Please see the [Transcriber’s Notes] at the end of this text.

A NEW ERA OF THOUGHT.

SCIENTIFIC ROMANCES.
By C. Howard Hinton, M.A.
Crown 8vo, cloth gilt, 6s.; or separately, 1s. each.

1. What is the Fourth Dimension? 1s.

GHOSTS EXPLAINED.

“A short treatise of admirable clearness. . . . Mr. Hinton brings us, panting but delighted, to at least a momentary faith in the Fourth Dimension, and upon the eye of this faith there opens a vista of interesting problems. . . . His pamphlet exhibits a boldness of speculation, and a power of conceiving and expressing even the inconceivable, which rouses one’s faculties like a tonic.”—Pall Mall.

2. The Persian King; or, The Law of the Valley, 1s.

THE MYSTERY OF PLEASURE AND PAIN.

“A very suggestive and well-written speculation, by the inheritor of an honoured name.”—Mind.

“Will arrest the attention of the reader at once.”—Knowledge.

3. A Plane World, 1s.

4. A Picture of our Universe, 1s.

5. Casting out the Self, 1s.

SECOND SERIES.

1. On the Education of the Imagination.

2. Many Dimensions, 1s.

LONDON: SWAN SONNENSCHEIN & CO.

A New Era of Thought.

BY
CHARLES HOWARD HINTON, M.A., Oxon.
Author of “What is the Fourth Dimension,” and other “Scientific Romances.”

London:
SWAN SONNENSCHEIN & CO.,
PATERNOSTER SQUARE.
1888.

Butler & Tanner,
The Selwood Printing Works,
Frome, and London.

PREFACE.

The MSS. which formed the basis of this book were committed to us by the author, on his leaving England for a distant foreign appointment. It was his wish that we should construct upon them a much more complete treatise than we have effected, and with that intention he asked us to make any changes or additions we thought desirable. But long alliance with him in this work has convinced us that his thought (especially that of a general philosophical character) loses much of its force if subjected to any extraneous touch.

This feeling has induced us to print Part I. almost exactly as it came from his hands, although it would probably have received much rearrangement if he could have watched it through the press himself.

Part II. has been written from a hurried sketch, which he considered very inadequate, and which we have consequently corrected and supplemented. Chapter XI. of this part has been entirely re-written by us, and has thus not had the advantage of his supervision. This remark also applies to Appendix E, which is an elaboration of a theorem he suggested. Appendix H, and all the exercises have, in accordance with his wish, been written solely by us. It will be apparent to the reader that Appendix H is little more than a brief introduction to a very large subject, which, being concerned with tessaracts and solids, is really beyond treatment in writing and diagrams.

This difficulty recalls us to the one great fact, upon which we feel bound to insist, that the matter of this book must receive objective treatment from the reader, who will find it quite useless even to attempt to apprehend it without actually building in squares and cubes all the facts of space which we ask him to impress on his consciousness. Indeed, we consider that printing, as a method of spreading space-knowledge, is but a “pis aller,” and we would go back to that ancient and more fruitful method of the Greek geometers, and, while describing figures on the sand, or piling up pebbles in series, would communicate to others that spirit of learning and generalization begotten in our consciousness by continuous contact with facts, and only by continuous contact with facts vitally maintained.

ALICIA BOOLE,
H. JOHN FALK.

N.B. Models.—It is unquestionably a most important part of the process of learning space to construct these, and the reader should do so, however roughly and hastily. But, if Models are required as patterns, they may be ordered from Messrs. Swan Sonnenschein & Co., Paternoster Square, London, and will be supplied as soon as possible, the uncertainty as to demand for same not allowing us to have a large number made in advance. Much of the work can be done with plain cubes by using names without colours, but further on the reader will find colours necessary to enable him to grasp and retain the complex series of observations. Coloured models can easily be made by covering Kindergarten cubes with white paper and painting them with water-colour, and, if permanence be desired, dipping them in size and copal varnish.

TABLE OF CONTENTS.

INTRODUCTORY NOTE TO PART I.

At the completion of a work, or at the completion of the first part of a work, the feelings are necessarily very different from those with which the work was begun; and the meaning and value of the work itself bear a very different appearance. It will therefore be the simplest and shortest plan, if I tell the reader briefly what the work is to which these pages are a guide, and what I consider to be its value when done.

The task was to obtain a sense of the properties of higher space, or space of four dimensions, in the same way as that by which we reach a sense of our ordinary three-dimensional space. I now prefer to call the task that of obtaining a familiarity with higher matter, which shall be as intuitive to the mind as that of ordinary matter has become. The expression “higher matter” is preferable to “higher space,” because it is a somewhat hasty proceeding to split this concrete matter, which we touch and feel, into the abstractions of extension and impenetrability. It seems to me that I cannot think of space without matter, and therefore, as no necessity compels me to such a course, I do not split up the concrete object into subtleties, but I simply ask: “What is that which is to a cube or block or shape of any kind as the cube is to a square?”

In entering upon this inquiry we find the task is twofold. Firstly, there is the theoretical part, which is easy, viz. to set clearly before us the relative conditions which would obtain if there were a matter physically higher than this matter of ours, and to choose the best means of liberating our minds from the limitations imposed on it by the particular conditions under which we are placed. The second part of the task is somewhat laborious, and consists of a constant presentation to the senses of those appearances which portions of higher matter would present, and of a continual dwelling on them, until the higher matter becomes familiar.

The reader must undertake this task, if he accepts it at all, as an experiment. Those of us who have done it, are satisfied that there is that in the results of the experiment which make it well worthy of a trial.

And in a few words I may state the general bearings of this work, for every branch of work has its general bearings. It is an attempt, in the most elementary and simple domain, to pass from the lower to the higher. In pursuing it the mind passes from one kind of intuition to a higher one, and with that transition the horizon of thought is altered. It becomes clear that there is a physical existence transcending the ordinary physical existence; and one becomes inclined to think that the right direction to look is, not away from matter to spiritual existences, but towards the discovery of conceptions of higher matter, and thereby of those material existences whose definite relations to us are apprehended as spiritual intuitions. Thus, “material” would simply mean “grasped by the intellect, become known and familiar.” Our apprehension of anything which is not expressed in terms of matter, is vague and indefinite. To realize and live with that which we vaguely discern, we need to apply the intuition of higher matter to the world around us. And this seems to me the great inducement to this study. Let us form our intuition of higher space, and then look out upon the world.

Secondly, in this progress from ordinary to higher matter, as a general type of progress from lower to higher, we make the following observations. Firstly, we become aware that there are certain limitations affecting our regard. Secondly, we discover by our reason what those limitations are, and then force ourselves to go through the experience which would be ours if the limitations did not affect us. Thirdly, we become aware of a capacity within us for transcending those limitations, and for living in the higher mode as we had lived in the previous one.

We may remark that this progress from the ordinary to the higher kind of matter demands an absolute attention to details. It is only in the retention of details that such progress becomes possible. And as, in this question of matter, an absolute and unconventional examination gives us the indication of a higher, so, doubtless, in other questions, if we but come to facts without presupposition, we begin to know that there is a higher and to discover indications of the way whereby we can approach. That way lies in the fulness of detail rather than in the generalization.

Biology has shown us that there is a universal order of forms or organisms, passing from lower to higher. Therein we find an indication that we ourselves take part in this progress. And in using the little cubes we can go through the process ourselves, and learn what it is in a little instance.

But of all the ways in which the confidence gained from this lesson can be applied, the nearest to us lies in the suggestion it gives,—and more than the suggestion, if inclination to think be counted for anything,—in the suggestion of that which is higher than ourselves. We, as individuals, are not the limit and end-all, but there is a higher being than ours. What our relation to it is, we cannot tell, for that is unlike our relation to anything we know. But, perhaps all that happens to us is, could we but grasp it, our relation to it.

At any rate, the discovery of it is the great object beside which all else is as secondary as the routine of mere existence is to companionship. And the method of discovery is full knowledge of each other. Thereby is the higher being to be known. In as much as the least of us knows and is known by another, in so much does he know the higher. Thus, scientific prayer is when two or three meet together, and, in the belief of one higher than themselves, mutually comprehend that vision of the higher, which each one is, and, by absolute fulness of knowledge of the facts of each other’s personality, strive to attain a knowledge of that which is to each of their personalities as a higher figure is to its solid sides.

C. H. H.

A NEW ERA OF THOUGHT.

PART I.

INTRODUCTION.

There are no new truths in this book, but it consists of an effort to impress upon and bring home to the mind some of the more modern developments of thought. A few sentences of Kant, a few leading ideas of Gauss and Lobatschewski form the material out of which it is built up.

It may be thought to be unduly long; but it must be remembered that in these times there is a twofold process going on—one of discovery about external nature, one of education, by which our minds are brought into harmony with that which we know. In certain respects we find ourselves brought on by the general current of ideas—we feel that matter is permanent and cannot be annihilated, and it is almost an axiom in our minds that energy is persistent, and all its transformations remains the same in amount. But there are other directions in which there is need of definite training if we are to enter into the thoughts of the time.

And it seems to me that a return to Kant, the creator of modern philosophy, is the first condition. Now of Kant’s enormous work only a small part is treated here, but with the difference that should be found between the work of a master and that of a follower. Kant’s statements are taken as leading ideas, suggesting a field of work, and it is in detail and manipulation merely that there is an opportunity for workmanship.

Of Kant’s work it is only his doctrine of space which is here experimented upon. With Kant the perception of things as being in space is not treated as it seems so obvious to do. We should naturally say that there is space, and there are things in it. From a comparison of those properties which are common to all things we obtain the properties of space. But Kant says that this property of being in space is not so much a quality of any definable objects, as the means by which we obtain an apprehension of definable objects—it is the condition of our mental work.

Now as Kant’s doctrine is usually commented on, the negative side is brought into prominence, the positive side is neglected. It is generally said that the mind cannot perceive things in themselves, but can only apprehend them subject to space conditions. And in this way the space conditions are as it were considered somewhat in the light of hindrances, whereby we are prevented from seeing what the objects in themselves truly are. But if we take the statement simply as it is—that we apprehend by means of space—then it is equally allowable to consider our space sense as a positive means by which the mind grasps its experience.

There is in so many books in which the subject is treated a certain air of despondency—as if this space apprehension were a kind of veil which shut us off from nature. But there is no need to adopt this feeling. The first postulate of this book is a full recognition of the fact, that it is by means of space that we apprehend what is. Space is the instrument of the mind.

And here for the purposes of our work we can avoid all metaphysical discussion. Very often a statement which seems to be very deep and abstruse and hard to grasp, is simply the form into which deep thinkers have thrown a very simple and practical observation. And for the present let us look on Kant’s great doctrine of space from a practical point of view, and it comes to this—it is important to develop the space sense, for it is the means by which we think about real things.

There is a doctrine which found much favour with the first followers of Kant, that also affords us a simple and practical rule of work. It was considered by Fichte that the whole external world was simply a projection from the ego, and the manifold of nature was a recognition by the spirit of itself. What this comes to as a practical rule is, that we can only understand nature in virtue of our own activity; that there is no such thing as mere passive observation, but every act of sight and thought is an activity of our own.

Now according to Kant the space sense, or the intuition of space, is the most fundamental power of the mind. But I do not find anywhere a systematic and thoroughgoing education of the space sense. In every practical pursuit it is needed—in some it is developed. In geometry it is used; but the great reason of failure in education is that, instead of a systematic training of the space sense, it is left to be organized by accident and is called upon to act without having been formed. According to Kant and according to common experience it will be found that a trained thinker is one in whom the space sense has been well developed.

With regard to the education of the space sense, I must ask the indulgence of the reader. It will seem obvious to him that any real pursuit or real observation trains the space sense, and that it is going out of the way to undertake any special discipline.

To this I would answer that, according to my own experience, I was perfectly ignorant of space relations myself before I actually worked at the subject, and that directly I got a true view of space facts a whole series of conceptions, which before I had known merely by repute and grasped by an effort, became perfectly simple and clear to me.

Moreover, to take one instance: in studying the relations of space we always have to do with coloured objects, we always have the sense of weight; for if the things themselves have no weight, there is always a direction of up and down—which implies the sense of weight, and to get rid of these elements requires careful sifting. But perhaps the best point of view to take is this—if the reader has the space sense well developed he will have no difficulty in going through the part of the book which relates to it, and the phraseology will serve him for the considerations which come next.

Amongst the followers of Kant, those who pursued one of the lines of thought in his works have attracted the most attention and have been considered as his successors. Fichte, Schelling, Hegel have developed certain tendencies and have written remarkable books. But the true successors of Kant are Gauss and Lobatchewski.

For if our intuition of space is the means by which we apprehend, then it follows that there may be different kinds of intuitions of space. Who can tell what the absolute space intuition is? This intuition of space must be coloured, so to speak, by the conditions of the being which uses it.

Now, after Kant had laid down his doctrine of space, it was important to investigate how much in our space intuition is due to experience—is a matter of the physical circumstances of the thinking being—and how much is the pure act of the mind.

The only way to investigate this is the practical way, and by a remarkable analysis the great geometers above mentioned have shown that space is not limited as ordinary experience would seem to inform us, but that we are quite capable of conceiving different kinds of space.

Our space as we ordinarily think of it is conceived as limited—not in extent, but in a certain way which can only be realized when we think of our ways of measuring space objects. It is found that there are only three independent directions in which a body can be measured—it must have height, length and breadth, but it has no more than these dimensions. If any other measurement be taken in it, this new measurement will be found to be compounded of the old measurements. It is impossible to find a point in the body which could not be arrived at by travelling in combinations of the three directions already taken.

But why should space be limited to three independent directions?

Geometers have found that there is no reason why bodies should be thus limited. As a matter of fact all the bodies which we can measure are thus limited. So we come to this conclusion, that the space which we use for conceiving ordinary objects in the world is limited to three dimensions. But it might be possible for there to be beings living in a world such that they would conceive a space of four dimensions. All that we can say about such a supposition is, that it is not demanded by our experience. It may be that in the very large or the very minute a fourth dimension of space will have to be postulated to account for parts—but with regard to objects of ordinary magnitudes we are certainly not in a four dimensional world.

And this was the point at which about ten years ago I took up the inquiry.

It is possible to say a great deal about space of higher dimensions than our own, and to work out analytically many problems which suggest themselves. But can we conceive four-dimensional space in the same way in which we can conceive our own space? Can we think of a body in four dimensions as a unit having properties in the same way as we think of a body having a definite shape in the space with which we are familiar?

Now this question, as every other with which I am acquainted, can only be answered by experiment. And I commenced a series of experiments to arrive at a conclusion one way or the other.

It is obvious that this is not a scientific inquiry—but one for the practical teacher.

And just as in experimental researches the skilful manipulator will demonstrate a law of nature, the less skilled manipulator will fail; so here, everything depended on the manipulation. I was not sure that this power lay hidden in the mind, but to put the question fairly would surely demand every resource of the practical art of education.

And so it proved to be; for after many years of work, during which the conception of four-dimensional bodies lay absolutely dark, at length, by a certain change of plan, the whole subject of four-dimensional existence became perfectly clear and easy to impart.

There is really no more difficulty in conceiving four-dimensional shapes, when we go about it the right way, than in conceiving the idea of solid shapes, nor is there any mystery at all about it.

When the faculty is acquired—or rather when it is brought into consciousness, for it exists in every one in imperfect form—a new horizon opens. The mind acquires a development of power, and in this use of ampler space as a mode of thought, a path is opened by using that very truth which, when first stated by Kant, seemed to close the mind within such fast limits. Our perception is subject to the condition of being in space. But space is not limited as we at first think.

The next step after having formed this power of conception in ampler space, is to investigate nature and see what phenomena are to be explained by four-dimensional relations.

But this part of the subject is hardly one for the same worker as the one who investigates how to think in four-dimensional space. The work of building up the power is the work of the practical educator, the work of applying it to nature is the work of the scientific man. And it is not possible to accomplish both tasks at the same time. Consequently the crown is still to be won. Here the method is given of training the mind; it will be an exhilarating moment when an investigator comes upon phenomena which show that external nature cannot be explained except by the assumption of a four-dimension space.

The thought of the past ages has used the conception of a three-dimensional space, and by that means has classified many phenomena and has obtained rules for dealing with matters of great practical utility. The path which opens immediately before us in the future is that of applying the conception of four-dimensional space to the phenomena of nature, and of investigating what can be found out by this new means of apprehension.

In fact, what has been passed through may be called the three-dimensional era; Gauss and Lobatchewski have inaugurated the four-dimensional era.

CHAPTER I.
SCEPTICISM AND SCIENCE. BEGINNING OF KNOWLEDGE.

The following pages have for their object to induce the reader to apply himself to the study, in the first place of Space, and then of Higher Space; and, therefore, I have tried by indirect means to show forth those thoughts and conceptions to which the practical work leads.

And I feel that I have a great advantage in this project, inasmuch as many of the thoughts which spring up in the mind of one who studies higher space, and many of the conceptions to which he is driven, turn out to be nothing more nor less than old truths—the property of every mind that thinks and feels—truths which are not generally associated with the scientific apprehension of the world, but which are not for that reason any the less valuable.

And for my own part I cannot do more than put them forward in a very feeble and halting manner. For I have come upon them, not in the way of feeling or direct apprehension, but as the result of a series of works undertaken purely with the desire to know—a desire which did not lift itself to the height of expecting or looking for the beautiful or the good, but which simply asked for something to know.

For I found myself—and many others I find do so also—I found myself in respect to knowledge like a man who is in the midst of plenty and yet who cannot find anything to eat. All around me were the evidences of knowledge—the arts, the sciences, interesting talk, useful inventions—and yet I myself was profited nothing at all; for somehow, amidst all this activity, I was left alone, I could get nothing which I could know.

The dialect was foreign to me—its inner meaning was hidden. If I would, imitating the utterance of my fellows, say a few words, the effort was forced, the whole result was an artificiality, and, if successful, would be but a plausible imposture.

The word “sceptical” has a certain unpleasant association attached to it, for it has been used by so many people who are absolutely certain in a particular line, and attack other people’s convictions. But to be sceptical in the real sense is a far more unpleasant state of mind to the sceptic than to any one of his companions. For to a mind that inquires into what it really does know, it is hardly possible to enunciate complete sentences, much less to put before it those complex ideas which have so large a part in true human life.

Every word we use has so wide and fugitive a meaning, and every expression touches or rather grazes fact by so very minute a point, that, if we wish to start with something which we do know, and thence proceed in a certain manner, we are forced away from the study of reality and driven to an artificial system, such as logic or mathematics, which, starting from postulates and axioms, develops a body of ideal truth which rather comes into contact with nature than is nature.

Scientific achievement is reserved for those who are content to absorb into their consciousness, by any means and by whatever way they come, the varied appearances of nature, whence and in which by reflection they find floating as it were on the sea of the unknown, certain similarities, certain resemblances and analogies, by means of which they collect together a body of possible predictions and inferences; and in nature they find correspondences which are actually verified. Hence science exists, although the conceptions in the mind cannot be said to have any real correspondence in nature.

We form a set of conceptions in the mind, and the relations between these conceptions give us relations which we find actually vibrating in the world around us. But the conceptions themselves are essentially artificial.

We have a conception of atoms; but no one supposes that atoms actually exist. We suppose a force varying inversely as the square of the distance; but no one supposes such a mysterious thing to really be in nature. And when we come to the region of descriptive science, when we come to simple observation, we do not find ourselves any better provided with a real knowledge of nature. If, for instance, we think of a plant, we picture to ourselves a certain green shape, of a more or less definite character. This green shape enables us to recognise the plant we think of, and to describe it to a certain extent. But if we inquire into our imagination of it, we find that our mental image very soon diverges from the fact. If, for instance, we cut the plant in half, we find cells and tissues of various kinds. If we examine our idea of the plant, it has merely an external and superficial resemblance to the plant itself. It is a mental drawing meeting the real plant in external appearance; but the two things, the plant and our thought of it, come as it were from different sides—they just touch each other as far as the colour and shape are concerned, but as structures and as living organisms they are as wide apart as possible.

Of course by observation and study the image of a plant which we bear in our minds may be made to resemble a plant as found in the fields more and more. But the agreement with nature lies in the multitude of points superadded on to the notion of greenness which we have at first—there is no natural starting-point where the mind meets nature, and whence they can travel hand in hand.

It almost seems as if, by sympathy and feeling, a human being was easier to know than the simplest object. To know any object, however simple, by the reason and observation requires an endless process of thought and looking, building up the first vague impression into something like in more and more respects. While, on the other hand, in dealing with human beings there is an inward sympathy and capacity for knowing which is independent of, though called into play by, the observation of the actions and outward appearance of the human being.

But for the purpose of knowing we must leave out these human relationships. They are an affair of instinct and inherited unconscious experience. The mind may some day rise to the level of these inherited apprehensions, and be able to explain them; but at present it is far more than overtasked to give an account of the simplest portions of matter, and is quite inadequate to give an account of the nature of a human being.

Asking, then, what there was which I could know, I found no point of beginning. There were plenty of ways of accumulating observations, but none in which one could go hand in hand with nature.

A child is provided in the early part of its life with a provision of food adapted for it. But it seemed that our minds are left without a natural subsistence, for on the one hand there are arid mathematics, and on the other there is observation, and in observation there is, out of the great mass of constructed mental images, but little which the mind can assimilate. To the worker at science of course this crude and omnivorous observation is everything; but if we ask for something which we can know, it is like a vast mass of indigestible material with every here and there a fibre or thread which we can assimilate.

In this perplexity I was reduced to the last condition of mental despair; and in default of finding anything which I could understand in nature, I was sufficiently humbled to learn anything which seemed to afford a capacity of being known.

And the objects which came before me for this endeavour were the simple ones which will be plentifully used in the practical part of this book. For I found that the only assertion I could make about external objects, without bringing in unknown and unintelligible relations, was this: I could say how things were arranged. If a stone lay between two others, that was a definite and intelligible fact, and seemed primary. As a stone itself, it was an unknown somewhat which one could get more and more information about the more one studied the various sciences. But granting that there were some things there which we call stones, the way they were arranged was a simple and obvious fact which could be easily expressed and easily remembered.

And so in despair of being able to obtain any other kind of mental possession in the way of knowledge, I commenced to learn arrangements, and I took as the objects to be arranged certain artificial objects of a simple shape. I built up a block of cubes, and giving each a name I learnt a mass of them.

Now I do not recommend this as a thing to be done. All I can say is that genuinely then and now it seemed and seems to be the only kind of mental possession which one can call knowledge. It is perfectly definite and certain. I could tell where each cube came and how it was related to each of the others. As to the cube itself, I was profoundly ignorant of that; but assuming that as a necessary starting-point, taking that as granted, I had a definite mass of knowledge.

But I do not wish to say that this is better than any kind of knowledge which other people may find come home to them. All I want to do is to take this humble beginning of knowledge and show how inevitably, by devotion to it, it leads to marvellous and far-distant truths, and how, by a strange path, it leads directly into the presence of some of the highest conceptions which great minds have given us.

I do not think it ought to be any objection to an inquiry, that it begins with obvious and common details. In fact I do not think that it is possible to get anything simpler, with less of hypothesis about it, and more obviously a simple taking in of facts than the study of the arrangement of a block of cubes.

Many philosophers have assumed a starting point for their thought. I want the reader to accept a very humble one and see what comes of it. If this leads us to anything, no doubt greater results will come from more ambitious beginnings.

And now I feel that I have candidly exposed myself to the criticism of the reader. If he will have the patience to go on, we will begin and build up on our foundations.

CHAPTER II.
APPREHENSION OF NATURE. INTELLIGENCE. STUDY OF ARRANGEMENT OR SHAPE.

Nature is that which is around us. But it is by no means easy to get to nature. The savage living we may say in the bosom of nature, is certainly unapprehensive of it, in fact it has needed the greatness of a Wordsworth and of generations of poets and painters to open our eyes even in a slight measure to the wonder of nature.

Thus it is clear that it is not by mere passivity that we can comprehend nature; it is the goal of an activity, not a free gift.

And there are many ways of apprehending nature. There are the sounds and sights of nature which delight the senses, and the involved harmonies and the secret affinities which poetry makes us feel; then, moreover, there is the definite knowledge of natural facts in which the memory and reason are employed.

Thus we may divide our means of coming into contact with nature into three main channels: the senses, the imagination, and the mind. The imagination is perhaps the highest faculty, but we leave it out of consideration here, and ask: How can we bring our minds into contact with nature?

Now when we see two people of diverse characters we sometimes say that they cannot understand one another—there is nothing in the one by which he can understand the other—he is shut out by a limitation of his own faculties.

And thus our power of understanding nature depends on our own possession; it is in virtue of some mental activity of our own that we can apprehend that outside activity which we call nature. And thus the training to enable us to approach nature with our minds will be some active process on our own part.

In the course of my experience as a teacher I have often been struck by the want of the power of reason displayed by pupils; they are not able to put two and two together, as the saying goes, and I have been at some pains to investigate wherein this curious deficiency lies, and how it can be supplied. And I have found that there is in the curriculum no direct cure for it—the discipline which supplies it is not one which comes into school methods, it is a something which most children obtain in the natural and unsupervised education of their first contact with the world, and lies before any recognised mode of distinction. They can only understand in virtue of an activity of their own, and they have not had sufficient exercise in this activity.

In the present state of education it is impossible to diverge from the ordinary routine. But it is always possible to experiment on children who are out of the common line of education. And I believe I am amply justified by the result of my experiments.

I have seen that the same activity which I have found makes that habit of mind which we call intelligence in a child, is the source of our common and everyday rational intellectual work, and that just as the faculties of a child can be called forth by it, so also the powers of a man are best prepared by the same means, but on an ampler scale.

A more detailed development of the practical work of Part II., would be the best training for the mind of a child. An extension of the work of that Part would be the training which, hand in hand with observation and recapitulation, would best develop a man’s thought power.

In order to tell what the activity is by the prosecution of which we can obtain mental contact with nature we should observe what it is which we say we “understand” in any phenomenon of nature which has become clear to us.

When we look at a bright object it seems very different from a dull one. A piece of bright steel hardly looks like the same substance as a piece of dull steel. But the difference of appearance in the two is easily accounted for by the different nature of the surface in the two cases; in the one all the irregularities are done away with, and the rays of light which fall on it are sent off again without being dispersed and broken up. In the case of the dull iron the rays of light are broken up and divided, so that they are not transmitted with intensity in any one direction, but flung off in all sorts of directions.

Here the difference between the bright object and the dull object lies in the arrangement of the particles on its surface and their influence on the rays of light.

Again, with light itself the differences of colour are explained as being the effect on us of rays of different rates of vibration. Now a vibration is essentially this, a series of arrangements of matter which follow each other in a closed order, so that when the set has been run through, the first arrangement follows again. The whole theory of light is an account of arrangements of the particles in the transmitting medium, only the arrangements alter—are not permanent in any one characteristic, but go through a complete cycle of varieties.

Again, when the movements of the heavenly bodies are deduced from the theory of universal gravitation, what we primarily do is to take account of arrangement; for the law of gravity connects the movements which the attracted bodies tend to make with their distances, that is, it shows how their movements depend on their arrangement. And if gravity as a force is to be explained itself, the suppositions which have been put forward resolve it into the effect of the movements of small bodies; that is to say, gravity, if explained at all, is explained as the result of the arrangement and altering arrangements of small particles.

Again, to take the idea which proceeding from Goethe casts such an influence on botanical observation. Goethe (and also Wolf) laid down that the parts of a flower were modified leaves—and traced the stages and intermediate states between the ordinary green leaf and the most gorgeous petal or stamen or carpel, so unlike a leaf in form and function.

Now the essential value in this conception is, that it enables us to look, upon these different organs of a plant as modifications of one and the same organ—it enables us to think about the different varieties of the flower head as modifications of one single plant form. We can trace correspondences between them, and are led to possible explanations of their growth. And all this is done by getting rid of pistil and stamen as separate entities, and looking on them as leaves, and their parts due to different arrangement of the leaf structure. We have reduced these diverse objects to a common element, we have found the unit by whose arrangements the whole is produced. And in this department of thought, as also to take another instance, in chemistry, to understand is practically this: we find units (leaves or atoms) combinations of which account for the results which we see. Thus we see that that which the mind essentially apprehends is arrangement.

And this holds over the whole range of mental work, from the simplest observation to the most complex theory. When the eye takes in the form of an external object there is something more than a sense impression, something more than a sensation of greenness and light and dark. The mind works as well as the sense, and these sense impressions are definitely grouped in what we call the shape of the object. The essential act of perceiving lies in the apprehension of a shape, and a shape is an arrangement of parts. It does not matter what these parts are; if we take meaningless dots of colour and arrange them we obtain a shape which represents the appearance of a stone or a leaf to a certain degree. If we want to make our representation still more like, we must treat each of the dots as in themselves arrangements, we must compose each of them by many strokes and dots of the brush. But even in this case we have not got anything else besides arrangement. The ultimate element, the small items of light and shade or of colour, are in themselves meaningless; it is in their arrangement that the likeness of the representation consists.

Thus, from a drawing to our notion of the planetary system, all our contact with nature lies in this, in an appreciation of arrangement.

Hence to prepare ourselves for the understanding of nature, we must “arrange.” In virtue of our activity in making arrangements we prepare ourselves to do what is called understand nature. Or we may say, that which we call understanding nature is to discern something similar in nature to that which we do when we arrange elements into compounded groups.

Now if we study arrangement in the active way, we must have something to arrange; and the things we work with may be either all alike, or each of them varying from every other.

If the elements are not alike then we are not studying pure arrangement; but our knowledge is affected by the compound nature of that with which we deal. If the elements are all alike, we have what we call units. Hence the discipline preparatory for the understanding of nature is the active arrangement of like units.

And this is very much the case with all educational processes; only the things chosen to arrange are in general words, which are so complicated and carry such a train of association that, unless the mind has already acquired a knowledge of arrangement, it is puzzled and hampered, and never gets a clear apprehension of what its work is.

Now what shall we choose for our units? Any unit would do; but it ought to be a real thing—it ought to be something which can be touched and seen, not something which no one has ever touched or seen, and which is even incapable of definition, like a “number.”

I would divide studies into two classes: those which create the faculty of arrangement, and those which use it and exercise it. Mathematics exercises it, but I do not think it creates it; and unfortunately, in mathematics as it is now often taught, the pupil is launched , into a vast system of symbols—the whole use and meaning of symbols (namely, as means to acquire a clear grasp of facts) is lost to him.

Of the possible units which will serve, I take the cube; and I have found that whenever I took any other unit I got wrong, puzzled and lost my way. With the cube one does not get along very fast, but everything is perfectly obvious and simple, and builds up into a whole of which every part is evident.

And I must ask the reader to absolutely erase from his mind all desire or wish to be able to predict or assert anything about nature, and he must please look with horror on any mental process by which he gets at a truth in an ingenious but obscure and inexplicable way. Let him take nothing which is not perfectly clear, patent and evident, demonstrable to his senses, a simple repetition of obvious fact.

Our work will then be this: a study, by means of cubes, of the facts of arrangement. And the process of learning will be an active one of actually putting up the cubes. In this way we do for the mind what Wordsworth does for the imagination—we bring it into contact with nature.

CHAPTER III.
THE ELEMENTS OF KNOWLEDGE.

There are two elements which enter into our knowledge with respect to any phenomenon.

If, for instance, we take the sun, and ask ourselves what we observe, we notice that it is a bright, moving body; and of these two qualities, the brightness and the movement, each seems equally predicable of the sun. It does move, and it is bright.

Now further study discloses to us that there is a difference between these two affirmations. The motion of the sun in its diurnal course round the earth is only apparent; but it is really a bright, hot body.

Now of these two assertions which the mind naturally makes about the sun, one—that it is moving—depends on the relation of the beholder to the sun, the other is true about the sun itself. The observed motion depends on a fact affecting oneself and having nothing to do with the sun, while the brightness is really a quality of the sun itself.

Now we will call those qualities or appearances which we notice in a body which are due to the particular conditions under which oneself is placed in observing it, the self elements; those facts about it which are independent of the observer’s particular relationship we will call the residual element. Thus the sun’s motion is a self element in our thought of the sun, its brightness is a residual element.

It is not, of course, possible to draw a line distinctly between the self elements and the residual elements. For instance, some people have denied that brightness is a quality of things, but that it depends on the capacity of the being for receiving sensations; and for brightness they would substitute the assertion that the sun is giving forth a great deal of energy in the form of heat and light.

But there is no object in pursuing the discussion further. The main distinction is sufficiently obvious. And it is important to separate the self elements involved in our knowledge as far as possible, so that the residual elements may be kept for our closer attention. By getting rid of the self elements we put ourselves in a position in which we can propound sensible questions. By getting rid of the notion of its circular motion round the earth we prepare our way to study the sun as it really is. We get the subject clear of complications and extraneous considerations.

It would hardly be worth while to dwell on this consideration were it not of importance in our study of arrangement. But the fact is that directly a subject has been cleared of the self elements, it seems so absurd to have had them introduced at all that the great difficulty there was in getting rid of them is forgotten.

With regard to the knowledge we have at the present day about scientific matters, there do not seem to be any self elements present. But the worst about a self element is, that its presence is never dreamed of till it is got rid of; to know that it is there is to have done away with it. And thus our body of knowledge is like a fluid which keeps clear, not because there are no substances in solution, but because directly they become evident they fall down as precipitates.

Now one of our serious pieces of work will be to get rid of the self elements in the knowledge of arrangement.

And the kind of knowledge which we shall try to obtain will be somewhat different from the kind of knowledge which we have about events or natural phenomena. In the large subjects which generally occupy the mind the things thought of are so complicated that every detail cannot possibly be considered. The principles of the whole are realized, and then at any required time the principles can be worked out. Thus, with regard to a knowledge of the planetary system, it is said to be known if the law of movement of each of the planets is recognized, and their positions at any one time committed to memory. It is not our habit to remember their relative positions with regard to one another at many intervals, so as to have an exhaustive catalogue of them in our minds. But with regard to the elements of knowledge with which we shall work, the subject is so simple that we may justly demand of ourselves that we will know every detail.

And the knowledge we shall acquire will be much more one of the sense and feeling than of the reason. We do not want to have a rule in our minds by which we can recall the positions of the different cubes, but we want to have an immediate apprehension of them. It was Kant who first pointed out how much of thought there was embodied in the sense impressions; and it is this embodied thought which we wish to form.

CHAPTER IV.
THEORY AND PRACTICE.

Both in science and in morals there is an important distinction to be drawn between theory and practice. A knowledge of chemistry does not consist in the intellectual appreciation of different theories and principles, but in being able to act in accordance with the facts of chemical combination, so that by means of the appliances of chemistry practical results are produced. And so in morals—the theoretic acquaintance with the principles of human action may consist with a marked degree of ignorance of how to act amongst other human beings.

Now the use of the word “learn” has been much restricted to merely theoretic studies. It requires to be enlarged to the scientific meaning. And to know, should include practice in actual manipulation.

Let us take an instance. We all know what justice is, and any child can be taught to tell the difference between acting justly and acting unjustly. But it is a different thing to teach them to act with justice. Something is done which affects them unpleasantly. They feel an impulse to retaliate. In order to see what justice demands they have to put their personal feeling on one side. They have to get rid of those conditions under which they apprehended the effects of the action at first, and they have to look on it from another point of view. Then they have to act in accordance with this view.

Now there are two steps—one an intellectual one of understanding, one a practical one of carrying out the view. Neither is a moral step. One demands intelligence, the other the formation of a habit, and this habit can be inculcated by precept, by reward and punishment, by various means. But as human nature is constituted, if the habit of justice is inculcated it touches a part of the being. There is an emotional response. We know but little of a human being, but we can safely say that there are depths in it, beyond the feelings of momentary resentment and the stimulus of pleasurable or painful sensation, to which justice is natural.

How little adequate is our physical knowledge of a human being as a bodily frame to explain the fact of human life. Now and again we see one of these isolated beings bound up in another, as if there was an undiscovered physical bond between them. And in all there is this sense of justice—a kind of indwelling verdict of the universal mind, if we may use such an expression, in virtue of which a man feels not as a single individual but as all men.

With respect to justice, it is not only necessary to take the view of one other person than oneself, but that of many. There may be justice which is very good justice from the point of view of a party, but very bad justice from the point of view of a nation. And if we suppose an agency outside the human race, gifted with intelligence, and affecting the race, in the way for instance of causing storms or disturbances of the ground, in order to judge it with justice we should have to take a standpoint outside the race of men altogether. We could not say that this agency was bad. We should have to judge it with reference to its effect on other sentient beings.

There are some words which are often used in contrast with each other—egoism and altruism; and each seems to me unmeaning except as terms in a contrast.

Let us take an instance. A boy has a bag of cakes, and is going to enjoy them by himself. His parent stops him, and makes him set up some stumps and begin to learn to play cricket with another boy. The enjoyment of the cakes is lost—he has given that up; but after a little while he has a pleasure which is greater than that of cakes in solitude. He enters into the life of the game. He has given up, or been forced to give up, the pleasure he knew, and he has found a greater one. What he thought about himself before was that he liked cakes, now what he thinks about himself is that he likes cricket. Which of these is the true thought about himself? Neither, probably, but at any rate it is more near the truth to say that he likes the cricket. If now we use the word self to mean that which a person knows of himself, and it is difficult to see what other meaning it can have, his self as he knew it at first was thwarted, was given up, and through that he discovered his true self. And again with the cricket; he will make the sacrifice of giving that up, voluntarily or involuntarily, and will find a truer self still.

In general there is not much difficulty in making a boy find out that he likes cricket; and it is quite possible for him to eat his cakes first and learn to play cricket afterwards—the cricket will not come to him as a thwarting in any sense of what he likes better. But this ease in entering in to the pursuit only shows that the boy’s nature is already developed to the level of enjoying the game. The distinct moral advance would come in such a case when something which at first was hard to him to do was presented to him—and the hardness, the unpleasantness is of a double kind, the giving up of a pursuit or indulgence to which he is accustomed, and the exertion of forming the habits demanded by the new pursuit.

Now it is unimportant whether the renunciation is forced or willingly taken. But as a general rule it may be laid down, that by giving up his own desires as he feels them at the moment, to the needs and advantage of those around him, or to the objects which he finds before him demanding accomplishment, a human being passes to the discovery of his true self on and on. The process is limited by the responsibilities which a man finds come upon him.

The method of moral advance is to acquire a practical knowledge; he must first see what the advantage of some one other than himself would be, and then he must act in accordance with that view of things. Then having acted and formed a habit, he discovers a response in himself. He finds that he really cares, and that his former limited life was not really himself. His body and the needs of his body, so far as he can observe them, externally are the same as before; but he has obtained an inner and unintellectual, but none the less real, apprehension of what he is.

Thus altruism, or the sacrifice of egoism to others, is followed by a truer egoism, or assertion of self, and this process flashed across by the transcendent lights of religion, wherein, as in the sense of justice and duty, untold depths in the nature of man are revealed entirely unexpressed by the intellectual apprehension which we have of him as an animal frame of a very high degree of development, is the normal one by which from childhood a human being develops into the full responsibilities of a man.

Now both in science and in conduct there are self elements. In science, getting rid of the self elements means a truer apprehension of the facts about one; in conduct, getting rid of the self elements means obtaining a truer knowledge of what we are—in the way of feeling more strongly and deeply and being bound and linked in a larger scale.

Thus without pretending to any scientific accuracy in the use of terms, we can assign a certain amount of meaning to the expression—getting rid of self elements. And all that we can do is to take the rough idea of this process, and then taking our special subject matter, apply it. In affairs of life experiments lead to disaster. But happily science is provided wherein the desire to put theories into practice can be safely satisfied—and good results sometimes follow. Were it not for this the human race might before now have been utopiad from off the face of the earth.

In experiment, manipulation is everything; we must be certain of all our conditions, otherwise we fail assuredly and have not even the satisfaction of knowing that our failure is due to the wrongness of our conjectures.

And for our purposes we use a subject matter so simple that the manipulation is easy.

CHAPTER V.
KNOWLEDGE: SELF-ELEMENTS.

I must now go with somewhat of detail into the special subject in which these general truths will be exhibited. Everything I have to say would be conceived much more clearly by a very little practical manipulation.

But here I want to put the subject in as general a light as possible, so that there may be no hindrance to the judgment of the reader.

And when I use the word “know,” I assume something else than the possession of a rule, by which it can be said how facts are. By knowing I mean that the facts of a subject all lie in the mind ready to come out vividly into consciousness when the attention is directed on them. Michael Angelo knew the human frame, he could tell every little fact about it; if he chose to call up the image, he would see mentally how each muscle and fold of the skin lay with regard to the surrounding parts. We want to obtain a knowledge as good as Michael Angelo’s. There is a great difference between Michael Angelo and us; but let that difference be expressed, not in our way of knowing, but in the difference between the things he knew and the things we know. We take a very simple structure and know it as absolutely as he knew the complicated structure of the human body.

And let us take a block of cubes; any number will do, but for convenience sake let us take a set of twenty-seven cubes put together so as to form a large cube of twenty-seven parts. And let each of these cubes be marked so as to be recognized, and let each have a name so that it can be referred to. And let us suppose that we have learnt this block of cubes so that each one is known—that is to say, its position in the block is known and its relation to the other blocks.

Now having obtained this knowledge of the block as it stands in front of us, let us ask ourselves if there is any self element present in our knowledge of it.

And there is obviously this self element present. We have learnt the cubes as they stand in accordance with our own convenience in putting them up. We put the lowest ones first, and the others on the top of them, and we distinctly conceive the lower ones as supporting the upper ones. Now this fact of support has nothing to do with the block of cubes itself, it depends on the conditions under which we come to apprehend the block of cubes, it depends on our position on the surface of the earth, whereby gravity is an all important factor in our experience. In fact our sight has got so accustomed to take gravity into consideration in its view of things, that when we look at a landscape or object with our head upside down we do not see it inverted, but we superinduce on the direct sense impressions our knowledge of the action of gravity, and obtain a view differing very little from what we see when in an upright position.

It will be found that every fact about the cubes has involved in it a reference to up and down. It is by being above or below that we chiefly remember where the cubes are. But above and below is a relation which depends simply on gravity. If it were not for gravity above and below would be interchangeable terms, instead of expressing a difference of marked importance to us under our conditions of existence. Now we put “being above” or “being below” into the cubes themselves and feel it a quality in them—it defines their position. But this above or below really comes from the conditions in which we are. It is a self element, and as such, to obtain a true knowledge of the cubes we must get rid of it.

And now, for the sake of a process which will be explained afterwards, let us suppose that we cannot move the block of cubes which we have put up. Let us keep it fixed.

In order to learn how it is independent of gravity the best way would be to go to a place where gravity has virtually ceased to act; at the centre of the earth, for instance, or in a freely falling shell.

But this is impossible, so we must choose another way. Let us, then, since we cannot get rid of gravity, see what we have done already. We have learnt the cubes, and however they are learnt, it will be found that there is a certain set of them round which the others are mentally grouped, as being on the right or left, above or below. Now to get our knowledge as perfect as we can before getting rid of the self element up and down, we have to take as central cubes in our mind different sets again and again, until there are none which are primary to us.

Then there remains only the distinction of some being above others. Now this can only be made to sink out of the primary place in our thoughts by reversing the relation. If we turned the block upside down, and learnt it in this new position, then we should learn the position of the cubes with regard to each other with that element in them, which comes from the action of gravity, reversed. And the true nature of the arrangement to which we added something in virtue of our sensation of up and down, would become purer and more isolated in our minds.

We have, however, supposed that the cubes are fixed. Then, in order to learn them, we must put up another block showing what they would be like in the supposed new position. We then take a set of cubes, models of the original cubes, and by consideration we can put them in such positions as to be an exact model of what the block of cubes would be if turned upside down.

And here is the whole point on which the process depends. We can tell where each cube would come, but we do not know the block in this new position. I draw a distinction between the two acts, “to tell where it would be,” and to “know.” Telling where it would be is the preparation for knowing. The power of assigning the positions may be called the theory of the block. The actual knowledge is got by carrying out the theory practically, by putting up the blocks and becoming able to realize without effort where each one is.

It is not enough to put up the model blocks in the reverse position. It is found that this up and down is a very obstinate element indeed, and a good deal of work is requisite to get rid of it completely. But when it is got rid of in one set of cubes, the faculty is formed of appreciating shape independently of the particular parts which are above or below on first examination. We discover in our own minds the faculty of appreciating the facts of position independent of gravity and its influence on us. I have found a very great difference in different minds in this respect. To some it is easy, to some it is hard.

And to use our old instance, the discovery of this capacity is like the discovery of a love of justice in the being who has forced himself to act justly. It is a capacity for being able to take a view independent of the conditions under which he is placed, and to feel in accordance with that view. There is, so far as I know, no means of arriving immediately at this impartial appreciation of shape. It can only be done by, as it were, extending our own body so as to include certain cubes, and appreciating then the relation of the other cubes to those. And after this, by identifying ourselves with other cubes, and in turn appreciating the relation of the other cubes to these. And the practical putting up of the cubes is the way in which this power is gained. It springs up with a repetition of the mechanical acts. Thus there are three processes. 1st, An apprehension of what the position of the cubes would be. 2nd, An actual putting of them up in accordance with that apprehension, 3rd, The springing up in the mind of a direct feeling of what the block is, independent of any particular presentation.

Thus the self element of up and down can be got rid of out of a block of cubes.

And when even a little block is known like this, the mind has gained a great deal.

Yet in the apprehension and knowledge of the block of cubes with the up and down relation in them, there is more than in the absolute apprehension of them. For there is the apprehension of their position and also of the effect of gravity on them in their position.

Imagine ourselves to be translated suddenly to another part of the universe, and to find there intelligent beings, and to hold conversation with them. If we told them that we came from a world, and were to describe the sun to them, saying that it was a bright, hot body which moved round us, they would reply: You have told us something about the sun, but you have also told us something about yourselves.

Thus in the apprehension of the sun as a body moving round us there is more than in the apprehension of it as not moving round, for we really in this case apprehend two things—the sun and our own conditions. But for the purpose of further knowledge it is most important that the more abstract knowledge should be acquired. The self element introduced by the motion of the earth must be got rid of before the true relations of the solar system can be made out.

And in our block of cubes, it will be found that feelings about arrangement, and knowledge of space, which are quite unattainable with our ordinary view of position, become simple and clear when this discipline has been gone through.

And there can be no possible mental harm in going through this bit of training, for all that it comes to is looking at a real thing as it actually is—turning it round and over and learning it from every point of view.

CHAPTER VI.
FUNCTION OF MIND. SPACE AGAINST METAPHYSICS. SELF-LIMITATION AND ITS TEST. A PLANE WORLD.

We now pass on to the question: Are there any other self elements present in our knowledge of the block of cubes?

When we have learnt to free it from up and down, is there anything else to be got rid of?

It seems as if, when the cubes were thus learnt, we had got as abstract and impersonal a bit of knowledge as possible.

But, in reality, in the relations of the cubes as we thus apprehend them there is present a self element to which the up and down is a mere trifle. If we think we have got absolute knowledge we are indeed walking on a thin crust in unconsciousness of the depths below.

We are so certain of that which we are habituated to, we are so sure that the world is made up of the mechanical forces and principles which we familiarly deal with, that it is more of a shock than a welcome surprise to us to find how mistaken we were.

And after all, do we suppose that the facts of distance and size and shape are the ultimate facts of the world—is it in truth made up like a machine out of mechanical parts? If so, where is there room for that other which we know—more certainly, because inwardly—that reverence and love which make life worth having? No; these mechanical relations are our means of knowing about the world; they are not reality itself, and their primary place in our imaginations is due to the familiarity which we have with them, and to the peculiar limitations under which we are.

But I do not for a moment wish to go in thought beyond physical nature—I do not suppose that in thought we can. To the mind it is only the body that appears, and all that I hope to do is to show material relations, mechanism, arrangements.

But much depends on what kind of material relations we perceive outside us. A human being, an animal and a machine are to the mind all merely portions of matter arranged in certain ways. But the mind can give an exhaustive account of the machine, account fairly well for the animal, while the human being it only defines externally, leaving the real knowledge to be supplied by other faculties.

But we must not under-estimate the work of the mind, for it is only by the observation of and thought about the bodies with which we come into contact that we know human beings. It is the faculty of thought that puts us in a position to recognize a soul.

And so, too, about the universe—it is only by correct thought about it that we can perceive its true moral nature.

And it will be found that the deadness which we ascribe to the external world is not really there, but is put in by us because of our own limitations. It is really the self elements in our knowledge which make us talk of mechanical necessity, dead matter. When our limitations fall, we behold the spirit of the world like we behold the spirit of a friend—something which is discerned in and through the material presentation of a body to us.

Our thought means are sufficient at present to show us human souls; but all except human beings is, as far as science is concerned, inanimate. One self element must be got rid of from our perception, and this will be changed.

The one thing necessary is, that in matters of thinking we will not admit anything that is not perfectly clear, palpable and evident. On the mind the only conceivable demand is to seek for facts. The rock on which so many systems of philosophy have come to grief is the attempt to put moral principles into nature. Our only duty is to accept what we find. Man is no more the centre of the moral world than he is of the physical world. Then relegate the intellect to its right position of dealing with facts of arrangement—it can appreciate structure—and let it simply look on the world and report on it. We have to choose between metaphysics and space thought. In metaphysics we find lofty ideals—principles enthroned high in our souls, but which reduce the world to a phantom, and ourselves to the lofty spectators of an arid solitude. On the other hand, if we follow Kant’s advice, we use our means and find realities linked together, and in the physical interplay of forces and connexion of structure we behold the relations between spirits—those dwelling in man and those above him.

It is difficult to explain this next self element that has to be removed from the block of cubes; it requires a little careful preparation, in fact our language hardly affords us the means. But it is possible to approach indirectly, and to detect the self-element by means of an analogy.

If we suspect there be some condition affecting ourselves which make us perceive things not as they are, but falsely, then it is possible to test the matter by making the supposition of other beings subject to certain conditions, and then examining what the effect on their experience would be of these conditions.

Thus if we make up the appearances which would present themselves to a being subject to a limitation or condition, we shall find that this limitation or condition, when unrecognized by him, presents itself as a general law of his outward world, or as properties and qualities of the objects external to him. He will, moreover, find certain operations possible, others impossible, and the boundary line between the possible and impossible will depend quite as much on the conditions under which he is as on the nature of the operations.

And if we find that in our experience of the outward world there are analogous properties and qualities of matter, analogous possibilities and impossibilities, then it will show to us that we in our turn are under analogous limitations, and that what we perceive as the external world is both the external world and our own conditions. And the task before us will be to separate the two. Now the problem we take up here is this—to separate the self elements from the true fact. To separate them not merely as an outward theory and intelligent apprehension, but to separate them in the consciousness itself, so that our power of perception is raised to a higher level. We find out that we are under limitations. Our next step is to so familiarize ourselves with the real aspect of things, that we perceive like beings not under our limitations. Or more truly, we find that inward soul which itself not subject to these limitations, is awakened to its own natural action, when the verdicts conveyed to it through the senses are purged of the self elements introduced by the senses.

Everything depends on this—Is there a native and spontaneous power of apprehension, which springs into activity when we take the trouble to present to it a view from which the self elements are eliminated? About this every one must judge for himself. But the process whereby this inner vision is called on is a definite one.

And just as a human being placed in natural human relationships finds in himself a spontaneous motive towards the fulfilment of them, discovers in himself a being whose motives transcend the limits of bodily self-regard, so we should expect to find in our minds a power which is ready to apprehend a more absolute order of fact than that which comes through the senses.

I do not mean a theoretical power. A theory is always about it, and about it only. I mean an inner view, a vision whereby the seeing mind as it were identifies itself with the thing seen. Not the tree of knowledge, but of the inner and vital sap which builds up the tree of knowledge.

And if this point is settled, it will be of some use in answering the question: What are we? Are we then bodies only? This question has been answered in the negative by our instincts. Why should we despair of a rational answer? Let us adopt our space thought and develop it.

The supposition which we must make is the following. Let us imagine a smooth surface—like the surface of a table; but let the solid body at which we are looking be very thin, so that our surface is more like the surface of a thin sheet of metal than the top of a table.

And let us imagine small particles, like particles of dust, to lie on this surface, and to be attracted downwards so that they keep on the surface. But let us suppose them to move freely over the surface. Let them never in their movements rise one over the other; let them all singly and collectively be close to the surface. And let us suppose all sorts of attractions and repulsions between these atoms, and let them have all kinds of movements like the atoms of our matter have.

Then there may be conceived a whole world, and various kinds of beings as formed out of this matter. The peculiarity about this world and these beings would be, that neither the inanimate nor the animate members of it would move away from the surface. Their movements would all lie in one plane, a plane parallel to and very near the surface on which they are.

And if we suppose a vast mass to be formed out of these atoms, and to lie like a great round disk on the surface, compact and cohering closely together, then this great disk would afford a support for the smaller shapes, which we may suppose to be animate beings. The smaller shapes would be attracted to the great disk, but would be arrested at its rim. They would tend to the centre of the disk, but be unable to get nearer to the centre than its rim.

Thus, as we are attracted to the centre of the earth, but walk on its surface, the beings on this disk would be attracted to its centre, but walk on its rim. The force of attraction which they would feel would be the attraction of the disk. The other force of attraction, acting perpendicularly to the plane which keeps them and all the matter of their world to the surface, they would know nothing about. For they cannot move either towards this force or away from it; and the surface is quite smooth, so that they feel no friction in their movement over it.

Now let us realize clearly one of these beings as he proceeds along the rim of his world. Let us imagine him in the form of an outline of a human being, with no thickness except that of the atoms of his world. As to the mode in which he walks, we must imagine that he proceeds by springs or hops, because there would be no room for his limbs to pass each other.

Imagine a large disk on the table before you, and a being, such as the one described, proceeding round it. Let there be small movable particles surrounding him, which move out of his way as he goes along, and let these serve him for respiration; let them constitute an atmosphere.

Forwards and backwards would be to such a being direction along the rim—the direction in which he was proceeding and its reverse.

Then up and down would evidently be the direction away from the disk’s centre and towards it. Thus backwards and forwards, up and down, would both lie in the plane in which he was.

And he would have no other liberty of movement except these. Thus the words right and left would have no meaning to him. All the directions in which he could move, or could conceive movement possible, would be exhausted when he had thought of the directions along the rim and at right angles to it, both in the plane.

What he would call solid bodies, would be groups of the atoms of his world cohering together. Such a mass of atoms would, we know, have a slight thickness; namely, the thickness of a single atom. But of this he would know nothing. He would say, “A solid body has two dimensions—height (by how much it goes away from the rim) and thickness (by how much it lies along the rim).” Thus a solid would be a two-dimensional body, and a solid would be bounded by lines. Lines would be all that he could see of a solid body.

Thus one of the results of the limitations under which he exists would be, that he would say, “There are only two dimensions in real things.”

In order for his world to be permanent, we must suppose the surface on which he is to be very compact, compared to the particles of his matter; to be very rigid; and, if he is not to observe it by the friction of matter moving on it, to be very smooth. And if it is very compact with regard to his matter, the vibrations of the surface must have the effect of disturbing the portions of his matter, and of separating compound bodies up into simpler ones.

Fig. 1.

Fig. 2.

Another consequence of the limitation under which this being lies, would be the following:—If we cut out from the corners of a piece of paper two triangles, A B C and A′ B′ C′, and suppose them to be reduced to such a thinness that they are capable of being put on to the imaginary surface, and of being observed by the flat being like other bodies known to him; he will, after studying the bounding lines, which are all that he can see or touch, come to the conclusion that they are equal and similar in every respect; and he can conceive the one occupying the same space as the other occupies, without its being altered in any way.

If, however, instead of putting down these triangles into the surface on which the supposed being lives, as shown in [Fig. 1], we first of all turn one of them over, and then put them down, then the plane-being has presented to him two triangles, as shown in [Fig. 2].

And if he studies these, he finds that they are equal in size and similar in every respect. But he cannot make the one occupy the same space as the other one; this will become evident if the triangles be moved about on the surface of a table. One will not lie on the same portion of the table that the other has marked out by lying on it.

Hence the plane-being by no means could make the one triangle in this case coincide with the space occupied by the other, nor would he be able to conceive the one as coincident with the other.

The reason of this impossibility is, not that the one cannot be made to coincide, but that before having been put down on his plane it has been turned round. It has been turned, using a direction of motion which the plane-being has never had any experience of, and which therefore he cannot use in his mental work any more than in his practical endeavours.

Thus, owing to his limitations, there is a certain line of possibility which he cannot overstep. But this line does not correspond to what is actually possible and impossible. It corresponds to a certain condition affecting him, not affecting the triangle. His saying that it is impossible to make the two triangles coincide, is an assertion, not about the triangles, but about himself.

Now, to return to our own world, no doubt there are many assertions which we make about the external world which are really assertions about ourselves. And we have a set of statements which are precisely similar to those which the plane-being would make about his surroundings.

Thus, he would say, there are only two independent directions; we say there are only three.

He would say that solids are bounded by lines; we say that solids are bounded by planes.

Moreover, there are figures about which we assert exactly the same kind of impossibility as his plane-being did about the triangles in [Fig. 2].

We know certain shapes which are equal the one to the other, which are exactly similar, and yet which we cannot make fit into the same portion of space, either practically or by imagination.

If we look at our two hands we see this clearly, though the two hands are a complicated case of a very common fact of shape. Now, there is one way in which the right hand and the left hand may practically be brought into likeness. If we take the right-hand glove and the left-hand glove, they will not fit any more than the right hand will coincide with the left hand. But if we turn one glove inside out, then it will fit. Now, to suppose the same thing done with the solid hand as is done with the glove when it is turned inside out, we must suppose it, so to speak, pulled through itself. If the hand were inside the glove all the time the glove was being turned inside out, then, if such an operation were possible, the right hand would be turned into an exact model of the left hand. Such an operation is impossible. But curiously enough there is a precisely similar operation which, if it were possible, would, in a plane, turn the one triangle in [Fig. 2] into the exact copy of the other.

Look at the triangle in [Fig. 2], A B C, and imagine the point A to move into the interior of the triangle and to pass through it, carrying after it the parts of the lines A B and A C to which it is attached, we should have finally a triangle A B C, which was quite like the other of the two triangles A′ B′ C′ in [Fig. 2].

Thus we know the operation which produces the result of the “pulling through” is not an impossible one when the plane-being is concerned. Then may it not be that there is a way in which the results of the impossible operation of pulling a hand through could be performed? The question is an open one. Our feeling of it being impossible to produce this result in any way, may be because it really is impossible, or it may be a useful bit of information about ourselves.

Now at this point my special work comes in. If there be really a four-dimensional world, and we are limited to a space or three-dimensional view, then either we are absolutely three-dimensional with no experience at all or capacity of apprehending four-dimensional facts, or we may be, as far as our outward experience goes, so limited; but we may really be four-dimensional beings whose consciousness is by certain undetermined conditions limited to a section of the real space.

Thus we may really be like the plane-beings mentioned above, or we may be in such a condition that our perceptions, not ourselves, are so limited. The question is one which calls for experiment.

We know that if we take an animal, such as a dog or cat, we can by careful training, and by using rewards and punishment, make them act in a certain way, in certain defined cases, in accordance with justice; we can produce the mechanical action. But the feeling of justice will not be aroused; it will be but a mere outward conformity. But a human being, if so trained, and seeing others so acting, gets a feeling of justice.

Now, if we are really four-dimensional, by going through those acts which correspond to a four-dimensional experience (so far as we can), we shall obtain an apprehension of four-dimensional existence—not with the outward eye, but essentially with the mind.

And after a number of years of experiment which were entirely nugatory, I can now lay it down as a verifiable fact, that by taking the proper steps we can feel four-dimensional existence, that the human being somehow, and in some way, is not simply a three-dimensional being—in what way it is the province of science to discover. All that I shall do here is, to put forward certain suppositions which, in an arbitrary and forced manner, give an outline of the relation of our body to four-dimensional existence, and show how in our minds we have faculties by which we recognise it.

CHAPTER VII.
SELF ELEMENTS IN OUR CONSCIOUSNESS.

It is often taken for granted that our consciousness of ourselves and of our own feelings has a sort of direct and absolute value.

It is supposed to afford a testimony which does not require to be sifted like our consciousness of external events. But in reality it needs far more criticism to be applied to it than any other mode of apprehension.

To a certain degree we can sift our experience of the external world, and divide it into two portions. We can determine the self elements and the realities. But with regard to our own nature and emotions, the discovery which makes a science possible has yet to be made.

There are certain indications, however, springing from our observation of our own bodies, which have a certain degree of interest.

It is found that the processes of thought and feeling are connected with the brain. If the brain is disturbed, thoughts, sights, and sounds come into the consciousness which have no objective cause in the external world. Hence we may conclusively say that the human being, whatever he is, is in contact with the brain, and through the brain with the body, and through the body with the external world.

It is the structures and movements in the brain which the human being perceives. It is by a structure in the brain that he apprehends nature, not immediately. The most beautiful sights and sounds have no effect on a human being unless there is the faculty in the brain of taking them in and handing them on to the consciousness.

Hence, clearly, it is the movements and structure of the minute portions of matter forming the brain which the consciousness perceives. And it is only by models and representations made in the stuff of the brain that the mind knows external changes.

Now, our brains are well furnished with models and representations of the facts and events of the external world.

But a most important fact still requires its due weight to be laid upon it.

These models and representations are made on a very minute scale—the particles of brain matter which form images and representations are beyond the power of the microscope in their minuteness. Hence the consciousness primarily apprehends the movements of matter of a degree of smallness which is beyond the power of observation in any other way.

Hence we have a means of observing the movements of the minute portions of matter. Let us call those portions of the brain matter which are directly instrumental in making representations of the external world—let us call them brain molecules.

Now, these brain molecules are very minute portions of matter indeed; generally they are made to go through movements and form structures in such a way as to represent the movements and structures of the external world of masses around us.

But it does not follow that the structures and movements which they perform of their own nature are identical with the movements of the portions of matter which we see around us in the world of matter.

It may be that these brain molecules have the power of four-dimensional movement, and that they can go through four-dimensional movements and form four-dimensional structures.

If so, there is a practical way of learning the movements of the very small particles of matter—by observing, not what we can see, but what we can think.

For, suppose these small molecules of the brain were to build up structures and go through movements not in accordance with the rule of representing what goes on in the external world, but in accordance with their own activity, then they might go through four-dimensional movements and form four-dimensional structures.

And these movements and structures would be apprehended by the consciousness along with the other movements and structures, and would seem as real as the others—but would have no correspondence in the external world.

They would be thoughts and imaginations, not observations of external facts.

Now, this field of investigation is one which requires to be worked at.

At present it is only those structures and movements of the brain molecules which correspond to the realities of our three-dimensional space which are in general worked at consistently. But in the practical part of this book it will be found that by proper stimulus the brain molecules will arrange themselves in structures representing a four-dimensional existence. It only requires a certain amount of care to build up mental models of higher space existences. In fact, it is probably part of the difficulty of forming three-dimensional brain models, that the brain molecules have to be limited in their own freedom of motion to the requirements of the limited space in which our practical daily life is carried on.

Note.—For my own part I should say that all those confusions in remembering which come from an image taking the place of the original mental model—as, for instance, the difficulty in remembering which way to turn a screw, and the numerous cases of images in thought transference—may be due to a toppling over in the brain, four-dimensionalwise, of the structures formed—which structures would be absolutely safe from being turned into image structures if the brain molecules moved only three-dimensionalwise.

It is remarkable how in science “explaining” means the reference of the movements and tendencies to movement of the masses about us to the movements and tendencies to movement of the minute portions of matter.

Thus, the behaviour of gaseous bodies—the pressure which they exert, the laws of their cooling and intermixture are explained by tracing the movements of the very minute particles of which they are composed.

CHAPTER VIII.
RELATION OF LOWER TO HIGHER SPACE. THEORY OF THE ÆTHER.

At this point of our inquiries the best plan is to turn to the practical work, and try if the faculty of thinking in higher space can be awakened in the mind.

The general outline of the method is the same as that which has been described for getting rid of the limitation of up and down from a block of cubes. We supposed that the block was fixed; and to get the sense of what it would be when gravity acted in a different way with regard to it, we made a model of it as it would be under the new circumstances. We thought out the relations which would exist; and by practising this new arrangement we gradually formed the direct apprehension.

And so with higher-space arrangements. We cannot put them up actually, but we can say how they would look and be to the touch from various sides. And we can put up the actual appearances of them, not altogether, but as models succeeding one another; and by contemplation and active arrangement of these different views we call upon our inward power to manifest itself.

In preparing our general plan of work, it is necessary to make definite assumptions with regard to our world, our universe, or we may call it our space, in relation to the wider universe of four-dimensional space.

What our relation to it may be, is altogether undetermined. The real relationship will require a great deal of study to apprehend, and when apprehended will seem as natural to us as the position of the earth among the other planets does to us now.

But we have not got to wait for this exploration in order to commence our work of higher-space thought, for we know definitely that whatever our real physical relationship to this wider universe may be, we are practically in exactly the same relationship to it as the creature we have supposed living on the surface of a smooth sheet is to the world of threefold space.

And this relationship of a surface to a solid or of a solid, as we conjecture, to a higher solid, is one which we often find in nature. A surface is nothing more nor less than the relation between two things. Two bodies touch each other. The surface is the relationship of one to the other.

Again, we see the surface of water.

Thus our solid existence may be the contact of two four-dimensional existences with each other; and just as sensation of touch is limited to the surface of the body, so sensation on a larger scale may be limited to this solid surface.

And it is a fact worthy of notice, that in the surface of a fluid different laws obtain from those which hold throughout the mass. There are a whole series of facts which are grouped together under the name of surface tensions, which are of great importance in physics, and by which the behaviour of the surfaces of liquids is governed.

And it may well be that the laws of our universe are the surface tensions of a higher universe.

But these expressions, it is evident, afford us no practical basis for investigation. We must assume something more definite, and because more definite (in the absence of details drawn from experience), more arbitrary.