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The locus of intersection of two moments is the assemblage of abstractive elements covered by both of them. Now two moments of the same temporal series cannot intersect. Two moments respectively of different families necessarily intersect. Accordingly in the instantaneous space of a moment we should expect the fundamental properties to be marked by the intersections with moments of other families. If M be a given moment, the intersection of M with another moment A is an instantaneous plane in the instantaneous space of M; and if B be a third moment intersecting both M and A, the intersection of M and B is another plane in the space M. Also the common intersection of A, B, and M is the intersection of the two planes in the space M, namely it is a straight line in the space M. An exceptional case arises if B and M intersect in the same plane as A and M. Furthermore if C be a fourth moment, then apart from special cases which we need not consider, it intersects M in a plane which the straight line (A, B, M) meets. Thus there is in general a common intersection of four moments of different families. This common intersection is an assemblage of abstractive elements which are each covered (or 'lie in') all four moments. The three-dimensional property of instantaneous space comes to this, that (apart from special relations between the four moments) any fifth moment either contains the whole of their common intersection or none of it. No further subdivision of the common intersection is possible by means of moments. The 'all or none' principle holds. This is not an
The two boundaries must have a common portion which is in fact a continuous three-dimensional locus of event-particles in the four-dimensional manifold. A three-dimensional locus of event-particles which is the common portion of the boundary of two adjoined events will be called a 'solid. A solid may or may not lie completely in one moment.
That is another thing you have given us. Attend!" At one end of the room, as upon a three-dimensional screen, the four Terrestrials saw themselves seated in the control-room of the Skylark.
It is by means of this correlation that the one three-dimensional space of physics is constructed; and it is because of the unconscious performance of this correlation that the distinction between perspective space and the percipient's private space has been blurred, with disastrous results for the philosophy of physics.
The artist who has given us a dozen first-rate things superb nudes, "felt" as solid, three-dimensional forms, and realized as such is always being forestalled by an astonishing caricaturist who can knock you off something brilliant, rapid, and telling while you wait for the boat.
Because it preserves the full three-dimensional presence of the body, sculpture is, next to the drama, the most realistic of the arts. This realism is not, however, an unmixed advantage for general appreciation.
The ship as a whole simply moves on a surface. The problem of three-dimensional movement does not ordinarily concern its steering. And thus with regard to ourselves all those movements and activities which characterize our bodily organs are three-dimensional; we never need to consider the ampler movements.
Goethe, on the other hand, ascribed to the human spirit the power of seeing the phenomenal world in all its three-dimensional multiplicity; that is, of seeing it in perspective and distinguishing between foreground and background.4 Things in the foreground he called ur-phenomena. Here the idea creatively determining the relevant field of facts comes to its purest expression.
For a finite event there is a continuity of boundary; for a duration the boundary consists of those event-particles which are covered by either of the two bounding moments. Thus the boundary of a duration consists of two momentary three-dimensional spaces. An event will be said to 'occupy' the aggregate of event-particles which lie within it.
Now for a leap into the abyss, which won't be so terrifying, since it involves no change of method. The cube must move into the fourth dimension, developing there a hyper-cube. This is impossible, for the reason the cube would have to move out of our space altogether three-dimensional space will not contain a hyper-cube.
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