Charles Howard Hinton

“ The course of knowledge is like the flow of some mighty river, which, passing through the rich lowlands, gathers into itself the contributions from every valley. Such a river may well be joined by a mountain stream, which, passing with difficulty along the barren highlands, flings itself into the greater river down some precipitous descent, exhibiting at the moment of its union the spectacle of the utmost beauty of which the river system is capable. ”

“ 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. ”

“ For some moments’ space the king could distinguish nothing, but soon he became aware of a luminousness over the mid ravine. Something palely bright was floating towards him. As the brightness came nearer he saw that it was a centre wherein innumerable bright rays met, and from which innumerable bright rays went forth in every direction.
“Take that,” the old man cried. “The rays go forth unto everything in the valley. They pass through everything unto everything. Through them thou canst touch whatsoever thou wilt.” ”

“ To a being standing on the rim of a plane world a straight line absolutely shuts out the prospect before him. If the straight line is infinite it cuts his world in two; he can never hope to get beyond it. ”

“ To cause a motion is the name for the action of our soul on matter—a thing shrouded in mystery. To be the antecedent in a chain of movements is the fact which we can observe about any movement in the external world. ”

“ And here, if we reflect on it, is the sign to us that we are limited in our notions of space—that we are really in a four-dimensional world.
Watching a ship as it recedes from the shore we see that it becomes hull down before it vanishes, and know that the earth is round. And no less certainly do our two hands, in their curious likeness and yet difference, afford to us a perpetual proof of our limitation, and indicate a larger world. ”

“ If there were no difference of level the state of things in nature would be as if one spring in order to unwind had to wind up an exactly equal spring of the same amount; as if a stone falling from a height had to raise an exactly equal stone to the same height from which it fell. Under such conditions of things no motion would begin. In such a state of things all nature would be like the inhabitants of the valley when the king bore no pain, for no course would be preferable to any other course. ”

“ 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? ”

“ First of all we must notice, that if a cube be formed from a square by the movement of the square in a new direction, each point of the interior of the square traces out part of the cube. It is not only the bounding lines that by their motion form the cube, but each portion of the interior of the square generates a portion of the cube. So if a cube were to move in the fourth dimension so as to generate a four-square, every point in the interior of the cube would start de novo, and trace out a portion of the new figure uninterfered with by the other points. ”

“ Space, as we know it, is subject to a limitation.
In order to obtain an adequate conception of what this limitation is, it is necessary to first imagine beings existing in a space more limited than that in which we move. Thus we may conceive a being who has been throughout all the range of his experience confined to a single straight line. Such a being would know what it was to move to and fro, but no more. The whole of space would be to him but the extension in both directions of the straight line to an infinite distance. It is evident that two such creatures could never pass one another. ”

“ And then the king was as one who enjoys the delights of thought. For in thought, delicate shades, impalpable nuances are ever passing. It is as the blended strains of an invisible orchestra, but more subtle far, that come and go in unexpected metres, and overwhelm you with their beauty when all seemed silent. ”

“ Hence as a will we must say of it that to it all that is is present—a will which by a fiat that to our notions is being acted on rather than acting, accepting pain rather than taking pleasure, sets the course of the world in motion, which holds all in one system, which creates all activities. ”

“ A plane and a line are mere abstractions. Every portion of matter is of three dimensions. If we consider beings on a plane not as mere idealities, we must suppose them to be of some thickness. If their experience is to be limited to a plane this thickness must be very small compared to their other dimensions. Transferring our reasoning to the case of four dimensions, we come to a curious result.
If a fourth dimension exists there are two possible alternatives.
One is, that there being four dimensions, we have a three-dimensional existence only. ”

“ And so we, when we conceive that from every particle of matter there is a new direction not connected with any of those which we know, but independent of all the paths we can draw in space, and at right angles to them all—we also must invent a new name for this new direction. And let us suppose a force acting in a definite way in this new direction. Let there be a force like gravitation. If there is such a direction, there will probably be a force acting in it; for in every known direction we find forces of some kind or another acting. ”

“ No material image will serve. Organised beings seem to us so complete that any addition to them would deface their beauty. Yet were we creatures confined to a plane, the outline of a Corinthian column would probably seem to be of a beauty unimprovable in its kind. We should be unable to conceive any addition to it, simply for the reason that any addition we could conceive would be of the nature of affixing an unsightly extension to some part of the contour. Yet, moving as we do in space of three dimensions, we see that the beauty of the stately column far surpasses that of any single outline. ”

“ As soon as the king had departed from the valley the 101 beings in it began to sink into the same state of apathy as those were whom he had first found there. Those who sank first were the ones in whose lives the stress of labour or thought was the most intense, for they first felt the loss of that bearing of pain by one beyond themselves which gave them a difference of pleasure. And slowly as the accumulated enjoyment was exhausted, a chill death in life crept over the land. ”

“ Thus the prince, apprehending the cause of existence, felt that it was pain, and dimly comprehending how the king was bearing pain, and himself feeling the strenuousness of the effort of using the rays for which the frame of the inhabitants was unstrung, longed that existence itself might cease. ”

“ The inhabitants of the valley would not have been right in saying that one act of a routine caused another: But they were right in saying that the amount of sensation was constant, and that some of it passed off in a form in which they could not feel it.
And so let us not say that one action causes another. Let us not say, for example, that the downward swing of a pendulum is the cause of its upward swing. But let us simply say that the one follows the other; that the amount of energy present is the same except for the small portion that passes off into the form of heat. ”

“ Just as a being living on a plane could tell about all the faces and edges of a cube or other simple solid figure by looking at what he could see when the cube was laid on his plane, and when it was twisted and laid down again; 225 so we can tell all about the sides, faces, and edges of a higher solid.
And the project seems less uninviting if we reflect on how complicated a matter the formation of our own conceptions of a solid are. What a lot of faces and edges a cube has! And, moreover, it must be remembered that we never touch or see a solid; we only see the surface and touch the surface. ”

“ If a body, which as a whole does not undergo a twist, has one part of it twisted, then there will be the image twist in the other part of it. I say that the poker as a whole is not twisted, and all that this means is that if it be removed from the electrical influence it is found to be not charged; and the idea which we may form is this: the strings of particles are twisted like the two strips of paper round the pencil; they are twisted so that they will exactly unwind if left alone. ”

“ Everything has its own powers of resistence, of moving, of affecting us in certain ways. Thus whatever we apprehend, we apprehend as powerful. Now since this quality of powerful comes in with regard to everything, it is probably introduced by the mind, and is rather a part of the mental action in giving an idea of reality than a quality of reality. If so, when we suppose a being to have the quality of ‘all powerful,’ we are not supposing anything at all about the being, but are only extending a quality quite barren of any correspondence with the absolute nature of things. ”

“ When I say that it is easy to make a set of objects, such as the higher children use, I do not mean to say that they can be made completely in every part at once. But we can make the ends and sides of them, and we can look at the ends and sides of them as they appear to us in space, and we can make up exactly what sides come into space when the simple objects are twisted and moved. ”

“ If we think of a man as existing in four dimensions, it is hard to prevent ourselves from conceiving him as prolonged in an already known dimension. The image we form resembles somewhat those solemn Egyptian statues which in front represent well enough some dignified sitting figure, but which are immersed to their ears in a smooth mass of stone which fits their contour exactly. ”

“ Now having cut out two men, whom we will call Homo and Vir, draw a line on a piece of paper to represent the rim of the world on which they stand, and, remembering that they cannot slide over each other, move them about. It must be remembered that the figures cannot leave the plane on which they are put. They must not be turned over. The only way in which they can pass each other is by one climbing over the other’s head. They can go forwards or backwards. ”

“ And perhaps the most mischievous is the expression, a curvature of space. Now of space as it is generally used, in its accepted significance, there can be no curvature. For space means a system of positions extending uniformly in the number of dimensions we choose to fix upon.
If we take the straight line as our space, we may call it 1 space; then the set of positions follow one on after the other without bending. If the line is bent it becomes a line, not a straight line. It should not be called 1 space, but a thing in 2 space. That is, it is a bent line in a plane. ”

“ Does this will not exist in those who are true personalities, and not mere pleasure-led creatures?—have they not some of this power, the power of accepting, suffering, of determining absolutely what shall be?—a creative power which, given to each who possesses it, makes him a true personality, distinct, and not to be merged in any other—a power which determines the chain of mechanical actions, of material sequences—which creates it in the very same way in which it seems to be coming to an end—by that which, represented in material terms, is the absorption of energy into an ultimate medium ”

“ Now if in all the course of time that has been, the sensation that has been passing away was pleasure, there would by this time have been left an excess of pain, and before now we should all have sunk into apathy. So it is either pleasure and pain mixed which passes away, or pain alone. I conceive that it is pain alone. These strange doctrines are true, only curiously expressed. The being over us is continually bearing pain and so making existence pleasant to us, thus causing us to move and live. So the pain of our life is that remaining pain which he does not take. ”

“ If now, however, Homo and Mulier be placed together, a very different relationship manifests itself. They cannot injure one another, and each is framed for the most delightful converse with the other. Nothing can be more secure from the outside world than a pair of approximately the same height; each protects the sensitive edge of each, and their armoured edges and means of offence are turned against all comers, either in one direction or the other. ”

“ Where the sun’s rays grazing the earth in January pass off and merge into darkness lies a strange world.
’Tis a vast bubble blown in a substance something like glass, but harder far and untransparent. ”

“ In many respects the inhabitants of this world are far more advanced than we are, having a simpler problem—how to deal with matter in one plane—they have advanced more nearly to a complete knowledge of its properties. Yet great as their knowledge is, their performance is small. If you but reflect on one single fact, you will see how limited all their efforts must be. They cannot fix the centre of a wheel, so that it rotates round an axis. For consider a wheel—a small disk lying on their plane. The centre on every part of it touches the surface of the bubble on which all things slide freely. ”

“ But in the world as a matter of fact positive and negative motion do not together come to nothing.
As in the valley the states of pleasure and of pain did not coalesce into a state of apathy, but always succeeded one another, in simple or complicated fashion, so on the earth it is impossible from two opposite moving bodies to get stillness. If the two come into contact in opposite directions the movement does not stop, but makes its appearance in an alteration of the shape of the bodies, in a disturbance of their particles, or in some such fashion. ”

“ And the king gave him some of his rays, straight rays going forth from the prince to others.
And immediately the prince awoke as it were from a dream. And he comprehended existence, and saw that in reality the pain and the pleasure were equal. And when he had seen this, and knew the power of the rays, and how by bearing pain he could make others pass through pleasure and pain, and call those sleeping into activity; when the prince knew this, he cried out:
“One thing succeeds another in the valley; pain follows pleasure, and pleasure follows pain. But the cause of all being is in bearing pain. ”

“ 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 cognisance of beings, whose consciousness was confined to the plane. The object would not vanish by moving in any direction, but disappear instantly as a whole. ”