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The theory is that the EPC passes from one moment, on one time-line, to the next moment on the next line, so that the true passage of the EPC from moment to moment is a two-dimensional diagonal.
When at the end of a day he lays aside his clothes that two-dimensional sheath of the three-dimensional body it is in full assurance that his body in turn will be abandoned by the inwardly retreating consciousness, and that he will range wherever he wills during the hours of sleep, clothed in his subtle four-dimensional body, related to the physical body as that is related to the clothes it wears.
In this way creatures which cannot leave the spherical surface, and cannot even peep out from the spherical surface into three-dimensional space, might discover, merely by experimenting with discs, that their two-dimensional "space" is not Euclidean, but spherical space.
For, although a building is a three-dimensional solid in reality, each view of it is a two-dimensional surface, bounded by lines and divided and diversified within by other lines. Now these lines have their life and beauty like the lines of a picture.
Ozma was the first to awaken. She felt refreshed and envigorated. The sound of birds chirping and the warm sun on her face brought her out of her deep restful slumber. The first thing that her eyes focused upon was a two-dimensional shadowy shape moving toward her along the ground in much the same manner as the shadow of an airplane would.
Her married years had taken her away from the environment which had enabled him to live his busy, uncomplicated life; where, the only medical man in a growing community, he had learned to form his own sturdy decisions and then to abide by them. Black and white, right and wrong, the proper course and the improper course he lived in a sort of two-dimensional ethical world.
Were he confined within it, escape would be impossible by any means known to him. Had he the ability to move in the third dimension, however, he could rise, pass over the enclosing line without disturbing it, and descend on the other side. The moment he forsook the plane he would disappear from two-dimensional space.
Its particular property of being closed prevents it from being definable as an abstractive element. When a moment intersects an event, it also intersects the boundary of that event. This locus, which is the portion of the boundary contained in the moment, is the bounding surface of the corresponding volume of that event contained in the moment. It is a two-dimensional locus.
Thus in the four-dimensional geometry of all event-particles there is a two-dimensional locus which is the locus of all event-particles on points lying on the straight line r. I will call this locus of event-particles the matrix of the straight line r. A matrix intersects any moment in a rect. Thus the matrix of r intersects the moment M in a rect ρ.
Our senses and thoughts are limited to a Space of three dimensions, and we can therefore only see or know that part of the Absolute which is or can be represented to us in three dimensions; a being whose senses were limited to a Universe of one dimension namely, a line, could have no real knowledge of another being who was in a Universe of two dimensions namely, a flat surface, except so far as the two-dimensional being could be represented within his line of sensation; so also the two-dimensional being, on a plane, could have no true knowledge of a being like ourselves in a Universe of three dimensions.
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