This is the theory. The practical work consisted in learning the names denoting these smaller cubes in connection with their positions, so that, the names being said, the small cubes meant were present to the mind, and a set of names being said, the shape, consisting of a set of cubes in definite relations to each other, came vividly before one. A complete knowledge of the block of cubes would be a complete appreciation of all the possible shapes which selections of the cubes would form, and this I strove to attain. Here at length I found real knowledge, and after a time I was able to reduce the size of the unknown still further, and to obtain a solid mass of knowledge fairly well worked all through. And now it all seemed satisfactory enough. There was real knowledge in knowledge of the arrangement; and the material cube, which must be assumed, could be made smaller and smaller, it could be turned into knowledge, thus affording a prospect of obtaining endless knowledge. Thus I found the real home of my mind, the only knowledge I had ever had, and I hoped always to continue to add to it, and always to reduce the unknown in size. Presently, too, the forms of the outward world began to fall in with this knowledge; and as the mass of known cubes became larger in number, a group of them would fairly well represent a wall, a door, a house, a simple natural object such as a stone or a fruit. Yet amidst all this delight I became conscious, dimly enough, of a self-element in the knowledge of blocks. If, putting up the block of cubes, we go to the left instead of the right, but in all other respects build up in the same way, we obtain a block which has a curious relation to the first block. The ordinary block is shown over again in Diagram III. Diagram IV. is the new block. The new block is like a looking-glass image of the old block. It is just the same, but that left and right is reversed. Also, if we take selections of blocks we get figures which are just reversed. Thus 1, 4, 7, 8, in Block III., means a figure turned to the right; in Block IV. a figure turned to the left. Again, consider the two figures formed by selecting the cubes 1, 4, 7, 8, 17, from Diagrams III. and IV. respectively. We get two figures which are just like one another as arrangements, but which we cannot turn into one another by twisting. [Illustration: Diagram III. is a block.] [Illustration: Diagram V.] Considered as arrangements in themselves, these figures and these blocks seem to be identical, for the relationships of cube to cube which are present in the one are all present in the other. But considered as shapes they are not identical. For they will not coincide. The whole matter becomes much more clear if we consider the relationship between the individual cube used and the block which it forms.