That’s Maths: The navigational skills of the Marshall Islanders

For thousands of years the Marshall Islanders of Micronesia have been finding their way around a broadly dispersed group of low-lying islands, navigating apparently without effort from one atoll to another one far beyond the horizon. They had no maps or magnetic compass, no clocks, no weather forecasts and certainly no GPS or SatNav equipment.

Traditionally fishing was the main source of food for the islanders, so it was vital to be able to steer to the fishing grounds and back home without too much effort. Seafarers who knew navigation had high status as the islanders depended upon them for their food supply.

The navigators used many methods to find their way. They could steer by the stars, they knew the habits of sea birds, they understood the clouds and were familiar with the ways of the winds. But foremost among the tools of their trade was an uncanny ability to comprehend the movements of the ocean, reading the many wave-trains that pattern the water surface, giving them vital clues about distant land masses.

The out-rigger canoes respond to the water and navigators can “feel” the waves and swell through the motion of the craft. They say that wave piloting is not done solely using visual clues but also involves the stomach.

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A one-dimensional signal, like a sound sequence, can be analysed into simple wave-like components, each with a different period. This is called spectral analysis. In a similar way patterns in two or more dimensions, like the waves on the ocean surface, can be spectrally partitioned, but now the components have different directions as well as periods. French mathematician Joseph Fourier was first to show how a general wave form can be separated into simple components.

Ocean waves are separated into sea and swell. The sea waves are generated locally by the direct action of the winds and tend to be steep, slow-moving, transient and chaotic. Swell is the long, regular and fast-moving wave motion generated by distant storms and often travelling thousands of kilometres.

Swell is persistent, often continuing unchanged for many days. Swell waves have long periods compared to sea-waves and are easily distinguished from them by an experienced sailor. The swell gives a steady reference direction, enabling an islander to maintain a straight course to a faraway destination.

The northeasterly trade winds that blow persistently in the neighbourhood of the islands generate their own trade-wind swell, of shorter period than the swells coming from farther away. This provides another reference as the direction of the trades tends to be quite persistent.

As a regular train of waves encounters an island it is distorted, producing complex patterns of reflected and refracted waves. The islanders can visually analyse these patterns, essentially performing a spectral analysis in their minds. It is as if they can do mental Fourier analysis.

This enables them to gauge the location of the island, even though there is no evidence visible on the horizon. As they get closer to land more complex patterns of shadowing and diffraction help them to find the openings through the reefs to the safety of the lagoon.

Scientists have been working with the islanders to gain a better understanding of their extraordinary navigational skills. Computer models can reproduce many of the effects they use but there is still much to learn. And time is running out: even a small increase in sea level may have drastic consequences for these low-lying islands.

Peter Lynch is emeritus professor at UCD school of mathematics & statistics — he blogs at thatsmaths.com