Fifth dimension

“ So, just change the situation a bit. A four dimensional being would have the same power over this three-dimensional world. He could make things appear and disappear, simply by transporting them through the fourth dimension. ”

“ To the question, where and what is the fourth dimension, the answer must be, it is here—in us, and all about us—in a direction toward which we can never point because at right angles to all the directions that we know. ”

“ The only two-dimensional objects which we know of in this world are merely illusions, projections of the third dimension, like a shadow. It is impossible for more than one dimension to live on any single plane. ”

“ Let us now leave this supposition of framework and threads. Let us investigate the conception of a four-dimensional existence in a simpler and more natural manner—in the same way that a two-dimensional being should think about us, not as infinite in the third dimension, but limited in three dimensions as he is in two. A being existing in four dimensions must then be thought to be as completely bounded in all four directions as we are in three. All that we can say in regard to the possibility of such beings is, that we have no experience of motion in four directions. ”

“ There are two directions of inquiry in which the research for the physical reality of a fourth dimension can be prosecuted. One is the investigation of the infinitely great, the other is the investigation of the infinitely small. ”

“ Suppose a person of the Fourth Dimension, condescending to visit you, were to say, ‘Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you infer a Solid (which is of Three) ; but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.’ What would you say to such a visitor? ”

“ Hence, may we not conclude that, so far from the fourth dimension being remote and far away, being a thing of symbolic import, a term for the explanation of dubious facts by a more obscure theory, it is really the most important fact within our knowledge. Our three-dimensional world is superficial. These processes, which really lie at the basis of all phenomena of matter, escape our observation by their minuteness, but reveal to our intellect an amplitude of motion surpassing any that we can see. ”

“ Our senses and thoughts are limited to a Space of three dimensions, and we can therefore only see or know that part [Pg 181] 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 ”

“ But although this supposition might be worked out at some length, it is hard to suppose that it could afford any definite test of the physical existence of a fourth dimension. No test has been discovered which is decisive. ”

“ In other words, time is made the fourth dimension. Psychic phenomena indicate that occasionally, in some individuals, the will is capable of producing physical movements for whose geometrico-mathematical definition a four-dimensional system of co-ordinates is necessary. ”

“ And in the first place, a being in four dimensions would have to us exactly the appearance of a being in space. A being in a plane would only know solid objects as two-dimensional figures—the shapes namely in which they intersected his plane. So if there were four-dimensional objects, we should only know them as solids—the solids, namely, in which they intersect our space. Why, then, should not the four-dimensional beings be ourselves, and our successive states the passing of them through the three-dimensional space to which our consciousness is confined? ”

“ We are as unable to imagine it as a creature living in the plane figure 2 would be to imagine a direction such that moving in it the square 2 would become the cube 3. The third dimension to such a creature would be as unintelligible as the fourth is to us. And at this point we have to give up the aid that is to be got from any presentable object, and we have simply to investigate what the properties of the simplest figure in four dimensions are, by pursuing further the analogy which we know to exist between the process of formation of 2 from 1 and of 3 from 2, and finally of 4 from 3. ”

“ A natural body extends in time as well as in space, and is therefore four-dimensional; but for the analogy to hold, the object must have one dimension less than the world, like the square seen from the third dimension. ”

“ To take one of the conceptions we have already formed, the turning of a real thing into its mirror image would be an occurrence which it would be hard to explain, except on the assumption of a fourth dimension.
We know of no such turning. But there exist a multitude of forms which show a certain relation to a plane, a relation of symmetry, which indicates more than an accidental juxtaposition of parts. ”

“ The Higher Space Hypothesis is of assistance here. It is only necessary to remember that from the fourth dimension the interior of a solid is as much exposed as the interior of a plane figure is exposed from the region of the third dimension. A four-dimensional being would experience no difficulty, under suitable conditions, in possessing itself of any part of the bodily mechanism of another. ”

“ If four dimensions exist and we cannot perceive them, because the extension of matter is so small in the fourth dimension that all movements are withheld from direct observation except those which are three-dimensional, we should not observe these double rotations, but only the effects of them in three-dimensional movements of the type with which we are familiar. ”

“ If we deal with one dimension only, the figure 1, that of a segment of a straight line, is cut out of and separated from the rest of an imaginary infinitely long straight line by the two points at its extremities. ”

“ If you were to step straight out of the looking-glass every one would think you left-handed. Such a change could be accomplished by revolving you in the fourth dimension, and in no other way. Therefore a mirror will show you at any moment exactly the effect of a fourth dimension. Then why is this not a proof of the actual existence of a fourth dimension? ”

“ Such a being would be able to make but a part of himself visible to us, for a cube would be apprehended by a two-dimensional being as the square in which it stood. Thus a four-dimensional being would suddenly appear as a complete and finite body, and as suddenly disappear, leaving no trace of himself, in space, in the same way that anything lying on a flat surface, would, on being lifted, suddenly vanish out of the cognizance of beings, whose consciousness was confined to the plane. ”

“ I. Not inconceivable, my Lord, to me, and therefore still less inconceivable to my Master. Nay, I despair not that, even here, in this region of Three Dimensions, your Lordship's art may make the Fourth Dimension visible to me; just as in the Land of Two Dimensions my Teacher's skill would fain have opened the eyes of his blind servant to the invisible presence of a Third Dimension, though I saw it not.
Let me recall the past. Was I not taught below that when I saw a Line and inferred a Plane, I in reality saw a Third unrecognized Dimension, not the same as brightness, called "height"? ”

“ There is another idea which modern science has been familiarizing us with, and which is bringing us towards the same conception—that, namely, of the fourth dimension. The supposition that the actual world has four space-dimensions instead of three makes many things conceivable which otherwise would be incredible. ”

“ That the majority of persons are still feeling their way over the surface of things is attested by the general mental ineptitude for the study of solid geometry. Depth and height play little part in our physical perception. For most of us the third dimension is practically unknown beyond the reach of a few feet. A Beachey soaring aloft - why all the bravado of curve and loop? Sooner or later he will fall to his death. Ay, verily! but his is a joyous martyrdom making for the evolution of consciousness. Not always shall we crawl like flies the surface of our globe! ”

“ To examine the actions of the very small portions of matter with the view of ascertaining if there is any evidence in the phenomena for the supposition of a fourth dimension of space, we must commence by clearly defining what the laws of mechanics would be on the supposition of a fourth dimension. It is of no use asking if the phenomena of the smallest particles of matter are like—we do not know what. ”

“ Our conscious life is in three dimensions, and naturally the idea occurs whether there may not be a fourth dimension. No inhabitant of flatland could realize what life in three dimensions would mean, though, if he evolved an analytical geometry applicable to the world in which he lived, he might be able to extend it so as to obtain results true of that world in three dimensions which would be to him unknown and inconceivable. ”

“ The method necessarily to be employed in the search for the evidences of a fourth dimension, consists primarily in the formation of the conceptions of four-dimensional shapes and motions. When we are in possession of these it is possible to call in the aid of observation, without them we may have been all our lives in the familiar presence of a four-dimensional phenomenon without ever recognising its nature. ”

“ We might then suppose that the matter we know extending in three dimensions has also a small thickness in the fourth dimension; that solids are rigid in the fourth as in the other three dimensions; that liquids are too coherent to admit of their spreading out in space, and becoming thinner in the fourth dimension, under the influence of an attractive center lying outside of our space ”

“ And in that light we have to regard what of worth and meaning the Exposition has for us.
Although the scientist has found it useful on occasion to postulate the fourth dimension, he has not thought necessary as yet to put it in the category of reality; much less has the layman. Consequently the mathematician holds the sole title to its knowledge unless we recognize the claims of the medium to a fourth-dimensional insight.
There is much, however, today which points to our coming to such perception as the natural result of our evolution and quite apart from geometrical abstractions or occultism. ”

“ If any real existence confined to a superficies could be shown to exist, there would be an argument for one relative to which our three-dimensional existence is superficial. But, both on the one side and the other of the space we are familiar with, spaces either with less or more than three dimensions are merely arbitrary conceptions. ”

“ The straight rays of light break against the mirror and are turned back. Our eyes give us no account of this break and turn, and so deceive us, putting before us, like the spiritualists, the effect of a fourth dimension. These are not questions which can be decided by reference to our space intuitions, for our intuitions are confined to Euclidean space, and even there are insufficient, approximative. For instance, you suppose you can imagine a curve on a plane, and so in physics curves are taken to represent functions. ”

“ It may be that in the very large or the very minute a fourth dimension of space will have to be postulated to account for parts—but with regard to objects of ordinary magnitudes we are certainly not in a four dimensional world. ”

“ Mathematicians have for long done problems in the seventh and eighth dimensions. They have told us that you cannot tie a knot in the second dimension, because there is no up or down, and the threads would not cross—​nor in the fourth, because the knot would pull out in a new direction and would not hold. ”

“ The fourth dimension is just as much here as anywhere else. Right here around you and me things exist and go forward in the fourth dimension: but we do not see them and are not conscious of them, because we are confined to our own three. Secondly: if we name the four coordinates as Einstein does, x, y, z, and t, then we exist in x, y, and z, and move freely about in them; but are powerless to move in t. ”

“ And this is so for the reason that when we proceed in the direction of multiple dimensions, that is, one dimension piled upon another dimension or inserted between two others we are traveling in a direction which, the more we multiply our dimensions, leads us farther and farther away from the truth. ”

“ The investigator going over each of these sections, noticing all their peculiarities, constructs in his mind the shape as it originally existed from the record afforded by an indefinite number of slices. So, to form an idea of a four-dimensional figure, a series of solid shapes bounded on every side differing gradually from one another, proceeding, it may be, to the most diverse forms, has to be mentally grasped and fused into a unitary conception. ”

“ If a third dimension exists, such figures are incapable of real existence. Thus he would admit that all his real objects had a certain, though very small thickness in the unknown dimension, and that the conditions of his existence demanded the supposition of an extended sheet of matter, from contact with which in their motion his objects never diverge. ”