Space has been defined as "room to move about." Let us accord to this definition the utmost liberty of interpretation. Let us conceive of space not alone as room to move ponderable bodies in, but as room to think, to feel, to strike out in unimaginable directions, to overtake felicities and knowledges unguessed by experience and preposterous to common sense. Space is not measurable: we attribute dimensionality to space because such is the method of the mind; and that dimensionality we attribute to space is progressive because progression is a law of the mind. The so-called dimensions of space are to space itself as the steps that a climber cuts in the face of a cliff are to the cliff itself. They are not necessary to the cliff: they are necessary only to the climber. Dimensionality is the mind's method of mounting to the idea of the infinity of space. When we speak of the fourth dimension, what we mean is the fourth stage in the apprehension of that infinity. We might as legitimately speak of a fifth dimension, but the profitlessness of any discussion of a fifth and higher stages lies in the fact that they can be intelligently approached only through the fourth, which is still largely unintelligible. The case is like that of a man promised an increase of wages after he had worked a month, who asks for his second month's pay before he is entitled to the first. THE SUBJECTIVITY OF SPACE Without going deep into the doctrine of the ideality--that is, the purely subjective reality--of space, it is easy to show that we have arrived at our conception of a space of three dimensions by an intellectual process. The sphere of the senses is two-dimensional: except for the slight aid afforded by binocular vision, sight gives us moving pictures _on a plane_, and touch contacts _surfaces_ only. What circumstances, we may ask, have compelled our intellect to conceive of _solid_ space? This question has been answered as follows: "If a child contemplates his hand, he is conscious of its existence in a double manner--in the first place by its tangibility, the second by its image on the retina of his eye. By repeated groping about and touching, the child knows by experience that his hand retains the same form and extension through all the variations of distance and position under which it is observed, notwithstanding that the form and extension of the image on the retina constantly change with the different position and distance of his hand in respect to his eye. The problem is thus set to the child's understanding: how to reconcile to his comprehension the apparently contradictory facts of the _invariableness_ of the object together with the _variableness_ of its appearance. This is only possible within a space of three dimensions, in which, owing to perspective distortions and changes, these variations of projection can be reconciled with the constancy of the form of a body."