The Case of
The Imaginary Islands
describes a rich set of models used by sailors in Micronesia to successfully navigate hundreds of miles of open ocean without instruments based on references to imaginary islands beyond the horizon.
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For hundreds of years, sailors in the Caroline Islands (so named by European interlopers) of Micronesia have used a sophisticated suite of models to manage sail travel over hundreds of miles of open ocean. These journeys were often conducted mostly out of sight of land and without technology such as compasses or chronometers. The domain of these sailors' navigation were the islands and atolls of Micronesia: (Placeholder image from

The importance of accurate navigation in this context cannot be overstressed, as missing one landfall might mean never making landfall at all. In contrast, navigators of the Mediterannean in early Western history had the advantage that steering a straight course after missing a landfall would eventually lead to landfall somewhere.

The navigation practices of these islanders has been studied for well over 150 years, but the first studies combined careful description with basic misunderstandings. By applying the models of Western navigation to the islanders' practices, they assumed that the navigators were performing an imperfect version of Western practice. Later studies, however, revealed that the navigators were doing a very different kind of navigation very well. The first analysis of this sort can be found in Thomas Gladwin's "East is Big Bird." A lengthy animated essay on the method can also be found on the web at The psychologist Edwin Hutchins brought this style of navigation and its initial misunderstanding to the well-deserved attention of the cognitive science communities. We will only sketch the contributions of these researchers enough to tell the story about models which we want to tell.

The Star Compass

One of the central models used by Micronesian navigators is a set of consistent compass directions based on the rising and setting of stars and constellations. As the night proceeds, stars rise and set around the horizon at particular times and in particular directions. The directions were named by the corresponding star or constellation: (Placeholder image from

Children in the Caroline Island culture start learning the names of these "compass points" when they are five or six years old. The simple directions are extended by memorization of reciprocal pairs of compass points (e.g. the rising of Vega is across from the setting of Antares) and by perpendicular reciprocal pairs (e.g. the Vega-Antares axis is perpendicular to the Shaula-Alpha Cassiopeia axis).

The rising and setting of stars does not change with the seasons (though the hours in which they are visible does), but it does change as one moves north and south. Fortunately, among the Caroline Islands, the range of north-south travel is fairly limited and doesn't substantially effect the star compass. And because they are near the equator, nights tend to be exactly the same length as days, so at least one rising or setting for each axis will always be visible.

Navigators also need to have a keen sense of the angular distance between star compass points, beyond the cardinal points behind-right-left. Seeing the setting of Gamma Corvus, they can steer a course towards the setting of the Pleiades, even if the Pleiades is not visible. They can also, with some accuracy, identify rising and setting points based on the position of the star in the sky and the general (apparent) motion of the heavens.

In addition to using the star compass to tell direction, sailors confirm directional information by using the alignment of ocean swells. Among the Micronesian islands, ocean swells at different times of year have particular alignments with particular distinct intervals. By considering the intervals and time of year, navigators can coordinate the motion of the ocean swells with the star compass.

Map In The Mind

The star compass is then used to describe the relative positions of the islands. In an exercise called "Island Looking," navigators memorize the directions between islands based on the star compass. From Woleai, they note, Eurapik is towards the setting of Antares. Learning this set of relations exhaustively lets them know how to set sail for any journey.

Like the idealized subway map of the introduction, the description of these directions only describes the paths between points and not their actual positions. Information which is irrelevant for starting the journey --- distance, physical context of launch and destination, points along the way, etc --- is not a part of this model. Instead, that sort of information is handled by other models.

Because these models are being stored in human memory conveyed and refreshed by an oral tradition, the simplicity of models is crucial. Just as the information presented on the subway map is constrained by the size of the map and other graphical constraints, the model of the positions of and paths between islands is constrained by the limits of the honed and practiced human memory.

When actually sailing between islands, the star compass is not always accurate enough alone to guarantee shore-to-shore paths. Instead, use of the star compass relies on the ability of sailors to find islands when they are near them. This may come out of sighting the actual island or of spotting the land birds which feed further out at sea.

Thus, using this star map is not a simple process, but requires substantial knowledge and skill beyond identifying points on the horizon. We like to think that a "direct model" like a map is natural and automatic to use, but in fact using maps typically involve many skills which everday map users take for granted (finding an island or identifying kinds of birds) but which are mysteries to strangers.

(An aside: Thousands of miles and some industrial centuries away, Westerners learn this lesson when riding the Tokyo subway system. The skill of "reading the map" and matching names on the map to signs in the stations is not one which we naturally have. Instead, it is slowly learned and many Westerners share the unpracticed experience of vigorous head motions from map to window, attempting to match the name at the station to some text on the map.)

The star compass and the relations learned by "island looking" provide directional information to sailors. But distance information is also important for many different purposes. Sailors use a different model --- island dragging --- to track and describe distances.

How Far?

If ocean sailing were like riding subway cars, it would only be neccessary to know the direction to sail between islands. Distance would be important for stocking provisions and for knowing when to look for one's destination, but for the journey itself we would need to know nothing more than the "star to steer by." However, ocean sailing is not so reliable.

Winds change. Currents change. And these changes distort the lines of travel between the islands as described by the star compass. If we steer from the island of Woleai towards the setting of Antares, we will arrive at the island of Eurapik only if there is no prevailing wind or current disrupting our travel. However, if there is some wind and/or current going to the North, we will not end up at Eurapik, but will overshoot and find ourselves lost in the Pacific. To compensate for this, we may need to aim for the setting of Shaula (in Scorpio) instead to ensure that we make landfall at Eurapik. But how do the navigators determine the strength and direction of these forces?

Some are directly available to the experienced sailor. One can sense the wind directly and identify its direction with respect to the star compass. The direction of currents cannot be identified directly, but it can be estimated by distortions in the shape of the wind-borne waves. Steeper waves result from current contrary to the wind, shallower waves from current moving along with the wind.

But though observation can determine direction, it is not so useful for determining absolute speed. For reasons much like those anticipated by physicists attempting to measure the Earth's speed, measuring the absolute speed of a ship at sea may be quite complicated. The problem is that speed is a relationship between distance and time and --- in the absence of landmarks --- distance may be difficult to determine. Small boat sailors can tell speed with respect to the water and its prevailing current, but that does not tell of actual progress along one's intended course.

Instead, to track distance, navigators begin by dividing a journey into segments called etaks or "drags" based on reference to some distant island and the star compass. They have memorized, of course, the points of rising and setting of the star compass and pick a distant island over which --- if they are on course --- particular star compass points will manfiest themselves by the rising or setting of particular stars. By using the actual events of rising and setting, sailors are using the "star compass" as a "star clock" which separates their journey into distinct segments called "drags" or "etaks."

But sailors have other models of drags, which serve to confirm the drags specified by their "star clock." The first drag, for instance, ends when their island of origin disappears beneath the horizon. The second drag ends when land birds feeding on the ocean disappear. In addition, some submarine features, such as reefs or even recurring fish populations, may coincide with drags.

Here we see the power of multiple models. The drags defined by the "star clock" reflect progress in time; the drags defined by the nearby visible cues (island, birds, reefs) reflect progress in distance. By comparing these two models, sailors can estimate the effect of current and other environmental conditions on their journey and compensate by steering a different course.

The double model is vitally important to "confirm" their drag-by-drag progress because the islands used to mark risings and settings are usually not even visible and may not even exist. And here we come to a second role for imagination in this suite of models.

Imaginary Islands

If a sailor is on course, the regular risings and settings occur over some distant island which is not along the course from origin to destination. However, this distant "reference" island is almost never visible to the navigator and may not even exist. Some of the islands used as reference points in this manner are simply constructions of "convenience" --- like the placeholder zero --- used to designate the series of risings and settings seen by the travellers as they move from drag to drag.

What is the point of maintaining these fictions? Why not simply use the "star clock" directly? The reason is that the navigators are not really using the star clock to tell time. They are using the star clock to estimate progress along their journey. Imagining islands and relative positions allows the navigator to compare expected positions directly rather than comparing time and position. The unseen island serves as a fixed point for converting time into distance.

There are assumptions lurking in these models. They assume that the current for the first few drags is consistent with the current for the rest of the voyage. They assume that the direction of the current remains roughly the same throughout the voyage. They assume that they have a good estimate of how quickly the boat is moving relative to wind and sea. Fortunately (or by design and practice), most of these assumptions hold for most of the time. It may be that decisions about scheduling journeys may seek conditions where the assumptions hold. But it is the assumptions which make the model --- and thus ambitious ocean journeys --- possible.

Frames of Reference

I have described these navigation practices from the point of view of the sailor crossing the ocean. However, the sailors think of them differently. In their imaginations, when they depart on their boat, they and their vehicle and their companions are fixed in place, and the world moves around them. Gladwin describes it beautifully:

Picture yourself on a Pulawat canoe at night. The weather is clear, the stars are out, but there is no land in sight. The canoe is a familiar little world. Men sit about, talk, perhaps move around a little in their microcosm. On either side of the canoe, water streams past, a line of turbulence and bubbles merging into a wake and disappearing into the darkness. Overhead there are stars, immovable, immutable. They swing in their paths across and out of the sky but invariably come up again in the same places. You may travel for days on the canoe, but the stars will not go away or change their positions aside from their nightly trajectories from horizon to horizon. Hours go by, miles of water have flowed past. Yet the canoe is still underneath and the stars are still above. Back along the wake however, the island you left falls further and further behind, while the one toward which you are heading is hopefully drawing closer. You can see neither of them, but know this is happening. You know too that there are islands on either side of you, some near, some far, some ahead, some behind. The ones that are ahead will, in due course, fall behind. Everything passes by the little canoe --- everything except the stars by night and the sun in the day.

This shift in perspective, akin to the shift involved in the inertial frames of Chapter 2, is more than just poetic. All of the navigator's cues for direction and correction are outside of the boat. Given that the world is moving in a particular way, the navigators arrange their own motion and direction to reflect the moving world.

This change of perspective simplifies the combination of factors. Rather than trying to resolve their position without landmarks, they are steering themselves to compensate for the motions they sense through multiple channels of different models. This shift in description simplifies the integration of multiple factors like wind, current, and the motion of the boat.

The specification of this frame of reference relies on, among other factors, the conversion of time into space through imaginary islands. The use of such "imaginary" objects is a common part of inference and we can see it recurring in the history of Western mathematical thought, to which our discussion of inference now turns.

Copyright (C) 1997, 1998 by Kenneth Haase
Draft, not for citation or circulation
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