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ANOTHER WORLD; 
 
 OR, 
 
 THE FOURTH DIMENSION. 
 
 A. T. SCHOFIELD, M.D. 
 
 •ol St KaTaitudei/res toS atwyot iKetroy nocew.' 
 
 THIRD 
 
 EDITION 
 
 SWAN SONNENSCHEIN & CO., LIM. 
 25 HIGH STREET, BLOOMSBURV 
 
 190S 
 

 First Edition, /««<;, 1888 ; Second Edition, May, 1897; 
 Third Edition, August, 1905. 
 
To 
 
 PROFESSOR J. H. GLADSTONE, 
 
 Ph.Di, F.R.S., F.G.S., Etc., ETa» 
 
 IN GRATEFUL RECOGNITION 
 
 OF VALUED HELP, 
 
 THIS BOOK IS DEDICATED 
 
 BY 
 
 THE AUTHOR. 
 
ANOTHER WORLD; 
 
 OR, 
 
 THE FOURTH DIMENSION. 
 
 INTRODUCTORY. 
 
 It is undoubtedly the cherished belief of the 
 vast majority of mankind, whether they be 
 Christian, Mohammedan, Hindoo, or Heathen, 
 whether they be savage or civilized, in every 
 quarter of the globe, that there is another world 
 besides the material universe in which we live. 
 
 All unite in considering that world to be 
 a higher sphere than ours, and its inhabitants 
 to be more or less spiritual beings. 
 
 It is also generally believed that the beings 
 of that spirit world can and do visit ours, 
 
 B 
 
The Fourth Dimension 
 
 manifesting themselves in a human or animal 
 shape. 
 
 When we come, however, to further details 
 of this higher world, we have every diversity 
 of belief and superstition. 
 
 The only account and description of it to 
 which we, as Christians, attach any credence, 
 is found in the Bible, a book which we regard 
 as a revelation of its rulers, inhabitants, and 
 laws, given to man by the supreme Ruler, not 
 only of the spiritual, but of our material world, 
 God. 
 
 In our own persons we get confirmation 
 of the existence of a higher sphere, in being 
 able consciously to distinguish between our 
 spiritual, intellectual, and moral selves and our 
 bodies and brains, through which we act and 
 by which we live. 
 
 Materialists will, we know, have none of this. 
 To them, if true to their creed, there is, and 
 can be, nothing beyond the material. Mind, 
 
Introductory. 
 
 morals, feelings, passions, are to them only 
 protoplasmic changes of ganglion nerve cells, 
 producing carbonic acid gas and water. 
 
 To them the almost universal consensus of 
 opinion in favour of a spirit world goes for 
 nothing, unless such a world can be demon- 
 strated, handled, and weighed. 
 
 We therefore propose, in the following pages 
 to discuss from a somewhat new point of view 
 the question of the existence of such a world, 
 what are its powers, its laws, and its relation- 
 ship, with this universe, and in doing so, will 
 observe how far these powers and laws, deduced 
 by analogy from mathematics, correspond to 
 the spiritual claims of the Christian religion. 
 
 I would here take the opportunity of acknow- 
 ledging my deep indebtedness to the anony- 
 mous author of a small book, called "Flatland," 
 which I have used extensively throughout, and 
 without which I am quite sure the public would 
 never have been troubled with these remarks ; 
 
The Fourth Dimension. 
 
 my object being to carry on the line of argu- 
 ment there brought forward, to what seems to 
 me its true and necessary conclusion. 
 
 Finally, let me ask the indulgence of my 
 more advanced mathematical readers for the 
 many fallacies and " non-sequiturs " that doubt- 
 less abound, in spite of my true endeavours 
 simply and impartially to draw none but 
 legitimate and logical conclusions from the 
 arguments and facts I have advanced. 
 
 PREFACE TO THIRD EDITION. 
 
 Many speculations concerning the fourth di- 
 mension have been made since this book was 
 first issued, notably that by Mr. Wells that it is 
 " Time." But no theory carries conviction, and 
 indeed the whole is a speculation, the interest 
 however of which remains untouched in the 
 close parallel afforded between what would be 
 true of a fourth dimension and all that is written 
 or known concerning the spirit world. A few 
 additions have been made in this edition. 
 
 A. T, SCHOFIELD. 
 6 Harley Street, W., 
 August, 1905. 
 
CHAPTER I. 
 
 THE LAND OF NO DIMENSIONS. 
 
 We are all so habituated to take visible 
 realities around us as a matter of course, and 
 so accustomed to every variety of solid or 
 material form, that why all the universe should 
 be limited to solidity, or three dimensions, is 
 only asked at rare intervals by a few of the 
 more thoughtful among us. 
 
 To make this plain. Even those unac- 
 customed to algebra will understand that if x 
 represents three inches, or a line of this length, 
 sf {x square) represents 3x3, or nine square 
 inches on a flat surface, three inches each way ; 
 x^ (x cube), again, represents 3 x 3 x 3, or twenty- 
 seven cubic or solid inches, or a solid body 
 measuring three inches every way. Hence we 
 
The Fourth Dimension. 
 
 consider x as representing lines, ^ squares, 
 x? solids, and then comes the question, What 
 does x^ represent? for mathematics passes as 
 easily from x^ to x^ as from x? to x^, and yet 
 while X, xf, x^, refer to objects known to all of 
 us, the wisest can form no possible conception 
 of what X*, or a world of four dimensions, is 
 like. 
 
 Perhaps, however, before disturbing our 
 minds, and entering seriously upon the question 
 as to whether there can be and is any object 
 or world represented by x*, and whether or no 
 we can comprehend it, my reader will not be 
 offended if, for the benefit of those less learned 
 than himself, I labour in the simplest language 
 further to explain these various dimensions. 
 
 To begin : No dimension, or size in no direc- 
 tion, is represented mathematically by a point, 
 which is an object described as having no parts 
 or magnitude, thus : — 
 
 One dimension {x), or size in one direction. 
 
The Land of No Dimensions. 
 
 is represented mathematically by a straight 
 line, which is described as having length with- 
 out breadth, thus : — 
 
 Two dimensions {xf), or size in two directions, 
 is represented mathematically by a superficies 
 or surface, which is described ,as having length 
 and breadth without thickness, thus : — 
 
 Three dimensions {x% or size in three direc- 
 tions, is represented mathematically by a solid 
 body, which is described as having length, 
 breadth, and thickness, thus :— 
 
8 The Fourth Dimension. 
 
 Four dimensions (ar»), or size in four direclions, 
 we cannot represent mathematically, nor can 
 we describe in what direction its fourth dimen- 
 sion lies, nor can we draw, or even imagine it ; 
 the fact being that the whole material world 
 which we can see, and of which we can speak, 
 is a world of three dimensions (or x^) and no 
 more, nor is it possible for the mind of man to 
 indicate or imagine any other direction than 
 three — length, breadth, and height (or depth 
 or thickness, etc.). 
 
 On this account it is that so many have 
 denied the possibility of there being anything 
 higher than a solid. To show the fallacy of 
 this argument, then, we will consider the 
 imaginary case of an inhabitant of a country 
 where nothing but perfectly flat objects exist, 
 when an endeavour is made to explain to him 
 our own world of solids ; and by putting our- 
 selves in his place, and carefully observing the 
 difficulty he, accustomed only to x' or flatness, 
 
The Land of No Dimensions. 9 
 
 would have in grasping x^, or solidity, which 
 nevertheless exists, we may understand better 
 that the difficulty we in x^, or solidity, have in 
 our turn of grasping x^, or the fourth dimension, 
 is no argument whatever against the existence 
 of such a world. 
 
 First of all, however, we will consider the 
 still lower conditions of no dimensions and of 
 one dimension. 
 
 Imagine, then, a world or universe consisting 
 entirely and absolutely of a single point, a 
 country which therefore possesses neither 
 length, breadth, depth, nor height. Imagine 
 (if you can) the sole being in such a world, and 
 observe what his experience would be, as 
 described in " Flatland." ' 
 
 " He is himself his own world, his own 
 universe; of any other than himself he can 
 form no conception ; he knows not length, or 
 breadth, or height, for he has no experience of 
 
 1 "Flatland." Seeleys. 
 
lo The Fourth Dimension. 
 
 them ; he has no cognizance even of the 
 number two ; for he is himself one and all, 
 being really nothing. Yet mark his perfect 
 self-complacency, and hence learn this lesson, 
 that to be self-contented is to be vile and 
 ignorant, and that to aspire is better than 
 to be blindly and impotently happy. Now 
 listen! There arose from the little buzzing 
 creature a tiny, low, monotonous tinkling, from 
 which I caught these words. ' It fills all 
 space, and what it fills it is, what it thinks 
 that IT utters; and what it utters, that it 
 hears, and it itself is thinker, utterer, hearer. 
 It is the one, and yet the all in all.'" 
 
 This then gives us an idea of what a 
 world would be that consisted only of one 
 being, and that being having no parts or 
 size. 
 
 Having duly performed this excruciating 
 effort of imagination, and succeeded in realizing 
 what nothing, or " Pointland," really is, the 
 
The Land of No Dimensions. 1 1 
 
 exhausted reader had better pause for five 
 minutes before taking the next step higher 
 into the more interesting world of one dimen- 
 sion, or " Lineland," 
 
CHAPTER II. 
 
 THE LAND OF ONE DIMENSION. 
 
 Let now my faithful reader, somewhat re- 
 cruited from the study of Chapter L, proceed 
 to picture a world of one dimension — a uni- 
 verse that consists only of innumerable straight 
 lines, long and short, all arranged in one and 
 the same interminable straight line — nothing 
 else at all, no deviation to right or left, no 
 right or left even existing to this linear 
 world, still less any height or depth. To 
 duly appreciate and grasp the phenomena of 
 such a world, it would greatly assist the mind 
 if my reader were to arrange a number of 
 pencils or matches in one long line, end to 
 end, and follow the fragments with his eye. 
 
The Land of One Dimension. 13 
 
 Let not any think that these preliminary 
 studies are needless, for every link in the 
 chain of analogy must be carefully followed, 
 if we are to reach the important conclusions 
 we are here aiming at. 
 
 Let my reader, then, now retire into his 
 inner consciousness, and proceed to imagine 
 a kingdom or world, as we have said, consist- 
 ing of an infinite number of inhabitants, each 
 one being a shorter or longer straight line, 
 and all arranged in one and the same straight 
 line, thus : 
 
 If one end of these creatures or lines be 
 furnished with an eye, it is obvious they will 
 each see the end of the line next in front of 
 them, which will be a simple point. 
 
 None, therefore, in this line (or world) can 
 ever see anything beyond a point. To see a 
 line one must obviously be out of the line (or 
 the Land of One Dimension) altogether. 
 
 If this is not clear, place your eye at the 
 
14 The Fotirth Dimension. 
 
 end of any straight line (a needle or knitting 
 needle), and you will only see a single point. 
 
 Let the mind now proceed to picture a being 
 of two dimensions, such as a square (illustrating 
 it at the same time by a piece of cardboard), 
 furnished with an eye at one of its angles, 
 approaching this world of Lineland (Slide the 
 cardboard square along the table towards the 
 long line of pencils or matches, etc.) ; and then 
 listen to the following remarks from our un- 
 known author. The square speaks. 
 
 " I saw before me a vast multitude of small 
 
 straight lines, all moving to and 
 
 fro in one and the same straight line. Ap- 
 proaching the largest, I accosted it (Here 
 bring the square close to a match), but re- 
 ceived no answer. Losing patience at what 
 appeared to me intolerable rudeness, I brought 
 my mouth into a position full in front of it 
 {Here slide a corner of the square into the 
 line in front of the match), and repeated my 
 
The Land of One Dimension. 15 
 
 question. ' What signifies this monotonous 
 motion to and fro in one and the same straight 
 line ? ' 
 
 *" I am the Monarch of the World,' replied 
 the small line. 'But thou, whence intrudes! 
 thou into my realm of Lineland ? ' 
 
 "Receiving this abrupt reply, I begged 
 pardon ; and by persevering questions ex- 
 tracted the following facts : — 
 
 "It seems that this poor ignorant monarch, 
 as he calls himself, was fully persuaded that 
 the straight line which he called his kingdom, 
 and in which he passed his existence, consti- 
 tuted the whole of the world, and indeed the 
 whole of space. Not being able either to 
 move or see, save in his straight line, he had 
 no conception of anything out of it 
 
 " Though he had heard my voice when I 
 first addressed him, the sound had come to 
 him in a manner so contrary to his own ex- 
 perience, that he had made no answer, ' seeing 
 
1 6 The Fourth Dimension. 
 
 no "man,' as he expressed it, and ' hearing a 
 voice, as it were, from his own inside.' 
 
 " Until the moment when I placed my mouth 
 in his world, he had not seen me ; nor had he 
 now the least conception of the region from 
 which I had come. Outside his world or line 
 all was blank to him ; nay, not even a blank, 
 for a blank implies space ; say rather, all was 
 non-existent. Such a life, with all vision 
 limited to a point, and all motion to a straight 
 line, seemed to me inexpressibly dreary, and 
 I was surprised to note the vivacity and cheer- 
 fulness of the king." 
 
 Such were the observations of our supposed 
 living square, and such would be the only life 
 possible, were the world but one straight line. 
 Our square, however, rejoicing in his own two 
 dimensions of breadth as well as length, tries 
 to enlighten the king of Lineland, and pro- 
 ceeds : — 
 
 " Thinking that it was time to bring down 
 
The Land of One Dimension. 17 
 
 the monarch from his raptures to the level of 
 common sense, I determined to endeavour to 
 open up to him some glimpses of the truth ; 
 that is to say, of the nature of flat things, or 
 two dimensions. 
 
 " So I began thus : ' Before I entered your 
 kingdom, I noticed that some of the lines 
 were larger ' 
 
 " ' You speak of an impossibility,' interrupted 
 the king ; ' you must have seen a vision, for to 
 detect the difference (even) between a line and 
 a point by the sense of sight is, as every one 
 knows, in the nature of things, impossible. 
 How could you see a line, that is to say, the 
 inside of any man ? ' * 
 
 " ' / can discern a line from a point, and let 
 me prove it. Before I came into your king- 
 dom I saw you dancing backwards and for- 
 
 * A line having no breadth, its outsides (so to speak) 
 are its two extremities, that which lies between being the 
 inside of the line ; and this inside is naked and open to the 
 eye of our square in two dimensions, but can never be seen 
 by a being in one. This will become clearer as we proceed. 
 
 C 
 
1 8 The Fourth Dimension. 
 
 wards, with seven lines and a dot in front of 
 you, and eight lines and a dot behind you.' 
 
 "He then proceeds to tell the king that there 
 is another motion possible, besides backwards 
 and forwards ; namely, from left to right. 
 
 " ^ Let me ask,' said the king, ' what you 
 mean by these words "left" and "right." I 
 suppose it is your way of saying northward 
 (forwards) and southward (backwards).' 
 
 " ' Not so,' replied I ; ' besides your motion 
 of forwards and backwards, there is another 
 motion ; which I call from left to right.' 
 
 " ' Exhibit to me, if you please, this motion 
 from left to right.' 
 
 " ' Nay, that I cannot do, unless you could 
 step out of your line altogether.' 
 
 " ' Out of my line ? Do you mean out of 
 the world ? Out of space ? ' 
 
 " ' Alas ! How shall I make it clear ? When 
 you move straight on, does it not sometimes 
 occur to you .that you could move in some 
 
The Land of One Dimension. 19 
 
 other way ? Instead of always moving in the 
 direction of one of your extremities, do you 
 never feel a desire to move in the direction, so 
 to speak, of your side ? ' 
 
 " ' Never ! And what do you mean ? How 
 can a man move in the direction of his inside ? ' 
 
 " ' Well then, I will try deeds ; I will gra- 
 dually move out of Lineland in the direction 
 which I desire to indicate to you.' 
 
 " At this word I began to move my body out 
 of Lineland. As long as any part of me re- 
 mained in his dominion, and in his view, the 
 king kept exclaiming, ' I see you,' But when I 
 had at last moved myself out of his line, he 
 cried, ' He is dead.' (Move card slowly out of 
 the straight line.) 
 
 '" I am not dead,' replied I; 'I am simply out 
 of Lineland, that is to say, out of the straight 
 line which you call space, and at this moment I 
 can see your line, or side, or inside, as you 
 ai-e pleased to call it.' 
 
20 The Fourth Dimension. 
 
 " But the monarch replied, ' If you were a man 
 of sense, you would listen to reason. You ask 
 me to believe that there is another line beside 
 that which my senses indicate, and another 
 motion beside that of which I am daily con- 
 scious. I, in return, ask you to describe in 
 words, or to indicate by motion, that other line 
 of which you speak. Instead of moving, you 
 merely exercise some magic art of vanishing 
 and returning to sight. Acknowledge your 
 folly, or depart from my dominion.' 
 
 " Furious at his perversity, I retorted, ' Be- 
 sotted being, ypu think yourself the perfection 
 of existence, while you are in reality the most 
 imperfect and imbecile. You profess to see, 
 whereas you can see nothing but a point' " 
 
 We have given these extracts at length, in 
 order that the reader may fully grasp what 
 would be the general conditions of life, pros- 
 pects, and intelligence in a world of one dimen- 
 sion, and also the necessary impossibility of 
 
The Land of One Dimension. 21 
 
 one in such a world being able to understand 
 the existence of another by argument or illus- 
 tration. Various other suggestive analogies 
 present themselves here, but we will defer their 
 discussion until we have the other dimensions 
 before us, and then consider them all together. 
 In the next chapter, therefore, we will move a 
 step higher, and attentively view life in a world 
 of two dimensions. 
 
CHAPTER III. 
 
 THE LAND OF TWO DIMENSIONS. 
 
 We must now again tax the imagination of 
 our readers, and ask them to picture a country 
 of two dimensions, where only length and 
 breadth are known. This country our author 
 aptly calls " Flatland," and in order to pre- 
 sent it vividly before our readers, we must 
 again quote extensively. Our old friend, the 
 animated square, speaks.* 
 
 " Imagine a vast sheet of paper, on which 
 straight lines, triangles, squares, and circles, 
 
 *This chapter will be better understood if the reader 
 provides himself with a few squares, 'circles, triangles, etc., 
 cut out of cardboard, to represent the inhabitants, — the 
 country being represented by the top of the table on which 
 they are laid ; while a house • in Flatland may be easily 
 made by enclosing a space with bits of cotton. 
 
The Land of Two Dimensions. 23 
 
 instead of remaining fixed in their places, move 
 freely about on the surface — very much like 
 shadows — and you will have a pretty correct 
 notion of my country and countrymen. In 
 such a country you will perceive at once that 
 it is impossible that there should be anything 
 of what you call a ' solid ' kind, but I daresay 
 you will suppose that we could at least see 
 the triangles, squares, and other figures mov- 
 ing, about as I have described them. On 
 the contrary, nothing was visible, nor could be 
 visible to us, except straight lines." 
 
 Our readers will see the strict analogy 
 here : that just -as those in one dimension 
 could only see points, not lines, — so those 
 in two dimensions can only see lines, not 
 squares, etc. If the eye is placed on a level 
 (that is, in the same world) with the edge of 
 one of the cardboard figures, whatever its 
 shape, only a straight line will be seen ; for 
 it is only as we rise above or go below it — 
 
24 The Fourth Dimension. 
 
 that is, enter the third dimension — that we see 
 the shape of the figure. 
 
 The houses in " Flatland," according to our 
 author and to reason, consist of spaces en- 
 closed by lines, openings being left for doors. 
 Of course the idea of a roof to such houses is 
 necessarily absurd, there being no space ex- 
 cept in length and breadth in that world ; 
 hence the houses are to our ideas open. There 
 is a north, south, east and west ; the first two 
 being equivalent to length and the latter two 
 to breadth. 
 
 Of course, any being in such a house, when 
 the door was shut, though inaccessible and 
 invisible to any inhabitant of Flatland, could 
 be as easily touched and seen by us if out- 
 side the house. (One of the pieces of card- 
 board placed inside a circle of thread will 
 illustrate this.) 
 
 Such a world, then, being imagined, thickly 
 peopled with flat figures gliding incessantly 
 
The Land of Two Dimensions. 25 
 
 to and fro on the surface, or in and out these 
 spaces surrounded by lines, which they call 
 houses, we will now try and understand the 
 extraordinary experiences of our animated 
 square in Flatland, when, after having tried 
 and failed to enlighten the king of one 
 dimension, he is, in his turn, instructed by 
 a being from our world of solids, or three 
 dimensions. The incident occurred thus : — 
 
 "It was the last day of the year 1999 of 
 our era. My four sons and two orphan 
 grandchildren had retired to their several 
 apartments, and my wife alone remained with 
 me to see the old millennium out and the 
 new one in. 
 
 " I was wrapt m thought, pondering In my 
 mind some words that had casually issued 
 from the mouth of my youngest grandson. 
 Taking nine squares, each an inch every way, 
 I had put them together so as to form one 
 largfi square with a side of three inches, and 
 
26 The Fourth Dimension. 
 
 I had proved to my grandson that, though 
 it was impossible for us to see the inside of 
 this, or indeed of any square, yet we might 
 ascertain the number of square inches in a 
 square, simply by squaring the number of 
 inches in the side ; ' and thus,' said I, ' we 
 know that 3°, or 9, represents the number 
 of square inches in a square whose side is 
 three inches long.' 
 
 "The little Hexagon (my grandson) medi- 
 tated on this awhile, and then said to me : 
 ' But you have been teaching me also to raise 
 numbers to the third power; I suppose 3* 
 must mean something in geometry. What 
 does it mean ? ' 
 
 " ' Nothing at all,' replied I, ' not at least 
 in geometry; for geometry has only two di- 
 mensions.' And then I began to show the 
 boy how a point, by moving through a length 
 of three inches, makes a line of three inches, 
 which may be represented by 3 ; and how 
 
The Land of Two Dimensions. 27 
 
 a line of three inches, moving parallel to itself 
 through a length of three inches, makes a 
 square of three inches every way, which may 
 be represented by 3'. 
 
 " Upon this my grandson, again returning 
 to his former suggestion, took me up rather 
 suddenly, and exclaimed, — 
 
 " ' Well, then, if a point by moving three 
 inches makes a line of three inches, represented 
 by 3, and if a straight line of three inches 
 moving parallel to itself makes a square of 
 three inches every way, represented by 3°, — 
 it must be that a square of three inches every 
 way moving somehow parallel to itself (but 
 I don't see how) must make a something 
 else (but I don't see what) of three inches 
 every way, — and this must be represented 
 
 by 3V " 
 
 Let the reader observe here how the Hexa- 
 gon, by reasoning strictly by analogy, thus dis- 
 covers and describes a cube or solid figure. 
 
28 The Fourth Dimension. 
 
 "'Go to bed,' said I, a little ruffled by 
 his interruption. ' If you would talk less non- 
 sense, you would remember more sense.' 
 
 " So my grandson had disappeared in dis- 
 grace. Rousing myself from my reverie, I 
 exclaimed, ' The boy is a fool ! ' 
 
 " Straightway I became conscious of a pre- 
 sence in the room, and a chilly breath thrilled 
 through my very being. Looking round in 
 every direction, I could see nothing. I re- 
 sumed my seat again, exclaiming, ' The boy 
 is a fool, I say ; 3' can have no distinct mean- 
 ing in geometry.' 
 
 " At once there came a distinctly audible 
 reply, * The boy is not a fool, and 3^ has an 
 obvious geometrical meaning.' 
 
 " My wife, as well as myself, heard the 
 words, although she did not understand their 
 meaning ; and both of us sprang forward in 
 the direction of the sound. What was our 
 horror when we beheld before us a figure ! 
 
The Land of Two Dimensions. 29 
 
 "My wife retreated to her apartment. I 
 began to approach the stranger with the in- 
 tention of taking a nearer view. He remained 
 motionless while I walked round him, begin- 
 ning from his eye, and returning to it again. 
 Circular he was throughout ; there could not 
 be a doubt of it. Then followed a dialogue. 
 
 (The reader will be much helped if he will 
 illustrate this by first placing a cardboard 
 square inside a large circle of thread, and then 
 place a ball inside the circle ; or, better still, 
 let the surface of a basin of water represent 
 Flatland, and a floating circle of thread and 
 piece of cardboard the house and its inhabit- 
 ant, and then a ball, half immersed, the visitor 
 — capable of sinking through or rising out of 
 Flatland at will.) 
 
 " /. ' Before your lordship enters into fur- 
 ther communication, would he deign to satisfy 
 the curiosity of one who would gladly know 
 whence his visitor came ? ' 
 
3© The Fourth Dimension. 
 
 " Stranger. 'From space, sir ; whence else ?' 
 
 " /. ' Pardon me, my lord ; but is not your 
 lordship already in space — even at this mo- 
 ment ? ' 
 
 " Stranger. ' Pooh ! What do you know of 
 space ? Define space.' 
 
 " /. ' Space, my lord, is length and breadth, 
 indefinitely prolonged.' 
 
 " Stranger. ' Exactly. You see you do not 
 even know what space is. You think it is of 
 two dimensions only ; but I have come to 
 announce to you a third — height, as well as 
 breadth and length.' 
 
 "/. 'Your lordship is. pleased to be meri-y. 
 We also speak of length and height (which 
 are the same), or breadth and thickness (which 
 are the same), thus denoting two dimensions 
 by four names. 
 
 " Stranger. ' But I mean not only three 
 names, but three dimensions.' 
 
 " /. ' Would your lordship indicate or ex- 
 
The Land of Two Dimensions. 31 
 
 plain to me in what direction is the third 
 dimension ? 
 
 " Stranger. ' I came from it. It is up above 
 and down below.' 
 
 " /. ' My lord means, seemingly, that it is 
 northward and southward.' 
 
 " Stranger. ' I mean nothing of the kind. 
 I mean a direction in which you cannot look, 
 because you have no eye in your side.' " 
 
 (If the reader makes a dot for an eye on 
 the cardboard square, he will see that such 
 an eye in the "side" of the square would 
 look upwards. Observe also that the borders 
 of the square form its outside, and all of it 
 that can be seen by any one on the same 
 level, and that the surface of the square is 
 its inside, enclosed by the four borders.) 
 
 " /. ' Pardon me, my lord ; a moment's in- 
 spection will convince your lordship that I 
 have a perfect luminary at the junction of 
 two of my sides.' " 
 
32 The Fourth Dimension. 
 
 The reader will see the square palls his 
 borders sides, whereas the stranger refers to 
 the surface of the square. Both may be 
 called sides ; thus a cardboard square has 
 four sides, or two sides.* 
 
 " Stranger. ' Yes ; but in order to see into 
 space you ought to have an eye, not in your 
 border, but in your side — that is, what you 
 would probably call your inside; but we in 
 Spaceland call it your side,' 
 
 " /. 'An eye in my inside ! An eye in my 
 stomach ! ! Your lordship jests.* 
 
 " Stranger. 'I am in no jesting humour, 
 I tell you I came from space. From that 
 position of advantage I discerned your houses, 
 yea, even your insides, all lying open to my view.' 
 
 "/. 'Such assertions are easily made, my 
 lord.' 
 
 " Stranger. ' How shall I convince him i* 
 Surely a plain statement of facts, followed by 
 * By analogy these are of course " insides." 
 
The Land of Two Dimensions. 33 
 
 ocular demonstration, ought to suffice. Now, 
 sir, listen to me. You are living in a plane. 
 I am not a plane (or flat) figure, but a solid. 
 You call me a circle, but I am a sphere. Your 
 country of two dimensions is not spacious 
 enough to represent me, — a being of three; 
 but can only exhibit a slice or section of me> 
 which is what you call a circle. See, now I 
 will rise, and the effect on your eye will be that 
 my circle will become smaller and smaller, till 
 It dwindles to a point, and finally vanishes.' 
 
 " There was no ' rising ' that I could see ; 
 but he diminished, and finally vanished, and 
 then, after a while, reappeared and regained 
 his original size. He heaved a deep sigh, 
 for he perceived I had altogether failed to 
 comprehend him. Indeed, I was now inclin- 
 ing to the belief that he was an extremely 
 clever juggler. 
 
 "After a long pause he continued our dia- 
 logue 
 
 D 
 
34 i he Fourth Dimension. 
 
 " ' How many sides has a square, and how 
 many angles ? ' 
 
 " /. ' Four sides and four angles,' 
 
 " Sphere. ' Now stretch your imagination a 
 little, and conceive a square in Flatland (you 
 are a square) with its side, or what you call 
 its inside, moving parallel to itself, up- 
 wards.' " 
 
 (The reader performs this by just gradually' 
 raising the cardboard square from the ■ table 
 and parallel with it.) 
 
 " /. ' What ! northward ? ' 
 
 " Sphere. ' No ; not northward ; upward- 
 out of Flatland altogether.' 
 
 " Restraining my impatience, I replied : 
 ' And what may be the nature of the figure 
 which I am to shape out by this motion 
 which you are pleased to denote by the word 
 " upward " ? ' 
 
 " Sphere. ' A cube, with eight terminal points 
 (or angles).' 
 
 * This is exactly what the grandson suggested. 
 
The Land of Two Dimensions. 35 
 
 " /. ' And how many sides will pertain to 
 this being whom I am to generate by the 
 motion of my " inside " in an " upward " 
 direction ? ' 
 
 " Sphere. ' The cube which you will generate 
 will be bounded by six sides — that is to say, 
 six of your insides. You see it all now, eh ? ' 
 
 " ' Monster ! ' I shrieked, ' be thou juggler, 
 enchanter, dream or devil, no more will I 
 endure thy mockeries. Either thou or I 
 must perish.' 
 
 "And saying these words, I precipitated 
 myself upon him. It was in vain. I could 
 feel him slowly slipping from my contact — 
 not edging to the right or left, but moving 
 somehow out of the world, and vanishing to 
 nothing. But I still heard the intruder's voice. 
 
 " Sphere. ' Why will you refuse to listen to 
 reason ? I had hoped to find in you a fit 
 apostle for the gospel of three dimensions. 
 
 * Observe the inside of one dimension is always the out- 
 side of the dimension higher. 
 
36 The Fourth Dimension. 
 
 Listen, my friend. I have told you I can see 
 from my position in space the inside of all 
 things that you consider closed. For ex- 
 ample, I see in yonder cupboard, near which 
 you are standing, several of what you call 
 boxes (but like everything else in Flatland, 
 they have no tops or bottoms) full of money. 
 I see also two tablets of accounts. I am 
 about to descend into that cupboard, and to 
 bring you one of those tablets. I saw you 
 lock the cupboard half an hour ago, and I 
 know you have the key in your possession. 
 But I descend from space ; the door, you see, 
 remains unmoved. Now I am in the cup- 
 board, and am taking the tablet. Now I have 
 it. Now I ascend with it.' 
 
 " I rushed to the closet, and dashed the 
 door open. One of the tablets was gone; 
 At the same time it appeared on the floor 
 of the room." 
 
 All this, however, failed to convince our 
 
The Land of Two Dtmensions. 37 
 
 square, who at last threw himself in impotent 
 rage upon the apparent circle again. 
 
 The sphere then, unwilling to leave him 
 in his ignorance, as a last resource lifted our 
 poor square right up out of Flatland — out of 
 the land of two dimensions altogether — into 
 our world of spar*\. of three dimensions. Here 
 we will follow him in the next chapter. 
 
CHAPTER IV. 
 
 THE LAND OF THREE DIMENSIONS. 
 
 The first object that met the bewildered gaze 
 of our square, when thus finally translated from 
 the world of two dimensions into that of three, 
 was the perfect figure of the sphere beside 
 him, still appearing as a curiously shaded flat 
 circle, this being the first surface he had ever 
 gazed upon ; all flat objects, when in his own 
 country, appearing, as we have seen, as straight 
 lines. 
 
 He then turned his wondering eyes down- 
 wards, and beheld to his amazement Flatland 
 as it really was, with its flat inhabitants of 
 different shapes all snugly ensconced in their 
 different rooms of their roofless houses, all of 
 which were of course now perfectly open to 
 
 38 
 
The Land of Three Dimensions. 39 
 
 his view. He could gaze down upon his own 
 house and the room he had just quitted, and 
 could see his wife and children. He, in his 
 turn, now could look into his own locked 
 cabinet, and discern the very tablets already 
 spoken of 
 
 But as he was carried higher he saw more. 
 His whole native city, hitherto known to him 
 only as lines, lay revealed, with the shape of 
 every inhabitant equally plainly to be seen, 
 whether in the street or within doors. 
 
 Naturally he thought at first he had become 
 a god, in thus seeing all that he had only sur- 
 mised before. 
 
 With the sphere as his guide, he then 
 travelled on through space, till beneath him he 
 saw the interior of the great judgment hall of 
 Flatland, with all its wise men assembled. He 
 then heard the following decree, to his dismay, 
 read out before them all. 
 
 " Whereas the States had been troubled by 
 
40 The Fourth Dimension. 
 
 divers ill-intentioned persons pretending to 
 have received revelations from another world, 
 it has been for this cause unanimously re- 
 solved by the Grand Council to make strict 
 search for such misguided persons, to scourge 
 and imprison any triangle, and to arrest any 
 one of higher rank, to be examined and judged 
 by the council." 
 
 " You hear your fate," the sphere re- 
 marked ; " death or imprisonment awaits the 
 apostle of the gospel of three dimensions." 
 
 " Not so," replied our square ; " the matter 
 is now so clear to me, the nature of real 
 space so palpable, that methinks I could make 
 a child understand it. Permit me but to de- 
 scend at this moment and enlighten them." 
 
 "Not yet," said the sphere, who then taking 
 our friend with him further into space, pro- 
 ceeded to introduce him to solid figures, be- 
 ginning with a cube. 
 
 Taking a number of square cards (the reader 
 
The Land of Three Dimensions. 41 
 
 can do this if he have enough), each the shape 
 of his friend, he placed them one on another 
 till they were as high as they were broad, and 
 thus he built up a cube. 
 
 To the uneducated eye of the square, how- 
 ever, accustomed only to see lines and points, 
 and to whom the sight of even a flat surface 
 was a new revelation, this solid form (like the 
 sphere) appeared to be an irregular six-sided 
 flat figure thus, (i) — not a solid like this, 
 (2)- 
 
 Fig. I. Fig. 2. 
 
 The reader can verify this by closing one 
 eye, and drawing the outlines of a cube seen 
 sideways, on paper. 
 
 It was not until some time after, when he 
 
42 
 
 The Fourth Dimension. 
 
 had by the direction of his friend carefully 
 felt its six sides and its eight angles, and 
 walked round and round and under and over 
 it, and had many views of it in different 
 lights, that the stupendous fact began to 
 dawn upon him, that this new world which 
 he had entered, not only enabled him to 
 see all objects in his own familiar Flatland 
 in a new and truer light, but contained 
 bodies of a fresh and glorious order, utterly 
 transcending all his powers of imagination 
 or description, and of a form so novel, so 
 unexpected, as to be incredible, were it not 
 that his senses convinced him of their ex- 
 istence. It took, indeed, a long time for him 
 to understand that the surfaces he saw of the 
 sphere and cube, thus, — 
 
The Land of Three Dimensions. 43 
 
 were not their interiors, thus : — 
 
 Once our friend the square had, however, 
 fairly grasped, as far as he could, the fact that 
 he now beheld in actual fact the realization 
 of the mathematical formula of 3^, and of that 
 problem of his grandson he had scouted as 
 being alike unreasonable and impossible, he 
 was not content to stop here. See now in the 
 words of our author to what he aspired. 
 
 " I thirsted," says he, " for yet deeper know- 
 ledge than he (the sphere) was offering to me. 
 
 " Pardon me," said I, " O thou whom I 
 
 must no longer address as the perfection of 
 
 beauty ; let me beg of thee to vouchsafe thy 
 
 servant a sight of thine interior." 
 
 * Observe the surface of a higher dimension appears to 
 be the interior to the dimension below. 
 
44 The Fourth Dimension, 
 
 "Sphere. 'My what?' 
 
 " /. ' Thine interior, thy stomach ! ' 
 
 " Sphere. 'Whence this ill-timed, impertinent 
 request ? And what mean you by saying 
 that I am no longer the perfection of all 
 beauty ? ' 
 
 " /. ' My lord, your own wisdom has taught 
 me to aspire to one even more great, more 
 beautiful, than yourself. As you yourself, 
 superior to all Flatland forms, combine many 
 circles in one, so doubtless there is one above 
 you, who combines many spheres in one 
 supreme existence, surpassing even the solids 
 of Spaceland. And even as we who are now 
 in space look down on Flatland, and see the 
 insides of all things, so of a certainty there 
 is yet above us some higher, purer region, 
 -whither thou dost surely purpose to lead me, 
 from the vantage ground of which we shall 
 look down upon the revealed insides of all 
 solid things.' 
 
The Land of Three Dimensions. 45 
 
 "Sphere. 'Pooh! Stuff! Enough of this 
 trifling.' 
 
 " /. ' Nay — deny me not what I know it is 
 in thy power to perform. Grant me but one 
 glimpse of thine interior.* 
 
 " Sphere. 'Well then, to content and silence 
 you, let me say at once, I cannot. Would you 
 have me turn my stomach inside out to oblige 
 you?' 
 
 " /. ' But my lord has shown me the insides 
 of all my countrymen in the land of two 
 dimensions by taking me into the land of 
 three. What therefore more easy than to take 
 his servant a second journey into the blessed 
 region of the fourth dimension, where I shall 
 look down with him once more upon this land 
 of three dimensions, and see the inside of 
 every three-dimensioned house, and the inside 
 of every solid living creature ? ' 
 
 ''Sphere. 'But where is this land of four 
 dimensions ? ' 
 
46 Thi Fourth Dimension. 
 
 "I. 'I know not ; but doubtless my teacher 
 knows.' 
 
 " Sphere. 'Not I. There is no such land. 
 The very idea of it is utterly inconceivable.' 
 
 " /. ' Trifle not with me, my lord. I crave 
 and thirst for more knowledge. Doubtless we 
 cannot see that other higher Spaceland now, 
 because we have no eye in our stomachs. 
 But, just as there was the realm of Flatland, 
 though that poor puny Lineland monarch could 
 turn neither to left nor right, and just as there 
 was close at hand, touching my frame, the land 
 of three dimensions, though I, blind and sense- 
 less wretch, had no power to touch it, no eye 
 in my interior to discern it ; so, of a surety, 
 there is a fourth dimension, which my lord 
 perceives with the inner eye of thought. 
 
 " ' In one dimension did not a moving point 
 produce a line with two terminal points ? 
 
 "'In two dimensions did not a moving line 
 produce a square with four terminal points ? 
 
The Land of Three Dimensions. 47 
 
 '"In three dimensions did not a moving square 
 produce a cube with eight terminal points ? 
 
 "'And in four dimensions shall not a cube — 
 alas for analogy, and alas for the progress of 
 truth, if it be not so-^result in a still more 
 divine organization with sixteen terminal points ? 
 Behold the infallible confirmation of the series, 
 2, 4, 8, 16. Is not this a geometrical progression 
 strictly according to analogy ? I ask, there- 
 fore, is it, or is it not, a fact that ere now your 
 countrymen also have witnessed the descent 
 of beings of a higher order than their own, 
 entering closed rooms, even as your lordship 
 entered mine, without the opening of doors or 
 windows, and appearing and vanishing at will ? 
 On the reply to this question I am ready to 
 stake everything.' 
 
 "Sphere. ' It is reported so. But men are 
 divided in opinion as to the facts. Therefore 
 pray have done with this trifling, and let us 
 return to business.' 
 
4^ The Fourth Dimension. 
 
 " /. 'I was certain of it.' 
 
 " Sphere. ' But most people say these visions 
 arose from the brain.' 
 
 " /. ' Say they so ? Oh ! believe them not ; 
 or if indeed it be so, that this other space is. 
 really Thoughtknd, then take me to that 
 blessed region where ' 
 
 " My words were cut short by a crash out- 
 side, which impelled me through space — down 
 — down — down to Flatland. Then a darkness, 
 and when I came to myself, I was once more 
 a common creeping square, in my study at 
 home, 
 
 " I awoke rejoicing, and began to reflect on 
 the glorious career before me. I would go 
 forth, methought, at once, and evangelize the 
 whole of Flatland. I would begin with my 
 wife. 
 
 "Just as I had decided, I heard a herald's 
 proclamation. Listening attentively, I recog- 
 nized the words of the resolution of the council. 
 
The Land of Three Dimensions. 49 
 
 enjoining the arrest or imprisonment of any 
 who should pervert the minds of the people 
 by delusions, and by professing to have re- 
 ceived revelations from another world. I re- 
 flected the danger was not to be trifled with. 
 Why not therefore make my first experiment 
 with my little grandson, with whom I should 
 be in perfect safety, for he would know nothing 
 of the proclamation of the council ? 
 
 " I therefore immediately sent for my grand- 
 son, and taught him once more how a point by 
 motion in one dimension produces a line ; and 
 how a straight line in two dimensions pro- 
 duces a square. After this, forcing a laugh, 
 I said, ' And now, you scamp, you wanted to 
 make me believe that a square may in the 
 same way, by motion "upward, not north- 
 ward," produce another figure, a sort of extra 
 square in three dimensions.' 
 
 " ' Dear grandpapa,' he said, ' that was only 
 my fun, and of course I meant nothing at all 
 
50. The Fourth Dimension. 
 
 by it ; and I don't think I said anything about 
 the third dimension; and I am sure I did 
 not say one word about " upward, not north- 
 ward," * for that would be such nonsense, you 
 know. How could a thing move upward, not 
 northward ? Even if I were a baby, I could 
 not be so absurd as that. How silly it is! 
 Ha! ha! hal' 
 
 " ' Not at all silly,' said I, losing my 
 temper ; ' here, for example, I take this square,' 
 — and at the word I grasped a movable 
 square which was lying at hand, — ' and move 
 it, you see, not northward but, yes, I move it 
 upward — that is to say, not northward, but 
 I move it somewhere — not exactly like this — 
 but somehow.' 
 
 * This diagram shows what is 
 meant by "upward, not north- 
 ward;" upward being the direc- 
 tion of the third dimension, a 
 direction impossible to be even 
 conceived by an inhabitant of two 
 dimensi'^ns, familiar as it is to us. 
 
 A. upward 
 
The Land of Three Dimensions. 51 
 
 " Here I brought my sentence to an 
 inane conclusion, shaking the square about 
 in a purposeless manner, much to the amuse- 
 ment of my grandson, who burst out laughing 
 louder than ever, and declaring I was joking 
 with him, ran away. Thus ended my first 
 attempt to convert a pupil to the gospel of 
 three dimensions." 
 
 Our poor square then shut himself up 
 and tried to write a book on the subject, 
 but was greatly hampered for want of illus- 
 trations, which he found impossible to draw, 
 or words to convey his meaning, which he 
 found he could not coin. 
 
 Meanwhile, his life was under a cloud. 
 He could not help comparing what he saw 
 in two dimensions with the reality of Flat- 
 land as seen from three. One day he tried 
 to see a cube with his eyes shut, but was 
 not quite certain he had realized the original. 
 This urged him to take some further steps 
 
52 The Fourth Dimension, 
 
 to make the revelation known, but how to 
 begin he knew not. 
 
 At times he could not restrain dangerous 
 utterances, dropping such expressions as the 
 "eye that discerns the interior of things," 
 " the all-seeing one," and " the third and 
 fourth dimensions"; and at last he was drawn 
 at a debating society, one day, to give a full 
 account of his glorious journey into Space 
 and of all he had seen and learned there. 
 
 He was at once arrested, and taken before 
 the great council, to whom he retold all his 
 story. At the close of a long examination 
 he was finally asked two questions : — 
 
 1. Whether he could indicate the direc- 
 tion which he meant when he used the words, 
 " upward, not northward " ? 
 
 2. Whether, by any diagrams or descriptions 
 (other than the enumeration of imaginary sides 
 and angles), he could indicate the figure he 
 called a cube ? 
 
The Land of Three Dimensions. 53 
 
 As it was obviously impossible for him to 
 comply with either of these apparently reason- 
 able demands, our unfortunate square was 
 finally sentenced to perpetual imprisonment. 
 
 Here, for many years, he ceaselessly tried 
 to teach the gospel of three dimensions to 
 his fellow-prisoners, but alas ! without the 
 slightest effect, being universally regarded as 
 a harmless monomaniac. 
 
 Here, then, we bid our square friend a final 
 adieu, and leave the little book in which his 
 story is enshrined, to consider further the laws 
 of a fourth dimension. 
 
CHAPTER V. 
 
 THE LAND OF FOUR DIMENSIONS MATHE- 
 MATICALLY CONSIDERED. 
 
 In now summing up the result of all that has 
 been said, and trying to carry the facts that 
 have been observed in the relation of the first 
 to the second, and the second to the third 
 dimension into the relations of the third to 
 the fourth, we will first of all consider this 
 higher and unknown dimension as a mathe- 
 matical figure, and secondly enumerate some 
 of the probable laws of a world of such 
 dimensions and its inhabitants, as deduced by 
 analogy, and their possible relations with our 
 world and its inhabitants. 
 
 Then we may further consider the actual 
 facts around us bearing on the question, and 
 
The Land of Four Dimensions. 55 
 
 compare these deduced laws of the fourth 
 dimension with some of the claims of Christi- 
 anity as stated in the Bible. 
 
 Let us then, first of all, consider the 
 mathematical or geometrical side of the ques- 
 tion, and inquire what would be the character 
 of regular figures in the fourth dimension, 
 arguing from analogy. 
 
 And in so doing, we must warn the reader 
 that the subject is necessarily somewhat in- 
 volved and intricate ; but that nevertheless 
 the conclusions arrived at are so fascinating 
 and novel, that if he will only traverse the 
 preliminary Sahara in patience, he will prob- 
 ably feel rewarded by the subsequent oasis 
 he reaches in the summing up and applica- 
 tion of the whole theory. 
 
 Let us therefore proceed to set forth the 
 facts in order. 
 
 IN ONE DIMENSION we get— 
 
 (i) Straight lines, 
 
56 The Fom'th Dimension. 
 
 (2) Varying only in one direction — length ; 
 
 (3) Having two terminal points (or sides or 
 outsides, the line between these being the in- 
 side) ; and 
 
 (4) Seen only (by a single eye in line with 
 them) as points. 
 
 IN r;^C> DIMENSIONS we get - 
 (i) Surface or flat figures, 
 
 (2) Varying in two directions — length and 
 breadth, also in number of sides and angles 
 (we also get irregular figures of one dimension, 
 but lying in two, as curved or crooked lines ;) 
 
 (3) Having not less than three * terminal 
 points or angles, and not less than three 
 borders or boundary lines, or sides or outsides 
 
 (the surface of the figure being the inside) ; and 
 
 (4) Seen only (by a single eye on a level 
 
 with them) as lines. 
 
 * No flat figure can have less than three angles and three 
 borders, viz., a triangle ; for two straight lines cannot en- 
 close a space. (Circles and curved lines are not considered, 
 being really an infinite number of straight lines.) 
 
The Land of Four Dimensions. 57 
 
 IN THREE DIMENSIONS we get— 
 (i) Solids, 
 
 (2) Varying only in three directions — length, 
 breadth, depth, also in number and regularity 
 of sides and angles (we also get irregular 
 figures of two dimensions, but lying in three, 
 as curved or crooked surfaces) ; 
 
 (3) Haying not less than four* terminal 
 points or angles, and not less than four borders, 
 surfaces, or sides or outsides (the contents being 
 the insides) ; and 
 
 (4) Seen only (by a single eye f) as surfaces. 
 
 IN FOUR DIMENSIONS we get (by 
 analogy) — 
 
 * A solid body cannot have fewer than four angles and 
 sides, viz., a solid triangle. (Circular and curved bodies are 
 not considered, being composed of an infinite number of 
 sides.) 
 
 t We see bodies as solids, not surfaces, simply because 
 we have two eyes, and can see them from two points of 
 view at once. The stereoscope is founded on this fact. 
 
58 The Fourth Dimension. 
 
 (i) Unnamed bodies, 
 
 (2) Varying only in foiir directions, lengthy 
 
 breath, depth, and , also in number and 
 
 regularity of size and angles (we also get 
 irregular bodies of three dimensions, but 
 lying in four ; as ) ; 
 
 (3) Having not less than five terminal 
 points or angles, and not less than five borders,, 
 solids, or sides or outsides ; and 
 
 (4) Seen only (by a double eye) as solids. 
 
 Turning now to consider some of the pro- 
 bable laws deducible by analogy from these data 
 and the foregoing chapters, we may suggest the 
 following, the general truth of which the reader 
 will probably be now prepared to admit. 
 
 Some of the relations of a being ik 
 <sm. dimension, with the dimension below 
 him and the beings in it, e.g., a being in 
 a fourth dimension with the third (our 
 
 world) and THOSE IN IT, ARE : — 
 
The Land of Four Dimensions. 59 
 
 1. He can enter or leave the world below 
 him, that is, appear and disappear at will, and 
 that without changing his form (pp. 14, 33). 
 
 2. However near to the world below him^ 
 he remains invisible till actually in it. 
 
 3. He can be in closest proximity with the 
 beings in the world below, and yet outside 
 
 that world altogether, and therefore invisible. 
 
 4. From his dimension he can see and enter 
 
 at will the inside of every living being and 
 thing in the world below him. 
 
 5. When he enters the world below, he can 
 never be wholly seen, and that part of him 
 that is seen is always in the form of the world 
 below him which he enters. 
 
 6. His voice, while still in his own dimen- 
 sion, would be heard (if hearing were possible) 
 by a being of the world below as an internal 
 voice, or a voice from his own inside (p. 16). 
 
 7. His appearance and disappearance in the 
 world below are not caused by any change of 
 
6o Tlte Fourth Dimension. 
 
 form or substance, but by his entering or leav- 
 ing that world. 
 
 8, A world and beings of any dimension 
 include all the shapes and characters of those 
 below them, adding to them that further shape 
 and character peculiar to the added dimension. 
 
 The relations of a being in one dimension 
 ■with that above him and its inhabitants, 
 
 e.g., ONE IN THE THIRD DIMENSION (oUR WORLd) 
 WITH THE FOURTH. 
 
 1. All conception of a higher dimension is 
 impossible, though capable of mathematical 
 •demonstration. 
 
 2. However vast and populous the dimen- 
 sion, to him it is absolutely and necessarily 
 non-existent. 
 
 3. If he could hear such beings, the sound 
 -would appear to come from his inner conscious- 
 ness, and not from his own world without 
 
 4. If such beings enter his world, he can 
 
The Land of Four Dimensions. 6 r 
 
 only see and comprehend that part of thent 
 that enters it. Such beings may directly enter 
 his own inside. 
 
 5. And to him such part always appears^ 
 in the likeness of an inhabitant of his world 
 (the inhabitants of one world being always a 
 partial likeness, or the likeness of a part, of 
 those in the world above them). 
 
 6. He can never, by his own power, leave 
 his own dimension or world. 
 
 7. While in his world, he can never see the 
 true appearance or shape of any being in it^ 
 but only its exterior. 
 
 8. If raised into the dimension above, he at 
 once perceives the true dimension and shape 
 of every being in his own world. 
 
 9. The beings of the dimension into which 
 he is raised, at first present the same appear- 
 ance as the beings (now first truly seen) in 
 his own dimension. 
 
 10. By close inspection and careful com 
 parison the real difference can be discerned. 
 
^2 The Fourth Dimension. 
 
 11. Even if the dimension above be visited 
 and understood, it is impossible to describe it 
 in the language, or to draw it in the figures, of 
 liis own dimension. 
 
 12. All such attempts are necessarily unin- 
 telligible, and sound foolish and irrational. 
 
 13. All attempts to understand or grasp the 
 dimension above, without having entered it, 
 are futile. 
 
 14. An eye in one's inside would, according 
 to analogy, look in the direction of the dimen- 
 sion above. 
 
 15. Each dimension adds one new direction 
 of size, space, capacity, and form to the one 
 below. 
 
 16. The visibility of a being does not 
 depend on physical properties, but on its 
 position inside or outside of the world below 
 him. 
 
'Ihe Land of Four Dmiensions. 
 
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CHAPTER VI. 
 
 THE LAND OF FOUR DIMENSIONS IN RELATION TO 
 OURS OF THREE. 
 
 Turning now from analogies and theories tc 
 facts, we find in the first place an almost 
 universal consensus of opinion amongst all 
 nations, throughout all ages (with few and 
 curious exceptions), that there does exist a 
 higher* world than ours, invisible to mortal 
 eyes. 
 
 Those among civilized nations who have 
 doubted or denied its existence have done so 
 in spite of their own feelings, and in virtue of 
 
 * By higher is meant greater in its qualities and powers. 
 In speaking of this world, though the whole of it is in- 
 cluded, it is mainly with that part of it that constitutes 
 God's spiritual kingdom that we are concerned. 
 
The Land of Four Dimensions. 65 
 
 a reasoning that denies anything that can- 
 not be apprehended by the senses, in short, 
 anything that is not "matter." The narrow- 
 ness of such reasoning gives it all its exact- 
 ness, and the materialist finds a satisfaction 
 in denying all he cannot account for, or 
 where the clear but limited light of his under- 
 standing fails to penetrate. Some minds, I 
 suppose, prefer the well-trimmed order of 
 a London square within its iron railing, or 
 a well-stocked kitchen garden with its four 
 high bHck walls, to the boundless prairie 
 or the rolling moorland. The known can at 
 any rate be made to yield a tribute to the 
 complacent human wisdom which can classify, 
 analyse, and otherwise ticket and name it ; 
 while the unknown is denied by our little 
 philosophers, partly because the human mind 
 cannot fully grasp it, and finds it easier to 
 ignore it, and partly because the unknowii 
 refuses to be measured, weighed, and arranged. 
 
66 The Fourth Dimension. 
 
 and thus furnish another trophy to the gfreat- 
 ness of man's intellect. 
 
 It must not be supposed, however, that our 
 patient reader has been asked to wade through 
 all these pages merely to prove to our material- 
 ists that there is a world that finds no place in 
 their philosophy ; for the reader himself doubt- 
 less already accepts the fact of this world in 
 a general way, and the number of absolute 
 materialists is too small, and their convictions 
 too strong, to be much shaken by the humble 
 methods adopted here. We seek to do far 
 more than this ; we hope to show by analogy 
 how the powers of this highei^ world, in 
 many an unlooked-for particular, correspond 
 with those that may justly be supposed to 
 belong \.Q x^. 
 
 Let us now proceed to consider some of the 
 phenomena of this unseen world, as current in 
 tradition, as experienced by individuals, and 
 as recorded in books — mainly in the Bible, 
 
The Land of Four Dimensions. 67 
 
 this being the authoritative history accepted 
 by all Christians of the spiritual kingdom. 
 
 All believe that this wtorld is a higher one 
 than ours ; 'higher in the sense of being greater, 
 wiser, more powerful ; that it, like ours, con- 
 tains inhabitants good and bad, and regions 
 fair, and dark, and terrible. But we all feel 
 that the goodness of some of its inhabitants 
 on the one hand, and the evil of the rest on 
 the other, alike transcend in every way all 
 standards of good and evil here ; and that, 
 in the same way, both the fairness and the 
 foulness and horror of its different regions 
 transcend all ever seen by mortal eye, or that 
 can be pictured by the human mind. 
 
 Most believe this unseen world to be densely 
 peopled, and that in some way it rules over 
 our own with a sway in every way greater, 
 again stronger, and more comprehensive than 
 that of any known earthly government. 
 
 Another curiously universal, instinctive belief 
 
68 The Fourth Dimension. 
 
 and one by no means confined to Christianity, 
 is, that when a man dies, part of him (his soul, 
 or spirit) leaves this world altogether, to enter 
 the higher one. And here we may turn aside 
 to remark that the general belief that man 
 has a spiritual nature — something beyond and 
 above the highest ganglion cell in his brain, 
 something that leaves the body at death, but 
 abides in it through life— may be well illus- 
 trated by algebra. 
 
 Let, for example, the body, material and 
 solid, be represented fairly enough by x^, and 
 the spirit, higher and possessing an unknown 
 power, by a;*.* Then (a;^+.ar*) represents the 
 
 * In taking x* here to represent spirits and hereafter the 
 spirit world, it must be remembered that we are absolutely 
 ignorant of what is really involved by this formula. As far 
 as we know, the "material" is strictly limited to three 
 dimensions, nothing in one or two being material, or having 
 any substance whatever. It must therefore be distinctly 
 understood that we firmly believe that God is a spirit, and 
 the other world a spiritual one, and that we have no wish 
 or intention of materializing it in enforcing the truUi of 
 
The Land of Four Dimensions. 69 
 
 man in life, while {x^+x*)—x* represents 
 the departure of the spirit (x*) at death, 
 which returns to its own dimension, while the 
 body (x^), which is left, returns to the earth to 
 which a belongs. 
 
 If this, then, be true, as is surely believed 
 amongst all Christians, that man is at any rate 
 a complex being, having as definite a relation 
 with the unseen world above him as with the 
 visible world around him, a relation which is 
 realized by all after death, then is explained 
 the instinctive craving of all the human race, 
 even apart from Bible revelation, after a higher 
 world ; hence, also, the capability to receive 
 and understand its mysteries, and the pos- 
 sibility of communion with it even now. 
 
 Turning from tradition to experience, we 
 have not only unnumbered instances of com- 
 munion between our spirits and the inhabitants 
 
 some of its laws by means of analogies drawn from a 
 supposed fourth dimension. 
 
70 The Fourth Dimension. 
 
 of the higher world, but equally numerous in- 
 stances of the entrance of these higher beings, 
 and their consequent appearance in our world. 
 
 Speaking of communion, and turning to the 
 Bible and to the lives of the saints and of 
 all good men in ancient and modern days, 
 and, on the other hand, to certain events 
 in the lives of bad men, especially in con- 
 nection with great crimes, no student of the 
 subject can doubt that the expressions, "We 
 see Jesus," " David sat before the Lord," 
 " God spake to Moses," " Satan tempted him," 
 " Daniel cried unto the Lord," " I sought the 
 Lord, and He heard me," and hundreds of 
 similar utterances in biographies and from the 
 lips of living men, represent the fact of com- 
 munion and intercourse between the two 
 worlds, just as faith, the evidence of things 
 not seen,* prayer, contemplation and abstrac- 
 tion represent the means. 
 
 * Hebrews xi. i. 
 
The Land of Four Dimensiotis. 7 1 
 
 Then, again, as to appearances. The Psy- 
 chical Research Society may be unable to dis- 
 cover a single authentic ghost, but nevertheless 
 innumerable appearances from the spirit world 
 are everywhere believed in, and, we think, 
 credibly attested. 
 
 The testimony of the Bible alone (if believed) 
 is of course overwhelming on the point. Angels 
 come and go at will, God Himself is seen in 
 Old Testament times in human form, and in 
 New Testament times, when our Lord takes a 
 spiritual body. He appears or disappears in this 
 world of ours at will. A hand wrote on 
 Belshazzar's wall. The form of the Son of 
 God was seen in the fiery furnace. Since then 
 appearances have been seen and voices heard 
 that cannot be explained by anything in three 
 dimensions. 
 
 Passing on to consider the history of this 
 higher world, more especially as recorded in 
 the Bible, we find its superiority as to its in- 
 
72 The Fourth Dimension. 
 
 habitants, its regions, and its powers, all amply 
 confirmed. Whether we consider the attributes 
 of God, or of an angel, or of a devil, whether 
 we read about heaven or hell, We are made 
 conscious. throughout, that all, from the omni- 
 potent Ruler of this higher world down to its 
 meanest servants, transcend our ideas in every 
 way. We find omniscience and omnividence 
 claimed, "all things being naked and open to 
 Him with whom we have to do" (Heb. iv. 13), 
 We find the angels described as unseen messen- 
 gers of good and evil, surrounding our path on 
 every side, and carrying out the will of their 
 Master for weal or woe. We find indications 
 that this unseen world itself surrounds us on 
 every side. We are positively told that our 
 soul definitely enters it at death, when it is 
 "absent from the body." 
 
 We have more. In the twelfth chapter of 
 the second epistle to the Corinthians we find a 
 detailed account given us by an educated man, 
 
The Land of Four Dimensions. 73 
 
 well read in the philosophy of his day — Paul, 
 of the fact of his being caught up into the 
 higher world (supposed, by referring to the date 
 which he gives, to have been when stoned 
 and dragged out of a city and left for dead), 
 and the curious statement made that although 
 he saw and heard much, he found it impossible 
 to describe or relate anything in human lan- 
 guage, on his return to this world. 
 
 We have also the account of Elijah and 
 Enoch and Christ suddenly leaving this world 
 for the higher one, while yet alive. 
 
 In some parts of the Bible, notably in the 
 Revelation, a definite endeavour is made to 
 describe some of these higher glories in human 
 language, and all that can be done is to picture 
 them by the commonest earthly symbols — gold, 
 glass, precious stones, pearls, thrones, palms, 
 lamps, trumpets, white linen, swords, suppers, 
 and so forth. No words existing to pourtray 
 the glories of the spiritual world. 
 
74 The Fotirth Dimension. 
 
 This world is described at length as passing 
 away altogether, and yet the foundations of 
 that world are not even shaken, it being de- 
 scribed as a " kingdom that cannot be moved." 
 
 The descent, as we have seen, of beings 
 from it to our earth is constantly recorded, 
 their appearance and disappearance spoken of, 
 the former always in human form, though this 
 latter is never spoken of as being assumed for 
 the occasion. When another form, as that 
 of a dove, is assumed, the fact on the con- 
 trary is always expressly mentioned. 
 
 Not only are mysterious appearances and 
 disappearances constantly recorded, but very 
 definitely in the case of our Lord, as entering a 
 room in a body "with flesh and bones," though 
 all entrance to it was barred. Also, at another 
 time, when, sitting at supper. He vanished out 
 of their sight, though in a body and capable of 
 eating and drinking.* 
 
 * We would ask the reader mo^t especially to note this 
 
The Land of Four Dimensions. 75 
 
 The Bible speaks also of our relationship 
 with that world. It tells us that the apprehen- 
 sion of its glories are not by means of the 
 seeing eye or the hearing ear, but by revelation 
 of the Spirit of God.* It reiterates the fact 
 that the natural (or finite) mind, though linked 
 with the fourth dimension, cannot of itself 
 grasp spiritual realities, but that they must be 
 revealed to us by spiritual means, and that 
 those alone to whom this is vouchsafed can 
 discern, judge, and weigh all earthly things in 
 their true and real light. 
 
 The third chapter of John tells us more. 
 It lays down the fact that by no education can 
 any man mentally or morally enter this higher 
 sphere. He must, in the language of our 
 Saviour, be positively born " again," or, as 
 better rendered, " from above," that is, intrd- 
 
 iii connection with paragraph 1, page 59, and paragraph 
 16, page 62. i\ 
 
 * I Corinthians if 9-13. 
 
76 The Fourth Dimension. 
 
 ■duced as truly into the higher world by birth, 
 as he was first introduced into this world in 
 the same manner. 
 
 All spiritual perception of this world is by 
 internal eyesight, the "eyes of our under- 
 standing."* 
 
 The language and descriptions of those who 
 profess to have been thus introduced, mentally 
 and morally (though not yet physically) into 
 this other world, are mostly unintelligible, and 
 foolishness to the inhabitants of this, t 
 
 Attempts, always unsuccessful, to penetrate 
 its mysteries beyond, or apart from what is 
 ■directly revealed, only help to fill our asylums 
 -and lists of suicides, while, on the other hand, 
 we are everywhere surrounded with large 
 bodies of sane people who claim to have been 
 introduced into it, to obey its laws, and to 
 •enjoy its privileges, and some of its powers. 
 
 With regard to our future relationship with 
 * Ephesians i. i8. f i Corinthians ii. 14. 
 
The Land of Four Dimensions. 77 
 
 this higher world, the Bible is equally clear. 
 It not only plainly shows that the soul ia 
 affinity with it in life, definitely enters it at 
 death, but points to a mysterious time, in the 
 hope of which thousands have closed their eyes, 
 on this world, of a resurrection, when the spirit 
 shal' be clothed again with a body, but differ- 
 ing from the present one in its origin and in its 
 properties and powers, being called a spiritual 
 body, and fitted to enter physically, for the 
 first time, those higher regions already familiar 
 to the departed soul. 
 
 These few detached remarks may serve to 
 point out some leading features of the world 
 " to come," in relation to our own ; we will now 
 consider them in connection with the mutual 
 relations of the various dimensions. 
 
CHAPTER VII. 
 
 THE LAND OF FOUR DIMENSIONS. FACfS 
 AND ANALOGIES. 
 
 Those who have -closely followed the allegory 
 of the different dimensions in the earlier chap- 
 ters of this treatise, must have been struck, in 
 the first place, by the absolute impossibility 
 of any inhabitant belonging purely and simply 
 to any one dimension even conceiving the 
 existence of a higher world than his own; 
 which to him, be it point, or line, or surface, 
 or solid space, is all that there is, or can be. 
 
 In the second place, a moment's reflection 
 will have shown them that in the very nature 
 of things, it obviously must be so. 
 
 To one living entirely on a surface and in a 
 
 78 
 
The Land of Four Dimensions. 79 
 
 world where there is nothing but length and 
 breadth indefinitely prolonged, the idea of 
 height and depth are absurd and impossible, 
 and there exists no mode of demonstrating 
 them, unless they are absolutely entered. 
 
 Having these facts before us, and applying 
 them to ourselves, we find, to our surprise, 
 they are not fully borne out in our experience. 
 
 We can to some extent understand the 
 existence of another world, even apart from all 
 revelation or entrance into it, and this is be- 
 cause we are something more than mere forms 
 of three dimensions. Were we such only, no 
 such traditions as we have alluded to would 
 be common to the human race ; the idea of a 
 higher world would be as impossible to us as 
 to the brute creation. 
 
 But there is a part of us that has been made 
 in the likeness of God, a part breathed into 
 us by the Divine breath, through which we 
 instinctively perceive the higher sphere, and 
 
8o The Fourth Dimension. 
 
 by means of which we are partly able to ap- 
 prehend its teachings. 
 
 Still, to a great extent, the analogies hold 
 good. We, like our friend the square, in Flat- 
 land, can see spiritual beings when they enter 
 our world, and like him, explain their appearing 
 and vanishing by magic or miracle, rather than 
 by the simple fact of their entering or leaving 
 our dimension. 
 
 Again, analogy has shown us how near, how 
 very near, the new dimension that characterizes 
 the world above us may be, with its inhabitants, 
 and yet be outside ours altogether. * 
 
 On the other hand, analogy shows us that 
 just as a point is comprehended in a line, a 
 line in a square, a square in a cube, so is our 
 world of three dimensions completely included 
 and swallowed up in the universe of four. 
 
 * This shows also the folly of those who, reasoning on 
 "three dimension" lines, assert that the spiritual world 
 must be beyond the confines of the material, and hence 
 millions of miles away, and farther than the farthest Etar. 
 
The Land of Four Dimensions. 8i 
 
 Analogy points out how omnividence is an 
 almost necessary property of a higher world. 
 
 The careful comparison of the analogies of the 
 third and fourth dimensions with the revealed 
 relation of our world to the spirit world, shows 
 such a likeness between the two, that it is not 
 too much to say that if we call our world a world 
 of three dimensions, we may fairly consider the 
 spirit world in many respects a world of four. 
 
 We conclude, therefore, that a higher world 
 than ours is not only conceivably possible, 
 but probable ; secondly, that such a world may 
 be considered as a world of four dimensions; 
 and, thirdly, that the spiritual world agrees 
 largely in its mysterious laws, in its language 
 which is foolishness to us, in its miraculous 
 appearances and interpositions, in its high and 
 lofty claims of omniscience, omnividence, etCj 
 and in other particulars, with what by analogy 
 would be the laws, language, and claims of a 
 fourth dimension. 
 
 G 
 
82 The Fourth Dimension. 
 
 Once these conclusions are admitted, and 
 our eventual destination, body and soul, seen 
 to be in this higher world, the transcendent 
 importance of understanding all about it, the 
 intense and real interest of all connected with 
 it, becomes overpoweringly evident. 
 
 If it be true that we are everywhere sur- 
 rounded by another world, which is our final 
 goal, how foolish to stop our ears to its history, 
 to shut our eyes to its facts, as recorded in 
 what is believed by us to be an authoritative 
 statement of them ! 
 
 The honest materialist has some excuse for 
 the total neglect of a Bible he disbelieves ; 
 but what shall we say of those who, professing 
 to accept these stupendous realities, are utterly 
 indifferent to them and the Book that reveals 
 them ? 
 
 Surely the study of what we will term this 
 fourth dimension far transcends the highest 
 earthly subjects, and dwarfs to their proper 
 
The Land of Four Dimensions. 83 
 
 level all objects of human ambition, for we 
 see at once that the lowest inhabitant of the 
 fourth dimension is necessarily of a different 
 and a higher order than the greatest monarch 
 in the third. The lowliest plant is of a 
 higher order than, and different beauty from, 
 the most precious mineral, possessing as it 
 does one sort of life ; the feeblest animal, 
 again, is of a higher order than, and different 
 beauty from, the oak or the cedar, possessing 
 as it does another sort of life; and in the 
 same way the humblest subject of God's 
 spiritual kingdom is of a higher order than, 
 and different beauty from the highest animal, 
 possessing as he does yet another sort of life. 
 
 Another great advantage these considera- 
 tions give is that, if admitted, they at once 
 rescue Christianity from being degraded to a 
 code of ethics, whereby men can better adorn 
 this third dimension, and present it in its true 
 and proper character of a new world and 
 
84 The Fourth Dimension. 
 
 kingdom, with its invisible inhabitants, laws, 
 houses, and rulers ; in a word, it becomes 
 objective instead of subjective. Light is also 
 thrown on the mysterious connection of soul 
 and body in us personally, and on the entrance 
 of the former into another world the moment 
 it is released from the body by death. 
 
 Conversion, the new birth, salvation, or 
 whatever the entrance of the light of Chris- 
 tianity into the heart of man is called, is now 
 seen not to be a process of education in 
 morality, in order to produce better members 
 of society, and of this world, but something 
 infinitely higher — z. positive resurrection into a 
 higher and purer world, where Christ now is, 
 an instruction in the heavenly principles, and 
 a glimpse into its transcendent glories, coupled 
 with a view into the hearts of men and of 
 the real nature of all earthly things, that reveal 
 their true value, the result being undoubtedly 
 to elevate the tone, life, and manners of the in- 
 
The Land of Four Dimensions. 85 
 
 dividual, but the object being to fit him to be 
 shortly removed altogether to that higher sphere 
 to which he now belongs, there to be clothed 
 with a spiritual (or fourth dimension) body. 
 
 Those who have followed, and who accept the 
 preceding lines of argument and thought, will 
 undoubtedly thus see more clearly the reason 
 and cause of a great many distinctive features 
 of Christianity. They will understand its lofty 
 claims, and know why, when its laws are truly 
 proclaimed, they are to men foolishness, where- 
 as, when adulterated with the wisdom of this 
 world (of the third dimension), they are more 
 or less intelligible. They will see why it is 
 insisted on so strongly that the natural man 
 cannot receive its mysteries (being of fhe third 
 dimension), and that they are only spiritually 
 discerned (that is, by revelation), why we must 
 be born again, or introduced by the power 
 of God into this new world. 
 
 They will now see how it is possible this 
 
86 The Fourth Dimension. 
 
 kingdom can be within us, and yet surrounding 
 us ; how angels may be by our very side, and 
 yet outside this world of space altogether. 
 
 They will see the impossibility of guessing 
 the direction of heaven or hell, seeing there 
 is an unknown direction around us, which we 
 cannot conceive, and the puerility of assuming 
 that it must be " up above " or " down below." 
 
 They will see that though the glorious 
 material universe extends beyond the utmost 
 limits of our vision, even artificially aided by 
 the most powerful telescopes, that does not 
 prevent the spiritual world and its beings, and 
 heaven and hell being by our very side. 
 
 They will see that, far from these spiritual 
 regions occupying some small corner of the 
 material universe, as surely as the greater 
 includes the less, so surely is the material 
 universe, vast as it is, swallowed up in the 
 spiritual. 
 
 The indications of the vast unknown extent 
 
The Land of Four Dimensions. 87 
 
 of this spiritual kingdom will be more clearly 
 understood in such references as Ephesians 
 i. 21. They will now more clearly discern 
 " the powers of the world to come," whereof we 
 speak, and understand the mysterious appear- 
 ances in the Bible of spiritual beings, always 
 in human form, necessarily so to be seen in 
 the third dimension. It will be no difficulty 
 to them to believe all thoughts and hearts are 
 naked and open to the Ruler of this world, still 
 less that every closed object and the inside of 
 every solid thing is and must be clearly seen. 
 
 Believing as we do that the soul, or immortal 
 part, of man is connected with this fourth 
 dimension, while the body belongs to the third, 
 the phenomena of death is clearly seen to be 
 the separation of these two dimensions, the 
 body remaining in this world while the soul 
 enters the other. 
 
 The simple and almost childish language of 
 Revelation, already alluded to, will no longer 
 
88 The Fourth Dimension. 
 
 appear strange, when it is seen that it is an 
 inspired attempt to put the glories of the 
 fourth dimension into the language of the 
 third ; hence the necessary use of such words 
 as glass, gold, etc. Nor will the language of 
 Paul, in 2 Cor. xii., fail to be better under- 
 stood as to what he heard when caught up out 
 of the third dimension into the fourth being im- 
 possible to utter or render into human language. 
 The arrogance of man will receive a severe 
 and salutary check when it is seen how, in the 
 very nature of things, it is impossible he can 
 understand even the new direction in which 
 this glorious world lies, while the Christian 
 will quite see why he is constantly misunder- 
 stood, and always so, indeed, when he lives 
 in the region of the fourth dimension; and 
 hence that saying is and must be true, that 
 he "discerns all things, yet he himself is 
 discerned of no man." * 
 
 * I Corinthians ii., end of chapter. 
 
The Land of Four Dimensions. 89 
 
 It is hardly too much to say that when the 
 possibility is proved of there being another 
 world in close proximity to ours, but necessarily 
 invisible to us, save as its beings enter or leave 
 ours, and when we discern a few of the lead- 
 ing laws, that by strict analogy may be taken 
 as found in such a world in relation to ours ; 
 that nearly the whole of Christianity becomes 
 clearer to us, its language more intelligible, 
 and some of its most difficult statements al- 
 most axiomatic. 
 
 If we consider such scriptures, for instance, 
 as Ephesians i., Colossians i., 2 Corinthians v., 
 and I Corinthians xv,, we find, just as Adam 
 is the principal being in the third dimension, 
 so is Christ in the fourth, and hence with 
 appropriateness is called " the Second Man." 
 
 The new creation is seen to be as literal 
 and real an introduction of beings into the 
 fourth dimension as the old was into the 
 third, and such a verse as Colossians i. 16, 
 
90 The Fourth Dimension. 
 
 descriptive of the Creator's power in both 
 dimensions, here designated visible and in- 
 visible, is apprehended. 
 
 The power whereby Christians are lifted 
 out of the third into the fourth, mentally, at 
 any rate, is graphically portrayed in Colossians 
 ii. 20-iii. 4. They are there spoken of as dead 
 and risen with Christ (into the fourth dimen- 
 sion), and are to be occupied with the superior 
 glories of their new sphere. 
 
 It is but little wonder, therefore, that those 
 who have really been made thus alive should 
 speak somewhat slightingly of the glories of 
 this world, when they consider the higher 
 glories of their own, or that they should be 
 enthusiastic in describing it, or earnest in 
 endeavouring to introduce others into it ; nor, 
 on the other hand, that by those who are 
 not thus alive, they should be accounted fools 
 and fanatics, and their language extravagant 
 and unintelligible. The wonder rather is, that 
 
The Land of Four Dimensions. 9 1 
 
 those who are thus alive should not be more 
 enthusiastic than they are, and appear more 
 foolish than they do. 
 
 In conclusion, we would briefly emphasize 
 these following points. 
 
 If we have to any degree succeeded in show- 
 ing the probability of that other world being 
 of a higher dimension than our own, and that 
 we have a link with it naturally in the spiritual 
 part of our beings ; we see most clearly estab- 
 lished by analogy, that by no development of 
 our mental faculties, by no advancement in 
 science, by no cultivation of conduct or morals, 
 in short, by no education or improvement of 
 the human race, per se, can we understand, 
 enter, or view this higher kingdom. Any 
 comprehension, in short, of it, is not by cul- 
 tivation, or strengthening even of that link we 
 already have with it in our souls, but by a 
 distinct revelation from that world to these 
 powers within us, and a consequent elevation 
 
92 The Fourth Dimension. 
 
 of these powers into this higher dimensien. 
 In relation therefore with Christianity (as we 
 call this scheme of revelation), we see why 
 the most highly cultured in the learning of 
 the third dimension possess little if any advan- 
 tage (nay, often the reverse) over the wayfaring 
 man, though a fool, inasmuch as it is to both of 
 them a distinct revelation, more easily received 
 indeed in the latter case, since there is here no 
 force of intellect to set aside, for the meaning 
 of our Lord's saying is now clearly apparent, 
 that except we become as little children, we 
 shall in no wise enter the kingdom of heaven. 
 
 If then these few remarks, and these mathe- 
 matical analogies, serve to show that the scrip- 
 tural way of entering the Kingdom of God is 
 the only way possible; if they assist to rouse 
 enthusiasm in believers, to convert unbelievers, 
 and to silence materialists, the object of the 
 writer will be fully gained.