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Chapter 7

The Spaces We Navigate and Their Horizons

Wherein I distinguish a variety of spaces we navigate and discern the boundaries at several of their horizons.

When it was time for the little overloaded boat to start back to the mainland, a wind came up and nudged it onto a large rock that was just below the surface of the water. We began, quite gently, to sink. . . . All together we went slowly deeper into the water. The boatman managed to put us ashore on a huge pile of rocks. . . .

The next day when I passed the island on a bus to Diyarbakir there, tied to the rock as we had left it, was a very small, very waterlogged toy boat in the distance, all alone.

—Mary Lee Settle, Turkish Reflections: A Biography of a Place, 1991

Navigating the Spaces We Perceive

Have you considered just how you navigate the spaces of your world? Fortunately, in our everyday living, we don’t have to; our brain is fine-tuned to do the job for us. Only when we encounter something exceptional do we need to pay attention. When we are climbing stairs, we see the stairs with our eyes. The space seen is called “occulocentric” because it centers on our eyeballs, but it is our body that is actually climbing the stairs. This body- centered space is called “egocentric.” The stairs inhabit their own space: some steps may be higher than others; some are wider, some may be curved. Stairs are objects, and each has its own “object-centered” space. Space, as we navigate it, is perceived as three-dimensional. Since we are moving within it, we must include time as a fourth dimension. We run up the stairs, navigating these occulocentric, egocentric, and object-centered spaces without hesitation. The brain must be simultaneously computing within 12 separate co-ordinates, four dimensions for each time-space. Cosmologists are puzzling the multidimensionality of “string” and “brane” theory: why aren’t scientists heeding the 12 navigational coordinates of brain theory?

Now imagine that the stairs are moving. You are in a hurry, so you climb these escalator stairs. You turn the corner and start climbing the next flight of stairs. Something is strange. The stairs seem to be moving but they are not, they are stationary. You stumble, stop, grab the railing, then you proceed cautiously. Your occulocentric (visual) cues still indicate that you are moving, but your egocentric (body) cues definitely shout “no.” The brain’s computations have been disturbed: occulocentric and egocentric cues are no longer meshed into a smoothly operating navigational space. It is this kind of separation—technically called “dissociation”— that alerts us to the possibility that the three types of space may be constructed by different systems of the brain.

Eye-Centered and Body-Centered Systems

While in practice in Jacksonville, Florida, I once saw a patient who showed an especially interesting dissociation after he’d been in an automobile accident. Every so often, he would experience a brief dizzy spell, and when it was over, he experienced the world as being upside down. This experience could last anywhere from a few minutes to several hours, when it was ended by another dizzy spell, after which his world turned right side up once more. This patient was an insurance case, and I had been asked by the insurance company to establish whether he was faking these episodes. Two factors convinced me that he was actually experiencing what he described: his episodes were becoming less frequent and of shorter duration; and his main complaint was that when the world was upside down, women’s skirts stayed up around their legs, despite gravity!

In the short time of this office visit I had failed to ask the patient what proved to be a critical question: Where were your feet when the world was upside down? Decades later I had the opportunity to find the answer to this question.

The story begins more than a hundred years ago when George Stratton, an early experimental psychologist, performed an experiment at Stanford University. He had outfitted himself with spectacles that turned the world upside down, just as the world had appeared to my patient. However, after continuously wearing these glasses for a week during his everyday activities, Stratton found that his world had turned right side up again.

Poincaré had stated that objects are relations; therefore, the perceived occulocentric space, which is made up of objects, is relational, something like a field whose polarity can change: Thus, “up” versus “down” is, in fact, a relationship that adjusts to the navigational needs of the individual. With respect to my question as to where one’s feet are located in such an upside-down/down-side-up world, why not repeat Stratton’s experiment and ask whether occulocentric and egocentric spaces become dissociated? My opportunity arose when two of my undergraduate students at Radford University in Virginia volunteered to repeat the experiment. One would wear the prism-glasses; the other would guide him around until his world was again negotiable, right side up.

Once the perceptions of the student wearing the glasses had stabilized, I had my chance to ask the long-held question: Where are your feet? “Down there,” my student said and pointed to his shoes on the ground. I placed my hand next to his and pointed down, as he had, and he saw my hand as pointing down.

Then I stepped away from him and placed my hand in the same fashion, pointing to the ground as I saw it. He, by contrast, saw my hand as pointing up! As I brought my hand closer to his body, there was a distance at which he became confused about which way my hand was pointing, until, when still closer to his body, my hand was perceived as pointing in the same direction as he had originally perceived it when my hand was next to his.

The region of confusion was approximately at the distance of his reach and slightly beyond.

Occulocentric and egocentric spaces are therefore dissociable, and each of these is also dissociable from object-centered spaces. After brain trauma, patients have experienced “micropsia,” a condition in which all objects appear to be miniscule, or “macropsia” where objects appear to be oversized. In these conditions, occulocentric and egocentric spaces remain normal.

Conceived as fields, it is not surprising that the objects in these spaces are subject to a variety of contextual influences. Some of these influences have been thoroughly investigated, such as the importance of frames in object perception; others, such as those in the Stratton experiment have been thoroughly studied, but no explanation has been given as to how such a process can occur, nor has an explanation been given for micropsia and macropsia.

I will venture a step toward explanation in noting that the Fourier theorem and symmetry group theory offer, at the least, a formal scaffolding for an explanation. The brain process that transforms the sensory input from the space-time domain optical image to the spectral domain at the primary visual cortex, and back to the space-time domain by way of movement, actually should end up with up-down mirror images of the occulocentric space. This is mathematically expressed in terms of “real” and “imaginary” numbers—that is, as a real and a virtual image. Ordinarily we suppress one of these images—probably by movement, but exactly how has not been studied as yet.

We noted in the previous chapter that symmetry groups have the characteristic that the group, the object, remains invariant across expansion and contraction. This means that we ordinarily adjust for what, in a camera, is the zoom of the lens. In my laboratory, my colleagues and I were able to change the equivalent of the zoom of receptive fields in the visual cortex by electrical stimulation of other parts of the cortex and of the basal ganglia of the brain. Patients experienced such a change in zoom during surgery at the University of California at San Francisco when their brains were electrically stimulated in the frontal and in the parieto-temporal regions of their cortex. Perhaps the adjustment of the zoom, which in our experiments was effected through lateral inhibition, becomes disturbed in patients who experience micropsia or macropsia.

Occulocentric space has been studied more thoroughly than the “spaces” of other senses, primarily because painters have been interested in portraying it. Painters needed to portray a three-dimensional perspective on a two-dimensional surface and to take into account the variety of constancies we perceive for objects, depending on the distance they are from us. This brings us to the topic of horizons, a topic that shows how our perceptions depend not only on the brain systems that are involved but also on how these systems become tuned by the culture in which we have been raised.

Nature and Nurture

At the dedication ceremonies of Brandeis University, Abraham Maslow, Wolfgang Köhler and I were discussing perception. Köhler insisted that the way we perceive is inborn. “If learning is involved, it isn’t perception,” he declared. With regard to perception, Köhler was what is referred to in psychology as a “nativist.” Today, it is hard to remember how entrenched this view was; so much evidence has since been obtained that indicates just how what we learn influences how we perceive. Much of this shift in viewpoint is due to the research and writings of Donald Hebb that drew attention to how dependent our current perception of perception is based upon what we have learned.

Hebb’s contribution came exactly at the right moment. During the mid-1950s, sitting at my dining room table, Jerome Bruner wrote a landmark paper entitled “The New Look in Perception.” Among other experiments, in this paper, Bruner recounted the demonstration that how large we perceive a particular coin to be—a quarter, for instance—depends on how wealthy or poor we are. Such an everyday experience attests to how much the context of our perception—in this case, what we have learned about the value of a coin—influences how we perceive it.

These insights were anticipated in anthropology and sociology, where studies of peoples of different cultures showed marked differences in their perceptions. For instance, in Somalia there is no appreciation for the color red but a great differentiation of the spectrum that we ordinarily classify as green. The brain processes reflecting such differences are now accessible to study with fMRIs and other brain-imaging techniques.

The argument can still be made that sensitivity to context is inherited. This is largely correct. In fact, the whole discourse on what is inherited and what is learned takes on a new significance when inheritance is considered as a potential rather than a full-blown established capacity received at birth. The Nobel laureate, behavioral zoologist Konrad Lorenz made this point with respect to learning: he pointed out that different species have different potentials for learning this or that skill.

Sandra Scarr, professor of psychology at the University of Virginia, has gone a step further in suggesting a test for determining “how much” of a skill is inherited: she has shown that, to the extent to which a perception or skill comes easily—that is naturally—to us, it is, to that extent, inherited. Thus, our ability to speak is highly inborn, but our ability to read is markedly less so. Though we all talk, whether we learn to speak English or Chinese depends on the culture in which we grow up. How fluent we may eventually become in Chinese or in English also depends on learning, which in turn depends on the stage of maturation of our brain when the learning is undertaken.

The Form Within

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