In the middle of the vast Pacific Ocean sit the remote islands of Polynesia. When arriving at these islands for the first time, Europeans were shocked to find them peopled, inhabited by individuals with no knowledge of continental landmasses—people for whom the world was only sea (Thompson 2019; Beaglehole 1955: 291). The residents of Polynesia were not bound to individual islands, but were highly mobile, frequently sailing between islands on multi-day voyages to engage in trade, to source natural resources, to pay religious tributes, to resolve civil matters, or to engage in military hostilities (Denning 1962: 121–125).

Figure 1: Tupaia’s chart (JB version), © British Library Board BL Add MS 21593.C.

One of the most curious artefacts to emerge from early European contact with Polynesian islanders is Tupaia’s chart (Figure 1). It was produced during James Cook’s first voyage to the Pacific (1768–1771) by Tupaia, a priest and master navigator from the island of Raʻiātea (Salmond 2004; 2010), in collaboration with crew members aboard Cook’s ship, Endeavour (Parsons 2015). Tupaia helped pilot the Endeavour between islands, and many of those present were impressed by his navigational ability: Joseph Banks, a naturalist aboard Endeavour, wrote that the crew had “a very good opinion of Tupias [sic] pilotage” (Beaglehole 1962: 323), and Cook, himself an expert cartographer, judged that Tupaia was “a very intelligent person” who “[knew] more of the Geography of the Islands situated in these seas ... then [sic] any one we had met with” (Beaglehole 1955: 117). Tupaia took an interest in European cartography, and “having perceived the meaning and use of charts, he gave directions for making one according to his own account” (Forster 1778: 511).

At first blush, Tupaia’s chart looks like a normal map. However, the islands’ positions do not correspond to their real-world coordinates, and their shapes do not resemble their shorelines. Critics have therefore suggested that Tupaia exaggerated his knowledge of the islands (Sharp 1963). Others, however, have argued that Tupaia was using a different representational system to encode geographic information (Hale 1846; Lewthwaite 1966; 1970; Finney 1998) and that interpreting the map is a matter of cross-cultural translation (Turnbull 1998; 2004). Tupaia’s chart has been dubbed the “Rosetta Stone of Polynesian navigation” (Turnbull 2019): a “puzzle” (Thompson 2019) containing secrets about the indigenous practices of seafaring Polynesians.

In this paper I use computational methods to derive a new account of Tupaia’s chart, and reveal a complex sailing network hidden within it. To facilitate this analysis, two versions of Tupaia’s chart are converted to vector graphics form—a well-known copy found in the papers of Joseph Banks (henceforth the JB version) and another copy surviving in a letter penned by Georg Forster (the GF version). Of the 74 islands that appear on the JB version, about 30 have never been reliably identified, in part because the names that Tupaia assigned to islands are different to those used now. Analyses are conducted using 41 islands whose identity is generally agreed upon (Denning 1962).

First, the shape of islands is considered. I test whether the area of islands on the map correlates with their size in real life. While there is a significant (α = 0.01) Pearson correlation (r = 0.747) in the GF version, no significant correlation is found in the JB version. Many islands in the JB version are a similar shape, as shown in Figure 2: they are vertically oriented, usually with depressed sides, and sometimes with an indentation on the top. This common island shape is not observed in the GF copy. In previous work, it has been hypothesised that the GF version represents an earlier draft of Tupaia’s chart than the JB copy (Eckstein / Schwarz 2019a); if this is true, it suggests that Tupaia initially followed European conventions for island sizing, but later discarded this approach, and perhaps used shape to encode other information about the islands.

Figure 2: Islands on Tupaia’s map with a similar shape.

Next the position of islands is considered. Various theories have been proposed about how Tupaia translated his knowledge of island locations onto paper. In an influential essay, Eckstein and Schwarz (2019) claim that Tupaia placed north in the centre of the chart, at a point he labelled avatea (“noon”). According to this theory, the bearing from island A to island B can be read by imagining two lines—one from island A to the centre of the chart (representing the north bearing), and the other from island A to island B—and finding the angle between them. A reading of this nature is illustrated in Figure 3: according to the avatea theory, the island of Moenatayo is depicted due east of Opoopooa.

Figure 3: Illustration of an avatea reading.

Eckstein and Schwarz (2019; 2023) present a complete identification of all 74 islands on Tupaia’s chart, predicting new identifications by finding islands which fall near to positions expected by the avatea system. This, however, leads to a problematic circularity in their argument, because they use the position of islands identified in this manner to justify the validity of the avatea theory itself.

An alternative theory has been put forward by Di Piazza and Pearthree (2007) based on observations made in ethnographic work. Oceanic navigators commonly oriented themselves relative to mental compasses, based either on the positions that familiar stars rise or set (Goodenough 1953; Alkire 1970; Gladwin 1970; Lewis 1972; Finney 1998), or on the directions notable winds blow (Beaglehole / Beaglehole 1938; Gill 1876; Lewis 1972). Di Piazza and Pearthree suggest that Tupaia used a mental compass of this nature to position islands on his chart. More specifically, they claim that each island can be interpreted as the centre of a compass on which other important islands are positioned. Importantly, these compasses are not all oriented with north pointed towards the top of the page, but are overlaid with different rotations. Di Piazza and Pearthree identify five candidate island compasses on the JB version, each with its own unique north direction. An example of one of the proposed island compasses is shown in Figure 4. In total, these five compasses correctly encode 27 inter-island connections within a 15° margin of error.

Figure 4: Illustration of an island compass.

I subject the avatea and compass theories to empirical scrutiny for the first time. For the compass theory, only five candidate compasses have been identified; to evaluate the theory, it is necessary to identify every compass on the map. Determining the orientation of an island compass can be framed as an optimisation problem, in which the goal is to identify a north bearing which aligns that island with as many other nearby islands as possible. I define a custom score function which, for a given island and a candidate north bearing, returns a measure of how well the bearings on the chart align with real life. This score function is based on a generalised bell function. Using this score function, a grid search is performed to find a unique north bearing for each identifiable island on Tupaia’s chart. These north bearings are shown in Figure 5 (unidentifiable islands are shown faded).

Figure 5: North bearings per island, according to the avatea theory (left) or to the compass-theory based model (right).

In this complete compass-based reading of Tupaia’s chart (JB), a total of 523 inter-island bearings are correct within a 15° margin of error, many more than the 27 connections tentatively identified by Di Piazza and Pearthree (2007). The avatea theory, on the other hand, yields only 78 connections that fall within this margin of error; this amount is statistically insignificant (α = 0.01). Using information about island elevation and the height of the Endeavour, I next identify paths on Tupaia’s chart which, had they been followed, would have resulted in island approaches proximate enough for successful landfall. If Tupaia’s chart (JB) is understood based on compass readings, then 356 island connections are accurate enough for landfall, while only 92 are if it is understood based on avatea readings. These connections are shown on a conventional map in Mercator projection in Figure 6. In sum, these results strongly favour a compass reading of Tupaia’s chart, and cast doubt on the legitimacy of the avatea system.

Figure 6: Navigable journeys on Tupaia’s chart when interpreted based on the avatea theory (top) versus the model-derived compass theory (bottom).

If my interpretation is correct, then these findings render Tupaia’s achievement all the more impressive. His map did not encode a small handful of common routes, but a dense nexus of inter-island connections spanning an area of around six million square kilometres. He possessed detailed knowledge, transmitted to him through oral tradition, about the location of all identifiable islands on the map, including many which were unknown to Europeans at the time. Remarkably, the precision of Tupaia’s knowledge was above the level required for landfall at all identifiable islands, including nearly 30 islands which he is not thought to have visited.