ANOTHER WORLD, by A.T. SCHOFIELD, M.D. Digitized by Cardinalis Etext Press, C.E.K. Posted to Wiretap in July 1993, as another.txt. Superscripts are marked with ^ symbol. Italics are marked with _Italics_. Footnotes are actual printed page numbers in [..]. This text is in the PUBLIC DOMAIN. ANOTHER WORLD; OR, THE FOURTH DIMENSION. BY A.T. SCHOFIELD, M.D. LONDON: GEORGE ALLEN & UNWIN LTD. RUSKIN HOUSE 40 MUSEUM STREET, W.C. FIRST EDITION JUNE, 1888. TO PROFESSOR J.H. GLADSTONE, PH.D., F.R.S., ETC., ETC., 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, 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, 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 demonstrated, 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 relationship, 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 acknowledging my deep indebtedness to the anonymous 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; my object being to carry on the line of argument 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 doubtless 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 dimension 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. CHAPTER I. THE LAND OF NO DIMENSION 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 unaccustomed to algebra will understand that if x represents three inches, or a line of this length, x^2 (x square) represents 3 x 3, or nine square inches on a flat surface, three inches each way; x^3 (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 consider x as representing lines, x^2 squares, x^3 solids, and then comes the question, What does x^4 represent? for mathematics passes as easily from x^3 to x^4 as from x^2 to x^3, and yet while x, x^2, x^3, refer to objects known to all of us, the wisest can form no possible conception of what x^4, 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^4, 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 direction_, 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_, is represented mathematically by a straight line, which is described as having length without breadth, thus:-- ---------------------- _Two dimensions_ (x^2), or _size in two directions_, is represented mathematically by a superficies or surface, which is described as having length and breadth without thickness, thus:-- FIGURE OF DIAMOND RECTANGLE AND A CIRCLE _Three dimensions_ (x^3), or _size in three directions_, is represented mathematically by a _solid body_, which is described as having length, breadth, and thickness, thus:-- FIGURE OF BOX, SPHERE AND A 3-D CROSS _Four dimensions_ (x^4), or _size in four directions_, we cannot represent mathematically, nor can we describe in what direction its fourth dimension 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^3) 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 ourselves in his place, and carefully observing the difficulty he, accustomed only to x^2 or flatness, would have in grasping x^3, or solidity, which nevertheless exists, we may understand better that the difficulty we in x^3, or solidity, have in our turn of grasping x^4, 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."[9] "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 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 exhausted reader had better pause for five minutes before taking the next step higher into the more interesting world of one dimension, or "Lineland." CHAPTER II. THE LAND OF ONE DIMENSION LET now my faithful reader, somewhat recruited from the study of Chapter I., proceed to picture a world of one dimension--a universe 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 l...
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