The fourth dimension is unknowable. If it exists and if at the same time we cannot know it, it evidently means that something is lacking in our psychic apparatus, in our faculties of perception; in other words, phenomena of the region of the fourth dimension are not reflected in our organs of sense. We must examine why this should be so, what are our defects on which this non-receptivity depends, and must find the conditions (even if only theoretically) which would make the fourth dimension comprehensible and accessible to us. These are all questions relating to psychology or, possibly, to the theory of knowledge.
Further, we know that the region of the fourth dimension (again, if it exists) is not only unknowable for our psychic apparatus, but is inaccessible in a purely physical sense. This must depend not on our defects, but on the particular properties and conditions of the region of the fourth dimension itself. It is necessary to examine what these conditions are, which make the region of the fourth dimension inaccessible to us, and to find the relation between the physical conditions of the region of the fourth dimension and the physical condition of our world. And having established this, it is necessary to see whether in the world surrounding us there is anything similar to these conditions, that is, whether there are any relations analogous to relations between the region of three dimensions and that of four dimensions.
Further, we know that the region of the fourth dimension (again, if it exists) is not only unknowable for our psychic apparatus, but is inaccessible in a purely physical sense. This must depend not on our defects, but on the particular properties and conditions of the region of the fourth dimension itself. It is necessary to examine what these conditions are, which make the region of the fourth dimension inaccessible to us, and to find the relation between the physical conditions of the region of the fourth dimension and the physical condition of our world. And having established this, it is necessary to see whether in the world surrounding us there is anything similar to these conditions, that is, whether there are any relations analogous to relations between the region of three dimensions and that of four dimensions.
