We've seen that touching nearby spots of skin will usually give rise to similar sensations: this is because the corresponding nerves run in parallel courses and thus cause similar activities inside the brain. The reverse is also usually true: the more similar two sensations are, the closer their origins in the skin. This has an important consequence:
The nerve pathways that preserve the physical nearness relations of our skin-sensors can make it easy for inner agencies to discover corresponding nearnesses about the outer world of space.
Moving your hand across an object tells you something about that object's shape. Imagine what must happen when a very young infant moves its hand across some object: each continuous motion produces a sequence of skin-sensor signals. Over time, various mapping agents can first use this information to learn, simply, which skin spots are nearest one another. Later, further layers of mapping agents could learn which skin spots lie between which others; this should be easy, too, because most small-scale motions tend to go in nearly straight lines. But then, since space itself is just a society of nearness relations between places, this is all the information we need to reconstruct the spatial structure of the skin. All this is in accord with a basic principle of mathematics:
Suppose you were lost in some unknown space — and could only tell which pairs of points were close to one another. That would be enough for you to figure a great deal about the space. From that alone, you could deduce if you were in a world of two dimensions or three. You could tell where there were obstacles and boundaries, holes and tunnels and bridges, and so on. You could figure out the global layout of that world from just those local bits of information about nearnesses.
It is a wonderful fact that, in principle, one can deduce the global geography of a space from nothing more than hints about which pairs of points lie near one another! But it is another matter to actually make such maps, and no one yet knows how the brain does this. To design a machine to accomplish such tasks, one could begin with a layer of correlation agents, one for each tiny patch of skin, each engineered to detect which other skin spots are most often aroused at nearly the same times; those will then be mapped as the nearest ones. A second layer of similar agents could then begin to make maps of larger regions, and several such layers would eventually assemble a sequence of maps on various scales, for representing several levels of detail.
If brains do something of this sort, it might illuminate a problem that has troubled some philosophers: Why do we all agree on what the outer world of space is like? Why don't different people interpret space in different, alien ways? In principle it is mathematically possible for each person to conclude, for example, that the world is three-dimensional — rather than two-or four-dimensional — just from enough experience with nearby pairs of points. However, if the wires from the skin to the brain were shuffled and scrambled around too much, we would probably never get them straightened out because the actual calculations for doing such things would be beyond our capabilities.