Mathematics of the Pacific Islands

Summary: The people of the Pacific Islands historically used sophisticated mathematics, including a unique method of navigation.

The Pacific Ocean covers more than one-fifth of the Earth’s surface and includes hundreds of islands. In the nineteenth century, few visitors to the Pacific Islands were able to match the skill of Pacific Islanders in solving arithmetic and algebra problems. The people of the Marshall Islands, scattered over dozens of atolls across the central Pacific, were master navigators who tracked their way over huge expanses of ocean without mechanical aids. The compass, sextant, and chronometer, which their European contemporaries were reliant upon for safe and successful voyaging, were completely unknown to them. What they possessed instead were a set of aids that relied upon an extremely complex type of knowledge related to what they could observe and even feel about the ocean around them. These aids were called Mattangs, Meddos, and Rebbelibs by their users and are known today as “stick charts.”

Some other instances of mathematics in Pacific Island culture and in the Pacific Islands region include the often-complex geometric patterns found in basket weaving, such as the design named “stars,” which has a tessellation pattern that is mathematically sophisticated and is reminiscent of Dutch graphic artist M.C. Escher’s drawings. These patterns can also be found in traditional tattoos, where the type of pattern had great cultural significance and represented the rank and bravery of the tattooed person. Scientists have also modeled the number of species on islands as a mathematical power function that depends on land area, and they continue to study island populations of birds and other species in this context. Researchers have explored barriers to success in mathematics in the Pacific Islands and recommended that teachers include culturally relevant content in their classrooms. Professional development programs and consortiums offer training for teachers and explore mathematics education for Pacific-region children.

Stick Charts

Stick charts were made from strips of the midrib of a coconut frond or pandanus root bound together with coconut sennit in geometric patterns meant to represent currents flowing around their low-lying atolls. Small shells or coral pebbles were attached to indicate the location of islands, and curved sticks were used to represent wave patterns.

The first of these charts, the Mattang, was a small square chart used to teach how waves reflect and refract, or bend, around a single island or atoll (see Figures 1 and 2). By detecting a change in the direction of the prevailing swell, a navigator could discern the presence of an island or atoll over the horizon. The Meddo was an actual chart covering a small set of atolls and used for voyages to nearby atolls. Meddo charts also showed the direction of the main ocean swell and how it curves around specific islands and the distance from a canoe at which an island could be detected. The Rebbelib was a more complex version of the Meddo and was used to represent an entire chain of islands or even the whole of the Marshall Islands. It showed the complex relationship between the islands and the major ocean swell.

Stick charts were not made and used by all Marshall Islanders. Only a select few knew the method for making and reading the charts, and the knowledge passed only from father to son. However, so that others could utilize the expertise of the navigator, 15 or more canoes sailed together in a squadron, accompanied by a lead navigator skilled in use of the charts. Because the knowledge contained in each chart was a closely guarded secret, they were not normally carried on a voyage. Instead, the navigator memorized the chart and gauged the wave patterns entirely by his sense of touch. Crouching in the bow of his canoe, he would literally feel the motion of his vessel.

It was not until 1862 that this unique navigational system was revealed in a public notice prepared by a resident missionary. It was an additional 30 years before it was comprehensively described by Captain Johann Winkler of the German Navy. He became so intrigued by the stick charts that he made a major effort to determine the navigational principles behind them and convinced the navigators to share how the stick charts were used. He recognized that the stick charts represented a significant contribution to the history of both navigation and cartography because they symbolized something that had never before been accomplished—a system of mapping and navigating by ocean swells. They are an indication that ancient maps may have looked far different, encoding different aspects from the natural world, than the maps commonly used today. The use of stick charts and navigation by swells apparently came to an end shortly after World War II. The venerable stick chart and ocean-going canoe were no match for large motorized vessels with modern navigational devices. They do, however, continue to be made in the Marshall Islands, though very few people are able to use them as navigation aids. They are primarily made and sold instead as tourist souvenirs.

Bibliography

Clark, Megan. “Cultural Cross-Purposes and Expectation as Barriers to Success in Mathematics.” Proceedings of the Ninth International Congress on Mathematical Education 3 (2004).

Tee, Garry. “Mathematics in the Pacific Basin.” British Journal for the History of Science 21 (1988).