The Han Matrix

math • 12/14/2025
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A small grid of stubborn facts

The bamboo skewers came in a little brown paper packet that had already started to go translucent in the corners, the way Kolkata humidity insinuates itself into everything—paper, pride, your plans for the day—until it all looks a bit damply apologetic, like it’s been caught doing something minorly shameful. I tipped the skewers onto my table—my table being a long-suffering slab that has held laptops, unpaid bills, half-read books, a mug with the fossilized ring of a thousand teas, and more existential regret than any piece of furniture deserves—and they made that dry, papery clatter that bamboo makes when it’s pretending it’s not a plant.

I had bought them to spear some aggressively average paneer cubes (I am a man of grand intellectual ambition and modest culinary execution), and now there they were, post-duty, looking innocent, like they hadn’t just been involved in the casual violence of tooth and jaw. And because I’m me—bookish, underfunded, a little feverish in the brain-pan even on good days—I didn’t throw them away. I lined them up.

First one. Then another. Then a little rectangle. Then, without asking permission from any sane part of myself, I started making columns. A 3. A 7. A 0. A negative—well, not a negative yet, because I didn’t have red rods and black rods like the Chinese did (more on that in a moment), so I just imagined the negative, which is how most of my adult life works: the minus sign exists in theory, but the real arithmetic arrives later, unpaid.

Within a minute I had a neat little arrangement of skewers that looked, from a distance, like I was either doing very earnest kindergarten math or preparing an extremely minimalist witchcraft ritual. The numbers were not even important; the shape was. A rectangle of coefficients. A small grid of stubborn facts.

This is the thing about matrices: they’re the rare mathematical object that looks like itself. You can see the idea in the air. You don’t need to squint through five layers of notation and academic self-regard. It’s right there—rows, columns, a little bureaucratic ledger of reality.

And then, as always, my mind did that hypomanic thing where one thought isn’t a thought, it’s a spark that leaps into a sack of dry coconut husk. Bamboo skewers. Counting rods. The Nine Chapters on the Mathematical Art. Han dynasty clerks and engineers solving systems of equations while Europe was still busy having spirited debates about whether bathing causes disease or merely invites it.

Two thousand years. Two thousand years of delay, not in the existence of the method—because the method was sitting there, plain as bamboo on a table—but in the naming, the credit, the myth-making, the whole pompous parade of “we invented this” that humans love because it lets them feel taller than their actual bodies, which are, in the end, just sacks of water and grievance.

I stared at my little bamboo rectangle and felt, absurdly, like I’d stumbled onto a message in a bottle—except the bottle had been floating for centuries and the message was: Dear future, we already did this. Please stop strutting. I sighed.

The Womb Called “Matrix”

The word “matrix” comes from Latin mater, mother—womb, source, origin, the place where things are formed. It’s a beautiful etymology, and like all beautiful etymologies it’s also a trap, because humans see beauty and immediately start building altars. “Matrix” sounds like something sacred, primordial, as if every grid of numbers is a little pregnancy.

Of course, half the time in math we use “matrix” the way government uses “framework”: it means “a box we can put things in so we can pretend we understand them.” But still. The womb idea sticks. A matrix is a container where relationships gestate.

Now, what’s deliciously ironic—delicious in the way irony is delicious, which is to say it tastes good and then gives you heartburn—is that long before European scholars polished the Latin and gave the thing a name that sounded suitably Roman and authoritative, Chinese mathematicians were already doing the womb-work. They had the baby. They were changing its diapers. They were teaching it to walk.

In The Nine Chapters on the Mathematical Art—compiled over time, polished around the Han period—the method for solving simultaneous linear equations appears in a chapter often translated as something like “Rectangular Arrays,” which is almost hilariously direct. Not “The Grand Unified Theory of Coefficients.” Not “Gauss’s Magnificent Staircase of Destiny.” Just: rectangles. Arrays. Here are the numbers. Do the work.

And the work is what we now call Gaussian elimination: you take a system of equations, you arrange the coefficients in a rectangular block, and you perform a sequence of row operations—add multiples of one row to another, swap rows, scale rows—until the block becomes triangular, then you back-substitute your way out like a man escaping a crowded Kolkata bus by sliding sideways through armpits and moral compromise.

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The math was literally tactile

What’s extraordinary is not merely that they had the method, but that they had it in a physical form: counting rods on a counting board. The coefficients were not ink; they were objects. You could touch the algebra. You could move it around. The math was literally tactile, which is a faintly obscene thought in a world where we’ve turned everything into glowing glass rectangles and forgotten what it means to handle an idea.

I am not romanticizing this as some mystical Eastern wisdom. No. It’s engineering. It’s grain yields. It’s taxes. It’s canals and land measurement and the eternal human obsession with “how much of this do I have, and how much of it can I extract from someone else.” The romance comes later, usually in languages with impressive-sounding nouns.

Fangcheng, or: Rectangles Don’t Care About Your Civilizational Pride

If you’ve ever watched the Western history of mathematics told in the lazy, chest-thumping mode—Greece, then a long sleepy nap, then Europe wakes up, then Newton sneezes and calculus falls out—you’ve seen the problem. It’s not that people are malicious (though plenty are); it’s that narratives are greedy. They want a clean arc. They want heroes. They want a lineage that ends in us, the presumed peak of everything.

But knowledge doesn’t behave like that. Knowledge is promiscuous. It wanders. It leaks. It gets lost in wars, burned in libraries, miscopied by tired scribes, translated badly, translated brilliantly, ignored for centuries because the wrong emperor was having a mood. It doesn’t care. It doesn’t salute.

So here’s this Han-era method—counting rods arranged as a rectangular array—and Europe, later, eventually, arrives at something similar and formalizes it and, being Europe, names it after a European man with the kind of gravitas that comes from having your portrait painted by people who could afford oil paint.

Gauss was a genius, no question. But calling the method “Gaussian elimination” the way we commonly do—without footnotes, without context—feels like naming rice “Newton’s grain” because Newton also ate food and occasionally needed carbohydrates to keep his brain from collapsing in on itself.

I can already hear the reflexive defense: “But Gauss popularized it in the West.” Yes. That’s true. And the West is very good at creating the impression that “popularized in the West” is the same as “invented by humanity.”

I grew up in an Indian education system that treats knowledge like a set of exam answers. It does not teach you the history of ideas as a messy, human, global thing. It teaches you a list of names and dates in the way people teach devotional chants: repeat, repeat, repeat, and do not ask why. This is how you get grown adults who can compute a determinant but cannot tell you what a determinant is in any sense that feels like reality. They can recite, they cannot see.

Which is why the counting rods hit me in the gut (the gut being the most honest organ, always making its opinions known with gas or hunger or cramps). The Chinese method is visual. It’s spatial. It’s literally a little theater of numbers on a board. It’s the thing my brain likes: pictures first, then overthinking. And then the other thing: it is unpretentious. It doesn’t need metaphysics. Humans, however, always do.

Two Thousand Years of People Mistaking a Label for a Discovery

Two thousand years is an embarrassing length of time to misunderstand what’s happening. Not to not know—ignorance is honest. To misunderstand. To think the label is the thing. To celebrate the naming as if naming is creation.

This is not only a math problem. It’s a civilization problem. It’s a human ego problem. It’s the same impulse that makes people take a river, slap a new name on it, and then act like they discovered water. The same impulse that makes empires redraw maps and call it “order.” The same impulse that makes a mediocre corporate manager rename a process, put it in a PowerPoint, and then become a “thought leader.”

I have worked in environments where I watched this happen in real time: someone takes a perfectly good idea—usually produced by underpaid people who do actual work—and then a more powerful person gives it a catchy label, wraps it in ceremony, and walks away with the credit like a thief who has the audacity to complain about pickpockets.

And because I am not immune to the species curse, I’ve done it too, in small ways. I’ve taken a thought, heard it from someone else, let it ferment in my brain, and later repeated it in my own words until it felt like mine. I am not proud. I am honest. This is where the depressive clarity comes in: the part of my brain that, on bad days, flattens everything into blunt statements. Here is one: I am not a special snowflake. I am a standard-issue Homo sapiens, with the same petty urges toward status and ownership, just less successful at satisfying them. The universe did not grant me moral superiority in exchange for poverty. Sometimes it feels like it did, but that’s just ego wearing a beggar’s shawl.

Counting Boards, Counting Bodies

There’s a vulgar beauty in the original counting board method. Numbers as objects. You move them. You line them up. You eliminate.

Eliminate is a harsh word. It sounds clean, surgical, almost noble. But it’s also what humans do to each other. We eliminate variables. We eliminate rivals. We eliminate inconvenient truths. In Gaussian elimination, you take a messy system and you reduce it to a form where the unknowns can be solved step by step. It’s orderly. It’s comforting. It’s the fantasy of control.

I have spent much of my adult life trying to perform Gaussian elimination on my own chaos—debts, mood swings, half-finished projects, the constant hum of envy when I see someone younger or dumber or merely luckier glide past me into comfort. I try to reduce, to simplify, to make the system triangular so I can solve it. But life is not a linear system. Life is a badly conditioned matrix with noise, missing entries, and a random adversary who occasionally kicks the table. Life has hidden variables. Life has constraints that change while you’re computing.

The Han mathematicians, bless them, were doing something grounded: grain, taxes, canals. My own system is more pathetic. It includes variables like “self-respect,” which is not even measurable, and “social standing,” which is measured entirely by people I don’t respect, and “mental stability,” which I can sometimes fake for weeks and then lose in an afternoon because a neighbor decided to burn trash and my lungs turned into a complaint department.

Sometimes I wish I could put my life on a counting board and move the rods around until something solvable appeared. I would happily swap rows. I would scale. I would add a multiple of my better self to my worse self until the worse self vanished. Of course, the worse self is stubborn. It has tenure.

A Brief Detour Through America

I lived in America from 1998 to 2014, and I still carry it in my head like an old map that no longer matches the roads. America then, in my memory, was a place where systems worked more often than not—where you could argue with the DMV and still leave with a license, where a bookshop had actual books and not just mugs with slogans, where a public library felt like a civic religion that didn’t ask you to kneel. There was still plenty of rot—capitalism always has a smell, like milk that’s been left out—but the plumbing of daily life felt less adversarial.

Now, watching from the distance of screens and headlines and the peculiar sadness of diaspora-in-reverse (I returned, but a part of me still stands there), it feels more brittle. Not because of any single leader or moment—history is rarely that neat—but because the whole culture seems to have leaned harder into spectacle, into branding, into the idea that shouting is a form of truth.

It’s the same disease as the naming problem. The label becomes the reality. The performance becomes the substance. And it’s not uniquely American, of course. India is a festival of labels. We label everything: patriotism, purity, tradition, success, sin. We turn labels into weapons and then wonder why we are bleeding.

Somewhere in all this, a Han mathematician is quietly moving rods on a board, solving a practical problem, not caring what any of us call it. That is the part that makes me laugh, bitterly and with affection. The universe keeps producing competence in small corners while the rest of us build monuments to our own noise.

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We build monuments to our own noise

The 2,000-Year Mirror

When I say “delay,” I don’t mean that the West sat around for two millennia incapable of elimination and then suddenly discovered it like a lost sock. I mean the recognition delay. The humility delay. The footnote delay. We are spectacularly bad at seeing knowledge as a shared human inheritance. We want it to be tribal loot. We want it to justify supremacy narratives—civilizational, national, religious, racial. We want math to be a trophy.

But math is the one arena where the universe refuses to play along. Two plus two does not change its mind because you sing a hymn. A system of equations does not yield a different solution because you wave a flag. The rods don’t care. The rectangle doesn’t care.

This should make us modest. It usually makes us more aggressive. I think of all the times I’ve seen people argue about who invented what—who had calculus first, who had zero first, who had the “right” astronomy, who was “ahead.” It’s like watching hungry men fight over who first discovered fire while standing next to a gas stove.

Meanwhile, the real story is that humans, scattered across continents, kept bumping into the same structures because reality has a limited vocabulary. If you have trade, you need accounting. If you have land, you need measurement. If you have grain, you need yields. If you have bureaucracy (and we always do, because we love hierarchy the way mosquitoes love ankles), you need systems. Systems lead to equations. Equations lead to arrays. Arrays lead to elimination. Not because Gauss was Gauss, but because the world is stubbornly consistent.

The Han “matrix” is not a quirky historical fact. It’s a reminder that intelligence is not the private property of any civilization. It’s a fungus that grows wherever conditions allow: curiosity, necessity, time, and enough stability that someone can sit down and push symbols around instead of dodging swords.

My Own Rectangular Array of Shame

I should confess something, because confession is the only currency I have that doesn’t inflate. When I first learned “Gaussian elimination,” I learned it the way most students do: as a procedure. Write the augmented matrix. Pivot. Reduce. Back-substitute. Get the answer. Done. I did not think about counting rods. I did not think about grain yields. I did not think about how a rectangle of numbers is a model of the world. I thought about grades.

Later, in the adult world, I found myself surrounded by people who also thought in procedures—people who could implement algorithms, write code, optimize traffic, move data—without any sense of history or meaning. The world rewarded them. It often punished me, because I kept asking: why? and who? and what story are we telling ourselves about this? which is not a lucrative hobby.

There is a perverse comfort in being a misfit. You can turn your failure into an identity: “I’m too honest for success.” That’s a lovely myth. It lets you avoid the more humiliating truth, which is that you are also lazy, fearful, inconsistent, sometimes arrogant, sometimes pathetic, and not always as brilliant as your inner monologue insists.

My mental health complicates this in the way a bad parameter complicates a system. In a hypomanic state, my mind becomes a counting board on fire: rods flying, connections forming, metaphors breeding like mosquitoes. In a depressive state, everything becomes a zero row: no pivot, no movement, no solution. I write and delete. Write and delete. Obsessive rewriting as exorcism. I tell myself it’s craft, and sometimes it is, but sometimes it’s just avoidance wearing a tweed jacket. The Han mathematicians would probably find this all very tiresome. They had grain to count.

Rectangles, Empires, and the Childish Need to Be First

The “who invented it” game is not just academic. It has political teeth. Empires love origin stories. They love being the source. They love being the womb. Matrix as mother becomes matrix as empire: the place where civilization is born, the place where everyone else is a footnote or a barbarian cameo.

But the history of mathematics, when you actually look at it without the costume jewelry, is a history of exchange—Silk Road, translation houses, merchants, stolen manuscripts, scholars fleeing wars with books under their arms, teachers teaching students who later teach enemies. Knowledge travels like a virus and like a gift, often both at once.

Colonial history tried to freeze that flow into a hierarchy: “We are the producers, you are the receivers.” It’s a lie that still echoes. You can hear it in the way people talk about “modernity” as if it’s a European invention rather than a messy global convergence. And then you find this Han rectangular array, sitting calmly in 179 AD, and the lie gets smaller. Not gone—lies are cockroaches, they survive everything—but smaller.

This is the part that gives me a modest, embarrassed hope. Not the motivational kind. Not the poster kind. The kind that shows up like a stray cat: unwanted, suspicious, but real. If a counting board can survive in a text across millennia, if a method can be rediscovered and rediscovered because reality keeps demanding it, then maybe our current noise—our supremacies, our slogans, our grandstanding—will also be reduced, row by row, into something simpler. Or maybe not. Humans are very good at preserving stupidity.

The Han Matrix on My Kolkata Table

My bamboo skewers are not counting rods. They are cheap, splintery, slightly oily, and the packet has the faint smell of the shopkeeper’s hands—soap, dust, old currency notes. Still, when I line them up, I feel something odd: a continuity that has nothing to do with nation or pride and everything to do with the shared human habit of trying to make the world legible.

I imagine a Han-era clerk, sleeves rolled up, moving rods with practiced fingers. I imagine the quiet satisfaction of reduction: the chaos becoming triangular, the unknowns revealing themselves one by one like reluctant confessions. I imagine him not caring whether some future German or French or Bengali will name the method after himself. He has work. He has a river to manage. He has grain to distribute. He has a life that is probably, in its own way, difficult and small and full of obligations.

And then I look at my own table—my books, my half-broken gadgets, my scribbled notes, my unpaid anxieties—and I feel, briefly, less special. Which is a relief. Being special is exhausting. The universe has been doing math through humans for a very long time. I am just one more nervous animal making rectangles out of sticks.

A Small Defiance

The two-thousand-year delay is not something we can fix retroactively. We can’t send a memo to history: “Please update the credits.” We can’t undo the way power shapes what gets remembered. But we can do one small thing, here, now, on a dusty Kolkata table with bamboo skewers that have already served their humble culinary purpose. We can tell the story correctly.

Not as a weapon. Not as a counter-supremacy—“See, they did it first, therefore we are superior,” which is just the same childish game with different jerseys—but as a reminder that intelligence is distributed, that history is messy, that the world doesn’t belong to any one narrative.

I gather the skewers back into a pile. The rectangle collapses. The matrix returns to bamboo. It’s late. The air outside has that winter heaviness, the kind that makes you feel like the city is wrapped in a damp blanket of exhaust. Somewhere a shrine is lit, someone is chanting, someone is honking, someone is being born, someone is dying, and none of it asks my permission.

I open my laptop. I stare at the draft. I consider deleting it—my favorite hobby, annihilating my own work before anyone else can—but I don’t. I just save, shut the screen, and put the bamboo packet back in the drawer, like a tiny, ridiculous relic. Two thousand years is a long time for a rectangle to wait to be seen.

© 2025 Suvro Ghosh.