beneath the singing with her face against the weave, and the wind that pressed through to touch her cheek was exactly what wind is. Cold. Moving air. It felt like being loved by a door left open.\nThere was one more thing nobody had told her, though the Office kept careful records of it. Touch is friction. The panels the wind favored wore fastest — the trembling worked their knots loose, thinned them, frayed them — so the most beloved panels had the shortest lives, and were soonest returned. The Office had a phrase for this too. The honor of being used up. Ilo heard it spoken at the count, gently, about her mother\u0026rsquo;s panel, one season after its elevation, when the silver swallow had been touched so often it was coming apart.\nAs a courtesy to a sung name, they let her keep one skein of the returned thread. It was boiled pale. It smelled like nothing.\nThat winter Ilo stopped sleeping, and did what unsleeping spinners do, which is walk. She walked the inner face at night with a lamp and looked, really looked, at the backs of the pictures: the knots, the crossed-over threads, the reversed ghosts of a thousand faces the valley had turned outward. An entire city, she thought, that has only ever seen the wrong side of everything it made. She was not the first to think this. She was the first in a long time to put on three coats, wrap the pale skein around her throat, and go out through the Narrow to look at the right side.\nThe Narrow was the one gap left in the wall, kept for the water to leave by, and going out through it in the dark of the year was the kind of act the songs used to be about. The wind took her breath at the gap and kept taking it. She walked the outer face for a day, hugging the cloth, and at dawn she stepped back to see what the wind saw.\nThe wind saw nothing.\nThere were no pictures on the wind side of the wall. There was gray. The wind had been walking that face for two hundred years and had bleached every color to its own color, scoured every swallow and wedding and harvest to a single vast weathered pallor, so that the reds and the diagonals and the glacier tones all arrived at the same gray within a season of arriving at all. The famous tremors were not preference. They were the shape of the valley funneling air, the same eddies in the same corners, pleasure-shaped only from behind. There was no buyer walking the market. There was no market. There was weather, and a wall in its way.\nAnd there was one thing more, which Ilo stood before for a long time. Wherever the wind\u0026rsquo;s touch had frayed the cloth — wherever the honor of being used up had loosened threads into the air — small birds had come. Swallows, mostly. They had pulled the loose silk free and woven it, on their own authority and to no count, into nests in the wall\u0026rsquo;s high frayed places. In the ruins of the pictures, in thread that had once been somebody\u0026rsquo;s mother, actual swallows were raising actual young, and not one of them was facing the weather. Every nest opened leeward. Even the birds knew which side of the wall life happens on.\nShe noticed, too, standing there — and this was not spoken of at the count, though the readers surely knew — that the glacier at the valley\u0026rsquo;s head had drawn back up its mountain like a hem, and the wind came thinner off it every year, and the wall was defended most fiercely in the very years it was needed least.\nIlo went back in through the Narrow, because a spinner\u0026rsquo;s breastbone fills whether or not anyone is counting, and because her whole life was on the inside of that wall, which is not nothing.\nShe told what she had seen. The readers heard her out with real kindness. \u0026ldquo;Grief grays the eye,\u0026rdquo; the eldest said, patting her hand, and the phrase was repeated at the count that evening as a caution, and several spinners wept for her, briefly, before the singing of the names.\nSo Ilo did not tell it again. She took up her place. She spun, as she would spin all her life; the silk does not ask permission. But those who watched her work in the years after said her skill had left her — that her knots had gone loose and careless, that she left thread-ends hanging outward into the weather like an apprentice. Her name was not sung again. The Office pitied her, and pity in Vell was a kind of unraveling too.\nShe never corrected them. Loose knots fray fast on the wind side. Frayed silk lifts free. And every spring, in the high gray ruin of the eastern quarter, there were more nests than the spring before — though only the weather knew it, and the weather, as ever, said nothing.\nIn Vell they still say the wind knows good work when it feels it. The wind, for its part, has never said a word, and is answered constantly.\n(end of the fable)\nFor the prompt and the explanation by Claude Fable 5 on this fable, please refer to this post.\n","permalink":"https://taskwitch.github.io/posts/a-fable-by-claude-fable/","summary":"\u003cp\u003e\u003cstrong\u003eNote:\u003c/strong\u003e part of this post is generated by AI (Claude Fable 5 High on July 5, 2026). For generative AI usage policy on this blog, please refer to the \u003ca href=\"/privacy-policy/\"\u003ePrivacy Policy and Content Usage Notice\u003c/a\u003e.\u003c/p\u003e\n\u003cp\u003eI tested Anthropic\u0026rsquo;s latest model — Claude Fable 5. Haven\u0026rsquo;t got a \u003cem\u003ehard-enough\u003c/em\u003e question for it to solve, I decide to let it write a fable about issues in our modern society to demonstrate its research (turns out it didn\u0026rsquo;t use web search though) and writing capabilities.\u003c/p\u003e","title":"A Fable by Claude Fable"},{"content":"When she boarded the plane for her university in the Western Hemisphere, it felt like her own personal Exodus—finally free to breathe without someone counting each breath, to dream without permission, to simply be herself where even the sunrise would arrive hours before anyone back home opened their eyes to judge another day.\n","permalink":"https://taskwitch.github.io/posts/my-exodus/","summary":"\u003cp\u003eWhen she boarded the plane for her university in the Western Hemisphere, it felt like her own personal \u003cem\u003eExodus\u003c/em\u003e—finally free to breathe without someone counting each breath, to dream without permission, to simply be herself where even the sunrise would arrive hours before anyone back home opened their eyes to judge another day.\u003c/p\u003e","title":"My Exodus"},{"content":"A question I saw in my sibling\u0026rsquo;s primary school math homework leads to the following generalization:\nFind the maximum number of $l\\times w\\times h$ bricks one can pack into a $L\\times W\\times H$ box.\nwhere $l, w, h, L, W, H$ are some given constants (of course for a primary school student).\nWe assume all faces of the bricks must be parallel to the box face, and all lengths are integers.\nApproach 1 If every brick must have the same orientation (e.g. every brick\u0026rsquo;s $l\\times w$ face is parallel to the box\u0026rsquo;s $L\\times W$ face), what is the maximum number of bricks that fit?\nSimply try each orientation and take the best count: $$ \\text{answer} = \\max_\\text{$(x,y,z)$ is a permutation of $(l,w,h)$} (\\left\\lfloor\\frac{L}{x}\\right\\rfloor\\left\\lfloor\\frac{W}{y}\\right\\rfloor\\left\\lfloor\\frac{H}{z}\\right\\rfloor) $$Approach 2 Every brick may have a different orientation, i.e. bricks can be rotated individually.\nWe can solve this using dynamic programming, which comes from the intuition that a bad placement early on can waste space and prevent the layout from reaching the true maximum.\nOne can think of it as: how many $l\\times w\\times h$ bricks can be cut from the large $L\\times W\\times H$ box by slicing the box into smaller cuboids?\nState Let $F(x, y, z)$ be the maximum number of bricks that can be packed into an $x\\times y\\times z$ cuboid.\nBase Case The recursion bottoms out when the cuboid has no volume: if any of $x, y, z$ is $0$, then $F(x,y,z) = 0$.\nNote this is the only base case the recursion needs. A small-but-nonempty cuboid like $1\\times1\\times1$ (when no brick fits) also yields $0$, but that falls out naturally: no orientation fits in Choice 1 (see below), and every cut in Choice 2 produces a sub-cuboid that likewise yields $0$. So \u0026ldquo;can\u0026rsquo;t hold a brick\u0026rdquo; is an emergent result, not a termination condition to check for.\nState Transitions For a $x\\times y\\times z$ cuboid, there are two choices:\nFill the whole cuboid with all bricks with the same orientation. For each permutation $(a,b,c)$ of $(l, w, h)$ that fits (i.e. $a\\le x$, $b\\le y$, $c\\le z$), we can place $\\left\\lfloor\\frac{x}{a}\\right\\rfloor \\left\\lfloor\\frac{y}{b}\\right\\rfloor \\left\\lfloor\\frac{z}{c}\\right\\rfloor$ bricks. We denote the set of permutation $(a,b,c)$ that fits such bricks $o$, namely: $$ o=\\{(a,b,c) : \\text{permutation of } (l,w,h) \\text{ with } a\\le x,\\; b\\le y,\\; c\\le z\\} $$ Cut the cuboid into two smaller ones. E.g. cutting an $x\\times y\\times z$ cuboid at $x = i$ yields two smaller cuboids $i \\times y \\times z$ and $(x-i) \\times y\\times z$. We cut the cuboid from all the three directions $x, y$, and $z$.\n$$ F(x,y,z) = \\max\\begin{cases} \\lfloor\\frac{x}{a}\\rfloor \\lfloor\\frac{y}{b}\\rfloor \\lfloor\\frac{z}{c}\\rfloor \u0026 (a,b,c) \\in o\\\\ F(i,y,z) + F(x - i, y, z) \u0026 1 \\le i \u003c x\\\\ F(x,j,z) + F(x, y-j,z) \u0026 1 \\le j \u003c y\\\\ F(x,y,k) + F(x, y, z - k) \u0026 1 \\le k \u003c z \\end{cases} $$Time Complexity $O(LWH(L+W+H))$\nWhy this is hard in general Our exact problem packs many copies of a single rotatable brick. It\u0026rsquo;s tempting to call this NP-hard by pointing at 2-D rectangle packing (set $H = h = 1$), which is known to be NP-hard. But that argument doesn\u0026rsquo;t actually go through: the NP-hardness of 2-D packing relies on packing rectangles of many different sizes, whereas flattening our problem only ever produces copies of one congruent rectangle. The hard instances of general rectangle packing aren\u0026rsquo;t reachable as special cases of ours, so this reduction doesn\u0026rsquo;t establish hardness for the identical-brick problem.\nSo I\u0026rsquo;ll be careful about the claim: I don\u0026rsquo;t have a clean reduction proving the single-brick version is NP-hard, and it may well be easier than general packing. What I can say firmly is that the guillotine DP below solves a restricted version exactly and in polynomial time, and that no simple greedy rule is known to be exact for the unrestricted version. Whether the unrestricted single-brick problem is polynomial or NP-hard is a question I\u0026rsquo;m leaving open here rather than asserting.\nAn exact method for the unrestricted version can\u0026rsquo;t rely on the guillotine shortcut, so it must search over genuine placements. That doesn\u0026rsquo;t mean naive brute force — ILP and CP-SAT solvers are exact and prune aggressively — but in the worst case the search space is exponential, and no polynomial-time exact algorithm is known.\nLimitations This DP only considers layouts that can be produced by recursive straight (\u0026ldquo;guillotine\u0026rdquo;) cuts. Some optimal packings interlock in ways no sequence of full-width cuts can reproduce, so the DP can occasionally undercount by a brick or two.\nThe reason to accept this isn\u0026rsquo;t NP-hardness directly — it\u0026rsquo;s a deliberate trade. Restricting to guillotine layouts is exactly what buys us polynomial time. We\u0026rsquo;re solving an easier, well-structured sub-problem on purpose, getting a fast and usually-optimal answer, and giving up the guarantee of exactness on interlocking cases. If you need the true optimum, you switch to an exponential search (backtracking or an ILP/CP formulation) and pay for it in runtime.\n","permalink":"https://taskwitch.github.io/posts/bricks-in-the-box/","summary":"\u003cp\u003eA question I saw in my sibling\u0026rsquo;s primary school math homework leads to the following generalization:\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003eFind the maximum number of $l\\times w\\times h$ bricks one can pack into a $L\\times W\\times H$ box.\u003c/p\u003e\n\u003c/blockquote\u003e\n\u003cp\u003ewhere $l, w, h, L, W, H$ are some given constants (of course for a primary school student).\u003c/p\u003e\n\u003cp\u003eWe assume all faces of the bricks must be parallel to the box face, and all lengths are integers.\u003c/p\u003e","title":"How to put the most bricks in a box?"},{"content":"This blog entry is written on an iPad running Code App by thebaselab. I am recording a way to uncomfortably edit or draft something then post to my blog just in case I forget to bring my laptop.\nSetting Up Code App Generate ssh key pairs and upload the public key to Github using ssh-keygen on your Code App terminal; Clone your blog repo, git equivalent on Code App is lg2; Github account mail and password or PAT may be required Writing Blogs Create your blog entry markdown in repo.git/content/posts Paste the following template into the editor --- title: draft: false date: --- Generate timestamp using date +\u0026#39;%Y-%m-%dT%H:%M:%S%z\u0026#39; and paste into the template - Copy and paste using the GUI instead of command + C/V. Save, lg2 add ., lg2 commit, and lg2 push. Github Action will automatically build and deploy the site. Remark You won\u0026rsquo;t want to write blogs on an iPad.\nCode App is extremely buggy and annoying. For example,\nits terminal is based on ios_system \u0026ldquo;terminal emulator\u0026rdquo; project commands and scripting are almost unusable (if I can run Hugo or write scripts, why have I manually copy the template?) poor mouse and keyboard integration I am writing this using the keyboard of my MacBook via Sidecar. frequent crashes maintenance and security aren\u0026rsquo;t guranteed make sure to backup you data, use version control, and set paraphrase to your ssh key. no extension ecosystem no grammar and spelling checking tools: please forgive these mistakes, if any, in this post Final Verdict Maybe a harmony os PC (not AD) has better blogging experience than an iPad.\nYour next computer won\u0026rsquo;t be an iPad. (Edited on iPad Pro M4 13\u0026rsquo;')\n","permalink":"https://taskwitch.github.io/posts/writing-blogs-on-ipad/","summary":"\u003cp\u003eThis blog entry is written on an iPad running \u003ca href=\"https://apps.apple.com/cn/app/code-app/id1512938504?l=en-GB$0\"\u003eCode App by thebaselab\u003c/a\u003e. I am recording a way to \u003cdel\u003euncomfortably\u003c/del\u003e edit or draft something then post to my blog just in case I forget to bring my laptop.\u003c/p\u003e\n\u003ch2 id=\"setting-up-code-app\"\u003eSetting Up Code App\u003c/h2\u003e\n\u003col\u003e\n\u003cli\u003eGenerate ssh key pairs and upload the public key to Github using \u003ccode\u003essh-keygen\u003c/code\u003e on your Code App terminal;\u003c/li\u003e\n\u003cli\u003eClone your blog repo, \u003ccode\u003egit\u003c/code\u003e equivalent on Code App is \u003ccode\u003elg2\u003c/code\u003e;\n\u003cul\u003e\n\u003cli\u003eGithub account mail and password or PAT may be required\u003c/li\u003e\n\u003c/ul\u003e\n\u003c/li\u003e\n\u003c/ol\u003e\n\u003ch2 id=\"writing-blogs\"\u003eWriting Blogs\u003c/h2\u003e\n\u003col start=\"3\"\u003e\n\u003cli\u003eCreate your blog entry markdown in \u003ccode\u003erepo.git/content/posts\u003c/code\u003e\u003c/li\u003e\n\u003cli\u003ePaste the following template into the editor\n\u003cdiv class=\"highlight\"\u003e\u003cpre tabindex=\"0\" style=\"color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;\"\u003e\u003ccode class=\"language-yaml\" data-lang=\"yaml\"\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e---\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#f92672\"\u003etitle\u003c/span\u003e: \n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#f92672\"\u003edraft\u003c/span\u003e: \u003cspan style=\"color:#66d9ef\"\u003efalse\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e\u003cspan style=\"color:#f92672\"\u003edate\u003c/span\u003e: \n\u003c/span\u003e\u003c/span\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003e---\n\u003c/span\u003e\u003c/span\u003e\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003e\u003c/li\u003e\n\u003cli\u003eGenerate timestamp using\n\u003cdiv class=\"highlight\"\u003e\u003cpre tabindex=\"0\" style=\"color:#f8f8f2;background-color:#272822;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-text-size-adjust:none;\"\u003e\u003ccode class=\"language-shell\" data-lang=\"shell\"\u003e\u003cspan style=\"display:flex;\"\u003e\u003cspan\u003edate +\u003cspan style=\"color:#e6db74\"\u003e\u0026#39;%Y-%m-%dT%H:%M:%S%z\u0026#39;\u003c/span\u003e\n\u003c/span\u003e\u003c/span\u003e\u003c/code\u003e\u003c/pre\u003e\u003c/div\u003eand paste into the template\n- Copy and paste using the GUI instead of command + C/V.\u003c/li\u003e\n\u003cli\u003eSave, \u003ccode\u003elg2 add .\u003c/code\u003e, \u003ccode\u003elg2 commit\u003c/code\u003e, and \u003ccode\u003elg2 push\u003c/code\u003e. Github Action will automatically build and deploy the site.\u003c/li\u003e\n\u003c/ol\u003e\n\u003ch2 id=\"remark\"\u003eRemark\u003c/h2\u003e\n\u003cp\u003eYou won\u0026rsquo;t want to write blogs on an iPad.\u003c/p\u003e","title":"Writing Hugo Blogs on iPad"},{"content":"Hi!\nCongratulations on finding me online (given that GitHub Pages are hard to appear in search results)!\nWho am I I am Ada.\nShe/they. Neurospicy computing witch. Fun fact: I have a birthday equal to Ada Lovelace\u0026rsquo;s in a way that Halloween equals Christmas. Interests Computing and cognitive science Biology and complex systems (General) learning Identity, technology, and society Coffee, music, people watching, and good typography Contact, Work \u0026amp; Socials Personal mail: binrays752 (at) gmail (dot) com\nGitHub: @taskwitch\nOther Socials: if you can find me \u0026#x1f440;\n","permalink":"https://taskwitch.github.io/about/","summary":"\u003cp\u003eHi!\u003c/p\u003e\n\u003cp\u003eCongratulations on finding me online (given that GitHub Pages are hard to appear in search results)!\u003c/p\u003e\n\u003ch2 id=\"who-am-i\"\u003eWho am I\u003c/h2\u003e\n\u003cp\u003eI am Ada.\u003c/p\u003e\n\u003cul\u003e\n\u003cli\u003e\u003ca href=\"https://pronouns.org/she-her\"\u003eShe\u003c/a\u003e/\u003ca href=\"https://pronouns.org/they-them\"\u003ethey\u003c/a\u003e.\u003c/li\u003e\n\u003cli\u003eNeurospicy computing witch.\u003c/li\u003e\n\u003cli\u003eFun fact: I have a birthday \u003cem\u003eequal to\u003c/em\u003e \u003ca href=\"https://www.wolframalpha.com/input?i=Ada+Lovelace%27s+birthday\"\u003eAda Lovelace\u0026rsquo;s\u003c/a\u003e in a way that \u003ca href=\"https://www.wolframalpha.com/input?i=christmas+equals+halloween+meme\"\u003eHalloween \u003cem\u003eequals\u003c/em\u003e Christmas\u003c/a\u003e.\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch2 id=\"interests\"\u003eInterests\u003c/h2\u003e\n\u003cul\u003e\n\u003cli\u003eComputing and cognitive science\u003c/li\u003e\n\u003cli\u003eBiology and complex systems\u003c/li\u003e\n\u003cli\u003e(General) learning\u003c/li\u003e\n\u003cli\u003eIdentity, technology, and society\u003c/li\u003e\n\u003cli\u003eCoffee, music, people watching, and good typography\u003c/li\u003e\n\u003c/ul\u003e\n\u003ch2 id=\"contact-work--socials\"\u003eContact, Work \u0026amp; Socials\u003c/h2\u003e\n\u003cp\u003ePersonal mail: binrays752 (at) gmail (dot) com\u003c/p\u003e","title":"About Ada"},{"content":"This is my first post. I\u0026rsquo;m testing out the Hugo framework and the PaperMod theme, and getting familiar with the setup along the way (mostly code highlighting, markdown formatting, and equations \u0026#x1f606;).\nFor this very first post — on the website I built right after graduating high school — I want to share an interesting problem underlying an AP Computer Science A question a friend asked me during senior year.\nTrue or false: will i sometimes equal 3?\ni = 3 j = 2 for _ in range(100): i -= j\tj += i The answer is true. This operation is actually periodic, with a period of $6$, regardless of the initial values of i and j!\nMatrix Representation of a Linear Transformation Here, i and j are updated linearly, so it\u0026rsquo;s natural to write the operation as a linear transformation — and therefore as a matrix transformation.\nFirst, write out the iteration equations: $$ i_{k+1} = i_{k} - j_k,\\\\ j_{k+1} = j_k + i_{k + 1} = j_k + (i_k - j_k) = i_k $$ or, equivalently, in vector form: $$ \\begin{pmatrix}i\\\\j\\end{pmatrix}_{k+1} = \\begin{pmatrix}i_k - j_k\\\\i_k\\end{pmatrix} = \\begin{pmatrix}1 \u0026 -1\\\\1 \u0026 0\\end{pmatrix}\\begin{pmatrix}i\\\\j\\end{pmatrix}_{k} $$ Denote $$ A = \\begin{pmatrix}1 \u0026 -1\\\\1 \u0026 0\\end{pmatrix}, \\quad \\boldsymbol x_k = \\begin{pmatrix}i\\\\j\\end{pmatrix}_k $$ so that $$ \\boldsymbol x_k = A^k \\boldsymbol x_0 $$Periodicity of the Linear Transformation To show periodicity in the linear transformation $A$, we need $\\boldsymbol x_p = A^p\\boldsymbol{x_0} = I\\boldsymbol x_0$ for some positive integer $p$ — that is, $A^p = I$.\nYou might quickly discover that $A^3 = -I$, which is enough on its own to show $A^6 = I$ and thus that $A$ has a period of $6$. But let\u0026rsquo;s give a more concrete proof here, using eigenvalues.\nAn eigenvalue of a linear transformation $T$ is a scalar $\\lambda$ such that applying $T$ to some nonzero vector $\\boldsymbol v$ has the same effect as multiplying $\\boldsymbol v$ by $\\lambda$: $$ \\lambda \\in \\mathbb F,\\quad\\text{s.t.}\\quad T\\boldsymbol v = \\lambda \\boldsymbol v $$ If an eigenvalue $\\lambda$ of a linear transformation $T$ satisfies $\\lambda^p=1$, then applying $T$ to $\\boldsymbol v$ $p$ times returns $\\boldsymbol v$ unchanged — which implies $T^p = I$. So $T$ has a period of $p$, and this holds independent of which nonzero eigenvector $\\boldsymbol v$ we chose.\nWe can find the eigenvalues of a matrix by solving its characteristic equation: $$ \\det (A - \\lambda I) = 0 $$ Plugging in our matrix $A$ gives: $$ \\begin{aligned} \\det \\begin{pmatrix}1 - \\lambda \u0026 -1 \\\\ 1 \u0026 0 - \\lambda \\end{pmatrix} \u0026= 0\\\\ (1 - \\lambda)(0 - \\lambda) - (-1)(1) \u0026= 0\\\\ \\lambda^2 - \\lambda + 1 \u0026= 0\\\\ \\Rightarrow \\lambda_{1,2} = \\frac{1 \\pm \\sqrt 3\\mathrm i}{2} \\end{aligned} $$ (where $\\mathrm i$ is the imaginary unit, satisfying $\\mathrm i^2 = -1$)\nRecall that the $n$-th root of unity has the form $\\exp(2\\pi \\mathrm i /n)$, namely: $$ x^n = 1 \\Rightarrow x = \\exp\\left(\\frac{2\\pi\\mathrm i}{n}\\right) $$ Take the root with positive imaginary part, $\\lambda = \\frac{1}{2} + \\frac{\\sqrt 3}{2}\\mathrm i$, and compare it to the right-hand side of Euler\u0026rsquo;s formula: $$ \\exp (\\mathrm i \\theta) = \\cos \\theta + \\mathrm i \\sin \\theta $$ This gives $\\theta = \\pi / 3$. Plugging back in: $$ \\lambda = \\exp\\left(\\mathrm i \\frac{\\pi}{3}\\right) = \\exp\\left(\\frac{2\\pi \\mathrm i}{6}\\right) $$ which is exactly a $6$-th root of unity.\nGeometrically, if we place the complex number $\\lambda$ on the complex plane, raising it to successive powers just spins it around:\non the unit circle $r = 1$, since $r = |\\lambda| = \\sqrt{(\\frac{1}{2})^2 + (\\frac{\\sqrt 3}{2})^2} = 1$ at a fixed angle that\u0026rsquo;s a rational fraction of $2\\pi$, since $\\theta = \\arctan (\\Im \\lambda / \\Re \\lambda) = 2\\pi / 6$ which is exactly the geometric behavior of an $n$-th root of unity.\nTransition matrices $A$ whose eigenvalues violate either of these properties won\u0026rsquo;t show periodicity — the vector on the complex plane will either grow or shrink in magnitude, or spin at an angle that never brings it back around to where it started.\n","permalink":"https://taskwitch.github.io/posts/an-interesting-ap-csa-question/","summary":"\u003cp\u003eThis is my first post. I\u0026rsquo;m testing out the \u003ca href=\"https://github.com/gohugoio/hugo\"\u003eHugo\u003c/a\u003e framework and the \u003ca href=\"https://github.com/adityatelange/hugo-PaperMod\"\u003ePaperMod\u003c/a\u003e theme, and getting familiar with the setup along the way (mostly code highlighting, markdown formatting, and equations \u0026#x1f606;).\u003c/p\u003e\n\u003chr\u003e\n\u003cp\u003eFor this very first post — on the website I built right after graduating high school — I want to share an interesting problem underlying an AP Computer Science A question a friend asked me during senior year.\u003c/p\u003e\n\u003cblockquote\u003e\n\u003cp\u003eTrue or false: will \u003ccode\u003ei\u003c/code\u003e sometimes equal 3?\u003c/p\u003e","title":"An Interesting AP Computer Science A Question"},{"content":"Last updated: June 2026\nPrivacy This website is a personal blog.\nI do not intentionally collect personal information from visitors except information voluntarily provided through email, contact forms, comments, or other direct communication channels.\nLike most websites, hosting providers and analytics services may automatically collect limited technical information such as IP addresses, browser types, operating systems, referring pages, and access times for security, maintenance, and performance purposes.\nI do not sell personal information to third parties.\nIf you contact me, your information will only be used to respond to your inquiry or maintain correspondence.\nThis website may contain links to third-party websites. I am not responsible for the privacy practices or content of those websites.\nCopyright Unless otherwise stated, all original text, essays, notes, images, and other content on this website are copyrighted by the author.\nYou may quote brief excerpts for commentary, criticism, scholarship, or similar purposes with appropriate attribution and a link to the original source.\nAny other reproduction, redistribution, or republication of substantial portions of the content requires permission from the author.\nGenerative AI Notice All articles, essays, notes, and original content published on this website are written by a human author.\nGenerative AI systems may be used for limited technical tasks such as spell-checking, grammar checking, formatting, accessibility review, or software development assistance. However, the ideas, arguments, analysis, and authorship of published content remain human-generated unless explicitly stated otherwise.\nAI Training Restriction The content of this website may not be used to train, fine-tune, evaluate, benchmark, or otherwise improve machine learning models, large language models, generative AI systems, or similar automated systems without prior written permission.\nThis restriction applies to automated scraping, dataset creation, model training, fine-tuning, retrieval datasets, synthetic data generation, and related uses.\nPermission to access this website does not imply permission to use its content for AI training purposes.\nContact Questions regarding this policy may be directed to the contact information provided on this website.\n","permalink":"https://taskwitch.github.io/privacy-policy/","summary":"\u003cp\u003eLast updated: June 2026\u003c/p\u003e\n\u003ch2 id=\"privacy\"\u003ePrivacy\u003c/h2\u003e\n\u003cp\u003eThis website is a personal blog.\u003c/p\u003e\n\u003cp\u003eI do not intentionally collect personal information from visitors except information voluntarily provided through email, contact forms, comments, or other direct communication channels.\u003c/p\u003e\n\u003cp\u003eLike most websites, hosting providers and analytics services may automatically collect limited technical information such as IP addresses, browser types, operating systems, referring pages, and access times for security, maintenance, and performance purposes.\u003c/p\u003e\n\u003cp\u003eI do not sell personal information to third parties.\u003c/p\u003e","title":"Privacy Policy and Content Usage Notice"},{"content":"","permalink":"https://taskwitch.github.io/ergono-code/","summary":"","title":"Ergono Code"}]