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168<br />
THE FOURTH DIMENSION<br />
first and last section. Hence the light blue tesseracts<br />
increase in number in two ways—in the right and left,<br />
and in the fourth dimension. <strong>The</strong>y ultimately form<br />
what we may call a plane surface.<br />
Now all those regions which contain a mixture of two<br />
simple colours, white, yellow, red, blue, increase in two<br />
ways. On the other hand, those which contain a mixture<br />
of three colours increase in three ways. Take, for instance,<br />
the ochre region; this has three colours, white, yellow,<br />
red; and in the cube itself it increases in three ways.<br />
Now regard the orange region; if we add blue to this<br />
we get a brown. <strong>The</strong> region of the brown tesseracts<br />
extends in two ways on the left of the second block,<br />
No. 2 in the figure. It extends also from left to right in<br />
succession from one section to another, from section 2<br />
to section 3 in our figure.<br />
Hence the brown tesseracts increase in number in three<br />
dimensions upwards, to and fro, fourth dimension. Hence<br />
they form a cubic, a three-dimensional region; this region<br />
extends up and down, near and far, and in the fourth<br />
direction, but is thin in the direction from left to right.<br />
It is a cube which, when the complete tesseract is represented<br />
in our space, appears as a series of faces on the<br />
successive cubic sections of the tesseract. Compare fig.<br />
103 in which the middle block, 2, stands as representing a<br />
great number of sections intermediate between 1 and 3.<br />
In a similar way from the pink region by addition of<br />
blue we have the light purple region, which can be seen<br />
to increase in three ways as the number of divisions<br />
becomes greater. <strong>The</strong> three ways in which this region of<br />
tesseracts extends is up and down, right and left, fourth<br />
dimension. Finally, therefore, it forms a cubic mass of<br />
very small tesseracts, and when the tesseract is given in<br />
space sections it appears on the faces containing the<br />
upward and the right and left dimensions.