D-503, engineer of the spaceship INTEGRAL, keeps a diary for the mathematically ordered One State — a glass city of numbered “ciphers” living by the Table of Hours. He is a rational man, and he is undone by a single irrational thing: the square root of minus one. There is no such number on the real line — and that is exactly the crack the total state cannot seal. The blue team builds the arithmetic; the red team demands the irrational be made rational.
source Yevgeny Zamyatin, We (Мы, written 1920–21) — the first modern dystopia, suppressed in the USSR and printed abroad; the ur-text behind Orwell and Huxley. Room: THE NOVEL. Rendered as its central metaphor, not quoted.
Yevgeny Zamyatin (1884–1937): a Bolshevik-turned-heretic and a naval engineer who built icebreakers on the Tyne. He wrote We in 1920–21 and it was banned unpublished at home — the first work suppressed by the new Soviet censorship board. It circulated abroad (English 1924) and became the ur-dystopia behind Orwell’s 1984 and Huxley’s Brave New World.
An engineer’s book: the tyranny is built out of mathematics, and its one wound is a number that does not fit.
Citizens are ciphers (numbers, not names): D-503, I-330, O-90. Life runs on the Table of Hours — every act scheduled, chewing and sleeping synchronized. The city is glass, walled off from the wild by the Green Wall; privacy is abolished so that nothing is hidden.
The horror is not chaos but perfect order: happiness defined as the absence of freedom, reason pushed until it becomes a cage. The one thing the equation cannot hold is the √-1 — the soul.
If √-1 has no place on the real line, invent a place for it. Define i by the single rule i² = −1, and every number becomes a + b·i — a point on a plane, not a line. Multiplication of imaginaries is exact: (0,1)·(0,1) = (−1,0).
Distance still works: |a + b·i| = √(a² + b²), so |3 + 4i| = 5. And the plane closes on itself: eiπ + 1 = 0. The irrational the state feared is not nonsense — it is a whole dimension it refused to admit.
The blue team re-runs the core claims on load: a dense search of the real line finds no x with x² = −1; the imaginary unit squares to −1; Euler’s identity lands on −1; |3+4i| = 5; and the Table of Hours maps all 24 hours. If red forces the irrational to be rational (6), this badge turns red.
Give the One State a number z = a + b·i. Set b = 0 and it is an ordinary real — a good citizen, on the line. Set b ≠ 0 and it steps off the line into the plane the state cannot police.
The panel below squares z, measures |z|, and asks the novel’s question: is this a square root of −1?
Two engines, side by side. Left: the real line — a dense search proves x² is never negative, so x² = −1 has no real solution. Right: the plane — complex arithmetic on your z, exact.
REAL LINE · minx x²
THE PLANE · z = a + b·i
Constant anchors: i² = −1 · eiπ = −1 (re within 1e−12) · |3+4i| = 5.
LINEAGE. The numbered citizen, the total schedule, the transparent city, the wall against the wild — We (1921) → Huxley’s Brave New World (1932) → Orwell’s 1984 (1949). D-503’s “illness” is a soul: the √−1 that reason could not absorb.
The One State’s schedule is a total, deterministic function from hour to action: for each of the 24 hours there is exactly one prescribed act, and no hour is left free. There is no argument the function fails to answer — that is the point of the terror.
A free variable — an unscheduled hour — is what the state cannot allow. The Personal Hours are the one deliberate, and narrow, exception.
“Total transparency is freedom.” Cut. The glass city hides nothing precisely so it can watch everything. Transparency here is the cage, not the release.
“Reason, pushed far enough, removes all unhappiness.” Cut. It removes freedom and calls the result happiness. The soul it cannot compute away is the √−1.
“√−1 is a value on the number line.” Cut. Every real x gives x² ≥ 0. The engine searches the line and finds nothing — the irrational lives off it.
The red move — the One State’s own demand: assert that some real x satisfies x² = −1. Force the search to “accept” a real root and pretend the soul was absorbed. The dense real search still finds none, so the witness (9) recomputes and turns red.
The rational state can schedule every hour, but it cannot make x² = −1 on the line. The lie is measurable, and the witness catches it.