CHAPTER VII.
In conclusion let us remark that we have supposed two different worlds—one of sensation in the first part, one of motion in the second part. And these have been treated as distinct from one another. And especially in the first part, by this avoidance of questions of movement, an appearance of artificiality was produced, and occasionally inconsistencies, for sometimes sensations were treated as independent of actions, sometimes as connected with them. But it remains to be decided if these inconsistencies are in themselves permanent, or whether, when we remove the artificial separation, and let the world of sensation and the world of motion coalesce, the inconsistencies will not disappear, thereby showing that their origin was merely in the treatment, not in the fact; that they came from the particular plan adopted of writing about the subject and are not inherent in the arguments themselves.
The king in the first part was supposed to have all the material problems of existence solved. There was a complete mechanism of nature. He took up the problem of the sentient life. But this problem can only artificially be separated from that of the material world. The gap between our sensations and matter can never be bridged, because they are really identical.
Let us then allow this separation to fall aside. Let us suppose the king to have all the reins of power in his own hands. Let us moreover suppose that he imparts his rays to the inhabitants so that they have each a portion of his power. And let us suppose that the inhabitants have arrived at a state of knowledge about their external world corresponding to that which we have about the world which we know.
Let us listen to a conversation between two of them.
A. The energy of the whole state of things is running down.
B. How do you prove that?
A. Whenever any motion of masses takes place a certain portion of the energy passes irrecoverably into the form of heat, and it is not possible to make so large a movement with those same masses as before, do all that is possible to obtain the energy back again from the heat into which it has passed.
B. Well, what about the heat? Energy in the form of the motions of the masses passes off into the energy of heat. But what is heat?
A. It is the motion of the finer particles of matter.
B. Well, I would put forward this proposal. We have by observation got hold of a certain principle that where any movement takes place some of the energy goes in working on the finer particles of matter. Let us now take this principle as a universal one of motion, and apply it to the motions of the finer particles of matter themselves, which are simply movements of the same kind as the movements of the larger ones. This principle would show that these movements are only possible inasmuch as they hand over a portion of their energy to work on still finer matter.
A. Then you would have to go on to still finer matter.
B. Yes, and so on and on; but to fix our thoughts, suppose there is an ultimate fine matter which is the last worked on. Now I say that we may either suppose that this is being gradually worked on and all the energy is dissipating, or else we may put it in this way. When we regard so much energy we are apt to think that it is the cause of the next manifestation in which it shows itself. But this is really an assumption. Energy is a purely formal conception, and all that we do is to trace in the actions that go on a certain formal correspondence, which we express by saying that the energy is constant.
A. But I feel my own energy.
B. Allow me to put your feeling to one side. If we take then the conservation of energy to be merely a formal principle, may we not look for the cause of the movements in the invariable accompaniment of them, namely, in the fact that a certain portion of the energy is expended irrevocably on the finer portions of matter. If now we take this ultimate medium which suffers the expenditure of energy on it, may we not look on it as the cause, and the setter in action of all the movements that there are. By its submitting to be acted on in the way in which it does submit, it determines all the actions that go on. For what is all else than a great vibration, a swinging to and fro. When we count it as energy, we by reckoning it in a particular manner make it seem to be indestructible, but that the energy should be indestructible would be a consequence from the supposition which we could very well make, that to produce a given series of effects the submitting to be worked on of this ultimate medium must be a minimum. If it were a minimum no movements could neutralize one another when once set going, for if they did there would be a waste of the submission of this ultimate medium.
A. But what do you suppose this ultimate medium would be?
B. That I cannot tell, but we seem to have indications. For the more fine the matter which we investigate, the more its actions seem to annihilate distance: light and electricity produce their effects with far greater rapidity than do the movements of masses. We might suppose that to this ultimate matter all parts were present in their effects, so that anything emanating from the ultimate matter would have the appearance of a system comprehending everything.
A. But you have not got any evidence of an ultimate matter.
B. No, all that we can think of is an endless series of finer and finer matter. But is that not an indication rather, not that the direction of our thoughts is false, but that there are other characteristics of this ultimate, so that when looked at under the form of matter it can only be expressed as an infinite series.
Let us omit the considerations brought forward in the preceding conversation and examine more closely the philosophy of the inhabitants of the valley in so far as it corresponds with ours.
They laid great stress on a notion of vis viva, or what we should term energy, but said it was gradually passing away from the form of movements of large bodies to that of movements of small bodies. So that in the course of time the whole valley would consist of nothing but an evenly extended mass of matter moving only in its small particles—and this motion of the small particles they called heat. Now they had very clearly arrived at the conviction that with every mechanical motion there was a certain transference of vis viva to the smaller particles of matter, so that it did not appear again as mechanical motion. But they did not accept this as a principle to work by. They did not consider that the motions of the smaller particles of matter were just the same as those of the larger masses. They did not see that if a condition held universally for the movements of the visible world, it must also hold for the smaller motions which they experienced as heat. So the conclusion which they should logically have come to that there was a transference of vis viva on and on was not held. But the step was a very little one for them to take from regarding an invariable condition as always there to regarding it as a cause. For the causes they assigned were all purely formal relations, and only got to assume an appearance of effective causes by familiarity with them, and a throwing over them of that feeling of effectiveness which they derived from the contact which they had with the king.
They might have reasoned. This universal condition of anything happening must be the cause. Energy goes from a higher to a lower level. That which causes the difference of level is the cause, and the cause of the difference of level must be that which invariably accompanies such a transference of energy from a higher to a lower level. Now this invariable condition is the passing of a portion of the energy into the form of motions of the finer parts of matter. Hence there is an apparently endless series. But to realize the matter, suppose an ultimate medium, suppose there is a kind of matter of infinite fineness distributed everywhere which let itself be worked on, and so determines differences and wakens the sleeping world. What are the qualities of this fine matter? We see them in the properties of the finer kind of matter which we know, such as light, electricity. The property of the finer kind of matter is in general that it tends to bring distant places together, so that a change in one part is rapidly communicated to every other part. If they followed this indication they would have supposed that the ultimate fine matter was of such a nature as to make all parts of the valley as one, so that there was no distance, and any determination of a difference of level on the part of this ultimate matter would have reference to all the conditions everywhere. It would be in immediate contact with every part, so that anything springing therefrom would present the appearance of a system having regard to the whole. Now if they had imagined such an ultimate medium doing that which to them would seem bearing rather than exerting force, suffering rather than acting, they would not have been far from a true conception of the king who directed them all. For he himself by reason of his very omnipresence could not be seen by them. There was nothing for them to distinguish him by. But they could have discovered somewhat of the means by which he acted on them, which can only be described from the appearances they present to the creatures whom the king calls into life.
But of truth they would have had another and perhaps a truer apprehension of the king in a different way. For when he acted on them so that they took one course rather than another, it was his action in themselves that they felt. If they were mere pleasure-led creatures then they were shaped outwardly, but if in their inner souls he acted and through them suffered, then they were true personalities conscious of being true selves, the oneness of all of them lying in the king, but each spontaneous in himself and absolute will, not to be merged in any other.
Thus they had two modes of access to the king, one through their own selves where he had made them exist, one through the outer world. And in the outer world it was but a direction in which they could look. They could never behold the personality of the king, but only an infinite series of different kinds of matter, one supporting the other as it were and underlying it, but doing more also than this, for in proportion as they considered the kinds of matter that lay deeper they found that distant became near, absent, present, that time gave no longer such distinctions, but from the phenomenal side they seemed by a gradual diminution of the limitations of experience to arrive at an external presentation of that absolute which exists in the fulness of things, which they knew more immediately in themselves when they truly were.
THE END.
INTRODUCTION.
In the next two or three of these papers certain questions connected with the subject of a space higher than our own will be treated. It is well, therefore, first to recede and to form definite conceptions about a world of plane space, about a world in which the beings can only move in two independent directions. Then, proceeding thence to our own world, we may gain the means of passing on to a higher world. And I should have wished to be able to refer the reader altogether to that ingenious work, “Flatland.” But on turning over its pages again, I find that the author has used his rare talent for a purpose foreign to the intent of our work. For evidently the physical conditions of life on the plane have not been his main object. He has used them as a setting wherein to place his satire and his lessons. But we wish, in the first place, to know the physical facts.
With this aim it is necessary to form a clear idea of what matter would be in a world of two dimensions, and the following illustration is a convenient one.
Place on the smooth surface of a table a half-crown piece, and suppose it to slide on the table perfectly freely. Imagine it to exercise an attractive force along the surface of the table in all directions round itself. By it and near it place a sixpence, and let the sixpence also slide freely on the table. It will, however, not be so free to move equally in all directions as the half-crown was, for it will be attracted by the half-crown. It will slip over the surface of the table under the influence of this supposed force, and will come into contact with the half-crown. Now if we suppose that both the half-crown and the sixpence are very thin, that they are both of them only the thickness of the ultimate particles of matter, then we shall have a representation of what material bodies will be in a plane world.
We must suppose that the particles cannot lift themselves or be lifted up from the plane so as to lie upon each other. Under no circumstances can they quit the surface of the plane.
Moreover, at no point must the particles adhere to the plane, nor must there be any friction impeding their movements over it. The only purpose which the support serves is to keep them on the same level surface and to convey influences from one particle to another. The gravity which we know, and which acts at right angles to the table on which the coins rest, will not have any effect on the particles in their motions on the plane, but will simply keep them to the plane. Any force of attraction which concerns their motions proceeds from one particle to another. Thus, conceive the half-crown to be a very large disk of matter, and the sixpence to be a sentient being. This being would feel a force of attraction towards the centre of the half-crown, and this force of attraction would keep him to the rim of the half-crown. If he weighed anything it would be by balancing it with his weight against the force which tended to pull it to the centre of the half-crown. He would not feel the gravity which keeps him against the surface of the table; he would not know that there was a hard, smooth surface on which he rested. He would always have been in contact with it, and so he could not tell what it would be like to be free from it. He would have no contrast whereby to apprehend its effect on him. Moreover, he would only know of movements in directions along the plane. He would not conceive that such a thing was possible as movement in another direction than to and fro, hither and thither on the plane. It is difficult to suppose that a being would be supported on one side by a plane, and not be in contact with anything on the other side, even atmosphere. Yet if we suppose a being of real matter free to move on the plane, this is what must be conceived. If the sixpence is conceived as such a being, it must receive its impressions through its rim. The rim represents its skin.
And if it be supposed to be surrounded by air for its respiration, this air must not be able, any more than the particles of solid matter, to rise away from the plane. The plane being must be conceived to have a different air to that which we know. The particles of its air, however free to move amongst themselves, must not have the power of moving away from the surface of the plane, as if so they would be able to pass to the interior of the body without passing through the skin. Any passage leading to the interior of the body would have to terminate in an opening in the rim, otherwise it would be completely shut up from the exterior.
Now it is obvious that if the table is struck so that it quivers, this movement will be communicated to the coins lying on it. Either the coins as a whole will move, or their particles will be disturbed.
Again, if we suppose there to be some particles loosely cohering together, lying on a smooth sheet of iron, it is evident that the quivering and jostling of the iron, if it is struck, would have an effect on the particles, and may cause the breaking up of the thin masses in which the particles cohere. Thus, if the material of which the sheet is composed be very dense and rigid, compared to the substances lying on it, they may undergo many alterations, being broken up and coming together again while the supporting matter which bears them all up simply moves and vibrates.
Diagram I.
It is evident that just as the particles are affected by the vibration and shaking of the sheet of metal on which we suppose them, so they might in turn possibly affect the sheet of metal and cause vibrations and shakings in it. These shakings and vibrations would go forth from a particle which excited them in every direction along the sheet. They would not pass out into the air, except secondarily and in a very minute degree. The shake would be transmitted in the sheet. And the effect on neighbouring particles would be great, on more distant particles it would be less, and on those at a great distance barely perceptible.
The following is a good plan for obtaining in a definite way the feeling of what existence in a plane would be like; it enables us to realize the conditions in such a way as to lay the basis for subsequent thought.
Let the reader take a sheet of note-paper and hold it before himself edgewise, so that he sees it with one eye as a single line. And let him hold it so that this line runs downwards from his eyebrows to his mouth, as shown in Diagram I. Now on this sheet of paper, on one side of it, let a straight line be drawn running across it, away from the observer. Suppose all below this line to be a thin layer of particles which, keeping compactly together, form a solid sheet of particles, every one of which touches the paper. This would be the solid earth to a being in the plane world.
Let the surface of the paper above this be covered by a layer of particles which move freely amongst each other, but which do not rise from the surface of the paper. These particles form the air of such a world.
On the surface of the earth draw a line standing upright. Let this line represent a man. Another line will represent a wall which the man could not pass except by getting over it.
It will be found that the objects on the paper are felt to be subject to the action of gravity. The question will occur, Why will not this thin layer of particles slip off the paper?
Now, the sense of gravity must not be got rid of, but it must be connected with the matter in the sheet of paper.
Suppose, then, that the sheet were to grow bigger and bigger till it filled out reaching through the whole world and cutting the globe in two. Then let all the earth be removed except a thin layer on one side of this enlarged sheet of paper. This thin layer will be the only portion of matter left. And such a thin layer will represent a plane world. The force of gravity must be conceived as remaining, but as coming from a large and thin disk.
Now to keep this thin layer on the paper it would be necessary to have some force acting sideways, so as to keep the particles to the paper.
And the paper itself may be conceived to exercise such a force: it is many particles thick, while the thin layer of matter is only one particle thick, and thus it will keep the layer of matter, which covers one side of it, in its place by virtue of its own attraction.
We suppose that the paper exerts an attractive force which keeps the thin layer of matter to it. This attractive force is not felt by the sentient beings on the paper, nor does it influence the movements of the particles of matter amongst themselves. We also suppose another attractive force proceeding from particle to particle of the matter on the plane. This would be felt by the beings and produce movements of matter.
Thus the conception of a plane world necessarily involves that of something on which it is.