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He concludes, "Either one of two things must be true, that four-dimensional conceptions give a wonderful power of representing the thought of the East, or that the thinkers of the East must have been looking at and regarding four-dimensional existence."
Four-dimensional geometry yields numberless other patterns whose beauty and interest could not possibly be impeached patterns beyond the compass of the cleverest designer unacquainted with projective geometry. The great need of the ornamentalist is this or some other solid foundation.
Because we lack the sense of four-dimensional space, we must here have recourse to analogy, and assume three-dimensional space to be the unsensed higher region encompassing a world of two dimensions, To a hypothetical flat-man of a two-space, any portion of his plane surrounded by an unbroken line would constitute an enclosure.
Even this description gives but a very partial idea of their appearance, for they are in reality four-dimensional vortices, so that the force which comes through them and is the cause of their existence seems to well up from nowhere.
Also in order to find the ideal simplicity of expressions of the relations between events, we restrict ourselves to event-particles. Thus the life of a material particle is its adventure amid a track of event-particles strung out as a continuous series or path in the four-dimensional space-time manifold. These event-particles are the various situations of the material particle.
It has been suggested that in the infinitely minute of organic bodies there is a power of movement in a fourth dimension. Proceed still further. Behind such organic change assumed to be four-dimensional there is the determination of some will-to-live, which manifests itself to consciousness as thought and as desire. Into these the idea of space does not enter: we think of them as in time.
In looking to nature for evidence of absolute position it is of no use to recur to the four-dimensional manifold of event-particles. This manifold has been obtained by the extension of thought beyond the immediacy of observation. We shall find nothing in it except what we have put there to represent the ideas in thought which arise from our direct sense-awareness of nature.
Out beyond the dense space that surrounds all stars, the long ship probed the ever-shifting currents in the four-dimensional universe. The long ship found a low-density flaw, where space could hardly be said to exist at all. The long ship, described mathematically, was half as long as the continuum the length being inversely proportional and related only to mass.
Every electron, in other words, must be the starting point of a pathway into and a terminal point out of four-dimensional space. Here we have another familiar higher space concept. The ether of space, because it has at last found entrance, must be given a grudging hospitality in these pages, even though the mysterious stranger prove but a ghost.
This complete family of parallel levels is also evidently a family lying in the moments of the time-system β. By introducing a third time-system γ, parallel rects are obtained. Also all the points of any one time-system form a family of parallel point-tracks. Thus there are three types of parallelograms in the four-dimensional manifold of event-particles.
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