Transcriber’s Notes
Text printed in italics is represented between _underscores_, bold
face text between ~tildes~. Small capitals have been transcribed as
ALL CAPITALS. A letter in square brackets preceded by an equal sign,
as [=X], represents a letter with bar above.
More Transcriber’s Notes may be found at the end of this text.
A NEW ERA OF THOUGHT.
SCIENTIFIC ROMANCES.
By C. HOWARD HINTON, M.A.
Crown 8vo, cloth gilt, 6_s._; or separately, 1_s._ each.
1. ~What is the Fourth Dimension?~ 1_s._
GHOSTS EXPLAINED.
“A short treatise of admirable clearness. . . . Mr. Hinton brings
us, panting but delighted, to at least a momentary faith in the Fourth
Dimension, and upon the eye of this faith there opens a vista of
interesting problems. . . . His pamphlet exhibits a boldness of
speculation, and a power of conceiving and expressing even the
inconceivable, which rouses one’s faculties like a tonic.”--_Pall
Mall._
2. ~The Persian King; or, The Law of the Valley~, 1_s._
THE MYSTERY OF PLEASURE AND PAIN.
“A very suggestive and well-written speculation, by the inheritor of
an honoured name.”--_Mind._
“Will arrest the attention of the reader at once.”--_Knowledge._
3. ~A Plane World~, 1_s._
4. ~A Picture of our Universe~, 1_s._
5. ~Casting out the Self~, 1_s._
_SECOND SERIES._
1. ~On the Education of the Imagination.~
2. ~Many Dimensions~, 1_s._
LONDON: SWAN SONNENSCHEIN & CO.
_A New Era of Thought._
BY
CHARLES HOWARD HINTON, M.A., OXON.
_Author of “What is the Fourth Dimension,” and other “Scientific
Romances.”_
[Illustration]
London:
SWAN SONNENSCHEIN & CO.,
PATERNOSTER SQUARE.
1888.
BUTLER & TANNER,
THE SELWOOD PRINTING WORKS,
FROME, AND LONDON.
PREFACE.
The MSS. which formed the basis of this book were committed to us by the
author, on his leaving England for a distant foreign appointment. It was
his wish that we should construct upon them a much more complete
treatise than we have effected, and with that intention he asked us to
make any changes or additions we thought desirable. But long alliance
with him in this work has convinced us that his thought (especially that
of a general philosophical character) loses much of its force if
subjected to any extraneous touch.
This feeling has induced us to print Part I. almost exactly as it came
from his hands, although it would probably have received much
rearrangement if he could have watched it through the press himself.
Part II. has been written from a hurried sketch, which he considered
very inadequate, and which we have consequently corrected and
supplemented. Chapter XI. of this part has been entirely re-written by
us, and has thus not had the advantage of his supervision. This remark
also applies to Appendix E, which is an elaboration of a theorem he
suggested. Appendix H, and all the exercises have, in accordance with
his wish, been written solely by us. It will be apparent to the reader
that Appendix H is little more than a brief introduction to a very large
subject, which, being concerned with tessaracts and solids, is really
beyond treatment in writing and diagrams.
This difficulty recalls us to the one great fact, upon which we feel
bound to insist, that the matter of this book _must_ receive objective
treatment from the reader, who will find it quite useless even to
attempt to apprehend it without actually building in squares and cubes
all the facts of space which we ask him to impress on his consciousness.
Indeed, we consider that printing, as a method of spreading
space-knowledge, is but a “pis aller,” and we would go back to that
ancient and more fruitful method of the Greek geometers, and, while
describing figures on the sand, or piling up pebbles in series, would
communicate to others that spirit of learning and generalization
begotten in our consciousness by continuous contact with facts, and only
by continuous contact with facts vitally maintained.
ALICIA BOOLE,
H. JOHN FALK.
N.B. Models.--It is unquestionably a most important part of the process
of learning space to construct these, and the reader should do so,
however roughly and hastily. But, if Models are required as patterns,
they may be ordered from Messrs. Swan Sonnenschein & Co., Paternoster
Square, London, and will be supplied as soon as possible, the
uncertainty as to demand for same not allowing us to have a large number
made in advance. Much of the work can be done with plain cubes by using
names without colours, but further on the reader will find colours
necessary to enable him to grasp and retain the complex series of
observations. Coloured models can easily be made by covering
Kindergarten cubes with white paper and painting them with water-colour,
and, if permanence be desired, dipping them in size and copal varnish.
TABLE OF CONTENTS.
PART I.
PAGE
INTRODUCTION 1-7
CHAPTER I.
Scepticism and Science. Beginning of Knowledge 8-13
CHAPTER II.
Apprehension of Nature. Intelligence. Study of Arrangement or
Shape 14-20
CHAPTER III.
The Elements of Knowledge 21-23
CHAPTER IV.
Theory and Practice 24-28
CHAPTER V.
Knowledge: Self-Elements 29-34
CHAPTER VI.
Function of Mind. Space against Metaphysics. Self-Limitation and
its Test. A Plane World 35-46
CHAPTER VII.
Self Elements in our Consciousness 47-50
CHAPTER VIII.
Relation of Lower to Higher Space. Theory of the Æther 51-60
CHAPTER IX.
Another View of the Æther. Material and Ætherial Bodies 61-66
CHAPTER X.
Higher Space and Higher Being. Perception and Inspiration 67-84
CHAPTER XI.
Space the Scientific Basis of Altruism and Religion 85-99
PART II.
CHAPTER I.
Three-space. Genesis of a Cube. Appearances of a Cube to a
Plane-being 101-112
CHAPTER II.
Further Appearances of a Cube to a Plane-being 113-117
CHAPTER III.
Four-space. Genesis of a Tessaract; its Representation in
Three-space 118-129
CHAPTER IV.
Tessaract moving through Three-space. Models of the Sections 130-134
CHAPTER V.
Representation of Three-space by Names and in a Plane 135-148
CHAPTER VI.
The Means by which a Plane-being would Acquire a Conception of
our Figures 149-155
CHAPTER VII.
Four-space: its Representation in Three-space 156-166
CHAPTER VIII.
Representation of Four-space by Name. Study of Tessaracts 167-176
CHAPTER IX.
Further Study of Tessaracts 177-179
CHAPTER X.
Cyclical Projections 180-183
CHAPTER XI.
A Tessaractic Figure and its Projections 184-194
APPENDICES.
A. 100 Names used for Plane Space 197
B. 216 Names used for Cubic Space 198
C. 256 Names used for Tessaractic Space 200-201
D. List of Colours, Names, and Symbols 202-203
E. A Theorem in Four-space 204-205
F. Exercises on Shapes of Three Dimensions 205-207
G. Exercises on Shapes of Four Dimensions 207-209
H. Sections of the Tessaract 209-217
K. Drawings of the Cubic Sides and Sections of the Tessaract
(Models 1-12) with Colours and Names 219-241
INTRODUCTORY NOTE TO PART I.
At the completion of a work, or at the completion of the first part of a
work, the feelings are necessarily very different from those with which
the work was begun; and the meaning and value of the work itself bear a
very different appearance. It will therefore be the simplest and
shortest plan, if I tell the reader briefly what the work is to which
these pages are a guide, and what I consider to be its value when done.
The task was to obtain a sense of the properties of higher space, or
space of four dimensions, in the same way as that by which we reach a
sense of our ordinary three-dimensional space. I now prefer to call the
task that of obtaining a familiarity with higher matter, which shall be
as intuitive to the mind as that of ordinary matter has become. The
expression “higher matter” is preferable to “higher space,” because it
is a somewhat hasty proceeding to split this concrete matter, which we
touch and feel, into the abstractions of extension and impenetrability.
It seems to me that I cannot think of space without matter, and
therefore, as no necessity compels me to such a course, I do not split
up the concrete object into subtleties, but I simply ask: “What is that
which is to a cube or block or shape of any kind as the cube is to a
square?”
In entering upon this inquiry we find the task is twofold. Firstly,
there is the theoretical part, which is easy, viz. to set clearly before
us the relative conditions which would obtain if there were a matter
physically higher than this matter of ours, and to choose the best
means of liberating our minds from the limitations imposed on it by the
particular conditions under which we are placed. The second part of the
task is somewhat laborious, and consists of a constant presentation to
the senses of those appearances which portions of higher matter would
present, and of a continual dwelling on them, until the higher matter
becomes familiar.
The reader must undertake this task, if he accepts it at all, as an
experiment. Those of us who have done it, are satisfied that there is
that in the results of the experiment which make it well worthy of a
trial.
And in a few words I may state the general bearings of this work, for
every branch of work has its general bearings. It is an attempt, in the
most elementary and simple domain, to pass from the lower to the higher.
In pursuing it the mind passes from one kind of intuition to a higher
one, and with that transition the horizon of thought is altered. It
becomes clear that there is a physical existence transcending the
ordinary physical existence; and one becomes inclined to think that the
right direction to look is, not away from matter to spiritual
existences, but towards the discovery of conceptions of higher matter,
and thereby of those material existences whose definite relations to us
are apprehended as spiritual intuitions. Thus, “material” would simply
mean “grasped by the intellect, become known and familiar.” Our
apprehension of anything which is not expressed in terms of matter, is
vague and indefinite. To realize and live with that which we vaguely
discern, we need to apply the intuition of higher matter to the world
around us. And this seems to me the great inducement to this study. Let
us form our intuition of higher space, and then look out upon the world.
Secondly, in this progress from ordinary to higher matter, as a general
type of progress from lower to higher, we make the following
observations. Firstly, we become aware that there are certain
limitations affecting our regard. Secondly, we discover by our reason
what those limitations are, and then force ourselves to go through the
experience which would be ours if the limitations did not affect us.
Thirdly, we become aware of a capacity within us for transcending those
limitations, and for living in the higher mode as we had lived in the
previous one.
We may remark that this progress from the ordinary to the higher kind of
matter demands an absolute attention to details. It is only in the
retention of details that such progress becomes possible. And as, in
this question of matter, an absolute and unconventional examination
gives us the indication of a higher, so, doubtless, in other questions,
if we but come to facts without presupposition, we begin to know that
there is a higher and to discover indications of the way whereby we can
approach. That way lies in the fulness of detail rather than in the
generalization.
Biology has shown us that there is a universal order of forms or
organisms, passing from lower to higher. Therein we find an indication
that we ourselves take part in this progress. And in using the little
cubes we can go through the process ourselves, and learn what it is in a
little instance.
But of all the ways in which the confidence gained from this lesson can
be applied, the nearest to us lies in the suggestion it gives,--and more
than the suggestion, if inclination to think be counted for
anything,--in the suggestion of that which is higher than ourselves. We,
as individuals, are not the limit and end-all, but there is a higher
being than ours. What our relation to it is, we cannot tell, for that is
unlike our relation to anything we know. But, perhaps all that happens
to us is, could we but grasp it, our relation to it.
At any rate, the discovery of it is the great object beside which all
else is as secondary as the routine of mere existence is to
companionship. And the method of discovery is full knowledge of each
other. Thereby is the higher being to be known. In as much as the least
of us knows and is known by another, in so much does he know the higher.
Thus, scientific prayer is when two or three meet together, and, in the
belief of one higher than themselves, mutually comprehend that vision of
the higher, which each one is, and, by absolute fulness of knowledge of
the facts of each other’s personality, strive to attain a knowledge of
that which is to each of their personalities as a higher figure is to
its solid sides.
C. H. H.
A NEW ERA OF THOUGHT.
PART I.
INTRODUCTION.
There are no new truths in this book, but it consists of an effort to
impress upon and bring home to the mind some of the more modern
developments of thought. A few sentences of Kant, a few leading ideas of
Gauss and Lobatschewski form the material out of which it is built up.
It may be thought to be unduly long; but it must be remembered that in
these times there is a twofold process going on--one of discovery about
external nature, one of education, by which our minds are brought into
harmony with that which we know. In certain respects we find ourselves
brought on by the general current of ideas--we feel that matter is
permanent and cannot be annihilated, and it is almost an axiom in our
minds that energy is persistent, and all its transformations remains the
same in amount. But there are other directions in which there is need of
definite training if we are to enter into the thoughts of the time.
And it seems to me that a return to Kant, the creator of modern
philosophy, is the first condition. Now of Kant’s enormous work only a
small part is treated here, but with the difference that should be found
between the work of a master and that of a follower. Kant’s statements
are taken as leading ideas, suggesting a field of work, and it is in
detail and manipulation merely that there is an opportunity for
workmanship.
Of Kant’s work it is only his doctrine of space which is here
experimented upon. With Kant the perception of things as being in space
is not treated as it seems so obvious to do. We should naturally say
that there is space, and there are things in it. From a comparison of
those properties which are common to all things we obtain the properties
of space. But Kant says that this property of being in space is not so
much a quality of any definable objects, as the means by which we obtain
an apprehension of definable objects--it is the condition of our mental
work.
Now as Kant’s doctrine is usually commented on, the negative side is
brought into prominence, the positive side is neglected. It is generally
said that the mind cannot perceive things in themselves, but can only
apprehend them subject to space conditions. And in this way the space
conditions are as it were considered somewhat in the light of
hindrances, whereby we are prevented from seeing what the objects in
themselves truly are. But if we take the statement simply as it is--that
we apprehend by means of space--then it is equally allowable to consider
our space sense as a positive means by which the mind grasps its
experience.
There is in so many books in which the subject is treated a certain air
of despondency--as if this space apprehension were a kind of veil which
shut us off from nature. But there is no need to adopt this feeling. The
first postulate of this book is a full recognition of the fact, that it
is by means of space that we apprehend what is. Space is the instrument
of the mind.
And here for the purposes of our work we can avoid all metaphysical
discussion. Very often a statement which seems to be very deep and
abstruse and hard to grasp, is simply the form into which deep thinkers
have thrown a very simple and practical observation. And for the present
let us look on Kant’s great doctrine of space from a practical point of
view, and it comes to this--it is important to develop the space sense,
for it is the means by which we think about real things.
There is a doctrine which found much favour with the first followers of
Kant, that also affords us a simple and practical rule of work. It was
considered by Fichte that the whole external world was simply a
projection from the _ego_, and the manifold of nature was a recognition
by the spirit of itself. What this comes to as a practical rule is, that
we can only understand nature in virtue of our own activity; that there
is no such thing as mere passive observation, but every act of sight and
thought is an activity of our own.
Now according to Kant the space sense, or the intuition of space, is the
most fundamental power of the mind. But I do not find anywhere a
systematic and thoroughgoing education of the space sense. In every
practical pursuit it is needed--in some it is developed. In geometry it
is used; but the great reason of failure in education is that, instead
of a systematic training of the space sense, it is left to be organized
by accident and is called upon to act without having been formed.
According to Kant and according to common experience it will be found
that a trained thinker is one in whom the space sense has been well
developed.
With regard to the education of the space sense, I must ask the
indulgence of the reader. It will seem obvious to him that any real
pursuit or real observation trains the space sense, and that it is going
out of the way to undertake any special discipline.
To this I would answer that, according to my own experience, I was
perfectly ignorant of space relations myself before I actually worked at
the subject, and that directly I got a true view of space facts a whole
series of conceptions, which before I had known merely by repute and
grasped by an effort, became perfectly simple and clear to me.
Moreover, to take one instance: in studying the relations of space we
always have to do with coloured objects, we always have the sense of
weight; for if the things themselves have no weight, there is always a
direction of up and down--which implies the sense of weight, and to get
rid of these elements requires careful sifting. But perhaps the best
point of view to take is this--if the reader has the space sense well
developed he will have no difficulty in going through the part of the
book which relates to it, and the phraseology will serve him for the
considerations which come next.
Amongst the followers of Kant, those who pursued one of the lines of
thought in his works have attracted the most attention and have been
considered as his successors. Fichte, Schelling, Hegel have developed
certain tendencies and have written remarkable books. But the true
successors of Kant are Gauss and Lobatchewski.
For if our intuition of space is the means by which we apprehend, then
it follows that there may be different kinds of intuitions of space. Who
can tell what the absolute space intuition is? This intuition of space
must be coloured, so to speak, by the conditions of the being which uses
it.
Now, after Kant had laid down his doctrine of space, it was important to
investigate how much in our space intuition is due to experience--is a
matter of the physical circumstances of the thinking being--and how much
is the pure act of the mind.
The only way to investigate this is the practical way, and by a
remarkable analysis the great geometers above mentioned have shown that
space is not limited as ordinary experience would seem to inform us, but
that we are quite capable of conceiving different kinds of space.
Our space as we ordinarily think of it is conceived as limited--not in
extent, but in a certain way which can only be realized when we think of
our ways of measuring space objects. It is found that there are only
three independent directions in which a body can be measured--it must
have height, length and breadth, but it has no more than these
dimensions. If any other measurement be taken in it, this new
measurement will be found to be compounded of the old measurements. It
is impossible to find a point in the body which could not be arrived at
by travelling in combinations of the three directions already taken.
But why should space be limited to three independent directions?
Geometers have found that there is no reason why bodies should be thus
limited. As a matter of fact all the bodies which we can measure are
thus limited. So we come to this conclusion, that the space which we use
for conceiving ordinary objects in the world is limited to three
dimensions. But it might be possible for there to be beings living in a
world such that they would conceive a space of four dimensions. All that
we can say about such a supposition is, that it is not demanded by our
experience. It may be that in the very large or the very minute a fourth
dimension of space will have to be postulated to account for parts--but
with regard to objects of ordinary magnitudes we are certainly not in a
four dimensional world.
And this was the point at which about ten years ago I took up the
inquiry.
It is possible to say a great deal about space of higher dimensions than
our own, and to work out analytically many problems which suggest
themselves. But can we conceive four-dimensional space in the same way
in which we can conceive our own space? Can we think of a body in four
dimensions as a unit having properties in the same way as we think of a
body having a definite shape in the space with which we are familiar?
Now this question, as every other with which I am acquainted, can only
be answered by experiment. And I commenced a series of experiments to
arrive at a conclusion one way or the other.
It is obvious that this is not a scientific inquiry--but one for the
practical teacher.
And just as in experimental researches the skilful manipulator will
demonstrate a law of nature, the less skilled manipulator will fail; so
here, everything depended on the manipulation. I was not sure that this
power lay hidden in the mind, but to put the question fairly would
surely demand every resource of the practical art of education.
And so it proved to be; for after many years of work, during which the
conception of four-dimensional bodies lay absolutely dark, at length, by
a certain change of plan, the whole subject of four-dimensional
existence became perfectly clear and easy to impart.
There is really no more difficulty in conceiving four-dimensional
shapes, when we go about it the right way, than in conceiving the idea
of solid shapes, nor is there any mystery at all about it.
When the faculty is acquired--or rather when it is brought into
consciousness, for it exists in every one in imperfect form--a new
horizon opens. The mind acquires a development of power, and in this use
of ampler space as a mode of thought, a path is opened by using that
very truth which, when first stated by Kant, seemed to close the mind
within such fast limits. Our perception is subject to the condition of
being in space. But space is not limited as we at first think.
The next step after having formed this power of conception in ampler
space, is to investigate nature and see what phenomena are to be
explained by four-dimensional relations.
But this part of the subject is hardly one for the same worker as the
one who investigates how to think in four-dimensional space. The work of
building up the power is the work of the practical educator, the work of
applying it to nature is the work of the scientific man. And it is not
possible to accomplish both tasks at the same time. Consequently the
crown is still to be won. Here the method is given of training the mind;
it will be an exhilarating moment when an investigator comes upon
phenomena which show that external nature cannot be explained except by
the assumption of a four-dimension space.
The thought of the past ages has used the conception of a
three-dimensional space, and by that means has classified many phenomena
and has obtained rules for dealing with matters of great practical
utility. The path which opens immediately before us in the future is
that of applying the conception of four-dimensional space to the
phenomena of nature, and of investigating what can be found out by this
new means of apprehension.
In fact, what has been passed through may be called the
three-dimensional era; Gauss and Lobatchewski have inaugurated the
four-dimensional era.
CHAPTER I.
SCEPTICISM AND SCIENCE. BEGINNING OF KNOWLEDGE.
The following pages have for their object to induce the reader to apply
himself to the study, in the first place of Space, and then of Higher
Space; and, therefore, I have tried by indirect means to show forth
those thoughts and conceptions to which the practical work leads.
And I feel that I have a great advantage in this project, inasmuch as
many of the thoughts which spring up in the mind of one who studies
higher space, and many of the conceptions to which he is driven, turn
out to be nothing more nor less than old truths--the property of every
mind that thinks and feels--truths which are not generally associated
with the scientific apprehension of the world, but which are not for
that reason any the less valuable.
And for my own part I cannot do more than put them forward in a very
feeble and halting manner. For I have come upon them, not in the way of
feeling or direct apprehension, but as the result of a series of works
undertaken purely with the desire to know--a desire which did not lift
itself to the height of expecting or looking for the beautiful or the
good, but which simply asked for something to know.
For I found myself--and many others I find do so also--I found myself in
respect to knowledge like a man who is in the midst of plenty and yet
who cannot find anything to eat. All around me were the evidences of
knowledge--the arts, the sciences, interesting talk, useful
inventions--and yet I myself was profited nothing at all; for somehow,
amidst all this activity, I was left alone, I could get nothing which I
could know.
The dialect was foreign to me--its inner meaning was hidden. If I would,
imitating the utterance of my fellows, say a few words, the effort was
forced, the whole result was an artificiality, and, if successful, would
be but a plausible imposture.
The word “sceptical” has a certain unpleasant association attached to
it, for it has been used by so many people who are absolutely certain in
a particular line, and attack other people’s convictions. But to be
sceptical in the real sense is a far more unpleasant state of mind to
the sceptic than to any one of his companions. For to a mind that
inquires into what it really does know, it is hardly possible to
enunciate complete sentences, much less to put before it those complex
ideas which have so large a part in true human life.
Every word we use has so wide and fugitive a meaning, and every
expression touches or rather grazes fact by so very minute a point,
that, if we wish to start with something which we do know, and thence
proceed in a certain manner, we are forced away from the study of
reality and driven to an artificial system, such as logic or
mathematics, which, starting from postulates and axioms, develops a body
of ideal truth which rather comes into contact with nature than is
nature.
Scientific achievement is reserved for those who are content to absorb
into their consciousness, by any means and by whatever way they come,
the varied appearances of nature, whence and in which by reflection they
find floating as it were on the sea of the unknown, certain
similarities, certain resemblances and analogies, by means of which they
collect together a body of possible predictions and inferences; and in
nature they find correspondences which are actually verified. Hence
science exists, although the conceptions in the mind cannot be said to
have any real correspondence in nature.
We form a set of conceptions in the mind, and the relations between
these conceptions give us relations which we find actually vibrating in
the world around us. But the conceptions themselves are essentially
artificial.
We have a conception of atoms; but no one supposes that atoms actually
exist. We suppose a force varying inversely as the square of the
distance; but no one supposes such a mysterious thing to really be in
nature. And when we come to the region of descriptive science, when we
come to simple observation, we do not find ourselves any better provided
with a real knowledge of nature. If, for instance, we think of a plant,
we picture to ourselves a certain green shape, of a more or less
definite character. This green shape enables us to recognise the plant
we think of, and to describe it to a certain extent. But if we inquire
into our imagination of it, we find that our mental image very soon
diverges from the fact. If, for instance, we cut the plant in half, we
find cells and tissues of various kinds. If we examine our idea of the
plant, it has merely an external and superficial resemblance to the
plant itself. It is a mental drawing meeting the real plant in external
appearance; but the two things, the plant and our thought of it, come as
it were from different sides--they just touch each other as far as the
colour and shape are concerned, but as structures and as living
organisms they are as wide apart as possible.
Of course by observation and study the image of a plant which we bear in
our minds may be made to resemble a plant as found in the fields more
and more. But the agreement with nature lies in the multitude of points
superadded on to the notion of greenness which we have at first--there
is no natural starting-point where the mind meets nature, and whence
they can travel hand in hand.
It almost seems as if, by sympathy and feeling, a human being was easier
to know than the simplest object. To know any object, however simple, by
the reason and observation requires an endless process of thought and
looking, building up the first vague impression into something like in
more and more respects. While, on the other hand, in dealing with human
beings there is an inward sympathy and capacity for knowing which is
independent of, though called into play by, the observation of the
actions and outward appearance of the human being.
But for the purpose of knowing we must leave out these human
relationships. They are an affair of instinct and inherited unconscious
experience. The mind may some day rise to the level of these inherited
apprehensions, and be able to explain them; but at present it is far
more than overtasked to give an account of the simplest portions of
matter, and is quite inadequate to give an account of the nature of a
human being.
Asking, then, what there was which I could know, I found no point of
beginning. There were plenty of ways of accumulating observations, but
none in which one could go hand in hand with nature.
A child is provided in the early part of its life with a provision of
food adapted for it. But it seemed that our minds are left without a
natural subsistence, for on the one hand there are arid mathematics, and
on the other there is observation, and in observation there is, out of
the great mass of constructed mental images, but little which the mind
can assimilate. To the worker at science of course this crude and
omnivorous observation is everything; but if we ask for something which
we can know, it is like a vast mass of indigestible material with every
here and there a fibre or thread which we can assimilate.
In this perplexity I was reduced to the last condition of mental
despair; and in default of finding anything which I could understand in
nature, I was sufficiently humbled to learn anything which seemed to
afford a capacity of being known.
And the objects which came before me for this endeavour were the simple
ones which will be plentifully used in the practical part of this book.
For I found that the only assertion I could make about external objects,
without bringing in unknown and unintelligible relations, was this: I
could say how things were arranged. If a stone lay between two others,
that was a definite and intelligible fact, and seemed primary. As a
stone itself, it was an unknown somewhat which one could get more and
more information about the more one studied the various sciences. But
granting that there were some things there which we call stones, the way
they were arranged was a simple and obvious fact which could be easily
expressed and easily remembered.
And so in despair of being able to obtain any other kind of mental
possession in the way of knowledge, I commenced to learn arrangements,
and I took as the objects to be arranged certain artificial objects of a
simple shape. I built up a block of cubes, and giving each a name I
learnt a mass of them.
Now I do not recommend this as a thing to be done. All I can say is that
genuinely then and now it seemed and seems to be the only kind of mental
possession which one can call knowledge. It is perfectly definite and
certain. I could tell where each cube came and how it was related to
each of the others. As to the cube itself, I was profoundly ignorant of
that; but assuming that as a necessary starting-point, taking that as
granted, I had a definite mass of knowledge.
But I do not wish to say that this is better than any kind of knowledge
which other people may find come home to them. All I want to do is to
take this humble beginning of knowledge and show how inevitably, by
devotion to it, it leads to marvellous and far-distant truths, and how,
by a strange path, it leads directly into the presence of some of the
highest conceptions which great minds have given us.
I do not think it ought to be any objection to an inquiry, that it
begins with obvious and common details. In fact I do not think that it
is possible to get anything simpler, with less of hypothesis about it,
and more obviously a simple taking in of facts than the study of the
arrangement of a block of cubes.
Many philosophers have assumed a starting point for their thought. I
want the reader to accept a very humble one and see what comes of it. If
this leads us to anything, no doubt greater results will come from more
ambitious beginnings.
And now I feel that I have candidly exposed myself to the criticism of
the reader. If he will have the patience to go on, we will begin and
build up on our foundations.
CHAPTER II.
APPREHENSION OF NATURE. INTELLIGENCE. STUDY OF ARRANGEMENT OR SHAPE.
Nature is that which is around us. But it is by no means easy to get to
nature. The savage living we may say in the bosom of nature, is
certainly unapprehensive of it, in fact it has needed the greatness of a
Wordsworth and of generations of poets and painters to open our eyes
even in a slight measure to the wonder of nature.
Thus it is clear that it is not by mere passivity that we can comprehend
nature; it is the goal of an activity, not a free gift.
And there are many ways of apprehending nature. There are the sounds and
sights of nature which delight the senses, and the involved harmonies
and the secret affinities which poetry makes us feel; then, moreover,
there is the definite knowledge of natural facts in which the memory and
reason are employed.
Thus we may divide our means of coming into contact with nature into
three main channels: the senses, the imagination, and the mind. The
imagination is perhaps the highest faculty, but we leave it out of
consideration here, and ask: How can we bring our minds into contact
with nature?
Now when we see two people of diverse characters we sometimes say that
they cannot understand one another--there is nothing in the one by which
he can understand the other--he is shut out by a limitation of his own
faculties.
And thus our power of understanding nature depends on our own
possession; it is in virtue of some mental activity of our own that we
can apprehend that outside activity which we call nature. And thus the
training to enable us to approach nature with our minds will be some
active process on our own part.
In the course of my experience as a teacher I have often been struck by
the want of the power of reason displayed by pupils; they are not able
to put two and two together, as the saying goes, and I have been at some
pains to investigate wherein this curious deficiency lies, and how it
can be supplied. And I have found that there is in the curriculum no
direct cure for it--the discipline which supplies it is not one which
comes into school methods, it is a something which most children obtain
in the natural and unsupervised education of their first contact with
the world, and lies before any recognised mode of distinction. They can
only understand in virtue of an activity of their own, and they have not
had sufficient exercise in this activity.
In the present state of education it is impossible to diverge from the
ordinary routine. But it is always possible to experiment on children
who are out of the common line of education. And I believe I am amply
justified by the result of my experiments.
I have seen that the same activity which I have found makes that habit
of mind which we call intelligence in a child, is the source of our
common and everyday rational intellectual work, and that just as the
faculties of a child can be called forth by it, so also the powers of a
man are best prepared by the same means, but on an ampler scale.
A more detailed development of the practical work of Part II., would be
the best training for the mind of a child. An extension of the work of
that Part would be the training which, hand in hand with observation
and recapitulation, would best develop a man’s thought power.
In order to tell what the activity is by the prosecution of which we can
obtain mental contact with nature we should observe what it is which we
say we “understand” in any phenomenon of nature which has become clear
to us.
When we look at a bright object it seems very different from a dull one.
A piece of bright steel hardly looks like the same substance as a piece
of dull steel. But the difference of appearance in the two is easily
accounted for by the different nature of the surface in the two cases;
in the one all the irregularities are done away with, and the rays of
light which fall on it are sent off again without being dispersed and
broken up. In the case of the dull iron the rays of light are broken up
and divided, so that they are not transmitted with intensity in any one
direction, but flung off in all sorts of directions.
Here the difference between the bright object and the dull object lies
in the arrangement of the particles on its surface and their influence
on the rays of light.
Again, with light itself the differences of colour are explained as
being the effect on us of rays of different rates of vibration. Now a
vibration is essentially this, a series of arrangements of matter which
follow each other in a closed order, so that when the set has been run
through, the first arrangement follows again. The whole theory of light
is an account of arrangements of the particles in the transmitting
medium, only the arrangements alter--are not permanent in any one
characteristic, but go through a complete cycle of varieties.
Again, when the movements of the heavenly bodies are deduced from the
theory of universal gravitation, what we primarily do is to take
account of arrangement; for the law of gravity connects the movements
which the attracted bodies tend to make with their distances, that is,
it shows how their movements depend on their arrangement. And if gravity
as a force is to be explained itself, the suppositions which have been
put forward resolve it into the effect of the movements of small bodies;
that is to say, gravity, if explained at all, is explained as the result
of the arrangement and altering arrangements of small particles.
Again, to take the idea which proceeding from Goethe casts such an
influence on botanical observation. Goethe (and also Wolf) laid down
that the parts of a flower were modified leaves--and traced the stages
and intermediate states between the ordinary green leaf and the most
gorgeous petal or stamen or carpel, so unlike a leaf in form and
function.
Now the essential value in this conception is, that it enables us to
look, upon these different organs of a plant as modifications of one and
the same organ--it enables us to think about the different varieties of
the flower head as modifications of one single plant form. We can trace
correspondences between them, and are led to possible explanations of
their growth. And all this is done by getting rid of pistil and stamen
as separate entities, and looking on them as leaves, and their parts due
to different arrangement of the leaf structure. We have reduced these
diverse objects to a common element, we have found the unit by whose
arrangements the whole is produced. And in this department of thought,
as also to take another instance, in chemistry, to understand is
practically this: we find units (leaves or atoms) combinations of which
account for the results which we see. Thus we see that that which the
mind essentially apprehends is arrangement.
And this holds over the whole range of mental work, from the simplest
observation to the most complex theory. When the eye takes in the form
of an external object there is something more than a sense impression,
something more than a sensation of greenness and light and dark. The
mind works as well as the sense, and these sense impressions are
definitely grouped in what we call the shape of the object. The
essential act of perceiving lies in the apprehension of a shape, and a
shape is an arrangement of parts. It does not matter what these parts
are; if we take meaningless dots of colour and arrange them we obtain a
shape which represents the appearance of a stone or a leaf to a certain
degree. If we want to make our representation still more like, we must
treat each of the dots as in themselves arrangements, we must compose
each of them by many strokes and dots of the brush. But even in this
case we have not got anything else besides arrangement. The ultimate
element, the small items of light and shade or of colour, are in
themselves meaningless; it is in their arrangement that the likeness of
the representation consists.
Thus, from a drawing to our notion of the planetary system, all our
contact with nature lies in this, in an appreciation of arrangement.
Hence to prepare ourselves for the understanding of nature, we must
“arrange.” In virtue of our activity in making arrangements we prepare
ourselves to do what is called understand nature. Or we may say, that
which we call understanding nature is to discern something similar in
nature to that which we do when we arrange elements into compounded
groups.
Now if we study arrangement in the active way, we must have something to
arrange; and the things we work with may be either all alike, or each of
them varying from every other.
If the elements are not alike then we are not studying pure arrangement;
but our knowledge is affected by the compound nature of that with which
we deal. If the elements are all alike, we have what we call units.
Hence the discipline preparatory for the understanding of nature is the
active arrangement of like units.
And this is very much the case with all educational processes; only the
things chosen to arrange are in general words, which are so complicated
and carry such a train of association that, unless the mind has already
acquired a knowledge of arrangement, it is puzzled and hampered, and
never gets a clear apprehension of what its work is.
Now what shall we choose for our units? Any unit would do; but it ought
to be a real thing--it ought to be something which can be touched and
seen, not something which no one has ever touched or seen, and which is
even incapable of definition, like a “number.”
I would divide studies into two classes: those which create the faculty
of arrangement, and those which use it and exercise it. Mathematics
exercises it, but I do not think it creates it; and unfortunately, in
mathematics as it is now often taught, the pupil is launched , into a
vast system of symbols--the whole use and meaning of symbols (namely, as
means to acquire a clear grasp of facts) is lost to him.
Of the possible units which will serve, I take the cube; and I have
found that whenever I took any other unit I got wrong, puzzled and lost
my way. With the cube one does not get along very fast, but everything
is perfectly obvious and simple, and builds up into a whole of which
every part is evident.
And I must ask the reader to absolutely erase from his mind all desire
or wish to be able to predict or assert anything about nature, and he
must please look with horror on any mental process by which he gets at
a truth in an ingenious but obscure and inexplicable way. Let him take
nothing which is not perfectly clear, patent and evident, demonstrable
to his senses, a simple repetition of obvious fact.
Our work will then be this: a study, by means of cubes, of the facts of
arrangement. And the process of learning will be an active one of
actually putting up the cubes. In this way we do for the mind what
Wordsworth does for the imagination--we bring it into contact with
nature.
CHAPTER III.
THE ELEMENTS OF KNOWLEDGE.
There are two elements which enter into our knowledge with respect to
any phenomenon.
If, for instance, we take the sun, and ask ourselves what we observe, we
notice that it is a bright, moving body; and of these two qualities, the
brightness and the movement, each seems equally predicable of the sun.
It does move, and it is bright.
Now further study discloses to us that there is a difference between
these two affirmations. The motion of the sun in its diurnal course
round the earth is only apparent; but it is really a bright, hot body.
Now of these two assertions which the mind naturally makes about the
sun, one--that it is moving--depends on the relation of the beholder to
the sun, the other is true about the sun itself. The observed motion
depends on a fact affecting oneself and having nothing to do with the
sun, while the brightness is really a quality of the sun itself.
Now we will call those qualities or appearances which we notice in a
body which are due to the particular conditions under which oneself is
placed in observing it, the self elements; those facts about it which
are independent of the observer’s particular relationship we will call
the residual element. Thus the sun’s motion is a self element in our
thought of the sun, its brightness is a residual element.
It is not, of course, possible to draw a line distinctly between the
self elements and the residual elements. For instance, some people have
denied that brightness is a quality of things, but that it depends on
the capacity of the being for receiving sensations; and for brightness
they would substitute the assertion that the sun is giving forth a great
deal of energy in the form of heat and light.
But there is no object in pursuing the discussion further. The main
distinction is sufficiently obvious. And it is important to separate the
self elements involved in our knowledge as far as possible, so that the
residual elements may be kept for our closer attention. By getting rid
of the self elements we put ourselves in a position in which we can
propound sensible questions. By getting rid of the notion of its
circular motion round the earth we prepare our way to study the sun as
it really is. We get the subject clear of complications and extraneous
considerations.
It would hardly be worth while to dwell on this consideration were it
not of importance in our study of arrangement. But the fact is that
directly a subject has been cleared of the self elements, it seems so
absurd to have had them introduced at all that the great difficulty
there was in getting rid of them is forgotten.
With regard to the knowledge we have at the present day about scientific
matters, there do not seem to be any self elements present. But the
worst about a self element is, that its presence is never dreamed of
till it is got rid of; to know that it is there is to have done away
with it. And thus our body of knowledge is like a fluid which keeps
clear, not because there are no substances in solution, but because
directly they become evident they fall down as precipitates.
Now one of our serious pieces of work will be to get rid of the self
elements in the knowledge of arrangement.
And the kind of knowledge which we shall try to obtain will be somewhat
different from the kind of knowledge which we have about events or
natural phenomena. In the large subjects which generally occupy the mind
the things thought of are so complicated that every detail cannot
possibly be considered. The principles of the whole are realized, and
then at any required time the principles can be worked out. Thus, with
regard to a knowledge of the planetary system, it is said to be known if
the law of movement of each of the planets is recognized, and their
positions at any one time committed to memory. It is not our habit to
remember their relative positions with regard to one another at many
intervals, so as to have an exhaustive catalogue of them in our minds.
But with regard to the elements of knowledge with which we shall work,
the subject is so simple that we may justly demand of ourselves that we
will know every detail.
And the knowledge we shall acquire will be much more one of the sense
and feeling than of the reason. We do not want to have a rule in our
minds by which we can recall the positions of the different cubes, but
we want to have an immediate apprehension of them. It was Kant who first
pointed out how much of thought there was embodied in the sense
impressions; and it is this embodied thought which we wish to form.
CHAPTER IV.
THEORY AND PRACTICE.
Both in science and in morals there is an important distinction to be
drawn between theory and practice. A knowledge of chemistry does not
consist in the intellectual appreciation of different theories and
principles, but in being able to act in accordance with the facts of
chemical combination, so that by means of the appliances of chemistry
practical results are produced. And so in morals--the theoretic
acquaintance with the principles of human action may consist with a
marked degree of ignorance of how to act amongst other human beings.
Now the use of the word “learn” has been much restricted to merely
theoretic studies. It requires to be enlarged to the scientific meaning.
And to know, should include practice in actual manipulation.
Let us take an instance. We all know what justice is, and any child can
be taught to tell the difference between acting justly and acting
unjustly. But it is a different thing to teach them to act with justice.
Something is done which affects them unpleasantly. They feel an impulse
to retaliate. In order to see what justice demands they have to put
their personal feeling on one side. They have to get rid of those
conditions under which they apprehended the effects of the action at
first, and they have to look on it from another point of view. Then they
have to act in accordance with this view.
Now there are two steps--one an intellectual one of understanding, one a
practical one of carrying out the view. Neither is a moral step. One
demands intelligence, the other the formation of a habit, and this habit
can be inculcated by precept, by reward and punishment, by various
means. But as human nature is constituted, if the habit of justice is
inculcated it touches a part of the being. There is an emotional
response. We know but little of a human being, but we can safely say
that there are depths in it, beyond the feelings of momentary resentment
and the stimulus of pleasurable or painful sensation, to which justice
is natural.
How little adequate is our physical knowledge of a human being as a
bodily frame to explain the fact of human life. Now and again we see one
of these isolated beings bound up in another, as if there was an
undiscovered physical bond between them. And in all there is this sense
of justice--a kind of indwelling verdict of the universal mind, if we
may use such an expression, in virtue of which a man feels not as a
single individual but as all men.
With respect to justice, it is not only necessary to take the view of
one other person than oneself, but that of many. There may be justice
which is very good justice from the point of view of a party, but very
bad justice from the point of view of a nation. And if we suppose an
agency outside the human race, gifted with intelligence, and affecting
the race, in the way for instance of causing storms or disturbances of
the ground, in order to judge it with justice we should have to take a
standpoint outside the race of men altogether. We could not say that
this agency was bad. We should have to judge it with reference to its
effect on other sentient beings.
There are some words which are often used in contrast with each
other--egoism and altruism; and each seems to me unmeaning except as
terms in a contrast.
Let us take an instance. A boy has a bag of cakes, and is going to enjoy
them by himself. His parent stops him, and makes him set up some stumps
and begin to learn to play cricket with another boy. The enjoyment of
the cakes is lost--he has given that up; but after a little while he has
a pleasure which is greater than that of cakes in solitude. He enters
into the life of the game. He has given up, or been forced to give up,
the pleasure he knew, and he has found a greater one. What he thought
about himself before was that he liked cakes, now what he thinks about
himself is that he likes cricket. Which of these is the true thought
about himself? Neither, probably, but at any rate it is more near the
truth to say that he likes the cricket. If now we use the word self to
mean that which a person knows of himself, and it is difficult to see
what other meaning it can have, his self as he knew it at first was
thwarted, was given up, and through that he discovered his true self.
And again with the cricket; he will make the sacrifice of giving that
up, voluntarily or involuntarily, and will find a truer self still.
In general there is not much difficulty in making a boy find out that he
likes cricket; and it is quite possible for him to eat his cakes first
and learn to play cricket afterwards--the cricket will not come to him
as a thwarting in any sense of what he likes better. But this ease in
entering in to the pursuit only shows that the boy’s nature is already
developed to the level of enjoying the game. The distinct moral advance
would come in such a case when something which at first was hard to him
to do was presented to him--and the hardness, the unpleasantness is of a
double kind, the giving up of a pursuit or indulgence to which he is
accustomed, and the exertion of forming the habits demanded by the new
pursuit.
Now it is unimportant whether the renunciation is forced or willingly
taken. But as a general rule it may be laid down, that by giving up his
own desires as he feels them at the moment, to the needs and advantage
of those around him, or to the objects which he finds before him
demanding accomplishment, a human being passes to the discovery of his
true self on and on. The process is limited by the responsibilities
which a man finds come upon him.
The method of moral advance is to acquire a practical knowledge; he must
first see what the advantage of some one other than himself would be,
and then he must act in accordance with that view of things. Then having
acted and formed a habit, he discovers a response in himself. He finds
that he really cares, and that his former limited life was not really
himself. His body and the needs of his body, so far as he can observe
them, externally are the same as before; but he has obtained an inner
and unintellectual, but none the less real, apprehension of what he is.
Thus altruism, or the sacrifice of egoism to others, is followed by a
truer egoism, or assertion of self, and this process flashed across by
the transcendent lights of religion, wherein, as in the sense of justice
and duty, untold depths in the nature of man are revealed entirely
unexpressed by the intellectual apprehension which we have of him as an
animal frame of a very high degree of development, is the normal one by
which from childhood a human being develops into the full
responsibilities of a man.
Now both in science and in conduct there are self elements. In science,
getting rid of the self elements means a truer apprehension of the facts
about one; in conduct, getting rid of the self elements means obtaining
a truer knowledge of what we are--in the way of feeling more strongly
and deeply and being bound and linked in a larger scale.
Thus without pretending to any scientific accuracy in the use of terms,
we can assign a certain amount of meaning to the expression--getting rid
of self elements. And all that we can do is to take the rough idea of
this process, and then taking our special subject matter, apply it. In
affairs of life experiments lead to disaster. But happily science is
provided wherein the desire to put theories into practice can be safely
satisfied--and good results sometimes follow. Were it not for this the
human race might before now have been utopiad from off the face of the
earth.
In experiment, manipulation is everything; we must be certain of all our
conditions, otherwise we fail assuredly and have not even the
satisfaction of knowing that our failure is due to the wrongness of our
conjectures.
And for our purposes we use a subject matter so simple that the
manipulation is easy.
CHAPTER V.
KNOWLEDGE: SELF-ELEMENTS.
I must now go with somewhat of detail into the special subject in which
these general truths will be exhibited. Everything I have to say would
be conceived much more clearly by a very little practical manipulation.
But here I want to put the subject in as general a light as possible, so
that there may be no hindrance to the judgment of the reader.
And when I use the word “know,” I assume something else than the
possession of a rule, by which it can be said how facts are. By knowing
I mean that the facts of a subject all lie in the mind ready to come out
vividly into consciousness when the attention is directed on them.
Michael Angelo knew the human frame, he could tell every little fact
about it; if he chose to call up the image, he would see mentally how
each muscle and fold of the skin lay with regard to the surrounding
parts. We want to obtain a knowledge as good as Michael Angelo’s. There
is a great difference between Michael Angelo and us; but let that
difference be expressed, not in our way of knowing, but in the
difference between the things he knew and the things we know. We take a
very simple structure and know it as absolutely as he knew the
complicated structure of the human body.
And let us take a block of cubes; any number will do, but for
convenience sake let us take a set of twenty-seven cubes put together
so as to form a large cube of twenty-seven parts. And let each of these
cubes be marked so as to be recognized, and let each have a name so that
it can be referred to. And let us suppose that we have learnt this block
of cubes so that each one is known--that is to say, its position in the
block is known and its relation to the other blocks.
Now having obtained this knowledge of the block as it stands in front of
us, let us ask ourselves if there is any self element present in our
knowledge of it.
And there is obviously this self element present. We have learnt the
cubes as they stand in accordance with our own convenience in putting
them up. We put the lowest ones first, and the others on the top of
them, and we distinctly conceive the lower ones as supporting the upper
ones. Now this fact of support has nothing to do with the block of cubes
itself, it depends on the conditions under which we come to apprehend
the block of cubes, it depends on our position on the surface of the
earth, whereby gravity is an all important factor in our experience. In
fact our sight has got so accustomed to take gravity into consideration
in its view of things, that when we look at a landscape or object with
our head upside down we do not see it inverted, but we superinduce on
the direct sense impressions our knowledge of the action of gravity, and
obtain a view differing very little from what we see when in an upright
position.
It will be found that every fact about the cubes has involved in it a
reference to up and down. It is by being above or below that we chiefly
remember where the cubes are. But above and below is a relation which
depends simply on gravity. If it were not for gravity above and below
would be interchangeable terms, instead of expressing a difference of
marked importance to us under our conditions of existence. Now we put
“being above” or “being below” into the cubes themselves and feel it a
quality in them--it defines their position. But this above or below
really comes from the conditions in which we are. It is a self element,
and as such, to obtain a true knowledge of the cubes we must get rid of
it.
And now, for the sake of a process which will be explained afterwards,
let us suppose that we cannot move the block of cubes which we have put
up. Let us keep it fixed.
In order to learn how it is independent of gravity the best way would be
to go to a place where gravity has virtually ceased to act; at the
centre of the earth, for instance, or in a freely falling shell.
But this is impossible, so we must choose another way. Let us, then,
since we cannot get rid of gravity, see what we have done already. We
have learnt the cubes, and however they are learnt, it will be found
that there is a certain set of them round which the others are mentally
grouped, as being on the right or left, above or below. Now to get our
knowledge as perfect as we can before getting rid of the self element up
and down, we have to take as central cubes in our mind different sets
again and again, until there are none which are primary to us.
Then there remains only the distinction of some being above others. Now
this can only be made to sink out of the primary place in our thoughts
by reversing the relation. If we turned the block upside down, and
learnt it in this new position, then we should learn the position of the
cubes with regard to each other with that element in them, which comes
from the action of gravity, reversed. And the true nature of the
arrangement to which we added something in virtue of our sensation of
up and down, would become purer and more isolated in our minds.
We have, however, supposed that the cubes are fixed. Then, in order to
learn them, we must put up another block showing what they would be like
in the supposed new position. We then take a set of cubes, models of the
original cubes, and by consideration we can put them in such positions
as to be an exact model of what the block of cubes would be if turned
upside down.
And here is the whole point on which the process depends. We can tell
where each cube would come, but we do not _know_ the block in this new
position. I draw a distinction between the two acts, “to tell where it
would be,” and to “know.” Telling where it would be is the preparation
for knowing. The power of assigning the positions may be called the
theory of the block. The actual knowledge is got by carrying out the
theory practically, by putting up the blocks and becoming able to
realize without effort where each one is.
It is not enough to put up the model blocks in the reverse position. It
is found that this up and down is a very obstinate element indeed, and a
good deal of work is requisite to get rid of it completely. But when it
is got rid of in one set of cubes, the faculty is formed of appreciating
shape independently of the particular parts which are above or below on
first examination. We discover in our own minds the faculty of
appreciating the facts of position independent of gravity and its
influence on us. I have found a very great difference in different minds
in this respect. To some it is easy, to some it is hard.
And to use our old instance, the discovery of this capacity is like the
discovery of a love of justice in the being who has forced himself to
act justly. It is a capacity for being able to take a view independent
of the conditions under which he is placed, and to feel in accordance
with that view. There is, so far as I know, no means of arriving
immediately at this impartial appreciation of shape. It can only be done
by, as it were, extending our own body so as to include certain cubes,
and appreciating then the relation of the other cubes to those. And
after this, by identifying ourselves with other cubes, and in turn
appreciating the relation of the other cubes to these. And the practical
putting up of the cubes is the way in which this power is gained. It
springs up with a repetition of the mechanical acts. Thus there are
three processes. 1st, An apprehension of what the position of the cubes
would be. 2nd, An actual putting of them up in accordance with that
apprehension, 3rd, The springing up in the mind of a direct feeling of
what the block is, independent of any particular presentation.
Thus the self element of up and down can be got rid of out of a block of
cubes.
And when even a little block is known like this, the mind has gained a
great deal.
Yet in the apprehension and knowledge of the block of cubes with the up
and down relation in them, there is more than in the absolute
apprehension of them. For there is the apprehension of their position
and also of the effect of gravity on them in their position.
Imagine ourselves to be translated suddenly to another part of the
universe, and to find there intelligent beings, and to hold conversation
with them. If we told them that we came from a world, and were to
describe the sun to them, saying that it was a bright, hot body which
moved round us, they would reply: You have told us something about the
sun, but you have also told us something about yourselves.
Thus in the apprehension of the sun as a body moving round us there is
more than in the apprehension of it as not moving round, for we really
in this case apprehend two things--the sun and our own conditions. But
for the purpose of further knowledge it is most important that the more
abstract knowledge should be acquired. The self element introduced by
the motion of the earth must be got rid of before the true relations of
the solar system can be made out.
And in our block of cubes, it will be found that feelings about
arrangement, and knowledge of space, which are quite unattainable with
our ordinary view of position, become simple and clear when this
discipline has been gone through.
And there can be no possible mental harm in going through this bit of
training, for all that it comes to is looking at a real thing as it
actually is--turning it round and over and learning it from every point
of view.
CHAPTER VI.
FUNCTION OF MIND. SPACE AGAINST METAPHYSICS. SELF-LIMITATION AND ITS
TEST. A PLANE WORLD.
We now pass on to the question: Are there any other self elements
present in our knowledge of the block of cubes?
When we have learnt to free it from up and down, is there anything else
to be got rid of?
It seems as if, when the cubes were thus learnt, we had got as abstract
and impersonal a bit of knowledge as possible.
But, in reality, in the relations of the cubes as we thus apprehend them
there is present a self element to which the up and down is a mere
trifle. If we think we have got absolute knowledge we are indeed walking
on a thin crust in unconsciousness of the depths below.
We are so certain of that which we are habituated to, we are so sure
that the world is made up of the mechanical forces and principles which
we familiarly deal with, that it is more of a shock than a welcome
surprise to us to find how mistaken we were.
And after all, do we suppose that the facts of distance and size and
shape are the ultimate facts of the world--is it in truth made up like a
machine out of mechanical parts? If so, where is there room for that
other which we know--more certainly, because inwardly--that reverence
and love which make life worth having? No; these mechanical relations
are our means of knowing about the world; they are not reality itself,
and their primary place in our imaginations is due to the familiarity
which we have with them, and to the peculiar limitations under which we
are.
But I do not for a moment wish to go in thought beyond physical
nature--I do not suppose that in thought we can. To the mind it is only
the body that appears, and all that I hope to do is to show material
relations, mechanism, arrangements.
But much depends on what kind of material relations we perceive outside
us. A human being, an animal and a machine are to the mind all merely
portions of matter arranged in certain ways. But the mind can give an
exhaustive account of the machine, account fairly well for the animal,
while the human being it only defines externally, leaving the real
knowledge to be supplied by other faculties.
But we must not under-estimate the work of the mind, for it is only by
the observation of and thought about the bodies with which we come into
contact that we know human beings. It is the faculty of thought that
puts us in a position to recognize a soul.
And so, too, about the universe--it is only by correct thought about it
that we can perceive its true moral nature.
And it will be found that the deadness which we ascribe to the external
world is not really there, but is put in by us because of our own
limitations. It is really the self elements in our knowledge which make
us talk of mechanical necessity, dead matter. When our limitations fall,
we behold the spirit of the world like we behold the spirit of a
friend--something which is discerned in and through the material
presentation of a body to us.
Our thought means are sufficient at present to show us human souls; but
all except human beings is, as far as science is concerned, inanimate.
One self element must be got rid of from our perception, and this will
be changed.
The one thing necessary is, that in matters of thinking we will not
admit anything that is not perfectly clear, palpable and evident. On the
mind the only conceivable demand is to seek for facts. The rock on which
so many systems of philosophy have come to grief is the attempt to put
moral principles into nature. Our only duty is to accept what we find.
Man is no more the centre of the moral world than he is of the physical
world. Then relegate the intellect to its right position of dealing with
facts of arrangement--it can appreciate structure--and let it simply
look on the world and report on it. We have to choose between
metaphysics and space thought. In metaphysics we find lofty
ideals--principles enthroned high in our souls, but which reduce the
world to a phantom, and ourselves to the lofty spectators of an arid
solitude. On the other hand, if we follow Kant’s advice, we use our
means and find realities linked together, and in the physical interplay
of forces and connexion of structure we behold the relations between
spirits--those dwelling in man and those above him.
It is difficult to explain this next self element that has to be removed
from the block of cubes; it requires a little careful preparation, in
fact our language hardly affords us the means. But it is possible to
approach indirectly, and to detect the self-element by means of an
analogy.
If we suspect there be some condition affecting ourselves which make us
perceive things not as they are, but falsely, then it is possible to
test the matter by making the supposition of other beings subject to
certain conditions, and then examining what the effect on their
experience would be of these conditions.
Thus if we make up the appearances which would present themselves to a
being subject to a limitation or condition, we shall find that this
limitation or condition, when unrecognized by him, presents itself as a
general law of his outward world, or as properties and qualities of the
objects external to him. He will, moreover, find certain operations
possible, others impossible, and the boundary line between the possible
and impossible will depend quite as much on the conditions under which
he is as on the nature of the operations.
And if we find that in our experience of the outward world there are
analogous properties and qualities of matter, analogous possibilities
and impossibilities, then it will show to us that we in our turn are
under analogous limitations, and that what we perceive as the external
world is both the external world and our own conditions. And the task
before us will be to separate the two. Now the problem we take up here
is this--to separate the self elements from the true fact. To separate
them not merely as an outward theory and intelligent apprehension, but
to separate them in the consciousness itself, so that our power of
perception is raised to a higher level. We find out that we are under
limitations. Our next step is to so familiarize ourselves with the real
aspect of things, that we perceive like beings not under our
limitations. Or more truly, we find that inward soul which itself not
subject to these limitations, is awakened to its own natural action,
when the verdicts conveyed to it through the senses are purged of the
self elements introduced by the senses.
Everything depends on this--Is there a native and spontaneous power of
apprehension, which springs into activity when we take the trouble to
present to it a view from which the self elements are eliminated? About
this every one must judge for himself. But the process whereby this
inner vision is called on is a definite one.
And just as a human being placed in natural human relationships finds in
himself a spontaneous motive towards the fulfilment of them, discovers
in himself a being whose motives transcend the limits of bodily
self-regard, so we should expect to find in our minds a power which is
ready to apprehend a more absolute order of fact than that which comes
through the senses.
I do not mean a theoretical power. A theory is always about it, and
about it only. I mean an inner view, a vision whereby the seeing mind as
it were identifies itself with the thing seen. Not the tree of
knowledge, but of the inner and vital sap which builds up the tree of
knowledge.
And if this point is settled, it will be of some use in answering the
question: What are we? Are we then bodies only? This question has been
answered in the negative by our instincts. Why should we despair of a
rational answer? Let us adopt our space thought and develop it.
The supposition which we must make is the following. Let us imagine a
smooth surface--like the surface of a table; but let the solid body at
which we are looking be very thin, so that our surface is more like the
surface of a thin sheet of metal than the top of a table.
And let us imagine small particles, like particles of dust, to lie on
this surface, and to be attracted downwards so that they keep on the
surface. But let us suppose them to move freely over the surface. Let
them never in their movements rise one over the other; let them all
singly and collectively be close to the surface. And let us suppose all
sorts of attractions and repulsions between these atoms, and let them
have all kinds of movements like the atoms of our matter have.
Then there may be conceived a whole world, and various kinds of beings
as formed out of this matter. The peculiarity about this world and these
beings would be, that neither the inanimate nor the animate members of
it would move away from the surface. Their movements would all lie in
one plane, a plane parallel to and very near the surface on which they
are.
And if we suppose a vast mass to be formed out of these atoms, and to
lie like a great round disk on the surface, compact and cohering closely
together, then this great disk would afford a support for the smaller
shapes, which we may suppose to be animate beings. The smaller shapes
would be attracted to the great disk, but would be arrested at its rim.
They would tend to the centre of the disk, but be unable to get nearer
to the centre than its rim.
Thus, as we are attracted to the centre of the earth, but walk on its
surface, the beings on this disk would be attracted to its centre, but
walk on its rim. The force of attraction which they would feel would be
the attraction of the disk. The other force of attraction, acting
perpendicularly to the plane which keeps them and all the matter of
their world to the surface, they would know nothing about. For they
cannot move either towards this force or away from it; and the surface
is quite smooth, so that they feel no friction in their movement over
it.
Now let us realize clearly one of these beings as he proceeds along the
rim of his world. Let us imagine him in the form of an outline of a
human being, with no thickness except that of the atoms of his world. As
to the mode in which he walks, we must imagine that he proceeds by
springs or hops, because there would be no room for his limbs to pass
each other.
Imagine a large disk on the table before you, and a being, such as the
one described, proceeding round it. Let there be small movable particles
surrounding him, which move out of his way as he goes along, and let
these serve him for respiration; let them constitute an atmosphere.
Forwards and backwards would be to such a being direction along the
rim--the direction in which he was proceeding and its reverse.
Then up and down would evidently be the direction away from the disk’s
centre and towards it. Thus backwards and forwards, up and down, would
both lie in the plane in which he was.
And he would have no other liberty of movement except these. Thus the
words right and left would have no meaning to him. All the directions in
which he could move, or could conceive movement possible, would be
exhausted when he had thought of the directions along the rim and at
right angles to it, both in the plane.
What he would call solid bodies, would be groups of the atoms of
his world cohering together. Such a mass of atoms would, we know,
have a slight thickness; namely, the thickness of a single atom. But
of this he would know nothing. He would say, “A solid body has two
dimensions--height (by how much it goes away from the rim) and thickness
(by how much it lies along the rim).” Thus a solid would be a
two-dimensional body, and a solid would be bounded by lines. Lines would
be all that he could see of a solid body.
Thus one of the results of the limitations under which he exists would
be, that he would say, “There are only two dimensions in real things.”
In order for his world to be permanent, we must suppose the surface on
which he is to be very compact, compared to the particles of his matter;
to be very rigid; and, if he is not to observe it by the friction of
matter moving on it, to be very smooth. And if it is very compact with
regard to his matter, the vibrations of the surface must have the effect
of disturbing the portions of his matter, and of separating compound
bodies up into simpler ones.
[Illustration: Fig. 1.]
[Illustration: Fig. 2.]
Another consequence of the limitation under which this being lies, would
be the following:--If we cut out from the corners of a piece of paper
two triangles, A B C and A′ B′ C′, and suppose them to be reduced to
such a thinness that they are capable of being put on to the imaginary
surface, and of being observed by the flat being like other bodies known
to him; he will, after studying the bounding lines, which are all that
he can see or touch, come to the conclusion that they are equal and
similar in every respect; and he can conceive the one occupying the same
space as the other occupies, without its being altered in any way.
If, however, instead of putting down these triangles into the surface on
which the supposed being lives, as shown in Fig. 1, we first of all turn
one of them over, and then put them down, then the plane-being has
presented to him two triangles, as shown in Fig. 2.
And if he studies these, he finds that they are equal in size and
similar in every respect. But he cannot make the one occupy the same
space as the other one; this will become evident if the triangles be
moved about on the surface of a table. One will not lie on the same
portion of the table that the other has marked out by lying on it.
Hence the plane-being by no means could make the one triangle in this
case coincide with the space occupied by the other, nor would he be able
to conceive the one as coincident with the other.
The reason of this impossibility is, not that the one cannot be made to
coincide, but that before having been put down on his plane it has been
turned round. It has been turned, using a direction of motion which the
plane-being has never had any experience of, and which therefore he
cannot use in his mental work any more than in his practical endeavours.
Thus, owing to his limitations, there is a certain line of possibility
which he cannot overstep. But this line does not correspond to what is
actually possible and impossible. It corresponds to a certain condition
affecting him, not affecting the triangle. His saying that it is
impossible to make the two triangles coincide, is an assertion, not
about the triangles, but about himself.
Now, to return to our own world, no doubt there are many assertions
which we make about the external world which are really assertions about
ourselves. And we have a set of statements which are precisely similar
to those which the plane-being would make about his surroundings.
Thus, he would say, there are only two independent directions; we say
there are only three.
He would say that solids are bounded by lines; we say that solids are
bounded by planes.
Moreover, there are figures about which we assert exactly the same kind
of impossibility as his plane-being did about the triangles in Fig. 2.
We know certain shapes which are equal the one to the other, which are
exactly similar, and yet which we cannot make fit into the same portion
of space, either practically or by imagination.
If we look at our two hands we see this clearly, though the two hands
are a complicated case of a very common fact of shape. Now, there is one
way in which the right hand and the left hand may practically be brought
into likeness. If we take the right-hand glove and the left-hand glove,
they will not fit any more than the right hand will coincide with the
left hand. But if we turn one glove inside out, then it will fit. Now,
to suppose the same thing done with the solid hand as is done with the
glove when it is turned inside out, we must suppose it, so to speak,
pulled through itself. If the hand were inside the glove all the time
the glove was being turned inside out, then, if such an operation were
possible, the right hand would be turned into an exact model of the left
hand. Such an operation is impossible. But curiously enough there is a
precisely similar operation which, if it were possible, would, in a
plane, turn the one triangle in Fig. 2 into the exact copy of the other.
[Illustration]
Look at the triangle in Fig. 2, A B C, and imagine the point A to move
into the interior of the triangle and to pass through it, carrying after
it the parts of the lines A B and A C to which it is attached, we should
have finally a triangle A B C, which was quite like the other of the two
triangles A′ B′ C′ in Fig. 2.
Thus we know the operation which produces the result of the “pulling
through” is not an impossible one when the plane-being is concerned.
Then may it not be that there is a way in which the results of the
impossible operation of pulling a hand through could be performed? The
question is an open one. Our feeling of it being impossible to produce
this result in any way, may be because it really is impossible, or it
may be a useful bit of information about ourselves.
Now at this point my special work comes in. If there be really a
four-dimensional world, and we are limited to a space or
three-dimensional view, then either we are absolutely three-dimensional
with no experience at all or capacity of apprehending four-dimensional
facts, or we may be, as far as our outward experience goes, so limited;
but we may really be four-dimensional beings whose consciousness is by
certain undetermined conditions limited to a section of the real space.
Thus we may really be like the plane-beings mentioned above, or we may
be in such a condition that our perceptions, not ourselves, are so
limited. The question is one which calls for experiment.
We know that if we take an animal, such as a dog or cat, we can by
careful training, and by using rewards and punishment, make them act in
a certain way, in certain defined cases, in accordance with justice; we
can produce the mechanical action. But the feeling of justice will not
be aroused; it will be but a mere outward conformity. But a human being,
if so trained, and seeing others so acting, gets a feeling of justice.
Now, if we are really four-dimensional, by going through those acts
which correspond to a four-dimensional experience (so far as we can), we
shall obtain an apprehension of four-dimensional existence--not with the
outward eye, but essentially with the mind.
And after a number of years of experiment which were entirely nugatory,
I can now lay it down as a verifiable fact, that by taking the proper
steps we can feel four-dimensional existence, that the human being
somehow, and in some way, is not simply a three-dimensional being--in
what way it is the province of science to discover. All that I shall do
here is, to put forward certain suppositions which, in an arbitrary and
forced manner, give an outline of the relation of our body to
four-dimensional existence, and show how in our minds we have faculties
by which we recognise it.
CHAPTER VII.
SELF ELEMENTS IN OUR CONSCIOUSNESS.
It is often taken for granted that our consciousness of ourselves and of
our own feelings has a sort of direct and absolute value.
It is supposed to afford a testimony which does not require to be sifted
like our consciousness of external events. But in reality it needs far
more criticism to be applied to it than any other mode of apprehension.
To a certain degree we can sift our experience of the external world,
and divide it into two portions. We can determine the self elements and
the realities. But with regard to our own nature and emotions, the
discovery which makes a science possible has yet to be made.
There are certain indications, however, springing from our observation
of our own bodies, which have a certain degree of interest.
It is found that the processes of thought and feeling are connected with
the brain. If the brain is disturbed, thoughts, sights, and sounds come
into the consciousness which have no objective cause in the external
world. Hence we may conclusively say that the human being, whatever he
is, is in contact with the brain, and through the brain with the body,
and through the body with the external world.
It is the structures and movements in the brain which the human being
perceives. It is by a structure in the brain that he apprehends nature,
not immediately. The most beautiful sights and sounds have no effect on
a human being unless there is the faculty in the brain of taking them in
and handing them on to the consciousness.
Hence, clearly, it is the movements and structure of the minute portions
of matter forming the brain which the consciousness perceives. And it is
only by models and representations made in the stuff of the brain that
the mind knows external changes.
Now, our brains are well furnished with models and representations of
the facts and events of the external world.
But a most important fact still requires its due weight to be laid upon
it.
These models and representations are made on a very minute scale--the
particles of brain matter which form images and representations are
beyond the power of the microscope in their minuteness. Hence the
consciousness primarily apprehends the movements of matter of a degree
of smallness which is beyond the power of observation in any other way.
Hence we have a means of observing the movements of the minute portions
of matter. Let us call those portions of the brain matter which are
directly instrumental in making representations of the external
world--let us call them brain molecules.
Now, these brain molecules are very minute portions of matter indeed;
generally they are made to go through movements and form structures in
such a way as to represent the movements and structures of the external
world of masses around us.
But it does not follow that the structures and movements which they
perform of their own nature are identical with the movements of the
portions of matter which we see around us in the world of matter.
It may be that these brain molecules have the power of four-dimensional
movement, and that they can go through four-dimensional movements and
form four-dimensional structures.
If so, there is a practical way of learning the movements of the very
small particles of matter--by observing, not what we can see, but what
we can think.
For, suppose these small molecules of the brain were to build up
structures and go through movements not in accordance with the rule of
representing what goes on in the external world, but in accordance with
their own activity, then they might go through four-dimensional
movements and form four-dimensional structures.
And these movements and structures would be apprehended by the
consciousness along with the other movements and structures, and would
seem as real as the others--but would have no correspondence in the
external world.
They would be thoughts and imaginations, not observations of external
facts.
Now, this field of investigation is one which requires to be worked at.
At present it is only those structures and movements of the brain
molecules which correspond to the realities of our three-dimensional
space which are in general worked at consistently. But in the practical
part of this book it will be found that by proper stimulus the brain
molecules will arrange themselves in structures representing a
four-dimensional existence. It only requires a certain amount of care to
build up mental models of higher space existences. In fact, it is
probably part of the difficulty of forming three-dimensional brain
models, that the brain molecules have to be limited in their own
freedom of motion to the requirements of the limited space in which our
practical daily life is carried on.
_Note._--For my own part I should say that all those confusions in
remembering which come from an image taking the place of the original
mental model--as, for instance, the difficulty in remembering which
way to turn a screw, and the numerous cases of images in thought
transference--may be due to a toppling over in the brain,
four-dimensionalwise, of the structures formed--which structures would
be absolutely safe from being turned into image structures if the
brain molecules moved only three-dimensionalwise.
It is remarkable how in science “explaining” means the reference of the
movements and tendencies to movement of the masses about us to the
movements and tendencies to movement of the minute portions of matter.
Thus, the behaviour of gaseous bodies--the pressure which they exert,
the laws of their cooling and intermixture are explained by tracing the
movements of the very minute particles of which they are composed.
CHAPTER VIII.
RELATION OF LOWER TO HIGHER SPACE. THEORY OF THE ÆTHER.
At this point of our inquiries the best plan is to turn to the practical
work, and try if the faculty of thinking in higher space can be awakened
in the mind.
The general outline of the method is the same as that which has been
described for getting rid of the limitation of up and down from a block
of cubes. We supposed that the block was fixed; and to get the sense of
what it would be when gravity acted in a different way with regard to
it, we made a model of it as it would be under the new circumstances. We
thought out the relations which would exist; and by practising this new
arrangement we gradually formed the direct apprehension.
And so with higher-space arrangements. We cannot put them up actually,
but we can say how they would look and be to the touch from various
sides. And we can put up the actual appearances of them, not altogether,
but as models succeeding one another; and by contemplation and active
arrangement of these different views we call upon our inward power to
manifest itself.
In preparing our general plan of work, it is necessary to make definite
assumptions with regard to our world, our universe, or we may call it
our space, in relation to the wider universe of four-dimensional space.
What our relation to it may be, is altogether undetermined. The real
relationship will require a great deal of study to apprehend, and when
apprehended will seem as natural to us as the position of the earth
among the other planets does to us now.
But we have not got to wait for this exploration in order to commence
our work of higher-space thought, for we know definitely that whatever
our real physical relationship to this wider universe may be, we are
practically in exactly the same relationship to it as the creature we
have supposed living on the surface of a smooth sheet is to the world of
threefold space.
And this relationship of a surface to a solid or of a solid, as we
conjecture, to a higher solid, is one which we often find in nature. A
surface is nothing more nor less than the relation between two things.
Two bodies touch each other. The surface is the relationship of one to
the other.
Again, we see the surface of water.
Thus our solid existence may be the contact of two four-dimensional
existences with each other; and just as sensation of touch is limited to
the surface of the body, so sensation on a larger scale may be limited
to this solid surface.
And it is a fact worthy of notice, that in the surface of a fluid
different laws obtain from those which hold throughout the mass. There
are a whole series of facts which are grouped together under the name of
surface tensions, which are of great importance in physics, and by which
the behaviour of the surfaces of liquids is governed.
And it may well be that the laws of our universe are the surface
tensions of a higher universe.
But these expressions, it is evident, afford us no practical basis for
investigation. We must assume something more definite, and because more
definite (in the absence of details drawn from experience), more
arbitrary.
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.
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.
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.
[1] The idea of space can “nicht aus den Verhältnissen der äusseren
Erscheinung durch Erfahrung erborgt sein, sondern diese äussere
Erfahrung ist nur durch gedachte Vorstellung allererst möglich.”
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.
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.
[2] “Science Romance,” No. I., by C. H. Hinton. Published by Swan
Sonnenschein & Co.
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.
[3] “Science Romances,” No. II.
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.
PART II.
CHAPTER I.
THREE-SPACE. GENESIS OF A CUBE. APPEARANCES OF A CUBE TO A PLANE-BEING.
The models consist of a set of eight and a set of four cubes. They are
marked with different colours, so as to show the properties of the
figure in Higher Space, to which they belong.
The simplest figure in one-dimensional space, that is, in a straight
line, is a straight line bounded at the two extremities. The figure in
this case consists of a length bounded by two points.
Looking at Cube 1, and placing it so that the figure 1 is uppermost, we
notice a straight line in contact with the table, which is coloured
Orange. It begins in a Gold point and ends in a Fawn point. The Orange
extends to some distance on two faces of the Cube; but for our present
purpose we suppose it to be simply a thin line.
This line we conceive to be generated in the following way. Let a point
move and trace out a line. Let the point be the Gold point, and let it,
moving, trace out the Orange line and terminate in the Fawn point. Thus
the figure consists of the point at which it begins, the point at which
it ends, and the portion between. We may suppose the point to start as a
Gold point, to change its colour to Orange during the motion, and when
it stops to become Fawn. The motion we suppose from left to right, and
its direction we call X.
If, now, this Orange line move away from us at right angles, it will
trace out a square. Let this be the Black square, which is seen
underneath Model 1. The points, which bound the line, will during this
motion trace out lines, and to these lines there will be terminal
points. Also, the Square will be terminated by a line on the opposite
side. Let the Gold point in moving away trace out a Blue line and end in
a Buff point; the Fawn point a Crimson line ending in a Terracotta
point. The Orange line, having traced a Black square, ends in a
Green-grey line. This direction, away from the observer, we call Y.
Now, let the whole Black square traced out by the Orange line move
upwards at right angles. It will trace out a new figure, a Cube. And the
edges of the square, while moving upwards, will trace out squares.
Bounding the cube, and opposite to the Black square, will be another
square. Let the Orange line moving upwards trace a Dark Blue square and
end in a Reddish line. The Gold point traces a Brown line; the Fawn
point traces a French-grey line, and these lines end in a Light-blue and
a Dull-purple point. Let the Blue line trace a Vermilion square and end
in a Deep-yellow line. Let the Buff point trace a Green line, and end in
a Red point. The Green-grey line traces a Light-yellow square and ends
in a Leaden line; the Terracotta point traces a Dark-slate line and ends
in a Deep-blue point. The Crimson line traces a Blue-green square and
ends in a Bright-blue line.
Finally, the Black square traces a Cube, the colour of which is
invisible, and ends in a white square. We suppose the colour of the cube
to be a Light-buff. The upward direction we call Z. Thus we say: The
Gold point moved Z, traces a Brown line, and ends in a Light-blue point.
We can now clearly realize and refer to each region of the cube by a
colour.
At the Gold point, lines from three directions meet, the X line Orange,
the Y line Blue, the Z line Brown.
Thus we began with a figure of one dimension, a line, we passed on to a
figure of two dimensions, a square, and ended with a figure of three
dimensions, a cube.
* * * * *
The square represents a figure in two dimensions; but if we want to
realize what it is to a being in two dimensions, we must not look down
on it. Such a view could not be taken by a plane-being.
Let us suppose a being moving on the surface of the table and unable to
rise from it. Let it not know that it is upon anything, but let it
believe that the two directions and compounds of those two directions
are all possible directions. Moreover, let it not ask the question: “On
what am I supported?” Let it see no reason for any such question, but
simply call the smooth surface, along which it moves, Space.
Such a being could not tell the colour of the square traced by the
Orange line. The square would be bounded by the lines which surround it,
and only by breaking through one of those lines could the plane-being
discover the colour of the square.
In trying to realize the experience of a plane-being it is best to
suppose that its two dimensions are upwards and sideways, _i.e._, Z and
X, because, if there be any matter in the plane-world, it will, like
matter in the solid world, exert attractions and repulsions. The matter,
like the beings, must be supposed very thin, that is, of so slight
thickness that it is quite unnoticed by the being. Now, if there be a
very large mass of such matter lying on the table, and a plane-being be
free to move about it, he will be attracted to it in every direction.
“Towards this huge mass” would be “Down,” and “Away from it” would be
“Up,” just as “Towards the earth” is to solid beings “Down,” and “Away
from it” is “Up,” at whatever part of the globe they may be. Hence, if
we want to realize a plane-being’s feelings, we must keep the sense of
up and down. Therefore we must use the Z direction, and it is more
convenient to take Z and X than Z and Y.
Any direction lying between these is said to be compounded of the two;
for, if we move slantwise for some distance, the point reached might
have been also reached by going a certain distance X, and then a certain
distance Z, or _vice versâ_.
Let us suppose the Orange line has moved Z, and traced the Dark-blue
square ending in the Reddish line. If we now place a piece of stiff
paper against the Dark-blue square, and suppose the plane-beings to move
to and fro on that surface of the paper, which touches the square, we
shall have means of representing their experience.
To obtain a more consistent view of their existence, let us suppose the
piece of paper extended, so that it cuts through our earth and comes out
at the antipodes, thus cutting the earth in two. Then suppose all the
earth removed away, both hemispheres vanishing, and only a very thin
layer of matter left upon the paper on that side which touches the
Dark-blue square. This represents what the world would be to a
plane-being.
It is of some importance to get the notion of the directions in a
plane-world, as great difficulty arises from our notions of up and down.
We miss the right analogy if we conceive of a plane-world without the
conception of up and down.
A good plan is, to use a slanting surface, a stiff card or book cover,
so placed that it slopes upwards to the eye. Then gravity acts as two
forces. It acts (1) as a force pressing all particles upon the slanting
surface into it, and (2) as a force of gravity along the plane, making
particles tend to slip down its incline. We may suppose that in a
plane-world there are two such forces, one keeping the beings thereon to
the plane, the other acting between bodies in it, and of such a nature
that by virtue of it any large mass of plane-matter produces on small
particles around it the same effects as the large mass of solid matter
called our earth produces on small objects like our bodies situated
around it. In both cases the larger draws the smaller to itself, and
creates the sensations of up and down.
If we hold the cube so that its Dark-blue side touches a sheet of paper
held upwards to the eye, and if we then look straight down along the
paper, confining our view to that which is in actual contact with the
paper, we see the same view of the cube as a plane-being would get. We
see a Light-blue point, a Reddish line, and a Dull-purple point. The
plane-being only sees a line, just as we only see a square of the cube.
The line where the paper rests on the table may be taken as
representative of the surface of the plane-being’s earth. It would be
merely a line to him, but it would have the same property in relation to
the plane-world, as a square has in relation to a solid world; in
neither case can the notion of what in the latter is termed solidity be
quite excluded. If the plane-being broke through the line bounding his
earth, he would find more matter beyond it.
Let us now leave out of consideration the question of “up and down” in
a plane-world. Let us no longer consider it in the vertical, or ZX,
position, but simply take the surface (XY) of the table as that which
supports a plane-world. Let us represent its inhabitants by thin pieces
of paper, which are free to move over the surface of the table, but
cannot rise from it. Also, let the thickness (_i.e._, height above the
surface) of these beings be so small that they cannot discern it. Lastly
let us premise there is no attraction in their world, so that they have
not any up and down.
Placing Cube 1 in front of us, let us now ask how a plane-being could
apprehend such a cube. The Black face he could easily study. He would
find it bounded by Gold point, Orange line, Fawn point, Crimson line,
and so on. And he would discover it was Black by cutting through any of
these lines and entering it. (This operation would be equivalent to the
mining of a solid being).
But of what came above the Black square he would be completely ignorant.
Let us now suppose a square hole to be made in the table, so that the
cube could pass through, and let the cube fit the opening so exactly
that no trace of the cutting of the table be visible to the plane-being.
If the cube began to pass through, it would seem to him simply to
change, for of its motion he could not be aware, as he would not know
the direction in which it moved. Let it pass down till the White square
be just on a level with the surface of the table. The plane-being would
then perceive a Light-blue point, a Reddish line, a Dull-purple point, a
Bright-blue line, and so on. These would surround a White square, which
belonged to the same body as that to which the Black square belonged.
But in this body there would be a dimension, which was not in the
square. Our upward direction would not be apprehended by him directly.
Motion from above downwards would only be apprehended as a change in the
figure before him. He would not say that he had before him different
sections of a cube, but only a changing square. If he wanted to look at
the upper square, he could only do so when the Black square had gone an
inch below his plane. To study the upper square simultaneously with the
lower, he would have to make a model of it, and then he could place it
beside the lower one.
Looking at the cube, we see that the Reddish line corresponds precisely
to the Orange line, and the Deep-yellow to the Blue line. But if the
plane-being had a model of the upper square, and placed it on the
right-hand side of the Black square, the Deep-yellow line would come
next to the Crimson line of the Black square. There would be a
discontinuity about it. All that he could do would be to observe which
part in the one square corresponded to which part in the other.
Obviously too there lies something between the Black square and the
White.
The plane-being would notice that when a line moves in a direction not
its own, it traces out a square. When the Orange line is moved away, it
traces out the Black square. The conception of a new direction thus
obtained, he would understand that the Orange line moving so would trace
out a square, and the Blue line moving so would do the same. To us these
squares are visible as wholes, the Dark-blue, and the Vermilion. To him
they would be matters of verbal definition rather than ascertained
facts. However, given that he had the experience of a cube being pushed
through his plane, he would know there was some figure, whereof his
square was part, which was bounded by his square on one side, and by a
White square on another side. We have supposed him to make models of
these boundaries, a Black square and a White square. The Black square,
which is his solid matter, is only one boundary of a figure in Higher
Space.
But we can suppose the cube to be presented to him otherwise than by
passing through his plane. It can be turned round the Orange line, in
which case the Blue line goes out, and, after a time, the Brown line
comes in. It must be noticed that the Brown line comes into a direction
opposite to that in which the Blue line ran. These two lines are at
right angles to each other, and, if one be moved upwards till it is at
right angles to the surface of the table, the other comes on to the
surface, but runs in a direction opposite to that in which the first
ran. Thus, by turning the cube about the Orange line and the Blue line,
different sides of it can be shown to a plane-being. By combining the
two processes of turning and pushing through the plane, all the sides
can be shown to the plane-being. For instance, if the cube be turned so
that the Dark-blue square be on the plane, and it be then passed
through, the Light-yellow square will come in.
Now, if the plane-being made a set of models of these different
appearances and studied them, he could form some rational idea of the
Higher Solid which produced them. He would become able to give some
consistent account of the properties of this new kind of existence; he
could say what came into his plane space, if the other space penetrated
the plane edge-wise or corner-wise, and could describe all that would
come in as it turned about in any way.
He would have six models. Let us consider two of them--the Black and the
White squares. We can observe them on the cube. Every colour on the one
is different from every colour on the other. If we now ask what lies
between the Orange line and the Reddish line, we know it is a square,
for the Orange line moving in any direction gives a square. And, if the
six models were before the plane-being, he could easily select that
which showed what he wanted. For that which lies between Orange line and
Reddish line must be bounded by Orange and Reddish lines. He would
search among the six models lying beside each other on his plane, till
he found the Dark-blue square. It is evident that only one other square
differs in all its colours from the Black square, viz., the White
square. For it is entirely separate. The others meet it in one of their
lines. This total difference exists in all the pairs of opposite
surfaces on the cube.
Now, suppose the plane-being asked himself what would appear if the cube
turned round the Blue line. The cube would begin to pass through his
space. The Crimson line would disappear beneath the plane and the
Blue-green square would cut it, so that opposite to the Blue line in the
plane there would be a Blue-green line. The French-grey line and the
Dark-slate line would be cut in points, and from the Gold point to the
French-grey point would be a Dark-blue line; and opposite to it would be
a Light-yellow line, from the Buff point to the Dark-slate point. Thus
the figure in the plane world would be an oblong instead of a square,
and the interior of it would be of the same Light-buff colour as the
interior of the cube. It is assumed that the plane closes up round the
passing cube, as the surface of a liquid does round any object immersed.
[Illustration: Fig. 1.]
[Illustration: Fig. 2.]
[Illustration: Fig. 3.]
[Illustration: Fig. 4.]
[Illustration: Fig. 5.]
But, in order to apprehend what would take place when this twisting
round the Blue line began, the plane-being would have to set to work by
parts. He has no conception of what a solid would do in twisting, but he
knows what a plane does. Let him, then, instead of thinking of the
whole Black square, think only of the Orange line. The Dark-blue square
stands on it. As far as this square is concerned, twisting round the
Blue line is the same as twisting round the Gold point. Let him imagine
himself in that plane at right angles to his plane-world, which contains
the Dark-blue square. Let him keep his attention fixed on the line where
the two planes meet, viz., that which is at first marked by the Orange
line. We will call this line the line of his plane, for all that he
knows of his own plane is this line. Now, let the Dark-blue square turn
round the Gold point. The Orange line at once dips below the line of his
plane, and the Dark-blue square passes through it. Therefore, in his
plane he will see a Dark-blue line in place of the Orange one. And in
place of the Fawn point, only further off from the Gold point, will be a
French-grey point. The Diagrams (1), (2) show how the cube appears as it
is before and after the turning. G is the Gold, F the Fawn point. In (2)
G is unmoved, and the plane is cut by the French-grey line, Gr.
Instead of imagining a direction he did not know, the plane-being could
think of the Dark-blue square as lying in his plane. But in this case
the Black square would be out off his plane, and only the Orange line
would remain in it. Diagram (3) shows the Dark-blue square lying in his
plane, and Diagram (4) shows it turning round the Gold point. Here,
instead of thinking about his plane and also that at right angles to it,
he has only to think how the square turning round the Gold point will
cut the line, which runs left to right from G, viz., the dotted line.
The French-grey line is cut by the dotted line in a point. To find out
what would come in at other parts, he need only treat a number of the
plane sections of the cube perpendicular to the Black square in the
same manner as he had treated the Dark-blue square. Every such section
would turn round a point, as the whole cube turned round the Blue line.
Thus he would treat the cube as a number of squares by taking parallel
sections from the Dark-blue to the Light-yellow square, and he would
turn each of these round a corner of the same colour as the Blue line.
Combining these series of appearances, he would discover what came into
his plane as the cube turned round the Blue line. Thus, the problem of
the turning of the cube could be settled by the consideration of the
turnings of a number of squares.
As the cube turned, a number of different appearances would be presented
to the plane-being. The Black square would change into a Light-buff
oblong, with Dark-blue, Blue-green, Light-yellow, and Blue sides, and
would gradually elongate itself until it became as long as the diagonal
of the square side of the cube; and then the bounding line opposite to
the Blue line would change from Blue-green to Bright-blue, the other
lines remaining the same colour. If the cube then turned still further,
the Bright-blue line would become White, and the oblong would diminish
in length. It would in time become a Vermilion square, with a
Deep-yellow line opposite to the Blue line. It would then pass wholly
below the plane, and only the Blue line would remain.
If the turning were continued till half a revolution had been
accomplished, the Black square would come in again. But now it would
come up into the plane from underneath. It would appear as a Black
square exactly similar to the first; but the Orange line, instead of
running left to right from Gold point, would run right to left. The
square would be the same, only differently disposed with regard to the
Blue line. It would be the looking-glass image of the first square.
There would be a difference in respect of the lie of the particles of
which it was composed. If the plane-being could examine its thickness,
he would find that particles which, in the first case, lay above others,
now lay below them. But, if he were really a plane-being, he would have
no idea of thickness in his squares, and he would find them both quite
identical. Only the one would be to the other as if it had been pulled
through itself. In this phenomenon of symmetry he would apprehend the
difference of the lie of the line, which went in the, to him, unknown
direction of up-and-down.