Lady Elliot Island, the southernmost coral cay of Australia's Great Barrier Reef, has two lighthouses. It also has a third that visitors describe in some detail, and which is not there.
Writing in The Conversation, Simon Cropper and Charles Kemp of the University of Melbourne have set out an explanation for what is known as the phantom lighthouse illusion, reported often enough on the island that its tourist guide mentions it.
The first lighthouse on Lady Elliot was built in 1873 and decommissioned in 1995, when a second tower took over the job. Visitors standing on the island after dark, however, regularly report beams shining from a lighthouse far out to sea, on the horizon, where there is open water.
The effect is not new and not local. The earliest known published account dates from 1937 and describes the same illusion off the coast of Brittany, in France.
To see it, the authors write, an observer should stand at least 70 metres from a lighthouse, between the tower and the sea, at night. Looking at the lighthouse, the rotating beam is plainly where it ought to be. Turning away to face the water, the beam appears to come from the horizon instead, and glancing back over one's shoulder does not dispel it.
Cropper and Kemp observed the illusion on the island and then rebuilt it in a relatively simple virtual reality environment, with the lighthouse placed 300 metres behind the observer. The laboratory results, they write, matched the real-world reports remarkably well. The study appears in the journal Open Mind.
The explanation turns on how little the eye has to work with after dark. With few cues to distance available, the brain leans on expectation, and people systematically judge points along a lighthouse beam to be much nearer than they are. The far end of the beam is in fact very distant and sweeping very fast. Perceive it as closer and slower, and the only consistent reading left is that the source lies ahead rather than behind.
The authors describe the brain as a prediction machine, combining expectation with whatever evidence is available. They compare the lighthouse case with the crater illusion familiar to astronomers, in which a photograph of a crater becomes a hill when rotated, because we assume that light falls from above.
The new work also moves the goalposts. Earlier observers had placed the illusion between roughly one and four kilometres from a lighthouse. The theory predicted it should emerge from about 70 metres, and both the virtual reality study and the authors' own night on the island bore that out. Someone misreading a beam this way can be wrong about the lighthouse's position by tens of kilometres.
It is worth being precise about what has now been established. The phantom is not a single mistake made once by one visitor in poor conditions. It is reliable, it appears at a stated distance, it has been reproduced in a laboratory, and it is printed in the island's own visitor material.
A lighthouse, considered strictly, is a navigational aid: a light, in a fixed bearing relation to an observer, visible at night from the sea. The phantom is visible at night. It is visible from the sea side of the island. It appears in the same place to successive observers. The Department of Unnecessary Research can find no criterion on that list which it fails.
The distance between the 1873 tower and the phantom is therefore narrower than the island's signage implies. One of them was built, staffed and maintained for 122 years, and was then decommissioned. The other was never built, has never been staffed, costs nothing to maintain, and has never been decommissioned.
On a strict reading of availability, the phantom is the island's best-performing light. It has not failed once since 1937.
Our analysts accept that it marks no hazard, guides no vessel and sits above empty water. They note that all three of those things are also true of a working lighthouse that no ship happens to be approaching.
The island will presumably go on advertising two. The third has outlasted one of them.