Every church, chapel and cathedral footprint in OpenStreetMap, measured for the direction it lies along. A street grid offers a building two perpendicular directions and no reason to prefer either. The churches take one of them.
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Both sliders are the admission test, exposed. Drag them and the population changes under you. That is the point of the section below: the number depends on a rule somebody chose, so the rule is on the page rather than behind it.
The measurement is the long axis of the building's outline: the direction of the larger principal moment of the filled polygon, taken as an axis rather than an arrow, because a footprint cannot say which end holds the altar. A nave gives a clean answer. A round chapel does not, and neither does a square tower or an octagonal baptistery.
That is not a nuisance, it is a trap. A shape whose two principal moments are equal has no principal axis at all: the eigenvectors of an isotropic covariance are arbitrary. A solver asked for one anyway does not return "undefined". It returns whatever the arithmetic's residual decides, and the residual is not random. Below, the same estimator runs on shapes built exactly regular. Every one of them is handed a bearing, and every bearing is exactly cardinal.
A cross-check between two estimators does not catch this. Area moments and the minimum-area rectangle are degenerate on exactly the same shapes, so they agree perfectly while both are meaningless: a control that cannot fail. What catches it is asking whether an axis exists before asking where it points.
So every footprint here faces two preregistered tests before it is allowed a bearing. Its elongation must reach 1.10, and its bearing must survive jittering every vertex by one OpenStreetMap coordinate quantum (about 1.1 cm) and moving the projection origin, staying within 5° across twelve trials. … footprints fail, and they are kept, labelled, and plotted, because they turn out to be the most useful control on the page.
The obvious objection to any eastward finding is the street. Cadastral surveys are frequently cardinal, from Roman centuriation to the United States Public Land Survey, so a building that simply obeys its street can land due east for reasons with nothing to do with liturgy.
But a grid is quadrantal. It offers two perpendicular directions and populates both. If the eastward peak were the grid, an equal peak would stand at due north. Here is the same corpus, split by whether the footprint has an axis at all:
| set | n | mean E-W score | within 5° of east | within 5° of north | ratio |
|---|
The second row is the control the corpus supplies for free. Those are church footprints too, in the same countries, traced by the same mappers off the same imagery, measured by the same estimator. They simply have no direction to have, and they show the cardinal spike arriving symmetrically: the signature of a grid, with no preference for east in it.
The single global number is a coverage-weighted average of places that behave completely differently, so it is not the headline. Countries with at least 2,000 admitted footprints, in order of eastward alignment. The last column is the same ratio computed on that country's own axis-less footprints.
| country | n | mean E-W | ≤5° east | ≤5° north | ratio | ratio, no axis |
|---|
Read the ordering, not the values: OpenStreetMap's coverage is wildly uneven, and a country's position here is partly a fact about who mapped it. What survives that caveat is the shape of the table. The eastward end is Orthodox (Greece, Serbia, Russia, Ukraine, Romania), the middle is the Latin West, and the far end is the colonial New World, where the ratio sits near 1 and the churches are indistinguishable from the street. Nothing in the estimator knows any of that.
One story survives the symmetry argument: perhaps churches sit in places whose grain happens to run east, or perhaps the church came first and the streets copied it. Both are answerable with the rest of the building stock. Slovenia is small enough to take whole, so every building in it was pulled and measured by the same engine.
| radius | matched | church − control |
|---|
Each church is paired with the nearest non-religious building whose area is within a factor of two and whose elongation is within 0.10, and the difference in east-west score is averaged. The radius is swept over a fifty-fold range because the point estimate alone cannot identify anything: a gap that grows with radius would mean the near neighbours were shaped by the church, and a gap that collapses would mean the grid explains the church. A flat gap means the two are separable and the effect survives.
Every figure above is recomputed here from axes.bin, the same 3.3 MB your browser already loaded, and compared with the frozen research payload. The button also runs a mutation: it corrupts one record and reports whether the comparison notices.
It does not show that anyone aimed a church at a sunrise. A footprint is an axis, not an arrow: it cannot say which end holds the sanctuary, so "east-west" here never means "facing east". It cannot date a building, so a shell rebuilt in 1890 on a 1200 foundation counts once, undated. It cannot see a church that OpenStreetMap has not drawn, and the coverage table is the honest bound on that. It cannot separate a patronal-feast orientation from an equinoctial one, which needs dedications and horizon profiles that no footprint carries.
What it shows is narrower and, being measured on every mapped instance rather than a survey of a few hundred, new: across the footprints OpenStreetMap holds, buildings tagged as churches lie east-west far more often than north-south; buildings tagged as churches that have no axis do not; and in a country taken whole, the entire secular building stock does not either.