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Eduardo Vargas was walking in Battery Park recently when he noticed a small memorial overlooking New York Harbor.

Mr. Vargas, in town from San Diego, squinted at a figure of a tugboat crewman depicted in weathered bronze on a stately pedestal situated at the southern tip of Manhattan. A plaque on the statue claimed it was erected in 1982 by Mayor Edward I. Koch and the longshoreman’s Local 333, to memorialize a little-known harbor tragedy from 1977.

All six crew members from a tugboat, the Maria 120, had “mysteriously vanished while investigating what appeared to be a private aircraft crash in New York Harbor,” the plaque reads.

“Wait, I’ve never heard of that before,” said Mr. Vargas, 38, while looking at the statue. His skepticism increased as the statue’s patina of officialdom gave way to weirdness.