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Society of Mind

11.2 the shape of space

The brain is imprisoned inside the skull, a silent, dark, and motionless place; how can it learn what it's like outside? The surface of the brain itself has not the slightest sense of touch; it has no skin with which to feel; it is only connected to skin. Nor can a brain see, for it has no eyes; it only is connected to eyes. The only paths from the world to the brain are bundles of nerves like those that come in from the eyes, ears, and skin. How do the signals that come through those nerves give rise to our sense of being in the outside world? The answer is that this sense is a complicated illusion. We never actually make any direct contact with the outside world. Instead, we work with models of the world that we build inside our brains. The next few sections try to sketch how that could come about.

The surface of the skin contains countless little touch-sensing agents, and the retina of the eye includes a million tiny light detectors. Scientists know a good deal about how these sensors send signals to the brain. But we know much less about how those signals lead to sensations of touch and of sight. Try this simple experiment:

Touch your ear.

What did that feel like? It seems impossible to answer that because there's scarcely anything to say. Now try a different experiment:

Touch your ear twice, in two different places, and also touch your nose.

Which two touches feel most similar? That question seems much easier to answer: one might say that the two ear touches feel more similar. Evidently, there is scarcely anything that one can say about a single sensation by itself, but we can often say much more when we can make comparisons.

Consider the analogy to how mathematics treats a perfect point. We shouldn't speak about its shape; it simply doesn't have a shape! But since we're used to things as having shapes,

we can't help thinking of points as round, like very tiny little dots. Similarly, we're not supposed to talk about the size of a point — since mathematical points, by definition, have no size. Still, we can scarcely help but think, in any case, they're very small. In fact, there's absolutely nothing to be said about a single point, except how it relates to other points. This is not because such things are too complicated to explain, but because they are too simple to explain. One cannot even speak about where a point is, by itself — since where has meaning only in relation to other points in space. But once we know some pairs of points, we can relate these to the lines that connect them, and then we can define new, different points where various pairs of lines may intersect. Repeating this can generate entire worlds of geometry. Once we understand the terrifying fact that points are nothing by themselves but exist only in relation to other points, then we can ask, as Einstein did, whether time and space are anything more than vast societies of nearnesses.

In the same way, there is little that one could say about any single touch — or about what any single sense-detecting agent does. However, there is much more to be said about the relations between two or more skin touches, because the closer together two skin spots are, the more frequently they'll both be touched at the same time.