The Geometry of Division

In short: We are not lonely because of what we believe but because every crisis added a new dividing line, and lines multiply: six axes make sixty-four tribes. The way back is not a better argument but holding contradiction and meeting real bodies in real rooms.

The Geometry of Division

How every crisis added an axis, and how eight billion people ended up alone

by Roman Balzan

The Domino Index. Weekly Intelligence.

Twenty years ago the map was simple. There was left, and there was right. One line, two sides. You could stand on it and know roughly where you were and roughly where your neighbor was, and even when you disagreed with him you could still sit at the same table, because the table only had two ends.

I want to walk through what happened to that line. Not the politics of it. The geometry of it. Because I think the reason we are so lonely has almost nothing to do with what we believe, and almost everything to do with the shape of how we have been cut.

One line

Start with the single axis. Left and right. Conservative and progressive. It is one dimension, and one dimension divides a population into two groups. That is the most a single line can do. Two tribes, each large enough to be a home.

For most of the twentieth century this held. The line moved, the parties drifted, but the number of dimensions stayed at one. And because there was only one line, the two groups it produced were enormous. Half the country on each side. You were never alone in your half. Your family was mostly in it. Your town was mostly in it. Disagreement existed, but it ran along a single seam, and a single seam is something a society can hold.

The first new axis

Then came the platform. Social media did something subtle that almost nobody named at the time: it made politics personal. Not personal as in "it affects your life." Personal as in "it is about persons." Faces. Names. Bodies.

The 2016 American election is the cleanest example, though the same thing happened in every democracy at slightly different times. The contest stopped being left against right in the abstract and became one specific man against one specific woman. And the moment it became a man against a woman, a new axis was born that had nothing to do with the old one. Gender got welded onto politics. Now you were not only left or right. You were also reacting, in public, to masculinity and femininity themselves.

Watch what that does to the geometry. You started with one line and two groups. You add a second line crossing it, and you do not get three groups or four in a row. You get four quadrants. Left-man, left-woman, right-man, right-woman. Two axes multiply. They do not add.

And each of those four quadrants is, by definition, smaller than either of the two halves you started with. The first cut halved the country. The second cut halved the halves.

The second, third, fourth

Then came the pandemic, and the pandemic was an axis factory.

It did not just add liberty against safety, though it added that too, and that one cut deep, because it split people who had agreed on everything else. It added masks and no-masks. It added vaccine and no-vaccine. It added trust-the-institutions against trust-yourself. It added lockdown-order against personal-freedom. Each of these was a fresh line, and each fresh line crossed all the lines already there.

Do the arithmetic, because the arithmetic is the whole point. One axis, two groups. Two axes, four. Three axes, eight. Four, sixteen. Five, thirty-two. The growth is not additive. It is exponential. Every crisis that arrives does not move you along the existing lines. It draws a new line perpendicular to all of them, and in doing so it cuts every existing group in half again.

Stack the ones we already have. Left and right. Man and woman. Boomer and zoomer. Vaxxed and unvaxxed. Native and immigrant. Believer and atheist. Six axes. Two to the sixth. Sixty-four tribes, and that is before we get to the ones forming right now.

By the time you have layered enough crises, the number of possible tribes races past the number of people who could ever fill them. And when the tribes outnumber the people, something breaks that has never broken before in human history: there is no longer a group large enough to hold you. You are sorted so finely that your particular combination of positions is shared by almost no one you will ever physically meet.

That is the loneliness. And here is the thing I most want you to see: it is not the loneliness of having too few groups. It is the loneliness of having too many, each one too small to be a home. We did not lose our tribes. We shattered them into a dust so fine that every grain is a single person.

The friends you lost on the way

Now bring it down from the abstract to the kitchen, because this is where it actually lives.

Think about the friendships that have quietly ended in the last ten years. Not with a fight, most of them. With a drift. Somebody posted something during the pandemic and you saw them differently. Somebody's politics became visible in a way it never used to be. Somebody landed on the wrong side of an axis you did not even know existed until the day it appeared, and the friendship, which had survived thirty years of the single old line, could not survive the crossing of the new one.

This is the mechanism of the modern loneliness, and it is worth stating plainly. Old friendships were built when there was one axis. They were strong enough to survive one disagreement, because a friendship can hold one seam. But each new crisis introduced a new axis, and with it a new chance for two people who had always been on the same side to suddenly find themselves on opposite sides of a line that did not exist when they became friends.

The more axes you add, the higher the odds that any two given people diverge on at least one of them. And in a culture that has learned to treat divergence on a single axis as grounds for exile, one divergence is enough. You do not lose friends because you changed. You lose them because the number of ways to be on opposite sides kept multiplying, until statistically nobody could stay on the same side of all of them.

The research has a cold name for the emotional half of this. They call it othering, aversion, and moralization: you stop seeing the other side as wrong and start seeing them as alien, then repellent, then evil. That is what turns a mere axis into a wall. Not the disagreement itself, but the moralizing of it. And every new axis is a new opportunity to moralize a stranger out of your life, or a friend.

The next line, forming now

Here is where the Domino tips forward, because the axes do not stop, and I can see the next one taking shape.

The next great dividing line is not political. It is ontological. It is about what is real, and what is human.

It is AI. And it will cut deeper than any line before it, because the earlier axes were all arguments about how to run the world, and this one is an argument about what a person is. Those who use these systems against those who refuse them. Those who make things with them against those who consider that making fraudulent. Human-made against machine-made. Real against generated. It is already here. I feel it every time someone praises a photograph of a meal and says nothing about a song, because some quiet instinct has already filed the song, correctly, under a new and suspicious category.

And notice what this axis does that no previous axis could. Every earlier line still assumed we were all the same kind of thing: humans, arguing. This new line questions the category itself. It does not just add a thirty-third or sixty-fifth tribe. It splits the ground the tribes are standing on. It asks whether the person you are talking to is even doing the same activity you are, whether their words are theirs, whether their art is art, whether their thinking is thinking.

When the dividing line stops being "what do you believe" and becomes "what are you," the fragmentation reaches the atom. There is nothing smaller to cut.

The counterfeit belonging

So what do people do, alone in a crowd of eight billion, sorted so finely that no physical tribe fits?

They reach for the only thing still offering membership. The algorithm.

And the algorithm is happy to oblige. It will find you the others who share your exact combination of positions, scattered across the planet, and it will gather them onto your screen and call it a community. For a moment it feels like the tribe you lost. It has the warmth of agreement, the relief of being understood, the pleasure of a shared enemy.

But it is a counterfeit, and the counterfeit is precise. It gives you belonging with no body behind it. A tribe of strangers who will never sit at your table, never carry your groceries, never carry your coffin. The feeling of belonging, extracted and served without the substance of it. And because the feeling is real even though the substance is absent, it satisfies just enough to stop you from going out to find the real thing, while never actually nourishing you. It is the sensation of connection engineered to replace connection.

This is the deepest cut of all, and it is the one the machine performs on us for profit. First the crises fragment us into tribes of one. Then the platform sells each isolated grain a picture of the tribe it lost, keeping it staring at the picture instead of walking out to build the real one.

What the Domino actually says

We keep saying trust collapsed. That trust in institutions eroded, that people stopped believing the news, the government, the experts, each other. That is true but it is the shallow reading.

The deeper reading is this. Trust did not simply erode, as if it wore away from use. Trust was subdivided. Every crisis cut the ground under it into finer and finer pieces, until there was no surface large enough left to lay it down on. You cannot place trust in a society sorted into eight billion tribes of one, because trust needs a group to rest in, and there are no groups left. Only grains.

That is the geometry of division. Not one wall down the middle. A hall of mirrors, each pane reflecting a slightly different you, until you cannot find another face that matches your own, and you mistake the reflection for company.

The way back is not a new argument

And so the way back cannot be winning the argument, because the argument is not the disease. The multiplication of axes is the disease, and you cannot argue your way out of geometry.

I spent a long time trying to name what actually holds a person together when the world is cutting them into finer and finer pieces, and I ended up with five things. Not beliefs. Not positions. Five things you carry, in your arms, with your eyes open. I called them the Five Holds, and only after writing the geometry above did I understand that they were never a spiritual list. They were a map out of exactly this. Two of them do the heavy lifting here.

The first is contradiction. The whole machinery of division runs on the refusal to hold two opposing things at once. Every axis demands you pick a side and stay pure, and the algorithm rewards the purity, because a person who can hold only one position is a person who can be sorted, targeted, sold to. To hold contradiction is to stand on an axis and refuse to be split by it. To say: I can love this and criticize it. I can agree with you here and disagree with you there and still keep you at my table. Contradiction is the muscle that lets a friendship survive the crossing of a new line, because it does not require the other person to be on your side of everything. It only asks that you refuse to moralize them out of your life over the one line where you differ. A person who can hold contradiction cannot be fragmented, because fragmentation needs your cooperation, and they will not give it.

The second is body. This is the thing no algorithm can counterfeit, because it requires meat in a room. The counterfeit belonging works precisely by removing the body: it gives you the feeling of the tribe with none of its substance, agreement without presence, a face on a screen that will never carry your coffin. The repair is the reverse move. It is physical, and small, and unglamorous. It is the walk, the meal, the hand, the person actually in front of you whose warmth is not being served to you by a system that profits from your isolation. The body is the one thing the machine cannot hand you, and so it is the one ground the fragmentation cannot reach.

The other three stand behind these two. Presence, because you cannot hold contradiction or meet a body while your attention is being harvested somewhere else; the algorithm's first theft is always your attention, and presence is taking it back. Shadow, because the person you moralize out of your life is often carrying the very thing you refuse to see in yourself, and the axis feels moral only because you have projected your own darkness onto the far side of it. And mortality, which is the closer, and the deepest of the five, because it is the one axis every grain shares. Sort the world into eight billion tribes of one and you will still find that every single one of them is going to die. The person across the table, on the wrong side of your sixty-fourth line, will also lose everyone they love and then lose themselves. That is not a small thing to have in common. It is the largest thing there is, and it sits underneath all the lines, older than any of them, dividing no one.

We were not divided by our beliefs. We were divided by the number of ways there were to differ, multiplied crisis by crisis until no two grains matched. The repair is not another belief. It is five holds, carried body to body: presence against the harvest of attention, shadow against the projection that builds the wall, contradiction against the demand to be pure, body against the counterfeit, and mortality underneath it all, reminding you that the person you were about to exile is, like you, briefly here and then gone.

The machine can show you the tribe you lost. It cannot hand you a person, and it cannot make you die, and those two facts are the whole of what is still ours. That is still, for now, enough.

The map. The territory. The compass.

Written with AI. Spoken by a human. Not less AI. More I.

Questions this answers

Why are people so lonely today?

Roman's view in July 2026 was that modern loneliness comes from geometry, not beliefs. Each crisis drew a new dividing line across all the old ones, so groups halved again and again until no group was big enough to feel like home.

How do dividing lines multiply?

One axis gives two groups, two give four, three give eight. Left and right, man and woman, boomer and zoomer, vaxxed and unvaxxed, native and immigrant, believer and atheist: six axes make sixty-four tribes, and every new crisis halves each group again.

Will AI become the next big social divide?

Roman's view in July 2026 was yes: users against refusers, human-made against machine-made, real against generated. He argued it cuts deeper than earlier lines, because it questions what a person is rather than what a person believes.

What is counterfeit belonging?

It is the sense of community an algorithm gives you by gathering strangers who share your exact positions on a screen. It feels like the tribe you lost but has no body behind it, and it satisfies just enough to stop you from building the real thing.

What are the Five Holds?

The Five Holds are presence, shadow, body, contradiction and mortality: five things Roman says a person carries to stay whole. Against division, contradiction lets a friendship survive a new line, and body, meeting people in person, is what no algorithm can counterfeit.

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