In a general way we may say, therefore, that a sensory continuum is -dimensional when, in order to render a path of continuous passage impossible between any two of its elements, it is necessary to remove a sub-continuum of dimensions. This sub-continuum itself is known to be dimensional because we can separate it into two parts only by removing from it a sub-continuum of dimensions, etc., till we finally get a sub-sub-sub ... continuum, which can be separated by removal of a single element. But such an element no longer constitutes a continuum, since passage in it is excluded; its dimensionality is then zero; so that the continuum it separates in two is obviously one-dimensional. A sensory continuum would also be given by a succession of weights placed on one’s hand, each only slightly heavier than the preceding one. Again our tactual impressions might yield a sensory continuum. In view of the fact that it is possible to account for the rise of the concept of space, even in the consciousness of a blind man, through the sole means of his tactual impressions, it may be of interest to discuss briefly an illustration of a tactual continuum—that obtained by exploring the surface of our skin by means of pinpricks. If these pinpricks are sufficiently close to one another, it will be impossible for us to differentiate between them and we shall always experience the sensation of one solitary pinprick. We can thus consider the sensory continuum obtained by some definite chain of pinpricks extending, let us say, from our elbow to our hand. This particular chain of sensations exhibits all the characteristics of a one-dimensional sensory continuum, since every one of its elements is indistinguishable from its immediate neighbours and since the removal of one of these elements (pinpricks) would create a hiatus rendering it impossible for us to pass in a continuous way from elbow to hand, along the chain. But if we should now consider all the possible chains of pinpricks extending from a point on our elbow to a point on our hand, the mere removal of one particular pinprick from one particular chain would be insufficient to interfere with the continuous passage. We might always follow one of the other chains, or even, following the same chain up to the missing element, skip round the latter without sensory continuity being interfered with. In the present case the only way to render this continuous passage impossible would be to remove some continuous chain of pinpricks—say, those circling round our wrist. The sensory skin-continuum would now be divided into two parts, and as the continuum removed was one-dimensional, we should conclude that the [Pg 26] skin continuum as manifesting its sensitivity to tactual stimuli was two-dimensional.