Distorted mental geography

Why do people confidently place one city east of another when the map says otherwise?

Answer quickly, without looking: is Reno further west than Los Angeles? Almost everyone says no. Reno sits at about 119.8 degrees west, Los Angeles at about 118.2 — Reno is the western one. Try two more. Is Rome north or south of New York? Rome, at 41.9 degrees north, is the northern city. And when a ship leaves the Atlantic end of the Panama Canal for the Pacific, does it travel west? It travels east, because the canal runs northwest to southeast.

Now, the interesting thing is not that people get these wrong. It is that they get them wrong the same way. If your head held a slightly blurry photograph of a map, the errors would scatter — some too far east, some too far west, cancelling out across a crowd. They do not scatter. They lean, together, in a direction you can predict before you ask. What kind of storage fails like that?

Start with what a scattering error would mean. Noise is what you get when a representation is of the right kind but imprecise — a photocopy of a photocopy. Systematic error means something else: the representation is of a different kind altogether, and the answer is being computed rather than read off.

So ask what is actually available to compute from. You have never seen your continent from above. What you have is a great many separate facts, most of them relational and most of them attached to named regions: California is on the west coast, Nevada is inland behind it, Italy is in southern Europe, New York is in the northeast. Notice that those facts are true, and notice that they are about containers, not about points.

Now watch how a question gets answered with only that material. "Is Reno west of Los Angeles?" You have no stored coordinates for either. What you do have is Reno-is-in-Nevada, Los Angeles-is-in-California, and Nevada-is-east-of-California. So the relation between the two regions is borrowed as the relation between the two cities. The inference is sound; the premise is a legitimate generalisation; the answer is wrong — because California's coastline swings sharply east as it runs south, and Los Angeles ends up behind the western edge of Nevada. This is the mechanism Stevens and Coupe demonstrated in 1978: people store geography as nested regions, and superordinate relations leak downward onto the things inside them.

Once you see that, a second family of errors follows naturally. If regions are the units, they must be stored with some orientation — and orientations get tidied. Barbara Tversky's work in the early 1980s found two habits: alignment, where separate bodies are remembered as lying more evenly beside or below one another than they do (the Americas remembered as stacked, when most of South America lies east of Florida), and rotation, where a feature is remembered swung towards a cardinal axis, so a coastline that actually runs northwest is recalled as running north. Both are the same economy: an approximate memory is cheaper if it is stored aligned to a grid.

Does the same tidying happen to distances? Test it on yourself. Which feels further — from your house to the cathedral, or from the cathedral to your house? Most people report the trip towards the landmark as shorter, an asymmetry that has no meaning on any map. And a route with many turns, junctions and remembered shopfronts is judged longer than an equally long empty stretch. Distance, it seems, is not retrieved either; it is reconstructed from how much stuff lies in between and how important the endpoints are.

Here I should be careful. That these distortions exist and reproduce across cultures is solid. Exactly what the underlying representation is — a hierarchy of regions, a graph of landmarks with rough metric annotations, or several overlapping systems used opportunistically — remains genuinely contested, and I would not want the crispness of the story to disguise that.

Two things are worth separating. The first is that this is not ignorance. Someone who has lived in both cities, driven between them, and can name every town on the road still makes the Reno error, because the error is produced by the inference procedure, not by a gap in the facts. Knowing more does not remove it; only checking a map does.

The second is that the distortion is not a defect to be engineered away. Consider what the hierarchy buys you. It compresses enormously — one fact about two states substitutes for millions of facts about pairs of towns. It generalises to places you have never been: told a town is in Nevada, you instantly inherit a workable guess about its climate, its distance from the sea, its relation to everything in California. And it is usually right, because political and physical regions genuinely are spatially coherent most of the time. The errors are the price of a representation that is right cheaply rather than right expensively.

Which suggests where to be suspicious. The hierarchy fails precisely where the world is not neatly nested — at coastlines that bend back on themselves, at borders that run diagonally, at a canal cut through an isthmus that curves. If you catch yourself certain about a spatial relation and you cannot recall ever seeing it, you are probably reading a drawer label.

• How map projections add a second, independent distortion on top of this one — and how the two interact.
• Whether people who navigate by cardinal directions in daily speech, as in some Australian and Mesoamerican languages, show the same rotation effects.
• What satellite navigation is doing to the hierarchy, given that it answers route questions without ever requiring a survey-level picture.

Every term the collection defines is gathered in the glossary.