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IT IS ROCKET SCIENCE!
In another desert, far from the home turf of the African desert ant, Robert Goddard toiled in the heat of Roswell, New Mexico, following a boyhood dream to send rockets far into space, a prelude to a mission to Mars. Goddard’s quest began at the dawn of the twentieth century when, as a seventeen-year-old boy, he sat in the bough of a cherry tree, looking down at the ground and imagining the view from Mars. He dreamed of a rocket that not only could escape from the earth’s atmosphere but could be guided to a target using some kind of navigational system. Later in life, as a rocket scientist in the New Mexican desert, Goddard designed a navigational system based on the gyroscope, a device invented 300 years earlier by the French scientist Léon Foucault.9
The wedding of Goddard’s solid rocket boosters and Foucault’s gyroscope produced one of the great shapers of twentieth-century world politics: the ballistic missile. The navigational problems of ballistic missiles are not very different from those of nursing gerbils finding their way home in the dark. In both cases, knowing where you are means understanding where you’ve been. In rocket mechanics, such problems are solved using a clever combination of accelerometers and gyroscopes.
A basic accelerometer can be thought of as nothing more than a mass, a spring, and a ruler. As the mass is accelerated, it exerts a force on the spring that causes the spring to stretch. The ruler measures the extent of the stretch, and this measurement yields the size of the acceleration.
As shown in Figure 3, gyroscopes are commonly constructed using a series of rotating rings called gimbals. As the object that carries the gyroscope rotates through space, the gimbals rotate. Measuring the size of the rotation can generate information about changes in heading, or direction.
Figure 3: The rotating wings of a gyroscope provide directional information
Both gyroscopes and accelerometers rely on some basic physical laws describing how things that contain mass move. Anything with mass contains inertia, which can be thought of as resistance to movement. Gyroscopes and accelerometers, because they rely on inertia, are said to be the instruments of “inertial navigation.” Together, these machines provide all the information necessary to calculate position, provided that the arithmetic can be worked out.
Inertial navigation is very difficult to do well over long periods of time. The path of a vehicle carrying accelerometers and gyroscopes can be reconstructed from the entire record of every change in heading or velocity, provided one knows exactly when these changes took place. But here’s the problem: no inertial guidance system has perfect precision. For that matter, no machine has perfect precision. Every measurement of acceleration or heading change contains an error, and these errors will accumulate as inexorably as the interest on delinquent income tax payments. This kind of inaccuracy, called integration drift, will become more and more serious as time goes by. There are two main ways to counteract this kind of error. One solution is to have a means of measuring velocity that does not depend on the inertial guidance system. Another is to allow the guidance system to come to rest. When the machine carrying the system halts, the velocity falls to zero and so does the value for integration drift. Both these error-correcting mechanisms are used, but the second one is obviously useful only on the surface of the planet, where friction and gravity can bring systems to a halt. It is not very good for rocket navigation, where making things stop can be tricky.
Though the gyroscopes and accelerometers in our middle ears look markedly different from those found in missiles and rockets, the principles involved are exactly the same, and the vestibular system found in mammals suffers from the same type of integration drift.
An animal using its vestibular system for navigation is subject to an accumulating error. Every time the animal turns or moves forward, the error for that movement segment is added to the error from all previous movement segments. Although ants also suffer from this cumulative error, the intrinsic error of their estimates of the sizes of turns is smaller than for mammals because the sun compass can yield more accurate estimates of turn size than can the vestibular system.
Given all this, we would expect path integration based on inertial guidance to be less accurate in mammals than it is in ants, and this is an expectation that has been confirmed in every case so far. But path integration can be carried out with other senses.
When furry creatures try to navigate in the lightless confines of a psychology experiment, they can be made to lose their way like human beings stumbling through a dark house during a power failure. It may take longer for them to stumble, but sooner or later, with enough twists and turns, integration drift will take its toll. A brief flash of light, though, like a bolt of lightning seen through a bedroom window, can reset our sense of position and turn integration drift back to zero. The details of how path integration works in darkness, and how brief visual “fixes” can reverse the accumulating errors of integration drift, have been worked out in experiments carried out with hamsters (their nice habit of stuffing food into cheek pouches and carrying it home to store in a larder makes them an excellent species for studying such problems). The main finding from these studies is that, provided there is not a great discrepancy between where a visual fix tells us we are and the location indicated by our inertial guidance system, a brief glimpse will wipe clean the slate, and re-zero integration drift. If the visual fix gives a surprising result, then it might be ignored.10
For example, imagine that you’ve arrived at your cottage, late at night, and need to find the main power switch to turn on the lights. You have a rough idea of which way to go from the front door, and you set off with your hands in front of you, feeling your way through darkness. A car drives past on a nearby road, and the sweep of headlights through the window provides you with a momentary visual fix. If the fix shows that you are walking at a slight angle to the target, you will correct your course. But if the flash of light suggests that you are walking in the completely wrong direction—back toward the door rather than toward the far wall where the power switch is located—you might be prone to disbelieve your eyes, wondering if the poor light has caused some kind of illusion.
WHAT’S GOOD FOR THE GOOSE MAY NOT BE GOOD FOR US
In a classic study of animal navigation, Ursula von St. Paul took a group of domestic geese on a country ride in a small covered cart. The ride began at their home and proceeded through a series of complicated switchback turns along narrow lanes through varying types of terrain. For some segments of the ride, von St. Paul covered the cart with a blanket so that the geese were not able to see anything. For other segments, the cart was uncovered so that the geese could see the sights as they rode. At the conclusion of the tour, von St. Paul took the geese out of the wagon and released them. Would they be able to find their way home?
The key finding in this experiment was that the geese picked a homeward route as if the only movements they had made had been those undertaken while the cart was uncovered. While carried around in the cart, the geese would have had very little access to inertial guidance because their vestibular systems would not function well while they traveled passively in such an unnatural conveyance. But the most interesting aspect of this finding was that the geese apparently were able to path integrate using the flow of visual motion that they received while the cart was uncovered, and this is a very different form of path integration from that using the vestibular senses for inertial guidance.11
Although this experiment showed clearly that path integration works well using vision, surprisingly few studies have aimed at determining how precisely this information can be used, especially in mammals. There are a few very intriguing suggestions, though, that geese are not the only animals capable of using path integration in this way.
In many laboratory studies of spatial navigation, animals are carried from their living quarters to another room that contains a testing apparatus. Many researchers have discovered that animals such as rats and mice are actually able to keep track of their orientati
on to the world as they are conducted passively through the hallways of a large laboratory. Some experiments require that animals lose all sense of spatial connection with the world outside the walls of the testing room, so that the experimenters can be confident that the behavior of the animals is under the complete control of cues present in the room. It can be extraordinarily difficult to produce that state of spatial detachment in an animal. In research in my laboratory (at the University of Waterloo), animals are sometimes conveyed from one place to another inside a light-free container that is rotated on a turntable en route to the testing room. If this is not done, animals often show signs that they have managed to maintain a consistent sense of direction and distance between the room in which they live and the room in which the experiment takes place, presumably by using a combination of optic flow and inertial guidance to keep track of their paths.
Findings such as these suggest that these animals hang on to their sense of place with great tenacity. Draconian disorientation procedures, including incarceration in dark boxes and on spinning turntables, can affect performance in some types of tasks, but even here one of the most peculiar things is that animals, rather than falling back on other sources of information not affected by such procedures (such as landmarks), will sometimes behave as though, having been robbed of their primal attachment to the earth, they cannot make proper sense of these other beacons of navigation.
Do human beings use the same strong sense of direction in solving navigation problems? Edward Atkinson’s experience in an Antarctic blizzard, the many anecdotal accounts of people becoming lost in wilderness, and our own tendency to become lost in relatively simple environments like shopping malls and office buildings suggest that we are built differently. Now we should see what the scientific studies have to say.
As a young woman is ushered into a psychology laboratory, she is asked to don a pair of opaque goggles to occlude her vision and a set of headphones to muffle ambient sounds. She communicates with the experimenter via a tiny earbud speaker. The woman is led about the room to one invisible target after another and is allowed to touch each one in turn. At the conclusion of this learning phase, she is led to a starting position and directed to walk to a specified target. Except for the fact that she is in a completely unfamiliar environment, this woman is in similar circumstances to the hapless cottage owner stumbling about looking for the light switch, or the exhausted mother trying to find her way out of a dark bedroom to the sounds of a crying infant. In experimental psychology labs, we can measure with great precision the extent to which people in such circumstances can find their way around, and the results are interesting, to say the least.
In one of the first such studies conducted in my laboratory, we had participants stand at one end of a standard squash court, take a good look around, and then let us lead them from place to place while they wore opaque goggles. We led participants to a series of different objects, one at a time, and then we led them back to the starting position and asked them to strike out by themselves to find the objects. One of the first odd things we noticed was that even though the participants had had a good look at the size and shape of the room, they would raise their hands before them so as to avoid collisions with the walls, even though in many cases the nearest obstacle was at least five meters away from them. Discussions with participants both during and after our procedures soon made it clear that they had very little idea where they were. Our formal measurements of their performance in simple tasks designed to test their knowledge of their own positions revealed that they were performing at levels barely distinguishable from chance. In these initial studies we made no deliberate attempt to disorient them—no lightproof carts or spinning turntables were required for our participants to become completely disoriented. The differences in behavior between people and other animals could not have been more striking.12
Through years of experience, we have learned many tricks that have helped us to extract reasonable performance from participants in experiments such as these, but there is still a massive contrast between the performances of non-humans in our laboratory and those of the people who volunteer for our studies. With animals, the challenge is usually to find a way to make them forget about the larger spatial context of the labyrinth of laboratory rooms so that we can be sure we’re controlling how our critters use space. With people, the challenge is to provide them with enough support that they can find their way across an ordinary rectangular room without banging their heads into the walls. Why do such differences exist? Though there’s still much that we don’t understand about this, there are some important clues.
In very simple situations, we can find our way to a target with reasonable accuracy. For example, imagine a task in which you are able to take a long look at a target that is lying on the ground some distance in front of you—say about 10 meters. Then, with eyes closed, you are asked to walk to the target. Provided that you are allowed to walk immediately after you close your eyes, you should be able to land within a few centimeters of the target. As you read these words, you may be very skeptical that you could perform well in such a “blindwalking” task. When you have a chance, try it out (ideally in a large, flat, outdoor space like a sports field). You will almost certainly be surprised by your accuracy.
When walking tasks like these are made slightly more complex, human performance unravels quickly. On a triangle-completion task, blindfolded people are walked along a path of a few meters and then, after changing direction, they are led along a second path. Their task is to complete the triangle by walking back to their starting point. There are two main differences between the triangle-completion task and the blindwalking task, both probably important. First, the triangle task does not contain an explicit visual preview of the target or of the stopping points (the corners of the triangle). We need to plan our homing route entirely on the basis of bodily information that we receive while walking (vestibular information, feedback from the muscles used in walking, and so on). Second, the triangle-completion task involves measuring both a pair of walked distances and the angle between them—considerably more complex than just estimating a visual distance. These two differences conspire to degrade our performance on this task sufficiently that, as ants, we would surely starve or fry in the blazing sun. In one typical study, after walking short triangles ranging in size from two to six meters, the average angular turning error in heading for home was more than 20 degrees, and the size of the distance error was around 50 percent of the distance walked.13
Except when the power fails or when we’re trying to creep around darkened rooms without disturbing sleeping family members, we human beings are not very likely to find ourselves trying to navigate entirely without using our visual sense. But the fact that we become disoriented so quickly and completely when deprived of visual fixes has a greater meaning. Our inability to tap into body-based senses to keep track of location may be a deficit rooted in our biology, a loss of an ability possessed by our ancestors that has fallen into dormancy through lack of use, or, what I think most likely, a combination of the two.
If we once possessed the ability to keep track of our location using path integration, perhaps even if not to the same degree seen in ants or even in rats or geese, what has caused our increasing tendency to lose contact with position, place, and space? Has some other way of understanding space come to supplant the ancient ways of gluing us to our place on the planet? The landmarks are now in place, our route is becoming slightly clearer, and some of the answers lie directly on our path.
CHAPTER 4
MAPS IN THE WORLD
HOW EXPERT NAVIGATORS USE SPECIALIZED
SENSES TO FIND THEIR WAY
Every cubic inch of space is a miracle.
WALT WHITMAN
Navigation using a map is a key transition from the simple kinds of tasks that I’ve been discussing thus far to the more complicated accomplishment of true wayfinding. In a wayfinding task, not only is the target invisible from the starting
point but it can be found only by carrying out the correct sequence of movements based on what can be seen, heard, or felt at each point in the sequence. You don’t need a map to complete a wayfinding task, and you certainly don’t need a map for any task that is simpler than the definition I’ve just given.
When you read the word map, the most likely thing that will spring to your mind (unless you’re a mathematician) is the folded paper that you might find in your glove compartment. There is no question that this is a map, albeit a very specialized one. The reason the map is taking up space in your car is that it is a useful tool for navigation, and what makes it useful is that the map is a model of the real world. A good map will contain replicas of things found in the real world that it is useful to know about, such as roads, schools, and shopping malls. Maps often have other useful features as well, such as a compass rose that allows you to orient the map properly to the real world and a scale so that you can work out the real distances between the points represented. But do all of these features have to be present for something to be called a map? To answer this question, we’ll want to stand back and take a much more general view of maps, where they come from, and how they are used.