Why not have beings for every kind of direction? Why are we three-dimensional beings unaware of any two-dimensional beings? How could beings of four dimensions escape detection as regards their three dimensions; and how could a being of one dimension, a fourth dimension, interfere with beings of dimensions to which it does not belong? The three-dimensional doctrine of space must be regarded with suspicion; for such a division merely selects certain few factors which are not what they appear to be. […] We may turn now to more general considerations. We look upon a piece of land, and we remark that there is _space_ to build twenty houses on; so, too, we glance into our purse, and say that it is _empty_. Now note, not only is vision three-dimensionsal, but it's field is unbroken by any points of no vision. Hence we never see nothing, never really gaze into vacancy. What do we mean, then, by an _empty_ purse? There is but one answer. Certain lines are observed, where certain other lines or complexes are imaginable. Instead of the worn lining, sovereigns might be seen; instead of heaps of refuse, houses might be seen. It is not that a full purse is an empty purse plus coins, it is a purse the lining of which is made of gold and not leather. […] What, then, is meant by _space_ and _empty space_? Are they a mysterious somewhere where lines are placed, a hole without walls where things are situated? One fails to catch the sense of these phrases, except in terms of lines. If the nearest row of houses which is within the view were pulled down, I could see the exterior of the next row behind it. So, too, the exterior of the row to be pulled down could be made to vanish, by building in front of it, by changing the lines. Similarly, since only one line in one position can be seen on a smooth two-dimensional plane, two things cannot simultaneously occupy the same space. Again, most lines may be displaced by others, and hence men speak of latent lines, of space. Infinite space, except as meaning infinite expanse, or infinite endeavour to see, is infinite nonsense: you might as well say you could imagine a room without boundaries. If we could stand on an overhanging promontory of a flat world and look outwards, we should have the immediate environment of the eyes, and around us, perhaps, some grey expanse. This expanse might be imagined indefinitely retreating as we advance into the gloom; but wipe out the lines, wipe out sight, and not space but nothing is left. Assume that we are beings but of one sense, that of vision, and there can be little doubt that by space we mean certain line relations and details, and that apart from these relations the word has no meaning. Thus space, being a relation between systems, cannot exist prior to systems, nor can it survive them. Large, small, round, square , are visual terms. When we are once convinced that space is not a glove into which the world fits, our difficulties are soon overcome.