The fourth dimension

232 THE FOURTH DIMENSION

plane being would represent three-dimensional space, only one of the catalogue cubes and one of the three blocks is needed.

APPLICATION TO THE STEP FROM PLANE TO SOLID.

Look at fig. 1 of the views of the tesseract, or, what comes to the same thing, take catalogue cube No, 1 and place it before you with the red line running up, the white line running to the right, the yellow line running away. ‘The three dimensions of space are then marked out by these lines or axes. Now take a piece of cardboard, or a book, and place it so that it forms a wall extending up and down not opposite to you, but running away parallei to the wall of the room on your left hand.

Placing the catalogue cube against this wall we see that it comes into contact with it by the red and yellow lines, and by the included orange face.

In the plane being’s world the aspect he has of the cube would be a square surrounded by red and yellow lines with grey points.

Now, keeping the red line fixed, turn the cube about it so that the yellow line goes out to the right, and the white line comes into contact with the plane.

In this case a different aspect is presented to the plane being, a square, namely, surrounded by red and white lines and grey points. You should particularly notice that when the yellow line goes out, at right angles to the plane, and the white comes in, the latter does not run in the same sense that the yellow did.

From the fixed grey point at the base of the red line the yellow line ran away from you. The white line now runs towards you. This turning at right angles makes the line which was out of the plane before, come into it