A molecule absorbs light at strictly defined frequencies, and each frequency is the difference between two energy levels. If levels are islands, then frequencies are the distances between them. Previously, to place the islands correctly, you needed to know their names and build a model. Now the map is assembled from distances alone.
The algorithm looks for repeated frequency differences. If two lines are separated by the same energy gap, it's like two paths between the same islands. Closing four such paths reveals the positions of the levels themselves. From 686 unlabeled water lines, the algorithm assembled 158 energy levels.
The accuracy turned out to be a thousand times better than in old databases. The map is assembled, even though the algorithm doesn't know the island names. They can be added later by matching against known maps. The key point is that the map already exists, and it's more accurate than previous ones.
The effective absorption path length in the SCALS cavity is about 28 km, which is like light passing through a sample the length of a marathon course, even though the cell itself is only 42 cm.
The idea of recovering hidden structure from indirect measurements recalls plots where a map of unknown territory is reconstructed from fragments of data. In Carl Sagan's novel Contact, the alien signal contains instructions for building a machine, and here too, a coherent network of levels is assembled from disparate frequencies.