Design of buildings within the discrete space

text: Kyrylo Komarov, Mykhailo Karnaukhov "A.C.C. Vaterpas". #1'2007. P. 38-41.

ТIt is difficult to find a person who doesn’t know rules for playing tag. The game seems to be very simple: it is a field of 16 cells, 15 of which contain squares with letters. The task of the game is to place squares to arrange the letters they have in the right order. But when one tries to solve this puzzle it appears that tag-game is an absolutely different world with its own laws and rules. The process of transference in this world doesn’t correspond with the transference in another world. It is the process that determines life within this game. For instance, it is impossible to move the square plainly one cell down. It is necessary to do at least three moves.

But there is also another possibility. With the help of a screwdriver one can pick two squares and out of the field, shift them and put back into the field. Thus, if we imagine that the field of the game is a different world, these moves represent the process of teleportation within this world as the squares changed their places without running the way between these positions. If one evaluates this process from inside the game world, following happened: squares A and B suddenly disappeared; for some time there was only vacuum instead of them and then they suddenly appeared being shifted from their positions to other. Not a bad trick indeed.

But we can change the rules of this game. Let us expand the field from 16 to endless number of cells and fill them all with squares to have none empty. This way we make the transference of the first type impossible. To keep this system dynamic let us make it possible to move squares shifting them. Hence, squares ? and B change their places. This process will not be teleportation if these two squares lie in the neighbor positions. In the other case, square A has must pass through all the squares on it’s way to position B.

Let us add the third dimension. Flatness turns into space, squares into cubes, and a flat square into spatial. Thus, we get an environmental model with a fine spatial net owing to which we have a possibility to distinguish every cube that fills in a cell. We can imagine this cube to be a three-dimensional pixel {by analogy with digital technologies}. The objects that fill the space are groups of pixels alike.

But let us get down to flatness and change the point of view. Let us imagine that there are no squares. Instead, every cell is filled in with information that determines all the physical characteristics of the cell through the depiction of the material it consists of. In this case, there is a possibility to scan the information of every of two cells and to give the information from the first one to the second and vice versa. Accordingly, the experiment with picking the squares out recurs but only on another level – “informational teleportation” is being realized. Moreover, it is possible to change the information of any cell to made-up and thus to change their characteristics to those which were impossible before.

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