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.

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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.

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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.

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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.

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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.

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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.

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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.

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, ABC 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, ABC, 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 AB and AC to which it is attached, we should have finally a triangle ABC, 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.

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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.

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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.

And we will assume that the conditions under which we human beings are, exactly resemble those under which the plane-beings are placed, which have been described.

This forms the basis of our work; and the practical part of it consists in doing, with regard to higher space, that which a plane-being would do with regard to our space in order to enable himself to realize what it was.

If we imagine one of these limited creatures whose life is cramped and confined studying the facts of space existence, we find that he can do it in two ways. He can assume another direction in addition to those which he knows; and he can, by means of abstract reasoning, say what would take place in an ampler kind of space than his own. All this would be formal work. The conclusions would be abstract possibilities.

The other mode of study is this. He can take some of these facts of his higher space and he can ponder over them in his mind, and can make up in his plane world those different appearances which one and the same solid body would present to him, and then he may try to realize inwardly what his higher existence is.

Now, it is evident that if the creature is absolutely confined to a two-dimensional existence, then anything more than such existence will always be a mere abstract and formal consideration to him.

But if this higher-space thought becomes real to him, if he finds in his mind a possibility of rising to it, then indeed he knows that somehow he is not limited to his apparent world. Everything he sees and comes into contact with may be two-dimensional; but essentially, somehow, himself he is not two-dimensional merely.

And a precisely similar piece of work is before us. Assuming as we must that our outer experience is limited to three-dimensional space, we shall make up the appearances which the very simplest higher bodies would present to us, and we shall gradually arrive at a more than merely formal and abstract appreciation of them. We shall discover in ourselves a faculty of apprehension of higher space similar to that which we have of space. And thus we shall discover, each for himself, that, limited as his senses are, he essentially somehow is not limited.

The mode and method in which this consciousness will be made general, is the same in which the spirit of an army is formed.

The individuals enter into the service from various motives, but each and all have to go through those movements and actions which correspond to the unity of a whole formed out of different members. The inner apprehension which lies in each man of a participation in a life wider than that of his individual body, is awakened and responds; and the active spirit of the army is formed. So with regard to higher space, this faculty of apprehending intuitively four-dimensional relationships will be taken up because of its practical use. Individuals will be practically employed to do it by society because of the larger faculty of thought which it gives. In fact, this higher-space thought means as an affair of mental training simply the power of apprehending the results arising from four independent causes. It means the power of dealing with a greater number of details.

And when this faculty of higher-space thought has been formed, then the faculty of apprehending that higher existence in which men have part, will come into being.

It is necessary to guard here against there being ascribed to this higher-space thought any other than an intellectual value. It has no moral value whatever. Its only connexion with moral or ethical considerations is the possibility it will afford of recognizing more of the facts of the universe than we do now. There is a gradual process going on which may be described as the getting rid of self elements. This process is one of knowledge and feeling, and either may be independent of the other. At present, in respect of feeling, we are much further on than in respect to understanding, and the reason is very much this: When a self element has been got rid of in respect of feeling, the new apprehension is put into practice, and we live it into our organization. But when a self element has been got rid of intellectually, it is allowed to remain a matter of theory, not vitally entering into the mental structure of individuals.

Thus up and down was discovered to be a self element more than a thousand years ago; but, except as a matter of theory, we are perfect barbarians in this respect up to the present day.

We have supposed a being living in a plane world, that is, a being of a very small thickness in a direction perpendicular to the surface on which he is.

Now, if we are situated analogously with regard to an ampler space, there must be some element in our experience corresponding to each element in the plane-being’s experience.

And it is interesting to ask, in the case of the plane-being, what his opinion would be with respect to the surface on which he was.

He would not recognize it as a surface with which he was in contact; he would have no idea of a motion away from it or towards it.

But he would discover its existence by the fact that movements were transmitted along it. By its vibrating and quivering, it would impart movement to the particles of matter lying on it.

Hence, he would consider this surface to be a medium lying between bodies, and penetrating them. It would appear to him to have no weight, but to be a powerful means of transmitting vibrations. Moreover, it would be unlike any other substance with which he was acquainted, inasmuch as he could never get rid of it. However perfect a vacuum be made, there would be in this vacuum just as much of this unknown medium as there was before.

Moreover, this surface would not hinder the movement of the particles of matter over it. Being smooth, matter would slide freely over it. And this would seem to him as if matter went freely through the medium.

Then he would also notice the fact that vibrations of this medium would tear asunder portions of matter. The plane surface, being very compact, compared to the masses of matter on it, would, by its vibrations, shake them into their component parts.

Hence he would have a series of observations which tended to show that this medium was unlike any ordinary matter with which he was acquainted. Although matter passed freely through it, still by its shaking it could tear matter in pieces. These would be very difficult properties to reconcile in one and the same substance. Then it is weightless, and it is everywhere.

It might well be that he would regard the supposition of there being a plane surface, on which he was, as a preferable one to the hypothesis of this curious medium; and thus he might obtain a proof of his limitations from his observations.

Now, is there anything in our experience which corresponds to this medium which the plane-being gets to observe?

Do we suppose the existence of any medium through which matter freely moves, which yet by its vibrations destroys the combinations of matter—some medium which is present in every vacuum, however perfect, which penetrates all bodies, and yet can never be laid hold of?

These are precisely observations which have been made.

The substance which possesses all these qualities is called the Æther. And the properties of the Æther are a perpetual object of investigation in science.

Now, it is not the place here to go into details, as all we want is a basis for work; and however arbitrary it may be, it will serve if it enables us to investigate the properties of higher space.

We will suppose, then, that we are not in, but on the Æther, only not on it in any known direction, but that the new direction is that which comes in. The Æther is a smooth body, along which we slide, being distant from it at every point about the thickness of an atom; or, if we take our mean distance, being distant from it by half the thickness of an atom measured in this new direction.

Then, just as in space objects, a cube, for instance, can stand on the surface of a table, or on the surface over which the plane-being moves, so on the Æther can stand a higher solid.

All that the plane-being sees or touches of a cube, is the square on which it rests.

So all that we could see or touch of a higher solid would be that part by which it stood on the Æther; and this part would be to us exactly like any ordinary solid body. The base of a cube would be to the plane-being like a square which is to him an ordinary solid.

Now, the two ways, in which a plane-being would apprehend a solid body, would be by the successive appearances to him of it as it passed through his plane; and also by the different views of one and the same solid body which he got by turning the body over, so that different parts of its surface come into contact with his plane.

And the practical work of learning to think in four-dimensional space, is to go through the appearances which one and the same higher solid has.

Often, in the course of investigation in nature, we come across objects which have a certain similarity, and yet which are in parts entirely different. The work of the mind consists in forming an idea of that whole in which they cohere, and of which they are simple presentations.

The work of forming an idea of a higher solid is the most simple and most definite of all such mental operations.

If we imagine a plane world in which there are objects which correspond to our sun, to the planets, and, in fact, to all our visible universe, we must suppose a surface of enormous extent on which great disks slide, these disks being worlds of various orders of magnitude.

These disks would some of them be central, and hot, like our sun; round them would circulate other disks, like our planets.

And the systems of sun and planets must be conceived as moving with great velocity over the surface which bears them all.

And the movements of the atoms of these worlds will be the course of events in such worlds. As the atoms weave together, and form bodies altering, becoming, and ceasing, so will bodies be formed and disappear.

And the plane which bears them all on its smooth surface will simply be a support to all these movements, and influence them in no way.

Is to be conscious of being conscious of being hot, the same thing as to be conscious of being hot? It is not the same. There is a standing outside, and objectivation of a state of mind which every one would say in the first state was very different from the simple consciousness. But the consciousness must do as much in the first case as in the second. Hence the feeling hot is very different from the consciousness of feeling hot.

A feeling which we always have, we should not be conscious of—a sound always present ceases to be heard. Hence consciousness is a concomitant of change, that is, of the contact between one state and another.

If a being living on such a plane were to investigate the properties, he would have to suppose the solid to pass through his plane in order to see the whole of its surface. Thus we may imagine a cube resting on a table to begin to penetrate through the table. If the cube passes through the surface, making a clean cut all round it, so that the plane-being can come up to it and investigate it, then the different parts of the cube as it passes through the plane will be to him squares, which he apprehends by the boundary lines. The cut which there is in his plane must be supposed not to be noticed, he must be able to go right up to the cube without hindrance, and to touch and see that thin slice of it which is just above the plane.

And so, when we study a higher solid, we must suppose that it passes through the Æther, and that we only see that thin three-dimensional section of it which is just about to pass from one side to the other of the Æther.

When we look on a solid as a section of a higher solid, we have to suppose the Æther broken through, only we must suppose that it runs up to the edge of the body which is penetrating it, so that we are aware of no breach of continuity.

The surface of the Æther must then be supposed to have the properties of the surface of a fluid; only, of course, it is a solid three-dimensional surface, not a two-dimensional surface.

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CHAPTER IX.
ANOTHER VIEW OF THE ÆTHER. MATERIAL AND ÆTHERIAL BODIES.

We have supposed in the case of a plane world that the surface on which the movements take place is inactive, except by its vibrations. It is simply a smooth support.

For the sake of simplicity let us call this smooth surface “the Æther” in the case of a plane world.

The Æther then we have imagined to be simply a smooth, thin sheet, not possessed of any definite structure, but excited by real disturbances of the matter on it into vibrations, which carry the effect of these disturbances as light and heat to other portions of matter. Now, it is possible to take an entirely different view of the Æther in the case of a plane world.

Let us imagine that, instead of the Æther being a smooth sheet serving simply as a support, it is definitely marked and grooved.

Let us imagine these grooves and channels to be very minute, but to be definite and permanent.

Then, let us suppose that, instead of the matter which slides in the Æther having attractions and repulsions of its own, that it is quite inert, and has only the properties of inertia.

That is to say, taking a disk or a plane world as a specimen, the whole disk is sliding on the Æther in virtue of a certain momentum which it has, and certain portions of its matter fit into the grooves in the Æther, and move along those grooves.

The size of the portions is determined by the size of the grooves. And let us call those portions of matter which occupy the breadth of a groove, atoms. Then it is evident that the disk sliding along over the Æther, its atoms will move according to the arrangement of the grooves over which the disk slides. If the grooves at any one particular place come close together, there will be a condensation of matter at that place when the disk passes over it; and if the grooves separate, there will be a rarefaction of matter.

If we imagine five particles, each slipping along in its own groove, if the particles are arranged in the form of a regular pentagon, and the grooves are parallel, then these five particles, moving evenly on, will maintain their positions with regard to one another, and a body would exist like a pentagon, lasting as long as the groves remained parallel.

But if, after some distance had been traversed by the disk, and these five particles were brought into a region where one of the grooves tended away from the others, the shape of the pentagon would be destroyed, it would become some irregular figure. And it is easy to see that if the grooves separated, and other grooves came in amongst them, along which other portions of matter were sliding, that the pentagon would disappear as an isolated body, that its constituent matter would be separated, and that its particles would enter into other shapes as constituents of them, and not of the original pentagon.

Thus, in cases of greater complication, an elaborate structure may be supposed to be formed, to alter, and to pass away; its origin, growth, and decay being due, not to any independent motion of the particles constituting it, but to the movement of the disk whereby its portions of matter were brought to regions where there was a particular disposition of the grooves.

Then the nature of the shape would really be determined by the grooves, not by the portions of matter which passed over them—they would become manifest as giving rise to a material form when a disk passed over them, but they would subsist independently of the disk; and if another disk were to pass over the same grooves, exactly the same material structures would spring up as came into being before.

If we make a similar supposition about our Æther along which our earth slides, we may conceive the movements of the particles of matter to be determined, not by attractions or repulsions exerted on one another, but to be set in existence by the alterations in the directions of the grooves of the Æther along which they are proceeding.

If the grooves were all parallel, the earth would proceed without any other motion than that of its path in the heavens.

But with an alteration in the direction of the grooves, the particles, instead of proceeding uniformly with the mass of the earth, would begin to move amongst each other. And by a sufficiently complicated arrangement of grooves it may be supposed that all the movements of the forms we see around us are due to interweaving and variously disposed grooves.

Thus the movements, which any body goes through, would depend on the arrangement of the Æthereal grooves along which it was passing. As long as the grooves remain grouped together in approximately the same way, it would maintain its existence as the same body; but when the grooves separated, and became involved with the grooves of other objects, this body would cease to exist separately.

Thus the separate existences of the earth might conceivably be due to the disposition of those parts of the Æther over which the earth passed. And thus any object would have to be separated into two parts, one the Æthereal form, or modification which lasted, the other the material particles which, coming on with blind momentum, were directed into such movements as to produce the actual objects around us.

In this way there would be two parts in any organism, the material part and the Æthereal part. There would be the material body, which soon passes and becomes indistinguishable from any other material body, and the Æthereal body which remains.

Now, if we direct our attention to the material body, we see the phenomena of growth, decay, and death, the coming and the passing away of a living being, isolated during his existence, absolutely merged at his death into the common storehouse of matter.

But if we regard the Æthereal body, we find something different. We find an organism which is not so absolutely separated from the surrounding organisms—an organism which is part of the Æther, and which is linked to other Æthereal organisms by its very substance—an organism between which and others there exists a unity incapable of being broken, and a common life which is rather marked than revealed by the matter which passes over it. The Æthereal body moreover remains permanently when the material body has passed away.

The correspondences between the Æthereal body and the life of an organism such as we know, is rather to be found in the emotional region than in the one of outward observation. To the Æthereal form, all parts of it are equally one; but part of this form corresponds to the future of the material being, part of it to his past. Thus, care for the future and regard for the past would be the way in which the material being would exhibit the unity of the Æthereal body, which is both his past, his present, and his future. That is to say, suppose the Æthereal body capable of receiving an injury, an injury in one part of it would correspond to an injury in a man’s past; an injury in another part,—that which the material body was traversing,—would correspond to an injury to the man at the present moment; injury to the Æthereal body at another part, would correspond to injury coming to the man at some future time. And the self-preservation of the Æthereal body, supposing it to have such a motive, would in the last case be the motive of regarding his own future to the man. And inasmuch as the man felt the real unity of his Æthereal body, and did not confine his attention to his material body, which is absolutely disunited at every moment from its future and its past—inasmuch as he apprehended his Æthereal unity, insomuch would he care for his future welfare, and consider it as equal in importance to his present comfort. The correspondence between emotion and physical fact would be, that the emotion of regard corresponded to an undiscerned Æthereal unity. And then also, just as the two tips of two fingers put down on a plane, would seem to a plane-being to be two completely different bodies, not connected together, so one and the same Æthereal body might appear as two distinct material bodies, and any regard between the two would correspond to an apprehension of their Æthereal unity. In the supposition of an Æthereal body, it is not necessary to keep to the idea of the rigidity and permanence of the grooves defining the motion of the matter which, passing along, exhibits the material body. The Æthereal body may have a life of its own, relations with other Æthereal bodies, and a life as full of vicissitudes as that of the material body, which in its total orbit expresses in the movements of matter one phase in the life of the Æthereal body.

But there are certain obvious considerations which prevent any serious dwelling on these speculations—they are only introduced here in order to show how the conception of higher space lends itself to the representation of certain indefinite apprehensions,—such as that of the essential unity of the race,—and affords a possible clue to correspondences between the emotional and the physical life.

The whole question of our relation to the Æther has to be settled. That which we call the Æther is far more probably the surface of a liquid, and the phenomena we observe due to surface tensions. Indeed, the physical questions concern us here nothing at all. It is easy enough to make some supposition which gives us a standing ground to discipline our higher-space perception; and when that is trained, we shall turn round and look at the facts.

The conception which we shall form of the universe will undoubtedly be as different from our present one, as the Copernican view differs from the more pleasant view of a wide immovable earth beneath a vast vault. Indeed, any conception of our place in the universe will be more agreeable than the thought of being on a spinning ball, kicked into space without any means of communication with any other inhabitants of the universe.

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CHAPTER X.
HIGHER SPACE AND HIGHER BEING. PERCEPTION AND INSPIRATION.

In the instinctive and sense perception of man and nature there is all hidden, which reflection afterwards brings into consciousness.

We are conscious of somewhat higher than each individual man when we look at men. In some, this consciousness reaches an extreme pitch, and becomes a religious apprehension. But in none is it otherwise than instinctive. The apprehension is sufficiently definite to be certain. But it is not expressible to us in terms of the reason.

Now, I have shown that by using the conception of higher space it is easy enough to make a supposition which shall show all mankind as physical parts of one whole. Our apparent isolation as bodies from each other is by no means so necessary to assume as it would appear. But, of course, a supposition of that kind is of no value, except as showing a possibility. If we came to examine into the matter closely, we should find a natural relationship which accounted for our consciousness being limited as at present it is.

The first thing to be done, is to organize our higher-space perception, and then look. We cannot tell what external objects will blend together into the unity of a higher being. But just as the riddle of the two hands becomes clear to us from our first inspection of higher space, so will there grow before our eyes greater unities and greater surprises.

We have been subject to a limitation of the most absurd character. Let us open our eyes and see the facts.

Now, it requires some training to open the eyes. For many years I worked at the subject without the slightest success. All was mere formalism. But by adopting the simplest means, and by a more thorough knowledge of space, the whole flashed clear.

Space shapes can only be symbolical of four-dimensional shapes; and if we do not deal with space shapes directly, but only treat them by symbols on the plane—as in analytical geometry—we are trying to get a perception of higher space through symbols of symbols, and the task is hopeless. But a direct study of space leads us to the knowledge of higher space. And with the knowledge of higher space there come into our ken boundless possibilities. All those things may be real, whereof saints and philosophers have dreamed.

Looking on the fact of life, it has become clear to the human mind, that justice, truth, purity, are to be sought—that they are principles which it is well to serve. And men have invented an abstract devotion to these, and all comes together in the grand but vague conception of Duty.

But all these thoughts are to those which spring up before us as the shadow on a bank of clouds of a great mountain is to the mountain itself. On the piled-up clouds falls the shadow—vast, imposing, but dark, colourless. If the beholder but turns, he beholds the mountain itself, towering grandly with verdant pines, the snowline, and the awful peaks.

So all these conceptions are the way in which now, with vision confined, we apprehend the great existences of the universe. Instead of an abstraction, what we have to serve is a reality, to which even our real things are but shadows. We are parts of a great being, in whose service, and with whose love, the utmost demands of duty are satisfied.

How can it not be a struggle, when the claims of righteousness mean diminished life,—even death,—to the individual who strives? And yet to a clear and more rational view it will be seen that in his extinction and loss, that which he loves,—that real being which is to him shadowed forth in the present existence of wife and child,—that being lives more truly, and in its life those he loves are his for ever.

But, of course, there are mistakes in what we consider to be our duty, as in everything else; and this is an additional reason for pursuing the quest of this reality. For by the rational observance of other material bodies than our own, we come to the conclusion that there are other beings around us like ourselves, whom we apprehend in virtue of two processes—the one simply a sense one of observation and reflection—the other a process of direct apprehension.

Now, if we did not go through the sense process of observation, we might, it is true, know that there were other human beings around us in some subtle way—in some mesmeric feeling; but we should not have that organized human life which, dealing with the things of the world, grows into such complicated forms. We should for ever be good-humoured babies—a sensuous, affectionate kind of jelly-fish.

And just so now with reference to the high intelligences by whom we are surrounded. We feel them, but we do not realize them.

To realize them, it will be necessary to develop our power of perception.

The power of seeing with our bodily eye is limited to the three-dimensional section.

But I have shown that the inner eye is not thus limited; that we can organize our power of seeing in higher space, and that we can form conceptions of realities in this higher space, just as we can in our ordinary space.

And this affords the groundwork for the perception and study of these other beings than man. Just as some mechanical means are necessary for the apprehension of our fellows in space, so a certain amount of mechanical education is necessary for the perception of higher beings in higher space.

Let us turn the current of our thought right round; instead of seeking after abstractions, and connecting our observations by ideas, let us train our sense of higher space and build up conceptions of greater realities, more absolute existences.

It is really a waste of time to write or read more generalities. Here is the grammar of the knowledge of higher being—let us learn it, not spend time in speculating as to whither it will lead us.

Yet one thing more. We are, with reference to the higher things of life, like blind and puzzled children. We know that we are members of one body, limbs of one vine; but we cannot discern, except by instinct and feeling, what that body is, what the vine is. If to know it would take away our feeling, then it were well never to know it. But fuller knowledge of other human beings does not take away our love for them; what reason is there then to suppose that a knowledge of the higher existences would deaden our feelings?

And then, again, we each of us have a feeling that we ourselves have a right to exist. We demand our own perpetuation. No man, I believe, is capable of sacrificing his life to any abstract idea; in all cases it is the consciousness of contact with some being that enables him to make the last human sacrifice. And what we can do by this study of higher space, is to make this consciousness, which has been reserved for a few, the property of all. Do we not all feel that there is a limit to our devotion to abstractions, none to beings whom we love. And to love them, we must know them.

Then, just as our own individual life is empty and meaningless without those we love, so the life of the human race is empty and meaningless without a knowledge of those that surround it. And although to some an inner knowledge of the oneness of all men is vouchsafed, it remains to be demonstrated to the many.

The perpetual struggle between individual interests and the common good can only be solved by merging both impulses in a love towards one being whose life lies in the fulfilment of each.

And this search, it seems to me, affords the needful supplement to the inquiries of one with whose thought I have been very familiar, and to which I return again, after having abandoned it for the purely materialistic views which seem forced upon us by the facts of science.

All that he said seemed to me unsupported by fact, unrelated to what we know.

But when I found that my knowledge was merely an empty pretence, that it was the vanity of being able to predict and foretell that stood to me in the place of an absolute apprehension of fact—when all my intellectual possessions turned to nothingness, then I was forced into that simple quest for fact, which, when persisted in and lived in, opens out to the thoughts like a flower to the life-giving sun.

It is indeed a far safer course, to believe that which appeals to us as noble, than simply to ask what is true; to take that which great minds have given, than to demand that our puny ones should be satisfied. But I suppose there is some good to some one in the scepticism and struggle of those who cannot follow in the safer course.

The thoughts of the inquirer to whom I allude may roughly be stated thus:—

He saw in human life the working out of a great process, in the toil and strain of our human history he saw the becoming of man. There is a defect whereby we fall short of the true measure of our being, and that defect is made good in the course of history.

It is owing to that defect that we perceive evil; and in the perception of evil and suffering lies our healing, for we shall be forced into that path at last, after trying every other, which is the true one.

And this, the history of the redemption of man, is what he saw in all the scenes of life; each most trivial occurrence was great and significant in relation to this.

And, further, he put forward a definite statement with regard to this defect, this lack of true being, for it lay, he said, in the self-centredness of our emotions, in the limitation of them to our bodily selves. He looked for a time when, driven from all thoughts of our own pain or pleasure, good or evil, we should say, in view of the miseries of our fellow-creatures, Let me be anyhow, use my body and my mind in any way, so that I serve.

And this, it seems to me, is the true aspiration; for, just as a note of music flings itself into the march of the melody, and, losing itself in it, is used for it and lost as a separate being, so we should throw these lives of ours as freely into the service of—whom?

Here comes the difficulty. Let it be granted that we should have no self-rights, limit our service in no way, still the question comes, What shall we serve?

It is far happier to have some concrete object to which we are devoted, or to be bound up in the ceaseless round of active life, wherein each day presents so many necessities that we have no room for choice.

But besides and apart from all these, there comes to some the question, “What does it all mean?” To others, an unlovable and gloomy aspect is presented, wherein their life seems to be but used as a material worthless in itself and ungifted with any dignity or honour; while to others again, with the love of those they love, comes a cessation of all personal interest in life, and a disappointment and feeling of valuelessness.

And in all these cases some answer is needed. And here human duty ceases. We cannot make objects to love. We can make machines and works of art, but nothing which directly excites our love. To give us that which rouses our love, is the duty of one higher than ourselves.

And yet in one respect we have a duty—we must look.

What good would it be, to surround us with objects of loving interest, if we bury our regards in ourselves and will not see?

And does it not seem as if with lowered eyelids, till only the thinnest slit was open, we gazed persistently, not on what is, but on the thinnest conceivable section of it?

Let it be granted that our right attitude is, so to devote ourselves that there is no question as to what we will do or what we will not do, but we are perfectly obedient servants. The question is, Whom are we to serve?

It cannot be each individual, for their claims are conflicting, and as often as not there is more need of a master than of a servant. Moreover, the aspect of our fellows does not always excite love, which is the only possible inducer of the right attitude of service. If we do not love, we can only serve for a self motive, because it is in some way good for ourselves.

Thus it seems to me that we are reduced to this: our only duty is to look for that which it is given us to love.

But this looking is not mere gazing. To know, we must act.

Let any one try it. He will find that unless he goes through a series of actions corresponding to his knowledge, he gets merely a theoretic and outside view of any facts. The way to know is this: Get somehow a means of telling what your perceptions would be if you knew, and act in accordance with those perceptions.

Thus, with regard to a fellow-creature, if we knew him we should feel what his feelings are. Let us then learn his feelings, and act as if we had them. It is by the practical work of satisfying his needs that we get to know him.

Then, may-be, we love him; or perchance it is said we may find that through him we have been brought into contact with one greater than him.

This is our duty—to know—to know, not merely theoretically, but practically; and then, when we know, we have done our part; if there is nothing, we cannot supply it. All we have to do is to look for realities.

We must not take this view of education—that we are horribly pressed for time, and must learn, somehow, a knack of saying how things must be, without looking at them.

But rather, we must say that we have a long time—all our lives, in which we will press facts closer and closer to our minds; and we begin by learning the simplest. There is an idea in that home of our inspiration—the fact that there are certain mechanical processes by which men can acquire merit. This is perfectly true. It is by mechanical processes that we become different; and the science of education consists largely in systematizing these processes.

Then, just as space perceptions are necessary for the knowledge of our fellow-men, and enable us to enter into human relationships with them in all the organized variety of civilized life, so it is necessary to develop our perceptions of higher space, so that we can apprehend with our minds the relationship which we have to beings higher than ourselves, and bring our instinctive knowledge into clearer consciousness.

It appears to me self-evident, that in the particular disposition of any portion of matter, that is, in any physical action, there can be neither right nor wrong; the thing done is perfectly indifferent.

At the same time, it is only in things done that we come into relationship with the beings about us and higher than us. Consequently, in the things we do lies the whole importance of our lives.

Now, many of our impulses are directly signs of a relationship in us to a being of which we are not immediately conscious. The feeling of love, for instance, is always directed towards a particular individual; but by love man tends towards the preservation and improvement of his race; thus in the commonest and most universal impulses lie his relations to higher beings than the individuals by whom he is surrounded. Now, along with these impulses are many instincts of a modifying tendency; and, being altogether in the dark as to the nature of the higher beings to whom we are related, it is difficult to say in what the service of the higher beings consists, in what it does not. The only way is, as in every other pre-rational department of life, to take the verdict of those with the most insight and inspiration.

And any striving against such verdicts, and discontent with them, should be turned into energy towards finding out exactly what relation we have towards these higher beings by the study of Space.

Human life at present is an art constructed in its regulations and rules on the inspirations of those who love the undiscerned higher beings, of which we are a part. They love these higher beings, and know their service.

But our perceptions are coarser; and it is only by labour and toil that we shall be brought also to see, and then lose the restraints that now are necessary to us in the fulness of love.

Exactly what relationship there is towards us on the part of these higher beings we cannot say in the least. We cannot even say whether there is more than humanity before the highest; and any conception which we form now must use the human drama as its only possible mode of presentation.

But that there is such a relation seems clear; and the ludicrous manner, in which our perceptions have been limited, is a sufficient explanation of why they have not been scientifically apprehended.

The mode, in which an apprehension of these higher beings or being is at present secured, is as follows; and it bears a striking analogy to the mode by which the self is cut out of a block of cubes.

When we study a block of cubes, we first of all learn it, by starting from a particular cube, and learning how all the others come with regard to that. All the others are right or left, up or down, near or far, with regard to that particular cube. And the line of cubes starting from this first one, which we take as the direction in which we look, is, as it were, an axis about which the rest of the cubes are grouped. We learn the block with regard to this axis, so that we can mentally conceive the disposition of every cube as it comes regarded from one point of view. Next we suppose ourselves to be in another cube at the extremity of another axis; and, looking from this axis, we learn the aspects of all the cubes, and so on.

Thus we impress on the feeling what the block of cubes is like from every axis. In this way we get a knowledge of the block of cubes.

Now, to get a knowledge of humanity, we must feel with many individuals. Each individual is an axis as it were, and we must regard human beings from many different axes. And as, in learning the block of cubes, muscular action, as used in putting up the block of cubes, is the means by which we impress on the feeling the different views of the block; so, with regard to humanity, it is by acting with regard to the view of each individual that a knowledge is obtained. That is to say, that, besides sympathizing with each individual, we must act with regard to his view; and acting so, we shall feel his view, and thus get to know humanity from more than one axis. Thus there springs up a feeling of humanity, and of more.

Those who feel superficially with a great many people, are like those learners who have a slight acquaintance with a block of cubes from many points of view. Those who have some deep attachments, are like those who know them well from one or two points of view.

Thus there are two definite paths—one by which the instinctive feeling is called out and developed, the other by which we gain the faculty of rationally apprehending and learning the higher beings.

In the one way it is by the exercise of a sympathetic and active life; in the other, by the study of higher space.

Both should be followed; but the latter way is more accessible to those who are not good. For we at any rate have the industry to go through mechanical operations, and know that we need something.

And after all, perhaps, the difference between the good and the rest of us, lies rather in the former being aware. There is something outside them which draws them to it, which they see while we do not.

There is no reason, however, why this knowledge should not become demonstrable fact. Surely, it is only by becoming demonstrable fact that the errors which have been necessarily introduced into it by human weakness will fall away from it.

The rational knowledge will not replace feeling, but will form the vehicle by which the facts will be presented to our consciousness. Just as we learn to know our fellows by watching their deeds,—but it is something beyond the mere power of observing them that makes us regard them,—so the higher existences need to be known; and, when known, then there is a chance that in the depths of our nature they will awaken feelings towards them like the natural response of one human being to another.

And when we reflect on what surrounds us, when we think that the beauty of fruit and flower, the blue depths of the sky, the majesty of rock and ocean,—all these are but the chance and arbitrary view which we have of true being,—then we can imagine somewhat of the glories that await our coming. How set out in exquisite loveliness are all the budding trees and hedgerows on a spring day—from here, where they almost sing to us in their nearness, to where, in the distance, they stand up delicately distant and distinct in the amethyst ocean of the air! And there, quiet and stately, revolve the slow moving sun and the stars of the night. All these are the fragmentary views which we have of great beings to whom we are related, to whom we are linked, did we but realize it, by a bond of love and service in close connexions of mutual helpfulness.

Just as here and there on the face of a woman sits the divine spirit of beauty, so that all cannot but love who look—so, presenting itself to us in all this mingled scene of air and ocean, plain and mountain, is a being of such loveliness that, did we but know with one accord in one stream, all our hearts would be carried in a perfect and willing service. It is not that we need to be made different; we have but to look and gaze, and see that centre whereunto with joyful love all created beings move.

But not with effortless wonder will our days be filled, but in toil and strong exertion; for, just as now we all labour and strive for an object, our service is bound up with things which we do—so then we find no rest from labour, but the sense of solitude and isolation is gone. The bonds of brotherhood with our fellow-men grow strong, for we know one common purpose. And through the exquisite face of nature shines the spiritual light that gives us a great and never-failing comrade.

Our task is a simple one—to lift from our mind that veil which somehow has fallen on us, to take that curious limitation from our perception, which at present is only transcended by inspiration.

And the means to do it is by throwing aside our reason—by giving up the idea that what we think or are has any value. We too often sit as judges of nature, when all we can be are her humble learners. We have but to drink in of the inexhaustible fulness of being, pressing it close into our minds, and letting our pride of being able to foretell vanish into dust.

There is a curious passage in the works of Immanuel Kant,[1] in which he shows that space must be in the mind before we can observe things in space. “For,” he says, “since everything we conceive is conceived as being in space, there is nothing which comes before our minds from which the idea of space can be derived; it is equally present in the most rudimentary perception and the most complete.” Hence he says that space belongs to the perceiving soul itself. Without going into this argument to abstract regions, it has a great amount of practical truth. All our perceptions are of things in space; we cannot think of any detail, however limited or isolated, which is not in space.

Hence, in order to exercise our perceptive powers, it is well to have prepared beforehand a strong apprehension of space and space relations.

And so, as we pass on, is it not easily conceivable that, with our power of higher space perception so rudimentary and so unorganized, we should find it impossible to perceive higher existences? That mode of perception which it belongs to us to exercise is wanting. What wonder, then, that we cannot see the objects which are ready, were but our own part done?

Think how much has come into human life through exercising the power of the three-dimensional space perception, and we can form some measure, in a faint way, of what is in store for us.

There is a certain reluctance in us in bringing anything, which before has been a matter of feeling, within the domain of conscious reason. We do not like to explain why the grass is green, flowers bright, and, above all, why we have the feelings which we pass through.

But this objection and instinctive reluctance is chiefly derived from the fact that explaining has got to mean explaining away. We so often think that a thing is explained, when it can be shown simply to be another form of something which we know already. And, in fact, the wearied mind often does long to have a phenomenon shown to be merely a deduction from certain known laws.

But explanation proper is not of this kind; it is introducing into the mind the new conception which is indicated by the phenomenon already present. Nature consists of many entities towards the apprehension of which we strive. If for a time we break down the bounds which we have set up, and unify vast fields of observation under one common law, it is that the conceptions we formed at first are inadequate, and must be replaced by greater ones. But it is always the case, that, to understand nature, a conception must be formed in the mind. This process of growth in the mental history is hidden; but it is the really important one. The new conception satisfies more facts than the old ones, is truer phenomenally; and the arguments for it are its simplicity, its power of accounting for many facts. But the conception has to be formed first. And the real history of advance lies in the growth of the new conceptions which every now and then come to light.

When the weather-wise savage looked at the sky at night, he saw many specks of yellow light, like fire-flies, sprinkled amidst whitish fleece; and sometimes the fleece remained, the fire-spots went, and rain came; sometimes the fire-spots remained, and the night was fine. He did not see that the fire-points were ever the same, the clouds different; but by feeling dimly, he knew enough for his purpose.

But when the thinking mind turned itself on these appearances, there sprang up,—not all at once, but gradually,—the knowledge of the sublime existences of the distant heavens, and all the lore of the marvellous forms of water, of air, and the movements of the earth. Surely these realities, in which lies a wealth of embodied poetry, are well worth the delighted sensuous apprehension of the savage as he gazed.

Perhaps something is lost, but in the realities, of which we know, there is compensation. And so, when we learn to understand the meaning of these mysterious changes, this course of natural events, we shall find in the greater realities amongst which we move a fair exchange for the instinctive reverence, which they now awaken in us.

In this book the task is taken up of forming the most simple and elementary of the great conceptions that are about us. In the works of the poets, and still more in the pages of religious thinkers, lies an untold wealth of conception, the organization of which in our every-day intellectual life is the work of the practical educator.

But none is capable of such simple demonstration and absolute presentation as this of higher space, and none so immediately opens our eyes to see the world as a different place. And, indeed, it is very instructive; for when the new conception is formed, it is found to be quite simple and natural. We ask ourselves what we have gained; and we answer: Nothing; we have simply removed an obvious limitation.

And this is universally true; it is not that we must rise to the higher by a long and laborious process. We may have a long and laborious process to go through, but, when we find the higher, it is this: we discover our true selves, our essential being, the fact of our lives. In this case, we pass from the ridiculous limitation, to which our eyes and hands seem to be subject, of acting in a mere section of space, to the fuller knowledge and feeling of space as it is. How do we pass to this truer intellectual life? Simply by observing, by laying aside our intellectual powers, and by looking at what is.

We take that which is easiest to observe, not that which is easiest to define; we take that which is the most definitely limited real thing, and use it as our touchstone whereby to explore nature.

As it seems to me, Kant made the great and fundamental statement in philosophy when he exploded all previous systems, and all physics were reft from off the perceiving soul. But what he did once and for all, was too great to be a practical means of intellectual work. The dynamic form of his absolute insight had to be found; and it is in other works that the practical instances of the Kantian method are to be found. For, instead of looking at the large foundations of knowledge, the ultimate principles of experience, late writers turned to the details of experience, and tested every phenomenon, not with the question, What is this? but with the question, “What makes me perceive thus?”

And surely the question, as so put, is more capable of an answer; for it is only the percipient, as a subject of thought, about which we can speak. The absolute soul, since it is the thinker, can never be the subject of thought; but, as physically conditioned, it can be thought about. Thus we can never, without committing a ludicrous error, think of the mind of man except as a material organ of some kind; and the path of discovery lies in investigating what the devious line of his thought history is due to, which winds between two domains of physics—the unknown conditions which affect the perceiver, the partially known physics which constitute what we call the external world.

It is a pity to spend time over these reflections; if they do not seem tame and poor compared to the practical apprehension which comes of working with the models, then there is nothing in the whole subject. If in the little real objects which the reader has to handle and observe does not lie to him a poetry of a higher kind than any expressed thought, then all these words are not only useless, but false. If, on the other hand, there is true work to be done with them, then these suggestions will be felt to be but mean and insufficient apprehensions.

For, in the simplest apprehension of a higher space lies a knowledge of a reality which is, to the realities we know, as spirit is to matter; and yet to this new vision all our solid facts and material conditions are but as a shadow is to that which casts it. In the awakening light of this new apprehension, the flimsy world quivers and shakes, rigid solids flow and mingle, all our material limitations turn into graciousness, and the new field of possibility waits for us to look and behold.

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CHAPTER XI.
SPACE THE SCIENTIFIC BASIS OF ALTRUISM AND RELIGION.

The reader will doubtless ask for some definite result corresponding to these words—something not of the nature of an hypothesis or a might-be. And in that I can only satisfy him after my own powers. My only strength is in detail and patience; and if he will go through the practical part of the book, it will assuredly dawn upon him that here is the beginning of an answer to his request. I only study the blocks and stones of the higher life. But here they are definite enough. And the more eager he is for personal and spiritual truth, the more eagerly do I urge him to take up the practical work, for the true good comes to us through those who, aspiring greatly, still submit their aspirations to fact, and who, desiring to apprehend spirit, still are willing to manipulate matter.

The particular problem at which I have worked for more than ten years, has been completely solved. It is possible for the mind to acquire a conception of higher space as adequate as that of our three-dimensional space, and to use it in the same manner.

There are two distinct ways of studying space—our familiar space at present in use. One is that of the analyst, who treats space relations by his algebra, and discovers marvellous relations. The other is that of the observer or mechanician, who studies the shapes of things in space directly.

A practical designer of machines would not find the knowledge of geometrical analysis of immediate help to him; and an artist or draughtsman still less so.

Now, my inquiry was, whether it was possible to get the same power of conception of four-dimensional space, as the designer and draughtsman have of three-dimensional space. It is possible.

And with this power it is possible for us to design machines in higher space, and to conceive objects in this space, just as a draughtsman or artist does.

Analytical skill is not of much use in designing a statue or inventing a machine, or in appreciating the detail of either a work of art or a mechanical contrivance.

And hitherto the study of four-dimensional space has been conducted by analysis. Here, for the first time, the fact of the power of conception of four-dimensional space is demonstrated, and the means of educating it are given.

And I propose a complete system of work, of which the volume on four space[2] is the first instalment.

I shall bring forward a complete system of four-dimensional thought—mechanics, science, and art. The necessary condition is, that the mind acquire the power of using four-dimensional space as it now does three-dimensional.

And there is another condition which is no less important. We can never see, for instance, four-dimensional pictures with our bodily eyes, but we can with our mental and inner eye. The condition is, that we should acquire the power of mentally carrying a great number of details.

If, for instance, we could think of the human body right down to every minute part in its right position, and conceive its aspect, we should have a four-dimensional picture which is a solid structure. Now, to do this, we must form the habit of mental painting, that is, of putting definite colours in definite positions, not with our hands on paper, but with our minds in thought, so that we can recall, alter, and view complicated arrangements of colour existing in thought with the same ease with which we can paint on canvas. This is simply an affair of industry; and the mental power latent in us in this direction is simply marvellous.

In any picture, a stroke of the brush put on without thought is valueless. The artist is not conscious of the thought process he goes through. For our purpose it is necessary that the manipulation of colour and form which the artist goes through unconsciously, should become a conscious power, and that, at whatever sacrifice of immediate beauty, the art of mental painting should exist beside our more unconscious art. All that I mean is this—that in the course of our campaign it is necessary to take up the task of learning pictures by heart, so that, just as an artist thinks over the outlines of a figure he wants to draw, so we think over each stroke in our pictures. The means by which this can be done will be given in a future volume.

We throw ourselves on an enterprise in which we have to leave altogether the direct presentation to the senses. We must acquire a sense-perception and memory of so keen and accurate a kind that we can build up mental pictures of greater complexity than any which we can see. We have a vast work of organization, but it is merely organization. The power really exists and shows itself when it is looked for.

Much fault may be found with the system of organization which I have adopted, but it is the survivor of many attempts; and although I could better it in parts, still I think it is best to use it until, the full importance of the subject being realized, it will be the lifework of men of science to reorganize the methods.

The one thing on which I must insist is this—that knowledge is of no value, it does not exist unless it comes into the mind. To know that a thing must be is no use at all. It must be clearly realized, and in detail as it is, before it can be used.

A whole world swims before us, the apprehension of which simply demands a patient cultivation of our powers; and then, when the faculty is formed, we shall recognize what the universe in which we are is like. We shall learn about ourselves and pass into a new domain.

And I would speak to some minds who, like myself, share to a large extent the feeling of unsettledness and unfixedness of our present knowledge.

Religion has suffered in some respects from the inaccuracy of its statements; and it is not always seen that it consists of two parts—one a set of rules as to the management of our relations to the physical world about us, and to our own bodies; another, a set of rules as to our relationship to beings higher than ourselves.

Now, on the former of these subjects, on physical facts, on the laws of health, science has a fair standing ground of criticism, and can correct the religious doctrines in many important respects.

But on the other part of the subject matter, as to our relationship to beings higher than ourselves, science has not yet the materials for judging. The proposition which underlies this book is, that we should begin to acquire the faculties for judging.

To judge, we must first appreciate; and how far we are from appreciating with science the fundamental religious doctrines I leave to any one to judge.

There is absolutely no scientific basis for morality, using morality in the higher sense of other than a code of rules to promote the greatest physical and mental health and growth of a human being. Science does not give us any information which is not equally acceptable to the most selfish and most generous man; it simply tells him of means by which he may attain his own ends, it does not show him ends.

The prosecution of science is an ennobling pursuit; but it is of scientific knowledge that I am now speaking in itself. We have no scientific knowledge of any existences higher than ourselves—at least, not recognized as higher. But we have abundant knowledge of the actions of beings less developed than ourselves, from the striking unanimity with which all inorganic beings tend to move towards the earth’s centre, to the almost equally uniform modes of response in elementary organized matter to different stimuli.

The question may be put: In what way do we come into contact with these higher beings at present? And evidently the answer is, In those ways in which we tend to form organic unions—unions in which the activities of individuals coalesce in a living way.

The coherence of a military empire or of a subjugated population, presenting no natural nucleus of growth, is not one through which we should hope to grow into direct contact with our higher destinies. But in friendship, in voluntary associations, and above all, in the family, we tend towards our greater life.

And it seems that the instincts of women are much more relative to this, the most fundamental and important side of life, than are those of men. In fact, until we know, the line of advance had better be left to the feeling of women, as they organize the home and the social life spreading out therefrom. It is difficult, perhaps, for a man to be still and perceive; but if he is so, he finds that what, when thwarted, are meaningless caprices and empty emotionalities, are, on the part of woman, when allowed to grow freely and unchecked, the first beginnings of a new life—the shadowy filaments, as it were, by which an organism begins to coagulate together from the medium in which it makes its appearance.

In very many respects men have to make the conditions, and then learn to recognize. How can we see the higher beings about us, when we cannot even conceive the simplest higher shapes? We may talk about space, and use big words, but, after all, the preferable way of putting our efforts is this: let us look first at the simplest facts of higher existence, and then, when we have learnt to realize these, We shall be able to see what the world presents. And then, also, light will be thrown on the constituent organisms of our own bodies, when we see in the thorough development of our social life a relation between ourselves and a larger organism similar to that which exists between us and the minute constituents of our frame.

The problem, as it comes to me, is this: it is clearly demonstrated that self-regard is to be put on one side—and self-regard in every respect—not only should things painful and arduous be done, but things degrading and vile, so that they serve.

I am to sign any list of any number of deeds which the most foul imagination can suggest, as things which I would do did the occasion come when I could benefit another by doing them; and, in fact, there is to be no characteristic in any action which I would shrink from did the occasion come when it presented itself to be done for another’s sake. And I believe that the soul is absolutely unstained by the action, provided the regard is for another.

But this is, in truth, a dangerous doctrine; at one Sweep it puts away all absolute commandments, all absolute verdicts of right about things, and leaves the agent to his own judgment.

It is a kind of rule of life which requires most absolute openness, and demands that society should frame severe and insuperable regulations; for otherwise, with the motives of the individual thus liberated from absolute law, endless varieties of conduct would spring forth, and the wisdom of individual men is hardly enough to justify their irresponsible action.

Still, it does seem that, as an ideal, the absolute absence of self-regard is to be aimed at.

With a strong religious basis, this would work no harm, for the rules of life, as laid down by religions, would suffice. But there are many who do not accept these rules as any absolute indication of the will of God, but only as the regulations of good men, which have a claim to respect and nothing more.

And thus it seems to me that altruism—thoroughgoing altruism—hands over those who regard it as an ideal, and who are also of a sceptical turn of mind, to the most absolute unfixedness of theory, and, very possibly, to the greatest errors in life.

And here we come to the point where the study of space becomes so important.

For if this rule of altruism is the right one, if it appeals with a great invitation to us, we need not therefore try it with less precaution than we should use in other affairs of infinitely less importance. When we want to know if a plank will bear, we entrust it with a different load from that of a human body.

And if this law of altruism is the true one, let us try it where failure will not mean the ruin of human beings.

Now, in knowledge, pure altruism means so to bury the mind in the thing known that all particular relations of one’s self pass away. The altruistic knowledge of the heavens would be, to feel that the stars were vast bodies, and that I am moving rapidly. It would be, to know this, not as a matter of theory, but as a matter of habitual feeling.

Whether this is possible, I do not know; but a somewhat similar attempt can be made with much simpler means.

In a different place I have described the process of acquiring an altruistic knowledge of a block of cubes; and the results of the laborious processes involved are well worth the trouble. For as a clearly demonstrable fact this comes before one. To acquire an absolute knowledge of a block of cubes, so that all self relations are cast out, means that one has to take the view of a higher being.

It suddenly comes before one, that the particular relations which are so fixed and important, and seem so absolutely sure when one begins the process of learning, are by no means absolute facts, but marks of a singular limitation, almost a degradation, on one’s own part. In the determined attempt to know the most insignificant object perfectly and thoroughly, there flashes before one’s eyes an existence infinitely higher than one’s own. And with that vision there comes,—I do not speak from my own experience only,—a conviction that our existence also is not what we suppose—that this bodily self of ours is but a limit too. And the question of altruism, as against self-regard, seems almost to vanish, for by altruism we come to know what we truly are.

“What we truly are,” I do not mean apart from space and matter, but what we really are as beings having a space existence; for our way of thinking about existence is to conceive it as the relations of bodies in space. To think is to conceive realities in space.

Just as, to explore the distant stars of the heavens, a particular material arrangement is necessary which we call a telescope, so to explore the nature of the beings who are higher than us, a mental arrangement is necessary. We must prepare our power of thinking as we prepare a more extended power of looking. We want a structure developed inside the skull for the one purpose, while an exterior telescope will do for the other.

And thus it seems that the difficulties which we first apprehended fall away.

To us, looking with half-blinded eyes at merely our own little slice of existence, our filmy all, it seemed that altruism meant disorder, vagary, danger.

But when we put it into practice in knowledge, we find that it means the direct revelation of a higher being and a call to us to participate ourselves too in a higher life—nay, a consciousness comes that we are higher than we know.

And so with our moral life as with our intellectual life. Is it not the case that those, who truly accept the rule of altruism, learn life in new dangerous ways?

It is true that we must give up the precepts of religion as being the will of God; but then we shall learn that the will of God shows itself partly in the religious precepts, and comes to be more fully and more plainly known as an inward spirit.

And that difficulty, too, about what we may do and what we may not, vanishes also. For, if it is the same about our fellow-creatures as it is about the block of cubes, when we have thrown out the self-regard from our relationship to them, we shall feel towards them as a higher being than man feels towards them, we shall feel towards them as they are in their true selves, not in their outward forms, but as eternal loving spirits.

And then those instincts which humanity feels with a secret impulse to be sacred and higher than any temporary good will be justified—or fulfilled.

There are two tendencies—one towards the direct cultivation of the religious perceptions, the other to reducing everything to reason. It will be but just for the exponents of the latter tendency to look at the whole universe, not the mere section of it which we know, before they deal authoritatively with the higher parts of religion.

And those who feel the immanence of a higher life in us will be needed in this outlook on the wider field of reality, so that they, being fitted to recognize, may tell us what lies ready for us to know.

The true path of wisdom consists in seeing that our intellect is foolishness—that our conclusions are absurd and mistaken, not in speculating on the world as a form of thought projected from the thinking principle within us—rather to be amazed that our thought has so limited the world and hidden from us its real existences. To think of ourselves as any other than things in space and subject to material conditions, is absurd, it is absurd on either of two hypotheses. If we are really things in space, then of course it is absurd to think of ourselves as if we were not so. On the other hand, if we are not things in space, then conceiving in space is the mode in which that unknown which we are exists as a mind. Its mental action is space-conception, and then to give up the idea of ourselves as in space, is not to get a truer idea, but to lose the only power of apprehension of ourselves which we possess.

And yet there is, it must be confessed, one way in which it may be possible for us to think without thinking of things in space.

That way is, not to abandon the use of space-thought, but to pass through it.

When we think of space, we have to think of it as infinity extended, and we have to think of it as of infinite dimensions. Now, as I have shown in “The Law of the Valley,”[3] when we come upon infinity in any mode of our thought, it is a sign that that mode of thought is dealing with a higher reality than it is adapted for, and in struggling to represent it, can only do so by an infinite number of terms. Now, space has an infinite number of positions and turns, and this may be due to the attempt forced upon us to think of things higher than space as in space. If so, then the way to get rid of space from our thoughts, is, not to go away from it, but to pass through it—to think about larger and larger systems of space, and space of more and more dimensions, till at last we get to such a representation in space of what is higher than space, that we can pass from the space-thought to the more absolute thought without that leap which would be necessary if we were to try to pass beyond space with our present very inadequate representation in it of what really is.

Again and again has human nature aspired and fallen. The vision has presented itself of a law which was love, a duty which carried away the enthusiasm, and in which the conflict of the higher and lower natures ceased because all was enlisted in one loving service. But again and again have such attempts failed. The common-sense view, that man is subject to law, external law, remains—that there are fates whom he must propitiate and obey. And there is a strong sharp curb, which, if it be not brought to bear by the will, is soon pulled tight by the world, and one more tragedy is enacted, and the over-confident soul is brought low.

And the rock on which such attempts always split, is in the indulgence of some limited passion. Some one object fills the soul with its image, and in devotion to that, other things are sacrificed, until at last all comes to ruin.

But what does this mean? Surely it is simply this, that where there should be knowledge there is ignorance. It is not that there is too much devotion, too much passion, but that we are ignorant and blind, and wander in error. We do not know what it is we care for, and waste our effort on the appearance. There is no such thing as wrong love; there is good love and bad knowledge, and men who err, clasp phantoms to themselves. Religion is but the search for realities; and thought, conscious of its own limitations, is its best aid.

Let a man care for any one object—let his regard for it be as concentrated and exclusive as you will, there will be no danger if he truly apprehends that which he cares for. Its true being is bound up with all the rest of existence, and, if his regard is true to one, then, if that one is really known, his regard is true to all.

There is a question sometimes asked, which shows the mere formalism into which we have fallen.

We ask: What is the end of existence? A mere play on words! For to conceive existence is to feel ends. The knowledge of existence is the caring for objects, the fear of dangers, the anxieties of love. Immersed in these, the triviality of the question, what is the end of existence? becomes obvious. If, however, letting reality fade away, we play with words, some questions of this kind are possible; but they are mere questions of words, and all content and meaning has passed out of them.

The task before us is this: we strive to find out that physical unity, that body which men are parts of, and in the life of which their true unity lies. The existence of this one body we know from the utterances of those whom we cannot but feel to be inspired; we feel certain tendencies in ourselves which cannot be explained except by a supposition of this kind.

And, now, we set to work deliberately to form in our minds the means of investigation, the faculty of higher-space conception. To our ordinary space-thought, men are isolated, distinct, in great measure antagonistic. But with the first use of the weapon of higher thought, it is easily seen that all men may really be members of one body, their isolation may be but an affair of limited consciousness. There is, of course, no value as science in such a supposition. But it suggests to us many possibilities; it reveals to us the confined nature of our present physical views, and stimulates us to undertake the work necessary to enable us to deal adequately with the subject.

The work is entirely practical and detailed; it is the elaboration, beginning from the simplest objects of an experience in thought, of a higher-space world.

To begin it, we take up those details of position and relation which are generally relegated to symbolism or unconscious apprehension, and bring these waste products of thought into the central position of the laboratory of the mind. We turn all our attention on the most simple and obvious details of our every-day experience, and thence we build up a conception of the fundamental facts of position and arrangement in a higher world. We next study more complicated higher shapes, and get our space perception drilled and disciplined. Then we proceed to put a content into our framework.

The means of doing this are twofold—observation and inspiration.

As to observation, it is hardly possible to describe the feelings of that investigator who shall distinctly trace in the physical world, and experimentally demonstrate the existence of the higher-space facts which are so curiously hidden from us. He will lay the first stone for the observation and knowledge of the higher beings to whom we are related.

As to the other means, it is obvious, surely, that if there has ever been inspiration, there is inspiration now. Inspiration is not a unique phenomenon. It has existed in absolutely marvellous degree in some of the teachers of the ancient world; but that, whatever it was, which they possessed, must be present now, and, if we could isolate it, be a demonstrable fact.

And I would propose to define inspiration as the faculty, which, to take a particular instance, does the following:—

If a square penetrates a line cornerwise, it marks out on the line a segment bounded by two points—that is, we suppose a line drawn on a piece of paper, and a square lying on the paper to be pushed so that its corner passes over the line. Then, supposing the paper and the line to be in the same plane, the line is interrupted by the square; and, of the square, all that is observable in the line, is a segment bounded by two points.

Next, suppose a cube to be pushed cornerwise through a plane, and let the plane make a section of the cube. The section will be a plane figure, and it will be a triangle.

Now, first, the section of a square by a line is a segment bounded by two points; second, the section of a cube by a plane is a triangle bounded by three lines.

Hence, we infer that the section of a figure in four dimensions analogous to a cube, by three-dimensional space, will be a tetrahedron—a figure bounded by four planes.

This is found to be true; with a little familiarity with four-dimensional movements this is seen to be obvious. But I would define inspiration as the faculty by which without actual experience this conclusion is formed.

How it is we come to this conclusion I am perfectly unable to say. Somehow, looking at mere formal considerations, there comes into the mind a conclusion about something beyond the range of actual experience.

We may call this reasoning from analogy; but using this phrase does not explain the process. It seems to me just as rational to say that the facts of the line and plane remind us of facts which we know already about four-dimensional figures—that they tend to bring these facts out into consciousness, as Plato shows with the boy’s knowledge of the cube. We must be really four-dimensional creatures, or we could not think about four dimensions.

But whatever name we give to this peculiar and inexplicable faculty, that we do possess it is certain; and in our investigations it will be of service to us. We must carefully investigate existence in a plane world, and then, making sure, and impressing on our inward sense, as we go, every step we take with regard to a higher world, we shall be reminded continually of fresh possibilities of our higher existence.

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