The fourth dimension

APPENDIX I 241

The fourth dimension appeared to us as the duration of the block.

If a bit of our matter were to be subjected to the same motion it would be instantly removed out of our space. Being thin in the fourth dimension it is at once taken out of our space by a motion in the fourth dimension.

But the tesseract block we represent having length in the fourth dimension remains steadily before our eyes for three minutes, when it is subjected to this transverse motion.

We have now to form representations of the other views of the same tesseract group which are possible in our space.

Let us then turn the block of tesseracts so that another face of it comes into contact with our space, and then by observing what we have, and what changes come when the block traverses our space, we shall have another view of it. The dimension which appeared as duration before will become extension in one of our known dimensions, and a dimension which coincided with one of our space dimensions will appear as duration.

Leaving catalogue cube 1 in the normal position, remoye the other two, or suppose them removed. We have in space the red, the yellow, and the white axes. Let the white axis go out into the unknown, and occupy the position the blue axis holds. Then the blue axis, which runs in that direction now will come into space. But it will not come in pointing in‘the same way that the white axis does now. It will point in the opposite sense. It will come in running to the left instead of running to the right as the white axis does now.

When this turning takes place every part of the cube 1 will disappear except the left-hand face—the orange face.

And the new cube that appears in our space will run to the left from this orange face, having axes, red, yellow, blue.

16