SCIENTIFIC ROMANCES.

BY
C. H. HINTON, B.A.

[What is the Fourth Dimension?] [The Persian King.] [A Plane World.] [A Picture of Our Universe.] [Casting Out the Self.]

FIRST SERIES.

London.
SWAN SONNENSCHEIN & CO., LIM.,
Paternoster Square.
1886.

What is the Fourth Dimension?

CHAPTER I.

At the present time our actions are largely influenced by our theories. We have abandoned the simple and instinctive mode of life of the earlier civilisations for one regulated by the assumptions of our knowledge and supplemented by all the devices of intelligence. In such a state it is possible to conceive that a danger may arise, not only from a want of knowledge and practical skill, but even from the very presence and possession of them in any one department, if there is a lack of information in other departments. If, for instance, with our present knowledge of physical laws and mechanical skill, we were to build houses without regard to the conditions laid down by physiology, we should probably—to suit an apparent convenience—make them perfectly draught-tight, and the best-constructed mansions would be full of suffocating chambers. The knowledge of the construction of the body and the conditions of its health prevent it from suffering injury by the development of our powers over nature.

In no dissimilar way the mental balance is saved from the dangers attending an attention concentrated on the laws of mechanical science by a just consideration of the constitution of the knowing faculty, and the conditions of knowledge. Whatever pursuit we are engaged in, we are acting consciously or unconsciously upon some theory, some view of things. And when the limits of daily routine are continually narrowed by the ever-increasing complication of our civilisation, it becomes doubly important that not one only but every kind of thought should be shared in.

There are two ways of passing beyond the domain of practical certainty, and of looking into the vast range of possibility. One is by asking, “What is knowledge? What constitutes experience?” If we adopt this course we are plunged into a sea of speculation. Were it not that the highest faculties of the mind find therein so ample a range, we should return to the solid ground of facts, with simply a feeling of relief at escaping from so great a confusion and contradictoriness.

The other path which leads us beyond the horizon of actual experience is that of questioning whatever seems arbitrary and irrationally limited in the domain of knowledge. Such a questioning has often been successfully applied in the search for new facts. For a long time four gases were considered incapable of being reduced to the liquid state. It is but lately that a physicist has succeeded in showing that there is no such arbitrary distinction among gases. Recently again the question has been raised, “Is there not a fourth state of matter?” Solid, liquid, and gaseous states are known. Mr. Crookes attempts to demonstrate the existence of a state differing from all of these. It is the object of these pages to show that, by supposing away certain limitations of the fundamental conditions of existence as we know it, a state of being can be conceived with powers far transcending our own. When this is made clear it will not be out of place to investigate what relations would subsist between our mode of existence and that which will be seen to be a possible one.

In the first place, what is the limitation that we must suppose away?

An observer standing in the corner of a room has three directions naturally marked out for him; one is upwards along the line of meeting of the two walls; another is forwards where the floor meets one of the walls; a third is sideways where the floor meets the other wall. He can proceed to any part of the floor of the room by moving first the right distance along one wall, and then by turning at right angles and walking parallel to the other wall. He walks in this case first of all in the direction of one of the straight lines that meet in the corner of the floor, afterwards in the direction of the other. By going more or less in one direction or the other, he can reach any point on the floor, and any movement, however circuitous, can be resolved into simple movements in these two directions.

But by moving in these two directions he is unable to raise himself in the room. If he wished to touch a point in the ceiling, he would have to move in the direction of the line in which the two walls meet. There are three directions then, each at right angles to both the other, and entirely independent of one another. By moving in these three directions or combinations of them, it is possible to arrive at any point in a room. And if we suppose the straight lines which meet in the corner of the room to be prolonged indefinitely, it would be possible by moving in the direction of those three lines, to arrive at any point in space. Thus in space there are three independent directions, and only three; every other direction is compounded of these three. The question that comes before us then is this. “Why should there be three and only three directions?” 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. We can conceive their coming out of the straight line and entering it again, but they having moved always in one straight line, would have no conception of any other direction of motion by which such a result could be effected. The only shape which could exist in a one-dimensional existence of this kind would be a finite straight line. There would be no difference in the shapes of figures; all that could exist would simply be longer or shorter straight lines.

Again, to go a step higher in the domain of a conceivable existence. Suppose a being confined to a plane superficies, and throughout all the range of its experience never to have moved up or down, but simply to have kept to this one plane. Suppose, that is, some figure, such as a circle or rectangle, to be endowed with the power of perception; such a being if it moves in the plane superficies in which it is drawn, will move in a multitude of directions; but, however varied they may seem to be, these directions will all be compounded of two, at right angles to each other. By no movement so long as the plane superficies remains perfectly horizontal, will this being move in the direction we call up and down. And it is important to notice that the plane would be different, to a creature confined to it, from what it is to us. We think of a plane habitually as having an upper and a lower side, because it is only by the contact of solids that we realize a plane. But a creature which had been confined to a plane during its whole existence would have no idea of there being two sides to the plane he lived in. In a plane there is simply length and breadth. If a creature in it be supposed to know of an up or down he must already have gone out of the plane.

Is it possible, then, that a creature so circumstanced would arrive at the notion of there being an up and down, a direction different from those to which he had been accustomed, and having nothing in common with them? Obviously nothing in the creature’s circumstances would tell him of it. It could only be by a process of reasoning on his part that he could arrive at such a conception. If he were to imagine a being confined to a single straight line, he might realise that he himself could move in two directions, while the creature in a straight line could only move in one. Having made this reflection he might ask, “But why is the number of directions limited to two? Why should there not be three?”

A creature (if such existed), which moves in a plane would be much more fortunately circumstanced than one which can only move in a straight line. For, in a plane, there is a possibility of an infinite variety of shapes, and the being we have supposed could come into contact with an indefinite number of other beings. He would not be limited, as in the case of the creature in a straight line, to one only on each side of him.

It is obvious that it would be possible to play curious tricks with a being confined to a plane. If, for instance, we suppose such a being to be inside a square, the only way out that he could conceive would be through one of the sides of the square. If the sides were impenetrable, he would be a fast prisoner, and would have no way out.

What his case would be we may understand, if we reflect what a similar case would be in our own existence. The creature is shut in in all the directions he knows of. If a man is shut in in all the directions he knows of, he must be surrounded by four walls, a roof and a floor. A two-dimensional being inside a square would be exactly in the same predicament that a man would be, if he were in a room with no opening on any side. Now it would be possible to us to take up such a being from the inside of the square, and to set him down outside it. A being to whom this had happened would find himself outside the place he had been confined in, and he would not have passed through any of the boundaries by which he was shut in. The astonishment of such a being can only be imagined by comparing it to that which a man would feel, if he were suddenly to find himself outside a room in which he had been, without having passed through the window, doors, chimney or any opening in the walls, ceiling or floor.

Another curious thing that could be effected with a two-dimensional being, is the following. Conceive two beings at a great distance from one another on a plane surface. If the plane surface is bent so that they are brought close to one another, they would have no conception of their proximity, because to each the only possible movements would seem to be movements in the surface. The two beings might be conceived as so placed, by a proper bending of the plane, that they should be absolutely in juxtaposition, and yet to all the reasoning faculties of either of them a great distance could be proved to intervene. The bending might be carried so far as to make one being suddenly appear in the plane by the side of the other. If these beings were ignorant of the existence of a third dimension, this result would be as marvellous to them, as it would be for a human being who was at a great distance—it might be at the other side of the world—to suddenly appear and really be by our side, and during the whole time he not to have left the place in which he was.

CHAPTER II.

The foregoing examples make it clear that beings can be conceived as living in a more limited space than ours. Is there a similar limitation in the space we know?

At the very threshold of arithmetic an indication of such a limitation meets us.

If there is a straight line before us two inches long, its length is expressed by the number 2. Suppose a square to be described on the line, the number of square inches in this figure is expressed by the number 4, i.e., 2 × 2. This 2 × 2 is generally written 2², and named “2 square.”

Now, of course, the arithmetical process of multiplication is in no sense identical with that process by which a square is generated from the motion of a straight line, or a cube from the motion of a square. But it has been observed that the units resulting in each case, though different in kind, are the same in number.

If we touch two things twice over, the act of touching has been performed four times. Arithmetically, 2 × 2 = 4. If a square is generated by the motion of a line two inches in length, this square contains four square inches.

So it has come to pass that the second and third powers of numbers are called “square” and “cube.”

We have now a straight line two inches long. On this a square has been constructed containing four square inches. If on the same line a cube be constructed, the number of cubic inches in the figure so made is 8, i.e., 2 × 2 × 2 or 2³. Here, corresponding to the numbers 2, 2², 2³, we have a series of figures. Each figure contains more units than the last, and in each the unit is of a different kind. In the first figure a straight line is the unit, viz., one linear inch; it is said to be of one dimension. In the second a square is the unit, viz., one square inch. The square is a figure of two dimensions. In the third case a cube is the unit, and the cube is of three dimensions. The straight line is said to be of one dimension because it can be measured only in one way. Its length can be taken, but it has no breadth or thickness. The square is said to be of two dimensions because it has both length and breadth. The cube is said to have three dimensions, because it can be measured in three ways.

The question naturally occurs, looking at these numbers 2, 2², 2³, by what figure shall we represent 2⁴, or 2 × 2 × 2 × 2. We know that in the figure there must be sixteen units, or twice as many units as in the cube. But the unit also itself must be different. And it must not differ from a cube simply in shape. It must differ from a cube as a cube differs from a square. No number of squares will make up a cube, because each square has no thickness. In the same way, no number of cubes must be able to make up this new unit. And here, instead of trying to find something already known, to which the idea of a figure corresponding to the fourth power can be affixed, let us simply reason out what the properties of such a figure must be. In this attempt we have to rely, not on a process of touching or vision, such as informs us of the properties of bodies in the space we know, but on a process of thought. Each fact concerning this unknown figure has to be reasoned out; and it is only after a number of steps have been gone through, that any consistent familiarity with its properties is obtained. Of all applications of the reason, this exploration is perhaps the one which requires, for the simplicity of the data involved, the greatest exercise of the abstract imagination, and on this account is well worth patient attention. The first steps are very simple. We must imagine a finite straight line to generate a square by moving on the plane of the paper, and this square in its turn to generate a cube by moving vertically upwards. Fig. 1 represents a straight line; Fig. 2 represents a square formed by the motion of that straight line; Fig. 3 represents perspectively a cube formed by the motion of that square A B C D upwards. It would be well, instead of using figure 3, to place a cube on the paper. Its base would be A B C D, its upper surface E F G H.

The straight line A B gives rise to the square A B C D by a movement at right angles to itself. If motion be confined to the straight line A B, a backward and forward motion is the only one possible. No sideway motion is admissible. And if we suppose a being to exist which could only move in the straight line A B, it would have no idea of any other movement than to and fro. The square A B C D is formed from the straight line by a movement in a direction entirely different from the direction which exists in A B. This motion is not expressible by means of any possible motion in A B. A being which existed in A B, and whose experience was limited to what could occur in A B, would not be able to understand the instructions we should give to make A B trace out the figure A B C D.

In the figure A B C D there is a possibility of moving in a variety of directions, so long as all these directions are confined to one plane. All directions in this plane can be considered as compounded of two, from A to B, and from A to C. Out of the infinite variety of such directions there is none which tends in a direction perpendicular to Fig. 2; there is none which tends upwards from the plane of the paper. Conceive a being to exist in the plane, and to move only in it. In all the movements which he went through there would be none by which he could conceive the alteration of Fig. 2 into what Fig. 3 represents in perspective. For 2 to become 3 it must be supposed to move perpendicularly to its own plane. The figure it traces out is the cube A B C D E F G H.

All the directions, manifold as they are, in which a creature existing in Fig. 3 could move, are compounded of three directions. From A to B, from A to C, from A to E, and there are no other directions known to it.

But if we suppose something similar to be done to Fig. 3, something of the same kind as was done to Fig. 1 to turn it into Fig. 2, or to Fig. 2 to turn it into Fig. 3, we must suppose the whole figure as it exists to be moved in some direction entirely different from any direction within it, and not made up of any combination of the directions in it. What is this? It is the fourth direction.

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

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.

Or, to look at the matter in another light, a being in three dimensions, looking down on a square, sees each part of it extended before him, and can touch each part without having to pass through the surrounding parts, for he can go from above, while the surrounding parts surround the part he touches only in one plane.

So a being in four dimensions could look at and touch every point of a solid figure. No one part would hide another, for he would look at each part from a direction which is perfectly different from any in which it is possible to pass from one part of the body to another. To pass from one part of the body to another it is necessary to move in three directions, but a creature in four dimensions would look at the solid from a direction which is none of these three.

Let us obtain a few facts about the fourth figure, proceeding according to the analogy that exists between 1, 2, 3, and 4. In the Fig. 1 there are two points. In 2 there are four points—the four corners of the square. In 3 there are eight points. In the next figure, proceeding according to the same law, there would be sixteen points.

In the Fig. 1 there is one line. In the square there are four lines. In the cube there are twelve lines. How many lines would there be in the four-square? That is to say that there are three numbers—1, 4, and 12. What is the fourth, going on accordingly to the same law?

To answer this question let us trace out in more detail how the figures change into one another. The line, to become the square, moves; it occupies first of all its original position, and last of all its final position. It starts as A B, and ends as C D; thus the line appears twice, or it is doubled. The two other lines in the square, A C, B D, are formed by the motions of the points at the extremities of the moving line. Thus, in passing from the straight line to the square the lines double themselves, and each point traces out a line. If the same procedure holds good in the case of the change of the square into the cube, we ought in the cube to have double the number of lines as in the square—that is eight—and every point in the square ought to become a line. As there are four points in the square, we should have four lines in the cube from them, that is, adding to the previous eight, there should be twelve lines in the cube. This is obviously the case. Hence we may with confidence, to deduce the number of lines in a four-square, apply this rule. Double the number of lines in the previous figure, and add as many lines as there are points in the previous figure. Now in the cube there are twelve lines and eight points. Hence we get 2 × 12 + 8, or thirty-two lines in the four-square.

In the same way any other question about the four-square can be answered. We must throw aside our realising power and answer in accordance with the analogy to be worked out from the three figures we know.

Thus, if we want to know how many plane surfaces the four-square has, we must commence with the line, which has none; the square has one; the cube has six. Here we get the three numbers, 0, 1, and 6. What is the fourth?

Consider how the planes of the cube arise. The square at the beginning of its motion determines one of the faces of the cube, at the end it is the opposite face, during the motion each of the lines of the square traces out one plane face of the cube. Thus we double the number of planes in the previous figure, and every line in the previous figure traces out a plane in the subsequent one.

Apply this rule to the formation of a square from a line. In the line there is no plane surface, and since twice nothing is nothing, we get, so far, no surface in the square; but in the straight line there is one line, namely itself, and this by its motion traces out the plane surface of the square. So in the square, as should be, the rule gives one surface.

Applying this rule to the case of the cube, we get, doubling the surfaces, 12; and adding a plane for each of the straight lines, of which there are 12, we have another 12, or 24 plane surfaces in all. Thus, just as by handling or looking at it, it is possible to describe a figure in space, so by going through a process of calculation it is within our power to describe all the properties of a figure in four dimensions.

There is another characteristic so remarkable as to need a special statement. In the case of a finite straight line, the boundaries are points. If we deal with one dimension only, the figure 1, that of a segment of a straight line, is cut out of and separated from the rest of an imaginary infinitely long straight line by the two points at its extremities. In this simple case the two points correspond to the bounding surface of the cube. In the case of a two-dimensional figure an infinite plane represents the whole of space. The square is separated off by four straight lines, and it is impossible for an entry to be made into the interior of the square, except by passing through the straight lines. Now, in these cases, it is evident that the boundaries of the figure are of one dimension less than the figure itself. Points bound lines, lines bound plane figures, planes bound solid figures. Solids then must bound four dimensional figures. The four-square will be bounded in the following manner. First of all there is the cube which, by its motion in the fourth direction, generates the figure. This, in its initial position, forms the base of the four-square. In its final position it forms the opposite end. During the motion each of the faces of the cube give rise to another cube. The direction in which the cube moves is such that of all the six sides none is in the least inclined in that direction. It is at right angles to all of them. The base of the cube, the top of the cube, and the four sides of the cube, each and all of them form cubes. Thus the four-square is bounded by eight cubes. Summing up, the four-square would have 16 points, 32 lines, 24 surfaces, and it would be bounded by 8 cubes.

If a four-square were to rest in space it would seem to us like a cube.

To justify this conclusion we have but to think of how a cube would appear to a two-dimensional being. To come within the scope of his faculties at all, it must come into contact with the plane in which he moves. If it is brought into as close a contact with this plane as possible, it rests on it by one of its faces. This face is a square, and the most a two-dimensional being could get acquainted with of a cube would be a square.

Having thus seen how it is possible to describe the properties of the simplest shape in four dimensions, it is evident that the mental construction of more elaborate figures is simply a matter of time and patience.

In the study of the form and development of the chick in the egg, it is impossible to detect the features that are sought to be observed, except by the use of the microscope. The specimens are accordingly hardened by a peculiar treatment and cut into thin sections. The investigator going over each of these sections, noticing all their peculiarities, constructs in his mind the shape as it originally existed from the record afforded by an indefinite number of slices. So, to form an idea of a four-dimensional figure, a series of solid shapes bounded on every side differing gradually from one another, proceeding, it may be, to the most diverse forms, has to be mentally grasped and fused into a unitary conception.

If, for instance, a small sphere were to appear, this to be replaced by a larger one, and so on, and then, when the largest had appeared, smaller and smaller ones to make their appearance, what would be witnessed would be a series of sections of a four-dimensional sphere. Each section in space being a sphere.

Again, just as solid figures can be represented on paper by perspective, four-dimensional figures can be represented perspectively by solids. If there are two squares, one lying over the other, and the underneath one be pushed away, its sides remaining parallel with the one that was over it, then if each point of the one be joined to the corresponding point of the other, we have a fair representation on paper of a cube. Fig. 3 may be considered to be such a representation if the square C D G H be considered to be the one that has been pushed away from lying originally under the square A B E F. Each of the planes which bound the cube is represented on the paper. The only thing that is wanting is the three-dimensional content of the cube. So if two cubes be placed with their sides parallel, but one somewhat diagonally with regard to the other, and all their corresponding points be supposed joined, there will be found a set of solid figures, each representing (though of course distortedly) the bounding cubes of the four-dimensional figure, and every plane and line in the four-dimensional figure will be found to be represented in a kind of solid perspective. What is wanting is of course the four-dimensional content.

CHAPTER III.

Having now passed in review some of the properties of four-dimensional figures, it remains to ask what relations beings in four dimensions, if they did exist, would have with us.

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?

Let us consider the question in more detail. And for the sake of simplicity transfer the problem to the case of three and two dimensions instead of four and three.

Suppose a thread to be passed through a thin sheet of wax placed horizontally. It can be passed through in two ways. Either it can be pulled through, or it can be held at both ends, and moved downwards as a whole. Suppose a thread to be grasped at both ends, and the hands to be moved downwards perpendicularly to the sheet of wax. If the thread happens to be perpendicular to the sheet it simply passes through it, but if the thread be held, stretched slantingwise to the sheet, and the hands are moved perpendicularly downwards, the thread will, if it be strong enough, make a slit in the sheet.

If now the sheet of wax were to have the faculty of closing up behind the thread, what would appear in the sheet would be a moving hole.

Suppose that instead of a sheet and a thread, there were a straight line and a plane. If the straight line were placed slantingwise in reference to the plane and moved downwards, it would always cut the plane in a point, but that point of section would move on. If the plane were of such a nature as to close up behind the line, if it were of the nature of a fluid, what would be observed would be a moving point. If now there were a whole system of lines sloping in different directions, but all connected together, and held absolutely still by one framework, and if this framework with its system of lines were as a whole to pass slowly through the fluid plane at right angles to it, there would then be the appearance of a multitude of moving points in the plane, equal in number to the number of straight lines in the system. The lines in the framework will all be moving at the same rate—namely, at the rate of the framework in which they are fixed. But the points in the plane will have different velocities. They will move slower or faster, according as the lines which give rise to them are more or less inclined to the plane. A straight line perpendicular to the plane will, on passing through, give rise to a stationary point. A straight line that slopes very much inclined to the plane will give rise to a point moving with great swiftness. The motions and paths of the points would be determined by the arrangement of the lines in the system. It is obvious that if two straight lines were placed lying across one another like the letter X, and if this figure were to be stood upright and passed through the plane, what would appear would be at first two points. These two points would approach one another. When the part where the two strokes of the X meet came into the plane, the two points would become one. As the upper part of the figure passed through, the two points would recede from one another.

If the line be supposed to be affixed to all parts of the framework, and to loop over one another, and support one another,[1] it is obvious that they could assume all sorts of figures, and that the points on the plane would move in very complicated paths. The annexed figure represents a section of such a framework. Two lines X X and Y Y are shown, but there must be supposed to be a great number of others sloping backwards and forwards as well as sideways.

Let us now assume that instead of lines, very thin threads were attached to the framework: they on passing through the fluid plane would give rise to very small spots. Let us call the spots atoms, and regard them as constituting a material system in the plane. There are four conditions which must be satisfied by these spots if they are to be admitted as forming a material system such as ours. For the ultimate properties of matter (if we eliminate attractive and repulsive forces, which may be caused by the motions of the smallest particles), are—1, Permanence; 2, Impenetrability; 3, Inertia; 4, Conservation of energy.

According to the first condition, or that of permanence, no one of these spots must suddenly cease to exist. That is, the thread which by sharing in the general motion of the system gives rise to the moving point, must not break off before the rest of them. If all the lines suddenly ended this would correspond to a ceasing of matter.

2. Impenetrability.—One spot must not pass through another. This condition is obviously satisfied. If the threads do not coincide at any point, the moving spots they give rise to cannot.

3. Inertia.—A spot must not cease to move or cease to remain at rest without coming into collision with another point. This condition gives the obvious condition with regard to the threads, that they, between the points where they come into contact with one another, must be straight. A thread which was curved would, passing through the plane, give rise to a point which altered in velocity spontaneously. This the particles of matter never do.

4. Conservation of energy.—The energy of a material system is never lost; it is only transferred from one form to another, however it may seem to cease. If we suppose each of the moving spots on the plane to be the unit of mass, the principle of the conservation of energy demands that when any two meet, the sum of the squares of their several velocities before meeting shall be the same as the sum of the squares of their velocities after meeting. Now we have seen that any statement about the velocities of the spots in the plane is really a statement about the inclinations of the threads to the plane. Thus the principle of the conservation of energy gives a condition which must be satisfied by the inclinations of the threads of the plane. Translating this statement, we get in mathematical language the assertion that the sum of the squares of the tangents of the angles the threads make with the normal to the plane remains constant.

Hence, all complexities and changes of a material system made up of similar atoms in a plane could result from the uniform motion as a whole of a system of threads.

We can imagine these threads as weaving together to form connected shapes, each complete in itself, and these shapes as they pass through the fluid plane give rise to a series of moving points. Yet, inasmuch as the threads are supposed to form consistent shapes, the motion of the points would not be wholly random, but numbers of them would present the semblance of moving figures. Suppose, for instance, a number of threads to be so grouped as to form a cylinder for some distance, but after a while to be pulled apart by other threads with which they interlink. While the cylinder was passing through the plane, we should have in the plane a number of points in a circle. When the part where the threads deviated came to the plane, the circle would break up by the points moving away. These moving figures in the plane are but the traces of the shapes of threads as those shapes pass on. These moving figures may be conceived to have a life and a consciousness of their own.

Or, if it be irrational to suppose them to have a consciousness when the shapes of which they are momentary traces have none, we may well suppose that the shapes of threads have consciousness, and that the moving figures share this consciousness, only that in their case it is limited to those parts of the shapes that simultaneously pass through the plane. In the plane, then, we may conceive bodies with all the properties of a material system, moving and changing, possessing consciousness. After a while it may well be that one of them becomes so disassociated that it appears no longer as a unit, and its consciousness as such may be lost. But the threads of existence of such a figure are not broken, nor is the shape which gave it origin altered in any way. It has simply passed on to a distance from the plane. Thus nothing which existed in the conscious life on the plane would cease. There would in such an existence be no cause and effect, but simply the gradual realisation in a superficies of an already existent whole. There would be no progress, unless we were to suppose the threads as they pass to interweave themselves in more complex shapes.

Can a representation, such as the preceding, be applied to the case of the existence in space with which we have to do? Is it possible to suppose that the movements and changes of material objects are the intersections with a three-dimensional space of a four-dimensional existence? Can our consciousness be supposed to deal with a spatial profile of some higher actuality?

It is needless to say that all the considerations that have been brought forward in regard to the possibility of the production of a system satisfying the conditions of materiality by the passing of threads through a fluid plane, holds good with regard to a four-dimensional existence passing through a three-dimensional space. Each part of the ampler existence which passed through our space would seem perfectly limited to us. We should have no indication of the permanence of its existence. Were such a thought adopted, we should have to imagine some stupendous whole, wherein all that has ever come into being or will come co-exists, which passing slowly on, leaves in this flickering consciousness of ours, limited to a narrow space and a single moment, a tumultuous record of changes and vicissitudes that are but to us. Change and movement seem as if they were all that existed. But the appearance of them would be due merely to the momentary passing through our consciousness of ever existing realities.

In thinking of these matters it is hard to divest ourselves of the habit of visual or tangible illustration. 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.

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. So all that we can do is to deny our faculty of judging of the ideal completeness of shapes in four dimensions.

CHAPTER IV.

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. The powers of such beings and their experience would be ampler, but there would be no fundamental difference in the laws of force and motion.

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. There would be no barrier, no confinement of our devising that would not be perfectly open to him. He would come and go at pleasure; he would be able to perform feats of the most surprising kind. It would be possible by an infinite plane extending in all directions to divide our space into two portions absolutely separated from one another; but a four-dimensional being would slip round this plane with the greatest ease.

To see this clearly, let us first take the analogous case in three dimensions. Suppose a piece of paper to represent a plane. If it is infinitely extended in every direction, it will represent an infinite plane. It can be divided into two parts by an infinite straight line. A being confined to this plane could not get from one part of it to the other without passing through the line. But suppose another piece of paper laid on the first and extended infinitely, it will represent another infinite plane. If the being moves from the first plane by a motion in the third dimension, it will move into this new plane. And in it it finds no line. Let it move to such a position that when it goes back to the first plane it will be on the other side of the line. Then let it go back to the first plane. It has appeared now on the other side of the line which divides the infinite plane into two parts.

Take now the case of four dimensions. Instead of bringing before the mind a sheet of paper conceive a solid of three dimensions. If this solid were to become infinite it would fill up the whole of three-dimensional space. But it would not fill up the whole of four-dimensional space. It would be to four-dimensional space what an infinite plane is to three-dimensional space. There could be in four-dimensional space an infinite number of such solids, just as in three-dimensional space there could be an infinite number of infinite planes.

Thus, lying alongside our space, there can be conceived a space also infinite in all three directions. To pass from one to the other a movement has to be made in the fourth dimension, just as to pass from one infinite plane to another a motion has to be made in the third dimension.

Conceive, then, corresponding to the first sheet of paper mentioned above, a solid, and as the sheet of paper was supposed to be infinitely extended in two dimensions, suppose the solid to be infinitely extended in its three dimensions, so that it fills the whole of space as we know it.

Now divide this infinite solid in two parts by an infinite plane, as the infinite plane of paper was divided in two parts by an infinite line. A being cannot pass from one part of this infinite solid to another, on the other side of this infinite plane, without going through the infinite plane, so long as he keeps within the infinite solid.

But suppose beside this infinite solid a second infinite solid, lying next to it in the fourth dimension, as the second infinite plane of paper was next to the first infinite plane in the third dimension. Let now the being that wants to get on the other side of the dividing plane move off in the fourth dimension, and enter the second infinite solid. In this second solid there is no dividing plane. Let him now move, so that coming back to the first infinite solid he shall be on the other side of the infinite plane that divides it into two portions. If this is done, he will now be on the other side of the infinite plane, without having gone through it.

In a similar way a being, able to move in four dimensions, could get out of a closed box without going through the sides, for he could move off in the fourth dimension, and then move about, so that when he came back he would be outside the box.

Is there anything in the world as we know it, which would indicate the possibility of there being an existence in four dimensions? No definite answer can be returned to this question. But it may be of some interest to point out that there are certain facts which might be read by the light of the fourth dimensional theory.

To make this clear, let us suppose that space is really four dimensional, and that the three-dimensional space we know is, in this ampler space, like a surface is in our space.

We should then be in this ampler space like beings confined to the surface of a plane would be in ours. Let us suppose that just as in our space there are centres of attraction whose influence radiates out in every direction, so in this ampler space there are centres of attraction whose influence radiates out in every direction. Is there anything to be observed in nature which would correspond to the effect of a centre of attraction lying out of our space, and acting on all the matter in it? The effect of such a centre of attraction would not be to produce motion in any known direction, because it does not lie off in any known direction.

Let us pass to the corresponding case in three and two dimensions, instead of four and three. Let us imagine a plane lying horizontally, and in it some creatures whose experience was confined to it. If now some water or other liquid were poured on to the plane, the creatures, becoming aware of its presence, would find that it had a tendency to spread out all over the plane. In fact it would not be to them as a liquid is to us—it would rather correspond to a gas. For a gas, as we know it, tends to expand in every direction, and gradually increase so as to fill the whole of space. It exercises a pressure on the walls of any vessel in which we confine it.

The liquid on the plane expands in all the dimensions which the two-dimensional creatures on the plane know, and at the same time becomes smaller in the third dimension, its absolute quantity remaining unchanged. In like manner we might suppose that gases (which by expansion become larger in the dimensions that we know) become smaller in the fourth dimension.

The cause in this case would have to be sought for in an attractive force, acting with regard to our space as the force of gravity acts with regard to a horizontal plane.

Can we suppose that there is a centre of attraction somewhere off in the fourth dimension, and that the gases, which we know are simply more mobile liquids, expanding out in every direction under its influence. This view receives a certain amount of support from the fact proved experimentally that there is no absolute line of demarcation between a liquid and a gas. The one can be made to pass into the other with no moment intervening in which it can be said that now a change of state has taken place.

We might then suppose that the matter we know extending in three dimensions has also a small thickness in the fourth dimension; that solids are rigid in the fourth as in the other three dimensions; that liquids are too coherent to admit of their spreading out in space, and becoming thinner in the fourth dimension, under the influence of an attractive centre lying outside of our space; but that gases, owing to the greater mobility of their particles, are subject to its action, and spread out in space under its influence, in the same manner that liquids, under the influence of gravity, spread out on a plane.

Then the density of a gas would be a measure of the relative thickness of it in the fourth dimension: and the diminution of the density would correspond to a diminution of the thickness in the fourth dimension. Could this supposition be tested in any way?

Suppose a being confined to a plane; if the plane is moved far off from the centre of attraction lying outside it, he would find that liquids had less tendency to spread out than before.

Or suppose he moves to a distant part of the plane so that the line from his position to the centre of attraction lies obliquely to the plane; he would find that in this position a liquid would show a tendency to spread out more in one direction than another.

Now our space considered as lying in four-dimensional space, as a plane does in three-dimensional space, may be shifted. And the expansive force of gases might be found to be different at different ages. Or, shifting as we do our position in space during the course of the earth’s path round the sun, there might arise a sufficient difference in our position in space, with regard to the attractive centre, to make the expansive force of gases different at different times of the year, or to cause them to manifest a greater expansive force in one direction than in another.

But although this supposition might be worked out at some length, it is hard to suppose that it could afford any definite test of the physical existence of a fourth dimension. No test has been discovered which is decisive. And, indeed, before searching for tests, a theoretical point of the utmost importance has to be settled. In discussing the geometrical properties of straight lines and planes, we suppose them to be respectively of one and two dimensions, and by so doing deny them any real existence. 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. The other is that we really have a four-dimensional existence, but are not conscious of it. If we are in three dimensions only, while there are really four dimensions, then we must be relatively to those beings who exist in four dimensions, as lines and planes are in relation to us. That is, we must be mere abstractions. In this case we must exist only in the mind of the being that conceives us, and our experience must be merely the thoughts of his mind—a result which has apparently been arrived at, on independent grounds, by an idealist philosopher.

The other alternative is that we have a four-dimensional existence. In this case our proportions in it must be infinitely minute, or we should be conscious of them. If such be the case, it would probably be in the ultimate particles of matter, that we should discover the fourth dimension, for in the ultimate particles the sizes in the three dimensions are very minute, and the magnitudes in all four dimensions would be comparable.

The preceding two alternative suppositions are based on the hypothesis of the reality of four-dimensional existence, and must be conceived to hold good only on that hypothesis.

It is somewhat curious to notice that we can thus conceive of an existence relative to which that which we enjoy must exist as a mere abstraction.

Apart from the interest of speculations of this kind they have considerable value; for they enable us to express in intelligible terms things of which we can form no image. They supply us, as it were, with scaffolding, which the mind can make use of in building up its conceptions. And the additional gain to our power of representation is very great.

Many philosophical ideas and doctrines are almost unintelligible because there is no physical illustration which will serve to express them. In the imaginary physical existence which we have traced out, much that philosophers have written finds adequate representation. Much of Spinoza’s Ethics, for example, could be symbolized from the preceding pages.

Thus we may discuss and draw perfectly legitimate conclusions with regard to unimaginable things.

It is, of course, evident that these speculations present no point of direct contact with fact. But this is no reason why they should be abandoned. 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. And such a stream is no inapt symbol of a line of mathematical thought, which, passing through difficult and abstract regions, sacrifices for the sake of its crystalline clearness the richness that comes to the more concrete studies. Such a course may end fruitlessly, for it may never join the main course of observation and experiment. But, if it gains its way to the great stream of knowledge, it affords at the moment of its union the spectacle of the greatest intellectual beauty, and adds somewhat of force and mysterious capability to the onward current.

The Persian King.

PART I.

CHAPTER I.

In Persia there was once a king. On one occasion when he was out hunting he came to the narrow entrance of a valley. It was shut in on either side by vast hills, seemingly the spurs from the distant mountains. These great spurs spread out including a wide tract of land. Towards the entrance where he stood they approached one another, and ended in abrupt cliffs. Across the mouth of the valley stretched a deep ravine. The king, followed by courtiers, galloped along, searching a spot where the deep fissure might be shallower, so that descending into it he might reach the valley by ascending on the opposite side.

But at every point the ravine stretched downwards dark and deep, from cliff to cliff, shutting off all access to the valley.

At one point only was there a means of crossing. There were two masses of rocks, jutting out one from either side like the abutments of a natural bridge, and they seemed to meet in mid air.

The mass trembled and shook as the king spurred his horse over it, and the dislodged stones reverberated from side to side of the chasm till the noise of their falling was lost.

Before the first of his courtiers could follow him one of the great piers or abutments gave way—the whole mass fell crashing down. The king was alone in the valley.

“So ho,” he cried, “the kingdom of Persia is shrunk to this narrow spot!” and without troubling himself for the moment how he should return, he sped onward.

But when he had ridden far into the valley on his steed that could outnumber ten leagues in an hour, and had returned to the entrance of it, he saw no trace of a living soul on the opposite brink of the cleft. No sign was left, save a few reeds bent down by the passage of the mounted train, that any human being had stood on the opposite side for ages.

The evening came on apace. Yet no one returned. Again he rode far into the valley. For the most part it was covered with long grass, but here and there a thick and tangled mass of vegetation attested to a great luxuriance of soil, while the surface was intersected here and there with rivulets of clear water, which finally lost their way in the dark gorge over which he had just so rashly adventured. But on no side did the steep cliffs offer any promise of escape.

When the night came on he stretched himself beneath one of the few trees not far from the ravine, while his faithful horse stood tranquilly at his head.

He did not awake till the moon had risen. But then suddenly he started to his feet, and walking to the edge of the cleft, peered over to the land from whence he had come. For he thought he heard sounds of some kind that were not the natural ones of the rustling wind or the falling water. Looking out he saw clearly opposite to him an old man in ragged clothing, leaning against a rock, holding a long pipe in his hands, on which he now and again played a few wild notes.

“Oho, peasant!” cried the king. “Run and tell the head man of your village that the king bids him come directly, and will have him bring with him the longest ropes and the strongest throwers under him.”

But the old man did not seem to give heed. Then the king cried, “Hearken, old man, run quickly and tell your master that the king is confined here, and will reward him beyond his dreams if he deliver him quickly.”

Then the old man rose, and coming nearer to the edge of the ravine stood opposite, still playing at intervals some notes on his long pipe. And the king cried, “Canst thou hear? Dost thou dare to refuse to carry my commands? For I am the king of Persia. Who art thou?”

Then the old man made answer, putting his pipe aside: “I am he who appears only when a man has passed for ever beyond the ken of all that have known him. I am Demiourgos, the maker of men.”

Then the king cried, “Mock me not, but obey my commands.”

The old man made answer, “I do not mock thee; and oh, my Lord, thou hast moved the puppets I have made, and driven them so to dance on the surface of the earth that I would willingly obey thee. But it is not permitted me to pass between thee and the world of men thou hast known.”

Then the king was silent.

At length he said, “If thou art really what thou sayest, show me what thou canst do; build me a palace.”

The old man lifted his pipe in both his trembling hands, and began to blow.

It was a strange instrument, for it not only produced the shriller sounds of the lute, and the piercing notes of the trumpet, but resounded with the hollow booming of great organ pipes, and amongst all came ever and again a sharp and sonorous clang as of some metal instrument resounding when it was struck.

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. And lo, as the strains sound, outside—palpable, large as the firmament, or real as the smallest thing you can take up and know it is there—outside stands some existence revealed—to be known and returned to for ever.

So the king, listening to this music, felt that something was rising behind him. And turning, beheld course after course of a great building. Almost as soon as he had looked it had risen completed, finished to the last embossure on the windows, the tracery on the highest pinnacles. All had happened while the old man was blowing on his pipe, and when he ceased all was perfect.

And yet the appearance was very strange, for a finished and seemingly habitable building rose out of waste unreclaimed soil, strewn with rocks and barren. No dwellings were near the palace to wait on it, no roads led to it or away from it.

“There should be houses around it, and roadways,” said the king; “make them, and fields sown with corn, and all that is necessary for a state.”

Blowing on his pipe in regular recurrent cadences, the old man called up houses close together, than scattered singly along roads which stretched away into the distance, to be seen every here and there perfectly clearly where they ascended a rising ground. And near at hand could be distinguished fields of grain and pasture land.

Yet as the king turned to walk towards the new scene, the old man laughed. “All this is a dream,” he cried; “so much I can do, but not at once.” And breathing peals of music from his pipe, he said, “This can be, but is not yet.”

“What,” asked the king, “is all a delusion?” and as he asked everything sank down. There was no palace, no houses or fields, only the steep precipice-locked valley, whither the king had ridden; and his horse cowering behind him.

Then the king cried, “Thou art some moonstruck hermit, leading out a life of folly alone. Get thee to the village thou knowest, and bring me help.”

But the old man answered him saying, “Great king, I am bound to obey thee, and all the creative might of my being I lay at thy feet; and lo, in the midst of this valley I make for thee beings such as I can produce. And all that thou hast seen is as nothing to what I can do for thee. The depths of the starry heavens have no limit, nor what I do for thee. Hast thou ever in thy life looked into the deep still ocean, and lost thy sight in the unseen depths? Even so thou wilt find no end in what I will give thee. Hast thou ever in thy life sought the depths of thy love’s blue eyes, and found therein a world which stretched on endlessly? Even so I bring all to thy feet. Now that all the gladness of the world has departed from thee, behold, I am a more willing servant than ever thou hast had.”

And again he played, and a hut rose up with a patch of cleared soil around it, and a spring near by.

Then the king said, “Here will I dwell, and if I am to be cut off from the rest of the world, I will lead a peaceful life in this valley.”

The sun was rising, the sounds had ceased, and the old man had disappeared.

CHAPTER II.

He made his way slowly to the patch of cultivated ground, he knocked at the door of the hut, and then he called out. No answer was made to the sound of his voice, he entered, and saw a rude, plain interior. There were two forms half lying, half propped up by the walls, and some domestic implements lay about. But when he spoke to the beings they did not answer, and when he touched their arms they fell powerless on the ground and remained there. A terrible fear came on the king lest he should become such as these. He left them and again sought a possible outlet, but fruitlessly. And that evening he sought the old man again and inquired what sort of beings these were.

“For though in form and body like children outwardly,” said the king, “they do nothing and seem unable to move; are they in an enchanted slumber?”

Then the old man came near to the edge of the ravine and, speaking solemnly and low, said:

“O king, thou dost not yet know the nature of the place wherein thou art. For these children are like the children thou hast known always both in form and body. I have worked on them as far as is within my power. But here in this valley a law reigns which binds them in sleepfulness and powerlessness. For here in everything that is done there is as much pain as pleasure. If it is pleasant to tread a downward slope there is as much pain in ascending the upward slope. And in every action there is a pleasant part and a painful part, and in the tasting of every herb the beings feel a bitter taste and a sweet taste, so indistinguishably united that the pleasure and the pain of eating it are equally balanced. And as hunger increases the sense of the bitterness in the taste increases, so it is never more pleasant to eat than not to eat. Everything that can be done here affords no more pleasure than it does pain, from the greatest action down to the least movement. And the beings as I can make them, they follow pleasure and avoid pain. And if the pleasure and the pain are equal they do not move one way or the other.”

“This is impossible,” said the king.

“Nay,” said the old man, “that it is as I have said I will prove to thee.” And he explained to the king how it would be possible to stimulate the children to activity, for he showed him how he could divest anything that was done of part of its pain and render it more pleasurable than painful. “In this way thou canst lead the beings I have given thee to do anything,” said the old man, “but the condition is that thou must take the painful part that thou sparest them thyself.” And he bade the king cut himself of the reeds that grew by the side of the ravine, and told him that putting them between himself and any being would enable him to take a part of the pain and leave in their feeling the whole of the pleasure and the pain diminished by that part which he bore himself.

Then the king cut of the reeds that grew by the side of the ravine. He went to the hut where these beings lay, and, taking the reeds in his hand, he placed one between the child’s frame and himself. And the child rose up and walked, while he himself felt a pain in his limbs. And he found that by taking a pain in each part of him the child would exercise that part; if he wished the child to look at anything he, by bearing a pain in his eyes, made looking at it pleasurable to the child, and accordingly the child did look at the object he wished him to regard. And again, by bearing a bitter taste in his mouth he made the child feel eating as pleasant, and the child gathered fruits and ate them.

Then the king by using two reeds made both the children move, and they went together wheresoever he wished them. But they had not the slightest idea of the king’s action on them. They recognized each other, and played with each other. They saw the king and had a certain regard for him, but of his action on them they knew nothing. For they felt his bearing the pain as this thing or that being pleasurable. They felt his action as a motive in themselves.

And all day long the king went with them, leading them through the valley, bearing the pain of each step, so that the children felt nothing but pleasure. But at nightfall he led them back to the rude dwelling where he had found them. He led them by taking the pain from their steps in that direction, and not taking any of the pain from steps in any other direction.

And when they had entered the dwelling-place he removed his reeds from them. Immediately they sank down into the state of apathy in which he had found them. They did not move.

And the king at nightfall sought again the side of the ravine.

Gazing across it he saw the sandy waste of the land from which he had come, he saw the great stones which were scattered about, looking pale and grey in the moonlight. And presently in the shadow of a rock near the opposite brink he discerned the form of the old man.

And he cried out to him, and bade him come near. And when the old man stood opposite to him, he besought him to tell him how he could make the beings go through their movements of life without his bearing so much pain.

And the old man took his staff in his hand, and he held it out towards the king, over the depth.

“Behold, O king, thy secret,” he cried. And with his other hand he smote the staff which was pointing down into the depths. The staff swung to and fro many times, and at last it came to rest again.

Then the king besought him to explain what this might signify.

“Thou hast been,” replied the old man, “as one who, wishing to make a staff swing to and fro, has made every movement separately, raising it up by his hand each time that it falls down. But, behold, when I set it in movement it goes through many swings of itself, both downward and upward, until the movement I imparted to it is lost. Even so thou must make these beings go through both pleasure and pain, thyself bearing but the difference, not taking all the pain.”

“Must I then,” asked the king, “by bearing pain give these beings a certain store of pleasure, and then let them go through their various actions until they have exhausted this store of pleasure?”

Then the old man made answer. “Can I have any secrets from thee? Hearken, O king, and I will tell thee what lies behind the shows of the world. What I have shown thee is an outward sign and symbol of what thou shouldst do, but it lies far outside those recesses whither I shall lead thee. Thou couldst indeed give these beings a store of pleasure, and they would go through their actions until it was all spent; but then thou wouldst be as one of themselves. Thou wouldst have to perform the painful part of some action and let them perform the pleasant part, and thus thou wouldst be immersed in the same chain of actions wherein they were. For regard my staff as it begins to swing. It is not I that make the movement that is imparted to it; that movement lay stored up in my arm, and when I struck the staff with my arm it was as if I had let another staff fall which in its falling gave up its movement to the one I held in my hand.”

“Where, then, does the movement go to when the staff ceases to swing,” asked the king.

“It goes to the finer particles of the air, and passes on and on. There is an endless chain. It is as if there were numberless staffs, larger and smaller, and when one falls it either raises itself or passes on its rising to another or to others. There is an endless chain of movement to and fro, and as one ceases another comes. But, O king, I wish to take thee behind this long chain and to place thee where thou mayest not say, I will do this or that; but where thou canst say, This whole chain of movement shall be or shall not. For as thou regardest this staff swinging thou seest that it moves as much up as it does down, as much to right as to left. And if the movements which it goes through came together it would be at rest. Its motion is but stillness separated into equal and opposite motions. And in what thou callest rest there are vast movements. It shall be thine, O king, to strike nothingness asunder and make things be. Nay, O king, I have not given thee these beings in the valley for thee to move by outward deeds, but I have given them to thee such that thou canst strike their apathy asunder and let them live. And know, O king, that even as those beings are whom thou hast found, so are all things in the valley down to the smallest. The smallest particle there is in the valley lies, unless it were for me, without motion. Each particle has the power of feeling pain and of feeling pleasure, but by the law of the valley these are equal. Hence of itself no particle moves. But I make it move, and all things in the valley sooner or later move back to whence they came. The streams which gather far off in the valley I lead along to where they fall into the depths between us. There they shiver themselves into the smallest fragments, and each fragment I cause to return whence it first came. And, O king, in all this movement, since it ends where it began, there is no more pleasure than pain. It is but the apathy of rest broken asunder. But the particles will not go through this round of themselves. I bear the pain to make them go through, each one the round I appoint it.”

“How then,” exclaimed the king, thinking of the pain he had felt in directing the movements of the children, “canst thou bear all this pain?”

“It is not much,” answered the old man; “and were it more I would willingly bear it for thee. For think of a particle which has made the whole round of which I spoke to you—it will make this journey if on the whole there is the slightest gain of pleasure over pain; and thus, although for each particle in its movement at every moment I bear the difference of pain, the pain for each particle is so minute that the whole course of natural movements in the valley weighs upon me but little. And behold all lies ready for thee, O king. I have done all that I can do. I can perfect each natural process, each quality of the ground, each plant and herb I make, up to the beings whom thou hast found. They are my last work, and into your hands I give them.”

And when he had said this, the old man let drop his staff, and placing both hands to his breast he seemed to draw something therefrom, and with both hands to fling it to the king.

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.”

The king took the rays and placed them on his breast; thence they went forth, and through them he touched and knew every part of the valley. And thinking of the hut where the children lay, the king perceived through the rays that went thither that the walls were tottering, and like to fall on the children. And through his rays he knew that the children perceived this in a dull kind of way; but since in their life there was no more pleasure than pain, they did not feel it more pleasant to rise up and move than to be still and be buried.

But the king through the rays, as before through the reeds, took the pain of moving, and the children rose and came out of the hut; and soon they were with the king, running and bounding as never children leapt and ran, with ecstasy of movement and unlimited exuberance of spirit. But as they leapt and ran the king felt an increasing pain in all his limbs. Still he liked to see them in their full and joyous activity, and he wished them to cast off that dull apathy in which they lay. So all through the night he roamed about with them thinking of all the wildest things for them to do, and leading them through dance and play, every movement and activity he could think of.

At length the rising sun began to warm the air, and the king, exhausted with pain, left off bearing it for them.

After a few languid movements the children sank down on a comfortable bank into a state of absolute torpor. The king looked at them; it seemed inconceivable that they could be the same children who had been running about so merrily a few moments ago. Thus far he had received no advantage from the rays the old man had given him, except that he could touch the children more easily.

He turned wearily and looked around. His horse stood there. But instead of whinnying and running up to greet him, the faithful animal stood still, looking across the ravine.

“Perchance without my burden, and with the strength these rays may impart,” thought the king, “he might manage the leap.”

The horse was standing opposite the remains of the natural bridge over which the two had so rashly crossed the day before. The king touched the horse with his rays. As with a sudden thrust of the spur, the noble animal rushed forward and leapt madly from the fragments of the arch. His fore feet gained the opposite brink, and with a terrible struggle he raised himself on the firm ground. Then he stood still. With a crash the remaining fragments of the bridge fell into the gulf, leaving the vast gap unnarrowed at any part. The horse stood looking over the ravine. But though the king called him by name, the faithful creature who used to come to him at the slightest whisper paid no heed. In a few moments he galloped off along the track the courtiers had pursued.

CHAPTER III.

The king being left thus with the children, applied himself to thought. He directed his rays to one of the children and caused it to stand up, and, following the counsel of the old man, he thought of an action. The action he thought of was that of walking, and he separated it into two acts; the one act moving the right foot, the other act moving the left foot. And he separated the apathy in which the child was into pleasure and pain; pleasure connected with the act of moving the right foot, pain connected with the act of moving the left foot. Immediately the child moved forward its right foot, but the left foot remained motionless. The child had taken the pleasure, but the pain was left; or, since the king had connected the pleasure and pain with two acts, it may be said, had done the pleasant act and left the painful act undone.

After waiting some time to see if the child would move, the king took the pain of moving the left foot; instantly the child moved it, and as soon as it had come to the ground again it moved the right foot, which was the pleasant act. But then it stopped. And by no amount of taking pains in the matter of the left foot could the king get the child into the routine of walking. As soon as he ceased to take the pain of moving the left foot, the child remained with the right foot forward. At last he removed his attention from the movement of the child, and it sunk back again torpor.

The rest of the day the king spent in reflection, and in making experiments with the children. But he did not succeed any better. Whatever action he thought of they went through the pleasant act, but made no sign of going through the painful act.

When darkness came the king perceived the faint luminousness of his rays: unless he had known of them he would hardly have perceived it.

And now he tried a new experiment. He took one of the rays, and, detaching it from the rest, he put it upon the body of one of the children, going out from its body and returning again to its body, so that it went forth from the child and returned to the child again. He then caused the child to stand up, and again tried it with the action of walking. His idea was this: the child required a power of bearing its own pain in order to go through a painful act, and as the rays enabled him to bear their pain, the ray proceeding from the child and coming back to it might enable it to bear its own pain. And now he separated the apathy into pleasure and pain as before. The child moved the right foot, and then when it had moved it, he saw that it actually began to move the left foot. But it did not move it a complete step, and after the next movement of the right foot the left foot did not stir.

Again and again the king tried the children, but his attempts came to nothing. One halting step of the left foot he could get them to go through, but no more.

He spent many hours. Suddenly the cause of his failure flashed upon him. “Of course,” he said to himself, “they don’t move, for I have forgotten to take part of the pain. If they went on moving their left feet they would have no balance of pleasure.”

And he tried one of them again. The child moved the right foot, then began to move the left foot. The king now by means of his rays took part of the pain of the movement of the left foot, and the child completed the step with it. Then of course it moved the right foot, for that was pleasant, and again the king took part of the pain of moving the left foot, and the child completed its second step. It walked.

The difficulty was surmounted. Soon both the children were moving hither and thither like shifting shadows in the night, and the king felt just a shade of pain.

The children would come up to him and talk with him, if he took the difference of pain which made it pleasant for them to do so. But they had no idea of his action on them, for by his taking the difference of pain they found an action pleasant, and felt a motive in themselves to do it, which they did not in the least connect with the being outside themselves to whom they spoke. They looked on him as some one more powerful than themselves, and friendly to them.

As soon as he was assured of the practical success of his plans, the king let the children relapse into their apathy while he thought. He conceived the design of forming with these children a state such as he had known on earth—a state with all the business and affairs of a kingdom, such as he had directed before. The vision of the palace which the old man had shown him rose up. He saw in imagination the fertile fields, with the roads stretching between them; he saw all the varied life of a great state. Accordingly from this time he was continually directing their existence, developing their powers, and learning how to guide them. And just as on first learning to read whole words are learnt which are afterwards split up into letters by the combinations of which other words are formed; so at first he thought of actions of a complicated nature, such as walking, and associated the moments of pleasure and pain with the acts of which such actions were composed. But afterwards he came to regard the simpler actions by the combination of many of which the beings were made to walk, and with the separate acts of these simple actions he associated pleasure and pain.

And at first the beings were conscious of these simple acts and nothing else, but in order that they might carry out more complicated actions, he developed the dim apprehension which they had, and led it on to the consciousness of more complicated actions. The simplest actions became instinctive to these beings, and they went through them without knowing why. But if at any time the king ceased to take the difference of pain, these actions, seemingly automatic as they were, ceased.

At certain intervals the king found his plans inconvenienced. Every now and then the beings went off into a state of apathy. Enough pain was borne for them to make it just worth their while to go through the actions of each routine. But any additional complication or hindrance unforeseen by the king was too much for them, and they sank under it. To remedy this he took in every action a slight portion of pain more than he had done at first. Thus he expended a certain portion of pain-bearing power to give stability to the routines. And the margin of pleasure over pain thus added was felt by the beings as a sort of diffused pleasure in existence, which made them cling to life.

Now in guiding these beings towards the end he wished to obtain, the king had to deal with living moving beings, and beings whose state was continually changing. And this led him to adopt as the type of the activity of these beings not a single action, but a succession of actions of the same kind, coming the one after the other. Thus a being having been given a certain activity, it continued going on in a uniform manner until the king wished to alter it.

Again it was important to keep the beings together, to prevent their being lost in the remote parts of the valley, and consequently the king took, other things being equal, a certain amount of the pain of motion towards the centre, and took none of the pain in any movement away from the centre of the valley. Thus the inhabitants had a tendency to come towards the centre, for there was a balance of pleasure in doing so, and thus they were continually presenting themselves to his notice, and not getting lost.

Of course, if there was any reason why he wanted them away from the centre, the king ceased his bearing of the pain of motion towards the centre, and then they were under the other tendency solely, which he imparted to them, in virtue of his bearing pain in another respect. And in everything that he did the king had regard to the circumstances in which the beings were placed, and the objects which he wanted to obtain. He did not spare any of his pain-bearing power to give them pleasure purely as a feeling, but always united the pleasure he obtained for them by his suffering with some external work.

And as time went on and the number of the inhabitants increased, he introduced greater order and regularity into the numberless activities which he conceived for them. The activities formed regular routines, conditioned by the surroundings of the being and the routines of those around it. A routine did not suddenly cease without compensation; but if the king wished it to stop he let another activity spring up at once in place of it, so that there was no derangement. The beings gradually became more intelligent, so that they could be entrusted with more difficult routines, and carried them out successfully, the king, of course, always taking the difference of pain necessary to make it worth their while. And they even became able to carry out single activities on a large scale, involving the co-operation of many single routines. For they had a sense of analogy, and observing some activity which the king had led them through on a small scale, and in which they had found a balance of pleasure, they were ready to try a similar one on a larger scale.

There was one feature springing from the advanced intelligence of the inhabitants which it is worth while to mention. Many of the possible activities which the beings could go through, instead of consisting of a pleasurable part first and a less painful part afterwards, consisted of a painful part first and a pleasurable part afterwards. This might happen by the particular arrangement of the acts of which the compounded activity consisted, the acts having already moments of pain or pleasure affixed to them, and happening to occur in such dispositions that the first part of the activity was painful, the next part pleasurable.

Now when the intelligence of the inhabitants was developed, the king, by leading them to think of such an activity, could induce them to go through with it. For the idea of the pleasure which would accompany the second part of the activity lightened the pain of the first. And this, combined with the portion of the pain which the king bore, almost counterbalanced the pain connected with the first part of the activity. Thus the beings were enabled to go through the painful part of the activity. But when they came to the second part of the activity the creatures were much disappointed. For by the law of the valley pleasure and pain were equal (except for the small part which the king bore). Now the pleasures of expectation had been so great that when the time came for the act usually associated in their minds with pleasure, the pleasure due had most of it been used up.

From this circumstance a saying arose amongst the inhabitants which was somewhat exaggerated, but which had a kernel of truth in what has just been described. The saying was that “The pleasure for which a labour has been undertaken flies away as soon as the labour has been finished, and nothing is left but to begin a new labour.” And, again, another saying: “The enjoyment of a thing lies in its anticipation, not in its possession.”

All this which has been so briefly described had in reality taken a long time. And now fields were cultivated, better houses were built. The inhabitants of the valley had increased greatly in number, and were divided up into several tribes, inhabiting different parts of the valley. But the most favoured position was the centre, and for the possession of the centre there were contentions and struggles. There the king’s activity in bearing was greatest, and the life was most developed.

All around the outskirts of the valley dwelt the ruder and less advanced people, who were called barbarians and savages by those nearer the centre.

CHAPTER IV.

Now when the king saw the inhabitants becoming more like the human beings he had known, he felt that he was solitary, and he desired to have some intercourse with them. But when he appeared amongst them they recognized him at once as some one more powerful than themselves, and were afraid of him. In their alarm they tried to lay hands on him. When he, to prevent their attacks, withdrew his continued bearing the difference of pain in their actions, those who were attacking him sank into apathy and became as the children whom he had first found.

And a horrible report sprang up amongst the inhabitants of a terrible being who came amongst them, and who struck all who looked on him with torpor and death. So the king ceased to walk amongst them. Still it was long since he had heard the sound of a voice speaking to him, and he wished for a companion. He sought again the old man, and standing at the edge of the chasm he called upon him.

And the old man appeared. “Art thou weary, O king, of thy task?”

“Nay,” replied the king; “but I wish to make myself known to the inhabitants that I may speak with them and they with me.”

And the old man counselled him to give some of his rays to one amongst the beings, for then this being having these rays and the power of bearing pain for another other than himself, would be like the king, and being like him would understand him.

Now the king sought over the whole of the valley, and of all the inhabitants he found one most perfect in form and in mind. He was the son of a king, and destined to reign in his turn over a numerous people. 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. Wherefore,” he cried, “let us seek an end to this show. Let us pray to be delivered, that at last, pain ceasing, we may pass into nothingness.”

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.

Yet all his life his deeds were noble, and he passed from tribe to tribe, bearing the burdens and calling forth the sleeping to activity.

CHAPTER V.

It is now the place in which to give a clear account of the king’s activity, and explain how he maintained the varied life of the valley.

And the best plan is to take a typical instance, and to adopt the Arabic method of description. By the Arabic method of description is meant the same method which the Arabs used for the description of numerical quantities. For instance, in the Arabic notation, if we are asked the number of days in the year, we answer first 300, which is a false answer, but gives the nearest approximation in hundreds; then we say sixty, which is a correction; last of all we say five, which makes the answer a correct one, namely, 365. In this simple case the description is given so quickly that we are hardly conscious of the nature of the system employed. But the same method when applied to more difficult subjects presents the following characteristics. Firstly, a certain statement is made about the subject to be described, and is impressed upon the reader as if it were true. Then, when that has been grasped, another statement is made, generally somewhat contradictory, and the first notion formed has to be corrected. But these two statements taken together are given as truth. Then when this idea has been formed in the mind of the reader, another statement is made which must likewise be received as a correction, and so on, until by successive statements and contradictions, or corrections, the idea produced corresponds to the facts, as the describer knows them.

Thus the activity of the king will be here described by a series of statements, and the truth will be obtained by the whole of the statements and the corrections which they successively bring in.

When the king wished to start a being on the train of activity he divided its apathy into pleasure and pain. The pleasure he connected with one act which we will call A. The pain he associated with another act which we will call B.

These two “acts,” A and B, which together form what we call an “action,” were of such a nature that the doing of A first and then of B was a process used in the organization of the life in the valley.

Thus the act A may be represented by moving the right foot, B by moving the left foot, then AB will be the action of taking a step. This however is but a superficial illustration, for the acts which we represent by A and B were fundamental acts, of which great numbers were combined together in any single outward act which could be observed or described.

Suppose for the present that there is only one creature in the valley. The king separates his apathy with regard to the action AB. Let us say he separates his apathy into 1000 pleasure and 1000 pain. Of the pleasure he lets the being experience the whole, of the pain he bears an amount which we will represent by 2. Thus the being has 1000 pleasure and 998 of pain, and the action is completed. His sensation is measured by the number 1000 in the first act, and by 998 in the second act.

But the king did not choose to make the fundamental actions of this limited and finishing kind. As the type of the fundamental activity, he chose an action, and made the being go through it again and again. Thus the being would go through the act A, then the act B. When the action AB was complete it would go through an act of the kind A again, then through an act of the kind B. Thus the creature would be engaged in a routine of this kind, AB, AB, AB, and so on.

And if the creature had been alone, and this had been the sole activity in which it was concerned, the king would have gone on bearing 2 of pain in each of these actions. The king would have kept the routine going on steadily, the creature bearing 1000 of pleasure in each A, and 998 of pain in each B.

At this point it may be asked that an example should be given of one of these elementary routines which the king set going. And this seems a reasonable request, and yet it is somewhat too peremptory. For in the world we may know of what nature the movements of the atoms are without being able to say exactly what the motion of any one is. In such a case a type is the only possible presentation. Again, take the example of a crystal. We know that a crystal has a definite law of shape, and however much we divide it we find that its parts present the same conformation. We cannot isolate the ultimate crystalline elements, but we infer that they must be such as to produce the crystal by their combination.

Now life on the valley was such in its main features as would be produced by a combination of routines of the kind explained. There were changes and abrupt transitions, but the general and prevailing plan of life was that of a routine of alternating acts of a pleasurable and a painful kind. It was just such as would be built up out of elementary routines, on which the king could count, and which, unless he modified their combinations, tended to produce rhythmic processes of a larger kind. And even the changes and abruptnesses had a recurrent nature about them, for if any routine in the valley altered suddenly, it was found that there were cases of other routines altering in like manner, when the conditions under which they came were similar. Thus the fundamental type of the action which the king instituted was that of a routine AB, AB, as described above. But there were two circumstances which caused a variation, so that this simple routine was modified.

Firstly, there was not one being only but many.

Secondly, the king wished to have some of his pain-bearing power set free from time to time. He did not wish to have to be continually spending it all in maintaining the routines he had started at first, and those immediately connected with them.

When he first began to organize the life of the beings he did not consciously keep back any of his pain-bearing power, but threw it all in the activities which he started. Still from time to time he wished to start new activities quite unconnected with the old, and for this reason he withdrew some of his pain-bearing power, as will be shown afterwards.

There were many beings. The king chose that the type of activity in each should be a routine. In that way he could calculate on the activity, and hold it in his mind as a settled process on whose operation he could count. But as the routines of the beings proceeded they came into contact with one another, and made, even by their simple co-existence, something different from what a routine by itself was. They interwove in various ways. Then, in order to take advantage of the combinations of these routines, or to modify them, it was necessary to set going other routines.

In order to be able to originate these connected routines the king adopted the following plan.

In the first action AB he separated the creatures’ apathy into 1000 pleasure and 1000 pain, bearing 2 of the pain himself. The creature thus went through 1000 of pleasure and 998 of pain. In the next action AB he did not separate the beings’ apathy up into so much pleasure and pain. He separated it up into 980 pleasure and 980 pain, that is, each moment of feeling was 20 less in sensation than the moments of feeling were in the first action.

Now it is obvious that if the bearing 2 of pain will make it worth while for a being to go through 1000 pleasure and 998 pain, then the bearing on the king’s part of 1 of pain would make it worth while for the being to go through 500 pleasure and 499 of pain.

And a similar relation would hold for different amounts of pleasure and pain. Thus clearly for the being to go through 980 of pleasure and the corresponding amount of pain, it would not be necessary for the king to bear so much as when the being went through 1000 of pleasure and the corresponding amount of pain.

Consequently when the king divided the beings’ apathy into 980 pleasure and 980 pain, it would not be necessary for him to bear 2 of pain to make it worth the beings’ while to go through the action. The king would not bear so much as 2 of pain, and thus he would have some of his pain-bearing power set free. He would have exactly as much as would enable him to make it worth a being’s while to go through an action with the moments of 20 of pleasure and 20 of pain.

And this—with a correction which will come later—is what the king did. He employed the pain-bearing power thus set free in starting other routines. Thus in the routine AB, AB, AB there would be first of all the action AB. Then along with the second action AB, the king (with the pain-bearing power set free) started an action CD—the beginning of a routine CD, CD, CD. Thus as the first routine went on and came into connection with other routines, new and supplementary routines sprang up which regulated and took advantage of the combinations of the old routines.

The amount of the moments of pleasure in the routine CD, was (with a slight correction explained below) measured in sensation, equal to 20. Thus the moment of pleasure in the first A being 1000, the moment of pleasure in the second A was 980, the moment of pleasure in the first C was 20 (subject to the correction spoken of). Thus the total amount of sensation in the second A and the associated act C, taken together (but for a small correction) was equal to the sensation in the first A. Hence the three points which were characteristic of the activity of the beings in the valley are obvious enough.

1. There is as fundamental type a routine AB, AB, AB, the sensation involved in which goes on diminishing.

2. There are routines CD, CD, &c., connected with AB, AB, in which the sensation which disappears in the routine AB, AB seems to reappear.

3. In the action AB itself there is a disappearance of sensation. The sensation connected with A is 1000, that connected with B is 998. Thus 2 of sensation seems to have disappeared. This 2 of sensation is of course the pain which the king bore, and which was the means whereby the creature was induced to go through the action at all. But looked at from the point of view of sensation, it seems like a diminution of amount. This diminution of amount, owing to the correction spoken of above, was to be found regularly all through the routine.

And now, with the exception of the final correction, the theory of the king’s activity is complete. There are certain mathematical difficulties which render an exhaustive account somewhat obscure in expression. When we take a general survey of a theory we want to see roughly how it all hangs together; but if we mean to adopt it, the exactitude of the numerical relations becomes a matter of vital importance.

It must be added that the numbers taken above were taken simply for purposes of illustration. In reality the pain born by the king was less in proportion.

The exhaustive account which follows deals with small numerical quantities. It had better be omitted for the present, and turned to later on for reference.

EXHAUSTIVE ACCOUNT.

We keep for the time being to the numbers used above. When the king had enough pain-bearing power set free in the second action of the routine AB, AB to start another routine CD, of 20 pleasure 20 pain, he did not use it all. He only used enough of it to set a routine going the moments of pleasure and pain in which were 16 in sensation. The routine CD was made up of acts with 16 of pleasure and 16 of pain.

The sensation in the first A was 1000, in the first B it was 998, giving a disappearance of 2. In the second A it was 980, and in C, which starts concurrently with the second A, it was not 20 as might have been expected, but 16, giving a loss of 4. The second A is less than the first A by 20. Searching for that 20 we find 16 in C. But there has been a disappearance of 4.

Looking now at the successive acts in the series we have in A 1000 sensation, in B 998 sensation, in A and C together 996 sensation.

The cause of the loss between A and B has already been explained. That between B and the second A with C remains to be accounted for.

It has been already said that the king withdrew some of his pain-bearing power from the routine AB and all routines connected with it, thus he was enabled to start activities altogether unconnected with those which he had originated, and was with regard to the products of his own activity as he had been at first, with regard to the beings in the valley before he started them on the path of life. And it was in consequence of his withdrawal of his pain-bearing power that the amount of sensation in C was not 20 but was less. This loss of 4 of sensation to the being corresponded to a setting free of a certain portion of pain-bearing power on the part of the king. And thus as the process went on, a portion of his power was continually being returned to him.

In the table below the first line of figures contains the amount of sensation in the actions AB, AB. The second line of figures contains the amount of sensation in the actions CD, CD. The third line of figures relates to another connected routine EF, EF, which originates in a manner similar to CD. The fourth line of figures represents the amount of pain borne by the king, the fifth line represents his pain-bearing power set free.

If the total amount of sensation which is experienced by the being in the original routine and the connected routines in the consecutive stages be summed up, it will be found to be

and so on.

Finally, the proportion of pain borne by the king was so small compared with the sensation experienced by the being, that A and B were apparently equal in sensation. Thus the sensation in the second A and in C together becomes apparently equal to that in B. And instead of the sensation diminishing quickly as shown above, it was only after a great many acts of the primary and connected routines had been gone through that any diminution of sensation in the form which the being could experience it was to be detected. Thus, as before stated, there was:

1. A routine of continually diminishing sensation.

2. Connected routines the sensation in which was apparently equal to that lost in A.

3. There was a continuous disappearance of sensation from the experience of the beings accompanying every step of the routine. The sensation which they could experience was less in every subsequent step and connected steps than in any one in which it was measured.

CHAPTER VI.

The history of the events which took place in the valley in their due order and importance must be sought elsewhere. But let us return and look at the condition of the valley and its inhabitants. Let us see what has become of them after a great lapse of time.

It is a fair, a beautiful land. The greater part of it is cultivated. There is no war—even to the extremest confines of the valley there is peace. Passing from the remote confines where still dwell a barbarous race, we come, as we approach the metropolis, amongst a more and more polite and refined people. In the metropolis itself the buildings are numerous and of great size. The palace which the king saw rise under the old man’s music is there, but another ruler dwells in it. Near the palace are two vast buildings standing on each side of a wide open court. There is no other building near save one between them, a comparatively small edifice of brick. These buildings are the assembly halls of the two most important councils in the valley. In the one on the left-hand side of the palace met the most distinguished of the inhabitants who from a special inclination or fitness were entrusted with the regulations about the pleasure and pain of the inhabitants. They framed the rules according to which each inhabitant must conform in his pursuit of pleasure, and they made the regulations whereby the whole body of inhabitants were supposed to gain an increase in pleasure and to avoid pain.

In the building on the right hand of the palace met those of the inhabitants who had studied the nature of feeling most deeply, and who from temperament or for other reasons had in their course of study not paid so much attention to whether feelings were painful or pleasurable, but who had studied their amount and regularity of their recurrence. They were the thinkers from whom all the practical inhabitants derived their rules of business. They devised the means and manner of putting into execution what was decided on in the other assembly. They did not often propose any positive enactment themselves, but were always able to show how the proposals of the other council could be carried into effect.

Their power was derived in this manner. The king had connected the feelings of pleasure and pain with certain acts, and had given each being a routine. Now as he himself made use of this routine and combined the routines of different individuals to bring about the results he desired, so also did the rulers of the valley. The routines of the individuals were studied and classified, and if any work was required to be done, those individuals whose routines were appropriate were selected and brought to the required spot. Now to effect this a careful study of the different routines was necessary, and also a knowledge of what stage they were at. For it would be no use bringing an individual whose routine was almost at an end to a work which was just beginning. Hence the most delicate instruments and processes had been devised for measuring the amount of feeling experienced by any individual, whether of pleasure or of pain, and a careful classification had been made of all routines.

But it is best to study the constitution of the state in a regular order, and the questions of pleasure and pain considered as such were esteemed the most important.

The inhabitants knew that they sought pleasure and avoided pain, and the great object was to make their life more pleasurable. Two means were adopted, the banishing of the causes of pain, and the obtaining causes of pleasure.

By causes of pain and pleasure they meant those objects with which the king had associated the feelings of pleasure and pain in the equal and opposite moments into which he had divided their apathy.

But in this respect they were in error to a certain extent, for it was not so much in respect to things as in respect to actions that the king separated their apathy into pleasure and pain. For instance, there was a peculiar species of shell which was found in many parts of the valley, covered with strange and involved lines and marks. Now the king had struck the apathy of the inhabitants into two moments with regard to this shell, one of pain connected with tracing out the twistings and interweavings of the hues on the shell, one of pleasure in contemplating the shell when the twistings and interweavings had been deciphered. Now it was the custom of the inhabitants to call the shell in its undeciphered condition a painful object, in its deciphered condition a pleasant object. And whoever could, would get as many deciphered shells as possible and experience the wave of pleasure in looking at them.

Now in the earlier ages those who deciphered the shells, or did work of a similar kind, had been forced to do it; they were a kind of slaves dependent on the will of their masters, who took away all the pleasures of their life. But in these earlier ages a great danger arose, for when all the pleasure was taken away by their masters, great masses of these slaves sank into apathy, and it seemed as if the valley was sinking into deadness.

Now this was a great terror with the inhabitants whose life was pleasurable, and at length they determined that there should not be any more of these slaves. But each of the inhabitants when he worked for another had to have it made worth his while.

In this way a great diminution took place in the pleasure-giving power of the so-called pleasurable things. For if a man had had it made worth his while to decipher one of these shells, he had had a great deal or nearly all of the pain he spent in doing it counterbalanced by the pleasure given him to induce him to do it. Hence when the shell was handed over there was not much to enjoy in it; for by the law of the valley the pleasure and the pain were equal, and the decipherer, not having gone through so much pain on the whole, there was but little pleasure to be got.

In fact, at this time the fashion of filling the houses of the more powerful of the inhabitants with the so-called pleasurable things had somewhat gone out, and it had passed into a proverb, “It is better to decipher your own shells.”

Now it may be considered strange how it was that some of the inhabitants could get other of the inhabitants to decipher the shells for them at all, or, at any rate, to decipher them so that there was any balance of pleasure left with the shells at all. But this power on the part of some of the inhabitants depended on the general action of the king. For by bearing the difference of pain in innumerable respects in the life of each he made life a pleasure (on the whole) to each, and they strove each to preserve their own life which was a source of pleasure. And some of the more powerful inhabitants had the power of denying to the rest, unless they laboured for them, the means of continuing to exist. Consequently it was possible for things to be obtained by the more powerful which had a balance of pleasure in them.

But the authorities who had studied the life of the valley in relation to pleasure and pain, saw that there was a danger in this relation of the more powerful to the less powerful. For as the numbers of the inhabitants increased the power grew more and more concentrated in the hands of a few, and there was a tendency for the inhabitants in general to be compelled more and more to go through the painful part of actions, leaving the pleasurable parts for the more powerful. And every now and then, before the council of wise men regulated the matter, great masses of the inhabitants passed off in a state of apathy. So they had many laws to restrict the action of the more powerful of the inhabitants; and, indeed, the more powerful of the inhabitants were ready to frame these laws themselves, and were willing to obey them, for they did not like to see portions of the inhabitants going off into a state of apathy.

But not only in this respect, but also in every other, the wise men regulated the affairs of the valley so as to make life more pleasurable. They had severe laws against any one who deprived another of pleasure without his consent, by violence or deceit. They did all they could to ward off a state of apathy. But in one respect beyond all others they were full of care and precaution. And this was in guarding against such sources of trouble, anxiety, and pain which could be removed from the community as a whole. Anything tending to lower the standard of comfort as a whole was carefully removed. Irregularities were reduced as much as possible; and, in one respect, a great step had been taken. It had not been carried in the council of wise men without great opposition, but it had at length been passed into law.

Any child born in the valley which had any incurable disease, or any gross deformity, or which by its delicacy seemed likely to cause more pain than pleasure in the valley, was at once put out of existence. The gain to the inhabitants of the valley of this was in their eyes immense; for their sight was offended by no deformities, and the painful offices of attending to the sick had undergone a considerable diminution since this edict had been passed into law.

The important duty of deciding on the claims of every infant that was born to a painless extinction was confined to a band of inspectors, who stayed for a short time only in any one part of the valley, lest they should become biassed by personal acquaintance with the individuals for whose children their offices were called into requisition.

CHAPTER VII.

Passing on to the other great building, where the other wise men meet, it is right to describe what may be called the intellectual development—as the foregoing was the moral development of the valley. The course which the opinions of the thinkers in the valley had gone through was the following.

At first they had no clear ideas, but all manner of mere opinions and fancies. At last they apprehended certain general tendencies—such as that towards the centre of the valley, and they explained many inclinations which had before been puzzling to them by this. And stimulated by this great discovery they examined more and more closely. And they found many special tendencies like that towards the centre of the valley, which the king had called into existence, and which he let go on as a general rule, unless he wished the contrary. And they also succeeded in nearly isolating the simplest routines, and so practically could observe the type of the king’s plan.

They saw that one act A was succeeded by another act B. And not taking into account that one was pleasant the other painful, they measured the amount of sensation present in the two acts. And then they took the next pair of acts, namely, A and B over again, and measured the amount of sensation present in them; and they found that the amount of sensation gradually diminished. And at first they thought that sensation gradually came to a stop; but afterwards they noticed that other actions were started in the neighbourhood of the routine A B as that diminished in point of feeling.

Now, of course, these other actions were started by the king with the pain-bearing power set free from the routine A B, as above described. But not knowing anything about this action on the part of the king, or about the king at all, the conclusion arrived at was this: That sensation transmits itself. If it does not continue in the routine A B, that part which does not continue passes on to the other routines, C D, E F, &c.

Then they measured very carefully; and they found, as nearly as they could measure, the routines which sprang up as the routine A B died away were equal in sensation to the loss in the routine A B, A B. And from this they concluded that the amount of sensation or feeling was constant. They called it living force, and said that it must transmit itself and, wherever it appeared, be equal in its total amount to what it was at first. But after a time, with more delicate measurements and more patient thought, they found that some of the sensation was still unaccounted for.

For consider any routine consisting of the acts A, B; A, B; A, B. In order to make any pair of acts A, B worth while, the king bore a certain amount of pain. Referring to the numbers which we took before, if there were 1000 of pleasure in A there would only be 998 of pain in B. Thus the sensation was not equal in the two acts A and B. Some of the sensations had gone, and the portion of sensation we are now considering—the portion by which B was less than A—had not gone in starting other routines. This loss could not be accounted for as they accounted for the difference in sensation between the first action A B and the second action, consisting of the acts A and B in the routine. There was a loss of sensation which was counterbalanced by the gain in sensation in other routines.

But besides this there was a further loss. Some sensation went off, not to be recovered in any routine they knew.

Now it was the bearing on the part of the king which produced the appearance of the passing away of sensation altogether, so that the act B was less in amount of sensation than the act A. But the inhabitants—at least the wise ones—were firmly convinced that sensation could not be annihilated or lessened. So they came to the conclusion that sensation was passing off into a form from which it never reappeared, so that it could affect them. They conceived it still to exist, but to be irrecoverably gone from the life of the inhabitants of the valley.

Taking the numbers we have taken, and the simple instances we have supposed, this course of reasoning appears straightforward enough. But in reality so complicated was the state of things in the valley, and the proportion of pain which the king bore in each single action so minute, that to have arrived at this result implied powers of investigation of no mean order.

It is interesting to mention the names which these investigators gave in the valley. In the performance of the pleasant act A, they said that the being acquired greater animation. In going through the painful act B, they said that he passed into a position of advantage. They used the term advantage because, having completed the painful act B, he was ready to begin the pleasant part of the action A over again. And in this part he manifested more animation.

And now although acts of greater animation and greater advantage succeeded one another, and although the new total of the sensation in the act of a being was very nearly equalled by that in a subsequent act, still there was not—they had to confess there was not—a complete equality. Some of the sensation had certainly gone from the sphere in which the inhabitants could feel it.

We see that this sensation which was gone was in reality the pain-bearing of the king, which set all their life going.

But they knew nothing of this, and formed a very different conclusion. They said: “If some of the sensation is continually going and disappearing from the life of the inhabitants of the valley—if this is the case, although the sensation may not be destroyed, it is certainly lost to us.”

And then they thought: “Surely the amount of sensation must be always the same; if some of it continually goes off into a form in which we cannot feel it, that portion which is left behind, and which we feel, must be continually growing less.”

Hence they concluded that the sensation in the valley was gradually running down. Less and less was being felt. After a time, which they calculated with some show of precision, all feeling will have left the inhabitants and gone off in some irrecoverable form. All the beings of the valley will sink into apathy.

Thus coming in the course of their investigations upon the action of the king, which was the continual cause of all life, they apprehended it as the gradual annihilation of life.

The small building between the two council halls remains to be noticed.

Now when the king had connected pleasure and pain with different acts to be performed by the inhabitants of the valley, he had of necessity to let the pleasant one be the one that came first in the order of its possible performance. And then by the device of the curved rays he had brought it about that the inhabitants went through the painful act consequent on the pleasurable one, the two together forming the complete action which the king had designed. But this chain was not very secure. The inhabitants had a tendency to go through the pleasurable act and leave the painful act undone.

Now in things which necessarily concerned their life, the king would, by repeatedly bearing the pain of the painful act, continually set the beings going again; for when they had performed the pleasant act they were landed in a state of torpor, until the pain of the painful act had been borne by them or for them. Now if this act of which they took the pleasant and left the painful part undone was in the main current of their lives, the king would over and over again, by bearing the pain, bring those who had shirked the painful part into a position of advantage again, so that they could begin the routine afresh with another pleasant act. And often when thus started again they would take to the routine, and bear the pain in the painful act themselves. But many, after assisting them again and again, the king was obliged to let sink into apathy, such namely as always left the painful part of the action undone.

Now the little building was the council hall or investigation chamber of the searchers out of new pleasures. And by new pleasures they meant something of the following kind. With the pleasant and painful acts which made up the main routines of their life, it was not safe to take the pleasant and leave the painful acts, for that gradually led to their sinking into apathy. But there were many routines which the king had instituted besides the main ones. And if the pleasant part of the action constituting these secondary routines were taken, then there followed no tendency to lethargy in the main current of their lives, but they simply had a pleasure the more. Of course the pain of the painful act had to be borne, but they not going through with it left it for the king to bear.

Long ago, through one of the inhabitants of the valley with whom he had communicated, the king had sent a message, asking the inhabitants not to take the pleasant part of an action without the connected painful part. But now all memory of this message was lost, and the little building had been built, as a council hall or investigation chamber for the searching out of pleasurable acts. In it all possible novelties of action were discussed. And the pleasant parts of them being described, exactly how far they were pleasurable, and in what degree they were pleasurable, the information was made public throughout the land.

CHAPTER VIII.

Besides these two principal buildings in the metropolis, there were other public buildings devoted to various purposes. And some of the most important were colleges devoted to the education of the young inhabitants.

Now there was in the college of applied sensations a student who, though outwardly as proficient as the average of his companions, was in reality the most backward of all. He learned by a kind of rote all the doctrines they understood, and he could explain apparently how one feeling caused another. But in himself he had no particle of understanding. He seemed deficient in the sense of cause and effect which the others had. Of this the following instance will suffice to show the nature.