Fig. 9
Now, if we continued in this manner till we had a very large block of thousands of cubes in each side Corvus would, in comparison to the whole block, be a minute point of a cubic shape, and Cuspis would be a mere line of minute cubes, which would have length, but very small depth or height. Next, if we suppose this much sub-divided block to be reduced in size till it becomes one measuring an inch each way, the cubes of which it consists must each of them become extremely minute, and the corner cubes and line cubes would be scarcely discernible. But the cubes on the faces would be just as visible as before. For instance, the cubes composing Mœna would stretch out on the face of the cube so as to fill it up. They would form a layer of extreme thinness, but would cover the face of the cube (all of it except the minute lines and points). Thus we may use the words Corvus and Nugæ, etc., to denote the corner-points of the cube, the words Mœna, Syce, Mel, Alvus, Proes, Murex, to denote the faces. It must be remembered that these faces have a thickness, but it is extremely minute compared with the cube. Mala would denote all the cubes of the interior except those, which compose the faces, edges, and points. Thus, Mala would practically mean the whole cube except the colouring on it. And it is in this sense that these words will be used. In the models, the Gold point is intended to be a Corvus, only it is made large to be visible; so too the Orange line is meant for Cuspis, but magnified for the same reason. Finally, the 27 names of cubes, with which we began, come to be the names of the points, lines, and faces of a cube, as shown in the diagram ([Fig. 9]). With these names it is easy to express what a plane-being would see of any cube. Let us suppose that Mœna is only of the thickness of his matter. We suppose his matter to be composed of particles, which slip about on his plane, and are so thin that he cannot by any means discern any thickness in them. So he has no idea of thickness. But we know that his matter must have some thickness, and we suppose Mœna to be of that degree of thickness. If the cube be placed so that Mœna is in his plane, Corvus, Cuspis, Nugæ, Far, Sors, Callis, Ilex and Arctos will just come into his apprehension; they will be like bits of his matter, while all that is beyond them in the direction he does not know, will be hidden from him. Thus a plane-being can only perceive the Mœna or Syce or some one other face of a cube; that is, he would take the Mœna of a cube to be a solid in his plane-space, and he would see the lines Cuspis, Far, Callis, Arctos. To him they would bound it. The points Corvus, Nugæ, Sors, and Ilex, he would not see, for they are only as long as the thickness of his matter, and that is so slight as to be indiscernible to him.
We must now go with great care through the exact processes by which a plane-being would study a cube. For this purpose we use square slabs which have a certain thickness, but are supposed to be as thin as a plane-being’s matter. Now, let us take the first set of 81 cubes again, and build them from 1 to 27. We must realize clearly that two kinds of blocks can be built. It may be built of 27 cubes, each similar to Model 1, in which case each cube has its regions coloured, but all the cubes are alike. Or it may be built of 27 differently coloured cubes like Set 1, in which case each cube is coloured wholly with one colour in all its regions. If the latter set be used, we can still use the names Mœna, Alvus, etc. to denote the front, side, etc., of any one of the cubes, whatever be its colour. When they are built up, place a piece of card against the front to represent the plane on which the plane-being lives. The front of each of the cubes in the front of the block touches the plane. In previous chapters we have supposed Mœna to be a Blue square. But we can apply the name to the front of a cube of any colour. Let us say the Mœna of each front cube is in the plane; the Mœna of the Gold cube is Gold, and so on. To represent this, take nine slabs of the same colours as the cubes. Place a stiff piece of cardboard (or a book-cover) slanting from you, and put the slabs on it. They can be supported on the incline so as to prevent their slipping down away from you by a thin book, or another sheet of cardboard, which stands for the surface of the plane-being’s earth.
We will now give names to the cubes of Block 1 of the 81 Set. We call each one Mala, to denote that it is a cube. They are written in the following list in floors or layers, and are supposed to run backwards or away from the reader. Thus, in the first layer, Frenum Mala is behind or farther away than Urna Mala; in the second layer, Ostrum is in front, Uncus behind it, and Ala behind Uncus.
| Third, or Top Floor. | - | | Mars Mala | Merces Mala | Tyro Mala | |
| Spicula Mala | Mora Mala | Oliva Mala | ||||
| Comes Mala | Tibicen Mala | Vestis Mala | ||||
| Second, or Middle Floor. | - | | Ala Mala | Cortis Mala | Aer Mala | |
| Uncus Mala | Pallor Mala | Tergum Mala | ||||
| Ostrum Mala | Bidens Mala | Scena Mala | ||||
| First, or Bottom Floor. | - | | Sector Mala | Hama Mala | Remus Mala | |
| Frenum Mala | Plebs Mala | Sypho Mala | ||||
| Urna Mala | Moles Mala | Saltus Mala | ||||
These names should be learnt so that the different cubes in the block can be referred to quite easily and immediately by name. They must be learnt in every order, that is, in each of the three directions backwards and forwards, e.g. Urna to Saltus, Urna to Sector, Urna to Comes; and the same reversed, viz., Comes to Urna, Sector to Urna, etc. Only by so learning them can the mind identify any one individually without even a momentary reference to the others around it. It is well to make it a rule not to proceed from one cube to a distant one without naming the intermediate cubes. For, in Space we cannot pass from one part to another without going through the intermediate portions. And, in thinking of Space, it is well to accustom our minds to the same limitations.
Urna Mala is supposed to be solid Gold an inch each way; so too all the cubes are supposed to be entirely of the colour which they show on their faces. Thus any section of Moles Mala will be Orange, of Plebs Mala Black, and so on.
Fig. 10.