The most apparently simple movements are those which we see taking place on the surface of the earth, connected with the agency which we call gravitation. We see the rivers flowing from a higher to a lower level, rocks when loosened from a mountain side rolling down, rain falling, and many minor changes of this sort.
But there are many actions besides these. For instance, suppose before us a spring coiled up. When it unwinds it “exerts force,” it transmits movement. In its first state it is like a stone at the top of a mountain. In its second state it is like a stone which has fallen to the bottom of the mountain. It had a power of movement and of communicating movement, now it has lost that power.
Again, the powder in a gun when it explodes expands and imparts movement to the shot. When the gun has been fired off the powder enters a different state. Before, the chemical affinities of its constituents were in a state of tension, now that it is fired off, they have formed fresh combinations. The power of transmitting movement has been lost by that which was the powder. It is like a portion of water at the top of a fall of water. If it remains at the top it has at any time the power of producing a shock, and of effecting, say, the movement of a water-wheel under it. But if it falls it has exerted and lost that power.
The difference of level associated with gravity is familiar to us. But we have no right, other than our own familiarity with it, to look on gravity as less in need of explanation than any other phenomenon of the external world. Newton did not suppose that there was any force inherent in matter which attracted othermatter inversely as the square of the distance. He showed that a great many astronomical facts were capable of being explained and calculated on this hypothesis. He left the explanation of how it is that matter gravitates unsolved, and it remains unsolved to the present day.
But gravitation affords us a useful term—“Level.”
Let us agree to call the following on a high level—a stone at the top of a precipice, a wound-up spring, oxygen and hydrogen mixed in the proportion to form water. Let us call the following at a low level—the stone at the foot of the precipice, a spring straightened so far as it tends to straighten, oxygen and hydrogen united in the form of water.
In passing from their first state to their last all these have manifested a power of movement and of communicating movement. They have now relatively to their former state lost that power.
Difference of level in this general sense is the most universal distinction of matter.
No motion takes place unless matter passes from a higher to a lower level.
The universal cause of motion is that which produces this difference of “level” in the general sense.
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.
What is the cause of the “Difference of Level?”Whenever matter passes from a higher to a lower level some of the energy which is given out passes away in the form of heat. This passing away of some of the energy into the form of heat is an invariable accompaniment of the transition from a higher to a lower level. Is it the cause of the difference of level?
In the valley the king by bearing some pain made action worth while. Is there any indication in nature of the production of a lower level which makes the course of things run on?
It is certain that energy in every action passes off into the form of heat, and unless it is through the power of the finer particles of matter to absorb the energy, it is difficult to see how any action can take place.
As with the other lines of thought, this line also terminates with a possibility. Nothing has been proved, but a place has been provided.
In the first part of this paper a possible mode of action was exhibited in the imaginary relations of a world subject to certain laws of pleasure and pain.
In the second part it has been shown that something is wanting in our conception of the natural processes. There is room for a central idea. No scientific doctrines properly understood would clash with one properly located.
Can the mode of action exhibited in terms of sensation in the fictitious world be applied to the case of the world of force and matter?
Before passing on, however, it is worth while to examine a little more closely into what is meant by the expression so often used: “Passing off into the form of heat.”
The modes in which energy passes off into the form of heat are in general those modes by which movement is brought to a standstill such as friction. And we are aptto think motion the primary fact, the cessation of motion a secondary and disagreeable fact. But both are equally existent phenomena, and the convenience to ourselves is not to mislead us as to their relative importance.
But what is this passing off of energy into the form of heat? The phrase is unsatisfactory, for we are told by science almost in the same breath that heat is the motion, the mechanical motion, of the particles of matter. So the statement resolves itself into this. Only when some of the motion passes off into the form of motion of the smaller particles of matter does motion take place in larger masses.
As a corollary it follows that at some date, however distant, all the motion of masses will have passed away into the form of motion of smaller masses.
It may be urged that when the larger masses move, the smaller particles also move. This is true; but motion in this sense is used to denote change of position amongst the smaller particles with regard to one another. The particles in a flying cannon-ball are relatively still with regard to one another as far as the motion of the cannon-ball as a whole is concerned.
We thus arrive at the following principle: The condition of the motion of masses taking place is that some of the motion passes off into the motion of the smaller particles.
But if the motion of the smaller particles is just the same as that of the larger portions, we are obviously not at the end. The very same principle just applied must be applied again.
These motions of the small particles of matter cannot take place unless some of their movement is transmitted and passed on, and transformed into the motion of still finer particles of matter.
But here obviously we are brought to the beginning ofan infinite series. An infinite series passing from finer matter to still finer matter, and so on endlessly.
The assumption by which we are led to this endless series of transmissions must be clearly apprehended. We take the law—that the motion of masses only takes place when some of the motion passes off into the motion of the finer particles of matter, and we assume that it holds always.
In a lever there is a fixed point, the fulcrum, which supports it, and the power raises the weight; but the weight may be fixed, and then the fulcrum can be lifted by the power. So we obtained this law from the consideration of material relations; and now we suppose this law to be the fixed point, and shift our notions of material relations.
Thus we are landed on an endless series. Before proceeding, however, to inquire what the significance of this endless series may be, let us assume an end to it. Let us assume that we come at last to a final transmission. Let us assume that the energy is transmitted to the ultimate particles of matter.
Or, if we have gone beyond matter, let us suppose an ultimate medium which by its modifications builds up matter, and which is the last and ultimate substance.
Let us suppose this ultimate medium absolutely to receive some of the energy. Let it absolutely receive and absorb some of the energy, and thereby give rise to the difference of level, to give the ultimate permission which sets all things going.
What are the properties of this medium? We obtain an indication of what they are when we examine the properties of the finer kinds of matter. Compared with the motions of masses, motions which affect the smaller particles of bodies are infinitely quick. Light and electricity are actions affecting the smaller particles ofbodies, and by them distances are speedily traversed, which relatively to moving masses are very great.
Now in point of speed of transmission the properties of this ultimate medium must be infinitely beyond those of luminiferous ether.
To this ultimate medium all movements at any distance from each other must be almost equally present at every part. At whatever distance from one another two affections of this ultimate medium be supposed to take place, the effect of the one will travel to the place of action of the other instantaneously.
Such a medium is a kind of visible symbol of the universe, being one system in which all motions should be co-determined.
To make this clear, suppose a transformation of energy was produced in one part of space of an absorption of energy on the part of this ultimate medium, this transformation of energy would be produced by a medium in instantaneous contact with every other part of space, and the transformation of energy thus originated would harmonize with, and have reference to, the transformations of energy in every other part of space.
There are two infinities—the infinite of space extending out each way, the infinite of the smaller and smaller divisions of matter. The ultimate medium we have supposed partakes of both infinities. It is infinite in extent, and infinitely fine in its particles.
Now this medium by absorbing energy sets movements going. And that movements do not neutralize one another—i.e., that movements in opposite directions do not mutually destroy one another—has this result, that a given amount of this absorption produces the greatest possible amount of motion. If motion came to a rest in any other way, more of this absorption by the ultimate medium would be needed. Hence, by a given amountof absorption in the ultimate medium the greatest possible amount of motion is produced. That is, the absorption of motion into the ultimate medium is a minimum, and the law of the conservation of energy is the expression of this being a minimum.
But here again a further remark is called for. We start by assuming energy to be an absolute existence. But why not assume this action on the part of the ultimate medium to be the real action, and consider the phenomena of motion and energy as the mode of its action.
What this action of the ultimate medium may be needs examination. All that we can say at present is that relatively to that which we call energy, the action of this medium is that of being acted on.
In the preceding, however, it must be remembered that this conception of an ultimate medium was merely a supposition to enable us to see and roughly map out the relations of the things we are investigating. Where we were really landed was in an infinite series—we were brought logically to the conception of an infinite series of media, one behind the other.
What does an infinite series indicate?
Let us turn to a region of thought where infinite series are familiar objects, and we can learn about them.
In algebra infinite series are common. Thus take series 1 -x²/2 +x⁴/4 and so on for ever. This is the attempt in algebra to represent a trigonometrical idea. In trigonometry it is expressed as cos.x. But in algebra it needs this infinite series.
In algebra infinite series occur when the object which it is wanted to represent in algebraical terms cannot be grasped by algebra. When there is no single term or set of them in algebra which will serve, the object is represented by means of an infinite series. Thus we may say that in any calculus, when the object to be treated of cannot be expressed in the terms of the calculus, it is represented by means of an infinite series.
Now, dealing with material considerations, going on in the calculus of matter, we have come to an infinite series. This indicates that we have gone as far as the material calculus will carry us. We have now to bring in an idea from a different quarter if we will simplify our expression.
It may well be that within our experience there is nothing which will serve. But let us suppose that that which in material terms we represent as an infinite series is a will—a will in contact with all existence, as shown by the properties it had when we conceived it as an ultimate medium. For, regarding it as an ultimate substance, we found that it would be affected by pulsations infinitely quicker than light and electricity; considered as a substance, it was such that distance to it tended to be annihilated. 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. For although we apprehend this will relatively to the appearances which we suppose we know, mechanical energy and feeling, still we see that both are caused by it, and that the sum of both is nothing, save for that which this will is in them.
Is there any other way of apprehending this will than through the external world?
We have two apprehensions of nature—one of external things, the other of our own wills.
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; which, represented in terms of sensation, is suffering; but which in itself is absolute being, though only to be known by us as a negation of negations.
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 energygoes 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 tobe 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 ofvis 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 thecourse 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 ofvis vivato 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 ofvis vivaon 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 ofinfinite 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 truepersonalities 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.
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 beso 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 nottell 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 thesheet 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.
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, exceptsecondarily 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.
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.
And just as a bubble blown by us consists of a distended film, so this bubble, vast beyond comparison, consists of a film distended and coherent.
On its surface in the course of ages has fallen a thin layer of space dust, and so smooth is this surface that the dust slips over it to and fro and forms densities and clusters as its own attractions and movements determine.
The dust is kept on the polished surface by the attraction of the vast film; but, except for that, it moves on it freely in every direction.
And here and there are condensations wherein have fallen together numbers of these floating masses, and where the dust condensing for ages has formed vast disks.
And these disks are glowing hot—yet no light comes from them into our universe.
For this world lies beyond the æther—far beyond. And however hot or glowing the masses are, if there is no medium to transmit the vibrations of heat the influence cannot travel.
Thus the only directions in which the heat can travelare on the film. From each of these glowing disks the luminous influence streams forth carried by the vibrations of the film which supports everything. For the heat and intense agitation of these glowing disks shakes and disturbs the bubble, and just as a thin soap bubble quivers and shakes, so this film quivers and shakes. And so elastic is it, and so rigid, that it carries the light and heat to all surrounding regions. Yet so vast is the bubble, so tremendous in its dimensions, that the agitation from these glowing disks travels almost in straight lines, till, spreading out on every side, it merges into darkness—like the ripples in the centre of a vast calm lake gradually become indistinguishable.
And round these central orbs of fire—for orbs of fire they are, though they only transmit their fire along the film of the bubble—round these orbs pass in due order and succession other disks, which, cold or warm, have not that energy of light and heat which the central orbs possess.
These disks, though large, are so immeasurably small compared with the vast surface of the all-supporting bubble, that their movements seem to lie on a plane flat surface; the curving of the film on which they rest is so slight compared to their magnitude, that they sail round and round their central fires as on a perfect level surface.
And one of these orbs is fitted by nature to be the habitation and home of living beings. For it is neither so hot as it was for long ages after it had condensed from the film of dust wherefrom all orbs are made, nor has it so cooled down as to render life unsupportable.
And, moreover, it is full of vast crevices and channels, for in many places the interior in cooling after the rim had set from its molten condition has left long caverns and passages, not only in one layer, but in many.
And on the rim and in these passages and caverns live the inhabitants of whom I speak.
They do not rise from the surface of the film, but as all matter lies on the smooth surface but one particle deep, so their bodies formed out of matter lie, as we should say, on this smooth surface.
Yet of this they know nothing. They say that they stand and walk.
For this orb has an attractive force.
Diagram II.—“Two beings walking round.”
Diagram II.—“Two beings walking round.”
By that very same impulse of coming together whereby it gathered its particles out of the dust on the bubble, by that very same force it draws towards its centre all that is near it or on it. Thus “up” is to these inhabitants a movement from the centre of the disk on the rim of which they live and away from it. “Down” is a movement from the rim towards the centre. The thin layer which forms the mass of the disk is their solid matter. They are not able even in thought to rise away from the surface of the bubble, and look from space upon their mode of existence. They ever pass to and fro upon a line, upon a rim; and no two can walk except after one another. If you look at the rude picture you will see that the two beings represented by two triangles cannot pass one another if they are unable to lift themselves up from lying on the surface of the paper. The surface ofthe paper represents the surface of the bubble, and sliding freely on it, but unable to lift up from it, are tenuous shapes that are the inhabitants, and that thin layer of particles that is to them solid matter.
Diagram III.—A section of the film of the bubble showing a disk BD lying on it, and a creature AB on the rim of the disk. CE is a section of the film, BD is a section of the disk, AB is a section of the creature. The thickness is enormously magnified and also the height AB of the creature compared with the diameter BD of the disk. The attraction which AB feels keeps him to BD; both AB and BD, the being and the disk, slide freely on the film CE without knowing of its existence.
Diagram III.—A section of the film of the bubble showing a disk BD lying on it, and a creature AB on the rim of the disk. CE is a section of the film, BD is a section of the disk, AB is a section of the creature. The thickness is enormously magnified and also the height AB of the creature compared with the diameter BD of the disk. The attraction which AB feels keeps him to BD; both AB and BD, the being and the disk, slide freely on the film CE without knowing of its existence.
Now were it not for the fact that the orb is reft into these chasms and passages, the only movement that these beings would have would be of passing round and round on the rim of their world.
Many words that we have, to them could bear no meaning. Thus “right and left” is to them unknown. For consider their faces bent in one direction along the rim. In following this direction, they go forward, in retracting from it they go backward. If they go away from the centre they go up, towards the centre is down. And by no means can they turn, raising themselves from the surface whereon they are. They do not even know that they have two sides; their movements, thoughts, and imaginations are all confined to that surface on which they are. This they call their space, their universe; nor does aught that lies beyond it, towards the interior of the bubble or away from it, directed outwards, come into their thoughts, even as an imaginary possibility of existence.
Life is extremely limited on such a world. To take a single instance, in order for two beings to pass each other, a complicated arrangement is necessary, shown in Diagram IV.
At intervals along the rim recesses and chambers areconstructed. Near the openings of these chambers lay movable plates or rods. When two beings wish to pass, one of them descends into the recess; the other one pushes the rod so as to form a bridge over the opening, walks across it, and then removes the plate so that the one who has descended can get up and go on his way.
Diagram IV.—Two beings passing.
Diagram IV.—Two beings passing.
If by any chance, while a being is in the recess, the plate or rod which acts as a bridge gets fixed, he is in a dangerous predicament. For suppose a being confined as shown. If he, suffering from want of air, cuts through the roof at AB, the whole part to the right of AB comes tumbling down. For its only support is severed when AB is cut through. It is impossible to make a hole which is not the whole width of matter as it lies on the surface. And with regard to this all constructions have to be made. There cannot be two openings in a wall of a house, unless when the one is open the other is so fashioned as closing to act as a rigid support to the wall, which now depends for its upholding entirely on it.
Diagram V.—A house.
Diagram V.—A house.
Thus, in the diagram, the house is held up entirely by the side opposite to the doorway EF, which is now open. The roof is supported by the side CD. If an openingAB be made in the wall CD before the doorway EF is closed, the roof will fall in. So, in order to pass through the house, EF must be firmly shut up before AB is opened. The houses are always built in the interior passages so as to leave the rim of the disk free for locomotion.
And there are many things to be said of the inhabitants on this disk with respect to their social and political life. It is hardly necessary for me to put down much about it here, for any one by using the method of the historian Buckle, and deducing the character of a people from their geographical influences and physical surroundings, could declare what the main features of their life and history must be.
But one or two remarks may be made here. First of all they are characterized by what I may venture to call a crude kind of polarity.
In dwellers in our world this polarity, which shows itself amongst other ways in the distinction of sexes, is tempered and modified.
In every man there is something of a woman, and in every woman there are some of the best qualities of a man.
But in the world of which we speak there is no physical possibility for such interfusion. In a linear existence there would be no consciousness of polarity. It makes its appearance first in the plane, and in a hard and unmitigated form.
It is impossible to do otherwise than caricature these beings when we write of them thus in brief. So let us accept the matter frankly, and, without scruple, look at them in the broadest possible manner.
If the reader will cut out the triangles in the corners of the two next pages he will obtain four plane beings, two of which are men, two of which are women. The lines down which the cutting is to be made are marked with a black line. 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. Much can be noticed from an inspection of these figures. Of course it is only symbolical in the rudest way, but in their whole life the facts which can be noticed in these simple figures are built up and organized into complicated arrangements.