Thus we decompose our stream of consciousness into a series of quantitatively different and qualitatively different things, upon each of which we confer independent existence. We attribute to these different aspects of our consciousness extension, but the extension is due only to our analysis; for the qualities of pitch, loudness, colour, odour, etc., which we disentangle from each other, did not exist apart from each other, any more than do the sine and cosine curves into which we decompose an arbitrarily drawn curved line. The multiplicity of our consciousness is intensive, like the multiplicity that we see to exist in the abstract number ten. This number stands for a group of things, but its multiplicity is intensive and only exists because we are able to subdivide anything in thought to an indefinite extent. Now, so far we have only separated what we agree to regard as the elemental parts of our general perception of the environment, but it is to be noted that we have not given to these elements anything like spatial extension. We may, if we like, regard our intuition of space as that of an indefinitely large, homogeneous, empty medium which surrounds us and in which we may, in imagination, place things. So regarded it is difficult to see in what way our notion of space differs from our idea of “nothing,” a pseudo-idea incapable of analysis, except into the idea of something which might be somewhere else. The more we think about it the more we shall become convinced that space, that is the “form” of space, represents our actual or potential modes of motion, that is, our powers of exertional activity. Space, we say, has three dimensions; in all our analysis of the universe, and of the activities that we can perceive in it, this idea of movement in three dimensions, forward and backward, up and down, and right and left, occurs; and we have to recognise that in it there is something fundamental, as fundamental as the intuitive knowledge that we possess of the direction of right and left. It is because we can move in such a way that any of our motions, no matter how complex, can be resolved into the components of backward and forward, right and left, and up and down, these directions all being at right angles to each other, that we speak of our movements as three-dimensional ones. Our geometry is founded, therefore, on concepts derived from our modes of activity; and there is nothing in the universe, apart from our own activity, that makes this the only geometry possible to us. Euclidean geometry does not depend on the constitution of the external universe, but on the nature of the organism itself.