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Such a disappearance would constitute an occult phenomenon in a world of two dimensions. Correspondingly, an evanishment from any three-dimensional enclosure such as a room with locked doors and windows might be effected by means of a movement in the fourth dimension.
This regular solid of four-dimensional space consists of sixteen cells, each a regular tetrahedron, thirty-two triangular faces, twenty-four edges and eight vertices. It is the correlative of the octahedron of three-dimensional space. First it is necessary to establish our four axes, all mutually at right angles.
I sat on the edge of a table ... and where I sat stood a supposed Greek vase of great antiquity and value. It is a law that prevails in three-dimensional space that two objects cannot occupy the same place at one time. I dislodged the vase. It came to the floor in a crash ... which stopped the music ... which stopped everything. There fell a dead silence.
West African manufacturing demonstrated a considerable amount of skill in a wide variety of crafts. These included basket-weaving, pottery making, woodworking and iron-working. Archeological evidence shows that West Africans were making pottery and terracotta sculpture as much as two thousand years ago. Three-dimensional forms seem to have held a particular interest for West African artists.
Upon these facts are constructed the laws of three-dimensional space which serve to carry mathematical thought to the remoter conceptual spaces of which we have spoken. It may seem that we are recording only one phase of mental evolution, but in fact we are dealing with a larger matter, namely, with the progressive evolution of knowledge in the Kantian category of number.
They didn't know that it was a molecule-model kit, but they soon found that the sticks would go into holes in the balls, and that they could be built into three-dimensional designs. This was much more fun than the colored stones. They made a few experimental shapes, then dismantled them and began on a single large design.
Epilogue The three-dimensional, moving, talking, almost living picture, being shown simultaneously in all the viewing areas throughout the innumerable planets of the Galaxy, faded out and the image of an aged, white-bearded Norlaminian appeared and spoke in the Galactic language.
We are there in the midst of a three-dimensional world, and the movements of the persons or of the animals or even of the lifeless things, like the streaming of the water in the brook or the movements of the leaves in the wind, strongly maintain our immediate impression of depth. Many secondary features characteristic of the motion picture may help.
The latter, knowing only length and breadth, and nothing of up or down, would see his three-dimensional friend as a line only. The moment the three-dimensional solid rose above or sank below his line of vision, it would seem to have disappeared like an apparition, although as really present as before. To the two-dimensional mind it would seem as though the solid were a ghost.
After Roger left them, Alan and Quantrell walked on through the Enclave together. Alan wondered whether it wasn't a good idea to have gone to the feelie with Roger after all; the Enclave was starting to depress him, too, and those three-dimensional shows had a way of taking your mind off things. But he was curious about Quantrell.
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