Hinton - The Fourth Dimension.pdf
Hinton - The Fourth Dimension.pdf Hinton - The Fourth Dimension.pdf
156 THE FOURTH DIMENSION taking the place of the preceding one. These sections appear to the plane being, counting from the first, to exactly coincide each with the preceding one. But the section of the string occupies a different plane in each to that which it does in the preceding section. The section of the string appears in the position marked by the dots. Hence the slant of the string appears as a motion in the frame work marked out by the cube sides. If we suppose the motion of the cube not be recognised, then the string appears to the plane being as a moving point. Hence extension on the unknown dimension appears as duration. Extension sloping in the unknown direction appears as continuous movement.
CHAPTER XII THE SIMPLEST FOUR-DIMENSIONAL SOLID A PLANE being, in learning to apprehend solid existence, must first of all realise that there is a sense of direction altogether wanting to him. That which we call right and left does not exist in his perception. He must assume a movement in a direction, and a distinction of positive and negative in that direction, which has no reality corresponding to it in the movements he can make. This direction, this new dimension, he can only make sensible to himself by bringing in time, and supposing that changes, which take place in time, are due to objects of a definite configuration in three dimensions passing transverse to his plane, and the different sections of it being apprehended as changes of one and the same plane figure. He must also acquire a distinct notion about his plane world, he must no longer believe that it is the all of space, but that space extends on both side of it. In order, then, to prevent his moving off in this unknown direction, he must assume a sheet, an extended solid sheet, in two dimensions, against which, in contact with which, all his movements take place. When we come to think of a four-dimensional solid, what are the corresponding assumptions which we must make? We must suppose a sense which we have not, a sense 157
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156<br />
THE FOURTH DIMENSION<br />
taking the place of the preceding one.<br />
<strong>The</strong>se sections appear to the plane being, counting from<br />
the first, to exactly coincide each with the preceding one.<br />
But the section of the string occupies a different plane in<br />
each to that which it does in the preceding section. <strong>The</strong><br />
section of the string appears in the position marked by<br />
the dots. Hence the slant of the string appears as a<br />
motion in the frame work marked out by the cube sides.<br />
If we suppose the motion of the cube not be recognised,<br />
then the string appears to the plane being as a moving<br />
point. Hence extension on the unknown dimension<br />
appears as duration. Extension sloping in the unknown<br />
direction appears as continuous movement.
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