The fourth dimension

144 THE FOURTH DIMENSION

is turning from its first position all of it except the red line leaves the plane—goes absolutely out of the range of the plane being’s apprehension. But when the yellow line points straight out from the plane then the pink face comes into contact with it. Thus the same red line remaining as he saw it at first, now towards him comes a face surrounded by white and red lines.

If we call the direction to the right the unknown direction, then the line he saw before, the yellow line, goes out into this unknown direction, and the line which before went into the unknown direction, comes in, It comes in in the opposite direction to that in which the yellow line ran before; the interior of the face now

A against the plane is pink. It is

a property of two lines at right angles that, if one turns out of

Le) B (e) a given direction and stands at right angles toit, then the other

B of the two lines comes in, but

Fig. 83. runs the opposite way in that

given direction, as in fig. 88.

Now these two presentations of the cube would seem, to the plane creature like perfectly different material bodies, with only that line in common in which they both meet.

Again our cube can be turned about the yellow line. In this case the yellow square would disappear as before, but a new square would come into the plane after the cube had rotated by an angle of 90° about this line. The bottom square of the cube would come in thus in figure 89. The cube supposed in contact with the plane is rotated about the lower yellow line and then the bottom face is in contact with the plane.

Here, as before, the red line going out into the unknown dimension, the white line which before ran in the