{"collection":"philosophy-ethics","full_text_available":true,"graph_url":"https://unchartedknowledge.5gfusion.net/v2/api/page/gutenberg_49289/graph","html_url":"https://unchartedknowledge.5gfusion.net/v2/page/gutenberg_49289","id":"gutenberg_49289","license":"Public Domain (US)","rights_basis":"gutenberg_metadata_copyright_false","source":"gutenberg","source_url":"https://www.gutenberg.org/ebooks/49289","summary":null,"tags":["Category: Philosophy & Ethics","Category: Science-Fiction & Fantasy","Fourth dimension"],"text":"SCIENTIFIC ROMANCES.\n\n\n                                   BY\n                           C. H. HINTON, B.A.\n\n  What is the Fourth Dimension?\n  The Persian King.\n  A Plane World.\n  A Picture of Our Universe.\n  Casting Out the Self.\n\n  [Illustration: _FIRST SERIES._]\n\n                               _London._\n                     SWAN SONNENSCHEIN & CO., LIM.,\n                          Paternoster Square.\n                                 1886.\n\n\n\n\n                     What is the Fourth Dimension?\n\n\n                               CHAPTER I.\n\nAt the present time our actions are largely influenced by our theories.\nWe have abandoned the simple and instinctive mode of life of the earlier\ncivilisations for one regulated by the assumptions of our knowledge and\nsupplemented by all the devices of intelligence. In such a state it is\npossible to conceive that a danger may arise, not only from a want of\nknowledge and practical skill, but even from the very presence and\npossession of them in any one department, if there is a lack of\ninformation in other departments. If, for instance, with our present\nknowledge of physical laws and mechanical skill, we were to build houses\nwithout regard to the conditions laid down by physiology, we should\nprobably\u2014to suit an apparent convenience\u2014make them perfectly\ndraught-tight, and the best-constructed mansions would be full of\nsuffocating chambers. The knowledge of the construction of the body and\nthe conditions of its health prevent it from suffering injury by the\ndevelopment of our powers over nature.\n\nIn no dissimilar way the mental balance is saved from the dangers\nattending an attention concentrated on the laws of mechanical science by\na just consideration of the constitution of the knowing faculty, and the\nconditions of knowledge. Whatever pursuit we are engaged in, we are\nacting consciously or unconsciously upon some theory, some view of\nthings. And when the limits of daily routine are continually narrowed by\nthe ever-increasing complication of our civilisation, it becomes doubly\nimportant that not one only but every kind of thought should be shared\nin.\n\nThere are two ways of passing beyond the domain of practical certainty,\nand of looking into the vast range of possibility. One is by asking,\n\u201cWhat is knowledge? What constitutes experience?\u201d If we adopt this\ncourse we are plunged into a sea of speculation. Were it not that the\nhighest faculties of the mind find therein so ample a range, we should\nreturn to the solid ground of facts, with simply a feeling of relief at\nescaping from so great a confusion and contradictoriness.\n\nThe other path which leads us beyond the horizon of actual experience is\nthat of questioning whatever seems arbitrary and irrationally limited in\nthe domain of knowledge. Such a questioning has often been successfully\napplied in the search for new facts. For a long time four gases were\nconsidered incapable of being reduced to the liquid state. It is but\nlately that a physicist has succeeded in showing that there is no such\narbitrary distinction among gases. Recently again the question has been\nraised, \u201cIs there not a fourth state of matter?\u201d Solid, liquid, and\ngaseous states are known. Mr. Crookes attempts to demonstrate the\nexistence of a state differing from all of these. It is the object of\nthese pages to show that, by supposing away certain limitations of the\nfundamental conditions of existence as we know it, a state of being can\nbe conceived with powers far transcending our own. When this is made\nclear it will not be out of place to investigate what relations would\nsubsist between our mode of existence and that which will be seen to be\na possible one.\n\nIn the first place, what is the limitation that we must suppose away?\n\nAn observer standing in the corner of a room has three directions\nnaturally marked out for him; one is upwards along the line of meeting\nof the two walls; another is forwards where the floor meets one of the\nwalls; a third is sideways where the floor meets the other wall. He can\nproceed to any part of the floor of the room by moving first the right\ndistance along one wall, and then by turning at right angles and walking\nparallel to the other wall. He walks in this case first of all in the\ndirection of one of the straight lines that meet in the corner of the\nfloor, afterwards in the direction of the other. By going more or less\nin one direction or the other, he can reach any point on the floor, and\nany movement, however circuitous, can be resolved into simple movements\nin these two directions.\n\nBut by moving in these two directions he is unable to raise himself in\nthe room. If he wished to touch a point in the ceiling, he would have to\nmove in the direction of the line in which the two walls meet. There are\nthree directions then, each at right angles to both the other, and\nentirely independent of one another. By moving in these three directions\nor combinations of them, it is possible to arrive at any point in a\nroom. And if we suppose the straight lines which meet in the corner of\nthe room to be prolonged indefinitely, it would be possible by moving in\nthe direction of those three lines, to arrive at any point in space.\nThus in space there are three independent directions, and only three;\nevery other direction is compounded of these three. The question that\ncomes before us then is this. \u201cWhy should there be three and only three\ndirections?\u201d Space, as we know it, is subject to a limitation.\n\nIn order to obtain an adequate conception of what this limitation is, it\nis necessary to first imagine beings existing in a space more limited\nthan that in which we move. Thus we may conceive a being who has been\nthroughout all the range of his experience confined to a single straight\nline. Such a being would know what it was to move to and fro, but no\nmore. The whole of space would be to him but the extension in both\ndirections of the straight line to an infinite distance. It is evident\nthat two such creatures could never pass one another. We can conceive\ntheir coming out of the straight line and entering it again, but they\nhaving moved always in one straight line, would have no conception of\nany other direction of motion by which such a result could be effected.\nThe only shape which could exist in a one-dimensional existence of this\nkind would be a finite straight line. There would be no difference in\nthe shapes of figures; all that could exist would simply be longer or\nshorter straight lines.\n\nAgain, to go a step higher in the domain of a conceivable existence.\nSuppose a being confined to a plane superficies, and throughout all the\nrange of its experience never to have moved up or down, but simply to\nhave kept to this one plane. Suppose, that is, some figure, such as a\ncircle or rectangle, to be endowed with the power of perception; such a\nbeing if it moves in the plane superficies in which it is drawn, will\nmove in a multitude of directions; but, however varied they may seem to\nbe, these directions will all be compounded of two, at right angles to\neach other. By no movement so long as the plane superficies remains\nperfectly horizontal, will this being move in the direction we call up\nand down. And it is important to notice that the plane would be\ndifferent, to a creature confined to it, from what it is to us. We think\nof a plane habitually as having an upper and a lower side, because it is\nonly by the contact of solids that we realize a plane. But a creature\nwhich had been confined to a plane during its whole existence would have\nno idea of there being two sides to the plane he lived in. In a plane\nthere is simply length and breadth. If a creature in it be supposed to\nknow of an up or down he must already have gone out of the plane.\n\nIs it possible, then, that a creature so circumstanced would arrive at\nthe notion of there being an up and down, a direction different from\nthose to which he had been accustomed, and having nothing in common with\nthem? Obviously nothing in the creature\u2019s circumstances would tell him\nof it. It could only be by a process of reasoning on his part that he\ncould arrive at such a conception. If he were to imagine a being\nconfined to a single straight line, he might realise that he himself\ncould move in two directions, while the creature in a straight line\ncould only move in one. Having made this reflection he might ask, \u201cBut\nwhy is the number of directions limited to two? Why should there not be\nthree?\u201d\n\nA creature (if such existed), which moves in a plane would be much more\nfortunately circumstanced than one which can only move in a straight\nline. For, in a plane, there is a possibility of an infinite variety of\nshapes, and the being we have supposed could come into contact with an\nindefinite number of other beings. He would not be limited, as in the\ncase of the creature in a straight line, to one only on each side of\nhim.\n\nIt is obvious that it would be possible to play curious tricks with a\nbeing confined to a plane. If, for instance, we suppose such a being to\nbe inside a square, the only way out that he could conceive would be\nthrough one of the sides of the square. If the sides were impenetrable,\nhe would be a fast prisoner, and would have no way out.\n\nWhat his case would be we may understand, if we reflect what a similar\ncase would be in our own existence. The creature is shut in in all the\ndirections he knows of. If a man is shut in in all the directions he\nknows of, he must be surrounded by four walls, a roof and a floor. A\ntwo-dimensional being inside a square would be exactly in the same\npredicament that a man would be, if he were in a room with no opening on\nany side. Now it would be possible to us to take up such a being from\nthe inside of the square, and to set him down outside it. A being to\nwhom this had happened would find himself outside the place he had been\nconfined in, and he would not have passed through any of the boundaries\nby which he was shut in. The astonishment of such a being can only be\nimagined by comparing it to that which a man would feel, if he were\nsuddenly to find himself outside a room in which he had been, without\nhaving passed through the window, doors, chimney or any opening in the\nwalls, ceiling or floor.\n\nAnother curious thing that could be effected with a two-dimensional\nbeing, is the following. Conceive two beings at a great distance from\none another on a plane surface. If the plane surface is bent so that\nthey are brought close to one another, they would have no conception of\ntheir proximity, because to each the only possible movements would seem\nto be movements in the surface. The two beings might be conceived as so\nplaced, by a proper bending of the plane, that they should be absolutely\nin juxtaposition, and yet to all the reasoning faculties of either of\nthem a great distance could be proved to intervene. The bending might be\ncarried so far as to make one being suddenly appear in the plane by the\nside of the other. If these beings were ignorant of the existence of a\nthird dimension, this result would be as marvellous to them, as it would\nbe for a human being who was at a great distance\u2014it might be at the\nother side of the world\u2014to suddenly appear and really be by our side,\nand during the whole time he not to have left the place in which he was.\n\n\n                              CHAPTER II.\n\nThe foregoing examples make it clear that beings can be conceived as\nliving in a more limited space than ours. Is there a similar limitation\nin the space we know?\n\nAt the very threshold of arithmetic an indication of such a limitation\nmeets us.\n\nIf there is a straight line before us two inches long, its length is\nexpressed by the number 2. Suppose a square to be described on the line,\nthe number of square inches in this figure is expressed by the number 4,\n_i.e._, 2 \u00d7 2. This 2 \u00d7 2 is generally written 2\u00b2, and named \u201c2 square.\u201d\n\nNow, of course, the arithmetical process of multiplication is in no\nsense identical with that process by which a square is generated from\nthe motion of a straight line, or a cube from the motion of a square.\nBut it has been observed that the units resulting in each case, though\ndifferent in kind, are the same in number.\n\nIf we touch two things twice over, the act of touching has been\nperformed four times. Arithmetically, 2 \u00d7 2 = 4. If a square is\ngenerated by the motion of a line two inches in length, this square\ncontains four square inches.\n\nSo it has come to pass that the second and third powers of numbers are\ncalled \u201csquare\u201d and \u201ccube.\u201d\n\nWe have now a straight line two inches long. On this a square has been\nconstructed containing four square inches. If on the same line a cube be\nconstructed, the number of cubic inches in the figure so made is 8,\n_i.e._, 2 \u00d7 2 \u00d7 2 or 2\u00b3. Here, corresponding to the numbers 2, 2\u00b2, 2\u00b3,\nwe have a series of figures. Each figure contains more units than the\nlast, and in each the unit is of a different kind. In the first figure a\nstraight line is the unit, viz., one linear inch; it is said to be of\none dimension. In the second a square is the unit, viz., one square\ninch. The square is a figure of two dimensions. In the third case a cube\nis the unit, and the cube is of three dimensions. The straight line is\nsaid to be of one dimension because it can be measured only in one way.\nIts length can be taken, but it has no breadth or thickness. The square\nis said to be of two dimensions because it has both length and breadth.\nThe cube is said to have three dimensions, because it can be measured in\nthree ways.\n\nThe question naturally occurs, looking at these numbers 2, 2\u00b2, 2\u00b3, by\nwhat figure shall we represent 2\u2074, or 2 \u00d7 2 \u00d7 2 \u00d7 2. We know that in the\nfigure there must be sixteen units, or twice as many units as in the\ncube. But the unit also itself must be different. And it must not differ\nfrom a cube simply in shape. It must differ from a cube as a cube\ndiffers from a square. No number of squares will make up a cube, because\neach square has no thickness. In the same way, no number of cubes must\nbe able to make up this new unit. And here, instead of trying to find\nsomething already known, to which the idea of a figure corresponding to\nthe fourth power can be affixed, let us simply reason out what the\nproperties of such a figure must be. In this attempt we have to rely,\nnot on a process of touching or vision, such as informs us of the\nproperties of bodies in the space we know, but on a process of thought.\nEach fact concerning this unknown figure has to be reasoned out; and it\nis only after a number of steps have been gone through, that any\nconsistent familiarity with its properties is obtained. Of all\napplications of the reason, this exploration is perhaps the one which\nrequires, for the simplicity of the data involved, the greatest exercise\nof the abstract imagination, and on this account is well worth patient\nattention. The first steps are very simple. We must imagine a finite\nstraight line to generate a square by moving on the plane of the paper,\nand this square in its turn to generate a cube by moving vertically\nupwards. Fig. 1 represents a straight line; Fig. 2 represents a square\nformed by the motion of that straight line; Fig. 3 represents\nperspectively a cube formed by the motion of that square A B C D\nupwards. It would be well, instead of using figure 3, to place a cube on\nthe paper. Its base would be A B C D, its upper surface E F G H.\n\n  [Illustration: Generating a line, square, and cube.]\n\nThe straight line A B gives rise to the square A B C D by a movement at\nright angles to itself. If motion be confined to the straight line A B,\na backward and forward motion is the only one possible. No sideway\nmotion is admissible. And if we suppose a being to exist which could\nonly move in the straight line A B, it would have no idea of any other\nmovement than to and fro. The square A B C D is formed from the straight\nline by a movement in a direction entirely different from the direction\nwhich exists in A B. This motion is not expressible by means of any\npossible motion in A B. A being which existed in A B, and whose\nexperience was limited to what could occur in A B, would not be able to\nunderstand the instructions we should give to make A B trace out the\nfigure A B C D.\n\nIn the figure A B C D there is a possibility of moving in a variety of\ndirections, so long as all these directions are confined to one plane.\nAll directions in this plane can be considered as compounded of two,\nfrom A to B, and from A to C. Out of the infinite variety of such\ndirections there is none which tends in a direction perpendicular to\nFig. 2; there is none which tends upwards from the plane of the paper.\nConceive a being to exist in the plane, and to move only in it. In all\nthe movements which he went through there would be none by which he\ncould conceive the alteration of Fig. 2 into what Fig. 3 represents in\nperspective. For 2 to become 3 it must be supposed to move\nperpendicularly to its own plane. The figure it traces out is the cube A\nB C D E F G H.\n\nAll the directions, manifold as they are, in which a creature existing\nin Fig. 3 could move, are compounded of three directions. From A to B,\nfrom A to C, from A to E, and there are no other directions known to it.\n\nBut if we suppose something similar to be done to Fig. 3, something of\nthe same kind as was done to Fig. 1 to turn it into Fig. 2, or to Fig. 2\nto turn it into Fig. 3, we must suppose the whole figure as it exists to\nbe moved in some direction entirely different from any direction within\nit, and not made up of any combination of the directions in it. What is\nthis? It is the fourth direction.\n\nWe are as unable to imagine it as a creature living in the plane Fig. 2\nwould be to imagine a direction such that moving in it the square 2\nwould become the cube 3. The third dimension to such a creature would be\nas unintelligible as the fourth is to us. And at this point we have to\ngive up the aid that is to be got from any presentable object, and we\nhave simply to investigate what the properties of the simplest figure in\nfour dimensions are, by pursuing further the analogy which we know to\nexist between the process of formation of 2 from 1, and of 3 from 2, and\nfinally of 4 from 3. For the sake of convenience, let us call the figure\nwe are investigating\u2014the simplest figure in four dimensions\u2014a\nfour-square.\n\nFirst of all we must notice, that if a cube be formed from a square by\nthe movement of the square in a new direction, each point of the\ninterior of the square traces out part of the cube. It is not only the\nbounding lines that by their motion form the cube, but each portion of\nthe interior of the square generates a portion of the cube. So if a cube\nwere to move in the fourth dimension so as to generate a four-square,\nevery point in the interior of the cube would start _de novo_, and trace\nout a portion of the new figure uninterfered with by the other points.\n\nOr, to look at the matter in another light, a being in three dimensions,\nlooking down on a square, sees each part of it extended before him, and\ncan touch each part without having to pass through the surrounding\nparts, for he can go from above, while the surrounding parts surround\nthe part he touches only in one plane.\n\nSo a being in four dimensions could look at and touch every point of a\nsolid figure. No one part would hide another, for he would look at each\npart from a direction which is perfectly different from any in which it\nis possible to pass from one part of the body to another. To pass from\none part of the body to another it is necessary to move in three\ndirections, but a creature in four dimensions would look at the solid\nfrom a direction which is none of these three.\n\nLet us obtain a few facts about the fourth figure, proceeding according\nto the analogy that exists between 1, 2, 3, and 4. In the Fig. 1 there\nare two points. In 2 there are four points\u2014the four corners of the\nsquare. In 3 there are eight points. In the next figure, proceeding\naccording to the same law, there would be sixteen points.\n\nIn the Fig. 1 there is one line. In the square there are four lines. In\nthe cube there are twelve lines. How many lines would there be in the\nfour-square? That is to say that there are three numbers\u20141, 4, and 12.\nWhat is the fourth, going on accordingly to the same law?\n\nTo answer this question let us trace out in more detail how the figures\nchange into one another. The line, to become the square, moves; it\noccupies first of all its original position, and last of all its final\nposition. It starts as A B, and ends as C D; thus the line appears\ntwice, or it is doubled. The two other lines in the square, A C, B D,\nare formed by the motions of the points at the extremities of the moving\nline. Thus, in passing from the straight line to the square the lines\ndouble themselves, and each point traces out a line. If the same\nprocedure holds good in the case of the change of the square into the\ncube, we ought in the cube to have double the number of lines as in the\nsquare\u2014that is eight\u2014and every point in the square ought to become a\nline. As there are four points in the square, we should have four lines\nin the cube from them, that is, adding to the previous eight, there\nshould be twelve lines in the cube. This is obviously the case. Hence we\nmay with confidence, to deduce the number of lines in a four-square,\napply this rule. _Double the number of lines in the previous figure, and\nadd as many lines as there are points in the previous figure._ Now in\nthe cube there are twelve lines and eight points. Hence we get 2 \u00d7 12 +\n8, or thirty-two lines in the four-square.\n\nIn the same way any other question about the four-square can be\nanswered. We must throw aside our realising power and answer in\naccordance with the analogy to be worked out from the three figures we\nknow.\n\nThus, if we want to know how many plane surfaces the four-square has, we\nmust commence with the line, which has none; the square has one; the\ncube has six. Here we get the three numbers, 0, 1, and 6. What is the\nfourth?\n\nConsider how the planes of the cube arise. The square at the beginning\nof its motion determines one of the faces of the cube, at the end it is\nthe opposite face, during the motion each of the lines of the square\ntraces out one plane face of the cube. Thus we double the number of\nplanes in the previous figure, and every line in the previous figure\ntraces out a plane in the subsequent one.\n\nApply this rule to the formation of a square from a line. In the line\nthere is no plane surface, and since twice nothing is nothing, we get,\nso far, no surface in the square; but in the straight line there is one\nline, namely itself, and this by its motion traces out the plane surface\nof the square. So in the square, as should be, the rule gives one\nsurface.\n\nApplying this rule to the case of the cube, we get, doubling the\nsurfaces, 12; and adding a plane for each of the straight lines, of\nwhich there are 12, we have another 12, or 24 plane surfaces in all.\nThus, just as by handling or looking at it, it is possible to describe a\nfigure in space, so by going through a process of calculation it is\nwithin our power to describe all the properties of a figure in four\ndimensions.\n\nThere is another characteristic so remarkable as to need a special\nstatement. In the case of a finite straight line, the boundaries are\npoints. If we deal with one dimension only, the figure 1, that of a\nsegment of a straight line, is cut out of and separated from the rest of\nan imaginary infinitely long straight line by the two points at its\nextremities. In this simple case the two points correspond to the\nbounding surface of the cube. In the case of a two-dimensional figure an\ninfinite plane represents the whole of space. The square is separated\noff by four straight lines, and it is impossible for an entry to be made\ninto the interior of the square, except by passing through the straight\nlines. Now, in these cases, it is evident that the boundaries of the\nfigure are of one dimension less than the figure itself. Points bound\nlines, lines bound plane figures, planes bound solid figures. Solids\nthen must bound four dimensional figures. The four-square will be\nbounded in the following manner. First of all there is the cube which,\nby its motion in the fourth direction, generates the figure. This, in\nits initial position, forms the base of the four-square. In its final\nposition it forms the opposite end. During the motion each of the faces\nof the cube give rise to another cube. The direction in which the cube\nmoves is such that of all the six sides none is in the least inclined in\nthat direction. It is at right angles to all of them. The base of the\ncube, the top of the cube, and the four sides of the cube, each and all\nof them form cubes. Thus the four-square is bounded by eight cubes.\nSumming up, the four-square would have 16 points, 32 lines, 24 surfaces,\nand it would be bounded by 8 cubes.\n\nIf a four-square were to rest in space it would seem to us like a cube.\n\nTo justify this conclusion we have but to think of how a cube would\nappear to a two-dimensional being. To come within the scope of his\nfaculties at all, it must come into contact with the plane in which he\nmoves. If it is brought into as close a contact with this plane as\npossible, it rests on it by one of its faces. This face is a square, and\nthe most a two-dimensional being could get acquainted with of a cube\nwould be a square.\n\nHaving thus seen how it is possible to describe the properties of the\nsimplest shape in four dimensions, it is evident that the mental\nconstruction of more elaborate figures is simply a matter of time and\npatience.\n\nIn the study of the form and development of the chick in the egg, it is\nimpossible to detect the features that are sought to be observed, except\nby the use of the microscope. The specimens are accordingly hardened by\na peculiar treatment and cut into thin sections. The investigator going\nover each of these sections, noticing all their peculiarities,\nconstructs in his mind the shape as it originally existed from the\nrecord afforded by an indefinite number of slices. So, to form an idea\nof a four-dimensional figure, a series of solid shapes bounded on every\nside differing gradually from one another, proceeding, it may be, to the\nmost diverse forms, has to be mentally grasped and fused into a unitary\nconception.\n\nIf, for instance, a small sphere were to appear, this to be replaced by\na larger one, and so on, and then, when the largest had appeared,\nsmaller and smaller ones to make their appearance, what would be\nwitnessed would be a series of sections of a four-dimensional sphere.\nEach section in space being a sphere.\n\nAgain, just as solid figures can be represented on paper by perspective,\nfour-dimensional figures can be represented perspectively by solids. If\nthere are two squares, one lying over the other, and the underneath one\nbe pushed away, its sides remaining parallel with the one that was over\nit, then if each point of the one be joined to the corresponding point\nof the other, we have a fair representation on paper of a cube. Fig. 3\nmay be considered to be such a representation if the square C D G H be\nconsidered to be the one that has been pushed away from lying originally\nunder the square A B E F. Each of the planes which bound the cube is\nrepresented on the paper. The only thing that is wanting is the\nthree-dimensional content of the cube. So if two cubes be placed with\ntheir sides parallel, but one somewhat diagonally with regard to the\nother, and all their corresponding points be supposed joined, there will\nbe found a set of solid figures, each representing (though of course\ndistortedly) the bounding cubes of the four-dimensional figure, and\nevery plane and line in the four-dimensional figure will be found to be\nrepresented in a kind of solid perspective. What is wanting is of course\nthe four-dimensional content.\n\n\n                              CHAPTER III.\n\nHaving now passed in review some of the properties of four-dimensional\nfigures, it remains to ask what relations beings in four dimensions, if\nthey did exist, would have with us.\n\nAnd in the first place, a being in four dimensions would have to us\nexactly the appearance of a being in space. A being in a plane would\nonly know solid objects as two-dimensional figures\u2014the shapes namely in\nwhich they intersected his plane. So if there were four-dimensional\nobjects, we should only know them as solids\u2014the solids, namely, in which\nthey intersect our space. Why, then, should not the four-dimensional\nbeings be ourselves, and our successive states the passing of them\nthrough the three-dimensional space to which our consciousness is\nconfined?\n\nLet us consider the question in more detail. And for the sake of\nsimplicity transfer the problem to the case of three and two dimensions\ninstead of four and three.\n\nSuppose a thread to be passed through a thin sheet of wax placed\nhorizontally. It can be passed through in two ways. Either it can be\npulled through, or it can be held at both ends, and moved downwards as a\nwhole. Suppose a thread to be grasped at both ends, and the hands to be\nmoved downwards perpendicularly to the sheet of wax. If the thread\nhappens to be perpendicular to the sheet it simply passes through it,\nbut if the thread be held, stretched slantingwise to the sheet, and the\nhands are moved perpendicularly downwards, the thread will, if it be\nstrong enough, make a slit in the sheet.\n\nIf now the sheet of wax were to have the faculty of closing up behind\nthe thread, what would appear in the sheet would be a moving hole.\n\nSuppose that instead of a sheet and a thread, there were a straight line\nand a plane. If the straight line were placed slantingwise in reference\nto the plane and moved downwards, it would always cut the plane in a\npoint, but that point of section would move on. If the plane were of\nsuch a nature as to close up behind the line, if it were of the nature\nof a fluid, what would be observed would be a moving point. If now there\nwere a whole system of lines sloping in different directions, but all\nconnected together, and held absolutely still by one framework, and if\nthis framework with its system of lines were as a whole to pass slowly\nthrough the fluid plane at right angles to it, there would then be the\nappearance of a multitude of moving points in the plane, equal in number\nto the number of straight lines in the system. The lines in the\nframework will all be moving at the same rate\u2014namely, at the rate of the\nframework in which they are fixed. But the points in the plane will have\ndifferent velocities. They will move slower or faster, according as the\nlines which give rise to them are more or less inclined to the plane. A\nstraight line perpendicular to the plane will, on passing through, give\nrise to a stationary point. A straight line that slopes very much\ninclined to the plane will give rise to a point moving with great\nswiftness. The motions and paths of the points would be determined by\nthe arrangement of the lines in the system. It is obvious that if two\nstraight lines were placed lying across one another like the letter X,\nand if this figure were to be stood upright and passed through the\nplane, what would appear would be at first two points. These two points\nwould approach one another. When the part where the two strokes of the X\nmeet came into the plane, the two points would become one. As the upper\npart of the figure passed through, the two points would recede from one\nanother.\n\n  [Illustration: Rectangle A B C D, crossed by two interlinked lines X\n  and Y two lines.]\n\nIf the line be supposed to be affixed to all parts of the framework, and\nto loop over one another, and support one another,[1] it is obvious that\nthey could assume all sorts of figures, and that the points on the plane\nwould move in very complicated paths. The annexed figure represents a\nsection of such a framework. Two lines X X and Y Y are shown, but there\nmust be supposed to be a great number of others sloping backwards and\nforwards as well as sideways.\n\nLet us now assume that instead of lines, very thin threads were attached\nto the framework: they on passing through the fluid plane would give\nrise to very small spots. Let us call the spots atoms, and regard them\nas constituting a material system in the plane. There are four\nconditions which must be satisfied by these spots if they are to be\nadmitted as forming a material system such as ours. For the ultimate\nproperties of matter (if we eliminate attractive and repulsive forces,\nwhich may be caused by the motions of the smallest particles), are\u20141,\nPermanence; 2, Impenetrability; 3, Inertia; 4, Conservation of energy.\n\nAccording to the first condition, or that of permanence, no one of these\nspots must suddenly cease to exist. That is, the thread which by sharing\nin the general motion of the system gives rise to the moving point, must\nnot break off before the rest of them. If all the lines suddenly ended\nthis would correspond to a ceasing of matter.\n\n2. Impenetrability.\u2014One spot must not pass through another. This\ncondition is obviously satisfied. If the threads do not coincide at any\npoint, the moving spots they give rise to cannot.\n\n3. Inertia.\u2014A spot must not cease to move or cease to remain at rest\nwithout coming into collision with another point. This condition gives\nthe obvious condition with regard to the threads, that they, between the\npoints where they come into contact with one another, must be straight.\nA thread which was curved would, passing through the plane, give rise to\na point which altered in velocity spontaneously. This the particles of\nmatter never do.\n\n4. Conservation of energy.\u2014The energy of a material system is never\nlost; it is only transferred from one form to another, however it may\nseem to cease. If we suppose each of the moving spots on the plane to be\nthe unit of mass, the principle of the conservation of energy demands\nthat when any two meet, the sum of the squares of their several\nvelocities before meeting shall be the same as the sum of the squares of\ntheir velocities after meeting. Now we have seen that any statement\nabout the velocities of the spots in the plane is really a statement\nabout the inclinations of the threads to the plane. Thus the principle\nof the conservation of energy gives a condition which must be satisfied\nby the inclinations of the threads of the plane. Translating this\nstatement, we get in mathematical language the assertion that the sum of\nthe squares of the tangents of the angles the threads make with the\nnormal to the plane remains constant.\n\nHence, all complexities and changes of a material system made up of\nsimilar atoms in a plane could result from the uniform motion as a whole\nof a system of threads.\n\nWe can imagine these threads as weaving together to form connected\nshapes, each complete in itself, and these shapes as they pass through\nthe fluid plane give rise to a series of moving points. Yet, inasmuch as\nthe threads are supposed to form consistent shapes, the motion of the\npoints would not be wholly random, but numbers of them would present the\nsemblance of moving figures. Suppose, for instance, a number of threads\nto be so grouped as to form a cylinder for some distance, but after a\nwhile to be pulled apart by other threads with which they interlink.\nWhile the cylinder was passing through the plane, we should have in the\nplane a number of points in a circle. When the part where the threads\ndeviated came to the plane, the circle would break up by the points\nmoving away. These moving figures in the plane are but the traces of the\nshapes of threads as those shapes pass on. These moving figures may be\nconceived to have a life and a consciousness of their own.\n\nOr, if it be irrational to suppose them to have a consciousness when the\nshapes of which they are momentary traces have none, we may well suppose\nthat the shapes of threads have consciousness, and that the moving\nfigures share this consciousness, only that in their case it is limited\nto those parts of the shapes that simultaneously pass through the plane.\nIn the plane, then, we may conceive bodies with all the properties of a\nmaterial system, moving and changing, possessing consciousness. After a\nwhile it may well be that one of them becomes so disassociated that it\nappears no longer as a unit, and its consciousness as such may be lost.\nBut the threads of existence of such a figure are not broken, nor is the\nshape which gave it origin altered in any way. It has simply passed on\nto a distance from the plane. Thus nothing which existed in the\nconscious life on the plane would cease. There would in such an\nexistence be no cause and effect, but simply the gradual realisation in\na superficies of an already existent whole. There would be no progress,\nunless we were to suppose the threads as they pass to interweave\nthemselves in more complex shapes.\n\nCan a representation, such as the preceding, be applied to the case of\nthe existence in space with which we have to do? Is it possible to\nsuppose that the movements and changes of material objects are the\nintersections with a three-dimensional space of a four-dimensional\nexistence? Can our consciousness be supposed to deal with a spatial\nprofile of some higher actuality?\n\nIt is needless to say that all the considerations that have been brought\nforward in regard to the possibility of the production of a system\nsatisfying the conditions of materiality by the passing of threads\nthrough a fluid plane, holds good with regard to a four-dimensional\nexistence passing through a three-dimensional space. Each part of the\nampler existence which passed through our space would seem perfectly\nlimited to us. We should have no indication of the permanence of its\nexistence. Were such a thought adopted, we should have to imagine some\nstupendous whole, wherein all that has ever come into being or will come\nco-exists, which passing slowly on, leaves in this flickering\nconsciousness of ours, limited to a narrow space and a single moment, a\ntumultuous record of changes and vicissitudes that are but to us. Change\nand movement seem as if they were all that existed. But the appearance\nof them would be due merely to the momentary passing through our\nconsciousness of ever existing realities.\n\nIn thinking of these matters it is hard to divest ourselves of the habit\nof visual or tangible illustration. If we think of a man as existing in\nfour dimensions, it is hard to prevent ourselves from conceiving him as\nprolonged in an already known dimension. The image we form resembles\nsomewhat those solemn Egyptian statues which in front represent well\nenough some dignified sitting figure, but which are immersed to their\nears in a smooth mass of stone which fits their contour exactly.\n\nNo material image will serve. Organised beings seem to us so complete\nthat any addition to them would deface their beauty. Yet were we\ncreatures confined to a plane, the outline of a Corinthian column would\nprobably seem to be of a beauty unimprovable in its kind. We should be\nunable to conceive any addition to it, simply for the reason that any\naddition we could conceive would be of the nature of affixing an\nunsightly extension to some part of the contour. Yet, moving as we do in\nspace of three dimensions, we see that the beauty of the stately column\nfar surpasses that of any single outline. So all that we can do is to\ndeny our faculty of judging of the ideal completeness of shapes in four\ndimensions.\n\n\n                              CHAPTER IV.\n\nLet us now leave this supposition of framework and threads. Let us\ninvestigate the conception of a four-dimensional existence in a simpler\nand more natural manner\u2014in the same way that a two-dimensional being\nshould think about us, not as infinite in the third dimension, but\nlimited in three dimensions as he is in two. A being existing in four\ndimensions must then be thought to be as completely bounded in all four\ndirections as we are in three. All that we can say in regard to the\npossibility of such beings is, that we have no experience of motion in\nfour directions. The powers of such beings and their experience would be\nampler, but there would be no fundamental difference in the laws of\nforce and motion.\n\nSuch a being would be able to make but a part of himself visible to us,\nfor a cube would be apprehended by a two-dimensional being as the square\nin which it stood. Thus a four-dimensional being would suddenly appear\nas a complete and finite body, and as suddenly disappear, leaving no\ntrace of himself, in space, in the same way that anything lying on a\nflat surface, would, on being lifted, suddenly vanish out of the\ncognisance of beings, whose consciousness was confined to the plane. The\nobject would not vanish by moving in any direction, but disappear\ninstantly as a whole. There would be no barrier, no confinement of our\ndevising that would not be perfectly open to him. He would come and go\nat pleasure; he would be able to perform feats of the most surprising\nkind. It would be possible by an infinite plane extending in all\ndirections to divide our space into two portions absolutely separated\nfrom one another; but a four-dimensional being would slip round this\nplane with the greatest ease.\n\nTo see this clearly, let us first take the analogous case in three\ndimensions. Suppose a piece of paper to represent a plane. If it is\ninfinitely extended in every direction, it will represent an infinite\nplane. It can be divided into two parts by an infinite straight line. A\nbeing confined to this plane could not get from one part of it to the\nother without passing through the line. But suppose another piece of\npaper laid on the first and extended infinitely, it will represent\nanother infinite plane. If the being moves from the first plane by a\nmotion in the third dimension, it will move into this new plane. And in\nit it finds no line. Let it move to such a position that when it goes\nback to the first plane it will be on the other side of the line. Then\nlet it go back to the first plane. It has appeared now on the other side\nof the line which divides the infinite plane into two parts.\n\nTake now the case of four dimensions. Instead of bringing before the\nmind a sheet of paper conceive a solid of three dimensions. If this\nsolid were to become infinite it would fill up the whole of\nthree-dimensional space. But it would not fill up the whole of\nfour-dimensional space. It would be to four-dimensional space what an\ninfinite plane is to three-dimensional space. There could be in\nfour-dimensional space an infinite number of such solids, just as in\nthree-dimensional space there could be an infinite number of infinite\nplanes.\n\nThus, lying alongside our space, there can be conceived a space also\ninfinite in all three directions. To pass from one to the other a\nmovement has to be made in the fourth dimension, just as to pass from\none infinite plane to another a motion has to be made in the third\ndimension.\n\nConceive, then, corresponding to the first sheet of paper mentioned\nabove, a solid, and as the sheet of paper was supposed to be infinitely\nextended in two dimensions, suppose the solid to be infinitely extended\nin its three dimensions, so that it fills the whole of space as we know\nit.\n\nNow divide this infinite solid in two parts by an infinite plane, as the\ninfinite plane of paper was divided in two parts by an infinite line. A\nbeing cannot pass from one part of this infinite solid to another, on\nthe other side of this infinite plane, without going through the\ninfinite plane, _so long as he keeps within the infinite solid_.\n\nBut suppose beside this infinite solid a second infinite solid, lying\nnext to it in the fourth dimension, as the second infinite plane of\npaper was next to the first infinite plane in the third dimension. Let\nnow the being that wants to get on the other side of the dividing plane\nmove off in the fourth dimension, and enter the second infinite solid.\nIn this second solid there is no dividing plane. Let him now move, so\nthat coming back to the first infinite solid he shall be on the other\nside of the infinite plane that divides it into two portions. If this is\ndone, he will now be on the other side of the infinite plane, without\nhaving gone through it.\n\nIn a similar way a being, able to move in four dimensions, could get out\nof a closed box without going through the sides, for he could move off\nin the fourth dimension, and then move about, so that when he came back\nhe would be outside the box.\n\nIs there anything in the world as we know it, which would indicate the\npossibility of there being an existence in four dimensions? No definite\nanswer can be returned to this question. But it may be of some interest\nto point out that there are certain facts which might be read by the\nlight of the fourth dimensional theory.\n\nTo make this clear, let us suppose that space is really four\ndimensional, and that the three-dimensional space we know is, in this\nampler space, like a surface is in our space.\n\nWe should then be in this ampler space like beings confined to the\nsurface of a plane would be in ours. Let us suppose that just as in our\nspace there are centres of attraction whose influence radiates out in\nevery direction, so in this ampler space there are centres of attraction\nwhose influence radiates out in every direction. Is there anything to be\nobserved in nature which would correspond to the effect of a centre of\nattraction lying out of our space, and acting on all the matter in it?\nThe effect of such a centre of attraction would not be to produce motion\nin any known direction, because it does not lie off in any known\ndirection.\n\nLet us pass to the corresponding case in three and two dimensions,\ninstead of four and three. Let us imagine a plane lying horizontally,\nand in it some creatures whose experience was confined to it. If now\nsome water or other liquid were poured on to the plane, the creatures,\nbecoming aware of its presence, would find that it had a tendency to\nspread out all over the plane. In fact it would not be to them as a\nliquid is to us\u2014it would rather correspond to a gas. For a gas, as we\nknow it, tends to expand in every direction, and gradually increase so\nas to fill the whole of space. It exercises a pressure on the walls of\nany vessel in which we confine it.\n\nThe liquid on the plane expands in all the dimensions which the\ntwo-dimensional creatures on the plane know, and at the same time\nbecomes smaller in the third dimension, its absolute quantity remaining\nunchanged. In like manner we might suppose that gases (which by\nexpansion become larger in the dimensions that we know) become smaller\nin the fourth dimension.\n\nThe cause in this case would have to be sought for in an attractive\nforce, acting with regard to our space as the force of gravity acts with\nregard to a horizontal plane.\n\nCan we suppose that there is a centre of attraction somewhere off in the\nfourth dimension, and that the gases, which we know are simply more\nmobile liquids, expanding out in every direction under its influence.\nThis view receives a certain amount of support from the fact proved\nexperimentally that there is no absolute line of demarcation between a\nliquid and a gas. The one can be made to pass into the other with no\nmoment intervening in which it can be said that now a change of state\nhas taken place.\n\nWe might then suppose that the matter we know extending in three\ndimensions has also a small thickness in the fourth dimension; that\nsolids are rigid in the fourth as in the other three dimensions; that\nliquids are too coherent to admit of their spreading out in space, and\nbecoming thinner in the fourth dimension, under the influence of an\nattractive centre lying outside of our space; but that gases, owing to\nthe greater mobility of their particles, are subject to its action, and\nspread out in space under its influence, in the same manner that\nliquids, under the influence of gravity, spread out on a plane.\n\nThen the density of a gas would be a measure of the relative thickness\nof it in the fourth dimension: and the diminution of the density would\ncorrespond to a diminution of the thickness in the fourth dimension.\nCould this supposition be tested in any way?\n\nSuppose a being confined to a plane; if the plane is moved far off from\nthe centre of attraction lying outside it, he would find that liquids\nhad less tendency to spread out than before.\n\nOr suppose he moves to a distant part of the plane so that the line from\nhis position to the centre of attraction lies obliquely to the plane; he\nwould find that in this position a liquid would show a tendency to\nspread out more in one direction than another.\n\nNow our space considered as lying in four-dimensional space, as a plane\ndoes in three-dimensional space, may be shifted. And the expansive force\nof gases might be found to be different at different ages. Or, shifting\nas we do our position in space during the course of the earth\u2019s path\nround the sun, there might arise a sufficient difference in our position\nin space, with regard to the attractive centre, to make the expansive\nforce of gases different at different times of the year, or to cause\nthem to manifest a greater expansive force in one direction than in\nanother.\n\nBut although this supposition might be worked out at some length, it is\nhard to suppose that it could afford any definite test of the physical\nexistence of a fourth dimension. No test has been discovered which is\ndecisive. And, indeed, before searching for tests, a theoretical point\nof the utmost importance has to be settled. In discussing the\ngeometrical properties of straight lines and planes, we suppose them to\nbe respectively of one and two dimensions, and by so doing deny them any\nreal existence. A plane and a line are mere abstractions. Every portion\nof matter is of three dimensions. If we consider beings on a plane not\nas mere idealities, we must suppose them to be of some thickness. If\ntheir experience is to be limited to a plane this thickness must be very\nsmall compared to their other dimensions. Transferring our reasoning to\nthe case of four dimensions, we come to a curious result.\n\nIf a fourth dimension exists there are two possible alternatives.\n\nOne is, that there being four dimensions, we have a three-dimensional\nexistence only. The other is that we really have a four-dimensional\nexistence, but are not conscious of it. If we are in three dimensions\nonly, while there are really four dimensions, then we must be relatively\nto those beings who exist in four dimensions, as lines and planes are in\nrelation to us. That is, we must be mere abstractions. In this case we\nmust exist only in the mind of the being that conceives us, and our\nexperience must be merely the thoughts of his mind\u2014a result which has\napparently been arrived at, on independent grounds, by an idealist\nphilosopher.\n\nThe other alternative is that we have a four-dimensional existence. In\nthis case our proportions in it must be infinitely minute, or we should\nbe conscious of them. If such be the case, it would probably be in the\nultimate particles of matter, that we should discover the fourth\ndimension, for in the ultimate particles the sizes in the three\ndimensions are very minute, and the magnitudes in all four dimensions\nwould be comparable.\n\nThe preceding two alternative suppositions are based on the hypothesis\nof the reality of four-dimensional existence, and must be conceived to\nhold good only on that hypothesis.\n\nIt is somewhat curious to notice that we can thus conceive of an\nexistence relative to which that which we enjoy must exist as a mere\nabstraction.\n\nApart from the interest of speculations of this kind they have\nconsiderable value; for they enable us to express in intelligible terms\nthings of which we can form no image. They supply us, as it were, with\nscaffolding, which the mind can make use of in building up its\nconceptions. And the additional gain to our power of representation is\nvery great.\n\nMany philosophical ideas and doctrines are almost unintelligible because\nthere is no physical illustration which will serve to express them. In\nthe imaginary physical existence which we have traced out, much that\nphilosophers have written finds adequate representation. Much of\nSpinoza\u2019s Ethics, for example, could be symbolized from the preceding\npages.\n\nThus we may discuss and draw perfectly legitimate conclusions with\nregard to unimaginable things.\n\nIt is, of course, evident that these speculations present no point of\ndirect contact with fact. But this is no reason why they should be\nabandoned. The course of knowledge is like the flow of some mighty\nriver, which, passing through the rich lowlands, gathers into itself the\ncontributions from every valley. Such a river may well be joined by a\nmountain stream, which, passing with difficulty along the barren\nhighlands, flings itself into the greater river down some precipitous\ndescent, exhibiting at the moment of its union the spectacle of the\nutmost beauty of which the river system is capable. And such a stream is\nno inapt symbol of a line of mathematical thought, which, passing\nthrough difficult and abstract regions, sacrifices for the sake of its\ncrystalline clearness the richness that comes to the more concrete\nstudies. Such a course may end fruitlessly, for it may never join the\nmain course of observation and experiment. But, if it gains its way to\nthe great stream of knowledge, it affords at the moment of its union the\nspectacle of the greatest intellectual beauty, and adds somewhat of\nforce and mysterious capability to the onward current.\n\n\n\n\n                           The Persian King.\n\n\n                               _PART I._\n\n\n                               CHAPTER I.\n\nIn Persia there was once a king. On one occasion when he was out hunting\nhe came to the narrow entrance of a valley. It was shut in on either\nside by vast hills, seemingly the spurs from the distant mountains.\nThese great spurs spread out including a wide tract of land. Towards the\nentrance where he stood they approached one another, and ended in abrupt\ncliffs. Across the mouth of the valley stretched a deep ravine. The\nking, followed by courtiers, galloped along, searching a spot where the\ndeep fissure might be shallower, so that descending into it he might\nreach the valley by ascending on the opposite side.\n\nBut at every point the ravine stretched downwards dark and deep, from\ncliff to cliff, shutting off all access to the valley.\n\nAt one point only was there a means of crossing. There were two masses\nof rocks, jutting out one from either side like the abutments of a\nnatural bridge, and they seemed to meet in mid air.\n\nThe mass trembled and shook as the king spurred his horse over it, and\nthe dislodged stones reverberated from side to side of the chasm till\nthe noise of their falling was lost.\n\nBefore the first of his courtiers could follow him one of the great\npiers or abutments gave way\u2014the whole mass fell crashing down. The king\nwas alone in the valley.\n\n\u201cSo ho,\u201d he cried, \u201cthe kingdom of Persia is shrunk to this narrow\nspot!\u201d and without troubling himself for the moment how he should\nreturn, he sped onward.\n\nBut when he had ridden far into the valley on his steed that could\noutnumber ten leagues in an hour, and had returned to the entrance of\nit, he saw no trace of a living soul on the opposite brink of the cleft.\nNo sign was left, save a few reeds bent down by the passage of the\nmounted train, that any human being had stood on the opposite side for\nages.\n\nThe evening came on apace. Yet no one returned. Again he rode far into\nthe valley. For the most part it was covered with long grass, but here\nand there a thick and tangled mass of vegetation attested to a great\nluxuriance of soil, while the surface was intersected here and there\nwith rivulets of clear water, which finally lost their way in the dark\ngorge over which he had just so rashly adventured. But on no side did\nthe steep cliffs offer any promise of escape.\n\nWhen the night came on he stretched himself beneath one of the few trees\nnot far from the ravine, while his faithful horse stood tranquilly at\nhis head.\n\nHe did not awake till the moon had risen. But then suddenly he started\nto his feet, and walking to the edge of the cleft, peered over to the\nland from whence he had come. For he thought he heard sounds of some\nkind that were not the natural ones of the rustling wind or the falling\nwater. Looking out he saw clearly opposite to him an old man in ragged\nclothing, leaning against a rock, holding a long pipe in his hands, on\nwhich he now and again played a few wild notes.\n\n\u201cOho, peasant!\u201d cried the king. \u201cRun and tell the head man of your\nvillage that the king bids him come directly, and will have him bring\nwith him the longest ropes and the strongest throwers under him.\u201d\n\nBut the old man did not seem to give heed. Then the king cried,\n\u201cHearken, old man, run quickly and tell your master that the king is\nconfined here, and will reward him beyond his dreams if he deliver him\nquickly.\u201d\n\nThen the old man rose, and coming nearer to the edge of the ravine stood\nopposite, still playing at intervals some notes on his long pipe. And\nthe king cried, \u201cCanst thou hear? Dost thou dare to refuse to carry my\ncommands? For I am the king of Persia. Who art thou?\u201d\n\nThen the old man made answer, putting his pipe aside: \u201cI am he who\nappears only when a man has passed for ever beyond the ken of all that\nhave known him. I am Demiourgos, the maker of men.\u201d\n\nThen the king cried, \u201cMock me not, but obey my commands.\u201d\n\nThe old man made answer, \u201cI do not mock thee; and oh, my Lord, thou hast\nmoved the puppets I have made, and driven them so to dance on the\nsurface of the earth that I would willingly obey thee. But it is not\npermitted me to pass between thee and the world of men thou hast known.\u201d\n\nThen the king was silent.\n\nAt length he said, \u201cIf thou art really what thou sayest, show me what\nthou canst do; build me a palace.\u201d\n\nThe old man lifted his pipe in both his trembling hands, and began to\nblow.\n\nIt was a strange instrument, for it not only produced the shriller\nsounds of the lute, and the piercing notes of the trumpet, but resounded\nwith the hollow booming of great organ pipes, and amongst all came ever\nand again a sharp and sonorous clang as of some metal instrument\nresounding when it was struck.\n\nAnd then the king was as one who enjoys the delights of thought. For in\nthought, delicate shades, impalpable nuances are ever passing. It is as\nthe blended strains of an invisible orchestra, but more subtle far, that\ncome and go in unexpected metres, and overwhelm you with their beauty\nwhen all seemed silent. And lo, as the strains sound, outside\u2014palpable,\nlarge as the firmament, or real as the smallest thing you can take up\nand know it is there\u2014outside stands some existence revealed\u2014to be known\nand returned to for ever.\n\nSo the king, listening to this music, felt that something was rising\nbehind him. And turning, beheld course after course of a great building.\nAlmost as soon as he had looked it had risen completed, finished to the\nlast embossure on the windows, the tracery on the highest pinnacles. All\nhad happened while the old man was blowing on his pipe, and when he\nceased all was perfect.\n\nAnd yet the appearance was very strange, for a finished and seemingly\nhabitable building rose out of waste unreclaimed soil, strewn with rocks\nand barren. No dwellings were near the palace to wait on it, no roads\nled to it or away from it.\n\n\u201cThere should be houses around it, and roadways,\u201d said the king; \u201cmake\nthem, and fields sown with corn, and all that is necessary for a state.\u201d\n\nBlowing on his pipe in regular recurrent cadences, the old man called up\nhouses close together, than scattered singly along roads which stretched\naway into the distance, to be seen every here and there perfectly\nclearly where they ascended a rising ground. And near at hand could be\ndistinguished fields of grain and pasture land.\n\nYet as the king turned to walk towards the new scene, the old man\nlaughed. \u201cAll this is a dream,\u201d he cried; \u201cso much I can do, but not at\nonce.\u201d And breathing peals of music from his pipe, he said, \u201cThis can\nbe, but is not yet.\u201d\n\n\u201cWhat,\u201d asked the king, \u201cis all a delusion?\u201d and as he asked everything\nsank down. There was no palace, no houses or fields, only the steep\nprecipice-locked valley, whither the king had ridden; and his horse\ncowering behind him.\n\nThen the king cried, \u201cThou art some moonstruck hermit, leading out a\nlife of folly alone. Get thee to the village thou knowest, and bring me\nhelp.\u201d\n\nBut the old man answered him saying, \u201cGreat king, I am bound to obey\nthee, and all the creative might of my being I lay at thy feet; and lo,\nin the midst of this valley I make for thee beings such as I can\nproduce. And all that thou hast seen is as nothing to what I can do for\nthee. The depths of the starry heavens have no limit, nor what I do for\nthee. Hast thou ever in thy life looked into the deep still ocean, and\nlost thy sight in the unseen depths? Even so thou wilt find no end in\nwhat I will give thee. Hast thou ever in thy life sought the depths of\nthy love\u2019s blue eyes, and found therein a world which stretched on\nendlessly? Even so I bring all to thy feet. Now that all the gladness of\nthe world has departed from thee, behold, I am a more willing servant\nthan ever thou hast had.\u201d\n\nAnd again he played, and a hut rose up with a patch of cleared soil\naround it, and a spring near by.\n\nThen the king said, \u201cHere will I dwell, and if I am to be cut off from\nthe rest of the world, I will lead a peaceful life in this valley.\u201d\n\nThe sun was rising, the sounds had ceased, and the old man had\ndisappeared.\n\n\n                              CHAPTER II.\n\nHe made his way slowly to the patch of cultivated ground, he knocked at\nthe door of the hut, and then he called out. No answer was made to the\nsound of his voice, he entered, and saw a rude, plain interior. There\nwere two forms half lying, half propped up by the walls, and some\ndomestic implements lay about. But when he spoke to the beings they did\nnot answer, and when he touched their arms they fell powerless on the\nground and remained there. A terrible fear came on the king lest he\nshould become such as these. He left them and again sought a possible\noutlet, but fruitlessly. And that evening he sought the old man again\nand inquired what sort of beings these were.\n\n\u201cFor though in form and body like children outwardly,\u201d said the king,\n\u201cthey do nothing and seem unable to move; are they in an enchanted\nslumber?\u201d\n\nThen the old man came near to the edge of the ravine and, speaking\nsolemnly and low, said:\n\n\u201cO king, thou dost not yet know the nature of the place wherein thou\nart. For these children are like the children thou hast known always\nboth in form and body. I have worked on them as far as is within my\npower. But here in this valley a law reigns which binds them in\nsleepfulness and powerlessness. For here in everything that is done\nthere is as much pain as pleasure. If it is pleasant to tread a downward\nslope there is as much pain in ascending the upward slope. And in every\naction there is a pleasant part and a painful part, and in the tasting\nof every herb the beings feel a bitter taste and a sweet taste, so\nindistinguishably united that the pleasure and the pain of eating it are\nequally balanced. And as hunger increases the sense of the bitterness in\nthe taste increases, so it is never more pleasant to eat than not to\neat. Everything that can be done here affords no more pleasure than it\ndoes pain, from the greatest action down to the least movement. And the\nbeings as I can make them, they follow pleasure and avoid pain. And if\nthe pleasure and the pain are equal they do not move one way or the\nother.\u201d\n\n\u201cThis is impossible,\u201d said the king.\n\n\u201cNay,\u201d said the old man, \u201cthat it is as I have said I will prove to\nthee.\u201d And he explained to the king how it would be possible to\nstimulate the children to activity, for he showed him how he could\ndivest anything that was done of part of its pain and render it more\npleasurable than painful. \u201cIn this way thou canst lead the beings I have\ngiven thee to do anything,\u201d said the old man, \u201cbut the condition is that\nthou must take the painful part that thou sparest them thyself.\u201d And he\nbade the king cut himself of the reeds that grew by the side of the\nravine, and told him that putting them between himself and any being\nwould enable him to take a part of the pain and leave in their feeling\nthe whole of the pleasure and the pain diminished by that part which he\nbore himself.\n\nThen the king cut of the reeds that grew by the side of the ravine. He\nwent to the hut where these beings lay, and, taking the reeds in his\nhand, he placed one between the child\u2019s frame and himself. And the child\nrose up and walked, while he himself felt a pain in his limbs. And he\nfound that by taking a pain in each part of him the child would exercise\nthat part; if he wished the child to look at anything he, by bearing a\npain in his eyes, made looking at it pleasurable to the child, and\naccordingly the child did look at the object he wished him to regard.\nAnd again, by bearing a bitter taste in his mouth he made the child feel\neating as pleasant, and the child gathered fruits and ate them.\n\nThen the king by using two reeds made both the children move, and they\nwent together wheresoever he wished them. But they had not the slightest\nidea of the king\u2019s action on them. They recognized each other, and\nplayed with each other. They saw the king and had a certain regard for\nhim, but of his action on them they knew nothing. For they felt his\nbearing the pain as this thing or that being pleasurable. They felt his\naction as a motive in themselves.\n\nAnd all day long the king went with them, leading them through the\nvalley, bearing the pain of each step, so that the children felt nothing\nbut pleasure. But at nightfall he led them back to the rude dwelling\nwhere he had found them. He led them by taking the pain from their steps\nin that direction, and not taking any of the pain from steps in any\nother direction.\n\nAnd when they had entered the dwelling-place he removed his reeds from\nthem. Immediately they sank down into the state of apathy in which he\nhad found them. They did not move.\n\nAnd the king at nightfall sought again the side of the ravine.\n\nGazing across it he saw the sandy waste of the land from which he had\ncome, he saw the great stones which were scattered about, looking pale\nand grey in the moonlight. And presently in the shadow of a rock near\nthe opposite brink he discerned the form of the old man.\n\nAnd he cried out to him, and bade him come near. And when the old man\nstood opposite to him, he besought him to tell him how he could make the\nbeings go through their movements of life without his bearing so much\npain.\n\nAnd the old man took his staff in his hand, and he held it out towards\nthe king, over the depth.\n\n\u201cBehold, O king, thy secret,\u201d he cried. And with his other hand he smote\nthe staff which was pointing down into the depths. The staff swung to\nand fro many times, and at last it came to rest again.\n\nThen the king besought him to explain what this might signify.\n\n\u201cThou hast been,\u201d replied the old man, \u201cas one who, wishing to make a\nstaff swing to and fro, has made every movement separately, raising it\nup by his hand each time that it falls down. But, behold, when I set it\nin movement it goes through many swings of itself, both downward and\nupward, until the movement I imparted to it is lost. Even so thou must\nmake these beings go through both pleasure and pain, thyself bearing but\nthe difference, not taking all the pain.\u201d\n\n\u201cMust I then,\u201d asked the king, \u201cby bearing pain give these beings a\ncertain store of pleasure, and then let them go through their various\nactions until they have exhausted this store of pleasure?\u201d\n\nThen the old man made answer. \u201cCan I have any secrets from thee?\nHearken, O king, and I will tell thee what lies behind the shows of the\nworld. What I have shown thee is an outward sign and symbol of what thou\nshouldst do, but it lies far outside those recesses whither I shall lead\nthee. Thou couldst indeed give these beings a store of pleasure, and\nthey would go through their actions until it was all spent; but then\nthou wouldst be as one of themselves. Thou wouldst have to perform the\npainful part of some action and let them perform the pleasant part, and\nthus thou wouldst be immersed in the same chain of actions wherein they\nwere. For regard my staff as it begins to swing. It is not I that make\nthe movement that is imparted to it; that movement lay stored up in my\narm, and when I struck the staff with my arm it was as if I had let\nanother staff fall which in its falling gave up its movement to the one\nI held in my hand.\u201d\n\n\u201cWhere, then, does the movement go to when the staff ceases to swing,\u201d\nasked the king.\n\n\u201cIt goes to the finer particles of the air, and passes on and on. There\nis an endless chain. It is as if there were numberless staffs, larger\nand smaller, and when one falls it either raises itself or passes on its\nrising to another or to others. There is an endless chain of movement to\nand fro, and as one ceases another comes. But, O king, I wish to take\nthee behind this long chain and to place thee where thou mayest not say,\nI will do this or that; but where thou canst say, This whole chain of\nmovement shall be or shall not. For as thou regardest this staff\nswinging thou seest that it moves as much up as it does down, as much to\nright as to left. And if the movements which it goes through came\ntogether it would be at rest. Its motion is but stillness separated into\nequal and opposite motions. And in what thou callest rest there are vast\nmovements. It shall be thine, O king, to strike nothingness asunder and\nmake things be. Nay, O king, I have not given thee these beings in the\nvalley for thee to move by outward deeds, but I have given them to thee\nsuch that thou canst strike their apathy asunder and let them live. And\nknow, O king, that even as those beings are whom thou hast found, so are\nall things in the valley down to the smallest. The smallest particle\nthere is in the valley lies, unless it were for me, without motion. Each\nparticle has the power of feeling pain and of feeling pleasure, but by\nthe law of the valley these are equal. Hence of itself no particle\nmoves. But I make it move, and all things in the valley sooner or later\nmove back to whence they came. The streams which gather far off in the\nvalley I lead along to where they fall into the depths between us. There\nthey shiver themselves into the smallest fragments, and each fragment I\ncause to return whence it first came. And, O king, in all this movement,\nsince it ends where it began, there is no more pleasure than pain. It is\nbut the apathy of rest broken asunder. But the particles will not go\nthrough this round of themselves. I bear the pain to make them go\nthrough, each one the round I appoint it.\u201d\n\n\u201cHow then,\u201d exclaimed the king, thinking of the pain he had felt in\ndirecting the movements of the children, \u201ccanst thou bear all this\npain?\u201d\n\n\u201cIt is not much,\u201d answered the old man; \u201cand were it more I would\nwillingly bear it for thee. For think of a particle which has made the\nwhole round of which I spoke to you\u2014it will make this journey if on the\nwhole there is the slightest gain of pleasure over pain; and thus,\nalthough for each particle in its movement at every moment I bear the\ndifference of pain, the pain for each particle is so minute that the\nwhole course of natural movements in the valley weighs upon me but\nlittle. And behold all lies ready for thee, O king. I have done all that\nI can do. I can perfect each natural process, each quality of the\nground, each plant and herb I make, up to the beings whom thou hast\nfound. They are my last work, and into your hands I give them.\u201d\n\nAnd when he had said this, the old man let drop his staff, and placing\nboth hands to his breast he seemed to draw something therefrom, and with\nboth hands to fling it to the king.\n\nFor some moments\u2019 space the king could distinguish nothing, but soon he\nbecame aware of a luminousness over the mid ravine. Something palely\nbright was floating towards him. As the brightness came nearer he saw\nthat it was a centre wherein innumerable bright rays met, and from which\ninnumerable bright rays went forth in every direction.\n\n\u201cTake that,\u201d the old man cried. \u201cThe rays go forth unto everything in\nthe valley. They pass through everything unto everything. Through them\nthou canst touch whatsoever thou wilt.\u201d\n\nThe king took the rays and placed them on his breast; thence they went\nforth, and through them he touched and knew every part of the valley.\nAnd thinking of the hut where the children lay, the king perceived\nthrough the rays that went thither that the walls were tottering, and\nlike to fall on the children. And through his rays he knew that the\nchildren perceived this in a dull kind of way; but since in their life\nthere was no more pleasure than pain, they did not feel it more pleasant\nto rise up and move than to be still and be buried.\n\nBut the king through the rays, as before through the reeds, took the\npain of moving, and the children rose and came out of the hut; and soon\nthey were with the king, running and bounding as never children leapt\nand ran, with ecstasy of movement and unlimited exuberance of spirit.\nBut as they leapt and ran the king felt an increasing pain in all his\nlimbs. Still he liked to see them in their full and joyous activity, and\nhe wished them to cast off that dull apathy in which they lay. So all\nthrough the night he roamed about with them thinking of all the wildest\nthings for them to do, and leading them through dance and play, every\nmovement and activity he could think of.\n\nAt length the rising sun began to warm the air, and the king, exhausted\nwith pain, left off bearing it for them.\n\nAfter a few languid movements the children sank down on a comfortable\nbank into a state of absolute torpor. The king looked at them; it seemed\ninconceivable that they could be the same children who had been running\nabout so merrily a few moments ago. Thus far he had received no\nadvantage from the rays the old man had given him, except that he could\ntouch the children more easily.\n\nHe turned wearily and looked around. His horse stood there. But instead\nof whinnying and running up to greet him, the faithful animal stood\nstill, looking across the ravine.\n\n\u201cPerchance without my burden, and with the strength these rays may\nimpart,\u201d thought the king, \u201che might manage the leap.\u201d\n\nThe horse was standing opposite the remains of the natural bridge over\nwhich the two had so rashly crossed the day before. The king touched the\nhorse with his rays. As with a sudden thrust of the spur, the noble\nanimal rushed forward and leapt madly from the fragments of the arch.\nHis fore feet gained the opposite brink, and with a terrible struggle he\nraised himself on the firm ground. Then he stood still. With a crash the\nremaining fragments of the bridge fell into the gulf, leaving the vast\ngap unnarrowed at any part. The horse stood looking over the ravine. But\nthough the king called him by name, the faithful creature who used to\ncome to him at the slightest whisper paid no heed. In a few moments he\ngalloped off along the track the courtiers had pursued.\n\n\n                              CHAPTER III.\n\nThe king being left thus with the children, applied himself to thought.\nHe directed his rays to one of the children and caused it to stand up,\nand, following the counsel of the old man, he thought of an action. The\naction he thought of was that of walking, and he separated it into two\nacts; the one act moving the right foot, the other act moving the left\nfoot. And he separated the apathy in which the child was into pleasure\nand pain; pleasure connected with the act of moving the right foot, pain\nconnected with the act of moving the left foot. Immediately the child\nmoved forward its right foot, but the left foot remained motionless. The\nchild had taken the pleasure, but the pain was left; or, since the king\nhad connected the pleasure and pain with two acts, it may be said, had\ndone the pleasant act and left the painful act undone.\n\nAfter waiting some time to see if the child would move, the king took\nthe pain of moving the left foot; instantly the child moved it, and as\nsoon as it had come to the ground again it moved the right foot, which\nwas the pleasant act. But then it stopped. And by no amount of taking\npains in the matter of the left foot could the king get the child into\nthe routine of walking. As soon as he ceased to take the pain of moving\nthe left foot, the child remained with the right foot forward. At last\nhe removed his attention from the movement of the child, and it sunk\nback again torpor.\n\nThe rest of the day the king spent in reflection, and in making\nexperiments with the children. But he did not succeed any better.\nWhatever action he thought of they went through the pleasant act, but\nmade no sign of going through the painful act.\n\nWhen darkness came the king perceived the faint luminousness of his\nrays: unless he had known of them he would hardly have perceived it.\n\nAnd now he tried a new experiment. He took one of the rays, and,\ndetaching it from the rest, he put it upon the body of one of the\nchildren, going out from its body and returning again to its body, so\nthat it went forth from the child and returned to the child again. He\nthen caused the child to stand up, and again tried it with the action of\nwalking. His idea was this: the child required a power of bearing its\nown pain in order to go through a painful act, and as the rays enabled\nhim to bear their pain, the ray proceeding from the child and coming\nback to it might enable it to bear its own pain. And now he separated\nthe apathy into pleasure and pain as before. The child moved the right\nfoot, and then when it had moved it, he saw that it actually began to\nmove the left foot. But it did not move it a complete step, and after\nthe next movement of the right foot the left foot did not stir.\n\nAgain and again the king tried the children, but his attempts came to\nnothing. One halting step of the left foot he could get them to go\nthrough, but no more.\n\nHe spent many hours. Suddenly the cause of his failure flashed upon him.\n\u201cOf course,\u201d he said to himself, \u201cthey don\u2019t move, for I have forgotten\nto take part of the pain. If they went on moving their left feet they\nwould have no balance of pleasure.\u201d\n\nAnd he tried one of them again. The child moved the right foot, then\nbegan to move the left foot. The king now by means of his rays took part\nof the pain of the movement of the left foot, and the child completed\nthe step with it. Then of course it moved the right foot, for that was\npleasant, and again the king took part of the pain of moving the left\nfoot, and the child completed its second step. It walked.\n\nThe difficulty was surmounted. Soon both the children were moving hither\nand thither like shifting shadows in the night, and the king felt just a\nshade of pain.\n\nThe children would come up to him and talk with him, if he took the\ndifference of pain which made it pleasant for them to do so. But they\nhad no idea of his action on them, for by his taking the difference of\npain they found an action pleasant, and felt a motive in themselves to\ndo it, which they did not in the least connect with the being outside\nthemselves to whom they spoke. They looked on him as some one more\npowerful than themselves, and friendly to them.\n\nAs soon as he was assured of the practical success of his plans, the\nking let the children relapse into their apathy while he thought. He\nconceived the design of forming with these children a state such as he\nhad known on earth\u2014a state with all the business and affairs of a\nkingdom, such as he had directed before. The vision of the palace which\nthe old man had shown him rose up. He saw in imagination the fertile\nfields, with the roads stretching between them; he saw all the varied\nlife of a great state. Accordingly from this time he was continually\ndirecting their existence, developing their powers, and learning how to\nguide them. And just as on first learning to read whole words are learnt\nwhich are afterwards split up into letters by the combinations of which\nother words are formed; so at first he thought of actions of a\ncomplicated nature, such as walking, and associated the moments of\npleasure and pain with the acts of which such actions were composed. But\nafterwards he came to regard the simpler actions by the combination of\nmany of which the beings were made to walk, and with the separate acts\nof these simple actions he associated pleasure and pain.\n\nAnd at first the beings were conscious of these simple acts and nothing\nelse, but in order that they might carry out more complicated actions,\nhe developed the dim apprehension which they had, and led it on to the\nconsciousness of more complicated actions. The simplest actions became\ninstinctive to these beings, and they went through them without knowing\nwhy. But if at any time the king ceased to take the difference of pain,\nthese actions, seemingly automatic as they were, ceased.\n\nAt certain intervals the king found his plans inconvenienced. Every now\nand then the beings went off into a state of apathy. Enough pain was\nborne for them to make it just worth their while to go through the\nactions of each routine. But any additional complication or hindrance\nunforeseen by the king was too much for them, and they sank under it. To\nremedy this he took in every action a slight portion of pain more than\nhe had done at first. Thus he expended a certain portion of pain-bearing\npower to give stability to the routines. And the margin of pleasure over\npain thus added was felt by the beings as a sort of diffused pleasure in\nexistence, which made them cling to life.\n\nNow in guiding these beings towards the end he wished to obtain, the\nking had to deal with living moving beings, and beings whose state was\ncontinually changing. And this led him to adopt as the type of the\nactivity of these beings not a single action, but a succession of\nactions of the same kind, coming the one after the other. Thus a being\nhaving been given a certain activity, it continued going on in a uniform\nmanner until the king wished to alter it.\n\nAgain it was important to keep the beings together, to prevent their\nbeing lost in the remote parts of the valley, and consequently the king\ntook, other things being equal, a certain amount of the pain of motion\ntowards the centre, and took none of the pain in any movement away from\nthe centre of the valley. Thus the inhabitants had a tendency to come\ntowards the centre, for there was a balance of pleasure in doing so, and\nthus they were continually presenting themselves to his notice, and not\ngetting lost.\n\nOf course, if there was any reason why he wanted them away from the\ncentre, the king ceased his bearing of the pain of motion towards the\ncentre, and then they were under the other tendency solely, which he\nimparted to them, in virtue of his bearing pain in another respect. And\nin everything that he did the king had regard to the circumstances in\nwhich the beings were placed, and the objects which he wanted to obtain.\nHe did not spare any of his pain-bearing power to give them pleasure\npurely as a feeling, but always united the pleasure he obtained for them\nby his suffering with some external work.\n\nAnd as time went on and the number of the inhabitants increased, he\nintroduced greater order and regularity into the numberless activities\nwhich he conceived for them. The activities formed regular routines,\nconditioned by the surroundings of the being and the routines of those\naround it. A routine did not suddenly cease without compensation; but if\nthe king wished it to stop he let another activity spring up at once in\nplace of it, so that there was no derangement. The beings gradually\nbecame more intelligent, so that they could be entrusted with more\ndifficult routines, and carried them out successfully, the king, of\ncourse, always taking the difference of pain necessary to make it worth\ntheir while. And they even became able to carry out single activities on\na large scale, involving the co-operation of many single routines. For\nthey had a sense of analogy, and observing some activity which the king\nhad led them through on a small scale, and in which they had found a\nbalance of pleasure, they were ready to try a similar one on a larger\nscale.\n\nThere was one feature springing from the advanced intelligence of the\ninhabitants which it is worth while to mention. Many of the possible\nactivities which the beings could go through, instead of consisting of a\npleasurable part first and a less painful part afterwards, consisted of\na painful part first and a pleasurable part afterwards. This might\nhappen by the particular arrangement of the acts of which the compounded\nactivity consisted, the acts having already moments of pain or pleasure\naffixed to them, and happening to occur in such dispositions that the\nfirst part of the activity was painful, the next part pleasurable.\n\nNow when the intelligence of the inhabitants was developed, the king, by\nleading them to think of such an activity, could induce them to go\nthrough with it. For the idea of the pleasure which would accompany the\nsecond part of the activity lightened the pain of the first. And this,\ncombined with the portion of the pain which the king bore, almost\ncounterbalanced the pain connected with the first part of the activity.\nThus the beings were enabled to go through the painful part of the\nactivity. But when they came to the second part of the activity the\ncreatures were much disappointed. For by the law of the valley pleasure\nand pain were equal (except for the small part which the king bore). Now\nthe pleasures of expectation had been so great that when the time came\nfor the act usually associated in their minds with pleasure, the\npleasure due had most of it been used up.\n\nFrom this circumstance a saying arose amongst the inhabitants which was\nsomewhat exaggerated, but which had a kernel of truth in what has just\nbeen described. The saying was that \u201cThe pleasure for which a labour has\nbeen undertaken flies away as soon as the labour has been finished, and\nnothing is left but to begin a new labour.\u201d And, again, another saying:\n\u201cThe enjoyment of a thing lies in its anticipation, not in its\npossession.\u201d\n\nAll this which has been so briefly described had in reality taken a long\ntime. And now fields were cultivated, better houses were built. The\ninhabitants of the valley had increased greatly in number, and were\ndivided up into several tribes, inhabiting different parts of the\nvalley. But the most favoured position was the centre, and for the\npossession of the centre there were contentions and struggles. There the\nking\u2019s activity in bearing was greatest, and the life was most\ndeveloped.\n\nAll around the outskirts of the valley dwelt the ruder and less advanced\npeople, who were called barbarians and savages by those nearer the\ncentre.\n\n\n                              CHAPTER IV.\n\nNow when the king saw the inhabitants becoming more like the human\nbeings he had known, he felt that he was solitary, and he desired to\nhave some intercourse with them. But when he appeared amongst them they\nrecognized him at once as some one more powerful than themselves, and\nwere afraid of him. In their alarm they tried to lay hands on him. When\nhe, to prevent their attacks, withdrew his continued bearing the\ndifference of pain in their actions, those who were attacking him sank\ninto apathy and became as the children whom he had first found.\n\nAnd a horrible report sprang up amongst the inhabitants of a terrible\nbeing who came amongst them, and who struck all who looked on him with\ntorpor and death. So the king ceased to walk amongst them. Still it was\nlong since he had heard the sound of a voice speaking to him, and he\nwished for a companion. He sought again the old man, and standing at the\nedge of the chasm he called upon him.\n\nAnd the old man appeared. \u201cArt thou weary, O king, of thy task?\u201d\n\n\u201cNay,\u201d replied the king; \u201cbut I wish to make myself known to the\ninhabitants that I may speak with them and they with me.\u201d\n\nAnd the old man counselled him to give some of his rays to one amongst\nthe beings, for then this being having these rays and the power of\nbearing pain for another other than himself, would be like the king, and\nbeing like him would understand him.\n\nNow the king sought over the whole of the valley, and of all the\ninhabitants he found one most perfect in form and in mind. He was the\nson of a king, and destined to reign in his turn over a numerous people.\nAnd the king gave him some of his rays, straight rays going forth from\nthe prince to others.\n\nAnd immediately the prince awoke as it were from a dream. And he\ncomprehended existence, and saw that in reality the pain and the\npleasure were equal. And when he had seen this, and knew the power of\nthe rays, and how by bearing pain he could make others pass through\npleasure and pain, and call those sleeping into activity; when the\nprince knew this, he cried out:\n\n\u201cOne thing succeeds another in the valley; pain follows pleasure, and\npleasure follows pain. But the cause of all being is in bearing pain.\nWherefore,\u201d he cried, \u201clet us seek an end to this show. Let us pray to\nbe delivered, that at last, pain ceasing, we may pass into nothingness.\u201d\n\nThus the prince, apprehending the cause of existence, felt that it was\npain, and dimly comprehending how the king was bearing pain, and himself\nfeeling the strenuousness of the effort of using the rays for which the\nframe of the inhabitants was unstrung, longed that existence itself\nmight cease.\n\nYet all his life his deeds were noble, and he passed from tribe to\ntribe, bearing the burdens and calling forth the sleeping to activity.\n\n\n                               CHAPTER V.\n\nIt is now the place in which to give a clear account of the king\u2019s\nactivity, and explain how he maintained the varied life of the valley.\n\nAnd the best plan is to take a typical instance, and to adopt the Arabic\nmethod of description. By the Arabic method of description is meant the\nsame method which the Arabs used for the description of numerical\nquantities. For instance, in the Arabic notation, if we are asked the\nnumber of days in the year, we answer first 300, which is a false\nanswer, but gives the nearest approximation in hundreds; then we say\nsixty, which is a correction; last of all we say five, which makes the\nanswer a correct one, namely, 365. In this simple case the description\nis given so quickly that we are hardly conscious of the nature of the\nsystem employed. But the same method when applied to more difficult\nsubjects presents the following characteristics. Firstly, a certain\nstatement is made about the subject to be described, and is impressed\nupon the reader as if it were true. Then, when that has been grasped,\nanother statement is made, generally somewhat contradictory, and the\nfirst notion formed has to be corrected. But these two statements taken\ntogether are given as truth. Then when this idea has been formed in the\nmind of the reader, another statement is made which must likewise be\nreceived as a correction, and so on, until by successive statements and\ncontradictions, or corrections, the idea produced corresponds to the\nfacts, as the describer knows them.\n\nThus the activity of the king will be here described by a series of\nstatements, and the truth will be obtained by the whole of the\nstatements and the corrections which they successively bring in.\n\nWhen the king wished to start a being on the train of activity he\ndivided its apathy into pleasure and pain. The pleasure he connected\nwith one act which we will call A. The pain he associated with another\nact which we will call B.\n\nThese two \u201cacts,\u201d A and B, which together form what we call an \u201caction,\u201d\nwere of such a nature that the doing of A first and then of B was a\nprocess used in the organization of the life in the valley.\n\nThus the act A may be represented by moving the right foot, B by moving\nthe left foot, then AB will be the action of taking a step. This however\nis but a superficial illustration, for the acts which we represent by A\nand B were fundamental acts, of which great numbers were combined\ntogether in any single outward act which could be observed or described.\n\nSuppose for the present that there is only one creature in the valley.\nThe king separates his apathy with regard to the action AB. Let us say\nhe separates his apathy into 1000 pleasure and 1000 pain. Of the\npleasure he lets the being experience the whole, of the pain he bears an\namount which we will represent by 2. Thus the being has 1000 pleasure\nand 998 of pain, and the action is completed. His sensation is measured\nby the number 1000 in the first act, and by 998 in the second act.\n\nBut the king did not choose to make the fundamental actions of this\nlimited and finishing kind. As the type of the fundamental activity, he\nchose an action, and made the being go through it again and again. Thus\nthe being would go through the act A, then the act B. When the action AB\nwas complete it would go through an act of the kind A again, then\nthrough an act of the kind B. Thus the creature would be engaged in a\nroutine of this kind, AB, AB, AB, and so on.\n\nAnd if the creature had been alone, and this had been the sole activity\nin which it was concerned, the king would have gone on bearing 2 of pain\nin each of these actions. The king would have kept the routine going on\nsteadily, the creature bearing 1000 of pleasure in each A, and 998 of\npain in each B.\n\nAt this point it may be asked that an example should be given of one of\nthese elementary routines which the king set going. And this seems a\nreasonable request, and yet it is somewhat too peremptory. For in the\nworld we may know of what nature the movements of the atoms are without\nbeing able to say exactly what the motion of any one is. In such a case\na type is the only possible presentation. Again, take the example of a\ncrystal. We know that a crystal has a definite law of shape, and however\nmuch we divide it we find that its parts present the same conformation.\nWe cannot isolate the ultimate crystalline elements, but we infer that\nthey must be such as to produce the crystal by their combination.\n\nNow life on the valley was such in its main features as would be\nproduced by a combination of routines of the kind explained. There were\nchanges and abrupt transitions, but the general and prevailing plan of\nlife was that of a routine of alternating acts of a pleasurable and a\npainful kind. It was just such as would be built up out of elementary\nroutines, on which the king could count, and which, unless he modified\ntheir combinations, tended to produce rhythmic processes of a larger\nkind. And even the changes and abruptnesses had a recurrent nature about\nthem, for if any routine in the valley altered suddenly, it was found\nthat there were cases of other routines altering in like manner, when\nthe conditions under which they came were similar. Thus the fundamental\ntype of the action which the king instituted was that of a routine AB,\nAB, as described above. But there were two circumstances which caused a\nvariation, so that this simple routine was modified.\n\nFirstly, there was not one being only but many.\n\nSecondly, the king wished to have some of his pain-bearing power set\nfree from time to time. He did not wish to have to be continually\nspending it all in maintaining the routines he had started at first, and\nthose immediately connected with them.\n\nWhen he first began to organize the life of the beings he did not\nconsciously keep back any of his pain-bearing power, but threw it all in\nthe activities which he started. Still from time to time he wished to\nstart new activities quite unconnected with the old, and for this reason\nhe withdrew some of his pain-bearing power, as will be shown afterwards.\n\nThere were many beings. The king chose that the type of activity in each\nshould be a routine. In that way he could calculate on the activity, and\nhold it in his mind as a settled process on whose operation he could\ncount. But as the routines of the beings proceeded they came into\ncontact with one another, and made, even by their simple co-existence,\nsomething different from what a routine by itself was. They interwove in\nvarious ways. Then, in order to take advantage of the combinations of\nthese routines, or to modify them, it was necessary to set going other\nroutines.\n\nIn order to be able to originate these connected routines the king\nadopted the following plan.\n\nIn the first action AB he separated the creatures\u2019 apathy into 1000\npleasure and 1000 pain, bearing 2 of the pain himself. The creature thus\nwent through 1000 of pleasure and 998 of pain. In the next action AB he\ndid not separate the beings\u2019 apathy up into so much pleasure and pain.\nHe separated it up into 980 pleasure and 980 pain, that is, each moment\nof feeling was 20 less in sensation than the moments of feeling were in\nthe first action.\n\nNow it is obvious that if the bearing 2 of pain will make it worth while\nfor a being to go through 1000 pleasure and 998 pain, then the bearing\non the king\u2019s part of 1 of pain would make it worth while for the being\nto go through 500 pleasure and 499 of pain.\n\nAnd a similar relation would hold for different amounts of pleasure and\npain. Thus clearly for the being to go through 980 of pleasure and the\ncorresponding amount of pain, it would not be necessary for the king to\nbear so much as when the being went through 1000 of pleasure and the\ncorresponding amount of pain.\n\nConsequently when the king divided the beings\u2019 apathy into 980 pleasure\nand 980 pain, it would not be necessary for him to bear 2 of pain to\nmake it worth the beings\u2019 while to go through the action. The king would\nnot bear so much as 2 of pain, and thus he would have some of his\npain-bearing power set free. He would have exactly as much as would\nenable him to make it worth a being\u2019s while to go through an action with\nthe moments of 20 of pleasure and 20 of pain.\n\nAnd this\u2014with a correction which will come later\u2014is what the king did.\nHe employed the pain-bearing power thus set free in starting other\nroutines. Thus in the routine AB, AB, AB there would be first of all the\naction AB. Then along with the second action AB, the king (with the\npain-bearing power set free) started an action CD\u2014the beginning of a\nroutine CD, CD, CD. Thus as the first routine went on and came into\nconnection with other routines, new and supplementary routines sprang up\nwhich regulated and took advantage of the combinations of the old\nroutines.\n\nThe amount of the moments of pleasure in the routine CD, was (with a\nslight correction explained below) measured in sensation, equal to 20.\nThus the moment of pleasure in the first A being 1000, the moment of\npleasure in the second A was 980, the moment of pleasure in the first C\nwas 20 (subject to the correction spoken of). Thus the total amount of\nsensation in the second A and the associated act C, taken together (but\nfor a small correction) was equal to the sensation in the first A. Hence\nthe three points which were characteristic of the activity of the beings\nin the valley are obvious enough.\n\n1. There is as fundamental type a routine AB, AB, AB, the sensation\ninvolved in which goes on diminishing.\n\n2. There are routines CD, CD, &c., connected with AB, AB, in which the\nsensation which disappears in the routine AB, AB seems to reappear.\n\n3. In the action AB itself there is a disappearance of sensation. The\nsensation connected with A is 1000, that connected with B is 998. Thus 2\nof sensation seems to have disappeared. This 2 of sensation is of course\nthe pain which the king bore, and which was the means whereby the\ncreature was induced to go through the action at all. But looked at from\nthe point of view of sensation, it seems like a diminution of amount.\nThis diminution of amount, owing to the correction spoken of above, was\nto be found regularly all through the routine.\n\nAnd now, with the exception of the final correction, the theory of the\nking\u2019s activity is complete. There are certain mathematical difficulties\nwhich render an exhaustive account somewhat obscure in expression. When\nwe take a general survey of a theory we want to see roughly how it all\nhangs together; but if we mean to adopt it, the exactitude of the\nnumerical relations becomes a matter of vital importance.\n\nIt must be added that the numbers taken above were taken simply for\npurposes of illustration. In reality the pain born by the king was less\nin proportion.\n\nThe exhaustive account which follows deals with small numerical\nquantities. It had better be omitted for the present, and turned to\nlater on for reference.\n\n\n                          EXHAUSTIVE ACCOUNT.\n\nWe keep for the time being to the numbers used above. When the king had\nenough pain-bearing power set free in the second action of the routine\nAB, AB to start another routine CD, of 20 pleasure 20 pain, he did not\nuse it all. He only used enough of it to set a routine going the moments\nof pleasure and pain in which were 16 in sensation. The routine CD was\nmade up of acts with 16 of pleasure and 16 of pain.\n\nThe sensation in the first A was 1000, in the first B it was 998, giving\na disappearance of 2. In the second A it was 980, and in C, which starts\nconcurrently with the second A, it was not 20 as might have been\nexpected, but 16, giving a loss of 4. The second A is less than the\nfirst A by 20. Searching for that 20 we find 16 in C. But there has been\na disappearance of 4.\n\nLooking now at the successive acts in the series we have in A 1000\nsensation, in B 998 sensation, in A and C together 996 sensation.\n\nThe cause of the loss between A and B has already been explained. That\nbetween B and the second A with C remains to be accounted for.\n\nIt has been already said that the king withdrew some of his pain-bearing\npower from the routine AB and all routines connected with it, thus he\nwas enabled to start activities altogether unconnected with those which\nhe had originated, and was with regard to the products of his own\nactivity as he had been at first, with regard to the beings in the\nvalley before he started them on the path of life. And it was in\nconsequence of his withdrawal of his pain-bearing power that the amount\nof sensation in C was not 20 but was less. This loss of 4 of sensation\nto the being corresponded to a setting free of a certain portion of\npain-bearing power on the part of the king. And thus as the process went\non, a portion of his power was continually being returned to him.\n\nIn the table below the first line of figures contains the amount of\nsensation in the actions AB, AB. The second line of figures contains the\namount of sensation in the actions CD, CD. The third line of figures\nrelates to another connected routine EF, EF, which originates in a\nmanner similar to CD. The fourth line of figures represents the amount\nof pain borne by the king, the fifth line represents his pain-bearing\npower set free.\n\n (1)   1000   998   980   978-40/1000      960         958-80/1000\n        A      B     A         B            A               B\n (2)                 16   15-998/1000  15-630/1000  15-658640/1000000\n                     C         D            C               D\n (3)                          16       15-998/1000\n                                            E               F\n (4)       2           1-992/1000        1-991/1000\n                                             +\n                                        360/1000000\n (5)       0             8/1000           8/1000 +\n                                        640/1000000\n\nIf the total amount of sensation which is experienced by the being in\nthe original routine and the connected routines in the consecutive\nstages be summed up, it will be found to be\n\n                 1000, 998, 996, 994-88/1000, 991-680/1000,\n\nand so on.\n\nFinally, the proportion of pain borne by the king was so small compared\nwith the sensation experienced by the being, that A and B were\napparently equal in sensation. Thus the sensation in the second A and in\nC together becomes apparently equal to that in B. And instead of the\nsensation diminishing quickly as shown above, it was only after a great\nmany acts of the primary and connected routines had been gone through\nthat any diminution of sensation in the form which the being could\nexperience it was to be detected. Thus, as before stated, there was:\n\n1. A routine of continually diminishing sensation.\n\n2. Connected routines the sensation in which was apparently equal to\nthat lost in A.\n\n3. There was a continuous disappearance of sensation from the experience\nof the beings accompanying every step of the routine. The sensation\nwhich they could experience was less in every subsequent step and\nconnected steps than in any one in which it was measured.\n\n\n                              CHAPTER VI.\n\nThe history of the events which took place in the valley in their due\norder and importance must be sought elsewhere. But let us return and\nlook at the condition of the valley and its inhabitants. Let us see what\nhas become of them after a great lapse of time.\n\nIt is a fair, a beautiful land. The greater part of it is cultivated.\nThere is no war\u2014even to the extremest confines of the valley there is\npeace. Passing from the remote confines where still dwell a barbarous\nrace, we come, as we approach the metropolis, amongst a more and more\npolite and refined people. In the metropolis itself the buildings are\nnumerous and of great size. The palace which the king saw rise under the\nold man\u2019s music is there, but another ruler dwells in it. Near the\npalace are two vast buildings standing on each side of a wide open\ncourt. There is no other building near save one between them, a\ncomparatively small edifice of brick. These buildings are the assembly\nhalls of the two most important councils in the valley. In the one on\nthe left-hand side of the palace met the most distinguished of the\ninhabitants who from a special inclination or fitness were entrusted\nwith the regulations about the pleasure and pain of the inhabitants.\nThey framed the rules according to which each inhabitant must conform in\nhis pursuit of pleasure, and they made the regulations whereby the whole\nbody of inhabitants were supposed to gain an increase in pleasure and to\navoid pain.\n\nIn the building on the right hand of the palace met those of the\ninhabitants who had studied the nature of feeling most deeply, and who\nfrom temperament or for other reasons had in their course of study not\npaid so much attention to whether feelings were painful or pleasurable,\nbut who had studied their amount and regularity of their recurrence.\nThey were the thinkers from whom all the practical inhabitants derived\ntheir rules of business. They devised the means and manner of putting\ninto execution what was decided on in the other assembly. They did not\noften propose any positive enactment themselves, but were always able to\nshow how the proposals of the other council could be carried into\neffect.\n\nTheir power was derived in this manner. The king had connected the\nfeelings of pleasure and pain with certain acts, and had given each\nbeing a routine. Now as he himself made use of this routine and combined\nthe routines of different individuals to bring about the results he\ndesired, so also did the rulers of the valley. The routines of the\nindividuals were studied and classified, and if any work was required to\nbe done, those individuals whose routines were appropriate were selected\nand brought to the required spot. Now to effect this a careful study of\nthe different routines was necessary, and also a knowledge of what stage\nthey were at. For it would be no use bringing an individual whose\nroutine was almost at an end to a work which was just beginning. Hence\nthe most delicate instruments and processes had been devised for\nmeasuring the amount of feeling experienced by any individual, whether\nof pleasure or of pain, and a careful classification had been made of\nall routines.\n\nBut it is best to study the constitution of the state in a regular\norder, and the questions of pleasure and pain considered as such were\nesteemed the most important.\n\nThe inhabitants knew that they sought pleasure and avoided pain, and the\ngreat object was to make their life more pleasurable. Two means were\nadopted, the banishing of the causes of pain, and the obtaining causes\nof pleasure.\n\nBy causes of pain and pleasure they meant those objects with which the\nking had associated the feelings of pleasure and pain in the equal and\nopposite moments into which he had divided their apathy.\n\nBut in this respect they were in error to a certain extent, for it was\nnot so much in respect to things as in respect to actions that the king\nseparated their apathy into pleasure and pain. For instance, there was a\npeculiar species of shell which was found in many parts of the valley,\ncovered with strange and involved lines and marks. Now the king had\nstruck the apathy of the inhabitants into two moments with regard to\nthis shell, one of pain connected with tracing out the twistings and\ninterweavings of the hues on the shell, one of pleasure in contemplating\nthe shell when the twistings and interweavings had been deciphered. Now\nit was the custom of the inhabitants to call the shell in its\nundeciphered condition a painful object, in its deciphered condition a\npleasant object. And whoever could, would get as many deciphered shells\nas possible and experience the wave of pleasure in looking at them.\n\nNow in the earlier ages those who deciphered the shells, or did work of\na similar kind, had been forced to do it; they were a kind of slaves\ndependent on the will of their masters, who took away all the pleasures\nof their life. But in these earlier ages a great danger arose, for when\nall the pleasure was taken away by their masters, great masses of these\nslaves sank into apathy, and it seemed as if the valley was sinking into\ndeadness.\n\nNow this was a great terror with the inhabitants whose life was\npleasurable, and at length they determined that there should not be any\nmore of these slaves. But each of the inhabitants when he worked for\nanother had to have it made worth his while.\n\nIn this way a great diminution took place in the pleasure-giving power\nof the so-called pleasurable things. For if a man had had it made worth\nhis while to decipher one of these shells, he had had a great deal or\nnearly all of the pain he spent in doing it counterbalanced by the\npleasure given him to induce him to do it. Hence when the shell was\nhanded over there was not much to enjoy in it; for by the law of the\nvalley the pleasure and the pain were equal, and the decipherer, not\nhaving gone through so much pain on the whole, there was but little\npleasure to be got.\n\nIn fact, at this time the fashion of filling the houses of the more\npowerful of the inhabitants with the so-called pleasurable things had\nsomewhat gone out, and it had passed into a proverb, \u201cIt is better to\ndecipher your own shells.\u201d\n\nNow it may be considered strange how it was that some of the inhabitants\ncould get other of the inhabitants to decipher the shells for them at\nall, or, at any rate, to decipher them so that there was any balance of\npleasure left with the shells at all. But this power on the part of some\nof the inhabitants depended on the general action of the king. For by\nbearing the difference of pain in innumerable respects in the life of\neach he made life a pleasure (on the whole) to each, and they strove\neach to preserve their own life which was a source of pleasure. And some\nof the more powerful inhabitants had the power of denying to the rest,\nunless they laboured for them, the means of continuing to exist.\nConsequently it was possible for things to be obtained by the more\npowerful which had a balance of pleasure in them.\n\nBut the authorities who had studied the life of the valley in relation\nto pleasure and pain, saw that there was a danger in this relation of\nthe more powerful to the less powerful. For as the numbers of the\ninhabitants increased the power grew more and more concentrated in the\nhands of a few, and there was a tendency for the inhabitants in general\nto be compelled more and more to go through the painful part of actions,\nleaving the pleasurable parts for the more powerful. And every now and\nthen, before the council of wise men regulated the matter, great masses\nof the inhabitants passed off in a state of apathy. So they had many\nlaws to restrict the action of the more powerful of the inhabitants;\nand, indeed, the more powerful of the inhabitants were ready to frame\nthese laws themselves, and were willing to obey them, for they did not\nlike to see portions of the inhabitants going off into a state of\napathy.\n\nBut not only in this respect, but also in every other, the wise men\nregulated the affairs of the valley so as to make life more pleasurable.\nThey had severe laws against any one who deprived another of pleasure\nwithout his consent, by violence or deceit. They did all they could to\nward off a state of apathy. But in one respect beyond all others they\nwere full of care and precaution. And this was in guarding against such\nsources of trouble, anxiety, and pain which could be removed from the\ncommunity as a whole. Anything tending to lower the standard of comfort\nas a whole was carefully removed. Irregularities were reduced as much as\npossible; and, in one respect, a great step had been taken. It had not\nbeen carried in the council of wise men without great opposition, but it\nhad at length been passed into law.\n\nAny child born in the valley which had any incurable disease, or any\ngross deformity, or which by its delicacy seemed likely to cause more\npain than pleasure in the valley, was at once put out of existence. The\ngain to the inhabitants of the valley of this was in their eyes immense;\nfor their sight was offended by no deformities, and the painful offices\nof attending to the sick had undergone a considerable diminution since\nthis edict had been passed into law.\n\nThe important duty of deciding on the claims of every infant that was\nborn to a painless extinction was confined to a band of inspectors, who\nstayed for a short time only in any one part of the valley, lest they\nshould become biassed by personal acquaintance with the individuals for\nwhose children their offices were called into requisition.\n\n\n                              CHAPTER VII.\n\nPassing on to the other great building, where the other wise men meet,\nit is right to describe what may be called the intellectual\ndevelopment\u2014as the foregoing was the moral development of the valley.\nThe course which the opinions of the thinkers in the valley had gone\nthrough was the following.\n\nAt first they had no clear ideas, but all manner of mere opinions and\nfancies. At last they apprehended certain general tendencies\u2014such as\nthat towards the centre of the valley, and they explained many\ninclinations which had before been puzzling to them by this. And\nstimulated by this great discovery they examined more and more closely.\nAnd they found many special tendencies like that towards the centre of\nthe valley, which the king had called into existence, and which he let\ngo on as a general rule, unless he wished the contrary. And they also\nsucceeded in nearly isolating the simplest routines, and so practically\ncould observe the type of the king\u2019s plan.\n\nThey saw that one act A was succeeded by another act B. And not taking\ninto account that one was pleasant the other painful, they measured the\namount of sensation present in the two acts. And then they took the next\npair of acts, namely, A and B over again, and measured the amount of\nsensation present in them; and they found that the amount of sensation\ngradually diminished. And at first they thought that sensation gradually\ncame to a stop; but afterwards they noticed that other actions were\nstarted in the neighbourhood of the routine A B as that diminished in\npoint of feeling.\n\nNow, of course, these other actions were started by the king with the\npain-bearing power set free from the routine A B, as above described.\nBut not knowing anything about this action on the part of the king, or\nabout the king at all, the conclusion arrived at was this: That\nsensation transmits itself. If it does not continue in the routine A B,\nthat part which does not continue passes on to the other routines, C D,\nE F, &c.\n\nThen they measured very carefully; and they found, as nearly as they\ncould measure, the routines which sprang up as the routine A B died away\nwere equal in sensation to the loss in the routine A B, A B. And from\nthis they concluded that the amount of sensation or feeling was\nconstant. They called it living force, and said that it must transmit\nitself and, wherever it appeared, be equal in its total amount to what\nit was at first. But after a time, with more delicate measurements and\nmore patient thought, they found that some of the sensation was still\nunaccounted for.\n\nFor consider any routine consisting of the acts A, B; A, B; A, B. In\norder to make any pair of acts A, B worth while, the king bore a certain\namount of pain. Referring to the numbers which we took before, if there\nwere 1000 of pleasure in A there would only be 998 of pain in B. Thus\nthe sensation was not equal in the two acts A and B. Some of the\nsensations had gone, and the portion of sensation we are now\nconsidering\u2014the portion by which B was less than A\u2014had not gone in\nstarting other routines. This loss could not be accounted for as they\naccounted for the difference in sensation between the first action A B\nand the second action, consisting of the acts A and B in the routine.\nThere was a loss of sensation which was counterbalanced by the gain in\nsensation in other routines.\n\nBut besides this there was a further loss. Some sensation went off, not\nto be recovered in any routine they knew.\n\nNow it was the bearing on the part of the king which produced the\nappearance of the passing away of sensation altogether, so that the act\nB was less in amount of sensation than the act A. But the inhabitants\u2014at\nleast the wise ones\u2014were firmly convinced that sensation could not be\nannihilated or lessened. So they came to the conclusion that sensation\nwas passing off into a form from which it never reappeared, so that it\ncould affect them. They conceived it still to exist, but to be\nirrecoverably gone from the life of the inhabitants of the valley.\n\nTaking the numbers we have taken, and the simple instances we have\nsupposed, this course of reasoning appears straightforward enough. But\nin reality so complicated was the state of things in the valley, and the\nproportion of pain which the king bore in each single action so minute,\nthat to have arrived at this result implied powers of investigation of\nno mean order.\n\nIt is interesting to mention the names which these investigators gave in\nthe valley. In the performance of the pleasant act A, they said that the\nbeing acquired greater animation. In going through the painful act B,\nthey said that he passed into a position of advantage. They used the\nterm advantage because, having completed the painful act B, he was ready\nto begin the pleasant part of the action A over again. And in this part\nhe manifested more animation.\n\nAnd now although acts of greater animation and greater advantage\nsucceeded one another, and although the new total of the sensation in\nthe act of a being was very nearly equalled by that in a subsequent act,\nstill there was not\u2014they had to confess there was not\u2014a complete\nequality. Some of the sensation had certainly gone from the sphere in\nwhich the inhabitants could feel it.\n\nWe see that this sensation which was gone was in reality the\npain-bearing of the king, which set all their life going.\n\nBut they knew nothing of this, and formed a very different conclusion.\nThey said: \u201cIf some of the sensation is continually going and\ndisappearing from the life of the inhabitants of the valley\u2014if this is\nthe case, although the sensation may not be destroyed, it is certainly\nlost to us.\u201d\n\nAnd then they thought: \u201cSurely the amount of sensation must be always\nthe same; if some of it continually goes off into a form in which we\ncannot feel it, that portion which is left behind, and which we feel,\nmust be continually growing less.\u201d\n\nHence they concluded that the sensation in the valley was gradually\nrunning down. Less and less was being felt. After a time, which they\ncalculated with some show of precision, all feeling will have left the\ninhabitants and gone off in some irrecoverable form. All the beings of\nthe valley will sink into apathy.\n\nThus coming in the course of their investigations upon the action of the\nking, which was the continual cause of all life, they apprehended it as\nthe gradual annihilation of life.\n\nThe small building between the two council halls remains to be noticed.\n\nNow when the king had connected pleasure and pain with different acts to\nbe performed by the inhabitants of the valley, he had of necessity to\nlet the pleasant one be the one that came first in the order of its\npossible performance. And then by the device of the curved rays he had\nbrought it about that the inhabitants went through the painful act\nconsequent on the pleasurable one, the two together forming the complete\naction which the king had designed. But this chain was not very secure.\nThe inhabitants had a tendency to go through the pleasurable act and\nleave the painful act undone.\n\nNow in things which necessarily concerned their life, the king would, by\nrepeatedly bearing the pain of the painful act, continually set the\nbeings going again; for when they had performed the pleasant act they\nwere landed in a state of torpor, until the pain of the painful act had\nbeen borne by them or for them. Now if this act of which they took the\npleasant and left the painful part undone was in the main current of\ntheir lives, the king would over and over again, by bearing the pain,\nbring those who had shirked the painful part into a position of\nadvantage again, so that they could begin the routine afresh with\nanother pleasant act. And often when thus started again they would take\nto the routine, and bear the pain in the painful act themselves. But\nmany, after assisting them again and again, the king was obliged to let\nsink into apathy, such namely as always left the painful part of the\naction undone.\n\nNow the little building was the council hall or investigation chamber of\nthe searchers out of new pleasures. And by new pleasures they meant\nsomething of the following kind. With the pleasant and painful acts\nwhich made up the main routines of their life, it was not safe to take\nthe pleasant and leave the painful acts, for that gradually led to their\nsinking into apathy. But there were many routines which the king had\ninstituted besides the main ones. And if the pleasant part of the action\nconstituting these secondary routines were taken, then there followed no\ntendency to lethargy in the main current of their lives, but they simply\nhad a pleasure the more. Of course the pain of the painful act had to be\nborne, but they not going through with it left it for the king to bear.\n\nLong ago, through one of the inhabitants of the valley with whom he had\ncommunicated, the king had sent a message, asking the inhabitants not to\ntake the pleasant part of an action without the connected painful part.\nBut now all memory of this message was lost, and the little building had\nbeen built, as a council hall or investigation chamber for the searching\nout of pleasurable acts. In it all possible novelties of action were\ndiscussed. And the pleasant parts of them being described, exactly how\nfar they were pleasurable, and in what degree they were pleasurable, the\ninformation was made public throughout the land.\n\n\n                             CHAPTER VIII.\n\nBesides these two principal buildings in the metropolis, there were\nother public buildings devoted to various purposes. And some of the most\nimportant were colleges devoted to the education of the young\ninhabitants.\n\nNow there was in the college of applied sensations a student who, though\noutwardly as proficient as the average of his companions, was in reality\nthe most backward of all. He learned by a kind of rote all the doctrines\nthey understood, and he could explain apparently how one feeling caused\nanother. But in himself he had no particle of understanding. He seemed\ndeficient in the sense of cause and effect which the others had. Of this\nthe following instance will suffice to show the nature.\n\nThe king had, in order to prevent the inhabitants from straying too far\nfrom the metropolis, kept a constant watchfulness over their movements,\nand had uniformly taken somewhat of the pain from any effort which they\nmade to move towards the metropolis, and had not taken any of the pain\nin efforts whose tendency was to remove them to a distance from the\nmetropolis. If there was any purpose to be served in going away from the\nmetropolis, he took enough pain from these movements to make it worth\nthe beings\u2019 while to go away from the metropolis. But when other things\nwere equal, it was a pleasurable thing to go towards the metropolis. The\nking made this general inclination, because if it had not been so,\nbeings lying out of the way of his immediate attention might have\ndrifted away and gone to the confines of the valley, away from where the\nbusy life he was calling out was manifested, and so have been lost to\nothers and themselves. As it was by imparting this general\npleasurableness of moving towards the metropolis he held all the\ninhabitants together, and knew the direction in which each would tend,\nunless for any special reason he had made it more pleasurable for the\nperson to move away from the metropolis.\n\nNow, as has been mentioned above, this general tendency had been\nobserved by the inhabitants; and they knew quite well that every\nindividual tended towards the metropolis, and was only prevented from\ncoming into it by strong local interests, or by all available positions\nin it or near it being already occupied. If any situation was vacant in\nthe metropolis, it was easily filled up by those from the surrounding\ncountry, for they all felt this tendency to press in.\n\nNow, the learned men in the valley had long recognized this as one of\nthe most important laws of the valley. And the students in the college\nof applied sensations felt this law to be true law, and anything which\nfollowed from it they felt to be self-evident. But the student of whom\nwe speak had not this happy, settled feeling with regard to this law. He\ncould not feel as if it were necessarily true.\n\nOne day the head of the college was talking to the foremost\nstudents\u2014those who had nearly finished their course and who would take\ntheir places in the valley shortly\u2014and he said incidentally in the\ncourse of his remarks, that those who were moving away from the\nmetropolis were as much attracted to it as those who were moving towards\nit.\n\n\u201cWhy do they move away, then?\u201d asked the backward student, who had by\ngreat diligence, after a long time, plodded his way by force of\nremembering by heart into the top class. He forgot his usual caution and\nhis acquired habit of only asking questions he had heard asked before in\norder to refresh his memory with the answers he had heard given before.\n\nThe professor frowned at the stupid question. \u201cThe supposed being,\u201d he\nanswered, \u201cwhile he is attracted to the metropolis in accordance with\nthe general law, may yet have some stronger inducement at the time to\nmove away from the metropolis. That he does move away shows of course\nthat his temporary inducement to move away is stronger than his\npermanent attraction towards the metropolis.\u201d\n\nThe student said that he was obliged for the explanation. \u201cBut\u2014\u2014\u201d\n\n\u201cWell?\u201d said the professor.\n\n\u201cThe only reason you have for supposing that the being is attracted\ntowards the metropolis is that he does move towards the metropolis. I\ndon\u2019t see why you should say it was pleasant for him to move towards the\nmetropolis when he does not do so.\u201d\n\n\u201cBut we know,\u201d said the professor.\n\n\u201cNo,\u201d said the student, \u201cyou only suppose; because you find it so on a\ngreat many occasions, you suppose it is so always. You are like a savage\nwho attacks the house of a civilized man. And he tries the window, the\ncivilized man meets him there; so he tries the door, the civilized man\nmeets him there; so he goes back to the window, and is met there again.\nAnd he concludes there are two men in the house; and after a time he\nconcludes there are as many men in the house as there are ways by which\nhe tries to get in.\u201d\n\nThe student had forgotten himself in speaking like this; and the\ncomparison to a savage, though made in haste and in good part as an\nillustration, offended the professor, so he said:\n\n\u201cYou do not believe that the law of attraction towards the metropolis is\nuniversal, and affects all the inhabitants?\u201d\n\n\u201cI cannot,\u201d said the student.\n\n\u201cThen you shall go to a place where you will feel it,\u201d said the\nprofessor. \u201cYou will go to-morrow to the extreme confines of the valley,\nand stop there until you are of a different mind.\u201d\n\nHe said this in a superior and gentle manner. But it was a terrible blow\nto the prospects of any student to be thus exiled. And yet the professor\nwas within his strict legal right, and the student knew it. He had\navoided this danger all through his college course, and now it came with\ncrushing effect on him. For just as long ago in the valley they had had\ndoctrines about the king, and had punished any one who did not feel them\nas true, and who was found out, so now when all the ideas about the king\nhad been disproved, they had severe regulations about the belief in the\nlaws. The learned class was a sect of priests, and whoever threatened to\nbring confusion and trouble by denying any of the known laws, and to\nlead the ignorant people to disregard them and deny them, was subject to\nsevere punishments. In the case of this student, the error did not so\nmuch matter, because he had committed his offence in the presence of\nwell-instructed people, who would only smile at his folly. But he had in\nhis presumption insulted the head of the college, and his punishment was\nuniversally considered to be mild and just. And yet he was not\naltogether in the wrong. For it was not as though the king (when he\nwanted a being to move away from the metropolis) took as usual a portion\nof his effort in going there; and at the same time counterbalanced this\nby taking a still larger portion of the pain involved in his moving away\nfrom the metropolis. By no means. When the king willed a man to move\naway from the metropolis, he let him start afresh, as it were, according\nto the conditions which every being was subject to in the valley\u2014that it\nwas just as pleasant as painful to move in any way, and he took a\nportion of the pain involved in moving away from the city.\n\nNow the student, when he was sent away, tried earnestly to see wherein\nhe had been wrong. The place where he was exiled was on the confines of\nthe valley, where a peaceable race of savages lived, engaged in\nagriculture. In the quiet, monotonous life of the place he thought over\nhis whole course of life, but could not obtain any different feeling.\nAnd while thus buried in thought, he fell into the way of going about\nwith the savages and doing as they did. Much to his surprise, when his\npreoccupation of mind passed away, he found himself singularly at home\nwith them. Their tastes seemed to agree with his. And he came to the\nconclusion that he was in reality a savage who by some mistake had been\nadmitted to the college. Having formed this conclusion, he threw himself\ninto the life around him heartily. In course of time he won the\nconfidence of the rude, uncultivated people, and they talked to him\nunreservedly.\n\nMany curious traditions were handed down amongst them. There were some\nwhich proceeded from the time when the king had walked and talked with\nthe children he called into activity. There were others proceeding from\ntimes when there had appeared amongst them one to whom the king had\ngiven some of his rays, so that that person had the power of making the\npain less in actions for others, and of giving them motives to act, and\nof rousing them thus to an active state. And all these traditions they\ntold to the exiled student.\n\nNow their own belief was this. They thought that there was a power over\nthem, and in this they recognized the king; but how it was that this\npower prompted them they did not know. Yet they connected him in some\nway with pleasure and pain. They thought it pained him when they had\npleasure, but not in the way in which was really the case. They thought\nsimply that it was pain to him to see them taking pleasure. They\nthought, moreover, that he would, if they displeased him much, take away\nall their pleasure and leave them nothing but pain.\n\nNow the student saw clearly some errors, some contradictions in their\nbelief. For instance, he knew that beings only followed pleasure, and\ndirectly pleasure was equalled by pain, sank into apathy, and then\ngradually vanished away. Hence he knew there need be no apprehension of\nthe power\u2019s acting as they thought. But the thing they said, that their\ntaking pleasure pained this power, struck him. He did not approve the\nresults in their life, for it was in consequence very gloomily framed,\nthough with a good deal of unconscious cheeriness. But he knew as a\nscientific fact that there was a constant diminution of feeling; and\nsince he also knew that beings in the valley did nothing except it was\nmore pleasant, he concluded that although pleasure and pain might both\nbe disappearing, still pain must be disappearing to a greater extent.\nNow since the feeling did not become nothing, but passed away out of the\nperception of the inhabitants, it followed that it must pass to some\nbeing. It did not disappear as feeling, but passed away from the\nsensation of the inhabitants. Is there a being, then, he asked\nhimself\u2014the power of whom these simple folks tell\u2014who bears the\ndifference of pain, and so makes existence pleasant to us? And is that\nthe meaning of what they say that our pleasure pains him? Is it just the\ntruth read backwards\u2014the truth, namely, that by his taking pain we have\npleasures, which they have had handed down to them as this\u2014that our\ntaking pleasure pains him.\n\nWhen he had thought thus far he remembered one of his books in which the\nancient beliefs of the valley were discussed. It happened to be one of\nthe books which he had brought into his exile with him. He took it down,\nand in the evening set himself to search through it. And in a footnote\ntowards the end of the book he read:\n\n\u201cThe existence of a power shaping the valley for the good of the beings\nin it is clearly disproved. First, by the amount of suffering there is\nin the valley. Secondly, by the fewness of the types of life, and the\nconstant modification of one plan to secure different results\u2014which\nwould be much better achieved by the use of radically different types\nand means. Thirdly, by the absence of any indication of such a power,\nexcept in the traditions of uncultivated tribes.\u201d\n\nWhen the student had read this he rose up and paced his chamber. For he\nsaw clearly that if it was in bearing part of the pain that the power of\nthe being lay, the first of these arguments fell to the ground. The\npresence of the pain in the valley would prove that this power took only\nsome of the pain and not all. As to the second argument, all it would\ncome to was that the being who, bearing pain, gave existence to the\ninhabitants, used economy in his actions\u2014he chose to effect his objects\nwith the least possible expenditure of means.\n\nReflecting thus he went out.\n\nNow it may be considered surprising that the king did not communicate in\nsome way with the student, for by means of his rays he was in possession\nof all that had gone on in his mind. But the king had found over and\nover again that if he manifested himself to any one of the inhabitants\nof the valley, the effect, though good at the immediate time, was most\ndisastrous for the following time. For the ends he was working towards,\nand leading the inhabitants towards, were much greater than any one of\nthem could grasp or conceive. And the inhabitants, as soon as they had\ncommunication with him, at once thought they knew his final will. And\nthey were a set most peculiarly stiff in their notions, and with the\nkind of sanction which communication with him gave them, even the most\nabsurd ideas if once conceived took a very long time to eradicate.\n\nSo when the student went out into the open air he saw nothing except the\nstars, and heard nothing except the wind. The way was so well known to\nhim, however, that he walked on quickly without stumbling in the\ndarkness. He had not gone far when he saw a kind of luminousness. Is it\nthe moon beginning to rise? he thought. But he found he had passed the\nlight and was leaving it behind. He could not have passed the moon thus.\nHe went towards the light, and when he had reached it, it seemed like a\nslender staff of light. He touched it with his hand, and although he did\nnot feel anything, yet he could take hold of it, and he walked on with\nthe slender beam in his hand.\n\nHe had not gone very far when in his walk he touched on something lying\nin the path. Bending down and touching it with his hand he found that it\nwas the form of a fellow creature. \u201cHe is overcome with fatigue; can I\nhelp him along?\u201d he thought. He rose up to look round, and let the beam\nof light which he held in his hand touch the prostrate form. \u201cI wish he\ncould get up by himself,\u201d he thought. No sooner had he felt this wish\nthan he had a sensation of pain in his limbs, and the figure rose up.\n\n\u201cI could not move,\u201d it said, \u201cuntil you came, with all my reasons to get\nalong; the pain was as much as the pleasure.\u201d\n\n\u201cWho are you?\u201d\n\n\u201cI am a wanderer, and am trying to reach the place where I was born;\nthey will help me there.\u201d\n\nNow in the valley there was a certain set of people called wanderers,\nwho had proved themselves unfit for any real work. These, if\ninoffensive, were allowed to roam about subsisting on charity. The\nstudent walked alongside this wanderer; and every step the wanderer made\nhe felt a sensation of pain in his limbs. But the two walked quickly on\ntill they came to the dwelling he had left so shortly before. The\nstudent led him in and let him rest in his chamber. And then he himself\nleft the dwelling again, taking with him a few necessaries.\n\n\n                              CHAPTER IX.\n\nWhen he had seen the wanderer safely housed he determined to go and\nvisit a friend who had lived in a town not very far from the metropolis.\nThis friend had been his most intimate companion when he first became a\nstudent, but being older had finished his studies sooner, and had left\nthe metropolis before the student\u2019s misfortune. In leaving his place of\nexile the student rendered himself liable to punishment, and he gave up\nthe means of subsistence which had been provided for him there. He was\nobliged to go as a wanderer, and trust to the liberality of the people\non the way.\n\nHe was hospitably received as a rule. The region was remote from the\nmetropolis, the inhabitants were glad to talk with a stranger\u2014and the\nwanderers were, in general, held to have a stock of exchangeable talk\nand news. But he did not speak with any one of what lay present to his\nmind, till one occasion.\n\nAs he was walking along early in the day, he was hailed by an inhabitant\nwho looked like a well-to-do farmer. Something in the student\u2019s\nappearance attracted him, for, learning that he was on his way to a\ndistant town, he asked him to stay and take the first meal of the day\nwith him. This inhabitant had been a clerk employed in the council of\npleasure and pain. But the sedentary life had been too trying for him;\nhe had come to live in the country on a small possession of his till he\nhad overcome the strain.\n\n\u201cDid you not find it very dull in the part you come from?\u201d\n\n\u201cNo; I found that the people had much of interest to tell me.\u201d\n\n\u201cThey have singular traditions. I remember when a deliberation was held\nin our council as to whether they were pernicious or harmless; it was\ndecided that they were harmless and little likely to spread.\u201d\n\n\u201cI have talked a good deal with them since I have lived amongst them,\nand have come to the conclusion that in what they believe a great deal\nis true.\u201d\n\n\u201cIndeed! you cannot surely believe that our pleasure is distasteful to\nany being outside us.\u201d\n\n\u201cNo; but I go back to the old notion of which you have heard, that there\nis a being who calls us into being, and who is over us; and I believe\nthat this being takes pain, and so makes life pleasurable to us. You\nknow that some sensation is passing away, and you know that there must\nbe more pain that passes away than pleasure.\u201d\n\n\u201cHow can I know that?\u201d\n\n\u201cWe know that there is not such a very great excess of pleasure over\npain. Now if in all the course of time that has been, the sensation that\nhas been passing away was pleasure, there would by this time have been\nleft an excess of pain, and before now we should all have sunk into\napathy. So it is either pleasure and pain mixed which passes away, or\npain alone. I conceive that it is pain alone. These strange doctrines\nare true, only curiously expressed. The being over us is continually\nbearing pain and so making existence pleasant to us, thus causing us to\nmove and live. So the pain of our life is that remaining pain which he\ndoes not take.\u201d\n\n\u201cThis seems to me a very dismal doctrine. I can imagine some poetry in\nthe idea of a being of infinite power, strong and glorious, but none in\nthe idea of a suffering being.\u201d\n\n\u201cWhen you were a child you thought your father could do everything; but\nas you grew up and found that he too had his difficulties, was your\nregard for him lessened, or your thankfulness for that which he did for\nyou?\u201d\n\n\u201cNo. And you mean that if we do not regard this being in the same way,\ngranting his existence, still we should feel gratitude towards him.\u201d\n\n\u201cCertainly we should feel gratitude to him; and, considering the\nattitude we have taken towards him, this feeling of gratitude comes over\nus with a kind of revulsion. But besides gratitude I do not see why we\nmust lose any other feeling such as you seem to miss. Do you not\nremember how, in the course of the studies we have all been through, we\nwere told that there were two parts in knowledge\u2014one corresponding to\nreality, one introduced by the action of our own minds\u2014so that certain\ncharacteristics which we at first think to be due to the nature of\nthings in themselves we find out on reflection are only our apprehension\nof our own mental action?\u201d\n\n\u201cYes; we do not perceive the reality absolutely, we apprehend it subject\nto the mind\u2019s mode of perceiving.\u201d\n\n\u201cAnd of course the mode of the mind\u2019s action makes it perceive certain\nqualities as parts of the real existence, which do not belong to real\nexistence at all. These qualities spring from our mind\u2019s own action. In\nold times these qualities were considered to be qualities of the reality\ninstead of introduced there. And much of the impressiveness of the idea\nformed of the being of whom we speak was due to a mere magnification and\nextension of these qualities\u2014qualities which do not correspond to\nanything in reality. So the impressiveness of the idea of this being was\ndue to the magnification of qualities which originate solely in our\nminds.\u201d\n\n\u201cThis accounts for the idea having faded away. But tell me definitely in\nan instance. Explain by taking some particular quality what you mean.\u201d\n\n\u201cI cannot do that, the thought but floats in my mind; still it is always\ngood to embody. Something of this sort. When we observe any object we\nalways attribute to it a certain power. Everything has its own powers of\nresistence, of moving, of affecting us in certain ways. Thus whatever we\napprehend, we apprehend as powerful. Now since this quality of powerful\ncomes in with regard to everything, it is probably introduced by the\nmind, and is rather a part of the mental action in giving an idea of\nreality than a quality of reality. If so, when we suppose a being to\nhave the quality of \u2018all powerful,\u2019 we are not supposing anything at all\nabout the being, but are only extending a quality quite barren of any\ncorrespondence with the absolute nature of things. We have left off\ntalking about the being, and are extending a conception which springs\nsolely from the only way in which we can perceive.\u201d\n\n\u201cSurely you would say that this being was powerful.\u201d\n\n\u201cOf course, if we think of him at all, we must conceive of him as\npowerful; the nature of our mental action demands this. But to dwell on\nthe notion of his powerfulness is quite barren, the only subject of\nthought which has content is to inquire what kind of power he has. There\nhas been a tendency on the part of those who have thought about this\nbeing to represent his greatness in every respect. But they have not\nalways been judicious in so doing, because being unable to separate his\nreal qualities from those which they attribute to him in virtue of their\nown mode of perception, they have come to lay stress on descriptions\nwhich on the one hand correspond to nothing in reality, and on the other\nhand fail to move those whom they are intended to impress. A cloak has\nbeen woven. The nature of this being is hidden. His nature has been\nconnected with introspective questions about the origin\u2014of, of all\nthings, the way in which we perceive. All this must be dashed aside.\nThis being is the cause of all our life, and yet he needs your help as\nyou understand help.\u201d\n\n\u201cI should like to accompany you to your friend and hear what he has to\nsay.\u201d\n\n\u201cCome, certainly.\u201d\n\nSo they went together to the town. On the way the clerk felt a\nbrightness of existence such as he had not enjoyed for a long time. They\ntalked together, and confided in one another. At length they came near\nthe town where the student\u2019s friend lived. They separated, the clerk\ngoing into the town, the student to the house of his friend. On his way\nthere the path led through a small wood of very thick growth. Passing\nalong, he found that he had left the path. Pausing to reflect in which\ndirection he ought to go, he thought he heard a sound. It was repeated.\nPenetrating deep into the obscurest part of the wood, he searched till\nat length he found\u2014carefully concealed\u2014a child, a mere infant.\n\nThe child was nearly perished with exposure. He took it up and warmed\nit. When the child was a little better the cause of its having been\nhidden away was apparent. Its breathing was distressed and laboured. It\nsuffered under some affection of the lungs, which made it gasp at every\nbreath. Still in other respects the child was well developed and seemed\nstrongly made. It seemed to have been left too long without care to\nrecover. The pain of exhaustion from the neglect, and added to this the\npain of its breathing, was too much for it, it was sinking.\n\n\u201cIf I could bear the pain of its breathing,\u201d thought the student, \u201cit\nmight not sink till I could get some nourishment for it.\u201d\n\nHe looked up, for it seemed to him as if some one struck him in the\nchest. There was no one there. The pain continued. He did not drop the\nchild but continued on his way to the house of his friend. When he got\nthere he noticed a stillness unusual in the houses of the inhabitants.\nHe entered, and was met by his friend\u2019s sister. He saw at once that\nsomething must have happened. She took him into a dimly lighted room,\nwhere he saw his friend lying motionless and his face quite white.\n\n\u201cHe has been suffering great pain for long,\u201d she said; \u201cit was hoped\nthat if he could bear up the pain would have run its course and he would\nnot sink. But all we could do was no use.\u201d The room was full of all\nthings accounted pleasurable, and she looked round as she spoke. \u201cIt was\nno good.\u201d Taking the child from his arms she left him with the form of\nher brother.\n\nSitting down by his side the student felt the strange oppression on his\nchest continue. He went out and found that the child had completely\nrevived. It had still the appearance of being agonized in its breathing,\nbut its eyes were bright, and it laughed.\n\n\u201cIt will be all right soon,\u201d said his friend\u2019s sister.\n\n\u201cTell me what was the matter with your brother.\u201d\n\nWhen he had heard about his malady he returned to the room. After he had\nsat there for some time he felt more and more the sorrow for the loss of\nhis friend, and the need of his counsel. This aimless, inert form, this\nlifeless mass, was that which he had come to seek\u2014was the being with\nwhom he had longed to confer.\n\nHe bent over him. \u201cCould I but snatch him back into life; could I but\nhave one hour\u2019s intercourse with him. If I had been with him I might\nhave borne some of the pain of his complaint before he was overpowered\nwith it.\u201d He touched the lifeless hands, they were cold and damp. He\ngazed into the expressionless face. He seemed to feel the pain of the\ninner struggle his friend had waged against the disease. The quiet of\nthat still chamber was gone for him; in his own person he felt the pangs\nof the struggle for life. A mist came over his eyes, and he sank down\nholding his friend\u2019s hands. Suddenly he heard a voice. He rose and\nlooked about him. The sound came faintly from the lips of his friend.\n\n\u201cI have been very ill,\u201d were the words he caught. \u201cI am so glad you have\ncome; I was thinking of you in my worst moments. You have come just as I\nam getting better.\u201d\n\nIndeed the features were regaining expression, the hands were warm. It\nwas his living friend again.\n\nAfter a few hours he was sufficiently recovered to hear about all that\nhad happened. They talked together long and earnestly. His friend was\nconvinced.\n\n\u201cLet us go to your companion,\u201d he said.\n\nThey went into the town together. They found that the clerk had gone to\nthe magistrates\u2019 hall where a trial was being held. They did not see the\nclerk at first, so they listened to the proceedings. A woman was brought\nin who had been kept in prison for some days, accused of concealing her\nchild. The case was clearly proved. The woman received her sentence with\nan appearance of apathy.\n\n\u201cShe will not come out of prison alive,\u201d said the student\u2019s friend,\nnoting her expression.\n\nBut he called out to her from where they stood in the body of the court,\n\u201cDo not fear, your child is safe.\u201d\n\nThe woman\u2019s face brightened, and she went with her jailers buoyantly.\n\nThe magistrate had remarked who it was that had spoken, and was about to\ngive orders for the disturber of order to be brought up for punishment.\nBut the clerk, who was sitting near to the magistrate with whom he was\nacquainted, said:\n\n\u201cThis is the one I have told you about; pray do not punish him.\u201d\n\nThe magistrate accordingly contented himself with warning the audience\nin general terms.\n\nBut he said to the clerk, \u201cSomething about him is very repulsive to me,\ndo not tell me anything more about him.\u201d\n\nThe three returned together, and together they deliberated as to how the\nnew idea about the king could be made known. It seemed best to go to the\nmetropolis and talk with the wisest and most learned there.\n\nThe student asked about the child. His friend\u2019s sister came and told him\nthat its breathing was not any better, but that the child itself was\nstrong and playful.\n\n\u201cIt belongs to the woman who was tried to day,\u201d said the student, \u201cand\nmust be kept safely till she is out of prison.\u201d\n\nHis friend after some deliberation gave it in charge to a faithful\nservant to take to the metropolis. A suffering child there would be much\nmore likely to be overlooked, \u201cand you,\u201d he said, \u201cwill be able to look\nafter it.\u201d\n\nAs the student and the clerk were about to set out on their way to the\nmetropolis his friend took him apart.\n\n\u201cMy sister tells me that I had sunk into apathy when you came.\u201d\n\n\u201cYes.\u201d\n\n\u201cAnd that you called me back?\u201d\n\n\u201cYes.\u201d\n\n\u201cHow can I thank you! had it not been for you I should never have\nenjoyed life again. I am grateful to you.\u201d\n\n\u201cDo not say grateful to me, but rather to that power which does for you\nall your life that which I do for you momentarily now. And even now it\nis not to me that you should be grateful, but to him, for it is only\nbecause he has enabled me to do so that I have taken of your pain.\u201d\n\nWith this he took farewell of his friend, and with the clerk proceeded\non their way.\n\nThey had not got very far when a train of servants came up behind them.\nThey stood by on one side, but from the midst of his attendants a youth\nstepped forward.\n\n\u201cI have learned what you have done, and I have overtaken you with great\nhaste.\u201d\n\n\u201cWhat is your wish?\u201d\n\n\u201cI want to come with you. I know that you have restored your friend from\napathy to life. No power is so great as that. I have riches in\nabundance. All that I have is at your service; teach me your power.\u201d\n\nNow in the valley riches meant abundance of pleasant things. At the time\nthe student was bearing the constant pain which he took of the child\u2019s\nbreathing, and the pain also of his friend\u2019s illness. He felt that\nbefore beginning to take pleasure\u2014which was the meaning of having\npleasant things\u2014it would be necessary to give up the power which he was\nexercising, so he said to the youth somewhat harshly:\n\n\u201cYou cannot compare riches and that which I do, nor can you exchange the\none for the other. First give up all your riches, then you can begin to\nlearn what I do.\u201d\n\nThe youth turned back, but once again spoke, saying:\n\n\u201cI will give up a great part of my riches if you will teach me.\u201d\n\n\u201cIf you want to keep any, however small a portion, you cannot do what I\ndo.\u201d\n\nThen the youth with all his attendants passed away.\n\n\n                               CHAPTER X.\n\nWhen they came to the metropolis the clerk brought many of his\nacquaintances to see the student. From his position in the council\nchamber, he was able to address and induce many of the ablest of the\ncouncillors to come and inquire. But as soon as they came into the\npresence of the student a sort of constraint sprang up between them.\nThey did not take his words as having any real meaning. They were\noccupied all the time on speculating what motive it was that made him\nsay these things, and as to what kind of difference it was which they\nfelt existing between him and them.\n\nIn fact, as time passed on, no one of any position or power would be\nbrought into any sort of approximation to him. On the other hand he used\nto speak continually with the poorer people. Those that were sick\nespecially delighted in his presence. There seemed to be in him a power\nof stimulating those that were sinking into apathy back again into life.\nThose who were worst off in the city seemed to feel when he spoke to\nthem a promise of an alleviation of their sufferings.\n\nOne day the clerk asked him\n\n\u201cHow is the child?\u201d\n\n\u201cIt is well.\u201d\n\n\u201cBut it still seems to breathe with as much difficulty.\u201d\n\n\u201cYes, but see how happily it runs about.\u201d\n\n\u201cHow do you manage to preserve it? Any child which I have seen would be\npining miserably with such an affliction. What is the power which the\nbeing you tell of has given you?\u201d\n\n\u201cIt is no power in the sense you mean.\u201d\n\n\u201cSurely it must be. Have I not followed you faithfully and done all I\ncould to get the wisest in the city to listen to you? Surely the time\nhas now come when you will tell me what this power is, and, if you can,\nlet me share it.\u201d\n\n\u201cYou do not know what you ask.\u201d\n\n\u201cTell me, I pray.\u201d\n\n\u201cIt is simply this, when I became aware through thought of the being\nthat is over us I had no message or command from him. But I found that I\ncould when I stood by any suffering being take some of the suffering and\nbear it myself. So as he of whom I tell does with us each moment of our\nlives I do occasionally and in a little manner.\u201d\n\n\u201cBut what pleasure do you get that makes all this worth your while?\u201d\n\n\u201cThere is no pleasure. I am glad to see the being freed from suffering,\nand living instead of sinking.\u201d\n\n\u201cDo you mean to say that there is nothing to hope for?\u201d\n\n\u201cI hope the time will come when I shall have a fuller knowledge of the\nbeing I know.\u201d\n\nThe clerk was silent. He went out. While he was still thinking over what\nhe had heard in answer to his inquiries, a messenger came to him from\nthe chief of the councillors of pleasure and pain, asking him to an\ninterview.\n\nWhen the clerk had been ushered into the presence of the chief\ncouncillor, and was alone with him, the latter said:\n\n\u201cI should like a little quiet conversation with you about your\ncompanion.\u201d\n\n\u201cI shall be glad.\u201d\n\n\u201cWhen you gave up your office and retired you had no expectation of\nbeing concerned in affairs of state again so soon.\u201d\n\n\u201cI did not expect, certainly, and I do not know what your meaning may be\nabout my being concerned in affairs of state.\u201d\n\n\u201cWhat I mean is very simple. The continued deliberations, generation\nafter generation, of the wise men who assemble in the council chamber\nhave been the cause of the continued progress of the inhabitants.\nNothing is done by them hurriedly or violently, but gradually\nimprovement after improvement is worked out. But besides this, there\nhave always been at every age certain disturbances in the state; certain\ndoctrines are brought forward, and sometimes these tend to good, and\nshould be encouraged; sometimes they are of unknown import, and must be\nstudied; sometimes they are against the happiness of the state, and then\nthe grave responsibility rests upon us of checking them. Now from your\nposition you have more opportunity of knowing than any one else in what\ndirection your companion\u2019s doctrines tend. I have sent for you to ask\nyou to share with me this grave responsibility.\u201d\n\n\u201cI do not think I can help you. I am sure he does not wish to do any\nharm. What harm can there be in his doctrines?\u201d\n\n\u201cIt is not so much about his doctrines which I want to speak to you as\nabout another subject. Many of those who have talked with him have\nagreed with one another in ascribing a singular oppressiveness to his\npresence. The expression was even used by a very worthy friend of mine,\n\u2018He made me feel like a puppet.\u2019 Now what right had he to inflict such a\nsensation on a very worthy individual? I want to ask you yourself if you\nhave ever felt this?\u201d\n\nThe clerk hesitated.\n\n\u201cAt least, tell me, have you ever found it easy to influence him?\u201d\n\n\u201cNo; I do not feel as if I could influence him in the least. He seems to\nlack the ordinary springs of motive.\u201d\n\n\u201cNow, should you say that it would be a gain to the community if many\nshould become like him? Would not they be difficult to govern?\u201d\n\n\u201cCertainly they would be difficult to govern.\u201d\n\n\u201cWould it be a gain in pleasure to the rest of the inhabitants or to\nthemselves?\u201d\n\n\u201cIt would not be a gain to themselves,\u201d said the clerk, recalling the\npain which his companion bore, \u201cbut it might be good for the rest of the\ninhabitants.\u201d\n\n\u201cYes,\u201d said the chief councillor, \u201cthat is where his strength lies; he\nis a very skilful physician or an impostor, and he has the people on his\nside from the cures he has effected. Can you tell me anything about his\nlife?\u201d\n\n\u201cI have heard from him that he was a student, and was exiled; and that\nin his place of exile he found out the new doctrines, and he left the\nplace he was sentenced to. On his way I joined him.\u201d\n\n\u201cSo much we know, and it is within our power, according to the\nregulations, to compel him to go back, and to punish him for having left\nthe region he was banished to.\u201d\n\n\u201cIf you have that power, why do you not send him back if you think it\nwould be best for the state for him to disappear?\u201d\n\n\u201cAh, my good friend, you have heard a great deal of our public\ndeliberations from your place in the council; but now that we are\nconsulting together, I must tell you that there are deeper secrets in\nthe art of government, which you will readily apprehend. Suppose we\narrested this individual and sent him away, the people would not see the\njustice of it. They want him now, and they would say that the forms of\nlaw were being used to get rid of him. Of course if his partizans became\nviolent something of this kind would have to be done. But it is only a\ndecree that seems just in the eyes of the people that we can prudently\ncarry out in such a case without attracting even more attention to him\nthan there is at present.\u201d\n\nThe clerk said nothing. The chief councillor went on:\n\n\u201cI am sorry that our conference has come to so little. I was hoping that\nI might have found in you a successor to the vacant seat in the chamber.\nI know you have the ability to fill it well. But before the advancements\nare made some proof of the wisdom of the successor is required. Hitherto\nyou have not had the chance, but I thought that in this difficult case,\nwhere you have so much better opportunities of observation than any one\nelse has, you might have shown your mental power and confirmed my\nopinion of you. Still, no doubt, on some future occasion you will have\nanother opportunity when this affair, difficult as it is, is forgotten.\u201d\n\nThe chief councillor made a sign that the interview was at an end, but\nthe clerk remained.\n\n\u201cAll that we want,\u201d the chief councillor resumed, \u201cis to form an opinion\nfrom inside knowledge of whether this innovator is likely to cause more\npain or more pleasure if he gains a hearing. Can you advise us? any\nparticle of knowledge of his inner life, apart from his public\nprofessions, is valuable.\u201d\n\n\u201cThere is a singular fact which I should like to tell you of, as it has\nbeen somewhat of a burden to me.\u201d\n\nThe chief councillor made a sign of assent, and the clerk told him about\nthe child, and how it had been preserved.\n\n\u201cAnd with this child,\u201d he said, \u201che and I sit when the day\u2019s work is\ndone.\u201d\n\n\u201cIt is indeed a strange story,\u201d said the chief councillor; \u201cyou are\nquite right in telling me. I was sure you were one on whose discretion\nconfidence might be placed. You have given me the highest proof I could\nhave expected. The bearings of this matter must be thought over.\u201d\n\nThat evening, as the clerk entered the room where they lived, the\nstudent was leaning over the child with a wearied expression. He went up\nto him and laid his hand on his shoulder. The child looked up at them\nand laughed. It was quite happy despite the apparent struggles of its\nbreathing. The student looked at his companion\u2019s face. His weariness\nvanished at once, and a strong warm light came into his eyes.\n\n\u201cYou seem oppressed, my friend. I know you regret the way in which all\nthe wise and important people you have brought here look on me, and you\nmust feel some sorrow for the partial loss of esteem they have showed\nyou in consequence. Can I help you to bear it?\u201d\n\nAt that moment the door opened, and a messenger came in and gave the\nclerk a sealed packet. He opened it and saw that it was his appointment\nto the vacant seat in the council chamber. But his face did not\nbrighten. He answered his companion moodily, and thus the day ended.\n\n\n                              CHAPTER XI.\n\nOn the next day the student rose early and went forth alone. He did not,\nas was his wont, go amongst the people, but he passed through the\nstreets towards the open country. On his way he was stopped by an old\nwoman, bent with age and many infirmities. She had no place amongst the\npeople, and had so many pains and such a barrenness of existence that\nany one who had thought of her would have wondered that she remained\nalive.\n\nShe stopped him and said, \u201cMaster, I have heard that you can take my\npain. Help me.\u201d\n\nBut he answered, looking at her, \u201cNo, I cannot, but I have a message for\nyou.\u201d\n\nAnd she said, \u201cA message for me? I do not know any one who would send me\na message.\u201d\n\nBut he answered, \u201cNevertheless, I have a message to you from my lord,\nand he bids me thank you.\u201d\n\nShe answered, \u201cIt cannot be. You must have made a mistake.\u201d\n\nBut he said, \u201cI have made no mistake; he thanks you.\u201d\n\nHe could not explain to her how by her bearing pain, according to the\nlaw of the valley, she took it from that which the king bore. Instead of\nsaying that, he gave her the message, and somehow the old woman believed\nit.\n\nThe rest of the day he spent in the open country. When he returned it\nwas getting towards dusk. There was an unusual movement in the streets.\nOn passing into the public market-place he saw a crowd collected; and\nwhen he had penetrated to their midst, he saw lying on the ground the\nchild he had kept so long. It had been lying uncared for and exposed for\nmany hours; and the want of food, the fright, and its gasping breathing\nmade it the most pitiable object. He at once stepped towards it and took\nit up in his arms.\n\n\u201cIs that your child?\u201d said one of the crowd.\n\n\u201cIt is not my own,\u201d he answered, \u201cbut I take care of it.\u201d\n\n\u201cThen it is you that are bringing pain upon us all,\u201d shouted several\nvoices from the back of the crowd. And some one shouted out:\n\n\u201cI know you. You pretend to take pain away and you really bring much\nmore in secret.\u201d\n\nAnd moved with a feeling of indignation against the one who had caused\nsuch a painful object to exist as the child was, the crowd closed on\nhim, and barred his way to his own place. But they did not lay hands on\nhim. As he stood with the child it gradually began to regain its\ncomposure. But with a sudden movement the crowd swept towards the\ncouncil chamber. And when they had come there they demanded that this\ncruel and wicked act of keeping pain in existence should be punished.\n\nThere happened to be several of the chief magistrates on the spot, and\nin obedience to the voices of the crowd they proceeded to sit in\njudgment at once. It was not known how the child had come into the\nstreets; but it was admitted by the prisoner to be his doing that it had\nbeen kept alive. The doctors unanimously said that it ought to have been\nput out of existence directly it was born. There was practically no\ndefence. The charge of subverting the laws was established. The people\nclamoured for the extreme penalty. The judges passed sentence on the\nstudent.\n\nBefore morning he was put to death.\n\nHe met his fate without sorrow, even with gladness. The pain in his life\nhad for long been as much as he could bear. He did not, like the prince\nof long ago, look upon nothingness as the desired end of existence. He\nfelt the presence of the one whom he had discerned through thought, and\nthis seemed more real to him than life or death.\n\nOn the following day, whether in reaction from the excitement of the\nprevious evening, or from some other cause, an unusual quiet pervaded\nthe streets of the city. There was not much discussion as to the event\nwhich had happened. The prevailing feeling was one of wonder that there\nshould have been so much commotion about an unimportant affair. For the\nmost part before the next evening the whole circumstances were on the\nway to be forgotten. And yet every here and there were persons in whose\nlives the loss of their friend was deeply felt. The joy and spring of\nlife seemed gone. The poor child lay pale and motionless, save when\nevery now and then it gasped convulsively for breath. None felt the\ndespondency more than the clerk. The interest and value of life seemed\nto have gone. He did not care for his new honours.\n\nThat day some most unexpected news went through the town. The chief of\nthe council of sensation had sunk into apathy. He was in the prime of\nhis life. It was most unexpected. Every one was astonished at the news,\nbut were still more astonished at how little they felt concerned.\n\nFollowing on these tidings came others. Many of the inhabitants of the\nmetropolis whose lives were most strenuous suddenly succumbed. The clerk\nhad made up his mind to go into the country. But tidings came from there\nalso that the poorer labourers, and those who were exposed to the\nfatigue of long journeys or exposure were in many cases sinking. The\nwave of torpor seemed passing over the whole valley and not to be\nconfined to the metropolis. The rich and unoccupied classes only were\ncomparatively unaffected. They betook themselves to the store of\nenjoyable things at their service, and so replaced the natural spring of\nlife which seemed tending to fail in every one.\n\nOn the confines of the valley, where the ravine struck its vast depth\nbetween this land and that, vast and endless as the sea stretched the\nplain whence the king had come. It was struck silvery grey by the light\nof the moon, dark shadows marked the nearer strands, and gradually the\nrocks which cast them showed their sharp outlines, hardly\ndistinguishable from the ground out of which they rose.\n\nOver the great gulf floated the sounds of a pipe, the strains were low,\nwinning the soul with the sweetness of an unearthly melody, throbbing as\nwith a call to a distant land away and beyond.\n\nAnd when the eye found the source of the sounds, there stood, once more,\nsolitary in the untenanted vast, the king\u2019s devoted friend, the same old\nman who before had hailed him. Gradually the music sank lower and lower,\ntill at length silence spread in folds unruffled. Then on the edge of\nthe valley a form appeared. It came and seemed to gaze across the gulf,\nstanding motionless and intent. At length a voice came.\n\n\u201cArt thou there?\u201d\n\n\u201cYea, O king, what wouldst thou? Art weary?\u201d\n\nNo answer came.\n\nThen the old man spoke. \u201cBehold the roads where they stretch gleaming\nwhite in the moonlight; behold the fields, the villages; see in the\ndistance the great walls of the palace. Have not these risen up for\nthee, O king?\u201d\n\nThen the king made answer: \u201cI am weary.\u201d\n\nSuddenly the old man raised his pipe with both his hands to his lips.\nWave after wave of triumphant sound pealed forth. Great harmonies such\nas marching nations might hear and rejoice, noble notes of unbounded\ngladness.\n\nThen, crossing by an unknown way, he came and stood by the king\u2019s side.\nAfter a while the two moved on together, and by a secret path passed\naway from the valley\u2014whither I know not.\n\nAs soon as the king had departed from the valley the beings in it began\nto sink into the same state of apathy as those were whom he had first\nfound there. Those who sank first were the ones in whose lives the\nstress of labour or thought was the most intense, for they first felt\nthe loss of that bearing of pain by one beyond themselves which gave\nthem a difference of pleasure. And slowly as the accumulated enjoyment\nwas exhausted, a chill death in life crept over the land. \u2019Tis useless\nto ask after the fate of any one of those that were there, for each was\ninvolved in the same calamity that overwhelmed all. Every hand forgot\nits cunning. The busy hum of life in the streets was hushed. In the\ncountry the slowly moving forms gradually sank to rest. At every spot\nwas such unbroken quiet as might have been had all the inhabitants gone\nto some great festival. But there was no return of life. No watchful\neye, no ready hand was there to stay the slight but constant inroads of\nruin and decay. The roads became choked with grass, the earth encroached\non the buildings, till in the slow consuming course of time all was\nburied\u2014houses, fields, and cities vanished, till at length no trace was\nleft of aught that had been there.\n\n\n                               _PART II._\n\n\n                               CHAPTER I.\n\nThere are certain respects in which our world resembles the valley.\nInstead of regarding pleasure, pain, and feeling, let us examine the\nworld we live in with regard to motion in one direction and another, and\nin respect of energy.\n\nIf we observe the movements which go on in the world, we find that in\ngreat measure they consist of movements which if put together would\nneutralize each other.\n\nA pendulum swings to and fro. If the two movements took place at the\nsame time the pendulum would be still. Taking a more ample motion\u2014that\nof the earth round the sun. The earth moves in the course of its orbit\nas much towards the sun as away from it, and as much towards the east as\ntowards the west. If all the motion were to be gone through at one and\nthe same time the earth would not move with regard to the sun.\n\nAgain, if we notice what goes on on the surface of the earth, we see\nthat there is a motion of rising up and of sinking down. There is an\napproximation of the chemical elements into some compounds, and a\nseparation of them again. Of all the myriad processes which go on, the\nswing of a pendulum is the type. But the downward swing may be very\ndifferent to the upward swing. It may be that the downward swing is\nrepresented by the violent action of the chemical affinities in a charge\nof gunpowder when exploded, and the upward swing may be represented by\nthe swift motion imparted to a cannon ball, and the swift motion of the\ncannon ball in its turn comes to rest, and as it comes to rest slowly or\nquickly other changes take place.\n\nAnd what we notice in our world is similar to what the inhabitants of\nthe valley noticed about pleasure and pain\u2014that they do not neutralize\none another as a matter of fact.\n\nThe contrary motions on the earth which, if they were put together,\nwould neutralize one another, do not as a matter of fact neutralize one\nanother. We call motion in one direction positive\u2014in the opposite\ndirection negative. But in the world as a matter of fact positive and\nnegative motion do not together come to nothing.\n\nAs in the valley the states of pleasure and of pain did not coalesce\ninto a state of apathy, but always succeeded one another, in simple or\ncomplicated fashion, so on the earth it is impossible from two opposite\nmoving bodies to get stillness. If the two come into contact in opposite\ndirections the movement does not stop, but makes its appearance in an\nalteration of the shape of the bodies, in a disturbance of their\nparticles, or in some such fashion.\n\nAgain in the valley, by measuring the pleasure and pain simply as\nfeeling, and not taking into account whether it was pleasure or pain,\nthe inhabitants found that the feeling was always the same in amount.\n\nSo we on the earth, measuring the amount of movement, and leaving out of\naccount whether it is positive or negative, come to the conclusion that\nthe quantity of movement, reckoned in the way in which we call it\nenergy, is always the same. The principle of the conservation of energy\nhas become a fundamental one in science.\n\nBut besides the discovery that the amount of sensation as such was\nalways constant, the inhabitants of the valley discovered that a portion\nof the sensation was passing away from a form in which they could feel\nit.\n\nAnd there is an analogous discovery in science. We know that a portion\nof the energy of our system is passing away. It is not being\nannihilated, but is disappearing. With the energy which can be collected\nfrom the falling of a stone, the same stone cannot be raised to its\nformer level again. Some of the energy has disappeared from the form in\nwhich it can be known as the energy of moving masses. The energy has in\nsome measure irrecoverably passed off in the form of heat.\n\nHence, just as the inhabitants of the valley came to the conclusion that\nin point of sensation they were \u201crunning down,\u201d and that after a time\nall sensation would have passed away from the form in which they could\nfeel it, so we have come to the conclusion that the energy of the system\nin which we live is running down, that the energy is passing out of the\nform in which it can be manifested as moving masses, that finally all\nmovement of masses will come to a standstill, and there be nothing left\nsave motionless matter, with warmth equally diffused through it.\n\nNow in coming to the conclusion about the valley, that the amount of\nsensation was gradually passing away, the inhabitants, as we have seen,\nhad come upon the very secret and cause of all the life in the valley.\nBut coming upon it from the outside they had not recognized the\nsignificance of what they had found. The cause and prime mover of all\ntheir existence indicated itself to them, coming thus upon it, as a\nprocess whereby all that went on was doomed to a distant but certain\nextinction.\n\nNow, is this process of the passing of mechanical energy into the form\nof heat to be interpreted by us in a way analogous to that in which the\ninhabitants of the valley could have interpreted the process they found?\n\nIn this cessation of sensation in the form in which they could\nexperience it lay the central fact of the life of the valley. Has this\npassing away of energy from the form in which we can experience it an\nanalogous significance to us?\n\nIn order to examine into the possibility thus suggested there are four\nconvergent lines of thought which it will be well to follow up\nseparately. Each of these lines of thought bears in an independent\nmanner on the central question\u2014the significance of the passing away of\nenergy. These lines of thought may be connected with the following\nwords, which indicate their significance: (1) Permission; (2) Causation;\n(3) Conservation of Energy; (4) Level.\n\n\n                              CHAPTER II.\n\nWhen we observe any movement taking place we ask what is the cause of\nit? what is the force which produces it? But surely, if we confine our\ninquiry to this point, we have made an omission. That we are not\nconscious of having made an omission may perhaps come from our living in\nthe air which yields so easily to any moving body. If we lived in a\nrigid medium we should, when we became aware of any moving body, ask two\nquestions. First, what urges it along? secondly, what prepared the\nchannel for its motion?\n\nBut seriously, without laying any stress on the above illustration, we\nsee that to every movement two conditions are necessary: a pushing and a\nyielding, a force and a permission. If the particles of the air could\nnot yield, a pendulum could not swing through it. If again the air could\nnot pass on the motion it has received, it could not yield to the motion\nof the pendulum.\n\nNow since every motion requires a permission, we are led to ask the\nquestion, What is the ultimate permission? What again is that which by\nyielding allows motion at all to take place?\n\nIf we trace any movement scientifically we find an indication of what\nthe ultimate permission is.\n\nA body swings through the air. Currents in the air are set up. These\ncurrents impinge on the objects with which the air is in contact, and in\nthem produce heat\u2014producing heat also by friction with other portions of\nthe same air. Every motion thus passes off finally, at however long an\ninterval, in the form of heat. Motion may reappear as motion through\nmyriads of phases, but at each change of form some of it passes off into\nthe form of heat, and finally all passes off into the form of heat.\nThus, unless matter admitted of being warmed, there would be no ultimate\npermission. A motion once started would never come to rest. Or, rather,\nno motion could take place at all.\n\nThe tendency of the above remarks is to avoid the conception of there\nbeing absolute laws of motion, true of bodies when surrounded by no\nmedium, modified when a medium is present. Surely such a conception is\nan instrument of the mind for exploring nature, not an absolute fact in\nnature. The abstract laws of motion are mental aids in creating\nknowledge; like scaffolding for the builder, even from their very\nusefulness they have probably but little to do with the permanent\nedifice.\n\nThis passing into the form of heat supplies a place analogous to that of\nthe \u201cvoid\u201d in the speculations of the Epicurean philosophers. They\nargued that motion was not possible without a void. Given a void,\nsomewhere into which matter could move, then any amount of motion could\nbe accounted for. But without a void into which a portion of matter\ncould move, how was it possible for motion to begin?\n\nThus repeating their inquiry with our altered conceptions, we ask this\nquestion about motion, or energy (which is a particular way of reckoning\nmotion).\n\nUnless motion can in some way pass off, how can there be all these\ntransformations of energy?\n\nNow the ultimate transformation of all energy of motion is into the form\nof heat. In this change into the form of heat is to be sought the\nultimate permission which makes all transformations of energy, all\nmotions, possible. It is this being acted on of the finer particles of\nmatter which permits the movements of the larger masses.\n\nThis passing of energy into the form of heat must not be regarded as a\nside circumstance, as less essential to the laws of nature than that law\nwhich we call the conservation of energy. It is at the same time the end\nof every motion, and that which makes every motion possible.\n\nThe passing of energy into the form of heat takes place in that which we\ncall friction, and in all those modes in which any movement is brought\nto a standstill. But so far from these being simply \u201chindrances\u201d to\nmotion, it is through them that we learn that which makes motion\npossible. It is with us as with the inhabitants of the valley, the\ngradual cessation of feeling from their life and the modes in which it\nceased were the way in which they regarded the action of the king who\nwas the cause of all. We have thought of motion as a thing in itself\nimpaired by the multitudinous obstacles it meets in the world. Let us\nlook on the circumstances more impartially. Let us look on them as\nsomething co-equal with motion. Let us find in that mode whereby all\nmotion comes to an end the originating cause also whereby all motion\ncomes to be.\n\nThe passing of the motion of masses into the form of heat is the\nultimate permission.\n\n\n                              CHAPTER III.\n\nIf we reflect cautiously on the history of our opinions, we find that we\noften fall into error in respect to our freedom in attributing causes.\nIf we are unfortunate we are apt to look on our neighbours, or the\nworld, or, if we are of a self-depreciatory turn of mind, ourselves as\nthe cause.\n\nAgain in past times people really felt sure about certain things being\ncauses which we now know had a very slight connection with the result.\nIncantations have been supposed to have an effect on physical phenomena,\nsuch as eclipses. Numbers and their properties have really been\nconceived as the causes of the modes of existence. Ideas have been\nsupposed to have causative power over the order of the world.\n\nWe should be very careful in attributing the notion of causation. If we\nsee a stone lying on the ground, and proceed to pick it up by the\nstrength of the arm, we say that the exertion of the arm is the cause of\nthe stone being lifted. But in this respect even we are too hasty. The\narm may exert itself and yet the stone not be lifted up\u2014if it is too\nheavy. All that we can say about it is that if the stone is lifted, a\ncertain set of muscular actions has gone on in the arm, and a certain\nmovement of the stone has taken place. If we look closely at the matter,\nthe movements in the arm are related to the movements in the stone in a\nstrictly measurable way. There has been so much exertion corresponding\nto the weight of the stone. But suppose the arm had done anything else,\nthere would have been the same relation traceable between the movements\nin the arm and the actions which followed its movements. The energy\nspent by the arm would be equal to the energy imparted to the object\nmoved, whether it be a stone sent flying through the air, or one lifted\nto a higher position (bearing in mind always the small quantity of\nenergy passing off in the form of heat).\n\nIt does not seem advisable that the notion of cause should be brought in\nto denote the relation of the movement of the arm and the movement of\nthe stone. These are two sets of actions between which the regular\nrelations which hold good between the consecutive states of moving\nsystems hold good.\n\nThe notion of \u201ccause\u201d should rather be applied to that act of the will\nwhereby the movements of the arm are connected with the movement of that\nparticular stone rather than the movement of any other object.\n\nWe are the cause of the actions we will. The notion of cause is derived\nfrom our \u201cwill\u201d action, and the notion of cause ought to be kept to this\nconnection.\n\nAll that goes on outside us can only be apprehended as consecutive\nstates following on one another. Between certain sets of consecutive\nevents we notice that the same relation holds good which we have\nobserved in other consecutive states. If some water is heated in England\nit passes off into steam; if water is heated in another part of the\nworld it also passes off into steam. There is an exact analogy in the\nbehaviour of water under the action of heat wherever we observe it. But\nall that we have obtained as knowledge is the fact that we may\npractically be confident of an analogous behaviour on the part of water\nwherever circumstances are similar. We may use the expression that heat\nis the cause of water boiling for convenience. But the expression should\nnot be used as containing any deep meaning. To say one external event is\nthe cause of another is to put an absolutely unknown and spiritual\nrelation in place of impartial observation.\n\nTo cause a motion is the name for the action of our soul on matter\u2014a\nthing shrouded in mystery. To be the antecedent in a chain of movements\nis the fact which we can observe about any movement in the external\nworld. We cannot strictly say what movements of gases, water, &c., cause\nthis volcano. We can only say what movements of gases, water, &c.,\nprecede this volcanic eruption analogous to movements which have\npreceded other volcanoes.\n\nThere are invariable sequences in the external world to which we do not\naffix the notion of cause and effect\u2014day and night, summer and winter.\nWhy we should do so in any case is not clear, except that by familiarity\nand mystery the sequences have become to us something like our own will\naction. Indeed, is it not the case that when we can trace intermediate\nlinks we say so and so comes from so and so in such a manner. But when\nno intermediate links can be traced we say one event causes another.\n\nIf, however, we omit the feeling of causation from the external chain of\nevents, it does not follow that there is no causation to be apprehended\nin the external world.\n\nLet us not introduce the notion of causation at haphazard. But if we\nfind in the external world signs of an action like our own will action,\nlet us then say, Here is causation.\n\nThe inhabitants of the valley would not have been right in saying that\none act of a routine caused another: But they were right in saying that\nthe amount of sensation was constant, and that some of it passed off in\na form in which they could not feel it.\n\nAnd so let us not say that one action causes another. Let us not say,\nfor example, that the downward swing of a pendulum is the cause of its\nupward swing. But let us simply say that the one follows the other; that\nthe amount of energy present is the same except for the small portion\nthat passes off into the form of heat.\n\n\n                              CHAPTER IV.\n\nSuppose certain sets of numbers were being presented to us one after the\nother, and amongst these three consecutive sets were the following.\nFirst set: 3, 5, 6. Second set: 8, -2, -1, 1. Third set: 7, 4, 2, -1.\n\nA little consideration will show us that there is a certain uniformity\nin these sets.\n\nTake the square of each of the numbers in the first set and add them\ntogether, the result is 70. Thus 3\u00b2 + 5\u00b2 + 6\u00b2 = 9 + 25 + 36 = 70.\n\nThe sums of the squares of the numbers in the second set come to the\nsame. 8\u00b2 + (-2)\u00b2 + (-1)\u00b2 + 1\u00b2 = 64 + 4 + 1 + 1 = 70. Also in the third,\n7\u00b2 + 4\u00b2 + 2\u00b2 + (-1)\u00b2 = 49 + 16 + 4 + 1 = 70, and so on.\n\nHaving noticed this we should regard it as a purely formal law, having\nnothing to do with why the numbers were presented to us. But we should\nconsider it likely that it would characterize all the numbers that were\npresented to us. And if this expectation were found to be realized, we\nshould after a time feel a certain assurance that the next set of\nnumbers presented would satisfy the same law. If this assurance was\nindefinitely satisfied we should get to regard the satisfying this law\nas an invariable condition of the numbers presented. But we should never\nregard this purely formal law\u2014that is, a law about the particular\ncharacteristics of the numbers\u2014we should never regard this formal law as\nthe cause of the next set of numbers appearing after the first had gone.\n\nWhen, however, we talk about the conservation of energy we are apt to\nthink of it as more than a merely formal law, more than a statement\nabout numbers which has been found to hold true.\n\nYet it is no more. The law of the conservation of energy asserts that in\nany system in motion the sum of the squares of the velocities of the\nparticles at any one moment is equal to the sum of the squares of the\nvelocities of the particles at the next moment.\n\nThe conservation of energy is but a mode of reckoning motion, by which\nit is found to be constant in all changes of a system. The system must\nembrace all the particles concerned in the motion. It may be made as\nlarge as we like.\n\nThe principle of the conservation of energy as here stated is confined\nto the case of moving bodies. Sometimes the energy is said to disappear\nfrom the form of motion and become potential energy. That case will be\ntreated under the fourth consideration of level, but it introduces no\nalteration in what has been said.\n\nAs to the practical truth of the law of conservation of energy there can\nbe no doubt; nor as to the value of the results obtained from tracing\nits validity in obscure actions. But there is nothing final about it. It\nis a numerical statement of extreme value, and it introduces a mode of\nreckoning by which motion can be looked upon as indestructible as matter\nis.\n\nThere is a possible objection to the law of conservation of energy.\n\nIt is no less a law in nature that in every one of a series of changes\nsome of the energy passes off into the form of heat. Now heat is\nreckoned as a mode of energy. And there is in science a method of\ncalculating how much energy any given quantity of heat is the equivalent\nof. And this equivalence is calculated on the supposition that no energy\nis lost. When heat is produced and motion passes away, the proportion\nbetween the motion that disappears and the heat that appears is\nrepresented by a number calculated on the assumption that no energy is\nlost. Thus whenever any quantity of energy takes the form of heat, the\nquantity of heat which is produced is exactly given by the calculation.\nBut the reverse process is not possible. It is not possible to turn back\nall the energy in the form of heat into the form of motion. Consequently\nit cannot be proved that the energy in the form of heat would, if all\nturned into motion, produce as much motion as that from which it was\nproduced. There may be an absolute loss of energy\u2014only a very small one.\nThe law of the conservation of energy may be the expression that this\nloss is a minimum.\n\nThis objection is not essential to the line of argument pursued above\nwith regard to the conservation of energy. It forms no necessary part of\nthe line of thought we are pursuing. It merely tends to show that the\nlaw of the conservation of energy is no axiom which we cannot suppose\nnot true. The real conclusion to which this part of our line of thought\ntends is that the conservation of energy is a purely formal law.\n\n\n                               CHAPTER V.\n\nThe most apparently simple movements are those which we see taking place\non the surface of the earth, connected with the agency which we call\ngravitation. We see the rivers flowing from a higher to a lower level,\nrocks when loosened from a mountain side rolling down, rain falling, and\nmany minor changes of this sort.\n\nBut there are many actions besides these. For instance, suppose before\nus a spring coiled up. When it unwinds it \u201cexerts force,\u201d it transmits\nmovement. In its first state it is like a stone at the top of a\nmountain. In its second state it is like a stone which has fallen to the\nbottom of the mountain. It had a power of movement and of communicating\nmovement, now it has lost that power.\n\nAgain, the powder in a gun when it explodes expands and imparts movement\nto the shot. When the gun has been fired off the powder enters a\ndifferent state. Before, the chemical affinities of its constituents\nwere in a state of tension, now that it is fired off, they have formed\nfresh combinations. The power of transmitting movement has been lost by\nthat which was the powder. It is like a portion of water at the top of a\nfall of water. If it remains at the top it has at any time the power of\nproducing a shock, and of effecting, say, the movement of a water-wheel\nunder it. But if it falls it has exerted and lost that power.\n\nThe difference of level associated with gravity is familiar to us. But\nwe have no right, other than our own familiarity with it, to look on\ngravity as less in need of explanation than any other phenomenon of the\nexternal world. Newton did not suppose that there was any force inherent\nin matter which attracted other matter inversely as the square of the\ndistance. He showed that a great many astronomical facts were capable of\nbeing explained and calculated on this hypothesis. He left the\nexplanation of how it is that matter gravitates unsolved, and it remains\nunsolved to the present day.\n\nBut gravitation affords us a useful term\u2014\u201cLevel.\u201d\n\nLet us agree to call the following on a high level\u2014a stone at the top of\na precipice, a wound-up spring, oxygen and hydrogen mixed in the\nproportion to form water. Let us call the following at a low level\u2014the\nstone at the foot of the precipice, a spring straightened so far as it\ntends to straighten, oxygen and hydrogen united in the form of water.\n\nIn passing from their first state to their last all these have\nmanifested a power of movement and of communicating movement. They have\nnow relatively to their former state lost that power.\n\nDifference of level in this general sense is the most universal\ndistinction of matter.\n\nNo motion takes place unless matter passes from a higher to a lower\nlevel.\n\nThe universal cause of motion is that which produces this difference of\n\u201clevel\u201d in the general sense.\n\nIf there were no difference of level the state of things in nature would\nbe as if one spring in order to unwind had to wind up an exactly equal\nspring of the same amount; as if a stone falling from a height had to\nraise an exactly equal stone to the same height from which it fell.\nUnder such conditions of things no motion would begin. In such a state\nof things all nature would be like the inhabitants of the valley when\nthe king bore no pain, for no course would be preferable to any other\ncourse.\n\nWhat is the cause of the \u201cDifference of Level?\u201d Whenever matter passes\nfrom a higher to a lower level some of the energy which is given out\npasses away in the form of heat. This passing away of some of the energy\ninto the form of heat is an invariable accompaniment of the transition\nfrom a higher to a lower level. Is it the cause of the difference of\nlevel?\n\nIn the valley the king by bearing some pain made action worth while. Is\nthere any indication in nature of the production of a lower level which\nmakes the course of things run on?\n\nIt is certain that energy in every action passes off into the form of\nheat, and unless it is through the power of the finer particles of\nmatter to absorb the energy, it is difficult to see how any action can\ntake place.\n\nAs with the other lines of thought, this line also terminates with a\npossibility. Nothing has been proved, but a place has been provided.\n\nIn the first part of this paper a possible mode of action was exhibited\nin the imaginary relations of a world subject to certain laws of\npleasure and pain.\n\nIn the second part it has been shown that something is wanting in our\nconception of the natural processes. There is room for a central idea.\nNo scientific doctrines properly understood would clash with one\nproperly located.\n\nCan the mode of action exhibited in terms of sensation in the fictitious\nworld be applied to the case of the world of force and matter?\n\nBefore passing on, however, it is worth while to examine a little more\nclosely into what is meant by the expression so often used: \u201cPassing off\ninto the form of heat.\u201d\n\nThe modes in which energy passes off into the form of heat are in\ngeneral those modes by which movement is brought to a standstill such as\nfriction. And we are apt to think motion the primary fact, the cessation\nof motion a secondary and disagreeable fact. But both are equally\nexistent phenomena, and the convenience to ourselves is not to mislead\nus as to their relative importance.\n\nBut what is this passing off of energy into the form of heat? The phrase\nis unsatisfactory, for we are told by science almost in the same breath\nthat heat is the motion, the mechanical motion, of the particles of\nmatter. So the statement resolves itself into this. Only when some of\nthe motion passes off into the form of motion of the smaller particles\nof matter does motion take place in larger masses.\n\nAs a corollary it follows that at some date, however distant, all the\nmotion of masses will have passed away into the form of motion of\nsmaller masses.\n\nIt may be urged that when the larger masses move, the smaller particles\nalso move. This is true; but motion in this sense is used to denote\nchange of position amongst the smaller particles with regard to one\nanother. The particles in a flying cannon-ball are relatively still with\nregard to one another as far as the motion of the cannon-ball as a whole\nis concerned.\n\nWe thus arrive at the following principle: The condition of the motion\nof masses taking place is that some of the motion passes off into the\nmotion of the smaller particles.\n\nBut if the motion of the smaller particles is just the same as that of\nthe larger portions, we are obviously not at the end. The very same\nprinciple just applied must be applied again.\n\nThese motions of the small particles of matter cannot take place unless\nsome of their movement is transmitted and passed on, and transformed\ninto the motion of still finer particles of matter.\n\nBut here obviously we are brought to the beginning of an infinite\nseries. An infinite series passing from finer matter to still finer\nmatter, and so on endlessly.\n\nThe assumption by which we are led to this endless series of\ntransmissions must be clearly apprehended. We take the law\u2014that the\nmotion of masses only takes place when some of the motion passes off\ninto the motion of the finer particles of matter, and we assume that it\nholds always.\n\nIn a lever there is a fixed point, the fulcrum, which supports it, and\nthe power raises the weight; but the weight may be fixed, and then the\nfulcrum can be lifted by the power. So we obtained this law from the\nconsideration of material relations; and now we suppose this law to be\nthe fixed point, and shift our notions of material relations.\n\nThus we are landed on an endless series. Before proceeding, however, to\ninquire what the significance of this endless series may be, let us\nassume an end to it. Let us assume that we come at last to a final\ntransmission. Let us assume that the energy is transmitted to the\nultimate particles of matter.\n\nOr, if we have gone beyond matter, let us suppose an ultimate medium\nwhich by its modifications builds up matter, and which is the last and\nultimate substance.\n\nLet us suppose this ultimate medium absolutely to receive some of the\nenergy. Let it absolutely receive and absorb some of the energy, and\nthereby give rise to the difference of level, to give the ultimate\npermission which sets all things going.\n\nWhat are the properties of this medium? We obtain an indication of what\nthey are when we examine the properties of the finer kinds of matter.\nCompared with the motions of masses, motions which affect the smaller\nparticles of bodies are infinitely quick. Light and electricity are\nactions affecting the smaller particles of bodies, and by them distances\nare speedily traversed, which relatively to moving masses are very\ngreat.\n\nNow in point of speed of transmission the properties of this ultimate\nmedium must be infinitely beyond those of luminiferous ether.\n\nTo this ultimate medium all movements at any distance from each other\nmust be almost equally present at every part. At whatever distance from\none another two affections of this ultimate medium be supposed to take\nplace, the effect of the one will travel to the place of action of the\nother instantaneously.\n\nSuch a medium is a kind of visible symbol of the universe, being one\nsystem in which all motions should be co-determined.\n\nTo make this clear, suppose a transformation of energy was produced in\none part of space of an absorption of energy on the part of this\nultimate medium, this transformation of energy would be produced by a\nmedium in instantaneous contact with every other part of space, and the\ntransformation of energy thus originated would harmonize with, and have\nreference to, the transformations of energy in every other part of\nspace.\n\nThere are two infinities\u2014the infinite of space extending out each way,\nthe infinite of the smaller and smaller divisions of matter. The\nultimate medium we have supposed partakes of both infinities. It is\ninfinite in extent, and infinitely fine in its particles.\n\nNow this medium by absorbing energy sets movements going. And that\nmovements do not neutralize one another\u2014_i.e._, that movements in\nopposite directions do not mutually destroy one another\u2014has this result,\nthat a given amount of this absorption produces the greatest possible\namount of motion. If motion came to a rest in any other way, more of\nthis absorption by the ultimate medium would be needed. Hence, by a\ngiven amount of absorption in the ultimate medium the greatest possible\namount of motion is produced. That is, the absorption of motion into the\nultimate medium is a minimum, and the law of the conservation of energy\nis the expression of this being a minimum.\n\nBut here again a further remark is called for. We start by assuming\nenergy to be an absolute existence. But why not assume this action on\nthe part of the ultimate medium to be the real action, and consider the\nphenomena of motion and energy as the mode of its action.\n\nWhat this action of the ultimate medium may be needs examination. All\nthat we can say at present is that relatively to that which we call\nenergy, the action of this medium is that of being acted on.\n\n\n                              CHAPTER VI.\n\nIn the preceding, however, it must be remembered that this conception of\nan ultimate medium was merely a supposition to enable us to see and\nroughly map out the relations of the things we are investigating. Where\nwe were really landed was in an infinite series\u2014we were brought\nlogically to the conception of an infinite series of media, one behind\nthe other.\n\nWhat does an infinite series indicate?\n\nLet us turn to a region of thought where infinite series are familiar\nobjects, and we can learn about them.\n\nIn algebra infinite series are common. Thus take series 1 - _x_\u00b2/2 +\n_x_\u2074/4 and so on for ever. This is the attempt in algebra to represent a\ntrigonometrical idea. In trigonometry it is expressed as cos. _x_. But\nin algebra it needs this infinite series.\n\nIn algebra infinite series occur when the object which it is wanted to\nrepresent in algebraical terms cannot be grasped by algebra. When there\nis no single term or set of them in algebra which will serve, the object\nis represented by means of an infinite series. Thus we may say that in\nany calculus, when the object to be treated of cannot be expressed in\nthe terms of the calculus, it is represented by means of an infinite\nseries.\n\nNow, dealing with material considerations, going on in the calculus of\nmatter, we have come to an infinite series. This indicates that we have\ngone as far as the material calculus will carry us. We have now to bring\nin an idea from a different quarter if we will simplify our expression.\n\nIt may well be that within our experience there is nothing which will\nserve. But let us suppose that that which in material terms we represent\nas an infinite series is a will\u2014a will in contact with all existence, as\nshown by the properties it had when we conceived it as an ultimate\nmedium. For, regarding it as an ultimate substance, we found that it\nwould be affected by pulsations infinitely quicker than light and\nelectricity; considered as a substance, it was such that distance to it\ntended to be annihilated. Hence as a will we must say of it that to it\nall that is is present\u2014a will which by a fiat that to our notions is\nbeing acted on rather than acting, accepting pain rather than taking\npleasure, sets the course of the world in motion, which holds all in one\nsystem, which creates all activities. For although we apprehend this\nwill relatively to the appearances which we suppose we know, mechanical\nenergy and feeling, still we see that both are caused by it, and that\nthe sum of both is nothing, save for that which this will is in them.\n\nIs there any other way of apprehending this will than through the\nexternal world?\n\nWe have two apprehensions of nature\u2014one of external things, the other of\nour own wills.\n\nDoes this will not exist in those who are true personalities, and not\nmere pleasure-led creatures?\u2014have they not some of this power, the power\nof accepting, suffering, of determining absolutely what shall be?\u2014a\ncreative power which, given to each who possesses it, makes him a true\npersonality, distinct, and not to be merged in any other\u2014a power which\ndetermines the chain of mechanical actions, of material sequences\u2014which\ncreates it in the very same way in which it seems to be coming to an\nend\u2014by that which, represented in material terms, is the absorption of\nenergy into an ultimate medium; which, represented in terms of\nsensation, is suffering; but which in itself is absolute being, though\nonly to be known by us as a negation of negations.\n\n\n                              CHAPTER VII.\n\nIn conclusion let us remark that we have supposed two different\nworlds\u2014one of sensation in the first part, one of motion in the second\npart. And these have been treated as distinct from one another. And\nespecially in the first part, by this avoidance of questions of\nmovement, an appearance of artificiality was produced, and occasionally\ninconsistencies, for sometimes sensations were treated as independent of\nactions, sometimes as connected with them. But it remains to be decided\nif these inconsistencies are in themselves permanent, or whether, when\nwe remove the artificial separation, and let the world of sensation and\nthe world of motion coalesce, the inconsistencies will not disappear,\nthereby showing that their origin was merely in the treatment, not in\nthe fact; that they came from the particular plan adopted of writing\nabout the subject and are not inherent in the arguments themselves.\n\nThe king in the first part was supposed to have all the material\nproblems of existence solved. There was a complete mechanism of nature.\nHe took up the problem of the sentient life. But this problem can only\nartificially be separated from that of the material world. The gap\nbetween our sensations and matter can never be bridged, because they are\nreally identical.\n\nLet us then allow this separation to fall aside. Let us suppose the king\nto have all the reins of power in his own hands. Let us moreover suppose\nthat he imparts his rays to the inhabitants so that they have each a\nportion of his power. And let us suppose that the inhabitants have\narrived at a state of knowledge about their external world corresponding\nto that which we have about the world which we know.\n\nLet us listen to a conversation between two of them.\n\n_A._ The energy of the whole state of things is running down.\n\n_B._ How do you prove that?\n\n_A._ Whenever any motion of masses takes place a certain portion of the\nenergy passes irrecoverably into the form of heat, and it is not\npossible to make so large a movement with those same masses as before,\ndo all that is possible to obtain the energy back again from the heat\ninto which it has passed.\n\n_B._ Well, what about the heat? Energy in the form of the motions of the\nmasses passes off into the energy of heat. But what is heat?\n\n_A._ It is the motion of the finer particles of matter.\n\n_B._ Well, I would put forward this proposal. We have by observation got\nhold of a certain principle that where any movement takes place some of\nthe energy goes in working on the finer particles of matter. Let us now\ntake this principle as a universal one of motion, and apply it to the\nmotions of the finer particles of matter themselves, which are simply\nmovements of the same kind as the movements of the larger ones. This\nprinciple would show that these movements are only possible inasmuch as\nthey hand over a portion of their energy to work on still finer matter.\n\n_A._ Then you would have to go on to still finer matter.\n\n_B._ Yes, and so on and on; but to fix our thoughts, suppose there is an\nultimate fine matter which is the last worked on. Now I say that we may\neither suppose that this is being gradually worked on and all the energy\nis dissipating, or else we may put it in this way. When we regard so\nmuch energy we are apt to think that it is the cause of the next\nmanifestation in which it shows itself. But this is really an\nassumption. Energy is a purely formal conception, and all that we do is\nto trace in the actions that go on a certain formal correspondence,\nwhich we express by saying that the energy is constant.\n\n_A._ But I feel my own energy.\n\n_B._ Allow me to put your feeling to one side. If we take then the\nconservation of energy to be merely a formal principle, may we not look\nfor the cause of the movements in the invariable accompaniment of them,\nnamely, in the fact that a certain portion of the energy is expended\nirrevocably on the finer portions of matter. If now we take this\nultimate medium which suffers the expenditure of energy on it, may we\nnot look on it as the cause, and the setter in action of all the\nmovements that there are. By its submitting to be acted on in the way in\nwhich it does submit, it determines all the actions that go on. For what\nis all else than a great vibration, a swinging to and fro. When we count\nit as energy, we by reckoning it in a particular manner make it seem to\nbe indestructible, but that the energy should be indestructible would be\na consequence from the supposition which we could very well make, that\nto produce a given series of effects the submitting to be worked on of\nthis ultimate medium must be a minimum. If it were a minimum no\nmovements could neutralize one another when once set going, for if they\ndid there would be a waste of the submission of this ultimate medium.\n\n_A._ But what do you suppose this ultimate medium would be?\n\n_B._ That I cannot tell, but we seem to have indications. For the more\nfine the matter which we investigate, the more its actions seem to\nannihilate distance: light and electricity produce their effects with\nfar greater rapidity than do the movements of masses. We might suppose\nthat to this ultimate matter all parts were present in their effects, so\nthat anything emanating from the ultimate matter would have the\nappearance of a system comprehending everything.\n\n_A._ But you have not got any evidence of an ultimate matter.\n\n_B._ No, all that we can think of is an endless series of finer and\nfiner matter. But is that not an indication rather, not that the\ndirection of our thoughts is false, but that there are other\ncharacteristics of this ultimate, so that when looked at under the form\nof matter it can only be expressed as an infinite series.\n\nLet us omit the considerations brought forward in the preceding\nconversation and examine more closely the philosophy of the inhabitants\nof the valley in so far as it corresponds with ours.\n\nThey laid great stress on a notion of _vis viva_, or what we should term\nenergy, but said it was gradually passing away from the form of\nmovements of large bodies to that of movements of small bodies. So that\nin the course of time the whole valley would consist of nothing but an\nevenly extended mass of matter moving only in its small particles\u2014and\nthis motion of the small particles they called heat. Now they had very\nclearly arrived at the conviction that with every mechanical motion\nthere was a certain transference of _vis viva_ to the smaller particles\nof matter, so that it did not appear again as mechanical motion. But\nthey did not accept this as a principle to work by. They did not\nconsider that the motions of the smaller particles of matter were just\nthe same as those of the larger masses. They did not see that if a\ncondition held universally for the movements of the visible world, it\nmust also hold for the smaller motions which they experienced as heat.\nSo the conclusion which they should logically have come to that there\nwas a transference of _vis viva_ on and on was not held. But the step\nwas a very little one for them to take from regarding an invariable\ncondition as always there to regarding it as a cause. For the causes\nthey assigned were all purely formal relations, and only got to assume\nan appearance of effective causes by familiarity with them, and a\nthrowing over them of that feeling of effectiveness which they derived\nfrom the contact which they had with the king.\n\nThey might have reasoned. This universal condition of anything happening\nmust be the cause. Energy goes from a higher to a lower level. That\nwhich causes the difference of level is the cause, and the cause of the\ndifference of level must be that which invariably accompanies such a\ntransference of energy from a higher to a lower level. Now this\ninvariable condition is the passing of a portion of the energy into the\nform of motions of the finer parts of matter. Hence there is an\napparently endless series. But to realize the matter, suppose an\nultimate medium, suppose there is a kind of matter of infinite fineness\ndistributed everywhere which let itself be worked on, and so determines\ndifferences and wakens the sleeping world. What are the qualities of\nthis fine matter? We see them in the properties of the finer kind of\nmatter which we know, such as light, electricity. The property of the\nfiner kind of matter is in general that it tends to bring distant places\ntogether, so that a change in one part is rapidly communicated to every\nother part. If they followed this indication they would have supposed\nthat the ultimate fine matter was of such a nature as to make all parts\nof the valley as one, so that there was no distance, and any\ndetermination of a difference of level on the part of this ultimate\nmatter would have reference to all the conditions everywhere. It would\nbe in immediate contact with every part, so that anything springing\ntherefrom would present the appearance of a system having regard to the\nwhole. Now if they had imagined such an ultimate medium doing that which\nto them would seem bearing rather than exerting force, suffering rather\nthan acting, they would not have been far from a true conception of the\nking who directed them all. For he himself by reason of his very\nomnipresence could not be seen by them. There was nothing for them to\ndistinguish him by. But they could have discovered somewhat of the means\nby which he acted on them, which can only be described from the\nappearances they present to the creatures whom the king calls into life.\n\nBut of truth they would have had another and perhaps a truer\napprehension of the king in a different way. For when he acted on them\nso that they took one course rather than another, it was his action in\nthemselves that they felt. If they were mere pleasure-led creatures then\nthey were shaped outwardly, but if in their inner souls he acted and\nthrough them suffered, then they were true personalities conscious of\nbeing true selves, the oneness of all of them lying in the king, but\neach spontaneous in himself and absolute will, not to be merged in any\nother.\n\nThus they had two modes of access to the king, one through their own\nselves where he had made them exist, one through the outer world. And in\nthe outer world it was but a direction in which they could look. They\ncould never behold the personality of the king, but only an infinite\nseries of different kinds of matter, one supporting the other as it were\nand underlying it, but doing more also than this, for in proportion as\nthey considered the kinds of matter that lay deeper they found that\ndistant became near, absent, present, that time gave no longer such\ndistinctions, but from the phenomenal side they seemed by a gradual\ndiminution of the limitations of experience to arrive at an external\npresentation of that absolute which exists in the fulness of things,\nwhich they knew more immediately in themselves when they truly were.\n\n\n                                THE END.\n\n\n\n\n                            _INTRODUCTION._\n\n\nIn the next two or three of these papers certain questions connected\nwith the subject of a space higher than our own will be treated. It is\nwell, therefore, first to recede and to form definite conceptions about\na world of plane space, about a world in which the beings can only move\nin two independent directions. Then, proceeding thence to our own world,\nwe may gain the means of passing on to a higher world. And I should have\nwished to be able to refer the reader altogether to that ingenious work,\n\u201cFlatland.\u201d But on turning over its pages again, I find that the author\nhas used his rare talent for a purpose foreign to the intent of our\nwork. For evidently the physical conditions of life on the plane have\nnot been his main object. He has used them as a setting wherein to place\nhis satire and his lessons. But we wish, in the first place, to know the\nphysical facts.\n\nWith this aim it is necessary to form a clear idea of what matter would\nbe in a world of two dimensions, and the following illustration is a\nconvenient one.\n\nPlace on the smooth surface of a table a half-crown piece, and suppose\nit to slide on the table perfectly freely. Imagine it to exercise an\nattractive force along the surface of the table in all directions round\nitself. By it and near it place a sixpence, and let the sixpence also\nslide freely on the table. It will, however, not be so free to move\nequally in all directions as the half-crown was, for it will be\nattracted by the half-crown. It will slip over the surface of the table\nunder the influence of this supposed force, and will come into contact\nwith the half-crown. Now if we suppose that both the half-crown and the\nsixpence are very thin, that they are both of them only the thickness of\nthe ultimate particles of matter, then we shall have a representation of\nwhat material bodies will be in a plane world.\n\nWe must suppose that the particles cannot lift themselves or be lifted\nup from the plane so as to lie upon each other. Under no circumstances\ncan they quit the surface of the plane.\n\nMoreover, at no point must the particles adhere to the plane, nor must\nthere be any friction impeding their movements over it. The only purpose\nwhich the support serves is to keep them on the same level surface and\nto convey influences from one particle to another. The gravity which we\nknow, and which acts at right angles to the table on which the coins\nrest, will not have any effect on the particles in their motions on the\nplane, but will simply keep them to the plane. Any force of attraction\nwhich concerns their motions proceeds from one particle to another.\nThus, conceive the half-crown to be a very large disk of matter, and the\nsixpence to be a sentient being. This being would feel a force of\nattraction towards the centre of the half-crown, and this force of\nattraction would keep him to the rim of the half-crown. If he weighed\nanything it would be by balancing it with his weight against the force\nwhich tended to pull it to the centre of the half-crown. He would not\nfeel the gravity which keeps him against the surface of the table; he\nwould not know that there was a hard, smooth surface on which he rested.\nHe would always have been in contact with it, and so he could not tell\nwhat it would be like to be free from it. He would have no contrast\nwhereby to apprehend its effect on him. Moreover, he would only know of\nmovements in directions along the plane. He would not conceive that such\na thing was possible as movement in another direction than to and fro,\nhither and thither on the plane. It is difficult to suppose that a being\nwould be supported on one side by a plane, and not be in contact with\nanything on the other side, even atmosphere. Yet if we suppose a being\nof real matter free to move on the plane, this is what must be\nconceived. If the sixpence is conceived as such a being, it must receive\nits impressions through its rim. The rim represents its skin.\n\nAnd if it be supposed to be surrounded by air for its respiration, this\nair must not be able, any more than the particles of solid matter, to\nrise away from the plane. The plane being must be conceived to have a\ndifferent air to that which we know. The particles of its air, however\nfree to move amongst themselves, must not have the power of moving away\nfrom the surface of the plane, as if so they would be able to pass to\nthe interior of the body without passing through the skin. Any passage\nleading to the interior of the body would have to terminate in an\nopening in the rim, otherwise it would be completely shut up from the\nexterior.\n\nNow it is obvious that if the table is struck so that it quivers, this\nmovement will be communicated to the coins lying on it. Either the coins\nas a whole will move, or their particles will be disturbed.\n\nAgain, if we suppose there to be some particles loosely cohering\ntogether, lying on a smooth sheet of iron, it is evident that the\nquivering and jostling of the iron, if it is struck, would have an\neffect on the particles, and may cause the breaking up of the thin\nmasses in which the particles cohere. Thus, if the material of which the\nsheet is composed be very dense and rigid, compared to the substances\nlying on it, they may undergo many alterations, being broken up and\ncoming together again while the supporting matter which bears them all\nup simply moves and vibrates.\n\n  [Illustration: Diagram I.]\n\nIt is evident that just as the particles are affected by the vibration\nand shaking of the sheet of metal on which we suppose them, so they\nmight in turn possibly affect the sheet of metal and cause vibrations\nand shakings in it. These shakings and vibrations would go forth from a\nparticle which excited them in every direction along the sheet. They\nwould not pass out into the air, except secondarily and in a very minute\ndegree. The shake would be transmitted in the sheet. And the effect on\nneighbouring particles would be great, on more distant particles it\nwould be less, and on those at a great distance barely perceptible.\n\nThe following is a good plan for obtaining in a definite way the feeling\nof what existence in a plane would be like; it enables us to realize the\nconditions in such a way as to lay the basis for subsequent thought.\n\nLet the reader take a sheet of note-paper and hold it before himself\nedgewise, so that he sees it with one eye as a single line. And let him\nhold it so that this line runs downwards from his eyebrows to his mouth,\nas shown in Diagram I. Now on this sheet of paper, on one side of it,\nlet a straight line be drawn running across it, away from the observer.\nSuppose all below this line to be a thin layer of particles which,\nkeeping compactly together, form a solid sheet of particles, every one\nof which touches the paper. This would be the solid earth to a being in\nthe plane world.\n\nLet the surface of the paper above this be covered by a layer of\nparticles which move freely amongst each other, but which do not rise\nfrom the surface of the paper. These particles form the air of such a\nworld.\n\nOn the surface of the earth draw a line standing upright. Let this line\nrepresent a man. Another line will represent a wall which the man could\nnot pass except by getting over it.\n\nIt will be found that the objects on the paper are felt to be subject to\nthe action of gravity. The question will occur, Why will not this thin\nlayer of particles slip off the paper?\n\nNow, the sense of gravity must not be got rid of, but it must be\nconnected with the matter in the sheet of paper.\n\nSuppose, then, that the sheet were to grow bigger and bigger till it\nfilled out reaching through the whole world and cutting the globe in\ntwo. Then let all the earth be removed except a thin layer on one side\nof this enlarged sheet of paper. This thin layer will be the only\nportion of matter left. And such a thin layer will represent a plane\nworld. The force of gravity must be conceived as remaining, but as\ncoming from a large and thin disk.\n\nNow to keep this thin layer on the paper it would be necessary to have\nsome force acting sideways, so as to keep the particles to the paper.\n\nAnd the paper itself may be conceived to exercise such a force: it is\nmany particles thick, while the thin layer of matter is only one\nparticle thick, and thus it will keep the layer of matter, which covers\none side of it, in its place by virtue of its own attraction.\n\nWe suppose that the paper exerts an attractive force which keeps the\nthin layer of matter to it. This attractive force is not felt by the\nsentient beings on the paper, nor does it influence the movements of the\nparticles of matter amongst themselves. We also suppose another\nattractive force proceeding from particle to particle of the matter on\nthe plane. This would be felt by the beings and produce movements of\nmatter.\n\nThus the conception of a plane world necessarily involves that of\nsomething on which it is.\n\n\n\n\n                             A Plane World.\n\n\nWhere the sun\u2019s rays grazing the earth in January pass off and merge\ninto darkness lies a strange world.\n\n\u2019Tis a vast bubble blown in a substance something like glass, but harder\nfar and untransparent.\n\nAnd just as a bubble blown by us consists of a distended film, so this\nbubble, vast beyond comparison, consists of a film distended and\ncoherent.\n\nOn its surface in the course of ages has fallen a thin layer of space\ndust, and so smooth is this surface that the dust slips over it to and\nfro and forms densities and clusters as its own attractions and\nmovements determine.\n\nThe dust is kept on the polished surface by the attraction of the vast\nfilm; but, except for that, it moves on it freely in every direction.\n\nAnd here and there are condensations wherein have fallen together\nnumbers of these floating masses, and where the dust condensing for ages\nhas formed vast disks.\n\nAnd these disks are glowing hot\u2014yet no light comes from them into our\nuniverse.\n\nFor this world lies beyond the \u00e6ther\u2014far beyond. And however hot or\nglowing the masses are, if there is no medium to transmit the vibrations\nof heat the influence cannot travel.\n\nThus the only directions in which the heat can travel are on the film.\nFrom each of these glowing disks the luminous influence streams forth\ncarried by the vibrations of the film which supports everything. For the\nheat and intense agitation of these glowing disks shakes and disturbs\nthe bubble, and just as a thin soap bubble quivers and shakes, so this\nfilm quivers and shakes. And so elastic is it, and so rigid, that it\ncarries the light and heat to all surrounding regions. Yet so vast is\nthe bubble, so tremendous in its dimensions, that the agitation from\nthese glowing disks travels almost in straight lines, till, spreading\nout on every side, it merges into darkness\u2014like the ripples in the\ncentre of a vast calm lake gradually become indistinguishable.\n\nAnd round these central orbs of fire\u2014for orbs of fire they are, though\nthey only transmit their fire along the film of the bubble\u2014round these\norbs pass in due order and succession other disks, which, cold or warm,\nhave not that energy of light and heat which the central orbs possess.\n\nThese disks, though large, are so immeasurably small compared with the\nvast surface of the all-supporting bubble, that their movements seem to\nlie on a plane flat surface; the curving of the film on which they rest\nis so slight compared to their magnitude, that they sail round and round\ntheir central fires as on a perfect level surface.\n\nAnd one of these orbs is fitted by nature to be the habitation and home\nof living beings. For it is neither so hot as it was for long ages after\nit had condensed from the film of dust wherefrom all orbs are made, nor\nhas it so cooled down as to render life unsupportable.\n\nAnd, moreover, it is full of vast crevices and channels, for in many\nplaces the interior in cooling after the rim had set from its molten\ncondition has left long caverns and passages, not only in one layer, but\nin many.\n\nAnd on the rim and in these passages and caverns live the inhabitants of\nwhom I speak.\n\nThey do not rise from the surface of the film, but as all matter lies on\nthe smooth surface but one particle deep, so their bodies formed out of\nmatter lie, as we should say, on this smooth surface.\n\nYet of this they know nothing. They say that they stand and walk.\n\nFor this orb has an attractive force.\n\n  [Illustration: Diagram II.\u2014\u201cTwo beings walking round.\u201d]\n\nBy that very same impulse of coming together whereby it gathered its\nparticles out of the dust on the bubble, by that very same force it\ndraws towards its centre all that is near it or on it. Thus \u201cup\u201d is to\nthese inhabitants a movement from the centre of the disk on the rim of\nwhich they live and away from it. \u201cDown\u201d is a movement from the rim\ntowards the centre. The thin layer which forms the mass of the disk is\ntheir solid matter. They are not able even in thought to rise away from\nthe surface of the bubble, and look from space upon their mode of\nexistence. They ever pass to and fro upon a line, upon a rim; and no two\ncan walk except after one another. If you look at the rude picture you\nwill see that the two beings represented by two triangles cannot pass\none another if they are unable to lift themselves up from lying on the\nsurface of the paper. The surface of the paper represents the surface of\nthe bubble, and sliding freely on it, but unable to lift up from it, are\ntenuous shapes that are the inhabitants, and that thin layer of\nparticles that is to them solid matter.\n\n  [Illustration: Diagram III.\u2014A section of the film of the bubble\n  showing a disk BD lying on it, and a creature AB on the rim of the\n  disk. CE is a section of the film, BD is a section of the disk, AB is\n  a section of the creature. The thickness is enormously magnified and\n  also the height AB of the creature compared with the diameter BD of\n  the disk. The attraction which AB feels keeps him to BD; both AB and\n  BD, the being and the disk, slide freely on the film CE without\n  knowing of its existence.]\n\nNow were it not for the fact that the orb is reft into these chasms and\npassages, the only movement that these beings would have would be of\npassing round and round on the rim of their world.\n\nMany words that we have, to them could bear no meaning. Thus \u201cright and\nleft\u201d is to them unknown. For consider their faces bent in one direction\nalong the rim. In following this direction, they go forward, in\nretracting from it they go backward. If they go away from the centre\nthey go up, towards the centre is down. And by no means can they turn,\nraising themselves from the surface whereon they are. They do not even\nknow that they have two sides; their movements, thoughts, and\nimaginations are all confined to that surface on which they are. This\nthey call their space, their universe; nor does aught that lies beyond\nit, towards the interior of the bubble or away from it, directed\noutwards, come into their thoughts, even as an imaginary possibility of\nexistence.\n\nLife is extremely limited on such a world. To take a single instance, in\norder for two beings to pass each other, a complicated arrangement is\nnecessary, shown in Diagram IV.\n\nAt intervals along the rim recesses and chambers are constructed. Near\nthe openings of these chambers lay movable plates or rods. When two\nbeings wish to pass, one of them descends into the recess; the other one\npushes the rod so as to form a bridge over the opening, walks across it,\nand then removes the plate so that the one who has descended can get up\nand go on his way.\n\n  [Illustration: Diagram IV.\u2014Two beings passing.]\n\nIf by any chance, while a being is in the recess, the plate or rod which\nacts as a bridge gets fixed, he is in a dangerous predicament. For\nsuppose a being confined as shown. If he, suffering from want of air,\ncuts through the roof at AB, the whole part to the right of AB comes\ntumbling down. For its only support is severed when AB is cut through.\nIt is impossible to make a hole which is not the whole width of matter\nas it lies on the surface. And with regard to this all constructions\nhave to be made. There cannot be two openings in a wall of a house,\nunless when the one is open the other is so fashioned as closing to act\nas a rigid support to the wall, which now depends for its upholding\nentirely on it.\n\n  [Illustration: Diagram V.\u2014A house.]\n\nThus, in the diagram, the house is held up entirely by the side opposite\nto the doorway EF, which is now open. The roof is supported by the side\nCD. If an opening AB be made in the wall CD before the doorway EF is\nclosed, the roof will fall in. So, in order to pass through the house,\nEF must be firmly shut up before AB is opened. The houses are always\nbuilt in the interior passages so as to leave the rim of the disk free\nfor locomotion.\n\nAnd there are many things to be said of the inhabitants on this disk\nwith respect to their social and political life. It is hardly necessary\nfor me to put down much about it here, for any one by using the method\nof the historian Buckle, and deducing the character of a people from\ntheir geographical influences and physical surroundings, could declare\nwhat the main features of their life and history must be.\n\nBut one or two remarks may be made here. First of all they are\ncharacterized by what I may venture to call a crude kind of polarity.\n\nIn dwellers in our world this polarity, which shows itself amongst other\nways in the distinction of sexes, is tempered and modified.\n\nIn every man there is something of a woman, and in every woman there are\nsome of the best qualities of a man.\n\nBut in the world of which we speak there is no physical possibility for\nsuch interfusion. In a linear existence there would be no consciousness\nof polarity. It makes its appearance first in the plane, and in a hard\nand unmitigated form.\n\nIt is impossible to do otherwise than caricature these beings when we\nwrite of them thus in brief. So let us accept the matter frankly, and,\nwithout scruple, look at them in the broadest possible manner.\n\nIf the reader will cut out the triangles in the corners of the two next\npages he will obtain four plane beings, two of which are men, two of\nwhich are women. The lines down which the cutting is to be made are\nmarked with a black line. Now having cut out two men, whom we will call\nHomo and Vir, draw a line on a piece of paper to represent the rim of\nthe world on which they stand, and, remembering that they cannot slide\nover each other, move them about. It must be remembered that the figures\ncannot leave the plane on which they are put. They must not be turned\nover. The only way in which they can pass each other is by one climbing\nover the other\u2019s head. They can go forwards or backwards. Much can be\nnoticed from an inspection of these figures. Of course it is only\nsymbolical in the rudest way, but in their whole life the facts which\ncan be noticed in these simple figures are built up and organized into\ncomplicated arrangements.\n\n  [Illustration: Diagram VI.]\n\n  [Illustration: Diagram VII.]\n\nIt is evident that the sharp point of one man is always running into\nanother man\u2019s sensitive or soft edge. Each man is in continual\napprehension of every other man: not only does each fear each, but their\nsensitive edges\u2014those on which they are receptive of all except the\nroughest impressions\u2014are turned away from each other.\n\nOn the sensitive edge is the face and all the means of expression of\nfeeling. The other edge is covered with a horny thickening of the skin,\nwhich at the sharp point becomes very dense and as hard as iron. It will\nbe evident, on moving the figures about that no two men could naturally\ncome face to face with each other.\n\nIn this land no such thing as friendship or familiar intercourse between\nman and man is possible. The very name of it is ridiculous to them. For\nthe only way in which one man can turn his sensitive edge to another man\nis if one of them will consent to stand on his head. Fathers hold their\nmale children in this way when little, but the first symptom of manhood\nis connected with a resentment against this treatment.\n\nIf now two women, Mulier and Femina, be looked at, the same relation\nwill be seen to hold good between them. By their nature they are\npredisposed, by accident, to injure one another, and their\nimpressionable sides are, by the very conditions of their being, turned\naway from each other.\n\nIf now, however, Homo and Mulier be placed together, a very different\nrelationship manifests itself. They cannot injure one another, and each\nis framed for the most delightful converse with the other. Nothing can\nbe more secure from the outside world than a pair of approximately the\nsame height; each protects the sensitive edge of each, and their\narmoured edges and means of offence are turned against all comers,\neither in one direction or the other. But, if the pair, through a mutual\nmisunderstanding, happen to be disadjusted, and, their feet on the rim,\nturn their sharpnesses against one another, they are absolutely exposed\nto the harms and arrows of the world.\n\nStill, even in this case they cannot wound one another\u2014a happy immunity.\n\nIn the annals of this race which I have by me I find a curious history,\nwhich, unintelligible for ages to them, admits by us of a simple\nexplanation.\n\nIt is said that two beings, the most ideally perfect Vir and Mulier,\nwere once living in a state of most perfect happiness, when, owing to\ncertain abstruse studies of the Mulier, she was suddenly, in all outward\nrespects, turned irremediably into a man. Vir recognized her as the same\ntrue Mulier. But she occupied the same position with regard to him which\nany other man would. It was only by standing on his head that he could,\nwith his sensitive edge, approach her sensitive edge. She refused to\nexplain how it was, or impart her secret to any one, but she had, she\nsaid, undergone a great peril. She manifested a strange knowledge of the\ninternal anatomy of the race, and most of their medical knowledge dates\nfrom her. But no persuasion would induce her to reveal her secret; all\nthe privacy of existence would be gone, she said, if she revealed it.\nShe was supposed to have acquired some magical knowledge.\n\nThis possession, however, did not make either of them happy, and one\nday, with fear, she said that she would either die or be restored to the\noutward semblance of her sex.\n\nShe disappeared\u2014absolutely; although she was surrounded by her friends,\nshe absolutely vanished. And had it not been that some days afterwards,\ncutting through the solid rock for the purposes of some excavations,\nthey accidentally came on a chasm, they would never have found her alive\nagain. For she was found in a cavity in the living rock, warm and\nbeautiful\u2014her old self again.\n\nHer secret died with her.\n\nFrom our point of view it is easy to see what had happened. If the\nfigure Mulier be taken up and turned over it will be easy to see that,\nthough still a woman, her configuration has become that of a man. To all\nintents and purposes she is a man. She is rendered incapable of that\nattitude which is the natural one between the men and women in this\nland, and the happy relationship between her and Vir is necessarily and\nentirely broken off. Move about as you will, keeping her figure turned\nthus on the plane, you will not be able to make her a fitting helpmate\nfor her unfortunate Vir. She must have discovered the secret of raising\nherself off the surface, and by some accident been turned over. Perhaps\nshe had used this new position to study anatomy\u2014for to an observer thus\nsituated the interior of every body would lie perfectly open\u2014and in\nprosecuting her studies had overbalanced herself.\n\nI have only mentioned this anecdote, however, for the sake of a curious\nobservation which was made at the time. It was found that when she was\nin this transformed condition she was absolutely without atmosphere. To\nexplain: ordinarily, apart from anything she said or did, there was a\nkind of influence proceeding from her which made her presence agreeable\nto Vir. When she was turned over she lost this. Now the explanation of\nthis is obvious. To these people light is the agitation of the surface\nof the bubble; transparent objects are those which do not hinder this\nagitation in its course. But most bodies and the physical frame of the\ninhabitants amongst them were not transparent, but stopped and reflected\nthese agitations of the film, thus sending off from their outer edge\nthose vibrations which excited sight in their fellows. But besides these\nvibrations of light there were finer ones still which were not damped or\ndeflected by the outer edge of the body, but came through the greater\npart of their frame as if it was transparent. In the interior, however,\nof their organizations there were certain regions which did arrest these\nsubtler vibrations, and which had (as the eye of light) the power of\nappreciating them. In connection with these regions there were certain\nstructures, extremely minute, which had the converse power of agitating\nthe film, and so sending forth through the periphery of the body these\nsame minute vibrations. These organs were not of any use, but they\nformed a sort of means of sympathetic communication between the\ninhabitants, acting in no very defined way, but certainly producing a\nsensation of a vague kind. Now when Mulier was turned in the way\ndescribed, the relation of her frame to the film of the bubble was\ndisarranged, and it was no wonder that this \u201catmosphere\u201d disappeared.\n\nIn many respects the inhabitants of this world are far more advanced\nthan we are, having a simpler problem\u2014how to deal with matter in one\nplane\u2014they have advanced more nearly to a complete knowledge of its\nproperties. Yet great as their knowledge is, their performance is small.\nIf you but reflect on one single fact, you will see how limited all\ntheir efforts must be. _They cannot fix the centre of a wheel, so that\nit rotates round an axis._ For consider a wheel\u2014a small disk lying on\ntheir plane. The centre on every part of it touches the surface of the\nbubble on which all things slide freely. To fix this point they would\nhave to drive down into the film\u2014a thing which they cannot do, and which\nthey are far from even imagining.\n\nIf they make an opening in the disk they can arrive at the centre of it.\nBut then the rod of matter which they put in will prevent the disk from\nrevolving.\n\n  [Illustration: Diagram VIII.\u2014The nearest approach to a wheel.]\n\nThe nearest approach to a wheel with a fixed centre which they can\nattain is shown in Diagram VIII., a portion of a circular disk which\noscillates about the smooth end of a rod built into the substance of the\ncut-away disk.\n\n  [Illustration: Diagram IX.\u2014A cart.]\n\nTheir carts are shown in the accompanying figure. They are simply rods\nplaced on rollers: as the rod is pulled along, the rollers turn, and the\nrod slides along\u2014just as a boat does on the rollers whereby sailors help\nthemselves in hauling it up the beach. As soon as these rollers roll\nfrom under the rod, as it goes on in its forward motion, they have to be\nsecured, and then lifted over the cart and put down in front. Thus there\nare to each cart a set of little disks or rollers, and, as the cart goes\non, these rollers have to be lifted over the cart from the back to the\nfront.\n\nThere is no means by which this can be made a continuous action. Each\nroller has to be waited for, lifted separately, and carried over\nseparately. And to put it down in front, the rope by which the cart is\ndragged along has to be unfastened and fastened up again.\n\nLooking at the Diagram IX. it will be seen that there is a hollow in the\nbody of the cart. On the part A B the driver sits. In the hollow from B\nto C is put the load. The load cannot then slip out over the ends of the\ncart. There is nothing in the cart to prevent it from falling out\nsideways.\n\nBut the contents, as the whole body of the cart, are kept to the smooth\nsurface of the bubble, and are thus supported by it on the side remote\nfrom the reader\u2019s eye, and also are kept from rising away from this\nsurface by the force of attraction exerted by the film.\n\nThus the surface of the bubble and its attractive force supply the other\ntwo sides of the cart.\n\nBut of these two sides, the beings are ignorant, and it seems to them\nperfectly natural that loads of any kind, even of fluids, should be kept\nsecurely in a cart with two ends.\n\n  [Illustration: Diagram X.\u2014How a rope is fixed to a cart.]\n\nThe method by which the rope is fastened to the cart is this: C is the\nbody of the cart; R is the rope ending in a wooden step B; A is an\noblong piece of wood. When the rope has to be taken out, A is lifted out\nby its handle, B is slipped back and taken out of the recess in C, and\nthen the rope is free from the cart. And in a similar way it is secured\nagain.\n\nOne very ordinary way of driving machinery with us is by shafting. A\nlong rod is driven round and carries wheels at different places along\nits length. Now with these inhabitants it was impossible to do this,\nbecause the twisting motion round a rod could not be imparted without\ngoing out of the thin layer in which they were. Their methods of\ntransmitting motion were by long rods, by a succession of short rods, by\npendulums attached to one another, or finally by wheels which drove one\nanother, but which were held by smooth sockets fitting round the rim far\nenough to steady them, but not so far as to hinder them from touching\neach other.\n\nAs to their science, the best plan is to give a short account of its\nrise.\n\nThey discovered that they were on a disk rotating round an inner centre,\nand also proceeding in a path round the source of light and heat.\n\nThey found that they were held in their path by a force of attraction.\nBut this attractive force was not with them as it is with us. With us,\nsince the effect which any particle has on the surrounding particles\nspreads out in our space if the distance is doubled from a centre of\nattraction, the force it exercises becomes one-quarter of what it was\nwhen at the less distance.\n\nWith them, however, when the distance doubled, the force of attraction\nbecame only one-half of what it was at the less distance. For the light,\nor attraction, or force of any kind emanating from a particle, only\nspreads along the film, and does not pass out into the space above or\nbeneath. If they had been on a thick globe instead of a bubble, the laws\nof attraction would have been the same as with us. But the bubble on\nwhich they were was thin compared with the paths along which the radiant\nforces spread forth. And thus every force being kept to one plane\ndiminished as the distance from the centre of its action.[2]\n\nNow it was a great problem with them how the light came from the central\norb. Their atmosphere, they knew, extended but a small distance above\nthe surface of their disk. And it was quite incapable, moreover, of\nconveying vibrations such as those of light and heat.\n\nBy studying the nature of light they became convinced that to transmit\nit there must be a medium of extreme rigidity between them and the great\nsource of light.\n\nIt is easy enough to see that what they thought was a medium between\nthem and their sun was in reality the rigid surface on which they\nrested. This elastic film vibrated in a direction transverse to the\nlayer they called matter, and carried the particles of matter with it.\nBut they, having no idea but that the surface on which they were was the\nwhole of space, thought that space must be filled with a rigid medium.\nThey found that the vibrations of the medium were at right angles to the\ndirection in which a ray was propagated. But they did not conceive of a\nmotion at right angles to their plane; they thought it must be in their\nplane.\n\nIt was a puzzle to them how their disk glided with so little friction\nthrough this medium. They concluded it was infinitely rare. They were\nstill more puzzled when they had reason to believe it was an opaque\nsubstance; and yet that it could be anything else than a medium which\nfilled their space was inconceivable to them. They could never get rid\nof it from a vacuum, however perfect. Indeed we see that in producing a\nvacuum they merely cleaned the surface on which they were.\n\nIn one respect it might have been advantageous if they had known, for,\ntheir law of attraction being what it was, their movement round their\nsun was not destined to go on for ever; but they were gradually falling\nnearer and nearer. Now, if only they had made the attempt, they might by\nsome means have got a hold on the surface on which they were, and, by\nmeans of a keel which tended to furrow it, have guided their world and\nthemselves in their path round their sun. Indeed, it is possible to\nimagine them navigating themselves whither they would through their\nuniverse\u2014that is, on the surface of their bubble.\n\nIt was also unfortunate in another respect that they did not realize the\nfact of the supporting surface, for the feeling which they came to have\nof being suspended in space, absolutely isolated, was a very unsettling\none, and tended to cause in them a certain lack of the feeling of\nsolidarity with the rest of the universe.\n\nWe have seen that their laws of mechanics were very different from ours.\nBut they had after all an experience of our mechanical principles,\nthough in a curious way. In all motions of any magnitude moving bodies\nwere confined to the surface of the plane. But where the small particles\nwere concerned there was more liberty of motion. The small particles\nwere free in their movement; although they could not go more than a very\nsmall distance away from the film on which they rested, still they were\ncapable of motion perpendicular to it. Thus a long line of particles\nconnected together could rotate as a whole, keeping straight like a\ntwisting wire, and by means of many strings of particles thus connected,\nmovements could be transmitted in a way which was totally unlike the\nmechanical movements to be seen in the case of large masses.\n\nThis motion of rotation round an axis lying in the plane was to them\nwhat electricity is to us. It was quite a mysterious force. But it was\nextremely useful in its applications. Having no idea of a rotation which\nin taking place went out of their surface, they could not conceive a\nreason for the results of such movements.\n\nIt can easily be seen how many kinds of forces they could have. There\nwas the spinning motion of the small particles on the surface. This they\nwere aware of\u2014it produced many appearances, but it was not fitted for\ntransmission across great distances, as each particle was apt to be\nhindered in its rotation by its neighbour. Sometimes, however, when\nconditions were favourable, many of these rotations were harmonious, and\nwaves were produced in their matter resembling the waves in our ocean.\n\nThere were only two other kinds of motion. One was an up and down\nvibration of the film carrying matter with it; the other was the\ntwisting of strings of particles which were rigidly connected together.\nThe up and down motion of the film was to them light. Those kinds of\nmatter which did not hinder this motion were said to be transparent;\nthose kinds which, lying on the film, hindered the motion or threw it\nback were said to be opaque.\n\nThe twisting motion round an axis was to them what electricity is to us.\nAnd when this twisting motion in one direction or another was conveyed\nto the particles of small masses which were free to move, many curious\neffects were produced analogous to the movements of electrified bodies.\nThere are obviously no other rotations or vibrations possible; hence in\nthat world there is nothing corresponding to magnetism. Their light was\nsimple, and could not be split into two kinds as our light can be\u2014into\ntwo kinds of polarized light.\n\nWas there no sign, then, by which the inhabitants of this world could\ngain a knowledge of their own limitation? There was. There was both a\nsign and the interpretation of it lying before them. They knew that they\ncould have two triangles precisely similar, and yet such as could not be\nturned the one into the other by any movement in the plane. How two\nthings could be so alike, and yet differ in some mysterious way, was to\nthem a puzzle. As an instance of such triangles may be taken those used\nin Diagram VI. to represent the man and the woman. They may be exactly\nequal, yet the beings in a plane world cannot turn them so that one\nwould coincide with the other.\n\nYet had they but considered the case of a being lower in the scale of\nspace existence than themselves, they would have seen the answer to\ntheir riddle. For consider a being confined altogether to a line\n\n                         _____________________\n                           C\u2032 B\u2032 A\u2032 M A B C.\n\nLet M be the being, and let him observe the three points A B C, and let\nhim form an idea of them and their positions with regard to each other,\nwhich he measures by the distance he has to travel to reach one after\npassing the other.\n\nLet him also become aware of the three points A\u2032 B\u2032 C\u2032, forming a\nprecisely similar set on the other side of him.\n\nIt may be objected that the being in the line could not conceive any\npoint lying beyond A, but that his experience would be limited to the\npoints A and A\u2032. If A and A\u2032 are material particles this would be the\ncase, but we may suppose them to be places in the line marked out by\ncold and heat, or some such means. Then a being could conceive a series\nof positions in his space such as A, B and C, A\u2032, B\u2032, C\u2032.\n\nIf now he remembers each set, and thinks about them, he finds that they\nare alike in every respect. But he cannot make them coincide with each\nother. For if he pushes the set A B C along the line, when A B and A\u2032 B\u2032\nare together C is just where it ought not to be. It is not on C\u2032. And if\nhe gets C on C\u2032, then A B has gone far away.\n\nHe would neither be able to make them coincide nor to conceive their\ncoincidence.\n\nThere would be no movement within the realm of his experience which\nwould make them coincide.\n\nYet the dweller in a plane world could easily make these sets of points\ncoincide, for he would bend the whole line round in his plane so that A\ncoming on A\u2032, B should come on B\u2032, and C on C\u2032. There would be no\ndifficulty to him in doing this. And he does it in virtue of there being\nto him a movement possible which is not possible to the being in the\nline. He has a liberty of motion unknown to the linear being.\n\nAnd now why should he not reason thus, \u201cSomething which to the linear\nbeing is inconceivable, to me is conceivable. Then may not things\ninconceivable to me be yet possible? May it not be possible that two\ntriangles which are like one another, but yet which cannot be thought by\nme as coinciding\u2014may not these triangles be able to be made coincident\u201d?\n\nIn this simple fact of his perpetual observation was really the proof of\nthe whole matter if he had but looked at it, the sign manual of his\nlimitation, the promise of his liberation from it in thought, the key to\nthe explanation of the mysterious minute actions by which he was\nsurrounded, and perchance a help to the comprehension of a higher life.\n\n\n                              _APPENDIX._\n\nIn our world a particle of matter which sends forth influence on the\nsurrounding matter does not send its radiant energy off along a plane,\nbut from the particle all the influence spreads out into space. And the\nmost convenient instance in our world to consider is that of a luminous\npoint from which rays spread out in every direction. Let M in Diagram\nXI. be such a point\u2014a particle of matter sending forth luminous rays in\nour three-dimensional space.\n\n  [Illustration: Diagram XI.\u2014Particles in space and in a plane exerting\n  force.]\n\nInstead of studying how these rays spread out in every way all around M,\nlet us only consider those which, passing out from M, fall on the square\nA B C D. A B C D casts a shadow, and this shadow extends, and is found\nto be bigger the further off from M it is measured. Suppose, at the\ndistance from M, M E, we put a square in the path of the shadow so as\njust to receive the shadow on it exactly. Let E F G H be this square. As\nis shown by the dotted lines, this square will be four times as large as\nthe square A B C D. So when the distance is doubled, the shadow becomes\nfour times as big.\n\nNow those rays of light which fall on A B C D would, if they were not\ninterrupted by it, spread out so as to exactly cover E F G H. Thus the\nsame amount of light which falls on the small square A B C D would, if\nit were taken away, fall on the large square E F G H.\n\nNow since the large square is four times the size of the small square,\nand the same amount of rays fall on it\u2014for it only receives those which\nwould fall on the small square\u2014there must be at any part of it an\nillumination one-quarter as strong as there would be at any point on the\nsmall square.\n\nThus the small square, if placed in its position, would seem four times\nas bright as the large square.\n\nThus, when the distance from the origin of light is doubled, the amount\nof light received by a surface of given area becomes one-fourth of what\nit was at the less distance.\n\nThis is what is meant by varying inversely as the square of the\ndistance. When the distance is doubled the intensity of the light is not\nsimply less, but is halved and halved, and becomes one-quarter of its\nprevious intensity.\n\nBut in the case of a particle resting on a thin sheet of metal, and\nshaking the metal\u2014as, for instance, a metal plate can be made to shake\nby a violin bow\u2014then this law would not hold.\n\nTake the second figure. Let P be the particle, and let the influence\nproceeding from it fall on the rod A B lying on the plane, and let us\nsuppose the rod to stop the vibrations from going beyond it, to receive\nthem and to turn them back just as a body does the light. Then the\n\u201cshadow\u201d of A B would spread out away from P; and if another rod E F\nwere put in at the distance P E, which is double of P A, then, to\nexactly fit the shadow, it would have to be double the length of A B;\nand the vibrations which fell on A B would exactly fall on E F. Now\nsince E F is twice as long as A B, the vibrations which fall on any part\nof it will be one-half as intense as the vibrations which fall on a\nportion of matter of the same size lying where A B lies.\n\nThus in a plane the influence or force sent out by any particle would\ndiminish as the distance. It would not \u201cvary inversely as the square of\nthe distance,\u201d but would \u201cvary inversely as the distance.\u201d\n\n\n\n\n                       A Picture of Our Universe.\n\n\n                               CHAPTER I.\n\nIt seems to me that the subject of higher space is becoming felt as\nserious, and fraught with much that is of the deepest interest, not only\nas a scientific problem, but in other ways also.\n\nIt seems also that when we commence to feel the seriousness of any\nsubject we partly lose our faculty of dealing with it. The intellect\nseems to be overweighted somehow, and clogged. Perhaps the suppositions\nwe make seem to us of too great importance, and we are not willing\nenough to let them go, fearing to lose the thing itself if we lose our\nhold of the means by which we have first apprehended it.\n\nBut whatever may be the cause, it does seem undoubtedly the fact that\nthe mind works more clearly and more freely on subjects which are of\nslight importance.\n\nAnd I propose, that without ignoring the real importance of the subject\nabout which we are treating, we should cast aside any tension from our\nminds, and look at it in a light and easy manner.\n\nWith this object in view let us contemplate a certain story which bears\non our problem.\n\nIt is said that once in a certain region of Ireland there took place a\ncurious contest. For in Kilkenny there were two cats so alike in size,\nvigour, determination, and prowess, that, fighting, they so clawed,\nscratched, bit, and finally devoured each other, that nothing was left\nof either of them save the tail.\n\nNow, on reflecting on this story, it becomes obvious that it originated\nwhen looking-glasses were first imported into Ireland from Italy. For\nwhen an Irishman sees for the first time anything new, he always\ndescribes it in an unexpected and yet genial and interesting manner.\nMoreover, we all know what contentious fellows they are, and how all\ntheir thoughts run on fighting. And I think if we put this problem to\nourselves, how by bringing in fighting to describe a looking-glass, we\nshall see that the story of the Kilkenny cats is the only possible\nsolution. For consider evidently how it arose. Depositing his favourite\nshillaly in a corner, the massively-built Irishman, to whom the\npossession was a novelty, saw reflected in his looking-glass the image\nof his favourite cat. With a scrutinizing eye he compared the two. Point\nfor point they were like. \u201cBegorra if I know which of the two would\nwin!\u201d he ejaculates. The combat becomes real to him, and the story of\nthe Kilkenny cats is made.\n\nNow, to our more sober mind, it is obvious that two cats\u2014two real\nmaterial things\u2014could not mutually annihilate each other to such an\nextent. But it is perfectly possible to make a model of the Kilkenny\ncats\u2014to see them fight, and to mark the issue.\n\nAnd I propose to symbolize or represent the Kilkenny cat by a twist.\nTake a pencil, and round it twist a strip of paper\u2014a flat spill will do.\nNow, having fastened the ends on to the pencil by two pins, so that it\nwill not untwist, hold the paper thus twisted on the pencil at right\nangles to the surface of a looking-glass: and in the looking-glass you\nwill see its image. In Diagram I., M represents the mirror, and on the\nleft hand is shown the twist, on the right hand the image twist. Now\ntake another pencil and another piece of paper, and make a model of what\nyou see in the glass. You will be able to twist this second piece of\npaper in a spiral round this second pencil so that it is an exact copy\nof what you see in the glass. Now put the two pencils together end to\nend, as they would be if the first pencil were to approach the glass\nuntil it touched it, meeting its image: you have the real copy of the\nimage instead of the image itself. Now pin together the two ends of the\npieces of paper, which are near together, and you have your two Kilkenny\ncats ready for the fray. To make them fight (remember that the\ntwists\u2014not the paper itself, but the paper twisted\u2014represent the cat),\nhold firmly and pull the other ends (the tail ends, so to speak), so as\nto let each twist exercise its nature on the other.\n\nYou will see that the two twists mutually annihilate each other. Without\nyour unwrapping the paper the twists both go, and nothing is left of\nthem.\n\n  [Illustration: Diagram I.]\n\nNow the image of the twist as a real thing was made by us. It did not\nexist in nature other than as a mere appearance.\n\nBut I want you to imagine this process of producing a real image as\nsomehow existing. I want you to lay aside for the present the question\nof how it could be done, and to conceive twists and image twists.\n\nThis is the mechanical conception I wish you to adopt\u2014there are such\nthings as twists. Suppose by some means to every twist there is produced\nits image twist. These two, the twist and its image, may exist\nseparately; but suppose that whenever a twist is produced its image\ntwist is also produced, and that these two when put together annihilate\neach other.\n\nWith this conception let us explore the domain of those actions which\nare called electrical.\n\nWhen a glass rod is rubbed with silk it becomes excited, its state is\ndifferent. It manifests many properties, such as that of attracting\nlight bodies, giving off a glow of light, &c. The silk also with which\nit was rubbed manifests similar properties. It also attracts light\nbodies, appears to glow in the dark, &c.\n\nAnd yet there is a difference between the state of excitement of the\nglass and of the silk. The electricity which is in them is of different\nkinds. And if the electricity of the silk and of the glass be brought\ntogether, all electrical effect disappears; they become glass and silk\nin an ordinary condition.\n\nIt may seem strange that, if this is so, they should become electrified\nwhen rubbed together. Yet this is the case, and must be taken as a fact.\nIt seems to depend partly on the circumstance that glass and silk are\nnot what is called conductors. In a conductor, if one part receives\nelectricity, this electricity at once runs over the whole of the\nconductor, whether it be an inch long or many feet. And if any part of\nthe conductor be touched by another conductor which is in contact with\nthe earth, every trace of electricity leaves the conductor, flowing, as\nit were, freely out of it.\n\nNow both glass and silk do not let the electricity run from them so\neasily. To discharge a glass rod it has practically to be touched in\nevery part. Thus, when by the rubbing with silk electricity is produced\non it, it is conceivable that this electricity should be kept to a\ncertain extent, and not combined immediately with the electricity on the\nsilk.\n\nBesides, the same cause\u2014the friction which produced the electricity on\nthe glass, and the other kind of electricity on the silk\u2014would probably\nprevent their combination as long as it was applied.\n\nNow let us suppose that the electrical charge which the glass has\nconsists in this.\n\nLet us suppose that the particles of the glass on the surface of it are\ntwisted, strained out of their natural position, and twisted.\n\nLet us also suppose that the particles of the silk are twisted too, but\nlet them have the image twist.\n\nNow these two twists, the glass twist and the silk twist, its image,\nwhen brought together, will run down. In unwinding each other they will\ngive off a certain amount of energy, which will manifest itself as a\nspark, make a crackling sound, and so on. But when they unwind each\nother there is no more tension of the particles.\n\nThis does not explain in the least why the glass particles should\nreceive a twist in one direction, the silk particles a twist of the\nimage kind.\n\nBut instead of inquiring into this, it is best to see if this\nsupposition is in accordance with other known facts of electrical\naction; because, if it is not, we may dismiss it more easily than we\ncould if we had to test it with regard to the very inaccessible question\nof why some bodies, when rubbed, get electrified in one way, others in\nanother.\n\nWhen the glass and silk are near together the twist on the glass and\nthat on the silk are related to each other as twist and image twist, and\nthere is no action on surrounding bodies from either of them, as they,\nso to speak, satisfy each other.\n\nBut when the glass rod and the silk are moved apart, and brought near\nother objects, then each of them calls up on those objects near which it\nis brought a twist of the kind which is the image of its own twist.\n\nIf the glass rod is brought near a mass of metal, which we will call a\nconductor, the following effect is observed:\u2014The part of the conductor\nnear the glass rod becomes charged with electricity of the silk kind;\nthe part of the conductor away from the rod becomes charged with\nelectricity of the glass kind.\n\nNow let us bring into play the supposition which we made before.\n\nLet us suppose that there is some process in nature which, when there is\na twist, makes a real image of that twist come into being. If we assume\nthis process, we see that, opposite to the silk, on whatever objects are\nnear it, will be a twist of the glass kind, and opposite the rod will be\na twist of the silk kind. That is to say, that on the conductor there\nwill be a twist of the silk kind when the glass rod is brought near it.\n\nBut there is nothing to make the particles of the conductor twist as a\nwhole. The glass rod is not supposed to touch the conductor\u2014it is simply\nbrought near it, and no actual communication takes place between them.\nNo force is actually applied to it, nor electricity communicated to it.\nHence, on the whole, the particles of the conductor will not be twisted.\nThat is to say, since there is a twist of the glass kind on one end,\nthere will be at the other end a twist of the image kind\u2014that is, of the\nsilk kind. And these two twists are like the two twists on the pencil\u2014if\nallowed to run together they will run each other out. So if the\nconductor were removed from the neighbourhood of the glass rod it would\nbe found to be no different from what it was at first. It would not be\n\u201ccharged.\u201d\n\nNow this is what actually happens.\n\nThus we have, firstly, a glass rod with its twist; secondly, a mass of\nmetal with two twists on it\u2014one near the glass rod, and of the image\nkind; the other at the other end of the mass of metal, and related to\nthe original twist in the following way. It is the image of its image.\n\nNow it will be found by using a mirror that the image of the image of a\ntwist is the twist itself.\n\nHence on the other end of the conductor there is a twist of the same\nkind as that on the glass rod.\n\nAnd it is obvious that the rod, with its twist, is connected with the\ntwist on the conductor nearest to it, and the twist on the other end of\nthe conductor will, by the same arbitrary process which we have assumed\nas real, call up a twist, the image of itself, on any object near it.\n\nIf it is touched by the object with this contrary twist the two will run\ntogether, and the conductor will, if it is left free, have only one\ntwist\u2014the silk kind, which has come up opposite the rod.\n\nIf now the rod be moved away, the conductor will be twisted as a whole;\nthat is, all the particles of which it is composed will be slightly\ntwisted with a twist of the silk kind.\n\nIn this state it is said to be charged.\n\nThus the assumption which we have made, that there is some process in\nnature in virtue of which, opposite to any twist, its image twist is\nproduced as a real thing\u2014this assumption is in harmony with the laws of\ninduction.\n\nInstead of working with a glass rod it is more convenient to use a metal\nrod. Suppose we take a poker and attach a handle of sealing wax to its\nmiddle. See A B below. This will be easily imagined, and its two ends,\nthe handle and the black end, will be easily retained in the mind.\n\nIf now electricity be communicated from the glass rod to the poker by\ntouching the two together, what happens is this: The particles of the\nglass being twisted communicate their twist to the particles of the\npoker. The twist on the poker is of the same kind as the twist on the\nglass rod, and the amount of twisting which the glass particles had is\ndivided between the glass rod and the poker. The use of the sealing-wax\nhandle is to keep the twist from communicating itself to the body of the\nperson holding it, and, through him, to the earth. It is found that\ncertain bodies, \u201cnon-conductors,\u201d will not communicate the twist and\nconvey it along; whereas metallic bodies, and conductors generally, will\ncommunicate this twist at once to great distances.\n\nWe will suppose that a metallic body consists of particles so arranged\ntogether that it easily acts as a set of minute threads or chains of\nparticles which will twist, each thread or chain twisting as a whole.\nThus the conception which should be formed of a metallic body conducting\nelectricity along it is this:\u2014Conceive a bundle of very fine but very\nrigid wires, each wire twisting separately but with the same kind of\ntwist as all the others, and each, as it twists, rotating amongst its\nfellow threads. If we have a metal rod we can twist it between the\nfinger and thumb. This is not the kind of twist we suppose, but that\neach separate string of particles is thus twisted, so that each set\ntwisting remains in the same part of the metal rod\u2014but is turning round\nin its fixed position. This is a body conveying an electric current. If\nthe current will not pass, the set of minute wires must be conceived as\nheld at the far end, and given a twist, starting from the point where\nthe electricity is communicated. Now if a conductor is thus charged and\nleft, it is found that it retains its charge; to be discharged it must\nbe touched with another conductor. Hence this twist of minute threads\ndiffers from a twist of a wire in that the threads cannot untwist of\nthemselves unless other threads come into contact with them to which\nthey can impart the twist. That this should be the case may depend on\nthe fact that the twisting strings are strings of molecules, and the\nends of them would thus be connected with other molecules with something\nof the same tenacity as that with which the strings themselves cohere\ntogether, and are unable to unlock themselves from these insulating or\nuntwisting molecules.\n\nLet us consider the state due to these twisting strings of particles.\n\nPlace two pennies lying on the table before you, and suppose them to be\nthe sections in which two strings of a conductor are cut across, so that\nyou are looking at two particles, represented by the pennies in the\ninterior of a conductor; the strings, of which the pennies are sections,\ncome up towards your eye. Now twist the two pennies each in the same\ndirection\u2014say that of the hands of a watch. From the outer edges you can\ntake the motion off; the edges are moving in the same direction. But\nwhere the two pennies meet you will see that the edge of each is going\nin a contrary direction to the other. And if one penny tends to move an\nobject in one way the other tends to move it in the contrary direction.\nHence these motions tend to neutralize each other in the interior of a\nconducting wire.\n\nHaving now formed a conception of the state of the particles in an\nelectrified poker, suppose another poker likewise held by an insulating\nhandle is brought near the first. Let the pokers be so arranged that the\nhandles both point one way, the black ends another way, and let the\nsecond poker be in the same line as the first, with its handle towards\nthe black end of the first.\n\nNow the first poker is charged, it contains electricity, its particles\nare twisted. What effect will it have on the second poker?\n\nIt is found that the second poker undergoes a certain change, but when\nit is removed to a distance from the first poker all trace of this\nchange disappears.\n\nOn the end nearest the first poker\u2014on the handle\u2014is found silk\nelectricity; on the end furthest from the first poker\u2014on the black\nend\u2014is found glass electricity.\n\n                               A B   C D\n                               ---   ---\n                               + +   - +\n\n  Let A B be one poker, the + representing the charge of glass\n  electricity. Let C D represent the other poker, the - representing the\n  induced silk electricity, the + the glass electricity in it.\n\nLet A be the handle of the first, B its black end. Let C be the handle\nof the second, and D its black end. To explain this let us bring in our\nimaginary principle. Let us suppose that when a charged body is brought\nnear an uncharged body, but is separated from it by some medium through\nwhich electricity cannot pass\u2014let us suppose that by some agency the\ntwist in the charged body calls up an image twist in the body opposite\nit. Thus, due to the twist in the first poker there will be an image\ntwist in the handle part of the second poker.\n\nBut the strings of particles in the second poker are not twisted as a\nwhole; they are twisted in such a way that if they are removed from the\nfirst poker, the twist, whatever it be, disappears.\n\nNow this would obviously be effected if we suppose the same thing to go\non in the second poker as took place between the first poker and the\nsecond. Let the twist in the handle end C of the second poker be\naccompanied by the production of an image twist in the black end D. And\nlet us take this as a fair account of our observations. If a body, which\nas a whole does not undergo a twist, has one part of it twisted, then\nthere will be the image twist in the other part of it. I say that the\npoker as a whole is not twisted, and all that this means is that if it\nbe removed from the electrical influence it is found to be not charged;\nand the idea which we may form is this: the strings of particles are\ntwisted like the two strips of paper round the pencil; they are twisted\nso that they will exactly unwind if left alone.\n\nNow of course all these suppositions are merely provisional, and must be\ndismissed unless seen to be mechanically possible; but for the present\nwe are trying to see if our assumption will fit in with facts. And our\nassumption is that there is in nature a power which amongst the\nmolecules produces that as a real thing which in our larger mode of\nexistence only occurs as a simulacrum and appearance. Our looking-glass\nimages are not real, but we suppose that real images are produced\namongst the molecules.[3]\n\nWe have seen that if we make a certain supposition as to the calling up\nof an image twist by a twist of molecular matter, then the main facts of\nelectricity are capable of an explanation, which, involving merely the\nmotion of ordinary matter, is far preferable to the idea of there being\na mysterious fluid, and more in harmony with our present ideas of\nelectricity.\n\nAnd yet it is impossible to retain this supposition unless a clear\nmechanical explanation can be given of how a real image of itself can be\ncalled up by the twist which we suppose electricity to be.\n\nWe can by intelligent agency produce a twist which is the real image of\na given twist. But it would be absurd to suppose amongst the molecules\nan agency which, acting with prescribed aim, gave in that domain those\nreal simulacra, those evident images, those phantoms with which we in\nour larger world of masses are for ever mocked.\n\nAnd yet it would be curious if such an hypothesis were to claim a\nrecognized position in our mental apparatus with which we think about\nnature.\n\nFor in that molecular world, if we imagine it to ourselves, there would\nbe a curious state.\n\nIf we consider a twist and its image, they are but the simplest and most\nrudimentary type of an organism. What holds good of a twist and its\nimage twist would hold good of a more complicated arrangement also. If a\nbit of structure apparently very unlike a twist, and with manifold parts\nand differences in it\u2014if such a structure were to meet its image\nstructure, each of them would instantly unwind the other, and what was\nbefore a complex and compound whole, opposite to an image of itself,\nwould at once be resolved into a string of formless particles. A flash,\na blaze, and all would be over.\n\nTo realize what this would mean we must conceive that in our world there\nwere to be for each man somewhere a counter-man, a presentment of\nhimself, a real counterfeit, outwardly fashioned like himself, but with\nhis right hand opposite his original\u2019s right hand. Exactly like the\nimage of the man in a mirror.\n\nAnd then when the man and his counterfeit met, a sudden whirl, a blaze,\na little steam, and the two human beings, having mutually unwound each\nother, leave nothing but a residuum of formless particles.\n\n\n                              CHAPTER II.\n\nWhat physical explanation is possible of this production of a real\nimage?\n\nFirst of all we may note that the production of a real image of any\ndisturbance is one of the commonest phenomena.\n\nIf a piece of indiarubber lying on the table be pressed downwards with\nthe finger it will move up when the finger is removed. The yielding and\nthe resuming its original form are movement and image movement.\n\nIf the disturbance is simply a displacement in one line, then, if the\nmedium in which this displacement is produced is not permanently\ndisplaced, but on the whole maintains its equilibrium, there invariably\naccompanies any displacement its image displacement.\n\nMoreover, to take the simple example of a wave propagated through\nwater\u2014the particles of the water on the whole move about a mean\nposition; they are not displaced permanently in any one direction; and,\ntaking the distance from the crest to the hollow of a wave, then from\nthe hollow to the next crest, is the real image of the first part. Thus\nin the complete movement in the wave measured from crest to crest, there\nis displacement and its real image.\n\nThus there seems some consistency about this supposition of an image,\nabout the production of a real image in nature.\n\nBut there are two observations which we can make.\n\n_Firstly_, if it is true in these complicated cases it ought to be true\nin simpler cases also. That is, if this supposition is in harmony with\nelectrical actions, it ought to fit in with other actions of a simpler\nkind.\n\n_Secondly_, a supposition of this kind has no permanent value; it is\nrather a feeler, by which we trace out our way in the darkness, than any\nactual vision itself. In default of an actual realization of what the\nelectrical relations are we can treat them by means of a supposition.\nBut we must be ready at any moment to give up the supposition if it does\nnot harmonize with the facts.\n\nAnd in the first case does the idea of a real image hold good about the\nsimplest possible actions?\n\nIf we push our fist towards a glass the image is that of a fist moving\nin the opposite direction.\n\nNow, suppose a pressure exerted on a wall, as, for instance, a hard\nstone hitting it. The wall undergoes a displacement, but not as a\nwhole\u2014only that part of it where the stone hits. And this displacement\nis followed by the image displacement, for the wall in the part where it\nhas been hit and pressed back moves forward, and by its reaction throws\nthe stone off.\n\nEvery case of action and reaction is a case of a motion and its image\nmotion.\n\nIf a bullet strikes the wall and goes with such velocity that it lodges\nin it, then the motion of the ball and the image motion of the wall\ndestroy one another, and the result is a shattering of the wall in the\npath of the bullet.\n\nNow in the case of a simple displacement of this kind there is a rule by\nwhich we can form the image displacement. Take a point on the wall, and\nabout this point as a centre turn the displacement half way round, so\nthat it does not come to be itself again, but is opposite to itself.\n\nBy this turning, the displacement becomes the image of itself; a\nmovement into the wall becomes a movement out from the wall; and these\nfollow one another if the wall is not injured. It should be noticed that\nthe displacement is moved round this point, using a direction which is\n_not_ in the displacement itself. The displacement goes straight into\nthe wall. The turning motion, which we suppose, needs another direction\nthan this.\n\nNow suppose, instead of a simple displacement like this, we take a\ndisplacement involving two directions, as in the case of a wave\ndisturbance\u2014it will be found that the conditions are just the same. If a\nwave movement falls on a medium which it does not destroy or move as a\nwhole, the displacement calls up its image displacement. And the image\ndisplacement can be found, as before, by twisting the displacement round\nso as to become opposite to itself\u2014by twisting it half-way round. But in\nthis case, too, a direction must be used which is not used in the\ndisplacement itself.\n\n  [Illustration: Diagram II.]\n\nLet us look at the wave disturbance more closely.\n\nThe horizontal central line in Diagram II. will represent the positions\nwhich a number of particles occupy when at rest. That is, let us suppose\nthere to be a number of particles lying in a series forming this line.\n\nWe can think of the portions of an elastic cord. An indiarubber tube may\nbe taken as an illustration, and made to vibrate by a motion of the\nhand.\n\nIf now one of the particles be deflected from its natural\nposition\u2014suppose it is moved to the position M\u2014then we should have one\nparticle at M out of its place, and all the others in their places.\n\nBut this does not happen. If the particle is pulled to M, the particles\nnear it follow after it, and are also disturbed from their places,\nthough not so much as the particle at M.\n\nWe should have a set of particles forming a shape like L M N, only much\nlonger; in fact, the particles all along the cord would be raised.\n\nIf the cord is struck suddenly we do have a set arranging themselves\nlike L M N, but only for a limited distance along the cord.\n\nAnd here we notice a curious thing.\n\nIf a set of particles is forced to go like L M N, removed from their\nposition of repose, then at once a set of particles goes like N O N\u2032.\n\nA displacement is accompanied by another displacement which is the\nopposite of it. And this displacement and opposite displacement travels\nalong the elastic cord.\n\nBut the point of view which is the most natural one to regard it from is\na little different from this. Let us consider a single point, P. When\nthis is disturbed it moves above its original position to M, and below\nto the other end of the dotted line. Its complete movement is from one\nof these extremes to the other. And if we take the complete disturbance\nas exhibited in all its phases by different points, we ought to look at\nthe portion of the diagram M N O. For here at N we have a point not\ndisplaced at all; at M, one displaced to its full extent upwards; at O,\none displaced to its full extent downwards. And intermediate particles\nhave intermediate displacements.\n\nNow when a complex displacement of this kind is put into a cord, its\nimage at once springs up. The displacement represented by M N O at once\ncalls up the displacement represented by O N\u2032 M\u2032, and this condition of\ndisplacement and image displacement continues repeating itself till the\ncord comes to rest.\n\nIf the diagram be closely looked at, it will be seen that it exhibits\nthe image relationship twice over. For the movement of the particle P\nfrom P to M has its image in the motion of another particle from its\nplace of repose to the position O. The disturbance itself, M N O,\nconsists of displacements and image displacements; and this disturbance,\nwith its image O N\u2032 M\u2032, makes the wave from crest to crest.\n\nThe \u201ctwist\u201d which we consider in these pages is like the wave motion,\nbut with a third component added, so that in the complete motion there\nis a displacement coming out from the plane of the paper, as well as the\ndisplacements in the plane of the paper itself.\n\nAnd just as the wave displacement produces a real image of itself in a\nmedium which it does not distort as a whole, so there is nothing\narbitrary in our assuming that an electric twist calls up the real image\nof itself in an insulating medium\u2014that is, a medium which it cannot\ntwist as a whole.\n\nIf L M N O is a wave motion, then L\u2032 M\u2032 N\u2032 O is its image, as produced\nby moving it round out of the plane of the paper\u2014Diagram II. If the wave\ndisturbance is moved round in the plane of the paper, the original wave\nL M N O becomes L\u2032 M\u2032 N\u2032 O\u2014Diagram III.\u2014a shape which bears no\nresemblance to the transmitted wave.\n\nConsider O N M L to be a bent piece of wire lying on the paper; if it is\nmoved round O, keeping on the paper, it becomes O N\u2032 M\u2032 L\u2032. To become\nlike O N\u2032 M\u2032 L\u2032 in Diagram II. it must move up from the paper and down\nagain on the right.\n\nThus adopting this artificial aid to thought\u2014that a displacement calls\nup an image displacement\u2014we get the rule that this displacement, the\nimage, can be got from the original displacement by moving the original\ndisplacement half-way round, using as the plane in which the turning is\nmade that plane which is given us by taking these two directions\u2014the\ndirection in which the wave is moving, and a direction at right angles\nto the directions in which the displacements which form the wave take\nplace.\n\nThus, with the wave motion shown, if we take the direction towards the\ntop of the page to be the up direction, and that from left to right to\nbe the sideways direction, then out of the paper towards us is the\n\u201cnear\u201d direction. So, too, in this case we have to turn the wave\ndisturbance out of the plane of the paper, and each point of it, to\nproduce the image, must turn in a circle (going half-way round it) lying\nin a plane which has the two directions near and sideways. The motions\nof the particles themselves are in the plane of the paper. So to get the\nimage by turning we use a direction\u2014the \u201cnear\u201d direction, which is not\ninvolved in the wave motion itself.\n\n  [Illustration: Diagram III.]\n\nHence we may state, as a tentative principle, that when a disturbance\ntakes place in a medium which will not be disturbed as a whole, then\nsuch disturbance is accompanied by a real image of itself; and this real\nimage of itself is the configuration which would be obtained by twisting\nthe original disturbance round in a direction not contained in the\noriginal disturbance.\n\nThus the disturbance O N\u2032 M\u2032 L\u2032 is obtained by twisting the disturbance\nL M N O round. The direction in which it is twisted is the direction\ncoming out from the plane of the paper.\n\nNow if this plane disturbance is in nature accompanied by its real\nimage, why should not a twist such as takes place in the electric\ncurrent also be accompanied by its image twist when it impinges on a\nmedium which it cannot twist as a whole\u2014that is, when it comes to an\ninsulator in its path?\n\nThe reason, obviously, is that we cannot conceive such an image produced\nmechanically. And the reason of this can be exhibited thus.\n\nWhen we had a plane disturbance like L M N O we only used up two\ndimensions of space, and we have a third coming up from the plane; and\nthis direction enables us to imagine a turning which will alter A B into\nits image.\n\nBut when we have a twist proceeding along an axis, as in the case of\nelectricity, we have no direction left over in space whereby we may\nconceive the twist turned round.\n\nNow when the displacement itself involves all these directions how will\nour rule hold?\n\nHow shall we get the image displacement? We can find what it is by using\na looking-glass; but the same rule which served in previous cases ought\nto work here also.\n\nWe want a direction which is neither up and down, right and left,\ntowards and away.\n\nNow let us adopt a mathematical device, and suppose there is such a\ndirection, and let us call it the X direction, the unknown direction.\n\nThen if we turn the twist round, using this X direction, we shall get\nthe image if our rule is correct. And as a matter of fact, by twisting a\nfigure round in this way, using a direction different from any of the\nthree mentioned above, we do get its image.\n\nHence the rule we have formed works consistently.\n\nIt will be found that if there was another direction so that the spiral\ndisturbance could be turned independently of the directions used up in\nit, that just as a plane disturbance can be turned into its image\ndisturbance, so the spiral disturbance of electricity could be turned\ninto its image spiral by a simple turning.\n\nIn this argument we have not looked at the matter directly, but from the\noutside. To see it immediately requires us to gain a familiarity with\nthe properties of space with four independent directions, and that would\ntake too long for the present paper. The same conclusion can be arrived\nat mathematically; but in these papers as far as possible we avoid\nsymbolism. We want to gain hold of scientific facts in a warm and living\nway, to unwrap them from conventionalities and formul\u00e6.\n\nThus if we suppose that in the minute motions which go on about us there\nis a possibility of moving in a four-dimensional way, then it is\nperfectly legitimate to assume that in a medium which cannot be twisted,\nbut which is elastic, a twist calls up a real image twist.\n\nAnd thus the assumptions which we have made as the basis of an\nelectrical theory are justified on the assumption of a four-dimensional\nspace, are untenable except on that supposition.\n\nThe matter is of course perfectly open. The only way is this, by\nadopting the assumption of a higher space to predict what the actions of\nthe molecules will be, then if a number of predictions are verified the\nevidence will become strong. And I feel sure that there are some very\ncurious things to be made out here. For my own part the evidence of the\nreality of four-dimensional space\u2014in the sense in which we say that our\nspace is real\u2014does not rest on the consideration of the molecular\nmovements about which it is not easy to get clear ideas, but on the\nstudy of the facts of space. I hardly think that any one who spent a few\nyears in becoming familiar with the facts of space, not by the means of\nsymbolism or reasoning but by pure observation, could doubt that there\nare really four dimensions.\n\nIn noticing the simpler actions and their image actions we find that the\nreal image does not coexist with its original, but rather follows and\nsucceeds it. If we push against a board the board yields, and springs\nback when we leave off pushing. If the original displacement is\npermanent as a point pressed against an elastic surface and making the\nsurface yield, then the image of this displacement is potential; it is\nnot actually there, but comes into play as soon as the original\ndisplacement is removed.\n\nNow in the electrical actions we have assumed both the original twist\nand the image twist as concurrently existing.\n\nIn certain cases there is no doubt that they are coexistent as when a\nglass rod is rubbed by silk.\n\nBut if the case of the action of a charged poker on an uncharged one be\nexamined it will be found that there is nothing to prove that the image\ntwist comes into existence until the original one is removed.\n\nWhen the charged poker is brought near the other, the remote end of the\nsecond is affected with the same kind of electricity as is on the\ncharged poker.\n\nThe appearance is just the same as if a thin wall were exposed to a\npressure on one side, and the other side were to bulge out. The\ndisplacement is transmitted through the conductor.\n\nIt is only when the original charged body is removed that the image\ncharge is found to be in existence on the second conductor. There are\nsome peculiarities, however, which make electrical displacements\ndifferent in their appearances from ordinary displacements.\n\nNo body can be made to move in any direction without imparting an equal\nmotion in an opposite direction to another body\u2014_e.g._, the motion of a\ncannon ball is equalled by the recoil of the cannon.\n\nAnd so no twist can be given to the particles of a body without an image\ntwist being given to other particles.\n\nNow the image displacement or rectilinear motion, in the case of a\nrectilinear motion, in straightforward movement seems to remain in the\nplace where it was produced. The recoil of the gun carriage produces a\nstrain on its bearings and friction, which produce heat, which gradually\ndissipates.\n\nBut the image displacement, in the case of electricity, seems to have a\nmarvellous facility for running through the earth and meeting the\noriginal displacement. An indefinitely long line of action seems in\nelectricity to take the place of a simple point. Our ordinary mechanical\nforces are located in centres, or points of action. In electricity the\nline seems to take the place of the point. Where the ordinary engineer\ndeals with points the electrical engineer deals with lines.\n\n\n                              CHAPTER III.\n                               THE \u00c6THER.\n\nThere are some expressions which, being somewhat vaguely used, are apt\nto cause confusion in the mind of those who read or hear about higher\nspace.\n\nAnd perhaps the most mischievous is the expression, a curvature of\nspace. Now of space as it is generally used, in its accepted\nsignificance, there can be no curvature. For space means a system of\npositions extending uniformly in the number of dimensions we choose to\nfix upon.\n\nIf we take the straight line as our space, we may call it 1 space; then\nthe set of positions follow one on after the other without bending. If\nthe line is bent it becomes a _line_, not a straight line. It should not\nbe called 1 space, but a thing in 2 space. That is, it is a bent line in\na plane.\n\nA being who was on the line might not perceive the fact of this bending,\nand it might not affect the measurements he made. But if the line ran\ninto itself again, and he found that he was moving on what we should\ncall a circle, this would in no way affect his idea of space. He would\nrecognize that what he called space, namely, his line, was not space,\nbut a curved thing in 2 space.\n\nSimilarly, taking a plane\u2014this is by definition not curved in any way,\nknown or unknown, and it can only be conceived to be bent by ampler\nspace being conceived, and its being imagined as having force applied to\nit so as to become a bent thing in this ampler space. In this case the\nterm \u201cplane\u201d is not the correct name.\n\nAnd so about our three-dimensional space; we cannot be robbed of that\nidea, although it might conceivably be proved that our earth and our\nwhole universe were on a curved thing in 4 space.\n\nWe will then keep the term \u201cspace\u201d for the ordinary conception; and call\nit 1, 2, 3, 4 space, according to the number of supposed independent\ndirections.\n\nA curved line or surface or solid we will call a 1, 2, or 3 thing,\naccording to the number of dimensions in it.\n\nA straight line is a 1 thing possible in 1 space. A circle is a 1 thing\npossible in 2 space. At any point of it a being in it is limited to\nmotion in one direction, while the circle itself involves two\ndimensions. The surface of a sphere is a 2 thing possible in 3 space.\nThe rind of an orange, or the orange itself, is a 3 thing possible in 3\nspace.\n\nIt will be observed that the surface of the sphere, although only a 2\nthing, involves the conception of 3 space, and cannot be understood\nwithout the use of the idea of 3 space. It is a 2 thing because at any\npoint of the surface a being can only move in two independent\ndirections. A crooked line drawn on the surface of a sphere is a 1 thing\nin a 2 thing in 3 space.\n\nAnother very common misconception is occasioned by the use of a figure\nof this kind [Illustration: symbol] to represent a \u201cknot\u201d in 2 space.\n\nIt obviously corresponds in 2 space to an iron rod welded together at\nthe crossing place of the loop, so that it is indistinguishable which is\nthe one free end, which the other. At the crossing point the two lines\nrepresented by the two ink marks must be absolutely one and the same.\n\nIf one line be supposed to go over the other, by however small a\ndistance, it would leave the plane. It would suddenly become invisible\nto the creature in the plane, and it would appear again at the other\nside of the line it crossed as if it came from nowhere.\n\nIt would be as extraordinary a sight as if we saw a pole going up to a\nbrick wall, then beyond the brick wall the rest of the pole\nappearing\u2014not going through the brick wall, nor coming round it\u2014but\nsomehow appearing; part of the same pole moving when it moved, obviously\nconnected with it, and yet with no joining part which we could possibly\ndiscover.\n\nAgain, it sometimes appears to be thought that the fourth dimension is\nin some way different from the three which we know. But there is nothing\nmysterious at all about it. It is just an ordinary dimension tilted up\nin some way, which with our bodily organs we cannot point to. But if it\nis bent down it will be just like any ordinary dimension: a line which\nwent up into the fourth dimension one inch will, when bent down, lie an\ninch in any known direction we like to point out. Only if this line in\nthe fourth dimension be supposed to be connected rigidly with any rigid\nbody, one of the directions in that rigid body must point away in the\nfourth dimension when the line that was in the fourth comes into a 3\nspace direction.\n\nIf the reader will refer back to the paper on the plane world he will\nfind a description of the means by which a being there might know that\nhe was in a limited world, and that his conception of space was not of\nwhat was really the whole of space, but of the limited portion of it to\nwhich he was confined by his manner of being.\n\nThe test by which such a being could discover his limitation was this.\nHe found two things, each consisting of a multitude of parts\u2014two\ntriangles; and the relationship of the parts of the one was the same as\nthe relationship of the parts of the other. For every point in the one\nthere was a corresponding point in the other. For every pair of points\nin the one there was a corresponding pair of points in the other. In\nfact, considered as systems made up of mutually related parts, each was\nthe same as the other.\n\nYet he could not make these two triangles coincide.\n\nNow this impossibility of bringing together two things which he felt\nwere really alike was the sign to him of his limitation; and by\nreflecting on the similar appearance which would present itself to a\nbeing limited to a straight line\u2014by thinking of two systems of points\nwhich were really identical, and which he could make coincide, but which\na line being could not make coincide, he would be led to conclude that\nhe in his turn was subject to a limitation.\n\nNow is there any object which we know which, considered as a whole\nconsisting of parts, is exactly like another whole, the two having all\ntheir parts similarly arranged, so as to form in themselves two\nidentical systems, and yet the one incapable of being made to coincide\nwith the other, even in thought?\n\nLet us look at our two hands.\n\nThey are (except for accidental variations) exactly alike. And yet they\ncannot be made to coincide.\n\nAnd here, if we reflect on it, is the sign to us that we are limited in\nour notions of space\u2014that we are really in a four-dimensional world.\n\nWatching a ship as it recedes from the shore we see that it becomes hull\ndown before it vanishes, and know that the earth is round. And no less\ncertainly do our two hands, in their curious likeness and yet\ndifference, afford to us a perpetual proof of our limitation, and\nindicate a larger world.\n\nThis sign really tells us more than the mere fact of our limitation: it\ntells us where to look for the possibility of four-dimensional\nmovements. It tells us that movements of any degree of magnitude\nrelative to us are not possible in the fourth dimension. It tells us to\nlook for four-dimensional movements in the minute particles of matter,\nnot in the movements of masses of about our own size.\n\nThe task before us is difficult. We have to make up from the outside\nwhat the appearances of a higher space existence are to us in our space,\nand then we have to look at the facts of nature and see if they\ncorrespond to these appearances.\n\nLet us take a few isolated points and look at them patiently.\n\nTo a being standing on the rim of a plane world a straight line\nabsolutely shuts out the prospect before him. If the straight line is\ninfinite it cuts his world in two; he can never hope to get beyond it.\n\nIt is to him what an infinite plane would be to us, stretching\nimpassably in front of us, cutting us off from all that lies on the\nother side.\n\nBut we know that a point can move round this line. It can revolve round\nit by going out of the plane, and coming down again into the plane on\nthe other side of the line.\n\nThis movement would be inconceivable to a plane being; for he can only\nconceive it possible to get to the other side of the line by going to\nthe end of it and coming back along the other side of the line.\n\nNow take a piece of paper and put a dot right in the middle and suppose\nthat it has no means of passing through the paper. We can only conceive\nthe dot getting to the other side of the paper by passing round the edge\nand coming back again to the position underneath where it was.\n\nBut by a four-dimensional movement it can slip round the paper without\ngoing to the edge.\n\nA set of words may help. In a plane a body rotates round a\npoint\u2014rotation takes place round a point. In space rotation is always\nround a line\u2014the axis. In four-dimensional space rotation takes place\nround a plane.\n\nTo take a farther consideration of this point\u2014a plane being can see one\nside or the opposite of a straight line. He can only see it in one\ndirection or in the reverse direction. But we can look at a straight\nline from a direction at right angles to that in which a plane being\nlooks at it. We can look at a straight line from points which go all\nround it.\n\nSimilarly, a being in four-dimensional space can look at a plane from a\ndirection at right angles to that in which we look at it. If we try to\nthink of this we shall imagine ourselves looking at the thin edge. But\nthis is not what a four-dimensional being would mean. He would see the\nplane exactly as we see it, but it would be from a direction at right\nangles to that in which we look.\n\nIn working with four-dimensional models it is a curious sensation until\nwe become used to it\u2014that of looking at a plane at one time, and then\nlooking at it again; and, although it seems just the same\u2014as square in\nfront of us as before\u2014realizing that we are looking at it from a\ndirection at right angles to that of our former view.\n\nAnd in four dimensions a point which is quite close to a plane can\nrevolve round it without passing through it, thus presenting to us the\nappearance of vibrating across the plane, but not passing through it.\n\nThe appearance is as wonderful to us as it would be for a plane being to\nsee a point which was in front of a line quickly passing behind it\nwithout having gone round the end. Such a point would appear to the\nplane being to vibrate across his line without passing through it.\n\nNow if we stand in front of a mirror we see the image of ourselves. If\nwe were to go round the mirror and take behind it the position which our\nimage seemed to occupy, we should not be able to make ourselves coincide\nwith it. In the mirror opposite to our left hand is the image of our\nleft hand; but if we passed round, our right hand would be in the place\nin which we imagined we saw the image of our left hand. And thus we\ncannot make ourselves coincide with our image. But by a rotation in\nfour-dimensional space we could put ourselves so as exactly to coincide\nwith our image. This can be seen by referring to the case of the\nstraight line, Diagram IV.\n\n  [Illustration: Diagram IV.]\n\n  [Illustration: Diagram V.]\n\nLet A B C be a triangle, and G a line. If A B C moves round the end of\nthe line, it can take up the position A\u2032 B\u2032 C\u2032; but it cannot anyhow be\nmade to take the position shown in Diagram V., A\u2032 B\u2032 C\u2032.\n\nBut if we move the triangle A B C out of the plane round the line G as\naxis, it will, in the course of its twisting round this axis, come into\nthe position A\u2032 B\u2032 C\u2032. It will come into this position when it has\ntwisted half-way round. The point A, for instance, twists round in a\ncircle lying in a plane which contains the direction A to A\u2032, and the\ndirection at right angles to the paper. Twisting half-way round in this\ncircle, it becomes A\u2032, and so on for the other points. Now a being who\ndid not know what a direction was which lay out of the plane would not\nbe able to conceive this twisting and turning movement. It would be as\nimpossible for him to conceive the triangle A B C turned into the\ntriangle A\u2032 B\u2032 C\u2032, as it would be for us to suppose ourselves turned\ninto the looking-glass image of ourselves by a simple twisting.\n\nYet just as a thing inconceivable to the plane creature can be done, so\nwe could be twisted round and turned into our image. But this only holds\ntheoretically; our relation to the \u00e6ther is such that we cannot be so\nturned, or any bodies of a magnitude appreciable to our senses.\n\nIf we consider the case of a being limited to a plane, we see that he\nwould have two directions marked out for him at every point of the rim\nof matter on which he must be conceived as standing. This is up and\ndown, and forwards and backwards\u2014the up being away from the attracting\nmass on which he is.\n\nNow, if he were to realize that he was in three-dimensional space, but\nconfined to a plane surface in it, his first conclusion would be that\nthere was a new direction starting from every point of matter, and that\nthis new direction was not one of those which he knew. This new\ndirection he could not represent in terms of the directions with which\nhe was familiar, and he would have to invent new terms for it.\n\nAnd so we, when we conceive that from every particle of matter there is\na new direction not connected with any of those which we know, but\nindependent of all the paths we can draw in space, and at right angles\nto them all\u2014we also must invent a new name for this new direction. And\nlet us suppose a force acting in a definite way in this new direction.\nLet there be a force like gravitation. If there is such a direction,\nthere will probably be a force acting in it; for in every known\ndirection we find forces of some kind or another acting. Let us call\naway from this force by the Greek word ana, and towards the centre of\nthis force kata. Then from every point in addition to the directions up\nand down, right and left, away from and towards us, is the new direction\nana and kata.\n\nNow we must suppose something to prevent matter passing off in the\ndirection kata. We must suppose something touching it at every point,\nand, like it, indefinitely extended in three dimensions.\n\nBut we need not suppose it\u2014this unknown\u2014to be infinitely extended in the\nnew direction ana and kata. If matter is to move freely, it must be on\nthe surface of this substratum. And when the word surface is used it\ndoes not mean surface in the sense that a table top is a surface; it is\nnot a plane surface, but a solid space surface. If from every point of a\nmaterial body a new direction goes off, the matter which fills up the\nspace produced by the solid moving in this new direction will have the\nsolid it started from as its surface, and will be to it as a solid cube\nis to the square which bounds it on the top.\n\nNow this body which extends thus, bearing all solid portions of matter\nin contact with its surface by every point of them, may be thick in the\nkata direction or thin.\n\nIf it is thick, then the influence of any point streaming out in radiant\nlines will pass as in all space directions, so out also in this new\ndirection.\n\nAnd then if its influence spreads out in this new direction, its effect\non any particle near it will diminish as the cube of the distance; for,\nbesides filling all space, it will have also to fill space extended in\nthis new direction.\n\nBut we know that the influence proceeding from a particle does not\ndiminish as the cube of the distance, but as the square of the distance.\n\nHence the body which, touching all solid bodies by every point in them,\nand supports them extending itself in the kata direction\u2014this body is\nnot thick in this direction, but thin. It is so thin that over distances\nwhich we can measure the influence proceeding from a body is not lost by\nspreading in this new kind of depth.\n\nThus the supporting body resembles, as far as we know it, a portion of a\nvast bubble. But moving on the surface of this bubble we can pass up and\ndown, near and far, right and left, without leaving the surface of the\nbubble. The direction in which it is thin is in a direction which we do\nnot know, in which we cannot move. But although we cannot make any\nmovements which we can observe with our eyes in this direction, still\nthe thin film\u2014thin though infinitely extended in any way which we can\nmeasure\u2014this thin film vibrates and quivers in this new direction, and\nthe effects of its trembling and quivering are visible in the results of\nmolecular motion. It only affects matter by its movement in directions\nat right angles to any paths which we can point to or observe, and these\nmovements are minute; but still they are incessant, all-pervading, and\nthe cause of movements of matter. It is smooth\u2014so smooth that it hinders\nnot at all the gliding of our earth in its onward path. Hence it does\nnot transmit a direct pull or push in any direction from one particle to\nanother; but by the twistings and vibrations of the material particles\nit is affected, and conveys from one to another these movements. Yet to\nbear up all matter, and thus hold it on its vast solid surface, it must\nbe extremely rigid and unshatterable; and hence it cannot be permanently\naltered or twisted by any force proceeding from matter; but receiving\nfrom matter any push or twist, it is impressed with it for some\ndistance; then, reasserting itself, it produces an image displacement or\ntwist, and this image it transfers to the particles of matter which it\ntouches.\n\nSometimes, as when light comes from the sun, this displacement and image\nis repeated and repeated innumerable times before at last we, receiving\nit, become aware of the origin of the disturbance.\n\nBut the properties and powers of this solid sheet\u2014this film quivering\nand trembling, yet infinite and solid\u2014are too many to begin to\nenumerate. The \u00e6ther is more solid than the vastest mountain chains, yet\nthinner than a leaf; undestroyed by the fiercest heat of any furnace,\nfor the heat of the furnace is but its shaking and quivering; bearing\nall the heavenly bodies on it, and conveying their influence to all\nregions of what we call space.\n\nAnd by some mysterious action it calls up magnetism from electricity; by\nits different movements it gives the different kinds of light their\nbeing.\n\nOf itself untrammelled and unclogged by matter, it vibrates and shakes\nwith the speed and rapidity of the vibrations of light. But when matter\nlies on it\u2014when air, even in its rarest condition, lies on it\u2014its proper\nmovement is damped and some of its quick shakings that are light, slow\ndown to the obscure vibrations of heat. Thus of itself it will not take\nup the vibration of a hot body, but selects only those orbs which are\nglowing with radiant light wherefrom to take its thrilling messages. But\nwhen matter lies on it, it takes obediently the less vivacious movements\nof terrestrial fires.\n\nA being able to lay hold of the \u00e6ther by any means would, unless he were\ninstantly lost from amongst us by his staying still while the earth\ndashes on\u2014he would be able to pass in any space direction in our world.\nHe would not need to climb by stairs, nor to pass along resting on the\nground.\n\nAnd such a being, even as thin as ourselves, and as limited, if not even\nin physical powers, but merely in thought he became aware of his true\nrelation to the \u00e6ther, he would see all things differently.\n\nFrom all shapes would fall that limitation of thought which makes us see\nthem differently to what they are; and in largeness and liberty of\npossible movement his mind would travel where ours but creeps, and soar\nand extend where ours journeys and diverges.\n\nIt is impossible in contemplating the rudiments of four-dimensional\nexistence to prevent a sense of largeness and liberty penetrating even\nthrough the profoundness of our ignorance.\n\nWhether we shall find beings other than ourselves, when we have explored\nthis larger space, cannot be said.\n\nBut there is a path which holds out a more distinct promise.\n\nWhen the conditions of life on a plane are realized it becomes evident\nthat much of that which is to us merely natural\u2014obvious from the very\nconditions of our life\u2014could only be attained by beings on the plane as\nthe result of artificial contrivances and modifications of their natural\ntendencies. In their progress and development they would, as it were,\nrepresent on the plane the features of the normal and undeveloped life\nof three-dimensional beings, and they would attain, as a result of moral\nlabour and energy, a position which children in our higher life are born\nto without trouble or thought.\n\nAnd so we in our advancing civilization may to the eyes of some higher\nbeings represent in our arrangements and institutions an approach to the\nsimplest matters of fact in their existence. We are separated from such\na view by our bodily conditions, but we are not to be prevented from\ntaking it with our minds.\n\nBy building up the conception of higher space, by framing the mechanics\nof such a higher world, we may arrive at a fairly accurate knowledge of\nthe conditions of life in it.\n\nAnd then, with that element in our thought, with the reasoned-out\ncharacteristics present to our minds of what life on a higher physical\nbasis would be, we may be able to judge amidst conflicting tendencies\nwith more certainty and calmness.\n\nIn one of the following papers of this series an account will be given\nof some of the facts which we can discern about the machinery and\nappliances of four-dimensional beings.\n\nBut the work of real discernment belongs to those who will from\nchildhood be brought up to the conception of higher space.\n\n\n                             _APPENDIX I._\n\nA supposition can be made with regard to the \u00e6ther which renders clearer\nan idea often found in literature.\n\nThis idea is that of the freedom of the will. If the will is free, then\nit must affect the world so as to determine chains of actions about\nwhich the mechanical laws hold true. We know that these mechanical laws\nare invariably true. Hence, if the will is an independent cause, it must\nact so that its deeds produce to us the appearance of a set of events\ndetermined by our known laws of cause and effect. The idea of the\nfreedom of the will is intimately connected with the assertion that\napparent importance, command of power, greatness and estimation, are\noutside considerations, not affecting the real importance and value of\nany human agent. These ideas can easily be represented using the idea of\nthe \u00e6ther as here given.\n\nFor suppose the \u00e6ther, instead of being perfectly smooth, to be\ncorrugated, and to have all manner of definite marks and furrows. Then\nthe earth, coming in its course round the sun on this corrugated\nsurface, would behave exactly like the phonograph behaves.\n\nIn the case of the phonograph the indented metal sheet is moved past the\nmetal point attached to the membrane. In the case of the earth it is the\nindented \u00e6ther which remains still while the material earth slips along\nit. Corresponding to each of the marks in the \u00e6ther there would be a\nmovement of matter, and the consistency and laws of the movements of\nmatter would depend on the predetermined disposition of the furrows and\nindentations of the solid surface along which it slips.\n\nThe sun, too, moving along the \u00e6ther, would receive its extreme energy\nof vibration from the particular region along which it moved, and the\nfurrows of the intervening distance give the phenomena actually observed\nof our relationship to the sun and other heavenly bodies.\n\nThus matter may be entirely passive, and the history of nations, stories\nof kings, down to the smallest details in the life of individuals, be\nphonographed out according to predetermined marks in the \u00e6ther. In that\ncase a man would, as to his material body, correspond to certain\nportions of matter; as to his actions and thoughts he would be a\ncomplicated set of furrows in the \u00e6ther.\n\nNow what the man is in himself may be left undetermined; but he would be\nmore intimately connected with the \u00e6ther than with the matter of his\nbody. And we may suppose that the \u00e6ther itself is capable of movement\nand alteration; that it moulds itself into new furrows and marks.\n\nThus the old woman smoking a pipe by the wayside years ago, and whom I\nsomehow so often remember, is not much different from me\u2014we are both\ncorrugations of the same \u00e6ther.\n\nNow our consciousness is limited to our bodily surroundings. Yet it may\nbe supposed that in an action of our wills we, whatever we are (and for\nthe present let us suppose that we are a part of the \u00e6ther), we may be\naltering these corrugations of the \u00e6ther. A single act of our wills,\nwhen we really do act, may be a universal affair with quite infinite\nrelations. Thus it may be the immediate presentation to us of an\nalteration proceeding from us of all that set of corrugations which\nrepresents our future life; it may be the whole disposition and lie of\nevents, which are prepared for the earth to phonograph out, being\ndifferently disposed. And it evidently is quite independent of the\nparticular furrows in which such alteration first occurs. That long\nstrip of \u00e6ther which is a very humble individual may, by an act of\nself-configuration, affect the neighbouring long strips and produce\ngreat changes. At any rate the intrinsic value of the will is quite\nindependent of the kind of furrows along which any material human body\nis proceeding.\n\n\n                             _APPENDIX II._\n\nIt is a good plan in fixing our attention to give definite names to the\ndirections of space. Let U stand for up. Then the up direction we will\ncall the U direction, or simply U.\n\nThen sideways, from left to right, we will call V, so that moving in the\nV direction, or moving V, means moving to the right hand.\n\nThen the away direction we will call W, so that a motion which goes away\nfrom us we call a W motion, and its direction we call W.\n\nThen any other direction which we suppose independent of these we will\ncall the X direction. Now the simple push or displacement takes place in\ndirection V, or left to right. It is turned into its image by turning in\nthe plane U V\u2014_i.e._, the plane of the paper.\n\nThe wave motion takes up the directions U V, and it can be turned into\nits image by a turning in the plane W V\u2014_i.e._, by turning out of the\npaper, as if the paper were folded over about the dotted line. Then\nfinally the twisting motion takes up the directions U V W, and can be\nturned into its image by being turned in the plane V X. That is, if each\npoint is turned half-way round in this plane it becomes the\ncorresponding point in the image twist. Thus on the supposition of the\npreceding pages, if a positively electrified particle could be turned in\n4 space, it would become a negatively electrified particle.\n\n\n                            _APPENDIX III._\n\nIt remains now to examine if the supposition that the particles of a\nwire are twisting in strings fits in with observed facts of electricity.\n\nAnd firstly, if the particles are twisting in this manner, it is only\nreasonable to suppose that they would take up a little more room than\nthey did when not subject to this movement\u2014that is, the wire would\nbecome a little thicker. But its volume remaining the same, if it\nbecomes thicker it must compensate for this thickening by becoming\nshorter. And it is found that a wire through which an electric current\nis sent tends to become shorter when the current comes into it.\n\nAgain, suppose a wire through which a current has been sent suddenly\nisolated. It has a twist in it, and will keep this twist. But if it is\nconnected up with any other wire forming a complete circuit through\nwhich it can untwist itself, it will probably do so, and in untwisting\nwould very likely overshoot the mark and become twisted in the opposite\ndirection. Thus it would make a series of twists, each less than the\nlast before becoming quiescent. And it is observed that a wire if so\nisolated does produce a rapidly alternating series of very minute\ncurrents before it comes to rest; just as if it were untwisting itself\nand overshot the mark each way many times before the electrical state\nhas altogether disappeared.\n\nThe question now comes before us, How is it that a wire gets twisted?\nThrough what agency is a current of electricity urged through a wire, or\na twist put into it?\n\nThis is often done by means of an electrical battery. We will take a\nsimple instance.\n\nSuppose a dish of sulphuric acid, and a bit of carbon and a piece of\nzinc put into it. Then the carbon and the zinc are connected outside the\nliquid by a wire. Along this wire electricity will pass. Now the twist\nput into the wire must come from somewhere. And it is found that the\nsulphuric acid, which is a very lively compound, and contains a great\ndeal of energy, becomes quieted down, and is quite different after the\nbattery has finished working. On examination afterwards it is found to\nconsist of sulphate of zinc.\n\nSulphuric acid can be looked upon as consisting of two bodies\u2014hydrogen\nand a sulphur and oxygen compound. This sulphur and oxygen compound is\ncalled SO\u2084. Now the SO\u2084 comes to the zinc, and with zinc forms quite a\ndead compound, with little energy in it, called zinc sulphate, or Zn\nSO\u2084. The hydrogen, on the other hand, comes off at the carbon in an\nenergetic state.\n\nHence evidently the SO\u2084 has given up its energy, the hydrogen has not.\nSo the twist in the wire probably comes from the SO\u2084 and thus the twist\nis started at the zinc end, and runs round the wire from zinc to carbon.\n\nAt the same time we may suppose that an image twist, starting also from\nthe zinc, runs through the fluid of the battery and then along the wire,\ntill meeting the twist the two mutually unwind each other.\n\nThus the battery will be as if one had a loop of thread, and at one\npoint twisted it between one\u2019s finger and thumb. Twist and image twist,\nstarting from this point, unwind each other on the opposite part of the\nloop. And if the loop is not joined, but the threads are held, each will\nbecome twisted with increasing tension till they can twist no longer.\nThe objects which hold the ends of the thread, and prevent them\ntwisting, represent insulators.\n\nIt is found that when a strong current of electricity passes through\nsome water which has had a little sulphuric acid added to it, two\neffects take place.\n\nIn the first place some of the current passes through as through a wire.\nIn the next place a part of the current is used up in producing an\neffect on the water. It splits the water up into two parts, each of them\ncontaining very much more energy than the water. One part is called\nhydrogen, and comes off at the wire which comes from the zinc, which we\nwill call the zinc wire. The other part of the water comes off at the\nwire coming from the carbon, or at the carbon wire, and is called\noxygen.\n\nLet us now suppose that the twist of the zinc wire calls up in the\nmolecule of water next to it an image twist. If it could pass on its\ntwist at once, the water would form an ordinary conductor; but the water\nis not a conductor. Hence we suppose the same relation to hold good\nbetween the end of the zinc wire and the water molecules as between the\nzinc wire and any other body to which the twist cannot be communicated.\n\nNow in the part of the molecule nearest the zinc wire an image twist is\ncalled up. And hence the molecule, being unable to twist as a whole, in\nthe end of it away from the zinc wire a twist is produced. Thus the\nwater molecule is strained into image twist and twist. Now let us\nsuppose that by a powerful current it is wrenched in two. It is\nseparated into a part having an image twist \u201chydrogen,\u201d which comes off\nat the zinc wire, and into a part with the twist \u201coxygen.\u201d\n\nBut this part with the twist calls up an image twist in the molecule\nnext to it, wrenches it in two. Thus the oxygen of the first molecule\nseparates up the next molecule into hydrogen and oxygen. The oxygen has\na twist, the hydrogen an image twist. These twists run each other out,\nand leave an oxygen part free.\n\nThis oxygen part does the same to the next molecule, and so this action\nis transmitted through the whole body of the water till the carbon wire\nis reached\u2014when, the oxygen part finding no other molecule to wrench\nasunder, is left isolated, and comes off in the form of gas.\n\nThus we see that oxygen and hydrogen would be bodies having in them\ntwist and image twist\u2014that is, that they would have an active rotation\neach of them; but the rotation would be different in the two cases, and\nsuch that if put together they would run each other out: the light and\nheat produced by the union of the two being probably the exhibition of\nthe effects of this running out.\n\nIf we adopt the supposition, which seems most in accordance with facts,\nthat there are in water two different elements occurring in distinct\nparticles, the one called oxygen, the other hydrogen; and if, moreover,\nwe suppose that these particles are perpetually changing places, and\nthat each oxygen particle is sometimes linked with this hydrogen\nparticle, sometimes with that, then it is obvious that the oxygen and\nthe hydrogen in the water are in such a state that, if collected\ntogether separately, they would form liquid oxygen and liquid hydrogen;\nand the effect of the electric twist is to give them those active image\nrotations, or strains, which make them take the gaseous form, and assume\nthat peculiar relation to each other which exhibits itself so strikingly\nin combustion.\n\nWith regard to magnetism, the same phenomenon of a particular state or\ndisturbance of matter and its image state or disturbance is very\nstrikingly obvious.\n\nFor take the case of a magnet. By the influence of an electric current\npassing round it, it can be turned into a magnet with opposite poles.\nThat is to say, the small particles of the iron have been so shifted\nthat, whatever their disposition was in the first case, they have now\nthe reverse disposition. If we suppose the small particles to be magnets\nlike the whole magnet, and all to have their north poles pointing in one\ndirection, then after the action of the current they have their north\npoles pointing in the opposite direction. But they have not turned in\nspace, for, if they were to turn, each must turn about some axis. But if\nthere was some axis then, with regard to this axis, the magnetic\ninfluence would have a definite relation; the turning of the particles\nwould take place in a certain plane, and there would be a certain plane\nin the magnet which would have special properties.\n\nBut a magnet is perfectly symmetrical in all its properties round its\naxis. The magnet which has had its poles reversed is, as an arrangement,\nthe image of itself in its first condition. In the solid mass of iron\nwhich forms the magnet, by the action of electricity, a particular\narrangement and its real image are alternately produced.\n\nThere are some very important electrical phenomena which have been left\nout of consideration altogether\u2014namely, the repulsions and attractions\nexercised by electrified bodies.\n\nAdopting the conceptions here laid down with regard to electricity\u2014that\nthe two kinds are in the relation of twist and image twist\u2014we find that\ncertain conclusions force themselves upon us.\n\nA positively electrified body attracts a negatively electrified body.\n\nA positively electrified body repels a positively electrified body.\n\nOr, as it is put in a shorter form, one kind of electricity attracts the\nopposite kind, and repels the same kind.\n\nNow, if our theory is true, a twist ought to attract its image twist,\nand repel a twist like itself.\n\nAnd as far as can be observed it is always a fact that a movement of any\nkind taking place in a medium does attract its image movement, and repel\na movement like itself.\n\nSome very instructive experiments have been made with bodies suspended\nin water, and caused to pulsate or twist. It would be found, on\nreferring to the details of these experiments, that if two spheres are\npulsating or throbbing, so that the movements of the one _are_ at any\ninstant what the movements of the other would _seem like_, if looked at\nin a mirror, then these two spheres will attract each other. If the one\nis a real copy of the other, then they repel each other. And this law\nholds good not only for throbbing movements, but also for twisting\nmovements.\n\nIf now we supposed that what held good for movements held good for\ntensions of the same nature as the movements, these results would be in\nexact accordance with our suppositions. If a twisting movement attracts\nits image twisting movement, will a twist attract its image twist by\nmeans of its effect on the medium in which it is, and on which it exerts\ntension? This point must be left undecided.\n\n\n\n\n                         Casting Out the Self.\n\n\nThe words which I have chosen as the title of this paper are the\nexpression for a process which has been asserted to be one that occurs\nalike in our mental and in our moral life. It has so happened that in\ncertain of my own inquiries I have applied this process; and the details\nmay be of interest. But I must warn the reader not to expect any wide\nviews on life, or far-reaching thoughts, or any of the warmth of human\naffairs. What I think about is Space; and it is the application of the\nprinciple of casting out the self in attaining a knowledge of Space\nabout which I have something to say.\n\nAnd, firstly, as a bit of absolute human experience is never without\nvalue, but that which we make up is often so, I may as well cast the\nfear of ridicule aside and enable the reader to take in, in a few lines,\nthe exact commencement of my inquiry.\n\nThe beginning of it was this. I gradually came to find that I had no\nknowledge worth calling by that name, and that I had never thoroughly\nunderstood anything which I had heard. I will not go into the matter\nfurther; simply this was what I found, and at a time when I had finished\nthe years set apart for acquiring knowledge, and was far removed from\ncontact with learned men. I could not take up my education again, but\nalthough I regretted my lost opportunities I determined to know\nsomething. With this view I tried to acquire knowledge in various ways,\nbut in all of them knowledge was too impalpable for me to get hold of\nit. And I would earnestly urge all students to make haste in acquiring\nreal knowledge while they are in the way with those that can impart it;\nand not rush on too quickly, thinking that they can get knowledge\nafterwards. For out in the world knowledge is hard to find.\n\nAt length I came to find that the only thing I could know was of this\nkind. If, for instance, there were several people in a room, I could not\nknow them themselves, for they were too infinitely complicated for my\nmind to grasp; but I could know if they were at right or left hand of\none another, close together, or far apart. And the same of, to take\nanother instance, botanical specimens in a book. I could not grasp the\nspecimens\u2014each was too infinitely complicated, and each part too\ninfinitely complex\u2014but I could tell which specimen was next which.\n\nAccordingly, being desirous to learn something thoroughly, and since, in\nthe arrangement of any different objects, there was such a lot of\nignorance introduced by the objects being different\u2014each bringing in its\nown ignorance and feeling of bewilderment\u2014I determined to learn an\narrangement of a number of objects as much alike as possible.\n\nAccordingly I took a number of cubes, which were as simple objects as I\ncould get, arranged them in a large block, and proceeded to learn how\nthey were placed with regard to each other. In order to learn them I\ngave each of them a name. The name meant the particular cube in the\nparticular position.\n\nThus, taking any three names, I could say, about the three cubes\ndenoted, how they were placed with regard to one another: one, say,\nwould be straight above the first with four intervening, the third would\ntouch the second on the right hand, or some similar arrangement.\n\nNow in this way I got what I conceived to be knowledge. It was of no use\nor beauty apparently, but I had no reason to use it or to show it.\n\nIt is about this bit of knowledge that I want to speak now\u2014a block of\ncubes, and the cubes are known each one where it is.\n\nSometimes I have been tempted to call this absolute knowledge, but have\nbeen reminded that I did not know the cube itself. Against this I have\nargued. But in argument we say many things which we do not understand,\nand my conclusion is, on the whole, that the objection is well founded.\nStill, if not knowledge absolute, the knowledge of this block approaches\nmore nearly to knowledge absolute than any other with which I am\nacquainted, because each cube is the same as its neighbour, and instead\nof an arrangement of all sorts of diverse ignorances we have only one\nkind of ignorance\u2014that of the cube. Each of the cubes was an inch each\nway, and I learnt a cubic yard of them. That is to say, when the name of\nany cube was said, I could tell at once those which it lay next to; and\nif a set of names were said, I could tell at once what shape composed of\ncubes was denoted. There were 216 primary names, and these, taken in\npairs, were enough to name the cubic yard.\n\nFor the practical purpose of this paper, however, it will suffice if the\nreader will imagine a block of twenty-seven cubes, forming a larger\ncube, each cube being denoted by a name (see Diagram I. below). Then it\nis evident that two names mean a certain arrangement consisting of two\ncubes in definite places with regard to one another\u2014three names denote\nthree cubes, and so on. And I would ask the reader not to mind taking a\nlittle trouble at this point, and to look at the diagram for a little\nwhile. If there is anything about which we can form perfectly clear\nideas, it is a little heap of cubes. And if the reader will simply look\nat them for a little space of time, he will realize clearly every word\nof what I have to say; for I am going to talk about nothing else than\nthis little block of cubes.\n\nThus, looking at the cube with the figure 1 upon it, this numeral will\nserve for the name of the cube, and similarly the number written on\nevery cube will serve for its name. So if I say cubes 1 and 2, I mean\nthe two which lie next to each other, as shown in the diagram; and the\nnumbers 1, 4, 7, denote three cubes standing above each other. If I say\ncubes 1 and 10, I mean the first cube and one behind it hidden by it in\nthe diagram.\n\n  [Illustration: Diagram I, a block consisting of 27 cubes.]\n\n  [Illustration: Diagram II.]\n\nNow this is the bit of knowledge on which I propose to demonstrate the\nprocess of casting out the self. It is not a high form of knowledge, but\nit is a bit of knowledge with as little ignorance in it as we can have;\nand just as it is permitted a worm or reptile to live and breathe, so on\nthis rudimentary form of knowledge we may be able to demonstrate the\nfunctions of the mind.\n\nAnd first of all, when I had learnt the cubes, I found that I invariably\nassociated some with the idea of being above others. When two names were\nsaid, I had the idea of a direction of up and down. But with regard to\nthe cubes themselves, there was no absolute direction of up or down. I\nonly conceive of an up and down in virtue of being on the earth\u2019s\nsurface, and because of the frequent experience of weight. Now this\ncondition affecting myself I found was present in my knowledge of the\ncubes. When certain of the names were said, I conceived of a figure\nhaving an upper part and a lower part. Now, considered as a set of cubes\nrelated to one another and not to me, the block had nothing to do with\nup and down. As long ago as Ptolemy, men have known that there is no\nsuch thing as an absolute up and an absolute down. And yet I found that\nin my knowledge of the set of cubes there was firmly embedded this\nabsolute up and this absolute down. Here, then, was an element arising\nfrom the particular conditions under which I was placed, and the next\nstep after recognizing it was to cast it out. This was easily done. The\nblock had to be turned upside down and learnt over again with the cubes\nall in their new positions. It was, I found, quite necessary to learn\nthem all over again, for, if not, I found that I simply went over them\nmentally the way first learnt, and then about any particular one made\nthe alteration required, by a rule. Unless they were learnt all over\nagain the new knowledge of them was a mere external and simulated\naffair, and the up and down would be cast out in name, not in reality.\nIt would be a curious kind of knowing, indeed, if one had to reflect\nwhat one knew and then, to get the facts, say the opposite.\n\nIt may seem as if, when the cubes were known in an upright position,\nthey would be easily imagined in an inverted position. But practice\nshows that this is very far from being the case. It requires\nconsiderable mental effort to determine the alterations in position, and\nto get an immediate knowledge requires a considerable time.\n\nIt may seem as if it were a dubious way of getting rid of gravity, or up\nand down, just to reverse the action of it.\n\nBut this way is the only way, for we, I have found, cannot conceive it\naway; we have to conceive it acting every way, then, affecting each view\nimpartially, it affects none more than another, and is practically\neliminated.\n\nThe cube had not only to be turned upside down, but also laid on each of\nits sides and then learnt. There were a considerable number of\npositions, twenty-four in number, which had to be brought close to the\nmind, so that the lie of each cube, relative to its neighbours and the\nwhole block, was a matter of immediate apprehension in each of the\npositions.\n\nIf a single cube be taken and moved about, it will be found that there\nare twenty-four positions in which it can be put by turning it, keeping\none point fixed, and letting each turning be a twist of a right angle.\nThe whole block had to be turned into each of these positions and learnt\nin each.\n\nThus the block of cubes seemed to be thoroughly known.\n\nAt any rate, up and down was cast out. And we can now attach a definite\nmeaning to the expression \u201ccasting out the self.\u201d One\u2019s own particular\nrelation to any object, or group of objects, presents itself to us as\nqualities affecting those objects\u2014influencing our feeling with regard to\nthem, and making us perceive something in them which is not really\nthere.\n\nThus up and down is not really in the set of cubes.\n\nNow these qualities or apparent facts of the objects can be got rid of\none at a time. To cast out the self is to get rid of them altogether.\n\nAs soon as I had got rid of Up and Down out of the set of cubes I was\nstruck by a curious fact.\n\nIf in building up the block of cubes one _goes_ to the left instead of\nto the right, keeping all other directions the same, a new cube is built\nup having a curious relation to the old cube. It is like the\nlooking-glass image of the old cube. Every cube in the new block\ncorresponds to every cube in the old block, but in the new figure it is\nas much to the left as before it was to the right. And any set of names\nin the block so put up gives a shape which is like the shape denoted by\nthe same set of names in the old block, but which cannot be made to\ncoincide with it, however turned about. It is the looking-glass image of\nthe old shape. The one block was just like the other block, except that\nright was changed into left. Now, was it necessary to cast out right and\nleft as had been done with up and down? or was right and left, as giving\ndistinctions in the block and in shapes formed of cubes, to remain? It\nseemed as if right and left belonged more to me than to the set of\ncubes. And yet the right-handed set of cubes could not be made by moving\nabout to coincide with the left-handed set of cubes. And this power of\ncoincidence was the test which had convinced me of the self nature of\n\u201cUp and Down.\u201d\n\nLet Diagram I. represent a small block of cubes. It is itself in the\nform of a cube, and it contains 27 cubes. For purposes of reference we\nwill give a number to each cube, and the number will denote the cube\nwhere it is.\n\nIn the front slice are cubes numbered from 1 up to 9, in the second\nslice are cubes numbered from 10 to 18, and so on. Thus behind 1 is the\ncube 10. This cube and the cube 11 are hidden, but the cube 12 is shown\nin the perspective.\n\nNow in this block of cubes there is a part which is known and a part\nwhich is unknown. The part which is known is how they come or the\narrangement of them. The part that is unknown is the cube itself,\nrepetitions of which in different positions forms the block.\n\nThe cube itself is unknown, because, being a piece of matter, it\npossesses endless qualities, each of which grows more incomprehensible\nthe more we study it. It is also unknown in having in it a multitude of\npositions which are not known. The cube itself is, amongst other things,\na vastly complicated arrangement of particles. Hence, _putting all\ntogether_, we are justified in calling the cube the unknown part; the\narrangement, the known part.\n\nThe single cube thus is unknown in two ways. It is unknown in respect to\nthe qualities of hardness, density, chemical composition, &c. It is also\nunknown as a shape. If it really consisted of a certain number of parts,\neach of which was clear and comprehensible in itself, then we should\nknow it if we grasped in our minds the relationship of all these parts.\nBut there are no definite parts of which a cube can be said to be made\nup. We can suppose it divided into a number of exactly similar parts,\nand suppose that all are like one of these parts. But this part itself\nremains, and the problem remains just the same about this part as about\nthe whole cube.\n\nNow there is a double perplexity: one about the nature of the matter,\nthe other about the cube as to the arrangement of its parts. We will\ngive up any question about the matter of which the cube is composed; to\nknow anything about that is out of the question. But, supposing it to be\nof some kind of matter, it presents an inexhaustible number of\npositions. It can be divided again and again.\n\nLet us look at the block again, and for the moment dismiss from our\nminds the question just raised as to the single cubes of which it is\nbuilt up. Let us look on each of these cubes as a unit. Then two of the\nunits, taken together, form a shape; three or five of them would form a\nmore complicated shape, and so on.\n\nWe can also suppose the cubes away, and think merely of the places which\nthey occupied. In this manner, by first thinking of the 27 cubes, and\nthen simply by keeping the places of them in our minds, we get 27\npositions, and in these positions we can suppose placed any small\nobjects we choose. Each of these positions may be called a unit\nposition, and we can form different arrangements of small objects by\nputting them in different ones of these positions. Now in all this we do\nnot divide the cube up. We simply think of it as a whole\u2014we think of it\nas a unit. Or if we take the room of the cube instead of the cube, and\nthink of the place it occupies, which I call a position, we do not\ndivide that position up. We take it, if I may use the expression, as a\nunit position. And _without asking any question as to the nature of\nthese positions, whether they are complicated ideas or not_, we have a\nkind of knowledge of the whole block, in that it consists of this\ncollection of 27 cubes, or of this set of 27 positions.\n\nThus in a rough and ready manner there is something which we can take.\nIf we do not inquire about one of the cubes itself, we are all right;\nthat being granted we can know the block.\n\nBut if we look into what each of these unit cubes, or what each of these\nunit positions is, we find quite an infinity opening before us. There is\nnothing definitely of which we can say that the whole unit cube is built\nup, and each of the positions has a perfectly endless number of\npositions in it, if we come to examine it closely. All that we can say\nis that our ignorance about each of the unit positions is of the same\nkind as our ignorance about every other, and, taking one as granted, we\nmay as well take the 27 as granted; and so out of a lot of similar\nignorances we get a kind of knowledge of the whole. And this knowledge\nis not a mere indefinite thing, but it can be worked at, improved, and\nmade perfect after its kind. For suppose we limit ourselves to the 27\npositions numbered in Diagram I. Two of these positions form one shape,\nthree of them will form another shape, and so on. And in going over each\nof these arrangements we gradually get to know the whole set of them\nwhich form the block.\n\nHaving given up for the time any question as to the possible\nsubdivisions of the cube, and looking on each cube as a unit position,\nwe have 27 positions. These positions can be taken in different\nselections, and each selection is a shape. To know the block or set of\npositions means to form a clear idea of every shape, consisting of\nselections of positions, which can be formed out of the 27.\n\nBut each of the cubes, 27 of which form the whole block, can be divided\nup. Each of these cubes contains a great many positions. There must, for\ninstance, be positions in each cube for every one of its molecules.\n\nThus it is evident that the cube supplies an inexhaustible number of\npositions to be learnt. I call the cube unknown in the sense that there\nare a great number of positions in it which are not clearly realized by\nthe mind.\n\nBy a very simple device it is possible to penetrate a little into the\nunknown part. The whole set of cubes forms a cube. Let us consider the\nsmall cube to be a model of the whole cube. Let us consider it as\nconsisting of 27 parts, each related to the other as the 27 first cubes\nwere related amongst themselves. Thus the unknown part, the material\ncube, which is used to build up the whole, becomes reduced in size.\nDiagram II. represents such a cube.\n\nThis is the theory. The practical work consisted in learning the names\ndenoting these smaller cubes in connection with their positions, so\nthat, the names being said, the small cubes meant were present to the\nmind, and a set of names being said, the shape, consisting of a set of\ncubes in definite relations to each other, came vividly before one. A\ncomplete knowledge of the block of cubes would be a complete\nappreciation of all the possible shapes which selections of the cubes\nwould form, and this I strove to attain. Here at length I found real\nknowledge, and after a time I was able to reduce the size of the unknown\nstill further, and to obtain a solid mass of knowledge fairly well\nworked all through.\n\nAnd now it all seemed satisfactory enough. There was real knowledge in\nknowledge of the arrangement; and the material cube, which must be\nassumed, could be made smaller and smaller, it could be turned into\nknowledge, thus affording a prospect of obtaining endless knowledge.\nThus I found the real home of my mind, the only knowledge I had ever\nhad, and I hoped always to continue to add to it, and always to reduce\nthe unknown in size.\n\nPresently, too, the forms of the outward world began to fall in with\nthis knowledge; and as the mass of known cubes became larger in number,\na group of them would fairly well represent a wall, a door, a house, a\nsimple natural object such as a stone or a fruit.\n\nYet amidst all this delight I became conscious, dimly enough, of a\nself-element in the knowledge of blocks.\n\nIf, putting up the block of cubes, we go to the left instead of the\nright, but in all other respects build up in the same way, we obtain a\nblock which has a curious relation to the first block.\n\nThe ordinary block is shown over again in Diagram III. Diagram IV. is\nthe new block. The new block is like a looking-glass image of the old\nblock. It is just the same, but that left and right is reversed.\n\nAlso, if we take selections of blocks we get figures which are just\nreversed. Thus 1, 4, 7, 8, in Block III., means a figure turned to the\nright; in Block IV. a figure turned to the left.\n\nAgain, consider the two figures formed by selecting the cubes 1, 4, 7,\n8, 17, from Diagrams III. and IV. respectively. We get two figures which\nare just like one another as arrangements, but which we cannot turn into\none another by twisting.\n\n  [Illustration: Diagram III. is a block.]\n\n  [Illustration: Diagram V.]\n\nConsidered as arrangements in themselves, these figures and these blocks\nseem to be identical, for the relationships of cube to cube which are\npresent in the one are all present in the other. But considered as\nshapes they are not identical. For they will not coincide.\n\nThe whole matter becomes much more clear if we consider the relationship\nbetween the individual cube used and the block which it forms.\n\nThere are two starting-points, either of which we can adopt. We can\nstart with the real material cube, or we can start with the act of\narranging. When I speak of the real material cube I do not want to call\nattention to the kind of matter of which it is composed, or to the\nnature of matter, but to the fact that it is to be a real cube such as\ncan be made, and which, if one edge or corner be marked, will retain\nthat mark just where it is\u2014a cube which is not a product of the\nimagination, but an object, with the properties of objects in general.\n\n  [Illustration: Diagram IV. is its image block.]\n\n  [Illustration: Diagram VI.]\n\nLet us start with the real material cube. Let us take the cube shown in\nDiagram V., which is the model on a small scale of the Block III. The\nnumbers in it show the small cubes of which we suppose it to be built up\nafter the pattern of Block III. The numbers also serve to show the\ndistinction of positions\u2014that is, we can refer to the right-hand corner\nor edge, &c., by saying the numbers of the small cube which lies there.\n\nNow, using the cube of Diagram V. to build up the block in Diagram III.\nwe get a perfectly orderly result, as shown in Diagram VII., and we can\ngo to bigger and bigger blocks, or down to smaller and smaller ones\nwithout any hitch. But if we use the cube of Diagram V. to build up the\nblock of Diagram IV., there is a disadjustment which can be discerned in\nDiagram VIII. Thus, when V. is used to build up III., the small cubes in\nV., 1, 4, 7, lie in same edge as the cubes 1, 4, 7, in the big Cube III.\nBut when V. is used to build up IV., the small cubes 3, 6, 9, lie on the\nedge which is occupied by the cubes 1, 4, 7, in big Cube IV.\n\n  [Illustration: Diagram VII.\u2014Block III. built up with Cube V.]\n\n  [Illustration: Diagram VIII.\u2014Block IV. built up with Cube V.\u2014a\n  disadjustment.]\n\nThus, if the same material cube is used, there is a disadjustment, and\nthe figure IV. cannot be considered the same as the figure III. even as\nan arrangement, for the same parts of the cubes do not lie in an\nanalogous manner. A certain corner of Cube V. is marked with the figure\n7; this corner would be on the outside in Block III., but in building up\nBlock IV. it would lie on the inside.\n\nIt is somewhat difficult to express this fact, but if the real cubes are\nlooked at it becomes perfectly obvious.\n\nImagine the whole Block III. to be built up of a number of cubes, every\none of which is alike. If the sides of these cubes be distinguished by\nany markings\u2014if, for instance, the left-hand side is blue and the other\nsides are each of some special colour, then on building up the whole\nblock the left-hand side of the whole block will be blue.\n\nIf, now, the same cubes be taken, and the attempt be made to build up\nthe looking-glass image of the block with them, it will be found that\nthere will be a disadjustment. If the blue sides are made to go to the\nright, as they must, to form an image block, then some other sides will\nbe in different places to what they should be in order to produce an\nimage of the original block. Although considered as an arrangement of\ncubes the new block will be an image of the original block, still,\nlooking at the individual cubes of which it is composed, it will be seen\nthat the new block is not an exact image of the old block.\n\nIf, however, we take the other starting-point, and, not assuming any\nfixed fundamental cube, look only at the act of arrangement, the two\nBlocks, III. and IV., are found to be identical in every internal\nrelationship.\n\nFor, taking the act of arrangement as the basis, if, when we have built\nup the Block IV., we look upon each of the cubes as an arrangement of\nthe same kind as the whole, then the cube 1 in Diag. IV. is represented\nin Diag. VI. And it is evident that if Diag. IV. is built up out of\ncubes like Diag. VI., the small cubes, 1, 4, 7, lie in the same edge as\nthe cubes 1, 4, 7, in Diag. IV. Thus it will be found for every\nrelationship in Diag. III. there is an exactly similar relationship in\nDiag. IV.\n\nIn this case if, for the sake of material illustration, we use marked\ncubes, it seems that we must not suppose each particular cube to have a\nfixed marking of its own, but that we must suppose the markings to\nspring up on the sides of the cubes in accordance with the places into\nwhich they are put.\n\nThere is another manner of regarding the matter which may help to bring\nout the point at issue.\n\nIf we suppose that we are putting up the cubes in one room while another\nperson is putting up cubes in an adjoining room; if we can tell him what\nwe are doing, using the words right and left, he will be able to put up\na block exactly like ours. But if we do not allow ourselves to use the\nwords right and left, but speak to the other person as if he were simply\nan intelligence without having the same kind of bodily organization as\nourselves, we should find that, supposing he could put up the block of\ncubes, it would be a mere matter of chance whether he had put up the\nblock as we had put it, or whether he had put it up in an image way. And\nthe same with regard to any shape. We could tell him that the cubes\nshould be put together, and we could tell him the relationship which\nthey should have with regard to one another; but the figure he put up\nwould just as likely be an image of our shape as not.\n\nAnd we could go on for ever building more and more complicated shapes\nand telling him to do the same, and no hitch or difficulty would come.\nBut at the end all his shapes might be ours just reversed, as if seen in\na mirror.\n\nAnd if, having put up the block, we coloured the sides of the cube we\nused as the fundamental cube, and told him how we had coloured it: if he\ncoloured his and brought it to us, and we compared them, his would just\nas likely be the image of our cube, and not able to be turned into it.\nSo that although, as arrangements, the structures we had put up were\nalike, still neither of us could use the other\u2019s fundamental cube; and\nif we exchanged the fundamental cubes there would be an inconsistency in\neach of our arrangements.\n\nNow, are these blocks of cubes really the same? Are III. and IV. really\nthe same in themselves, as all relationships in the one are to be found\nin the other? If so, the feeling on my part that they are different, and\nthe inconceivability of their coinciding, must be due to some\nself-element which is mixed up with my apprehension of the cube.\n\nThe Block IV. is like the Block III. in its known part\u2014in its\narrangement. It is unlike Block III. in its unknown part\u2014the cube which\nmust ultimately be supposed as the fundamental cube, by using which over\nand over again the whole is built up.\n\nNow, the properties of the unknown part\u2014the little cube of matter which\nof some size or another, we must assume, are so mysterious that one does\nnot feel any argument very safe which rests on it.\n\nMoreover, there is a very obvious consideration which reduces the\nimportance of the part played by the material cube very considerably.\n\nIt is possible to consider the Cube V., which is used to build up III.,\nas the total of 27 cubes.\n\nBut each of these cubes\u2014the small cubes in Diag. V.\u2014can be considered to\nbe made up of 27 still smaller cubes.\n\nBy going on in this way we can get our fundamental cube very small\nindeed. The difference between the Cubes III. and IV., in respect to\nthis fundamental cube, will still remain. But omitting this difference\nthey will be, considered as arrangements, identical.\n\nTo state the matter over again. We start with a real cube, one inch each\nway, and build up the block in Diagram III. with it. If we try to build\nup the block in Diagram IV. with this same inch cube, we find that there\nis a disadjustment.\n\nBut we are not obliged to have our fundamental cube one inch in size. We\ncan take it as small as we like, and build up the block, using a greater\nnumber of such cubes. We can take it the twenty-seventh of the\ntwenty-seventh of an inch cube; or, in fact, as small as ever we like.\nAnd if we take a very small cube as the fundamental one with which we\nbuild up the Block III., then, using this same fundamental cube to build\nup Block IV., we should find a disadjustment, although this\ndisadjustment would only come in when we come down to the very minute\ncube, and studied its relationship to the whole Block IV.\n\nThus, apparently, the Block IV. could never be built up consistently,\nusing as its fundamental cube the fundamental cube out of Block III. But\nin saying this we have really made an assumption.\n\nIt is obvious that Cubes V. and VI., just like Cubes III. and IV.,\nconsidered as shapes made up of matter, are very different, and could\nnot be shifted one on to the other.\n\nBut all our laws and feelings about movements and possibilities are\nfounded on the observation of objects having a certain degree of\nmagnitude.\n\nBut the fundamental cube, which we must assume, may be supposed to be of\na degree of magnitude less than any known degree.\n\nIn cubes of a certain size V. and VI. are different, and cannot be made\nto coincide.\n\nBut we are absolutely unable to say anything about cubes beyond a\ncertain degree of smallness. With cubes of a certain degree of\nminuteness, V. and VI. might be able to be made coincide.\n\nThus, for instance, we feel as if we could divide a piece of matter on\nand on for ever. But chemists tell us that, after a certain number of\ndivisions, the next division would split it up into two different kinds\nof matter. Since all our reasoning is founded on the behaviour of\nobjects of known size, we can tell nothing at all by inference about the\nbehaviour of very small objects.\n\nIt is obvious that, from our customary experience, we can assert\nabsolutely nothing at all about the extremely minute or the extremely\nlarge. All reasoning which is founded on the likeness between the\nextremely small and the ordinary objects of our observation is\nabsolutely valueless as telling us any truth.\n\nOf course, by saying this we have not got rid of the argument for the\ndifference of III. and IV. But we have put the thing from the\nobservation of which that argument is drawn out of the region of known\nthings. We have put it into the hazy land of the extremely minute. Its\nargument is good, but it depends on its being of a certain size. We\nsuppose it less than that size, and we can consider the subject without\nregard to its argument.\n\nThe question then before me was, Is \u201cRight and Left\u201d to be cast out? And\nconnected with this was the consideration of whether it was possible for\nextremely minute cubes to be \u201cpulled through,\u201d that is, to be treated\nsomehow which would turn one like V. into one like VI.\n\nNow, if \u201cright and left\u201d was a self-element, it could be cast out; if it\nwas a permanent distinction in the cubes themselves, it could not be\ncast out. The thing to do was evidently to try. The method was to learn\nthe cubes over again, in a set of new positions. For every one of the\nways in which they were learnt before, there was an inverted or pulled\nthrough way to be learnt.\n\nWhile I was engaged in this attempt another inquiry suddenly coincided\nwith this, and explained it all.\n\nMuch has been said about the fourth dimension of space and the\ninconceivability of it to us. Now, if there are beings who live in a\nfour-dimensional world, they must feel as habituated to it as we do to\nours, and the conceptions which seem so impossible to us must be\nevery-day matters to them. It would be impossible for us to try to enter\nat once into the serious thoughts of these denizens of higher space. But\namongst them there would probably be some with whose occupations we\nmight become familiar, and with whose ideas we might gain some\nacquaintance. Amongst these beings there must be children, and just as\nchildren on the earth gain their familiarity with space by means of\nbricks and blocks and toys, so these higher children must have their own\nsimple objects wherewith they grow into familiarity with their complex\nworld.\n\nNow it is easy to make a set of simple objects such as these higher\nchildren would use. And it seemed a practical thing to do with regard to\nthe conceivability or inconceivability of the fourth dimension to give\nthe matter a fair trial, by going through those processes and those\nexperiences which must be gone through by the beings in higher space to\ngain their acquaintance with it.\n\nWhen I say that it is easy to make a set of objects, such as the higher\nchildren use, I do not mean to say that they can be made completely in\nevery part at once. But we can make the ends and sides of them, and we\ncan look at the ends and sides of them as they appear to us in space,\nand we can make up exactly what sides come into space when the simple\nobjects are twisted and moved.\n\nJust as a being living on a plane could tell about all the faces and\nedges of a cube or other simple solid figure by looking at what he could\nsee when the cube was laid on his plane, and when it was twisted and\nlaid down again; so we can tell all about the sides, faces, and edges of\na higher solid.\n\nAnd the project seems less uninviting if we reflect on how complicated a\nmatter the formation of our own conceptions of a solid are. What a lot\nof faces and edges a cube has! And, moreover, it must be remembered that\nwe never touch or see a solid; we only see the surface and touch the\nsurface. If we cut away the surface that we first saw or touched, we\ncome on another surface, and so on.\n\nNow, of course, the surfaces of a solid are given to us by nature in\ntheir right connection and relation. Each of the edges of the cube, for\ninstance, can be noticed and remarked without any difficulty, and they\nare all on the same bit of space, to be looked at one at the same time\nas another.\n\nBut the sides, faces, and edges of a higher solid cannot be in our space\nall at once. They must come separately, be looked at one by one.\n\nThus a being in a plane could not see the lower side and the front of a\ncube at once. He would first have to look at the lower side as the cube\nrested on his plane, then if the cube were turned over he would see the\nfront, and the lower side would be gone. If he got the set of right\nappearances which a cube would present to him when, turning about in a\nsystematic way, it came at intervals into his plane, and if, moreover,\nhe fixed his mind on these appearances, he might at last, if it was in\nhim, rise to the conception of a cube as we know it.\n\nNow, the parts by which a higher solid comes into our space are solids,\nand what we have to form is a set of solids coming and going in a\nsystematic way, as the higher figure is moved about in a systematic way.\n\nThis afforded a welcome exercise, for conceiving the solid shapes, and\nhow they went and came, increased my familiarity with the set of cubes.\n\nMoreover, in trying to get the piece of ignorance\u2014the necessary real\ncube\u2014as small as possible, I had got the block which I knew to a\nsomewhat fine state of division, and could, by picking out a particular\nset of cubes from the whole number, obtain a mental model of any shape I\nwanted. The whole block of cubes formed a kind of solid paper in which\none could mentally put down any solid shape one wanted. And just as it\nis a great convenience to have a piece of paper for drawing figures one\nwants to think about, so it was a great convenience to have this solid\npaper.\n\nThe subject, however, abounds in abysses for stupidity to fall into, and\nI had to clamber out of each of them; so it took me several years before\nI got quite on the right tack. Then it was easy enough: any one in a few\nweeks could learn to conceive four-dimensional figures. Not only is it\neasy, but there are abundant traces that we do it continually without\nbeing aware of it. I am sure if the loveliness of the work while one is\ndoing it, and the simplicity and self-evident nature of the results when\nobtained, were generally known, it would be a favourite amusement.\n\nNow one of the first things that presented itself to my attention when I\nbegan to move the four-dimensional figures about was a fact which bore\ncurious reference to my difficulty about the fundamental cube. If the\nreader remembers, it seemed to me as if the cube out of which the whole\nblock of known cubes was built ought to be able to be inverted. That is\nto say, it seemed to me that there was a self-element present in my\nknowledge of the cubes. But in order to cast out that self-element the\nfundamental cube which lay at the basis of the whole block would have to\nbe able to be inverted, or pulled through.\n\nNow I found that when I took a four-dimensional figure which came into\nspace by a cube\u2014that is, a figure which rested on space by a cube, or\none of whose sides was a cube\u2014when I took a figure of that sort up in\nthe fourth dimension and twisted it round and brought it down again,\nthis cube would sometimes be inverted or pulled through\u2014although I had\ndone nothing to it, but had simply twisted the whole figure round\nwithout disturbing the arrangement of its parts.\n\nThus evidently to a higher child it would be no more difficult to invert\nor pull through a cube or a figure than it would be to me to twist one\nround.\n\nHence it was obvious that right and left was really a self-element in my\nblock of cubes. I being in our space was under a certain limitation, and\nthat limitation made me feel as if a right-handed arrangement was\ndifferent from a left-handed arrangement.\n\nA being who was not limited as I was would see that they were one and\nthe same. Hence, in knowing the set of blocks it was necessary to cast\nout \u201cright and left,\u201d and the names had to be learnt over again in new\npositions.\n\nThus it is evident that there are three expressions which may be\nconsidered in reference to a knowledge of a block of cubes as almost\nidentical: \u201cCasting out the self\u201d\u2014\u201cSeeing as a higher child\u201d\u2014and\nthirdly, \u201cAcquiring an intuitive knowledge of four-dimensional space.\u201d\n\nThus, taking the simplest and most obvious facts\u2014the arrangement of a\nfew cubes\u2014we found that there was a known part and an unknown part; the\nknown part corresponding to our act of putting, the unknown part the\ncube which, of some size or another, must be taken as given in the\nexternal world. Then there was obviously a self-element present in the\nUp and Down felt as in the cubes. This being removed, Right and Left had\nalso to go. So, to get the knowledge of this simple set of objects clear\nof self-elements, two universe transforming thoughts have to be used;\nand when these thoughts are thus incorporated the cubes become\ndifferent.\n\nIt will be obvious to the reader that in these pages I have merely\ntouched the surface of the subject. But the deeper matters which are\ncontained in the knowledge of a block of cubes are difficult to express,\nand are so mixed up with the practical work, as far as I conceive them\nat present, that it is best to consider in some detail the applications\nto the world about us of those truths of which we have already got a\nclear apprehension from the block of cubes.\n\nInstead, then, of going on, let us conclude the present paper by going\nback, and taking a simple instance of the general truth that progress in\nthe knowledge of a block of cubes is casting out the self.\n\nLet the reader turn to Diagram I. and make out the shape which the\nfollowing numbers denote\u2014namely, 1, 4, 5. If the following numbers be\nsaid, 18, 27, 26, it will be found that they denote the same shape, but\nin a different position. Now if the block of cubes be well known, these\ntwo sets of names, 1, 4, 5, and 18, 27, 26, ought to convey instantly to\nthe mind the same idea. However quickly they are realized, it ought to\nbe evident that they are the same shape.\n\nAnd a good deal of the practical work in learning a block of cubes\nconsists in gaining this faculty of immediate apprehension. But when it\nis gained it is seen to consist much more of getting rid of an\nimperfection than in being any real advance. For if the two shapes are\nidentical we need not ask ourselves how it is we see them as the same,\nbut we have to ask ourselves what is the reason why we do not recognize\ntheir identity; and the answer evidently is that, if we do not recognize\ntheir identity, it is due to the particular relationship of each shape\nto ourselves. One is down on our left hand, another is up on our right,\nand they are turned relatively to us different ways. Now these\ndifferences, which are merely relative to us, we impress upon the\nshapes, and really feel the shapes to be different. The practice\nconsists in getting rid of the influence of these self-elements, so that\ntwo shapes, however complicated, being alike, when their names are said,\nwe feel them to be alike without calculation or reflection. Thus the\npower of seeing likeness and analogy in this domain is merely another\nname for the power of casting out the self-elements from our mental\npresentation of any objects with which we come into contact.\n\n\n\n\n                               Footnotes\n\n\n[1]A B C D framework, X and Y two lines interlinked.\n\n[2]_See_ Appendix.\n\n[3]For details, see Appendix III.\n\n\n\n\n                          Transcriber\u2019s Notes\n\n\n--Retained publication information from the printed edition: this eBook\n  is public-domain in the country of publication.\n\n--Silently corrected a few palpable typos; left intentionally\n  nonstandard usage unchanged.\n\n--In the text versions only, text in italics is delimited by\n  _underscores_.\n\n--In the text versions only, superscript text is preceded by ^caret.\n\n--In the text versions only, subscript text is preceded by _underscore.","title":"Scientific Romances (First Series)","tradition":"philosophy-ethics","translated_text":null,"word_count":68698}