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I have a friend who has spent much of his life traveling from one country to another in search of many of life’s greatest pleasures, including fine beers. Because the consumption of fine beer is often incompatible with razor-sharp accuracy in calculations of currency conversions, my friend has learned a useful trick. He carries a card in his wallet that lists a series of dollar amounts and their equivalents in local currency. To a mathematician, this relationship of one set of values to another constitutes a map just as surely as the one in the glove compartment. The main difference between this kind of map and a road map is really only that the road map contains two dimensions whereas the currency chart contains one. Direction isn’t part of a one-dimensional map, so a compass is not required. In both cases, a scaling factor is used to relate one variable to another.
Mathematicians who are interested in different ways of mapping one quantity on to another are called topologists. The formal definition of topology is almost guaranteed to cause you to put this book down and run away screaming, so I will give only an informal idea of what topologists do.1 Imagine taking a sheet of something flexible, like rubber or latex, and drawing a simple map of your neighborhood on it. Now think of all of the ways that you could distort that sheet by, for example, stretching it over your face or stepping on one side and tugging at a corner. The only things that are against the rules are ripping the sheet or gluing any of its edges together. A topologist is interested in understanding which properties are preserved by your wanton handling of this map and which ones are altered.
For mathematicians, the importance of topology is hard to overestimate. Not only does it draw links between major areas of mathematics such as algebra, geometry, and mathematical analysis but it has also led to the mathematical field called graph theory, which has been pivotal in providing the tools to help provide solutions to such practical matters as how to prevent traffic jams and how to design networks of computers. Many problems in applied mathematics involve finding the most direct and efficient routes between one place and another. One classic example of this sort is the “traveling salesman problem,” in which one has to find the most efficient route that provides one visit each to a group of randomly arranged targets. The traveling salesman problem is of interest not only to, well, salesmen but also to those who design such things as circuit boards (to minimize production costs) and robotic devices that carry out repetitive tasks.
In psychology, the field of topology has helped us to understand the ways in which maps can be used to navigate. For example, think of the last time you drew a sketch map for someone to help them find their way from one place to another. Typically, such maps contain only the bare minimum of features that you deem necessary for them to find their way without becoming lost, so the major emphasis is placed on those points where people need to make explicit decisions (“Which way do I turn when I see the post office?”). Scale is seldom well preserved on sketch maps. A long, straight stretch of highway is likely to be compressed compared with another part of the map where a complicated cluster of intersections needs to be negotiated. So your map is a good topological map in the sense that it preserves the connectedness of places and the order in which they will be encountered, but it is not what is called a metric map because dimension and angle have not been preserved. For the most part, we expect the paper maps that we buy at gas stations to be metric in this sense. We expect there to be a proper scale to them, so that they represent accurate two-dimensional models of the real world.
In a later chapter, we’ll revisit the artifactual maps—the kinds of representations of space that have been drawn by human beings for thousands of years—to help us to understand how humans mentally represent space. Right now, though, we want to step back and take a somewhat broader view of the different types of maps that are used by both animals and human beings to guide themselves through space. As with some of the earlier parts of our story, some key differences between humans and animals will emerge from our exploratory forays through the animal world.
HOW HOMING PIGEONS FIND THEIR WAY
Racing, or homing, pigeons have a distinguished history as long-distance navigators. These birds, the same species as the common city-dwelling pigeons, have been used to assist with human communication for thousands of years. Before the widespread adoption of the telegraph in the nineteenth century, sending messages by pigeon was one of the fastest ways to communicate over long distances. Ancient Egyptians may even have used pigeons to announce the coronation of Ramses II. In a tradition perhaps beginning with Genghis Khan, Julius Caesar is said to have used pigeons extensively to convey battle knowledge, especially in his conquest of Gaul. The Reuters news service began as a system by which financial information could be conveyed from Germany to Belgium via telegraph wires, but the gaps were filled using what some pundits have recently referred to as the wi-fly method—pigeon telegraph. For as long as humans have used pigeons to carry bits of paper over great distances, we’ve also been interested in the mechanisms that they use to find their way reliably from one place to another. The scientific history of our interest in pigeons begins with Pliny the Elder in the first century A.D. In his astonishing encyclopedia, Naturalis historia, Pliny reports that Decimus Brutus used pigeons to convey news of the outcome of a battle at Modena.2
Consider this scenario. A homing pigeon is removed from its loft and placed inside an opaque box, which is fastened to the back of a truck, and transported over a sinuous route for a distance of 100 kilometers. The box is opened and the pigeon flies away. The initial flight direction of the pigeon seems random, but within a short time the bird is flying in a direct path back toward the loft. In a matter of hours, it has returned home. Such acts of successful homing can take place over distances of thousands of kilometers. As with so many of the navigational feats of animals in long-distance migration and homing, we know less than we’d like to about how such prodigious accomplishments come about, but it seems clear enough that in order to carry out such journeys, pigeons need two things: they need to know where they are and they need to know where they are going.3
Many useful sources of directional information exist in nature. Sun, moon, and stars, provided one knows something about the passage of time, can be used as a compass. Our own pocket compasses rely on something different—the earth’s magnetic field. The magnetic field of the earth is often portrayed as something like a huge bar magnet thrust through the center of the planet, with one pole roughly corresponding to each of the planetary poles. Though this is a handy diagrammatic shorthand for understanding how a compass works, it would be a mistake to believe that the physical processes that give rise to the earth’s magnetic field share much with a bar magnet. The real cause of the field is something that geophysicists call the dynamo effect, which is caused by the movements of massive amounts of conductive molten iron deep within the planet’s core. These movements, caused in turn by the rotation of the earth, throw gigantic magnetic field lines across the surface of the planet and far out into the space surrounding it. When we hold a small navigational compass in our hand and watch the needle align with magnetic north, we are witnessing an alignment between the slender rod of metal in our hand and these huge churning seas of molten rock and metal deep beneath us.
Do pigeons use a magnetic compass to find direction? An animated battle rages among scientists who study pigeons, but those who believe that pigeons can use magnetic fields to navigate are slowly gaining ground. Some early studies showed that forcing pigeons to fly while wearing tiny coils that disrupted the magnetic fields surrounding their heads caused them to become lost. Though this would seem to be incontrovertible evidence for some kind of use of magnetic fields to navigate, the effect was largely confined to young, inexperienced birds. The old hands were much less disrupted by such treatment, for reasons that are now becoming clear and which we will look at in a moment. The biggest obstacle to establishing the use of magnetic fields for compass orientation in birds has been the difficulty of finding the ma
gnetic receptor. Sounds are detected by ears, smells by nostrils, and sights by eyes. What sense organ detects magnetic fields? It turns out that the answer to this question might have eluded us for so long because the receptor organ was, so to speak, staring us in the face the whole time. Though the fine details remain to be worked out, it appears that pigeon photoreceptors, the cells in the back of the eye that convert light into electrical impulses, are sensitive to magnetic field orientation. Just as ant eyes can detect polarization angles, pigeon eyes seem to be able to detect magnetic field properties. We have no way of knowing whether pigeons can actually “see” magnetic fields, but there is at least good evidence that the direction of these fields can influence the way pigeon photoreceptors work. Regardless of whether these influences rise to pigeon consciousness (whatever that might be), they might be enough to influence flight direction.
The evidence for a magnetic sense in pigeons helps explain how they complete their long journeys, but one major piece of the puzzle continues to elude us. In the example that I described earlier, in which a pigeon was released from a box into an unfamiliar neighborhood, it was able to find its way back to its loft. Because the pigeon had never been to the release area before, it wouldn’t be enough for it to know which direction was which. It would also need to know something about where it was. Without a map, our pigeon is still lost.
Though pigeons may be the most intensively studied case of this type, some other animals share the pigeon’s ability to find home from an unknown location, suggesting that they too can map their own location on the planet’s surface, even when they are released in an entirely new location. Current thinking suggests that the only way to accomplish a feat like this is to have what is called a gradient map.
Imagine that you are standing in a large, square field. On one side of the field a noisy road crew is doing some repairs with a pneumatic drill. On an adjacent side of the field a street vendor with a food cart is playing a loud, repetitive jingle. With your eyes closed, you could wander around in the field and work out your distance from either the road crew or the food cart by gauging the loudness of the sounds. Knowing both distances would allow you to triangulate your position on the field with an accuracy limited only by your ability to discriminate loudness. What is even more interesting about this example is that you could work out your position in the field even from locations that you had never visited before, provided you had a basic understanding of the principle— two sources of sound in two different locations provide unambiguous cues to position.
Maps based on these principles work by taking advantage of some kind of gradient—some feature of an environment that changes in a regular manner depending on the observer’s position. Sounds are louder when we are closer to them. Smells are more intense. Lights are brighter. What about magnetic fields? It turns out that these fields vary systematically across the surface of the planet as well.
Indeed, the properties of magnetic fields that are used by navigating animals are more complicated than the properties that are used to help us point ourselves toward north in a cluttered forest. Geomagnetic fields have both intensity and direction. So for any point on the ground, imagine that there is a set of invisible arrows representing the geomagnetic field in that area. The arrows not only point in a particular direction but also have a specific length (which corresponds to intensity). Both direction and length vary systematically according to one’s position. From the standpoint of the gradient map principle, one of the most useful things about this is that the two properties of the geomagnetic field are somewhat independent of one another. Because field direction can change independently of field intensity, knowing both of these values can uniquely define one’s position in space. In addition, there are lots of interesting irregularities in the gradient map formed by the earth’s magnetic field. These irregularities are most commonly caused by gigantic pieces of rock with their own magnetic properties that interfere with magnetic field lines from the earth’s iron core. The beauty of these features is that they can help to further define the magnetic environment of the pigeon’s neighborhood and allow it to localize itself more precisely in space.
So much for theory. Do pigeons actually use magnetic gradient maps? Some convincing evidence suggests that they do. For one thing, experienced birds become disoriented when their ability to read magnetic maps is disturbed either by the presence of anomalous sources of magnetism or by interference with the system thought to be involved in magnetic map reading. In one of the most interesting of recent studies, homing pigeons were released in the vicinity of the Auckland Junction Magnetic Anomaly, an area in New Zealand with an extraordinarily high and unusual spike in magnetic field intensity and direction. Pigeons released here showed wildly disordered flight paths that seemed to be under the control of the local anomaly, but as their distance from the geomagnetic spike increased, their flight directions became more ordered and they began to fly in the right direction for home.4 Interestingly, the detector system for reading magnetic maps may be entirely separate from the magnetic compass found in the pigeon’s retina. Nerve fibers embedded in the nostrils of pigeons and other birds contain specialized magnetite molecules—much like those thought to have been discovered in Martian bacteria—and it is these nerve fibers that appear to be involved in map reading.
It isn’t very likely that homing pigeons rely entirely on magnetic fields to find their way around. Although the use of a gradient map might be the only way to account for navigation over vast distances from unknown origins to familiar home sites, some of the more mundane “everyday” navigational problems faced by pigeons could be solved by other means. Like many other animals, pigeons use visual landmarks (including human-built artifacts such as systems of highways), and some intriguing evidence suggests that they might be able to navigate over considerable distances using their finely tuned sense of smell. It has even been proposed that pigeons are able to construct a kind of mosaic map of space based on olfactory panoramas in much the same way as they can use magnetic fields.5
Homing pigeons are far from being the only animals that can use magnetic fields to navigate based on gradient maps. Many other birds, as well as aquatic creatures, have a keen magnetic sense. Even some mammals, such as the naked mole rat, an unusually social rodent living a subterranean life in conditions where landmarks are sparse, have been shown to rely on magnetic fields to navigate.
Other than pigeons, one of the best-studied examples of navigation by magnetic field is the sea turtle. Green turtles live and forage near the coast of Brazil, but a large number of them lay their eggs on the beaches of Ascension Island, in the south Atlantic. This small island, conveniently located about halfway between South America and the coast of Africa, has long been used as a stopping-over point for mariners and a staging area for military actions ranging from government raids on slaving ships in the nineteenth century to the Falkland Islands conflict in 1982. Green turtles had the misfortune to become a handy source of fresh protein for sailors, who at one time engaged in the barbaric practice of capturing these huge animals and tying them upside down to the decks of their ships as a kind of living larder. The turtles were hardy enough to survive under these conditions for weeks, waiting to be turned into soup for the ship’s crew. Because green turtle soup was also a prized delicacy in Europe, turtles were occasionally captured with the objective of returning them alive to the home port and delivering them with much fanfare to the wealthy and the titled. It was common for such captured turtles to be branded or otherwise labeled with the name of the anticipated recipient. The illness and death of the Duke of Wellington—a turtle destined for the royal table—was a noteworthy enough event to be recorded in a ship’s log.
In 1865, Carl Cornelius described one of the most extraordinary features of green sea turtles when he recounted an episode in which such a turtle had been captured near Ascension, branded, and then released in the English Channel when it appeared to be unwell. Two years later, this same turtle was recapture
d at Ascension, suggesting that it had found its way through thousands of kilometers of entirely unfamiliar waters from the English Channel back to its foraging ground near Brazil and from there back to Ascension Island.6 Though this was one of the first reports of the impressive navigational abilities of sea turtles, it is now well known that these animals enjoy a life cycle requiring them to carry out several long-distance migrations. It is virtually impossible to imagine these being completed unless turtles possess a gradient map.
Loggerhead turtles lay their eggs in the sand on the eastern shore of Florida, and the young, following subtle contours of light and terrain, find their way to water. Assuming they avoid being eaten by shorebirds that lie in wait for the hatchling turtles to make their dash to the sea, loggerheads find deep water by sensing the directions of wave patterns and, once free of the beach, rely on magnetic fields to guide them across the ocean to the Atlantic’s eastern shore. Like many other ultra-long-distance navigators, loggerheads probably rely on simple combinations of cues, such as the direction of major ocean currents and of magnetic field lines to carry them to favored waters. Though not impossible, it is unlikely that these turtles use a gradient map for the initial transatlantic voyage because the scenery would be entirely new to them. But in addition to these long-haul voyages, loggerheads are capable of surprising finesse in localizing their breeding grounds on the Florida beaches near Melbourne. Displacement experiments in which loggerheads are picked from the sea and returned to it far from their favored breeding grounds have shown that loggerheads show a well-developed ability to find their way back to traditional nesting sites that seems to rely on the magnetic sense. This sense probably includes an ability to read local microvariations in magnetic fields caused by the peculiarities of rock formations underlying the ocean floor.7