Charles Howard Hinton

“ In none of his writings, as far as we know, did he carry it to its legitimate conclusion on the side of matter, but in the direction of the formal qualities he was led to his limiting conception of that existence of pure form which lies beyond all known determination of matter. The unmoved mover of all things is Aristotle’s highest principle. Towards it, to partake of its perfection all things move. The universe, according to Aristotle, is an active process—he does not adopt the illogical conception that it was once set in motion and has kept on ever since. ”

“ We must suppose a direction in which we can never point extending from every point of our space. We must draw a distinction between a geometrical cube and a cube of real matter. The cube of real matter we must suppose to have an extension in an unknown direction, real, but so small as to be imperceptible by us. From every point of a cube, interior as well as exterior, we must imagine that it is possible to draw a line in the unknown direction. ”

“ Parmenides, and the Asiatic thinkers with whom he is in close affinity, propound a theory of existence which is in close accord with a conception of a possible relation between a higher and a lower dimensional space. This theory, prior and in marked contrast to the main stream of thought, which we shall afterwards describe, forms a closed circle by itself. It is one which in all ages has had a strong attraction for pure intellect, and is the natural mode of thought for those who refrain from projecting their own volition into nature under the guise of causality. ”

“ Our space conceptions are so intimately connected with those which we derive from the existence of gravitation that it is difficult to realise the condition of a plane being, without picturing him as in material surroundings with a definite direction of up and down. Hence the necessity of our somewhat elaborate scheme of representation, which, when its import has been grasped, can be dispensed with for the simpler one of a thin object slipping over a smooth surface, which lies in front of us. ”

“ We have never had a demand to conceive what our own most intimate powers are. But, [Pg 258] just as little as by immersing himself in the steering of his ship over the plane surface of the ocean, a captain can lose the faculty of thinking about what he actually does, so little can the soul lose its own nature. It can be roused to an intuition that is not derived from the experience which the senses give. ”

“ Thus, in exploring the facts of geometry from the simplest logical relations to the properties of space of any number of dimensions, we are merely observing ourselves, becoming aware of the conditions under which we must perceive. Do any phenomena present themselves incapable of explanation under the assumption of the space we are dealing with, then we must habituate ourselves to the conception of a higher space, in order that our logic may be equal to the task before us. ”

“ In reply to this I would remark that a plane being having one less dimension than our three would have one-third of our possibilities of motion, while we have only one-fourth less than those of the higher space. It may very well be that there may be a certain amount of freedom of motion which is demanded as a condition of an organised existence, and that no material existence is possible with a more limited dimensionality than ours. ”

“ Plato said that behind the phenomena of mind that Meno’s slave boy exhibited, there was a vast, an infinite perspective. And his singularity, his originality, comes out most strongly marked in this, that the perspective, the complex phenomena beyond were, according to him, phenomena of personal experience. A footprint in the sand means a man to a being that has the conception of a man. But to a creature that has no such conception, it means a curious mark, somehow resulting from the concatenation of ordinary occurrences. ”

“ In those complex structures which men build up and direct, such as a ship or a railway train (and which, if seen by an observer of such a size that the men guiding them were invisible, would seem to present some of the phenomena of life) the appearance of animation is not due to any diffusion of life in the material parts of the structure, but to the presence of a living being.
The old hypothesis of a soul, a living organism within the visible one, appears to me much more rational than the attempt to explain life as a form of motion. ”

“ All that is necessary is to present some few of those appearances which, while inconsistent with three-dimensional matter, are yet consistent with our formal knowledge of four-dimensional matter, in order for the soul to wake up and not begin to learn, but of its own intimate feeling fill up the gaps in the presentiment, grasp the full orb of possibilities from the isolated points presented to it. ”

“ He takes account of everything; he does not separate matter and the manifestation of matter; he fires all together in a conception of a vast world process in which everything takes part—the motion of a grain of dust, the unfolding of a leaf, the ordered motion of the spheres in heaven—all are parts of one whole which he will not separate into dead matter and adventitious modifications. ”

“ If the place of this universe is a meeting of two, there would be a one-sideness to space. If it lies so that what stretches away in one direction in the unknown is unlike what stretches away in the other, then, as far as the movements which participate in that dimension are concerned, there would be a difference as to which way the motion took place. This would be shown in the dissimilarity of phenomena, which, so far as all three-space movements are concerned, were perfectly symmetrical. To take an instance, merely, for the sake of precising our ideas, not for any inherent probability in it ”

“ According to Parmenides of the school of Elea the all is one, unmoving and unchanging. The permanent amid the transient—that foothold for thought, that solid ground for feeling on the discovery of which depends all our life—is no phantom; it is the image amidst deception of true being, the eternal, the unmoved, the one. ”

“ As the real world is to this shadow world, so is the higher world to our world. I accept his analogy. As our world in three dimensions is to a shadow or plane world, so is the higher world to our three-dimensional world. That is, the higher world is four-dimensional; the higher being is, so far as its existence is concerned apart from its qualities, to be sought through the conception of an actual [Pg 3] existence spatially higher than that which we realise with our senses.
Here you will observe I necessarily leave out all that gives its charm and interest to Plato’s writings. ”

“ Now, if rotation in one direction corresponds to positive electricity, rotation in the opposite direction corresponds to negative electricity, and the smallest electrified particles would have their charges reversed by being turned over—an absurd supposition.
If we fix on a mode of motion as a definition of electricity, we must have two varieties of it, one for positive and one for negative; and a body possessing the one kind must not become possessed of the other by any change in its position. ”

“ From every point a line can be drawn in a direction unknown to him, and there is a solidity of a kind greater than that which he knows. This solidity can only be realised by him by his supposing an unknown direction, by motion in which what he conceives to be solid matter instantly disappears. The higher solid, however, which extends in this dimension as well as in those which he knows, lasts when a motion of that kind takes place, different sections of it come consecutively in the plane of his apprehension, and take the place of the solid which he at first conceives to be all. ”

“ If we suppose the being represented by the piece of paper to have no knowledge of the thickness by which he projects above the surface of the table, it is obvious that he can have no knowledge of objects of a similar description, except by the contact with their edges. His body and the objects in his world have a thickness of which however, he has no consciousness. Since the direction stretching up from the table is unknown to him he will think of the objects of his world as extending in two dimensions only. ”

“ Plato uses this illustration to portray the relation between true being and the illusions of the sense world. He says that just as a man liberated from his chains could learn and discover that the world was solid and real, and could go back and tell his bound companions of this greater higher reality, so the philosopher who has been liberated, who has gone into the thought of the ideal world, into the world of ideas greater and more real than the things of sense, can come and tell his fellow men of that which is more true than the visible sun—more noble than Athens, the visible state. ”

“ That eternal corrector of our aspirations and ideals, the material universe draws sublimely away from the simplest things we can touch or handle to the infinite depths of starry space, in one and all uninfluenced by what we think or feel, presenting unmoved fact to which, think it good or think it evil, we can but conform, yet out of all that impassivity with a reference to something beyond our individual hopes and fears supporting us and giving us our being. ”

“ It can be argued that the occurrence of symmetry in two dimensions involves the existence of a three-dimensional process, as when a stone falls into water and makes rings of ripples, or as when a mass of soft material rotates about an axis. It can be argued that symmetry in any number of dimensions is the evidence of an action in a higher dimensionality. Thus considering living beings, there is an evidence both in their structure, and their different mode of activity, of a something coming in from without into the inorganic world. ”

“ Thinking of such a being in man, was not Plato’s line well divided?
It is noteworthy that, if Plato omitted his doctrine of the independent origin of ideas, he would present exactly the four-dimensional argument; a real thing as we think it is an idea. A plane being’s idea of a square object is the idea of an abstraction, namely, a geometrical square. Similarly our idea of a solid thing is an abstraction, for in our idea there is not the four-dimensional thickness which is necessary, however slight, to give reality. ”

“ But in the lofty march of his reason he never loses sight of the whole; and that wherein our views differ from his lies not so much in a superiority of our point of view, as in the fact which he himself enunciates—that it is impossible for one principle to be valid in all branches of enquiry. The conceptions of one method of investigation are not those of another; and our divergence lies in our exclusive attention to the conceptions useful in one way of apprehending nature rather than in any possibility we find in our theories of giving a view of the whole transcending that of Aristotle. ”

“ Kant asserts that whenever we think we think of objects in space and time, but he denies that the space and time exist as independent entities. He goes about to explain them, and their universality, not by assuming them, as most other philosophers do, but by postulating their absence. How then does it come to pass that the world is in space and time to us?
Kant takes the same position with regard to what we call nature—a great system subject to law and order. “How do you explain the law and order in nature?” we ask the philosophers. ”

“ And as the plane is the matter relatively to determinations in the plane, so the plane itself exists in virtue of the determination of space. A plane is that wherein formless space has form superimposed on it, and gives an actuality of real relations. We cannot refuse to carry this process of reasoning a step farther back, and say that space itself is that which gives form to higher space. As a line is the determination of a plane, and a plane of a solid, so solid space itself is the determination of a higher space. ”

“ It is indeed curious that we are able to talk and converse on every subject of thought except the fundamental one of space. The only way of speaking about the spatial configurations that underlie every subject of discursive thought is a co-ordinate system of numbers. This is so awkward and incommodious that it is never used. In thinking also, in realising shapes, we do not use it; we confine ourselves to a direct visualisation. ”

“ When we have formed the conception of four-dimensional motion, we can ask a rational question of Nature. Before we have elaborated our conceptions we are asking if an unknown is like an unknown—a futile inquiry.
As a matter of fact, four-dimensional movements are in every way simple and more easy to calculate than three-dimensional movements, for four-dimensional movements are simply two sets of plane movements put together. ”

“ A lack of mathematical knowledge will prove of no disadvantage to the reader, for I have used no mathematical processes of reasoning. I have taken the view that the space which we ordinarily think of, the space of real things (which I would call permeable matter) , is different from the space treated of by mathematics. Mathematics will tell us a great deal about space, just as the atomic theory will tell us a great deal about the chemical combinations of bodies. But after all, a theory is not precisely equivalent to the subject with regard to which it is held. ”

“ The world of sentient experience, according to the modern view, is closed and limited; only the physical world is ample and large and of ever-to-be-discovered complexity. Plato’s world of soul, on the other hand, is at least as large and ample as the world of things.
Let us now try a crucial experiment. Can I form an intuition of a four-dimensional object? Such an object is not given in the physical range of my sense contacts. All I can do is to present to myself the sequences of solids, which would mean the presentation to me under my conditions of a four-dimensional object. ”

“ Let us imagine the cube in our space, which is the base of a tesseract, to turn about one of its edges. The rotation will carry the whole body with it, and each of the cubic sections will rotate. The axis we see in our space will remain unchanged, and likewise the series of axes parallel to it about which each of the parallel cubic sections rotates. The assemblage of all of these is a plane.
Hence in four dimensions a body rotates about a plane. There is no such thing as rotation round an axis. ”

“ And our logic is simply spatiality in the general sense—that resultant of a selection of the permanent from the unpermanent, the ordered from the unordered, by the means of the group and its underlying duality.
We can predicate nothing about nature, only about the way in which we can apprehend nature. All that we can say is that all that which experience gives us will be conditioned as spatial, subject to our logic. ”

“ Let us trace out the consequences of defining positive electricity as an A motion and negative electricity as a B motion. The combination of positive and negative [Pg 228] electricity produces a current. Imagine a vortex in the ether of the A kind and unite with this one of the B kind. An A motion and B motion produce rotation round a plane, which is in the ether a vortex round an axial surface. It is a vortex of the kind we represent as a part of a sphere turning inside out. Now such a vortex must have its rim on a boundary of the ether—on a body in the ether. ”

“ 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. ”

“ 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. ”