§ 6. Tactual Perception of the Third Dimension.— There is one point which ought to be made clear from the outset. We do not and can not have a perception of solid volume of the same kind as the perception of surfaces. The reason in the case of touch may be easily stated. We cannot touch one thing behind another. We come in contact with things only at their surfaces. What lies behind a surface in the solid volume of the object is intercepted by the parts in front of it. When we apprehend a surface, we have presented at once all its parts. The points, lines, and areas which we distinguish within it may be found by analysis of the total presentation as simultaneously given to synthetic touch. But the indefinite multiplicity of surfaces intersecting each other and connected by cross surfaces in an indefinite multiplicity of ways which compose solid volume, can never be presented to synthetic touch.

It is free movement which plays the leading part in our fully developed perception of the third dimension. We have seen in § 3 (The Spatial Significance of Free Movements) that "the sweep of a limb, or the movement of the whole body, comes to mean extension, differing in amount and direction according to the direction and amount of the movement." Now, the extended arm starting from any given position may move either up and down, or right and left, or in any intermediate direction. Each sweep of the arm to and fro means for consciousness an extended surface; and all these surfaces intersect each other in a line corresponding to the original position of the arm. Or again, consider the movements by which the extended palm becomes the clenched fist. The various intermediate positions form a continuous series: and each of them has an acquired spatial significance, which has arisen through the actual grasping of objects of varying size and shape. When the surface of the fingers meets the surface of the palm, the two surfaces become for perception one. At each intermediate position, they are distinguishable, and are apprehended not merely as part of the superficies of the body, but as surfaces of objects which might possibly be clasped in the hand. Thus we have a series of surfaces which, instead of forming part of one surface, overlie and underlie each other in layers. Hence in clasping an actual object, the position of the hand derives a spatial significance from its place in this serial movement by which we pass from the outstretched palm to the clenched fist. In this way we may account for that peculiarly distinct presentation of solidity which accompanies the grasping of an object.

In exploring an object with the hand by way of active touch, the actual path of the movement as determined by the configuration of the object is only one of an indefinite number of possible paths of free movement. At any given moment the surface which has been actually explored may have an indefinite number of possible continuations. The relation of the actual continuation to these possible continuations, each of which might have been actual in the case of a different object, is a relation in the third dimension of space. Finally, the constant presentation of our own organism as extended, is a great help towards the presentation of the third dimension. For whenever we touch either our own organism or an external body, two surfaces must be presented simultaneously, with a common part and independent continuations. This is only saying over again what we have already said in § 4 (Perception of the Organism as Extended). When the palm of one hand is laid upon the palm of the other, the area of contact is apprehended on the one hand as a portion of the total surface of the right hand and arm, on the other as a portion of the total surface of the left hand and arm. When the palm of the hand is applied to an external object, the area of contact is apprehended both as a part of the body surface and of the surface of the object. It has thus two independent continuations, which diverge from each other in the third dimension.

Many other details might be referred to. But the principle is the same in all. We apprehend the third dimension by touch, in so far as we apprehend the same surface as having more than one independent continuation.