The corners are not neutral. They are how hard the system has to hit you to stay where it is.
The 2×2 is usually drawn as a coordinate plane — two clean axes, four quiet quadrants. It isn't. The corners are the extremities of coercion: the maximum force a political arrangement is prepared to apply to a human body in order to remain that arrangement. The center is calmer not because it is wiser, but because no single principle is being pushed to its breaking point.
Closer to the edges, more violence is required against the masses to keep the configuration standing. Closer to the center, the violence is diluted, distributed, deniable. This page redraws the grid with that fact left in.
The figure
The same 2×2, with the violence drawn in.
Layer
Each corner is a coercion peak. The intensity falls off toward the center, where no single principle is being driven to its limit. The peaks differ in kind — who hits whom, with what apparatus, in whose name — but not in fact. Switch to Vectors to see the asymmetry of direction: three peaks project force outward at their populations; the fourth is the corner those forces converge on.
coercion peak / outward force force projected at the bottom-left self-coercion (the cop in the head) low-coercion trough
The argument
Why the corners burn.
A political arrangement is a claim about who owns what and who decides what. The further a corner pushes its claim — total collective ownership, total private ownership, total central control, total decentralization — the more bodies have to be moved, broken, watched, or starved to keep that claim true against everyone whose life it doesn't fit.
That force does not vanish in the center. It is just diluted across compromises — a little of each principle, none of them load-bearing, none of them worth killing for in large numbers. The center is not virtuous. It is mixed.
Each of the four corners pays for its purity in a different currency of harm. The next four boxes name the currency.
↖ Top-left peak
Authoritarian communism
collective ownership · high control
To make ownership collective against the will of those who hold property — and to keep it collective against the drift of incentives, kinship, and time — requires a permanent apparatus aimed inward at the population. The peasant who hides grain, the engineer who quotes a foreign paper, the cousin of an émigré: all become enforcement problems for the state.
Forced collectivization of agriculture
Internal passport and residence control
Re-education through labour
Party-administered famine as policy outcome
Denunciation infrastructure inside the family unit
NamedHolodomor (1932–33). Great Leap Forward (1958–62). Gulag archipelago. The party did not abolish the kulak by argument.
↗ Top-right peak
Authoritarian fascism
private ownership · high control
Private hierarchy held by central command requires an enemy whose elimination explains the inequalities the system refuses to flatten. The state delivers labour discipline, racial sorting, and territorial expansion for the owning class; the owning class delivers the budgets. The violence is not residual — it is the offer.
Camps and selection: industrial murder of designated populations
Strike-breaking by paramilitary, then by police, then by law
Sterilization and eugenic regimes
Wars of conquest framed as national hygiene
Disappearance squads under client dictatorships
NamedAuschwitz. Operation Condor. The Pinochet stadium. The corporate-state fusion does not ask the workers' permission to enter the workplace.
↙ Bottom-left peak
Libertarian socialism
collective ownership · low control
This corner is the one whose violence the standard reading hides — not because the corner is innocent, but because it is the one that has spent the most time on the receiving end of the other three. Anarchist and libertarian-socialist traditions do not pretend coercion has disappeared. They internalize the threat of the surrounding state into protocol: federation against capture, affinity groups against infiltration, accountability process against the cop in the head, mutual aid against the slow violence of the market. The defence is horizontal because the offence is vertical.
Federation as defence against state and capital capture
Security culture: compartmentalization, need-to-know, no names
Transformative-justice processes in place of police
Mutual aid networks as redundancy against state withdrawal
Self-defence formations: the CNT militias, the YPJ, the Zapatista bases
NamedBarcelona, 1936–37 — crushed by Stalinists from the left and Francoists from the right inside eighteen months. Rojava, under blockade. Chiapas, under low-intensity siege since 1994. The corner that does not start the violence still has to survive it.
↘ Bottom-right peak
Libertarian capitalism
private ownership · low control
The corner that markets itself as the absence of violence. It isn't. The violence is outsourced — to the bailiff, the bouncer, the private prison contractor, the algorithm that decides who eats — and rebranded as natural outcome. The state appears small because it has been hollowed into a property-rights enforcement layer for private parties. Eviction is a court order executed by a uniform; the uniform is just not federal.
Eviction as routine administrative violence
Workplace coercion under at-will and right-to-work doctrine
Medical bankruptcy and care withheld for non-payment
Private security, ALPRs, gated zones, segregated school finance
Debt bondage of the global south through structural adjustment
NamedPinochet's Chile was the laboratory. The Chicago Boys wrote the textbook. The eviction notice does not feel like state violence until you read who signs it.
A scale question
Equal in height, unequal in direction.
The first thing readers ask is whether the peaks should be drawn at different heights — taller for the regimes with bigger death tolls, shorter for the corners that never had a state-scale instantiation. The answer is no, and the refusal is part of the argument.
Heightening by body count requires picking a tally, and every available tally was assembled to win an argument. The Black Book of Communism's figures count famine deaths, unborn children, and contested overlaps with the Second World War. The fascist column gets routinely understated by the same actors who inflate the communist column. Heightening by population reached makes the bottom-right corner look like the worst by default — which may be true but isn't the structural claim this page is making. And the bottom-right is deliberately undercountable: eviction-attributable deaths, deaths of despair, medical-bankruptcy deaths, structural-adjustment famines in the global south — none of it appears in any "regime deaths" ledger because none of it is attributed to a regime. The same hollowing-out that makes the corner look like the absence of violence makes its violence statistically invisible. Heightening the peak short there would reproduce the erasure.
The scale that is defensible is directional. Switch the figure above to Vectors and the asymmetry surfaces: three corners project force outward from a state or property apparatus at their own populations. The fourth absorbs force projected at it by the other three, and adds a small self-arrow — the cop in the head, the only honest entry of self-coercion in the grid.
The four peaks are equal in coercive intensity and unequal in coercive direction. Three point outward. One is the corner those three are pointed at.
— the scale that survives the body-count problem
This is also the cleanest reply to the horseshoe. A line cannot show direction; it can only show position. Once you allow the corners to have vectors, the claim that the extremes secretly agree dissolves into a claim that they happen to be the same distance from the middle — which is geometry, not politics.
The center, honestly
Why the trough is calmer — and why that isn't a virtue.
If each corner is a peak, the center is a trough. Mixed economies with mixed control structures do less of each kind of damage because they refuse to commit fully to any of the four pure claims. Social democracy taxes private ownership without abolishing it; representative democracy permits central authority without surrendering all decisions to it. The compromises absorb force the way a damper absorbs vibration.
This is not a moral achievement. It is a structural fact about commitment. A regime that refuses to make any principle load-bearing also refuses to make any principle work. The trough is shallow precisely because it is not standing for anything in particular.
The center is not where the violence ends. It is where the violence stops being attributable.
— the read this page proposes
Three observations
What drawing the grid this way commits you to.
One — the four peaks are not interchangeable.
The horseshoe argument says the extremes meet. The topography says they don't: they peak in different corners, with different apparatuses, against different bodies. The peaks are equal in height and unequal in everything else. Saying "all extremes are the same" requires erasing two axes of difference to make the line work.
Two — three of the four peaks are state-built. One is state-defended-against.
The top-left, top-right, and bottom-right peaks are constructed by states (or by states-of-property) projecting force outward onto populations. The bottom-left peak is constructed by populations absorbing force projected at them by the other three, and converting that absorption into protocol. The asymmetry matters for honest accounting. It does not make the corner safe.
Three — the line erases the violence that doesn't fit.
The left/right line places authoritarian communism and authoritarian fascism near the ends, libertarian capitalism somewhere on the right, and libertarian socialism… nowhere it can plot. The line cannot resolve the bottom half of the grid at all. It is not a coincidence that the corner most concerned with surviving state violence is the one the line was built to disappear.
What this is, what it isn't
Method.
The corner labels follow the rest of theaxes.fyi — ownership on the horizontal, control on the vertical. The added claim is interpretive: that each corner has a maximum coercive force required to hold it in place, and that the force decays toward the center.
The heatmap is illustrative, not measured. The intensities at the four corners are drawn equal because the argument is about structure, not body count. Tallying the dead across regimes is a separate, well-trodden exercise and not the work of this page. The claim here is narrower: the corners are not coordinates. They are peaks. The line cannot show that.