The fourth dimension

170 THE FOURTH DIMENSION

as drawn by a plane being, are not the cubes themselves, but represent the faces or the sections of acube. Thus in the plane being’s diagram a cube of twenty-seven cubes “null” represents a cube, but is really, in the normal position, the orange square of a null cube, and may be called null, orange square.

A plane being would save himself confusion if he named his representative squares, not by using the names of the cubes simply, but by adding to the names of the cubes a word to show what part of a cube his representative square was.

Thus a cube null standing against his plane touches it by null orange face, passing through his plane it has in the plane a square as trace, which is null white section, if we use the phrase white section to mean a section drawn perpendicular to the white line. In the same way the cubes which we take as representative of the tesseract are not the tesseract itself, but definite faces or sections of it. In the preceding figures we should say then, not null, but “null tesseract ochre cube,” because the cube we actually have is the one determined by the three axes, white, red, yellow.

There is another way in which we can regard the colour nomenclature of the boundaries of a tesseract.

Consider a null point to move tracing out a white line one inch in length, and terminating in a null point, see fig. 103 or in the coloured plate.

Then consider this white line with its terminal points itself to move in a second dimension, each of the points traces out a line, the line itself traces out an area, and gives two lines as well, its initial and its final position.

Thus, if we call “a region” any element of the figure, such as a point, or a line, etc., every “region” in moving traces out a new kind of region, “a higher region,” and gives two regions of its own kind. an initial and a final

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