On comparing the two lists of the Mala view and Vesper view, it will be seen that the cubes presented in the Vesper view are new sides of the tessaract, and that the arrangement of them is different from that in the Mala view. (This is analogous to the changes in the slabs from the Moena to Alvus view of the cubic Block.) Of course, the Vespers of all these tessaracts are not visible at once in our space, any more than are the Moenas of all three walls of a cubic Block to a plane-being. But if the tessaractic Set be supposed to move through space in the unknown direction at the rate of an inch a minute, the Second Block will present its Vespers after the First Block has lasted a minute. The relative position of the Mala Block and the Vesper Block may be represented in our space as in the diagram, [Fig. 20]. But it must be distinctly remembered that this arrangement is quite conventional, no more real than a plane-being’s symbolization of the Moena Wall and the Alvus Wall of the cubic Block by the arrangement of their Moena and Alvus faces, with the solidity omitted, along one of his known directions.

The Vespers of the First and Second Blocks cannot be in our space simultaneously, any more than the Moenas of all three walls in plane space. To render their simultaneous presence possible, the cubic or tessaractic Block or Set must be broken up, and its parts no longer retain their relations. This fact is of supreme importance in considering higher space. Endless fallacies creep in as soon as it is forgotten that the cubes are merely representative as the slabs were, and the positions in our space merely conventional and symbolical, like those of the slabs along the plane. And these fallacies are so much fostered by again symbolizing the cubic symbols and their symbolical positions in perspective drawings or diagrams, that the reader should surrender all hope of learning space from this book or the drawings alone, and work every thought out with the cubes themselves.

If we want to see what each individual cube of the tessaractic faces presented to us in the last example is like, we have only to consider each of the Malas similar in its parts to Model 1, and each of the Vespers to Model 5. And it must always be remembered that the cubes, though used to represent both Mala and Vesper faces of the tessaract, mean as great a difference as the slabs used for the Moena and Alvus faces of the cube.

If the tessaractic Set move Kata through our space, when the Vesper faces are presented to us, we see the following parts of the tessaract Urna (and, therefore, also the same parts of the other tessaracts):

(1) Urna Vesper, which is Model 5.

(2) A parallel section between Urna Vesper and Urna Idus, which is Model 11.

(3) Urna Idus, which is Model 6.

When Urna Idus has passed Kata our space, Moles Vesper enters it; then a section between Moles Vesper and Moles Idus, and then Moles Idus. Here we have evidently observed the tessaract more minutely; as it passes Kata through our space, starting on its Vesper side, we have seen the parts which would be generated by Vesper moving along Cuspis—that is Ana.

Two other arrangements of the tessaracts have to be learnt besides those from the Mala and Vesper aspect. One of them is the Pluvium aspect. Build up the Set in Z X Y, letting Arctos run Z, Cuspis X, and Ops Y. In the common plane Moena, Urna Pluvium coincides with Urna Mala, though they cannot be in our space together; so too Moles Pluvium with Moles Mala, Ostrum Pluvium with Ostrum Mala. And lying towards us, or Y, is now that tessaract which before lay in the W direction from Urna, viz., Thyrsus. The order will therefore be the following (a star denotes the cube whose corner is at point of intersection of the axes, and the name Pluvium must be understood to follow each of the names):

ZXYW
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