Field notes

Two hundred citizens sit on a plane with two independent dials: economics (left = state control, right = free market) across, and social freedom (bottom = liberty, top = control) up. That is the Nolan / Political-Compass two-axis picture from the lesson.

The classic "left–right line" is a single ruler. To place a 2D person on it you must project them — drop them straight onto the line. Spin the line and you choose a different camera angle. Nothing about the citizens changes; only what the ruler can see.

Every angle throws one whole dimension away. Variance kept is how much of the real spread survives the squash; distortion is the rest — the information one line destroys. It is never zero.

The dashed-gold PCA ghost is the least-lying angle: the one direction that keeps the most variance. It is a diagonal, not the economic axis — so the usual left–right line is not even the honest one. Square to it lies the faint dashed max-lie axis, where almost everything real vanishes.

Tap two citizens to compare. Some angles fuse a libertarian and a socialist into "neighbors" on the line while splitting true allies apart. That is the trap: a single line reports strangers as twins.

Controls: drag the gold line (or arrow keys) to rotate. Drag a citizen to move them; tap two to probe their real vs. projected distance. PROBE picks a far-apart pair for you; ECON and SOCIAL snap to 0° / 90°.