*** START OF THE PROJECT GUTENBERG EBOOK 64055 ***

  A THEORY OF THE
  MECHANISM OF SURVIVAL




  A THEORY OF THE
  MECHANISM OF SURVIVAL

  _THE FOURTH DIMENSION AND ITS
  APPLICATIONS_

  BY

  W. WHATELY SMITH

  LONDON:
  KEGAN PAUL, TRENCH, TRUBNER & CO., LTD.
  NEW YORK: E.P. DUTTON & CO.

  1920




  _TO
  MY MOTHER_




"_When we can no longer interpret a phenomenon by the known, we must
needs try to do so by the unknown...._"

"_It is well, in spite of everything, to seek an explanation of the
inexplicable; it is by attacking it on every side at all hazards that
we cherish the hope of overcoming it._"

  MAETERLINCK. "The Unknown Guest."




CONTENTS


  CHAPTER                                                  PAGE

  I. The meaning of Four-Dimensional Space                    1

  II. The scope of application and probable
  importance of the higher space concepts                    21

  III. Application to certain of the facts
  elicited by Psychic Research                               39

  IV. Some other possible applications of the
  hypothesis                                                 92

  V. Vitality and Will                                      113

  VI. Higher Space and Physical Science                     122

  VII. The Connecting Link                                  136

  VIII. The Religious Aspects of the hypothesis             168

  IX. Summary and Conclusion                                181

  Appendix                                                  187

  Index                                                     196




PREFACE


The highly speculative and extrapolatory character of this book will be
evident to all who are bold enough to read it.

I wish to make it perfectly clear that I have no intention of
dogmatising on so obscure a subject. The suggestions which follow are
purely tentative, and I am well aware that some of them are likely to
prove mutually incompatible.

But it is only by the bold formulation and ruthless rejection of
hypotheses that progress is made, and even if we are compelled
to abandon the Higher Space Hypothesis altogether--as is very
possible--the negative information so gained will be of the greater
value if the hypothesis has first been given the fullest possible trial.

  W.W.S.




A Theory of The Mechanism of Survival




CHAPTER I

THE MEANING OF FOUR-DIMENSIONAL SPACE.


The main line of thought developed in these pages has no claims to
originality. Professor Zöllner of Leipsic was an ardent exponent of the
theory in the "seventies" and some authors hold that even the ancient
writings of the East contain attempts to express Four-Dimensional
concepts.

Whether this is actually so is open to doubt but it must be remembered
that in the days when these writings were produced mathematical
knowledge was itself in its infancy and that there was, therefore,
no terminology available in which the Higher Space concepts could be
suitably expressed even supposing that the ancient philosophers had
them in mind.

It is only through accumulated knowledge, especially the work of Gauss,
Lobatschewsky, Bolyai, Riemann, and others that modern mathematicians
are able to deal easily with space of more than three dimensions.

It may be noted that Kant says:

"If it be possible that there are developments of other dimensions of
space, it is very probable that God has somewhere produced them. For
His works have all the grandeur and glory that can be comprised."

According to Mr. G.R.S. Mead similar ideas are to be found in certain
of the Gnostic cosmogonies.

 (Fragments of a Faith forgotten, p. 318.)

But a detailed historical review would be out of place here and I will
therefore proceed at once to a discussion of what is meant by the
term "fourth dimension" and will try to explain how it is that we can
determine some of the necessary properties of four-dimensional space,
even although we cannot picture it to ourselves.

At this point I would urge the reader to try to believe that the
subject is not one of great difficulty. As a matter of fact it is
really exceptionally straightforward if only one faces it and does not
allow oneself to be frightened.

I know that it is impossible to form any clear mental picture of
four-dimensional conditions, but that does not matter. The ideas
involved are admittedly unprecedented in our experience, but they
are not contrary to reason and I do not ask more than a formal and
intellectual assent to the propositions and analogies concerned.

Let me start, then, by defining what is meant by a Dimension. The
best definition I can think of is to say that, in the sense in which
the word is used here, a Dimension means "An independent direction in
space."

I must amplify this by saying that, "Two directions in space are to be
considered as independent when they are so related that no movement,
however great, along one of them will result in the slightest movement
along, or parallel to, the other. That is to say, at right angles, or
perpendicular to one another."

Thus in Fig. 1 AOA´ and BOB´ are independent directions. One might move
for ever along OA or OA´ and yet one would not have moved in the very
least in the direction of OB or of OB´.

[Illustration: _Fig. 1_]

Now on a flat surface, such as a sheet of paper, it is not possible to
draw more than _two_ such directions. Any other line that can be drawn,
XOX´ for instance, is in a compound direction, so to speak. That is to
say it is partly in the direction AOA´ and partly in the direction BOB´
and it is possible to reach any point in it, Y for example, by moving
along OA´ to _a_ and then moving in the direction of OB´ a distance
equal to O_b_, or _vice versa_ or by doing the two simultaneously.

For the benefit of those who are absolutely ignorant of the rudiments
of Geometrical knowledge, I would point out that Parallel lines are
said to point, in fact _do_ point, in the same direction.

[Illustration: _Fig. 2_]

Thus, in Fig. 2, the direction of the line ZZ´ is the same as that of
AOA´ and the direction of the line PP´ is the same as that of XOX´.

Thus we see that in a flat surface we find only _two_ dimensions
and consequently we can refer to a flat surface as "Space of two
dimensions" or "Two-dimensional space."

But if we refuse to be restricted to a flat surface we find that it is
possible to draw a third line through O which is quite "independent"
of the directions of the two lines we have previously drawn. We can do
this by drawing it vertically, that is to say, perpendicular to the
plane of the paper. Call this line COC´.

[Illustration: _Fig. 3_]

I have shown it _in perspective_ in Fig. 3. This line fulfils the
definition we gave of an independent direction in space for it is at
right angles both to AOA´ and to BOB´. But we have now exhausted our
resources. Try as we will we are unable to draw a fourth line which
shall be at right angles to AOA´, BOB´, and COC´ simultaneously.

On other words--In the space we know we find only three dimensions and
consequently we can refer to it as "Space of three dimensions" or
"Three-dimensional space."

Now the idea of a fourth dimension of space is simply this: That,
whereas in three-dimensional space, we can draw, through any point
in it, _three_, and only three, lines mutually at right angles: in
four-dimensional space, it would be possible to draw, through any point
in it, _four_, and only four, lines mutually at right angles.

Extending the idea to "Higher space" in general, we may say that,--In
space of "n" dimensions we can draw, through any point in it, "n," and
only "n," lines mutually at right angles.

Now I admit, that, at first sight, the idea that it might be possible,
under any circumstances, to draw more than three such lines through a
point, seems utterly staggering and inconceivable. And indeed the more
one thinks of it and the more thoroughly one grasps what it means, the
more absolutely impossible does it appear.

All the same, as I hope to show very soon, it _is_, as a matter of
fact, quite possible that there may be another independent direction
fulfilling the prescribed conditions, in spite of the fact that we are
at present ignorant of it.

This we can only realize by a consideration of the time-honoured but
indispensable analogy of a two-dimensional world, or "Flatland."

This analogy I propose to examine in some detail in the paragraphs
which follow.

But before doing so I wish to point out, and I do not think it will
be necessary to do more, that a "line" which has length, but neither
breadth nor thickness, can be correctly described as "One-dimensional
space" _i.e._:--space having only one dimension.

A mathematical "point," which has only position and neither length nor
breadth nor thickness, can similarly be called space of no dimensions
or "Zero-dimensional space." Also I wish to take the opportunity of
defining one or two words which I may have occasion to use and have the
merit of brevity.

 (1) Lines which are drawn through a point for the sake of determining
 direction are called in Geometrical parlance, "Axes."

 Thus in Fig. 1 AOA´ and BOB´ are axes. The former would be known as
 "the axis of A," the latter as "the axis of B." Similarly in Fig. 3
 COC´ is "the axis of C."

 (2) The point in which two or more axes meet, is called the "Origin"
 and is commonly denoted by the letter O.

 (3) When convenient, I shall use the terms, "Two space," "Three
 space," "Four space," etc., instead of writing "Two-dimensional
 space," "Three-dimensional space," "Four-dimensional space," etc. in
 full each time.


THE ANALOGY OF A TWO-DIMENSIONAL WORLD.

The consideration of the analogy of a two dimensional world is
necessary because, as Mr. C.H. Hinton says in his book, "The Fourth
Dimension," p. 6.

 "The change in our conceptions, which we make in passing from the
 shapes and motions in two dimensions to those in three, affords a
 pattern by which we can pass on still further to the conception of an
 existence in four-dimensional space."

Let us start then by imagining a very large, flat and perfectly smooth
surface; such for instance as the top of a highly polished table or the
surface of a sheet of still liquid.

We have seen that such a surface constitutes space of two dimensions,
because through any point in it we can only draw two lines at right
angles to one another. In order to draw a third such line we must get
out of the surface altogether and draw the line perpendicular to it.

Next we must try to imagine that this surface is populated by a race of
beings of an extraordinary thinness.

In order to grasp the analogy properly we must imagine them to be so
constituted that they are incapable of realising any direction in space
which does not lie in the aforementioned flat surface on which they
live.

We can imagine this by supposing that their thickness, _i.e._:--their
extension in the third dimension perpendicular to their surface,--is so
small as to be invisible to them and also that their "nerve endings"
all lie on their periphery. This last is equivalent to saying that they
have no "sense organs" facing the third dimension and that therefore
they cannot receive impressions, or respond to any stimuli that come to
them from that direction.

It follows, therefore, that unless they develope special sense organs
which face the third dimension they will be acquainted only with such
objects and events as lie, or take place, in their surface.

It is of course inconceivable that they should be truly "plane" beings
in the mathematical sense and possess no thickness at all. But if we
suppose that their thickness is of the same order as the diameter of
a chemical "Atom"--that they are "one atom thick" so to speak,--the
conditions laid down as to their limitation will be fulfilled.

Now we have supposed the flat surface in our analogy to be _perfectly_
smooth in the true sense of the word. That is to say of such a nature
as to offer no resistance whatever to the passage of objects over it.

This means that plane beings will not be sensible of any opposition to
their movement as far as the surface is concerned. Also, as we have
supposed that they have no nerve endings facing it, it follows that
they cannot feel any pressure from it. In short they will be totally
unaware of its existence.

But for the purpose of strict analogy this is insufficient, because a
being placed on such a surface would be as incapable of movement as
we should be if we were freely suspended in infinite space, remote
from all the material objects we know. There would be nothing, in
any direction known to him, from which he could "push off." We must
therefore further suppose that the force of gravity operates in his
world in a manner similar to that which we know,--every particle of
matter attracting every other particle.

This will mean two things; first, that every particle on the surface
will be held against that surface and that plane beings will,
therefore, never be able to move away from it; and, second, that matter
on the surface will tend to collect together in a manner precisely
analogous to what we observe in our space.

Finally, we may suppose that these hypothetical beings whom we are
considering live on the rim of a very large disc of plane matter, which
has collected and is held together by the action of gravity, just as we
live on the surface of a very large sphere of solid matter. They will
be kept up against the rim of the disc by the force of gravity, which
will attract them towards its centre, in the same way that we are kept
against the surface of the earth.

It is easy to realise that the existence of such a plane being will be
very limited indeed. He will be conscious of two directions only. One
will be "up and down" that is to say, towards or away from the centre
of his plane earth: the other will be "forwards and backwards" along
its rim. Again any object, that projects beyond the rim of the disc on
which he lives, will be for him an obstacle, which can only be passed
by climbing over or burrowing under it. He cannot go round it, because
that would mean coming out of the flat surface, which he is unable to
do. Thus in Fig. 4, if the curved line AB represents a portion of the
rim of the disc or "plane earth," and C a plane being, then he can only
pass from A to B by "climbing over" any intervening object such as D,
_i.e._:--by following the path indicated by the dotted line. Otherwise
he would have to get out of the plane of the paper, which is impossible
for him.

[Illustration: _Fig. 4_]

Now that I have described in outline the strict analogy of a race of
plane beings inhabiting a smooth surface, I shall take the liberty,
in the course of developing the idea more fully, of treating it in
a slightly less rigid fashion. That is to say I shall assume that
the reader has grasped the main idea and I shall not trouble about
the "Plane earth" etc., unless it is desirable to do so for the sake
of bringing out some special point; and I shall substitute for the
foregoing somewhat elaborate representation the simpler one of a thin
object free to slide on a smooth surface lying in front of us.

But before doing so I would point out that already we begin to see our
way a little. We can understand for instance that the fact of a Fourth
dimension of space being unknown and inconceivable to us, is no proof
that it does not exist. We have seen that a Third dimension would be
equally unknown and inconceivable to a being limited in the manner
described above; although we know that a third dimension does exist.

We have only to suppose that analogous limitations obtain in our own
case to see that a Fourth dimension might well exist of which we would
still be unaware.

We must, for instance, suppose that we have no sense organs facing that
way and that we are prevented from moving in that direction by some
circumstance analogous to the smooth sheet on which we supposed the
plane being to live. The plane being would think that he could see all
round his plane objects although we know that he could not really do
so, and similarly our conviction that we can see all round our solid
objects may be an illusion.

Thus we are already in a position to appreciate the fact that our
inability to perceive or imagine Four-dimensional space or objects
in it, is no argument against its existence. There is, therefore, no
'a priori' reason for supposing that four dimensional space is not
a reality. It is a point which must be settled by an appeal to the
evidence.

If, in the course of our investigation, we find that there are in our
space phenomena, which closely resemble those which would in "two
space" indicate the existence of a third dimension, then we shall be
entitled to say that these phenomena indicate the probable existence of
a fourth dimension.

We can now proceed with our consideration of a two dimensional world,
remembering that,--

 Shapes and events in four space bear to shapes and events in three
 space, the same relation that those in three space bear to those in
 two space.

[Illustration: _Fig. 5^{[a=]}_]

[Illustration: _Fig. 5^{[b=]}_]

The very small three-dimensional thickness which we have supposed to
exist in all the objects of our plane world is imperceptible to the
plane beings which inhabit it and the objects which they perceive
they will accordingly think of as geometrical figures and of their
boundaries as geometrical lines, having length but no breadth. A circle
will appear to a plane being as a completely closed space. He will, as
he thinks, be able to go all round it without being able to find any
opening in its bounding line. It will in fact be to him what a sphere
is to us. A two space room will be a thing like the figure shown in
Fig. 5_a_. He will be able to get into or out of it by the gap in the
wall which is shown and which corresponds to the door. But he will not
be able to conceive of any other mode of entry or exit, although we can
see that from the direction of the third dimension it is not closed at
all. Similarly, if Fig. 5_b_ represents a closed two-dimensional box,
we see that this is absolutely open to us, who are three dimensional
beings, though appearing to be closed on all sides to a plane being. If
we took advantage of this fact we could play all sorts of tricks on him
for we could put things into the box or take them out of it, by way of
the third dimension, while to the plane being the box would appear to
be tightly closed the whole time. It will be noticed that as the path
of an object in transference would lie wholly outside the plane being's
space he would not be able to form any conception of the nature of the
process involved. If he tried to understand it at all he would probably
imagine that the object has been disintegrated into particles inside
the box, passed in this condition through the minute interstices
which he might suppose to exist in its walls, and reintegrated on the
other side. Whereas the true explanation is far simpler. The very
great importance of this will become apparent when we come to consider
the question of the positive evidences for the existence of a fourth
dimension.

It is because of this importance that I have dwelt on a point which to
many readers will have been obvious as soon as stated.

Similarly we could make things appear "from nowhere" and disappear
equally mysteriously simply by putting them down on to his flat surface
and picking them up again.

I may as well repeat here that I do not for a moment expect that the
reader will have been able to visualise four-dimensional space. But
I do hope that he will have seen the force of the analogy and will
be prepared to admit that so far as we have gone at present four
dimensional space is by no means inconceivable though it may not be
distinctly imaginable.

The foregoing is really all that is necessary on the mathematical or
theoretical side for the understanding of the basic ideas with which
I am dealing but for the benefit of those readers who like that sort
of thing I have added a few simple propositions and extensions of the
analogy in the form of an appendix.

The only other question that need really concern us here is that of the
phenomena of _change_ in a two-dimensional world.

We have already seen that a cube laid on a flat surface will present
to a plane being, in that surface, the appearance of a square. It is
also clear that if it is pushed through the surface it will continue to
present the same appearance until it has passed right through, when it
will suddenly vanish away.

He would be unconscious of any movement on the part of the cube unless
there was some difference between the first and last sections which he
perceived.

If, for instance, the bottom face was red and the top face blue he
would be conscious of a colour change on the part of the square which
he perceived. It would start by being red and would pass through
various shades of purple till, just before its final disappearance, it
would be pure blue. But now suppose that it was pressed through his
surface not "normally" but corner wise as indicated in Fig. 6--that
is to say with one of its corners leading and one of its diagonals
vertical. The plane being would then see quite a different set of
figures. First would be a point; this would grow into a triangle which
would increase in size until it reached a certain maximum when it would
begin to develope three new sides at its corners which would grow, at
the expense of the original sides, until a regular hexagon was produced
when the reverse process would set in and the hexagon gradually change
back into a triangle which in turn would dwindle away and disappear.
It is easy to work out what would happen in the case of other solids,
_e.g._, Sphere, Cone, Tetrahedron, etc. All such changes would appear
very mysterious to the plane being if he had formed no conception of
three-dimensional space or the shapes of bodies therein.

[Illustration: _Fig. 6._]

Let us now extend this idea rather further.

Suppose we were to take a series of cinematograph pictures of the
two-dimensional world, from the direction of the third dimension. We
should obtain a succession of pictures each representing the precise
state of affairs at some given moment in the two space world. Every
thing in it would be represented in each. There would be no question
of one thing being hidden by another because we are regarding them
all from the direction of the third dimension in which they have an
inappreciable extension. If we imagine the two space world to be
very small or our camera to be very large there is no difficulty in
supposing that each of our pictures includes the whole of the two space
universe,--plane beings, earth, sun, planets, etc., all complete.

Imagine further that these pictures are reproduced, as cinematograph
films actually are, on a transparent substance and then let us
superimpose these successive pictures on one another in order so as to
form a block. By this means we can represent the disposition of all the
objects in a two space system at a number of successive instants in
one single three space figure. For instance, the motion of a two space
planet round its sun would become a part of a helix or spiral. If we
now cut away from our block all the blank material which intervenes
between the representations of the various two space objects we shall
have a complete synthesis in three space of a succession of two space
arrangements. If we were now to pass this three space object through a
penetrable two space surface, _e.g._, a soap film, we should exactly
reproduce for the two space beings in it the changes which we had
originally recorded.

By analogy we can see that it would be possible to account for all the
changes in our three-dimensional space by supposing them to be due to
the passage through it of suitably shaped and arranged four-dimensional
solids, of which we only perceive at any moment a section whose
extension in the fourth dimension is imperceptibly small.

It will appear later that I do not think that this is literally the
case. The point I want to make here is that the phenomena of change or
successive arrangement in space of a given dimensionality are capable
of explanation in terms of forms in the next space higher, which latter
do not change within themselves.

The precise import of this will appear when we come to consider the
bearing of the higher space theory on the problem of the nature of
Time.




CHAPTER II

THE SCOPE OF APPLICATION AND PROBABLE IMPORTANCE OF THE HIGHER-SPACE
CONCEPTS.


In the preceding chapter I have tried to explain what is meant by the
term "four-dimensional space" and to demonstrate some of its more
important properties from the point of view of ourselves who live in
space of three dimensions.

I am now in a position to state the basic hypothesis which I propose to
discuss in the pages which follow.

Briefly stated it is this:--

"Higher space is a Physical reality and not a mere mathematical
idea. In waking life the individual consciousness functions in a
three-dimensional 'vehicle,' namely the physical body. But it may also
possess at least one other vehicle--a four-dimensional one--and in
this it may function after death and, possibly, during sleep, trance,
anæsthesia and other forms of insensibility."

This hypothesis is not my own and I am not prepared to defend it
as being necessarily correct. But, as I hope to show, there are a
number of considerations which tend to support it and I do think it
is sufficiently plausible to make it worthy of serious consideration
before it is finally rejected by those who are students of these
matters.

In this chapter I propose to deal with the different ways in which it
is likely to prove of importance.

First of all, then, it has strong claims to be adopted as a working
hypothesis by those who are students of Psychical Research, especially
by those who are convinced of the validity of the Spiritistic
explanation of communications purporting to emanate from the deceased.

Secondly, I believe that if accepted as valid it would do much to
provide a common meeting ground for opposite schools of religious
and scientific thought. Between these there was a most marked and
unfortunate cleavage during last century and though there has been a
very considerable rapprochement since the days when controversy was
at its height there is still much to be done before we can hope for a
complete community of thought and expression.

It is hardly necessary to say that these two spheres of application are
very closely allied, but it is none the less convenient to separate
them for purposes of discussion.


THE NEED OF A WORKING HYPOTHESIS IN PSYCHIC SCIENCE.

The studies of Psychical Researchers must necessarily cover a very
wide area which is bounded on the one hand by Physical science proper,
on another by Philosophy, on a third by Psychology and on a fourth by
Religion. With each of these subjects it has close relations and yet
possesses features which serve to distinguish it from any of them.

Sir William Barrett writes as follows of the scope of Psychical
Research:

 "The subjects to be considered cover a wide range, from unconscious
 muscular action to the mysterious operation of our sub-conscious self;
 from telepathy to apparitions at the moment of death; from hypnotism
 and the therapeutic effects of suggestion to crystal-gazing and the
 emergence of hidden human faculties; from clairvoyance, or the alleged
 perception of objects without the use of the ordinary channels of
 sense, to dowsing, or the finding of under-ground water and metallic
 lodes with the so-called divining-rod; from the reported hauntings
 of certain places to the mischievous pranks of poltergeists (or
 boisterous but harmless ghosts whose asserted freaks may have given
 rise both to fetishism and fairies); from the inexplicable sounds and
 movement of objects without assignable cause to the thaumaturgy of the
 spiritualistic séance; from the scribbling of planchette and automatic
 writing generally to the alleged operation of unseen and intelligent
 agents and the possibility of experimental evidence of human survival
 after death."

  (_Psychical Research, p. 10_).

In view of the heterogeneous nature of this list I do not think
it practicable to frame any hard and fast definition of Psychical
Research. Moreover certain of the phenomena which it once studied--such
as Hypnotism--have been largely taken over by "orthodox" science,
and others, such as Telepathy and Clairvoyance, although of great
intrinsic interest and some relevance, may ultimately be regarded as
comparatively remote from the main body of psychic phenomena.

Roughly speaking, the characteristic feature of the latter is a
suspicion, or _prima facie_ appearance, or allegation that they emanate
from, or are in some way connected with the activities of extra-mundane
intelligences--notably the "spirits of" the deceased.

It is this feature which has caused their rejection by the sciences
with which they would naturally appear to be associated and although
our studies may in many cases show that the appearance is wholly
spurious it must be remembered that, until every phenomenon is so
disposed of and relegated to its appropriate "orthodox" science, the
ultimate problem of Psychical Research is largely a matter of the
provision of answers to such questions as:--

"Is there any scientifically valid reason for supposing that Individual
Human Personality survives bodily death?"

"If so, under what conditions does it persist?"

"What is the relation between these new conditions and those with which
we are acquainted?"

Any investigation into Human Personality of a scope less than this
can be included under the heads of Physiology or Psychology which are
prepared to investigate any conceivable intricacy in the mental or
bodily states of the living.

It is only when the investigator refuses to be limited by bodily death
that Psychic science differentiates itself as a separate study.

I do not propose to consider here whether psychical research has yet
given any satisfactory answer to the above mentioned questions or even
whether there is any considerable chance of its ever being able to do
so.

I merely wish to point out the nature of the problems with which it is
concerned and which alone distinguish it as a separate science.

It follows that any hypothesis advanced with a view to co-ordinating
the observed facts _may_ find itself called upon to give an
intelligible explanation of discarnate personalities, that is to say of
human personalities not functioning through the flesh and blood bodies
in which we are accustomed to meet them.

So far as our present knowledge goes and on the balance of all the
available evidence I am inclined to think that this necessity is at
least imminent.

The adoption of some form of working hypothesis is moreover imperative
in the light of scientific history.

All who are interested in psychical research will agree that it is in
the highest degree desirable that it should be recognised as a Science
of a dignity commensurate with its intrinsic importance and on a level
with the sciences more generally accepted as such.

That it has not, hitherto, attained this position in the eyes of the
world in general is largely due to the fact that it has not yet fully
reached that stage of development which chiefly distinguishes a
science properly so called from mere speculatory observation.

This is no reflection on the many able and genuinely scientific men
who have worked on the subject ever since it first became prominent
in modern times some seventy years ago but is, on the contrary, a
necessary and inevitable stage in the growth of any science whatsoever.

The processes of acquiring scientific knowledge are as invariable as
those of logical thought. Just as all accurate reasoning may be reduced
to a series of syllogisms, so the process of acquiring exact knowledge
may be reduced to a series of analogous sequences.

  These are:--(1) Observation.
              (2) Induction.
              (3) Deduction.
              (4) Experiment.--A special form
                    of observation.

I do not say that this sequence of operations is always consciously
performed any more than when "thinking a thing out" we always
consciously reduce our reasoning to its simplest syllogistic
constituents.

But every time we acquire a new item of knowledge it would be possible
to reduce the process by which we acquired it to a series of the
sequences mentioned above.

It is worth while considering these steps in slightly greater detail.

OBSERVATION in the last analysis means no more than the recording and
classifying of sensations, which are the only form in which we get any
information as to the outer world.

INDUCTION means the process of concluding from a study of the observed
and collected facts that there is some specific co-ordinating principle
at work by virtue of which the facts exist. This is the process known
as forming a working hypothesis.

DEDUCTION. In this stage we consider more closely the working
hypothesis which we have formulated, and we conclude that if it be true
certain other consequences must inevitably follow.

EXPERIMENT. This simply means that we turn again to the outside world
and examine it to see whether these deduced results do actually obtain
in practice.

If they do we argue that our hypothesis is, probably, a correct one and
we retain it until it is shown that if it be correct some result must
inevitably occur which in fact does not.

There is a difference between a _valid_ hypothesis and a _true_
one--or, as the latter is commonly termed, a Law.

Any hypothesis is valid which explains the observed facts or at least
explains some of them and contradicts none. But the epithet "true" can
only properly be applied when it has been shown that all necessary
deductions are invariably borne out in practice. As a matter of fact we
can never say this with absolute certainty for it is always conceivable
that some exception may some day be found which would necessitate the
remoulding of the hypothesis.

The most we can say is that certain hypotheses have stood the test in
such a very large number of cases without a single failure that there
is a very high degree of probability that they are really true.

The hypothesis that the Chemical "Atom" was the ultimate and
indivisible unit of matter was a perfectly valid one in the light of
the facts that had been observed at the time of its formation and of
its apparent proof by Lavoisier and others.

It is only the facts which have been elicited by the study of
Ionisation, of Radio-active substances and similar phenomena that have
proved it to be untenable and necessitated the substitution of the
electronic theory.

Again the Corpuscular theory of light affords a very pertinent
illustration of the point I wish to make.

A number of facts regarding the phenomena of light were observed and
classified and it was found that these could be explained by the
hypothesis that light consisted of a stream of very minute particles
moving at very high speed which impinged upon the eye and thus gave
rise to the sensations observed. Up to a point this explanation was
perfectly satisfactory and for a long time it held the field, partly
because of the great prestige of Newton to whom much of its development
was due and partly because it continued to explain subsequently
observed facts without much straining.

But among other things it was demonstrated that in order to account for
the observed phenomena of refraction it was necessary to suppose that
the "Corpuscles" travelled faster in water than in air.

At first there was no means of determining directly whether this was so
or not. But later the researches of Foucault made it possible to settle
the point by direct measurement. When the velocity of light in air
and water respectively was measured directly by Foucault's method it
was found that the velocity in water was _less_ than that in air. The
Corpuscular theory was therefore untenable.

It is only by this process of forming, testing and, if necessary,
rejecting hypotheses that we gradually attain to exact knowledge. As
Prof. Richet says:

 "La science n'a jamais été qu'une serie d'erreurs, approximations
 constamment evoluant constamment boulversé, et cela d'autant plus vite
 qu'elle était plus avancée."

  (Annales des sciences psychiques, 1905, p. 15.)

From this brief resumé of the steps involved in scientific progress
it is clear that the formation of a working hypothesis, by inductive
reasoning from the observed facts, is a normal, necessary, and
invariable step in the progress of any science whatsoever.

For this reason I do not think it likely that Psychical research
will attain any widespread recognition as a science until it is in
possession of a valid working hypothesis capable of explaining at least
the more important of the observed facts. I believe that the higher
space hypothesis fulfills this condition and if so it is clearly worth
while adopting, purely provisionally and tentatively of course, by
those who concern themselves with the subject.

I have said that I think that the conception of higher space has a
bearing on the relations between Religious and Scientific thought.

I shall reserve for a later chapter the treatment of the question
from the purely religious stand-point, and shall only examine here
the reasons which seem to me to have led so many sincere and able
scientific men to a position at variance with the religious and
spiritual point of view.

This is, of course, closely bound up with the whole topic of the
various attempts which have been made to satisfy the perennial demand
for light on the mysteries of life and death and on the spiritual and
non-material aspects of the universe.

It is out of the question for me to attempt to classify here the
countless religions, sects, and philosophies which have arisen from
time to time. But they do seem to fall into three main groups and
although it is impossible to label these in any really satisfactory
manner I think one may say that the Materialistic Scientists are the
representatives of one school, the Orthodox Theologians of another, and
the Occultists of a third.

By the Materialistic Scientists I mean those who see in matter or ether
the ultimate and only permanent reality and who attempt to explain
every experienced phenomenon in terms of matter and ether and of these
only.

According to their view, Thought, Emotion, Consciousness, are no more
than electro-chemical changes in the protoplasmic constituents of the
brain cells. "The brain secretes consciousness as the liver secretes
bile."

The idea of "spirit" is inconceivable to them; for the whole essence of
Spirit is that it is not matter nor, so far as we can imagine, ether.

Now although this attitude is utterly repugnant to me, I can yet easily
understand and sympathise with the state of mind which occasions it.
I, too, feel that if there is one thing above all others to which
one's intellect must cling at all costs it is the general proposition
of the coherence and continuity of the universe--in other words the
great Law of Causation. If ever we let go of that we find ourselves in
chaos--which is insanity.

Within the "ring-fence," so to speak, of matter and energy the
law holds good, but anything outside appears to the scientist as
"discontinuous" and therefore, quite rightly, revolting. As against
this point of view my contention is that it is quite possible to form
an intelligible concept of Reality, different from and yet perfectly
continuous with, the physical reality of the scientist.

This first purely materialistic school admits of fairly easy
delimitation whereas the other two schools mingle together and
diverge within themselves in so complex a manner that it is much
more difficult to distinguish them from each other than to separate
either of them from the first. But I think the difference is something
of this kind. The school of which the Occultists are typical seem
to me to tend to replace logically coherent explanation by mere
descriptive nomenclature. On the other hand the Orthodox Theologians,
while dogmatically asserting the existence of spirit and constantly
emphasising the supreme importance of the spiritual life, are apt to
ignore the intellectual demand for intelligible explanation altogether.

It is merely foolish to ignore or to ridicule on 'a priori' grounds
the statements of those who claim to have investigated the problems
with which we are concerned by the cultivation of abnormal or commonly
latent faculties.

If such faculties exist, as is very possible, it is clearly no more
than common sense that they should be exercised to the full in the
solution of problems which present especial difficulties to the more
normal methods of investigation. The results might be of the very
highest possible value. Indeed, it may well be that the cultivation
of such faculties is by far the best way of attacking the whole
question. I am by no means prepared dogmatically to deny it. None the
less I think we are entitled to expect that those who claim to have
attained knowledge by these means should take some pains to make their
results continuous with existing knowledge and to eliminate needless
obscurities.

At present the application of the word "Science" to the utterances of
the Occult schools--as commonly presented--is a complete misnomer.

In Theosophical literature, for instance, we are confronted with a
scheme of things built up of such terms as "Astral Plane," "Etheric
Double," "Causal Body," "Karma" and so forth.

With all due deference to my Theosophical friends I submit that this is
not scientific explanation and cannot be so unless its exponents are
prepared to tell us what is the relation between the astral plane and
the physical world, between the etheric double and the body as known to
physiologists.

Thus it is intellectually unsatisfying and little calculated to arouse
the sympathetic interest of the strictly logical thinker.

I do not mean to say that none of the words of the type quoted have
any real significance. On the contrary I think it very probable that
many of them have and that they do represent real parts of the actual
scheme of things. The trouble is that they are only names; and to name
a thing is not the same as to explain it. In common fairness I ought,
however, to admit that in several passages Mr. Leadbeater--one of the
best known Theosophical writers--makes a distinct effort to escape
from this tendency and it has further been opined by a very eminent
Occultist that the bulk of contemporary literature on the subject will
be out of date in a few years.

I am inclined to suspect that this failing was the cause he had in mind.

I repeat that my primary quarrel is not with the accuracy or otherwise
of the statements made. Every word of them may be perfectly correct,
but so long as they are expressed in terms wholly unrelated to
pre-existing concepts I must, _qua_ scientist, remain unconvinced.

The third school which includes the Orthodox Theologians sometimes
resembles the Occultists in the use of unintelligible terms but their
chief weakness is their failure to recognise and to cater for the
intellectual demand for coherent explanation.

They never weary of insisting, quite rightly, on the paramount
importance of Spiritual things, but no effort is made to show the
continuity which must, in a sane Cosmos, exist between Matter and
Spirit, or to state the "common factor," so to speak, which unites
them as parts of a coherent whole.

For myself I refuse to believe that no such common factor is
discoverable. As Sir Oliver Lodge says, "I have learned to believe in
intelligibility."

This omission on the part of theologians did not so much matter in the
days before Physical Science had attained to its present degree of
development. Men knew so little about the material Universe that they
experienced little difficulty in finding a place in it for Spirit and
the Spiritual life. "Heaven" was conveniently represented as being
somewhere "above" and "Hell" as somewhere "below." But now things have
altered and we know quite a fair amount about the material world.
Consequently the scientist demands--not unreasonably, I think--an
explanation of "Spirit" which shall not conflict with the fundamental
laws of continuity and causation.

So far the theologians have failed to meet this demand and to provide
the necessary habitat for consciousness which shall be independent
of, and yet causally continuous with, the material world which the
scientist knows.

It is this illogical discontinuity which has alienated the sympathies
of so many men of scientific mind and forced them to attempt to reduce
all mental and spiritual phenomena to terms of matter.

The foregoing should be sufficient to show how important it is that
Psychical Research--the connecting link between the study of the
material and that of the purely spiritual--should adopt as soon as
possible some form of working hypothesis which is not repugnant either
to religious or scientific thought. It is only by doing this that we
can hope to retain the sympathies of both classes of thinkers and this
is surely worth an effort quite apart from all other considerations.
Here again I believe that the higher space hypothesis meets the
requirements of the case and this is my second chief reason for urging
its adoption.




CHAPTER III

APPLICATION TO CERTAIN OF THE FACTS ELICITED BY PSYCHIC RESEARCH


In this chapter I propose to give some instances of the way in which
the higher space hypothesis throws light on certain Psychic Phenomena
which, without its aid, appear extremely obscure and difficult of
explanation, but I shall make no attempt to cover the whole range of
phenomena known to students.

Some are not yet, in my opinion, sufficiently well authenticated
to necessitate consideration, and those which are, some--such as
Telekinesis, Prevision, and certain aspects of unconsciousness--are
more conveniently treated in later chapters; others are so mysterious
as to render any attempt at explanation premature until we have a wider
and firmer foundation of fact on which to build; others again, such
as thought transference or Telepathy, will probably prove explicable
without introducing the Higher Space hypothesis in any direct
connection.

There are some, however, which may well be considered here.

The first, and by far the most important problem which confronts us
in attempting to form an idea of post-mortem conditions, or of the
existence of personality apart from the physical body, lies in the fact
that we cannot conceive of personality as absolutely disembodied--as
pure essence. Yet we know that if personality does in fact survive
physical death, it must do so in some form, completely non-material
in the ordinary sense of the word, which is invisible, impalpable, in
short entirely imperceptible, to our normal senses.

Probably it is the difficulty of conceiving such a mode of existence
which has chiefly prevented physical scientists, as a whole, from
accepting the obvious interpretation of the evidence for Survival
offered by various Psychic phenomena.

Few people, I think, who have studied the literature of the subject,
would be prepared to deny that Survival is, at least, strongly
indicated by the evidence in question.

But this difficulty of conceiving a state of existence, at once
real and non-physical, has induced scientists to prefer to seek an
explanation of the observed facts in terms of Thought transference,
Secondary personality and so forth.[1]

But as soon as we introduce the concept of the Fourth Dimension this
difficulty disappears.

We have but to suppose that after physical death the Individual
consciousness is embodied in a vehicle organised, not from physical
matter, but from Four-dimensional matter, _i.e._, that which, in four
space, corresponds to what we call "Matter" in three space.

Such a vehicle fulfills the required conditions in every way. It is
scientifically real--that is to say, it has its habitat in a region as
subject to law and as susceptible to mathematical analysis as the three
dimensional world in which we at present live.

And yet it must be supposed to be, of its very nature, inapprehensible
by our normal physical senses.

We are thus enabled to understand how those who have left this physical
world may, although discarnate, be none the less as truly _alive_ as
ever, close to us and yet invisible, constantly in touch with us and
yet beyond our normal ken.

This is the first and supremely important application of the
hypothesis and it is impossible to over-emphasise it.

       *       *       *       *       *

Of the more specific phenomena suitable for discussion here, I will
first deal with Clairvoyance.

This is probably far from being a simple phenomenon of unvarying
nature. There would appear to be at least four varieties and it is
possible that as our knowledge of the subject increases we shall come
to recognise still more.

The four at present distinguishable may be denoted as follows:--

 (1) So-called "Etheric Clairvoyance." This is apparently no more than
 a heightening of the ordinary powers of vision.

 (2) Perception of objects and contemporary events more or less removed
 in space from the percipient and invisible by ordinary means.

 (3) Perception of non-material objects or events; as when a
 clairvoyant describes the appearance of a deceased person alleged to
 be present in "spirit form."

 (4) Clairvoyance in time. That is to say the perception of future
 events--Prevision--or of past events--Postvision.

Instances of each of these four forms are abundant and amply verified
except, perhaps, in the case of class 3 where verification is scarcely
possible.

It is easy to understand how clairvoyance of the first type arises. We
know that light consists of very rapid vibrations in the ether which
impinge upon the retina and cause the sensation of sight. We also know
that if a beam of white light is passed through a triangular glass
prism it is bent aside and split up into the seven colours of the
rainbow, viz., Red, Orange, Yellow, Green, Blue, Indigo, and Violet.
The resulting band of colour is called a Spectrum. If the Spectrum so
obtained is thrown upon a screen and a number of people are asked to
mark thereon the limits of what they can see it will be found that
these limits vary considerably.

We know, too, that there is a wide range of light-vibrations beyond
the furthest of these visible limits, for although our eyes do not
respond to them the photographic plate does. We also know that some
of these vibrations will penetrate substances which are opaque to
ordinary light although the opposite is the case for some substances.
This is particularly the case with "ultra-violet" light which consists
of vibrations more rapid even than those of violet light which are
themselves the most rapid in all the visible spectrum. It seems
reasonable therefore to suppose that certain people with abnormal
retinæ or in an abnormal condition might be especially sensitive
to these ultra-violet rays and that they might not only see things
invisible to us but even see them _through_ obstacles which are opaque
to the sort of light to which normal eyes respond.

This explanation may serve for certain simple cases of clairvoyant
vision but it soon breaks down because the visual image of any object
seen in this way must be liable to confusion by the superimposed images
of intervening objects.

Suppose for instance that a clairvoyant wishes to see, by this method,
what is written on page 100 of a closed book. We will suppose that
the covers and paper of the book are transparent to some kind of
ultra-violet light to which the eye of the clairvoyant responds,
whereas the ink is opaque to the same light.

On looking at the book the writing on page 100 would be visible
all right, but so would that on the preceding 99 pages; it would,
therefore, be practically impossible to read the 100th page.

It will be seen, therefore, that clairvoyance of this type must be
of very limited scope and cannot be held to account for cases of the
second type where the clairvoyant perceives events happening at a
considerable distance, amounting in some instances to a matter of
hundreds of miles.

I freely admit that at present I am not prepared to give an explanation
of all cases where the distances involved are very large.

But to cases where the incidents or objects perceived are reasonably
near the percipient, the higher space hypothesis offers a simple and
elegant solution.

Consider the two dimensional analogue.

[Illustration: _Fig. 7_]

Suppose that "A" Fig. 7, represents a two-dimensional observer and that
X, Y, and Z are two-dimensional closed spaces, rooms, houses, or what
not. The interiors of these closed spaces will be invisible to "A."
All he will be able to see will be a straight line as at "B," for the
boundaries of X, Y, and Z will be opaque and impassable to him.

But now suppose that he were to be lifted up vertically, out of the
plane of the paper altogether. He would from this new position be
able to see the interiors of X, Y, and Z, together with any two space
incidents occurring therein. They would present approximately the
appearance shown in Fig. 7 and the degree of foreshortening would
diminish with the height to which he ascended above the plane of the
paper.

In a precisely analogous manner we must suppose that three-dimensional
obstructions do not exist for, and that the interiors of closed
three-dimensional spaces are entirely open to, anyone who could regard
them from a point situated in four space, _i.e._, removed from three
space to a suitable distance in the direction of the fourth dimension.
The greater this distance the less will be the foreshortening and the
greater will be the range of vision.

There would be no question of intervening objects obscuring the
view, simply because, in four space, three space objects do not
intervene--the view of X in Fig. 7 is in no way obscured by the
presence of Y or Z.

Compare with this the statements of many clairvoyants to the effect
that when in the clairvoyant state they can, and do, see the front,
sides, back, and every internal point of three space objects
simultaneously.

The parallel is almost irresistible in its significance. Compare also
the following case given by Professor de Morgan, and which is typical
of the very numerous cases of this nature on record.

In this case the percipient was a little girl who was undergoing
mesmeric treatment for fits by Mrs. de Morgan. While in the mesmeric
state she was desired to follow Professor de Morgan mentally to the
house at which he was dining and which was totally unknown to the
child. The girl got there at once and gave an accurate description of
the room in which the Professor was, the furniture which it contained,
the people to whom he was talking and various small incidents which
took place. On his return Professor de Morgan confirmed every detail of
the description.

This is, of course, a very condensed resumé of the occurrence.
Interested readers should consult contemporary Psychic literature
which abounds with such cases. The point is that no amount of retinal
hypersensibility will so much as begin to explain this sort of case,
whereas it is not so utterly incomprehensible when we introduce the
idea that the percipient may have been seeing four-dimensionally.

It is hardly necessary to observe that the sense organs involved cannot
be the physical eyes. They must be supposed to belong to the four
dimensional vehicle.

In attempting to explain this second type of clairvoyance along these
lines, there seem to be two main difficulties involved and these are
admittedly very great.

First, how is it that the four space vehicle possesses organs capable
of perceiving three space objects and incidents? One would expect it to
respond to four space impressions only.

Secondly, as soon as the distances involved become more than quite
small it is very difficult to conceive how the percipient can
simultaneously describe the events by the use of physical speech
mechanism and also perceive them from a point of view which must be
supposed to be very considerably removed in the direction of the fourth
dimension.

A correspondent of my own who appears to possess this power of
clairvoyance at a distance in a remarkable degree and to be able to
exercise it at will, tells me that when she is seeing a distant scene,
she is yet so closely in touch with her physical body that she is
conscious of moving her hand, for example.

It is difficult to account for this on the four dimensional or any
other theory.

I have no wish to minimise these difficulties or to claim that the
introduction of the Higher space hypothesis clears up the whole matter.
It does nothing of the sort.

But it does give us a dim inkling of what the general nature of the
causes at work may be, especially as regards the power of "internal
vision" mentioned above and which I particularly wish to emphasise.

This is more than can be said of any alternative theory with which I am
acquainted.

Future study will probably show that this class of phenomena is far
from simple and is really capable of being resolved into a number of
sub-classes, each requiring its own appropriate explanation.

It is interesting to note that Mr. C.W. Leadbeater, the well-known
Theosophical writer and clairvoyant, definitely introduces the
four-dimensional concept in his book on Clairvoyance and ascribes the
power of long-range perception to the intervention of what he calls an
"astral telescope"; but there would appear to be no evidence in support
of this idea beyond the _ipse dixit_ of the writer and even he is very
vague on the point.

The third form of clairvoyance, namely, the perception of non-physical
things, is readily explicable on the hypothesis which we are
considering.

Just as the physical body has sense organs adapted for the perception
of physical things, so the four-dimensional body or "vehicle" will
presumably possess analogous organs adapted for the perception of
four-dimensional things.

In ordinary persons, we must suppose either that these organs are
almost completely undeveloped, or else that the mechanism, whereby the
impressions received are conveyed to the consciousness and recorded as
memories, is defective or inhibited.

In the clairvoyant on the contrary we may suppose that they are well
developed and active and that he is able consciously to perceive by
their aid.

In advancing this explanation of the third form of clairvoyance, I do
not wish it to be thought that I attribute an objective origin to all
visions of objects which have no obviously physical reality.

Hallucination is often a _vera causa_ and indeed it is comparatively
seldom that we can eliminate it with certainty.

But I do not think it can legitimately be applied to all visions of
this class.

The point is of some interest and worthy of a moment's thought even
though it involves a digression from the main topic.

The essence of hallucination is that it should have a purely subjective
origin and be unfounded on objective reality.

If I were to look round and find my sofa occupied by three green
cassowaries playing nap I should, I think, be justified in assuming
that I was the victim of an hallucination having no foundation in
objective fact. It would, presumably, have arisen from a simultaneous
excitation of the memory centres associated with the game of nap,
cassowaries, the number three, and the sensation of greenness,
occasioned, more or less fortuitously, by over-work or alcoholic excess.

On the other hand if I were to see the figure of an old man with a
long white beard, one front tooth missing, shaggy eyebrows, black
velvet smoking jacket, gold watch and chain, and so forth and were
subsequently to find that such a person, answering the description in
every detail, and previously entirely unknown to me, had really once
lived, or was still living, then the view that this vision was the
result of pure hallucination, would be untenable.

The probabilities against any chance stimulation of memory centres
giving rise to precisely that combination of characteristics, are
immeasureably large.

In such cases--and they are by no means unknown--we must attribute some
degree of objectivity to the origin of the vision.

This is of importance in view of the tendency in some quarters to
dismiss all such visions as purely hallucinatory.

We shall see later that the problems connected with Prevision and
Postvision are also, if not completely explained, at least rendered
less utterly incomprehensible by the introduction of the higher space
hypothesis.

With the third class of clairvoyant phenomena is closely associated
that group of facts known as "Phantasms of the Living, of the Dying,
and of the Dead."

Certain aspects of the dream state, again, seem to be related to
clairvoyance at a distance and are conveniently dealt with here.

Let us follow up the idea of a four-dimensional vehicle and see what
light, if any, it throws on these questions.

Let us suppose that the four-dimensional vehicle becomes detached
from, and loses touch with, the three-dimensional physical body
during unconsciousness; or rather that unconsciousness is due to this
detachment.

It follows that the "Ego" embodied in this four-dimensional vehicle
can no longer receive impressions through the three-dimensional sense
organs and that it is wholly dependent for communication with the
outside world on those which belong to the four-dimensional vehicle.
The nature of the impressions received will depend on the degree of
development of these organs.

If they are completely undeveloped the Ego will be utterly oblivious
of its surroundings, whereas if they are well developed the reverse
will be the case and we may suppose the Ego to be as fully cognizant
of the surrounding world as we are in ordinary waking life. It is
interesting to compare with this the statements of those who claim
to have consciously explored the "Astral plane" or four space world.
They often describe sleepers as being present, but "in a brown study."
Compare also the statement often found in communications purporting to
emanate from discarnate personalities to the effect that, "We have seen
so-and-so, but do not know whether he is dead or not."

Of course, it by no means follows that it will be possible, even under
these latter conditions, to remember in waking life the impressions
received during unconsciousness. On the contrary we should expect this
to be the exception rather than the rule.

In their passage from sense organ to consciousness the impressions
received will, _ex hypothesi_, not pass through the physical brain and
the memory centres with which they become associated may be located in
a position which is inaccessible to consciousness when embodied in the
physical vehicle.

It would be possible, though not perhaps absolutely necessary, to
account on these lines for the impression which most people have
sometimes had, of apparently "remembering" a place which they have
certainly never visited previously in waking life. They might, however,
on this theory, have done so in sleep.

It would also account for those dreams in which the dreamer perceives
an incident at a distance which is subsequently verified.

As for the ordinary chaotic dream, this, it seems to me may be
accounted for in either of two main ways. If we suppose that the
stimulation of certain cells (memory centres) in the brain causes
an uprush into consciousness of the associated item of memory or
"souvenir," it is not unreasonable to suppose that such stimulation is
going on _in the body_ all the time. But it will only be in the state,
intermediate between profound sleep and waking, that these aroused
souvenirs will, on the one hand get through to the consciousness--which
in deep sleep is separated from the body altogether--and, on the other
will escape over-ruling by the Will or obliteration by the influx of
normal sensory impressions.

This would account for the fact that the majority of dreams appear to
be of very short duration and to take place in the very act of waking.

The other cause of ordinary dreams is probably in its general nature
suggestive. That is to say the Ego cut off from the outside world by
the imperfections of its four-dimensional senses is quiescent, and in
a state peculiarly favourable for the telepathic picking up of stray
thoughts which suggest dreams.

This of course is especially the case when the dream is deliberately
suggested by a hypnotic specialist, as is sometimes done.[2]

The subject of Phantasmal apparitions is also both complex in its
varieties and obscure as to its causes.

The commonest explanation, namely, the telepathic influence of the
percipient by the agent, does not seem to me to be applicable to every
case. For instance, it is difficult to conceive how a man shot through
the head can visualise himself sufficiently clearly at that moment to
project a telepathic image of himself, including the wound, to the
percipient. And, more generally, it is probable that few of us could
visualise our own appearance with sufficient accuracy to do more than
convey, telepathically, a vague general impression. On the other hand,
if we are to suppose that the details are filled up, so to speak, by
the percipient, how are we to explain accurate perception of clothing
and so forth of which the percipient could have no knowledge?

Finally, the whole telepathic theory seems weak in this respect. If
I in the act of death, vehemently long for, or think of, a certain
person, it is clear that the thought in my mind which is most likely
to be transmitted to the brain of a percipient will not be the thought
of myself--still less of my own appearance--but rather of the other
person. Why should this suggest _me_ to his mind?

In experimental telepathy it is the idea on which the agent
concentrated his mind that is transmitted to the percipient, not some
other idea, and I see no reason for supposing that this is not always
the case.

In cases where the apparition has been deliberately produced as the
result of an act of will on the part of the agent, the apparition has
invariably been preceded by the agent concentrating his mind on the
person to whom he wishes to appear, _not_ on himself.

In view of these considerations I frankly do not see how the telepathic
theory can be unreservedly maintained.

When we add that in some of these experimentally produced cases the
agent has himself seen the percipient and given details, subsequently
verified, of the circumstances prevailing at the percipient's end; and
then compare this with certain of the varieties of clairvoyance at a
distance, we must surely admit that the supposition that the agent was
really present, though not in the physical body, is by far the simplest
explanation.

For cases of this sort the reader should consult "Phantasms of the
Living." Some good selected instances are also given in "Death, it's
Causes and Phenomena," by Messrs. Carrington and Meader.

The idea that conscious existence in a vehicle other than the physical
body is possible even during life is borne out to some extent by the
evidence of those who testify to having seen their own body, from
outside, while in a state of unconsciousness. An interesting one is
given in the above mentioned work. The narrator describes how as he lay
in bed he felt a cold sensation creeping up his legs from the feet and
gradually extending throughout his body. After this had gone on for
some time he became momentarily unconscious and on coming to himself
again "seemed to be walking on air" and to be entirely free from his
body. He thought of a friend who was some hundreds of miles distant
and in a few seconds he found himself in the presence of his friend in
circumstances which he describes. His friend spoke to him but he could
not stay. After much difficulty and perplexity he decided that he ought
to return to his body and as soon as he had made up his mind on the
point he found himself looking at his apparently dead body propped up
in bed as he had been when this experience began. He tried to control
it and in due course was able to do so and after a time successfully
"re-embodied" himself apparently none the worse for his experiences.

The credentials of this case are good, and it is important to note that
the friend referred to wrote spontaneously to say that he had seen
the narrator at the time and in the circumstances which the latter
describes.

For this reason it can hardly be dismissed as a mere hallucination or
dream and it is relevant to the present discussion because the narrator
saw his own body from outside and was apparently embodied all the time
in a vehicle of some sort.

Another somewhat similar and equally remarkable case is given in the
same work. This I shall deal with in a later chapter. In view of the
foregoing considerations, I think it fair to say that the idea of
a non-physical vehicle of consciousness capable, under the proper
conditions, of temporary detachment from the physical body, has strong
claims to be adopted as a working hypothesis for future investigations
even though it is too early, as yet, to accept it as a proven fact.

It certainly seems to clear up certain cases of apparition and abnormal
acquisition of information as to distant events, in a way which other
theories do not do without being strained to an extent which I regard
as unwarrantable.

It seems probable that the chief reason why such an hypothesis has
not been adopted before is simply the difficulty of conceiving the
nature of such a vehicle. But this is overcome if we suppose that it is
four-dimensional.

The theory has, of course, its own attendant difficulties and I have no
desire disingenuously to ignore them.

First it may be asked: How does the percipient see the apparition?
For four-dimensional objects are, _ex hypothesi_ invisible to
three-dimensional sight.

Second: Why does the four-dimensional vehicle present the exact
appearance of the three-dimensional body--clothes and all?

Third: How can it speak, _i.e._, set up vibrations in three-dimensional
matter, as it is sometimes recorded as doing?

It is admittedly far from easy to answer these questions, in the light
of our present knowledge.

As regards the first, I should feel disposed to say that such
apparitions would be the rule rather than the exception, were it not
for the fact that only those whose four-dimensional organs are fairly
well developed can see them. Even so it may be that they are only
called into activity as a result of some special "rapport" existing
between the agent and the percipient.

Professor Joire, in his book "Psychical and Supernormal Phenomena"
points out that in nearly every case the percipient is in a state
which he describes as "superficial somnambulism or passive mediumship"
_i.e._, in some condition which from the facts of Hypnosis we may
consider to be especially favourable to the receiving of supernormal
impressions of any kind.

This observation appears highly relevant and important.

The second difficulty may be met, though not, I must admit, in a
particularly convincing manner, by supposing that the four-dimensional
vehicle is so mobile and plastic, in respect to appropriate forces,
that it is capable of being moulded by the mere power of will.

It would thus take the form which the agent commonly associated with
himself, or which he observed his physical body to have after he had
left it.

It would be possible to adduce a number of considerations in support of
this view, but none of them are in any way conclusive and I therefore
leave the reader to form his own opinion on the matter.

As regards the third point, there are two possible answers which might
be offered.

On the one hand it might be suggested that the words heard are really
objective; the result, that is to say of actual vibrations in the
atmosphere, and that this result is produced because, in all such
cases, the percipient is sufficiently mediumistic to provide the
necessary material for the agent to "work up" some form of speaking
apparatus. This is very difficult to conceive as possible, and yet we
must suppose some such process to be involved in the production of
the "Direct Voice," a phenomenon which, though baffling, seems well
authenticated.

But this is rendered improbable by the cases where the speaking agent
has been a living person, who records no such process as having taken
place.

Besides, it is grossly improbable that a living person, or for that
matter a newly 'dead' person, would know how to perform this operation.

The most probable explanation seems to be a combination of telepathic
communication between the agent and the percipient accompanied by an
auditory hallucination on the part of the latter. This would be, I
think, quite natural.

These difficulties are much reduced, though not entirely removed, if
we suppose that the agent is embodied, not in the four-dimensional
vehicle, but in what, for lack of a better word, is called the "Etheric
Double." This appears to be of a semi-material nature and is discussed
at length in the chapter dealing with "The Connecting Link."

But this supposition would involve special difficulties of its own.

There is reason to suppose that the "Etheric Double," if it exists at
all, is incapable of moving far from the physical body during life and
it does not appear well adapted for use as a vehicle after death.

But on this point I shall have more to say later.

Generally speaking, it seems probable that no one of these explanations
will be found to cover all the cases in question. But each is likely to
prove applicable to some of them, although much careful investigation
and analysis will be necessary before we can hope to be able to allot
each case to its true cause with any degree of assurance.

None the less I am convinced that the hypothesis of a four-dimensional
vehicle, detachable on occasion from the physical body, puts us, at
least, on the right track.

I will now turn to the consideration of a series of phenomena which,
from the point of view of the higher space hypothesis, are of far
greater interest and significance than any we have yet considered.

I refer to the phenomena of "apport" and of "apparent penetration of
matter by matter."

If we have a closed room, of which all the windows, doors, and other
apertures have been carefully shut and sealed, it is clearly impossible
to introduce any solid object into that room, by normal means, without
breaking the seals and opening one of the apertures. The same would
apply to a closed, locked and sealed box.

But the literature of Psychical research abounds with instances where
objects are alleged to have been introduced into such closed and
sealed rooms and boxes--or removed from them, which comes to the same
thing--_without_ breaking the seals. This is the phenomenon of "apport"
properly so called and it forms a special case of the more general
class of "apparent penetration of matter by matter."

Other cases of the latter are the tying of knots in an endless cord
of such a nature that they can only be untied by breaking the cord or
separating its previously sealed ends; or the passing, on to the wrist
or ankle of some person or other, of a ring so small that it could not
possibly be pushed on over the hand or foot.

A very good test would be the interlinking of two rings turned from
different sorts of wood--as was attempted without success in the
Slade-Zöllner investigation; or the passing of a piece of weldless
drawn steel tube on to the middle portion of an ordinary wooden
dumb-bell.

With regard to these phenomena I propose, first, to show in what their
very great importance lies and then to discuss the nature of the
evidence we have for their actual occurrence.

If the reader will refer back to the first chapter, he will at once
perceive why I laid what must have appeared to be unnecessary
stress on the fact that "rooms" and "boxes" which would appear to be
absolutely closed to a two space being would be perfectly open to us
who live in a three space world. Just as every point in the interior
of a two space figure is absolutely open in the direction of the third
dimension, so we must suppose from analogy that the interior of a
closed three space figure--a box or room--is perfectly accessible from
the direction of the fourth dimension.

Consequently on the hypothesis that four space actually exists as
a reality, and is peopled by intelligent beings, possessed of the
necessary "apparatus"--whatever that may be--the explanation of the
phenomenon of apport is quite simple.

We have only to suppose that the object in question is moved out of the
containing space, in the direction of the fourth dimension, and then
put down again into three space outside the box or room in which it
originally was. Or conversely, when it is a question of introducing an
object _into_ a closed space.

During transit, the object would, of course, be located entirely
outside of three space.

I will not go at length into the question of how the tying of knots
in an endless cord could be performed in four space. Any reader who
cares to tie together the two ends of a piece of string for himself,
will soon realise that it is not possible then to tie a simple knot
in the string without untying the ends. If such an operation were to
be performed, under test conditions, it would clearly be a case of
apparent penetration of matter by matter.

Consider this case which is analogous to that of the steel tube and the
dumb-bell suggested above:

Let A and B be two space objects. Fig 8. A two space being could not
conceive of their being brought into the second position shown in the
figure.

[Illustration: _Fig. 8_]

But we, having the advantage of a third dimension of space could very
easily pick up the object A and put it down in the second position with
regard to B. Similarly a four space being of sufficient knowledge and
manipulative ability could, theoretically, slip on to the middle part
of the dumb-bell a piece of steel tube of a diameter too small to be
passed over the two large ends. There are, of course, a large number of
variations which could be introduced into this class of experiment but
the foregoing will be sufficient to indicate their salient features.

For the purpose of detailed consideration I shall deal only with the
case of the removal of a solid object from the interior of a closed and
sealed box, which is typical of the whole of this class of phenomena.

Let it be clearly understood that at the moment I am not expressing
any opinion as to whether this or any allied phenomenon has actually
occurred. I am concerned merely with the inferences we should
be compelled to draw if such an occurrence were substantiated
scientifically beyond all possibility of doubt.

We have seen that given four-dimensional space as a reality and
an intelligent four-dimensional being equipped with the necessary
knowledge, powers, facilities and so forth, which I have included
under the general term of "apparatus" the thing could be done in a
comparatively comprehensible manner, although the actual manipulative
details would still require clearing up.

The question now arises: Is this the only conceivable _modus operandi_
that could bring about the same result? It is not. There is one other,
and so far as I know only one other, theory which has been advanced to
account for this type of phenomenon.

It has been supposed that the solid object in question is dissociated,
by some obscure means, into ultra-atomic particles, is passed in this
condition through the walls of the box and finally "integrated" again
into its original form outside the box.

Now, apart from the obvious difficulty of imagining how these
ultra-atomic particles are integrated into the precise form originally
possessed by the object, this theory has at first sight a certain
plausibility.

We know that all matter is probably susceptible of dissociation in a
fashion that was originally supposed to be the exclusive property of
Radium and other Radio-active substances.[3]

If, then, we postulate the existence of intelligent beings in a
non-physical state of existence, there is nothing to prevent us from
supposing that certain of them have acquired a sufficient knowledge
of physical laws to enable them to effect a process of this nature
artificially.

I do not say that this idea commends itself to me; but it is the
explanation most commonly offered for the phenomena in question, and
this fact taken in conjunction with its _prima facie_ plausibility,
entitles it to careful consideration before we dismiss it as untenable.

The real objection to it is a mere matter of Physics. The work of
the scientists mentioned above goes to show that what we call matter
is no more than a condensation of energy in the ether; and that the
dissociation of matter is invariably accompanied by an enormous
liberation of energy.

For calculations on this point the reader may refer to M. Le Bon's book
"The Evolution of Matter."

Without going into such calculations it may be said that the amount
of energy that would be liberated in the dissociation of a gramme of
matter, would be amply sufficient, if it were produced in the form of
heat, to fuse, and for that matter vaporise, the experimenters, the
room, the whole house, and probably about half the town as well!

What becomes of this enormous quantity of energy which must be
liberated during the process if the dissociation theory of the
phenomena is correct? Why is its liberation not apparent, and painfully
apparent, to the experimenters? How is it prevented from being
dissipated and how is it collected again and recondensed into matter?

This point seems to me to be insuperable.

If the object within the box is dissociated, then energy must
inevitably be liberated. If energy is liberated, then it cannot
conceivably escape detection in such quantities.

I hope I have made my point clear. I am quite sure that any scientist
accustomed to think in terms of energy will at once see the difficulty
to which I allude.

I can see only one way out and that is to suppose that in some
mysterious manner the liberated energy is stored in a "reservoir," so
to speak, _which is not situated in our space at all_, and this at once
lets us in for the original idea of a fourth dimension and higher space
and all the rest of it.

Hence I maintain, and I think I have reason to maintain, that if
these phenomena do actually occur at all, then we are compelled to
admit that four-dimensional space does actually exist; and this no
matter whether we accept as the proximate cause of the phenomena a
simple four-dimensional movement or the far more elaborate and less
satisfactory notion of dissociation and re-integration.

The reader will now understand why it is that I attach such great
importance to these phenomena of apport and of the "apparent
penetration of matter by matter."

If one of these phenomena could be established by absolutely
incontrovertible experimental evidence, with the same degree of
certainty, for instance, as the phenomenon of levitation without
contact has been established by the recent researches of Crawford, I
should regard the four-dimensional hypothesis as virtually proven.

I should be much interested to hear whether any interested reader can
get out of the difficulty, assuming the authenticity of the phenomenon
for the sake of argument, but I do not think that it will prove
possible.

       *       *       *       *       *

I will now pass to the consideration of the nature of the evidence that
exists for the actual occurrence of this sort of phenomenon.

I will preface my remarks by two quotations from writers who appear to
hold somewhat different views on the subject.

In "The Physical Phenomena of Spiritualism" Mr. Hereward Carrington
says:

 "Without now stopping to consider any _a priori_ speculations as to
 the scientific possibility or impossibility of such a thing; the
 mere historic evidence in the case would certainly seem to point to
 the conclusion that fraud and nothing but fraud has been operative
 throughout and is quite sufficient to account for all the phenomena
 observed (save in the case of W.S. Moses, perhaps, that stumbling
 block to the rationalistic psychical researcher), in the presence of
 professional mediums.... In fact _all_ these cases sift themselves
 down to the one primary consideration: could the medium, in spite of
 the searching, have introduced into the séance room, unseen by his
 sitters, the objects materialised."

It should be noted that the above refers to cases where the séance room
is found, after the sitting, to contain objects which were certainly
not there before. In this connection the last sentence of the passage
quoted above is eminently justifiable and it is for this reason that I
prefer to deal with varieties of the phenomenon which are more amenable
to experimental control on the part of the experimenter; as for
instance the removal of a solid object from the sealed box which we are
considering.

Compare with this first quotation the following taken from Mr. Gambier
Bolton's book "Psychic Force."

 "During my sixteen years of experimental investigation into the
 question of the existence of this Psychic Force, the apparent
 penetration of matter by matter has been such a common occurrence at
 our experimental meetings, that unless this happens to take place
 in connection with some unusually large and ponderous object that
 is suddenly brought into our midst, or removed from the place where
 we are holding our meetings, I take but very little note of it. I
 could fill a large volume with instances where this has taken place
 in my own presence.... I am not engaged in an attempt to explain
 such things, but am merely recording phenomena which I myself have
 witnessed and which have been witnessed hundreds, nay thousands, of
 times by well-known investigators like Sir William Crookes and Dr.
 Alfred Russel Wallace under the strictest test conditions."

These two views are, to say the least of it, somewhat divergent. We
must, therefore, see what is to be gathered from such original records
as are available.

The _locus classicus_ of this sort of phenomenon is the Slade-Zöllner
investigation of 1877-9.

This investigation has received so much attention that it is impossible
to avoid giving it somewhat careful consideration here.

Johann Carl Friedrich Zöllner was born in 1834. He was Professor
of Physics and Astronomy at the University of Leipsic, a member of
many learned and scientific societies and the author of a number of
scientific treatises.

He was assisted, from time to time, in his investigations by Professors
Weber, Fechner, and Scheibner all of whom were men of considerable
eminence in one branch or another of mathematical or physical science.

The medium in whose presence the phenomena were produced was the
well-known "Dr." Slade. This medium has been demonstrated to have
resorted to fraud with a certainty that admits of no dispute.

But, as Mr. Hereward Carrington points out, we ought not to allow this
fact to influence us in the consideration of any particular case. In
the first place it is fairly certain that mediums who are capable of
producing genuine phenomena under suitable conditions are also liable
to resort to trickery when the genuine thing does not come off. (Cp.
the case of Eusapia Palladino.) In the second, too great a reliance
on antecedents is apt to produce an unreliable _a priori_ prejudice.
Every case should be considered on its merits alone and the medium's
past history should only be allowed to influence our judgment if it can
be shown that fraud has not been rigorously excluded and that the only
argument against it is the argument from moral integrity.

In this case the argument from integrity is obviously inadmissible and
as a matter of fact the precautions taken to guard against fraud were
so very inadequate that we cannot accept the experiments in question
as worth anything at all from the scientific point of view.

Zöllner's account of his experiments is to be found in his book
"Transcendental Physics," translated into English by Mr. C.C. Massey
in whom the author found an able and enthusiastic champion against his
many critics.

Among the more important of his experiments were:

Production of knots in an endless string.

Slate writing under "test" conditions.

Disappearance and reappearance of solid objects.

Coins transferred from closed and fastened boxes.

Other instances of the apparent penetration of matter by matter.

The careful study of this book is of the greatest value as an exercise
in the criticism of evidence and as a guide for anyone who proposes to
study such matters at first hand.

I do not think that I can illustrate my meaning better than by a
description of my own impressions in connection with the book.

When I first read it I was much impressed by the scientific eminence of
those who bore witness to the authenticity of the events described.

I reflected that here we had a Physicist of no mean order, assisted
by other scientists of European reputation, men trained, presumably,
in the art of exact observation and not likely to be deceived by the
manipulations of a conjuror. Surely we must believe their testimony if
we are to assign any value to human evidence at all!

Then, as I thought over the matter more and became more convinced of
the importance of the conclusions to be drawn from these experiments,
if genuine, I felt that these considerations, although possessed of
their own importance, were yet not sufficient to warrant acceptance of
the evidence without careful examination of the intrinsic qualities of
the latter.

On further study of the book I was struck by the fact that not
one of the special experiments, carefully designed by Zöllner to
establish the genuineness of the phenomena and the validity of the
four-dimensional explanation beyond all doubt, had succeeded. This was
suspicious, although not, of course, conclusive. Specially devised test
experiments may very likely fail simply because they may involve the
upsetting of some essential condition which is not fully understood
by the experimenter. But when such experiments fail, while others of,
apparently, identical general nature succeed, it gives one cause for
thought.

Finally, when I came to examine the records of individual experiments
in the light of the criticisms of Mr. Carrington, of Dr. Hyslop and
others, I realised that the nature of the evidence was emphatically
_not_ good enough to justify our accepting as demonstrated the facts
which Zöllner claimed to have established.

I shall not waste my own time and that of the reader by giving numerous
instances of the sort of thing I mean.

I will confine myself to the case that we are more especially
considering as being typical of the whole of this class of phenomena,
_i.e._, the case of the removal of a coin from a closed and fastened
box.

Zöllner describes how in December 1877 he put some coins in a small
cardboard box and had closed it by glueing a strip of paper round the
sides. He had done this in the expressed hope that Slade might be able
to remove them and thus give a proof of the reality of the fourth
dimension which was Zöllner's pet hobby. In May 1878 Slade came again
to Leipsic and performed the feat, at any rate to the satisfaction of
Zöllner.

The box was put on a table together with some slates and other objects
and Slade and Zöllner and his colleagues sat round. Zöllner satisfied
himself by shaking the box that the coin was still inside and in
answer to Slade's enquiries explained the purpose of the experiment
and its importance if successful. There was a little preliminary slate
writing and then Slade began staring into a corner of the room and
saying "I see funf and eighteen hundred seventy six." Then a hard
object was heard to fall on the slate which Slade had held under the
table all the time and on withdrawing the slate it was found to be a
five mark piece of date 1876. Zöllner then snatched up the cardboard
box and shook it only to find that it was empty.

This is a very highly condensed description of the proceedings but I
do not think I have been guilty either of "_suggestio falsi_" or of
"_suppressio veri_".

Interested readers can refer to the original.

Now, if Zöllner had been writing no more than a casual account of a
well-known experiment, inserted for the sake of completeness or for
similar reasons, it would be well enough.

But to offer his account, in the face of a very natural scientific
incredulity, as a conclusive demonstration of a highly controversial
point, was an insult to one's intelligence.

There are numerous criticisms that might be made, but I shall confine
myself to pointing out only the more conspicuous of them.

In this experiment there are two main methods by which the result might
have been obtained by fraudulent means.

There seems no doubt that the coin was really in the box at the
beginning of the sitting. We may equally accept the statement that the
box shaken at the end of the experiment did not contain a coin.

On the hypothesis of fraud, therefore, one of two things must have
happened.

Either Slade must have contrived, during the sitting, to possess
himself of the box, open it, abstract the coin, close the box again,
and return it to the table; or else he must have substituted for the
box, which at the beginning of the sitting contained the coin, another
(empty) box, previously prepared to resemble the original.

I do not think the former method to be at all likely.

One cannot unstick a length of glued paper and stick it up again in a
few seconds unobserved.

On the other hand everything lends itself to the supposition that the
second method was actually adopted.

In the first place we know that the box was prepared some six months
previous to the experiment.

It is true that Zöllner is a trifle hazy as to dates, saying at the
outset that Slade's first visit to Leipsic was in December 1877, and,
later, that the first and second visits were in November and December
1877.

But this is comparatively immaterial, the point being that Slade had
presumably had ample time and opportunity for finding out all about
these boxes and for preparing substitutes. I say "presumably" because
in the absence of definite evidence to the contrary, we have no reason
to suppose that these boxes were kept in an inaccessible place or that
Zöllner had never mentioned his intentions with regard to them to
Slade himself or to anyone else. I consider then that so far as the
records go, we are perfectly entitled to suppose that Slade was able to
prepare, and, in fact, actually did prepare, an empty counterfeit box,
externally similar to that prepared by Zöllner. The second, and almost
incredible, point to be noticed is that apparently no steps of any sort
were taken by Zöllner to identify either the box or the coin after the
sitting with those originally prepared by him.

In fact, he definitely says that he had completely forgotten, indeed
had never so much as observed, the value or dates of the coins used!

With such gross carelessness in the control, the trick becomes
exceptionally easy to perform.

Slade goes to the séance armed, among other things, with an empty,
counterfeit box resembling Zöllner's, also with a five-mark piece of
the right date--I think that even Zöllner would have been suspicious
if the coin that fell on the slate had been dated 1878! Zöllner shakes
_his_ box--the genuine one--and satisfies himself that the coin is
really there. Then follows a little preliminary play with the slate and
so on, the simplest matter in the world to an artist like Slade. At the
critical moment Slade diverts the attention of the experimenters from
the table by the world-old conjuror's dodge of gazing fixedly in some
other direction and murmuring "I see--see--funf," etc. While Zöllner
and his colleagues are glancing in the same direction to see what he
is looking at, Slade swiftly substitutes his counterfeit box for the
original, and the trick is to all intents and purposes done. All he has
now to do is to drop the coin which he brought with him on to the slate
at any convenient moment and draw out the latter in triumph!

Given the astounding guilelessness of Zöllner and the complete lack of
control revealed by the records, the thing was absurdly simple.

And yet Zöllner refers to it as having been performed under "such
stringent conditions!"

The foregoing example will, I hope, make quite clear how much
importance I attach to the Slade-Zöllner investigations.

I am not prepared to say that Slade never produced genuine phenomena,
either with Zöllner or with anyone else.

On the contrary, I think it probable that he possessed a certain amount
of genuine mediumistic power which, however, he did not hesitate to
supplement by cheating when occasion offered.

Some, or for that matter all, of the Slade-Zöllner experiments may
happen to have been genuine. But in view of the known untrustworthiness
of Slade and the complete lack of proper scientific control revealed
by a study of the published records we must write them off as quite
valueless from a scientific point of view.

I have dealt with this particular case at some length partly on account
of the vehemence of the controversies which have raged round it and
partly because the discrediting of Zöllner's observations has done much
to bring the whole idea of the fourth dimension into disfavour and even
into ridicule. This, I feel, is unfair and I wish to make it clear that
my present advocacy of the claims of the higher space hypothesis is in
no way based on the Zöllner experiments.

There are, of course, in the literature of the subject a large number
of other cases which are not so obviously unreliable--some, in fact,
which are distinctly good.

Dr. S.A. Peters gives an account of an early experiment by Dr.
Hare--one of the pioneer investigators--in which two small balls of
platinum were transferred to the inside of two hermetically sealed
glass tubes. It is not a bad case but is a very old one and the record
gives no particulars of any special precautions taken to exclude fraud.

The Milan Committee appointed to investigate the mediumship of Eusapia
Palladino failed to obtain any confirmation of Zöllner's experiments,
but they seem to have been puzzled by an unaccountable incident where
the medium managed to get into, or partially into, a coat while her
hands were being held by the Committee. I do not myself regard this
case as convincing.

The American Society for Psychical Research recorded some observations
with a Mrs. Roberts of New York, who managed to liberate herself from a
carefully made and sealed cage which was closed and sealed by members
of the investigating committee. I do not know anything at first-hand
about the credentials of this case. Dr. Paul Joire quotes it and I
suppose, therefore, that he considers it reliable.

The same author also quotes at length a case observed by Dr. Pogorelsky
and other Russian investigators with the medium Sambor. In this case a
cane chair was passed on to the arms of two of the experimenters whose
hands were clasped and bound together. That is to say, whereas to start
with the chair was by itself and independent of them it was, at the
end of the proceedings, found suspended from their arms by the opening
at the back. As the opening was too small for either of them to have
wriggled through even if they had wished to do so this was a clear case
of apparent penetration of matter by matter.

The evidence in this case seems to be well above the average although
it cannot be said to amount to mathematical certainty.

Mr. Gambier Bolton gives a distinctly good case in his book "Psychic
Force," p. 65. Under exceptionally favourable conditions he observed
the removal of a light table from a sort of tent which he had
constructed and very carefully closed and secured. This is one of the
best cases I know; it took place in the observer's own room, it was
done impromptu, it was well observed in light, and all the objects
concerned were the observer's property and not of a kind to admit of
prestidigitation. It is difficult to see any way out of it and yet I
must confess that I am not wholly satisfied. I feel that in every case
there is just something more needed to carry complete conviction and I
should very much like to see a good case myself.

Other instances are common. The records of the mediumship of Stainton
Moses, for instance, abound with them. But as there were never any
test conditions imposed, so far as I am aware, it follows that the
question of the genuineness of the phenomena is simply a matter of
the integrity of the medium. On this point every reader must be left
to form his own opinion. Many authorities have professed the greatest
confidence in Moses. Mr. Podmore, on the other hand, presents the
suspicious features of the case in a very able criticism in his "Modern
Spiritualism." Anyway on a point of such importance as this I do not
think it would be right to allow the matter to be settled by any purely
moral considerations of the type adduced in the case of Moses.

In general, then, I should say that the phenomena of the apparent
penetration of matter by matter are not established with the same
degree of certainty which characterises certain other phenomena, and
which we ought to demand before accepting them as scientifically proven
or utilising them without reserve as a basis for the construction of
theories.

In the interests of the science it is in the highest degree important
that experiments of this nature should be carried out under real test
conditions.

Should any of my readers be so fortunate as to be acquainted with any
medium capable of producing these very rare phenomena with regularity,
I should esteem it a great favour if they would kindly inform me. I
would very much like to arrange some definite experiments to settle the
matter--if possible once and for all.

There is one other direction from which, in my opinion, we receive a
strong hint that four-dimensional space is intimately connected with
Psychic phenomena.

I refer to Crawford's work on table levitation. This investigation
is undoubtedly destined to take rank as a "classical" research of
the first magnitude and no one who professes to take an intelligent
interest in the scientific and experimental aspects of Psychic
investigations can afford to be without his book.[4]

In a later chapter I shall have occasion to refer to certain aspects
of his results and to show how they fit in with those of other
investigators working on very different lines.

In the present context I propose only to call attention to the rigidity
of his "cantilever," a phrase which perhaps needs some explanation.

As a result of the most careful and painstaking researches extending
over a period of nearly three years and performed under conditions
which were singularly favourable for observation, he has been enabled
to arrive at certain definite conclusions as to the mechanical causes
of telekinesis in general and table levitation without contact in
particular.

He finds that when the table is lifted clear of the floor it is
supported by a definite structure or cantilever. This structure is
invisible and impalpable, or nearly so, and appears to be organised out
of some form of matter actually taken from the body of the medium.

Dr. Crawford has been able to work out the form and size of this
structure with considerable accuracy. For the details of method and
results the reader should consult his book. It is possible to pass a
thin rod through this structure in any direction without causing a
breakdown, and without encountering any perceptible resistance.

Nevertheless the structure can resist compressional, tensional and
torsional stresses of very considerable magnitude as I am able to
testify from personal experience.

I may mention here that I have witnessed these phenomena myself under
good observing conditions and that I am prepared to certify in the most
unequivocal manner that they are absolutely authentic; that is to say
the result neither of fraud--conscious or unconscious--nor of illusion.

Indeed, I do not suppose that an intelligent person could suppose
them to be due to anything of the sort after a careful study of Dr.
Crawford's book, quite apart from any personal observation and I only
add my own testimony as a small make-weight for what it may be worth.

We are here confronted with a sort of mechanical paradox. How can we
conceive that the structure manages to combine the contrary attributes
of rigidity and impalpability? Rigidity means simply the power of
resisting deformation under stress. That is to say that in order for a
body to be rigid it must be capable of developing within itself forces
which shall counteract those which tend to deform it. If we apply a
stress--a deforming force--to a rigid body, then this force must be met
by some opposing force; otherwise the body will be deformed. Normally
this is a matter of molecular cohesion, etc.

Now, this structure resists deformation under stress, and it therefore
follows that the deforming forces must be counteracted by opposing
forces.

But the structure is impalpable, and we can pass a rod through it in
any direction without encountering any resistance.

This being so it is difficult to conceive how the forces resisting
deformation can be applied from any direction in which we can move the
rod, _i.e._, from any direction known and accessible to us.

The more one tries to think out what is involved in the idea of an
impalpable and yet rigid structure, the more hopeless it seems.

But I think that the concept of four-dimensional space will help us
even here.

We know two things. First that the structure is rigid and therefore
that the deforming stresses are counteracted by opposing forces and,
second, that these opposing forces are apparently not applied from
any direction with which we are acquainted. But is it not possible
that they may be applied from some direction with which we are _not_
acquainted?

From some direction, in fact, of which the hypothetical fourth
rectangular axis of space is a component.

Is it possible that the matter which is drawn from the body of the
medium, and which forms the structure, is composed of molecules whose
atoms are arranged not in space of three dimensions but in space of
four dimensions?

I do not say that this is necessarily so; but I must confess that to
me it looks rather like it. Still less am I prepared to say that the
atoms are arranged four dimensionally. We do not know enough for that
yet. But it is, I think, a possibility, although for all I know to the
contrary there may be many other ways in which forces operating in four
space might act on three-dimensional atoms and molecules.

Consider a two-dimensional analogy again.

Imagine a number of flat-headed drawing pins lying points upward on
a flat surface. Taken collectively as a system they will have no
rigidity. Now imagine a board pressed down on those points so that
they penetrate into the board. The points and the board alike will
be invisible to the two space beings inhabiting the surface and yet
the drawing-pins, taken collectively as a system would have acquired
rigidity. Deforming stresses would be resisted by cohesive forces
operating outside the two space surface altogether.

This analogy is, naturally, imperfect; but I think that it enables us
to form some idea of the way in which the rigidity of the levitating
structure might result from its being held together by binding forces
operating outside our space.

The only alternative is to suppose that the particles of which the
structure is composed are rendered rigid by virtue of some peculiar
motion of the ether of a nature entirely unknown to us and different
from any type of ethereal motion with which we are at present
acquainted. This is palpably unsatisfactory and has the grave defect,
in an explanation, of failing even to begin to explain.

In an article published in "Light," for July 14, 1917, I discussed this
point in somewhat greater detail.

This is all that I have to say with respect to the phenomena which are
essentially "Psychical." In the next chapter I shall deal with two
other applications of the theory to more general questions.

FOOTNOTES:

[Footnote 1: Far be it from me to suggest that these last-mentioned
factors play no part in the phenomena. On the contrary, their effect is
at least very considerable, and does much to obscure and complicate the
work of interpretation.]

[Footnote 2: NOTE.--The foregoing remarks on the subject of Dreams
might be taken to imply an ignorance of the views inaugurated by
Freud, and extended by Jung, Pfister, and others of the Psychoanalytic
school. But I do not think that there is any fundamental contradiction
involved. Even if, as this school tends to maintain, there is no
dream without it's hidden and esoteric meaning, it is still perfectly
legitimate to suppose that the _form_ which a dream takes may be
determined by causes of the type which I have been discussing here.
These would provide the raw material so to speak which would be worked
up into the finished dream in accordance with Freudian principles.]

[Footnote 3: Compare the recent work of Rutherford, Soddy, Le Bon and
others.]

[Footnote 4: "The Reality of Psychical Phenomena" (Watkins).]




CHAPTER IV

SOME OTHER POSSIBLE APPLICATIONS OF THE HYPOTHESIS


In this chapter I propose to deal first with the questions of Time and
prevision and in the next to show how the higher space ideas help us to
clear up certain difficulties in connection with Vitality and Will.

The question of the nature of time is one which brings us into close
contact with Philosophic and Metaphysical thought and one is apt to
find oneself in very deep waters indeed. Still I think it is possible
to show how the higher space ideas come in without involving myself in
controversial statements. I shall leave it to others to decide whether,
as I am inclined to suspect, the acceptance of higher space concepts as
actualities would provide Metaphysicians with a somewhat new field of
speculation or modified methods of expression.

It has been suggested by some writers that "the fourth dimension is
time."

At first sight this definition would seem to conflict with our original
statement that it is an unknown direction in space at right angles
to every direction which we can find. But, as a matter of fact there
is a certain amount to be said for the idea. It might be pointed
out, for instance that for an object to exist at all it must possess
some "extension" in time. It must, that is to say, not only possess
a certain length and breadth and thickness but must also exist for a
certain time. Otherwise it simply does not exist. Then, again, if we
were able to "travel" in time we might fairly claim to be travelling in
a previously unknown direction, different that is from any direction at
present known to us.

Moreover, as I showed at the end of the first chapter, changes in
our space could be accounted for by supposing them to represent
our perception of a series of parallel sections made by our
three-dimensional space cutting an assemblage of suitably shaped and
arranged four-dimensional solids. It is here that I think we find a
clue which may perhaps be relevant to the present discussion.

I am far from being prepared to say that the fourth dimension _is_ time
because I doubt whether time as commonly understood is an "absolute"
thing. It seems to me to be rather a limitation of our finite
consciousness.

In the Divine Consciousness which I take to be alone Absolute there can
be, surely, no Past or Future; all must be comprehended in the Eternal
Now.

But I do think it possible that if we were not limited to three
dimensions in thought and experience we might be able greatly to modify
our present conceptions of time and to understand many things with
regard to it which at present appear obscure.

Let us start by considering for a moment our ordinary idea of "Time."
To start with we associate it with clocks and next, if we go a step
further back, with the movement of the earth relative to the sun and
stars. A clock is merely a mechanical device for subdividing into equal
parts of suitable size the intervals between successive recurrences of
certain astronomical events. In fact our ordinary ideas of time are
determined by a wholly fortuitous arrangement of the component parts of
the Solar System. If the masses etc. were other than they are, our day
and year would be altered accordingly. It is quite conceivable that in
some highly complex system of several "suns" moving under the influence
of their mutual attractions and attended each by its own sub-system
of satellites, there might be a world from which all the observable
astronomical phenomena would be so complicated that its inhabitants
could detect no regularity in them at all.

If, for instance, any given astronomical grouping of the observable
bodies only recurred once in a hundred generations of the inhabitants,
the measurement of time from astronomical data would be scarcely
practicable.

A similar state of things would result if the average life of a man on
earth lasted about ten minutes.

Again we know that the regularity of the changes in our system is
really only apparent, for all the motions by which we habitually
measure time are gradually altering under the influence of tidal
friction.

So we see that all our ordinary ideas of time are based on the
fissiparous assumption that certain distributions of matter will occur
regularly; that is to say in such a manner that if we could observe any
two successive cycles simultaneously they would appear coincident.

The same can be shown to apply to any other system of time measurement
which we can substitute for the observation of astronomical phenomena.

This is so because, apart from all other reasons, every conceivable
method must be based on the assumption that the properties of matter
are invariable. But these seem to be functions of the properties of
ether and since the solar system is certainly, and the whole universe
probably, moving through ether-filled space, this means that our
methods of time measurement must ultimately be based on the assumption
that the ether is homogeneous.

Very probably it is; but there is no reason why it should be--on _a
priori_ grounds.

Now M. Bergson has been at pains to discriminate between this time "of
succession" which we know and true time--the time "of duration." His
view, as I understand it, is that the succession of events or "spatial
simultaneities" by which we _measure_ time no more _is_ time than the
succession of marks on a foot-rule _is_ the material which we measure
with it.

What we actually experience as time does not necessarily correspond
with the spatial recurrences which measure it.

We all of us say, when we are bored, that "the time passed slowly" or,
when we are happy and amused, that "the time flew" and although this
may appear at first sight to be no more than a loose way of speaking I
think that there is more in it than that. It is here, in fact, that we
find what I can only call a "check" on the measurement of time.

It is the apprehension of something capable of undergoing change, of
Psychic states to wit, whose changes are yet totally independent of
the spatial changes by which we ordinarily measure time. A man who is
hanging by a frayed rope over a precipice waiting for someone to come
and rescue him might very likely say that "It seemed hours" although it
might really have been no more than a very few minutes.

Yet in one sense he might be speaking the literal truth. The changes
which took place in his mental states during those few minutes might
well be as complex and extensive as those he would normally experience
in the course of hours.

This should suffice to make clear the difference between the "real time
process" which we measure and the recurrence of spatial simultaneities
by which we measure it.

If we consider the latter alone we soon find that they are difficult
of comprehension. As Mr. Lindsay says in his book "The Philosophy of
Bergson," p. 128.

 "If we eliminate real time altogether we get a number of
 simultaneities whose relation to each other we cannot understand....
 For the relation between the simultaneities is taken to be that of
 the parts to the whole, but ... that is itself a simultaneity ...
 the relation of the simultaneities which are now taken as in their
 aggregate constituting change must be conceived of as necessary, as
 somehow all existing at once."

And again:

"We can only understand change by realising that it is incapable of
spatial expression...."

This quotation seems to me to be important because it brings out
clearly the points with regard to which I think that the higher space
hypothesis may be important.

For although I am entirely in accord with the idea that there are, so
to speak, two sorts of time I feel that in the light of the hypothesis
we cannot allow the statement that "change is something which is
incapable of spatial expression" to pass unchallenged.

If it were put in the form, "material change is incapable of expression
in terms of space of three dimensions," I should have nothing to say.

But in the course of my remarks on the phenomena of change in
a two-dimensional world, I pointed out that it is possible to
integrate an infinite number of three-spatial simultaneities into a
four-dimensional whole.

The introduction of this concept seems to me calculated to modify the
whole aspect of the question.

For, by its light, we see that all the three-spatial simultaneities by
which we mark time _can_ exist at once.

They can do so because the arrangement of material particles which
constitutes a given simultaneity may be regarded, if we so wish, as a
thin section of a four dimensional solid.

We can say, then, that there are two sorts of time.

First there is ordinary Physical "time" which is measured by the
recurrence of three-spatial simultaneities and this, if we choose, may
be regarded as produced by the passage across our space of something
which has extension in four dimensions.

Secondly, there is what I am inclined to call Subjective time,
consisting of changes in Psychic states; and which may be regarded,
provisionally, as being perceived by virtue of changes in "objects,"
including the vehicles of our own consciousnesses, in space of four
dimensions, or, at any rate, in space of a dimensionality higher than
three.

I do not mean the foregoing remarks to be taken too literally for I do
not regard three-dimensional change as produced by the passage across
our space of actual four-dimensional solids. This seems to me to be
altogether too crude an idea and was only introduced to bring out my
point that three-dimensional change is _capable of expression_ in terms
of four space.

Whether it is solely a phenomenon of consciousness or whether there may
be something in the nature of four-dimensional "lines of force" which
cut three-dimensional space and determine material distributions I am
not at all prepared even to surmise.

A side light on this matter of the two sorts of time is given by the
phenomena of time in dreams. It is well known that we may be awakened
by a noise and that in the very few seconds between the occurrence
of the noise and our becoming completely conscious we may experience
a long and complicated dream in which we may do and say things which
would take quite a long time in actual life and this without any sense
of hurry.

This seems to show that the "time scale" for the dream state is not
the same as that to which we are accustomed in our waking hours.
The difference should be sought, as Mr. Bragdon points out, in the
differing vehicle of consciousness.

This idea can be pushed much further.

I have suggested that there is a sort of time which is, so to speak,
peculiar to our space and which is expressible in terms of four space;
and that there is another sort of time which appertains to four space
itself, associated, that is, with four space change in the same way
that three space time is associated with three space change.

But if we accept the idea that there are more dimensions of space than
three we cannot refuse to consider the possibility that there are
more than four. If so we must say that four space change is in turn
expressible in terms of five space in just the same way that three
space change is expressible in terms of four space.

Now, it is evident that a being embodied in four space and possessing,
either temporarily or permanently, no three-space vehicle, will be
unaffected by three space change and will, therefore, be independent
of three space time. Four space change would take the place of the
three spatial simultaneities by which we, embodied in three space,
reckon time, and five space change would take the place of the changes
in Psychic states which for us give rise to the second aspect of time
which we have been discussing.

The whole dual nature of time would be repeated but with the difference
of being one dimension higher.

The same may be applied to five space and six space and so on,
indefinitely.

In each case the changes giving rise to the experience of subjective
time would presumably be the resultant of the changes of all spaces
higher than that of the lowest vehicle, but that of the next higher
space would predominate.

Hence Consciousness could never be altogether free of the experience of
time until it was embodied only in the highest space of all, which we
must suppose to possess the attributes of infinitely dimensional space.

And this will only apply to the Divine Consciousness.

All this is admittedly highly speculative but seems to me the natural
deduction if we assume the existence of spaces of dimensionality higher
than four.

The nature of maximally dimensional space is a question which I do not
propose to discuss here as it is somewhat conspicuously outside the
sphere of practical politics. For other observations on this subject,
including some remarks on the concept of "curved time," the interested
reader may profitably refer to Mr. Bragdon's book "Four Dimensional
Vistas."

Mr. Klein treats the question in a rather different, but highly
interesting, manner in his book "Science and the Infinite."


PREVISION.

The subject of prevision is obviously closely allied to that of time,
since the only considerable difficulty lies in the fact that the
incidents forseen are removed in time. They are wrapped in the darkness
of the future and we say that they "have not happened yet."

There are two forms which an attempt to explain the fairly numerous
good cases of prevision may take.

One way is to say that the future is latent in the present in that
it is determined by factors at present in existence. The other is
to say that there is no such thing as Past or Future, but that both
are comprehended in the Now and that it is merely on account of the
limitations of our Consciousness that we cannot apprehend them.

According to the former view the power of prevision is the result of a
mere heightening of the faculties by which we can always foresee the
future to some slight extent. If we see a blind man walking towards the
edge of a cliff it is not difficult to foresee that he will, probably,
fall off it and be smashed at the bottom. Such a sight could easily be
supposed to give rise to a visualisation of the corpse at the bottom of
the cliff, which might pass for a prophetic vision.

In such simple matters it is not difficult to imagine that a suitable
clairvoyant state, combined with unconscious but accurate reasoning and
subsequent visualisation, would enable the percipient to forecast the
future.

But clearly the accuracy of such a forecast would depend on the
perception of _all_ the factors involved, as well as on the precision
of the unconscious reasoning.

Hence, although we might readily accept this explanation in the case of
prevision of events in the immediate future, or in the case of vague
presentiments, it becomes increasingly difficult to do so, as the
event prevised becomes more remote and the number of factors which may
possibly influence the issue are proportionately increased.

I need hardly say that these factors of which I speak must include
Psychic states and so forth.

To use the terminology to which we have by this time become accustomed,
we could, theoretically, forecast the distribution of every particle
of matter in three space, provided we knew present distribution and
velocities; and provided also that no interference could arise from
external, _i.e._, four space, sources. But in order to be certain of
the latter, we must know all about four space dispositions and so on to
the "N"th degree.

Absolute prevision could therefore only result from a complete
knowledge of all the factors in _every_ space combined with absolutely
perfect reasoning powers.

Although, as will be seen, certain of the ideas in the above have
a place in what I believe to be the true theory of prevision, the
explanation as above described does not appear to me to be satisfying.

The heightening of faculty required in all but the very simplest cases
is too great to be accepted except in the last resort.

Now, as regards the other theory, that the future does actually exist
_now_ and that only our own limitations prevent us from apprehending it.

Consider again the crude and metaphorical representation of change as
resulting from the passage across our three space of a congeries of
four space solids which supposes that the distribution of matter at any
moment is simply a very thin cross section of this congeries.

If this were the case it is evident that to anyone who had the power of
moving freely in four dimensions it would be possible to move up the
mass and see what some cross section was like which had not yet arrived
at our space.

This is desperately crude but it gives the general idea.

In order to grasp it better we will transpose it into terms of two-and
three space at the same time altering it slightly. Suppose that a two
space world consists of a colossal soap film. Imagine a thin thread
passing through the film and stretched between two points, one above
the film and one below. If these two points move perpendicularly to
the film the thread will move accordingly. The point where the thread
cuts the film will remain stationary if the thread was perpendicular to
the latter to start with, but will move if the thread was originally
slanting.

To a two space being inhabiting the film, all that will be visible of
the thread will be a minute circle, an atom of two-space matter let us
say.

Now let us imagine an enormous number of such threads, sufficient
to produce all the atoms necessary to make up a complete two space
universe. Suppose also that these are twisted and intertwined in the
most complicated possible manner. Then as they pass across the soap
film they will give rise to the most complex changes in the two space
world.

A three space being, however, could see the filamentary structure as a
whole and would not be limited to the particular section which happened
to be crossing the film at any given moment.

I must again insist that I do not for a moment regard this as being
anything like a true picture of what actually occurs. The point I wish
to make is merely that if, as seems to be the case, three space change
can be represented spatially by the use of four space ideas, then it
is not utterly inconceivable that a consciousness free to move in four
space and independent of three space limitations, should be able in
some obscure way to foresee coming changes.

       *       *       *       *       *

There is a prevalent notion to the effect that if we admit the
possibility of prevision we are bound to become involved in the slough
of Fatalism.

"If we can foresee what is going to happen," it is urged, "then the
future must be already settled, and we have no power of altering it."

This view appears to me to be fallacious.

Consider again for a moment the filamentary world.

Our forecast of events therein is based on the assumption that the
filamentary structures remain unaltered, that the cross-sections which
will be traversed by the film will not be changed before it gets there.

This is pure assumption and quite unwarranted.

In the first place the two space beings themselves might be able to
alter the arrangement of the threads during their passage across the
film, implying of course the exercise of three space forces, and the
possession of a certain degree of three-dimensionality, on their part.
In the second place all sorts of extraneous three space forces might be
applied.

The argument does not perhaps apply especially felicitously to this
particular analogy, but translated into more general terms it means
that three space change, although expressible in terms of four space,
and perhaps for the very reason that it is thus expressible, is
susceptible to modification under the influence of factors which have
no three-dimensionality.

As stated at the outset, absolute prevision necessitates _every_ factor
being accounted for, and these factors may appear, not merely in three
space or four space, but in N-space too.

In fact, the more accurate prevision is to be, the wider survey must
the percipient take.

In order to attain absolute prevision the precipient must be able to
function consciously in maximally-dimensional space. But this ability
I take to be the exclusive prerogative of the Divine Consciousness.

The purely speculatory character of the foregoing will be evident and I
do not wish it to be taken as more than an attempt to convey a general
impression of ideas which seem somewhat suggestive.

It seems appropriate to end a chapter frankly given over to inchoate
and somewhat formless speculations, with some remarks on the
objectivity or otherwise of space in general.

These remarks have been more especially prompted by Mr. E.L. Gardner's
article on "The Fourth Dimension" which appeared in the _Theosophist_
for October 1916, by a pamphlet for private circulation written by Mr.
T. Olman Todd, 1915, and by Mr. Klein's remarks on Space in his book
"Science and the Infinite."

Throughout this work I have treated four-dimensional space as an
objective reality and, as will appear, I consider that this is
perfectly justifiable.

The general tendency of the above-mentioned writers seems to be to
suggest that this attitude is fallacious and that all space, of
whatever dimensionality, is rather to be regarded as a phenomenon of
consciousness. In saying this I do not pretend to be reflecting with
precision the views expressed by the writers in question. I am merely
giving the general effect produced on my mind by their ideas.

I may say at once that I think that they are probably perfectly right
and that no space of any kind is really objective.

I am, for instance, disposed to agree with Mr. Gardner when he says
that "However willingly we may grant that behind the description
'Fourth Dimension' there stands something that is real, it is of
importance that that reality should be described in terms of Life and
Consciousness and not be regarded as a further extension of Matter or
Form."

Mr. Klein concludes that "our very conception of space is one of the
modes only under which motion or physical phenomena are presented to
our consciousness."

I have neither the knowledge nor the temerity to embark upon a
discussion of the point from the metaphysical point of view and all
I wish to do is to show that I am aware that all our ideas regarding
space are liable to be modified at the hands of the philosophers
and that I have no desire to minimise the importance of their
contributions. On the contrary I think it probable that these may prove
to be of the utmost value. They may, for instance, by interpreting
spatial experience in terms of consciousness, throw light on the very
considerable difficulty to which I drew attention on page 48.

But I submit that for the present purpose we can legitimately disregard
the whole thing. It may well be that the change in passing from
our present state of consciousness to that which I have described
as consciousness in four dimensions is subjective rather than
objective, that the change would be in our consciousness rather than
in spatial conditions. But whatever may be the real nature of our
three-dimensional space from the strictly academic point of view we can
and habitually do treat it as an objective reality and I think it fair
to claim an equal licence in dealing with four-dimensional space.

Pure consciousness is an elusive thing to handle and if we find
evidence to the effect, for example, that the state of consciousness
in which we exist when separated from the body can be accurately
represented by the higher space hypothesis, then surely we had better
say that it is existence in four-dimensional space and have done with
it, just as we say that our normal existence is existence in three
dimensional space.

After all the whole matter is one of "relativity" so to speak. The
final effect with which we are concerned is the reaction of reality
on our minds and, just as we can in dynamics reduce any one member of
a system to rest and treat all motions as relative to that so here it
makes no practical difference whether it is our mind or reality which
changes provided that the changed relation between them is correctly
expressed.




CHAPTER V

VITALITY AND WILL


Another and particularly happy illustration of the way in which the
higher space concepts enable one to solve awkward dilemmas is to be
found in the problems of Vitality and Will. Readers who are interested
in these topics would do well to refer to Mr. Hereward Carrington's
"Problems of Psychical Research" or to his "Vitality, Fasting, and
Nutrition."

There are in general two main views which may be taken about Vitality.
We may either suppose that Life is purely a product of the body, that
it is a mere physiological function and nothing more, or one may
suppose that so far from the body being the primary cause of Life the
exact converse is the case--that Life is the _raison d'etre_ of the
body. It may be that everything that we recognize as "vital," every
attribute which enables us to distinguish animate from inanimate
objects, is no more than a purely physical phenomenon the product
of unusually complicated chemical actions: or it may be that the
chemico-physical complex which we call the body is only the means
whereby the pressing tide of Life manages to manifest itself in the
world. This latter is the view held by M. Bergson, by Mr. Carrington
and by myself.

 "M. Bergson regards matter as the dam which keeps back the rush of
 life. Organise it a little (as in the protozoa), _i.e._, slightly
 raise the sluice,--and a little life will squeeze through. Organise
 it elaborately (as in man), _i.e._, raise the sluice a good deal, and
 much life will squeeze through."

  (The Right Hon. A.J. Balfour.)

This is the "transmissive" as opposed to the "productive" theory and
the whole position is very like that which obtained in Psychology some
years ago. William James then showed that although it was possible to
interpret the observed facts of Psychology on the hypothesis that the
brain "produced" consciousness it was equally legitimate to do so on
the hypothesis that it "transmitted" it.

As he said " ... Mere coincidence in two sets of phenomena does
not prove that they are causally connected, that one produces the
other. They may be quite separate from one another (psycho-physical
parallelism) or both may be aspects of something else."

Personally I should be prepared to admit only the latter possibility.
Causeless parallelism is incredible; as James himself admits elsewhere.

The analogy is very close. Just as consciousness is usually conceived
to be due to the functioning of the brain but may, on the contrary
exist apart from it and merely use the brain as a channel of
manifestation, so also may Life exist apart from and use the body.

I will not go into the various arguments which support this view.
Perhaps the most striking is that from the necessity for sleep--a
phenomenon which appears to be exclusively associated with Life.
A mechanism needs replenishing with fuel, it must have worn parts
replaced and both these processes are accurately paralleled in the
body of any living organism. But an engine does not need sleep,
whereas a living organism not only needs it but cannot be satisfied
with any substitute for it. It looks therefore as if Life could not be
maintained from purely physical sources and this lends support to the
view that it is an essentially extra-physical thing transmitted by, but
not arising from, physical actions.

But this view leaves us with the difficulty that if we suppose that
Life is transcendent to the Physical and uses it only as a means of
manifestation we cannot see how it can do so without partaking of the
nature of the physical and so losing its "selective," "guiding" or
"intelligent" qualities. For in order that things should be causally
connected they must have qualities in common. Are then we to say that
life is a form of energy or that it is not?

As Mr. Carrington says: "We are ... driven into this dilemma: life must
be an energy--but, as such, it cannot be purposive! Life is purposive,
yet it must be an energy--for otherwise it could not affect the bodily
energies and the material world."

M. Bergson adopts the "hair trigger" theory and supposes the Life only
affects the physical energies of the body _very slightly_, just enough
to deflect them this way or that. But this is not getting out of the
difficulty at all, for the problem is one not of degree but of kind;
it is just as difficult to imagine "non-energy" affecting energy "very
slightly" as to imagine it affecting it a good deal.

Nor does it help matters to suppose, with Mr. Carrington and other
authorities, that Life is a wholly distinct and unique kind of energy;
an "absolutely separate force _per se_ different from any other mode
of energy of which we have any knowledge." If this is so we must ask
"How is it that this force combines sufficient of the qualities
common to all the physical forces to enable it to affect them, with
characteristics of so different a nature that we can call it an
absolutely different force _per se_ and emancipate it from the ordinary
laws and limitations of physical forces?"

A very similar, if not identical, dilemma arises in the case of Will
which must either be supposed to be a purely physical force--which
hypothesis commits us at once to a creed of thoroughgoing materialistic
determinism or else we must suppose it to be distinct from physical
energy by virtue of some added non-physical quality which must be
wholly outside the physical realm. Yet this extra quality of "conscious
intent" which is the essential characteristic of the act of willing
does, as a matter of common experience, enable us to control physical
matter and forces.

In fact, the whole trouble is simply this.

The universe presents a closed circle of matter and energy. Anything
within it must be bound by law, blind and unintelligent. Nothing
without it can affect anything within it--if for no other reason
than that if it could it would violate the fundamental law of the
conservation of energy. But Will _does_ affect matter, therefore it
must be within the circle: it is _not_ blind, for its very essence is
initiative, independence, and intelligence and it must, therefore, be
outside the circle.

Now let us introduce the idea of higher space and see where it leads us.

Suppose that the energy which we term "Life" is located to start with
in higher space--in four-dimensional space for example. Suppose that
it is really pressing against the "dam" of three-dimensional matter
trying to use it for a vehicle of manifestation. The extent to which
it will be able to do so will depend on the presence or absence in the
matter concerned of those qualities which enable it to be acted on by
four-dimensional forces. What these qualities are it is at present
impossible to say although one might hazard a guess to the effect
that the essential factor might be one of greater or less molecular
extension in the direction of the fourth dimension.

But wherever matter exists which possesses the suitable properties,
there will Life "squeeze through the dam" to a greater or less extent
and we shall have a "living" organism which will continue to live until
the matter through which Life is--in each particular case--manifesting,
loses the properties which enable it to be made use of.

Whether there is any sort of matter which can truly be called
completely inanimate or whether, as some people hold, all matter is to
some extent "alive" I am not prepared to say. Personally I should be
sorry to have to draw a distinct dividing line anywhere and it seems
more in accordance with the general continuity of things to suppose
that no such line can really be drawn.

For myself I tend more and more to the view that Life, Vitality,
Consciousness--call it what you will--is something which dips down, as
it were, for the purpose of gaining experience and of self-evolution,
from its original location--wherever and whatever that may be--through
successive limitations of consciousness until it reaches this, the
lowest, the most restricted and the most individual state of all.

These successive limitations may conveniently be represented by saying
that consciousness functions in spaces of successively decreasing
dimensionality although it must be borne in mind, as was pointed out at
the end of the last chapter, that this may be only a convenient way of
expressing the effect of a change which belongs to the consciousness
itself more properly than to its environment.

At each successive descent consciousness must find a suitably
organised vehicle in which to function and through which it can
receive impressions. But each such vehicle will involve corresponding
circumscriptions and, conversely, each upward stage will involve an
extension of consciousness, until finally, when our evolution is
entirely accomplished, we shall be completely and fully Conscious and
independent of all limitations of any sort or kind. On the downward
half of the journey the characteristic process would, on this theory,
be the gaining of individual at the cost of "communal" consciousness,
whereas during the second half the latter would continually increase
and at last lead to complete "communion" in the widest possible sense
without any loss of individuality. This view, which has a good deal
to support it especially in point of continuity and general coherence
with other well established ideas, has much in common with that held by
the Theosophists, which is, to my mind, the strongest plank in their
platform.

But to revert to the original idea of Life as primarily a
four-dimensional force.

This does not involve any contravention of the Law of the Conservation
of energy for we have only to suppose that the Law is exact only for
the Cosmos and for the physical universe, as commonly understood, no
more than a very close approximation.

The amounts of energy which we must suppose to enter the physical or
three-dimensional universe from four-dimensional space may be very
small, so small as to defy detection by the methods we are able to
apply to the study of living organisms in which alone they could be
observed; and yet, by virtue of the "hair-trigger" theory to which I
have already referred they might produce effects as large as we please.

The foregoing is clearly incomplete, but I think I may fairly claim to
have removed the fundamental dilemma which first confronted us.

We have seen that life may be supposed to exist entirely apart from
ordinary physical matter and yet to affect it so long as we suppose it
to do so from some region of higher space. It is a form of energy if we
wish to call it so and yet it is distinct from the ordinary forms of
physical energy and free from the limitations which would be imposed
upon it if we reckoned it as subject to the Law of Conservation as
commonly understood.

And yet the latter is not broken but rather strengthened; for we now
suppose it to be not merely of Universal but of Cosmic application.




CHAPTER VI

HIGHER SPACE AND PHYSICAL SCIENCE.


In an earlier chapter I defined a valid hypothesis as one which
explained at least _some_ of the observed facts and did not contradict
any of them.

Since then I have been trying to show that the Higher Space ideas do
throw a certain amount of light on quite a number of difficulties and
enable us to clear up certain anomalies and dilemmas which seem to be
insoluble without its aid.

We must now consider rather more definitely than we have hitherto done
whether there is any thing in the hypothesis to conflict with those
established conclusions of scientists which are the nearest approach
we have to absolute certainties. I think we shall find not only that
there is no such conflict but that there are here and there distinct
indications that the higher space ideas may some day find applications
in the exegesis of even the most strictly physical sciences.

These indications are admittedly very nebulous at present, it may be
that they are all illusory and as will appear later they cannot _all_
lead to anything, for some are mutually exclusive.

I do not propose to express any very definite opinions on their
comparative values but shall simply state them and leave it to my
readers to decide what they are worth.

It must be remembered throughout that we cannot expect to find any very
definite indications of the existence of higher space as a reality for
the simple reason that physical science is concerned solely with those
phenomena of matter and force which are "_ex hypothesi_" essentially
three-dimensional.

It is worth noting at the outset that physical scientists have evinced
no especial hostility to the concept of the fourth dimension, as such,
however much they may have opposed to the more definitely Psychic
researches which I, personally, believe to be closely associated with
it.

Lord Kelvin, for instance, saw in it nothing repugnant to scientific
thought and professed himself quite willing to adopt it should such
a course seem to be indicated by the evidence. Another distinguished
physicist has gone so far as to evolve a theory of "ether squirts"
from the direction of the fourth dimension in connection with the
ultimate constitution of matter.

Again M. Poincaré the distinguished French Physicist has said "The
characteristic property of space, that of having three dimensions is
only ... a property residing, so to speak, in human intelligence."

Mathematical physicists also find that certain experimental anomalies
are resolved if they refer phenomena to four interchangeable axes
involving homogeneous co-ordinates instead of to three space axes and
one time axis. If this is not dealing in four-dimensional space it is
first cousin to it.

M. Poincaré also pointed out that the postulates of Euclid are not
experimentally verifiable facts and as a matter of fact much work
has been done in the elaboration of non-Euclidean geometries. This
is too mathematical a subject to be dealt with in detail here, but
I can indicate the general drift of it, so far as it is relevant to
the present discussion by means of the time honoured analogy of the
two-dimensional world.

Most of my readers will know what are meant by the terms "latitude" and
"longitude" and that the lines of longitude are "great circles" which
pass through the poles and cut the earth's equator at right angles.
It is also a matter of common knowledge that if on a plane surface two
lines are drawn each of which cuts another line at right angles these
two lines will be parallel--that is to say they will never meet however
far they may be produced. This holds good provided that the surface
in which they are drawn is truly plane--_i.e._, flat. But it breaks
down, as we see in the case of the "great circles" of longitude, if
the lines are drawn on a sphere. Now imagine two-dimensional beings,
having no conception of the existence of a third dimension, living on
the surface of a very large sphere. They might discover this principle
about parallel lines and all would go well until they began making
measurements over very large distances. Then their Geometry would begin
to go wrong. They would find that lines drawn in their surface which
ought not to meet however far produced would begin to show a tendency
to do so. This would be an indication to them that there was such a
thing as a third dimension of space and that their two-dimensional
world was curved in this third dimension.

Now if a two-dimensional space can be curved in three dimensions there
is no sort of reason why three-dimensional space should not be curved
in four and in a precisely similar way three-dimensional geometry
would, if such were the case, begin to "go wrong" where very large
measurements were involved. Now, the largest measurements we ever make
are astronomical measurements and as a matter of fact, according to
Mr. Bragdon, there does seem to be a tendency for Geometry to go wrong
in certain cases. He says that the number of negative parallaxes of
stars is larger than would be expected having regard to the probable
experimental errors. The parallax of an object is the angle which it
subtends at two different points of observation, and so long as it is
at a finite distance from these two points--which in the case of a star
are the two opposite ends of the earth's orbit--this angle must be
positive. That is to say the lines drawn in the observed direction of
the star from the two points must converge.

If, as in certain cases seems to happen, they _diverge_, then one of
three things must be the case; either the observations are wrong or
else light does not, as is commonly believed, travel in straight lines
(for after all what we call a straight line in astronomy is only the
path of a ray of light) or else our geometry is breaking down and we
must suppose that our space is curved, which would necessitate the
acceptance of the existence of a fourth dimension.

It must be admitted that the explanation of negative parallaxes is more
likely to be found in one or both of the two first alternatives than in
the third.

Mr. Hinton has a good deal to say in his books about various
four-dimensional theories of electricity involving four-dimensional
vortices. These are highly ingenious but there does not seem to be
any considerable reason for supposing them to be anything more and I
shall therefore not describe them here. Two of his ideas however are so
striking, although for different reasons, that I think a brief outline
will not be out of place.

In his book "A new Era of Thought" he points out the remarkable
analogy which exists between the properties of ether as postulated by
physicists and those which a perfectly smooth solid sheet would present
to the intelligence of two-dimensional beings living on it.

The hypothesis of the ether was introduced to account for the
transmission of light, heat, electricity, and so forth, and has proved
of the utmost service to physicists. Most of my readers are probably
acquainted with the general idea and I need not therefore discuss it in
detail.

It will be sufficient here to say that it is supposed to be a
weightless, homogeneous medium extending throughout all space and
permeating all bodies. Indeed Matter itself is supposed to be no more
than the result of more or less complex disturbances in it.

But although it accounts for the phenomena in connection with which
it was called into being it is necessary to ascribe to it very
contradictory properties. On the one hand it has been calculated that
in order for it to transmit the forces which we know that it does
transmit, for instance the force of gravitation, it must possess a
rigidity some 3,000 times greater than that of the strongest known
steel. On the other hand we must suppose it to be of a tenuity far in
excess of the most perfect vacuum which we can obtain, for otherwise
the earth and other planets which are moving at immense speed through
this medium would be slowed down; which is not in practice the case.

Now Hinton points out that to a two-dimensional being, a perfectly
smooth solid sheet on the surface of which he lived would possess many
of these properties. Being perfectly smooth it would be imperceptible
to him and would offer no opposition to the passage of bodies over it.
Yet it could, being solid, transmit vibration just as we know the ether
does for us. Also it could be as rigid as you please without losing any
of its imperceptibility. It could not be weighed and it could not be
eliminated from any vessel no matter what care was taken to do so.

The analogy is striking but it does not appeal to me and I do not
think that even Mr. Hinton means it to be taken strictly, for in other
passages he gives quite different suggestions as to the ether.

One of the latter is derived from a consideration of the phenomena of
rotation in four-dimensional space and is of some intrinsic interest.

In two space rotation takes place about a point, in three space about
a line and we should therefore expect that in four space it would do
so about a plane. This is easily shown to be the case although I do
not propose to go into the proof here. The only important point is
that whereas it is impossible to conceive a mass of three-dimensional
spheres in a state of continuous rotation,--because they would be
trying to drive each other in different directions and so would prevent
the rotation,--in four dimensions this is not the case and a mass of
"hyper-spheres" could be "self-driving," that is to say the rotation
of each could be such as to assist and not to retard that of its
neighbours. This fact is of interest because Lord Kelvin showed that
the contradictory properties of the ether referred to above could only
be reconciled by supposing it to be animated throughout by a motion of
a vortical character.

This "self-driving" effect of rotating hyper-spheres is worth glancing
at a little more closely. It arises from the fact that there are
two distinct sorts of rotation which such a sphere may possess. In
three-dimensional rotation the motion may take place about any axis
we please and the other two axes which can be drawn will change one
into the other, so to speak, as the rotation takes place. But in
four-dimensional space we have four axes and while the X and Y axes
change place, say, there is nothing to prevent the W and Z axes doing
so too. Thus we might have the X axis changing into the Y and the
W into the Z. To reverse both of these motions so as to have the Y
axis changing into the X and the Z into the W does not give us a new
kind of motion any more than reversing the direction of an ordinary
three-dimensional rotation does--it is only equivalent to looking
at it from a different point of view. But if in the case of the
four-dimensional rotation we reverse one only of the two rotational
components we do get a new kind of motion, and this is of interest in
view of the fact that electricity like other forces is regarded as a
mode of etheric motion, and if this be so there would seem to be a
certain need for two distinct kinds of it in order to correspond to
positive and negative electricity respectively.

It is just possible that there is some connection, as Mr. Hinton
suggests, between this need and the two kinds of four-dimensional
rotation referred to above.

       *       *       *       *       *

Most writers on the subject of higher space make great play with the
phenomena of symmetry and adduce its occurrence in nature as evidence
of the existence of a fourth dimension. This view is not warranted by
the facts and I shall therefore touch on it only very briefly.

[Illustration: _Fig. 9_]

The point arises in the following way. Consider the two triangles ABC
and DEF in Fig. 9. If these were cut out and laid on a smooth surface
exactly as shown, no amount of sliding about would enable us to fit
one exactly over the other. In order to do this it would be necessary
to pick one up out of the plane of the paper and turn it over. In a
precisely similar manner two asymmetrical three-dimensional objects
such as a right and left hand, each of which is the mirror image of
the other, could not be made to coincide unless one of them were to be
turned over in four-dimensional space. The point made by Mr. Hinton and
other writers who attach importance to the phenomena of symmetry, is
that there seems to be a general tendency in nature towards a right and
left handed symmetry in which the whole organism is symmetrical about a
central plane, each half being the mirror image of the other and that
this symmetry is unlikely to have arisen through equal increments on
either side of the central plane. They suppose as an alternative that
"the ultimate elements of living matter" are not right and left handed
_ab initio_, but become so by virtue of some of them being "folded
over" in four-dimensional space.

This view seems to me to lack foundation especially in view of the fact
that the work of Le Bel and Van't Hoff fully cleared up the analogous
phenomena in the case of crystals without introducing the concept of
higher space at all. In general therefore I agree with Schubert who
says:--

 " ... the only inference we can here make is that the idea of a
 four-dimensioned space is competent, from a mathematical point of
 view, to throw some light on the phenomena of symmetry."

  (Mathematical Essays, p. 91.)

None the less Bragdon is right in his contention that "Could it be
shown that the two-dimensional symmetry in nature is the result of
a three dimensional movement, the right and left-handed symmetry of
solids would by analogy be the result of a four-dimensional movement."

I need hardly say that if we could experimentally obtain the changing
of an asymmetrical right-handed object into the corresponding
left-handed one it would be of the very first importance as a proof of
the reality of higher space.

Far more important than any of the foregoing, however, are the
considerations arising from what is known as the Principle of
Relativity. This subject, which has received much attention at the
hands of mathematical physicists in recent years, is far too abstruse
to be dealt with in detail here and a partial and popularised account
would almost certainly fail to satisfy those who are not wholly
ignorant of mathematical physics and would weary those who are. I
propose, therefore, to dismiss it in very few words in spite of its
great importance and relevance.

"The Principle of Relativity is the hypothesis that it is impossible by
means of physical experiments to determine the absolute velocity of a
body through space." (Cunningham "Relativity and the Electron Theory,"
p. 2).

We cannot, for example, determine the velocity of the earth relative to
the ether.

This is of importance when we are dealing with the idea of
"simultaneity"--an idea which, as we saw in Chapter IV. is closely
associated with our notion of Time. For our criterion of simultaneity
has in practice been based on optical communication. (Cp. Ibid, pp. 5
and 28). But it is easy to show that "the setting up of a standard of
simultaneity by means of light signals is not possible until a definite
velocity is assigned to the observer. Thus the hypothesis of relativity
requires a reconsideration of the way in which we measure time." (Ibid,
pp. 5, 28, 29).

"This again reacts on the measurement of the length of a material
body, the 'distance between two points' being the distance between
simultaneous positions of those points. Thus it becomes necessary also
to examine the way in which we measure space. It becomes impossible to
consider space and time separately; the two measures are interrelated
to such an extent that Minkowski felt himself constrained to say that
'from henceforth time by itself and space by itself are mere shadows,
that they are only two aspects of a single and indivisible manner of
co-ordinating the facts of the physical world.'" (Ibid, pp. 5 and 6.)

When it is remembered that the Principle of Relativity is firmly
established in scientific thought it will be realised that this
conclusion arrived at as a result of purely physical considerations is
of the very utmost importance as an independent confirmation of the
general line of thought developed in the preceding pages.

I therefore feel it legitimate to claim that in so far as physical
science throws any light on the subject at all its testimony is
distinctly favourable.




CHAPTER VII

THE CONNECTING LINK


In the foregoing chapters I have tried to show that there are,
scattered here and there over the field of Psychic Research,
sufficient indications to warrant our adopting, as a tentative
working hypothesis, the idea that four-dimensional space is a reality
and that the Individual consciousness is capable of functioning in
a four-dimensional vehicle quite apart from the three-dimensional
physical body.

I hope that I have made it quite clear that in my opinion the two
vehicles are entirely separate and independent, and that I do not
regard the three-dimensional body as being a mere section of a
four-dimensional whole.

I propose in this chapter to consider in some detail the question of
the nature of the connection which must perforce exist between the two
vehicles.

We know that there must be some form of connection because impressions
which are received by the three-dimensional sense organs are
transmitted to the conscious Ego, which is, _ex hypothesi_, embodied in
the four-dimensional vehicle.

Furthermore it is clear that the connection can be interrupted with
comparative ease, since in sleep, anæsthesia, and analogous conditions,
the conscious Ego does not receive these impressions although the sense
organs may still be subject to stimuli to a greater or less degree.

We are not, of course, able to draw detailed conclusions as to the
precise nature of this connection by the exercise of pure deductive
reason.

But I think that my readers will agree with me that the first and most
obvious place to look for it will be in the realm of the nervous system.

Further we may safely say that, assuming the hypothesis we are
considering to be correct, the sense impression must, at some stage in
its transmission, be deflected, so to speak, out of three space into
four space.

In order for this to happen it is necessary that some part of the
transmitting mechanism should be capable of producing this deflection
and it is reasonable to suppose that a substance or mechanism specially
differentiated for the purpose of deflecting impressions in this manner
out of three space into four space, will be distinguished by an
abnormal four-dimensional complexity as compared with ordinary matter,
which, as we have already seen, probably possesses a very slight
four-dimensional extension.

As a result of this abnormal four-dimensional complexity it is to be
anticipated that the part of the transmitting mechanism concerned will
possess characteristics sufficient to differentiate it from ordinary
matter.

I submit, then, that we may reasonably deduce that if the
four-dimensional hypothesis which I have outlined be correct, there
should exist, either as an integral part of the nervous system or
in close association with it, some constituent or substance which,
in spite of having many of the properties of ordinary matter, will
also possess characteristics peculiar to itself--as, for instance,
susceptibility to four-dimensional forces imperceptible to us.

At this point I would recall to the reader's attention the remarks
which I made in Chapter II regarding the processes of scientific
thought and the sequence of operations whereby we attain to exact
knowledge.

So far we have considered a number of observed facts and framed
a working hypothesis which, I believe, explains some, and is not
contradicted by any, of them.

In the immediately preceding paragraphs we have, by deductive
reasoning, concluded that if this hypothesis be correct then something
else must follow. There must, in fact, be some sort of connecting link
whereby sense impressions are deflected out of three space into four
space and are thus enabled to get through to the consciousness.

We have also concluded that this connecting link is likely to consist
of matter in some curious condition such as to invest it with
properties unlike those of ordinary matter. If on turning again to the
realm of observation, we find that this deduction is substantiated in
practice, we shall receive distinct confirmation of the correctness of
our working hypothesis.

In the pages which follow I propose to show that there are a number of
facts which strongly indicate, even if they cannot at present be held
conclusively to demonstrate, the existence of some such connecting link.

I am well aware that there are numerous gaps in the body of evidence
which I shall bring forward on this subject. To some of these I shall
draw specific attention in the hope that by doing so I may induce some
of my readers to experiment on the points in question. There is an
enormous amount of research work to be done before we shall be able to
have any considerable confidence in our speculations or to feel that we
are working on anything like a firm foundation. Much of the evidence to
which I shall refer in this chapter is in urgent need of confirmation
and there is very little indeed which I should care to guarantee
personally. Still the indications, slight though they are, do seem to
point rather in the same direction and as my object is to stimulate
investigation and, perhaps to indicate some of the lines on which it
may profitably proceed rather than to lay down the law on obscure
points, I have thought it worth while to deal with them fairly fully.

Historically the first relevant experiments were probably those of
Reichenbach in the middle of last century. But so little was known
in those days about a variety of factors which might have vitiated
his results, and his work has been so strongly criticised by later
authorities that I will not do more than mention him for the benefit of
any reader who may have a fancy for probing into the historical origins
of the subject. None the less great credit is due to Reichenbach for
the thorough and painstaking character of his researches to which he
brought immense industry and a truly scientific spirit which led him
to fantastic and erroneous conclusions only because he had not our
present knowledge to guard him from the many pitfalls which abound in
these investigations.

The first phenomena to which I wish to call attention is that known as
Exteriorisation of Sensibility.

This has been investigated by de Rochas and later by Joire and by
Boirac, and I believe it is well established.

The gist of the phenomenon is that in certain hypnotic states the skin
of the subject becomes insensitive to pain but the "sensibility" is
transferred to a sensitive layer a few centimetres distant from the
skin. Pinching or pricking the skin itself produces no effect but
doing so in the region of the sensitive layer arouses the appropriate
sensation in the subject. Furthermore, according to Joire, this
sensibility can be localised and transferred to various objects--a fact
which gives the investigator a most desirable power of experimental
control.

Dr. Joire performed a number of experiments to determine whether
the results could be attributed to auto-suggestion, to unconscious
suggestion by the investigator or to unconscious connivance on the part
of the subject, but concluded that they could not. Any reader who has
doubts on the subject should read his book "Psychical and Supernormal
Phenomena." Dr. Joire was unable to give any explanation of these
phenomena, nor shall I attempt to do so at the moment beyond pointing
out that on the face of it, it looks as if some definite substance of
sensitive properties were exteriorised which, however, must be supposed
to be to some extent under the control of the will, since it was found
that the seat of sensibility could be shifted at the word of command.

Leaving this for a moment I would draw attention to the subject of the
"aura." Certain persons claim to be able to see this normally as a
regular thing and describe it as being a bluish-grey haze surrounding
the body and at a little distance from it. Dr. Kilner in his book "The
Human Atmosphere" describes how he found it possible to induce this
power of vision in normal persons by causing them to gaze at the light
through suitably coloured screens which seemed to affect the retina in
such a way as to make it more sensitive to the particular wave length
of light which emanates from, or is reflected by, the aura.

In the course of his investigations he found among other things that
the aura was apparently under the control of the will since it could
in certain cases be made to change colour or to extrude rays by mere
volition.

Through the courtesy of Dr. Kilner I have myself been able to try the
effect of the screens and I certainly saw, or thought I saw, an aura of
the type which he describes.

At the same time I am not altogether prepared to swear that the
appearance could not be some sort of optical illusion or "artifact"
and I should accept the aura with less reserve if it could be recorded
photographically.

On the other hand some of Dr. Kilner's experiments, notably as regards
colour of the aura and its uses in diagnosis, are very remarkable and
seem unlikely to be due to either of the above mentioned causes.

If we accept these experiments at their face value they certainly
support the idea to which the phenomena of Exteriorisation of
Sensibility faintly pointed, namely that there may be some
exteriorisable _substance_ under the control of the Will.

There are other experiments which also point the same way. Consider
for example those of MacDougal who weighed a number of patients at
the moment of death and found in each case that this coincided with a
_sudden_ loss of weight of about threequarters of an ounce, more than
could be accounted for by loss from perspiration or from the emptying
of the lungs. He claims that "We have experimental proof that a
substance capable of being weighed does leave the body at death." It is
of course most important that these experiments should be confirmed by
independent investigators but there seems no reason to doubt the facts
as stated, although I cannot agree with MacDougal's view that what
leaves the body _is_ the "soul."

Dr. Baraduc, again, took photographs of his son and wife shortly after
death and found that in each case a luminous, cloudlike mass or masses
were visible over the bodies.

This case is of exceptional interest in that the observations were not
personal but were photographic records. Unless the case is inaccurately
reported it follows that there must have been some objective foundation
for the results, and it would also seem that, since the object
photographed affected the plate but was invisible to the eye, it must
not only have been material or quasi-material in nature but also have
emitted light of a frequency above the range of normal vision, _i.e._,
"ultra-violet" light. Here again there is great need for confirmation
but so far as it goes the evidence continues to point the same way.

Surely this concatenation of evidences from such different sources
cannot be purely fortuitous?

The foregoing are the most important and representative experiments on
these lines but the whole of the literature of Psychic Research abounds
with minor pointers which all indicate the same sort of thing.

Let us turn again to the work of Crawford, to which I have already
referred.

He started out to investigate the causes of telekinetic phenomena and
had at the outset no sort of notion of what the explanation was likely
to be and he found that his table is supported, during levitation
without contact, by a rigid structure.

This structure is invisible to the eye and is practically impalpable.
It appears to be composed of matter taken from the medium. The main
conclusion is, I think, inevitable, but for the experiments and
reasoning which have led to it the reader must consult Dr. Crawford's
book.

Again we have this same curious substance exteriorised from the body.

But there are two points in particular which bring it closely into line
with the phenomena which we have been considering.

The first is that although Dr. Crawford has not yet succeeded in
photographing the structure _in situ_, he has obtained a photograph of
what appears to be the same substance issuing out of the medium.

Furthermore, the existence of the structure has been confirmed by
clairvoyants, and this fact, taken in conjunction with the photographic
results and with what I said about "etheric" or "ultra-violet"
clairvoyance in Chapter III, forces us once more to the conclusion that
this elusive substance possesses the property of emitting or reflecting
ultra-violet light.

The second point is that the extrusion of this substance from the
medium results in superficial insensibility, although she is in full
possession of all her normal faculties.

Dr. Crawford discusses this point at some length in an article which
appeared in the _Psychic Gazette_ for September 1916. Into the minutiæ
of the discussion I need not enter here. It is sufficient to say that
the medium is to some extent insensitive and that in Dr. Crawford's
opinion "It seems likely that the want of sensibility to heavy and
varied reactions which undoubtedly occur upon the medium is due to some
peculiar condition of her organism during the period of phenomena."

Now, these various experiments although they may be individually weak
do seem rather to hang together. There is an appearance of possible
connection between the experiments of Joire and recent views on the
"aura"; and it is possible that what MacDougal weighed and Baraduc
photographed are the same thing.

It is obvious that all these experiments ought to be checked and
re-checked by independent investigators and further experiments
undertaken to discover whether there is any real connection between
them.

But for the present purpose I think it legitimate to extrapolate and to
assume that they are reliable and connected in the way that I suspect.

The experiments of de Rochas, of Joire and of Kilner suggest that a
temporary loss of sensibility is accompanied by the extrusion from the
body of a sensitive substance of peculiar properties.

In the Baraduc and MacDougal experiments a total and permanent loss of
sensibility seems to be accompanied by the extrusion of a substance of
somewhat similar properties.

Finally in the case of Dr. Crawford's researches we find that the
extrusion of an apparently very similar substance is again accompanied
by a certain insensitivity.

Somewhat similar conditions are to be found in cases of
"materialisation"--compare, for example, the work of Dr.
Schrenk-Notzing and Mme. Bisson or Dr. Geley's paper in
Part I. of the "Annales des Sciences Psychiques" for 1919.

It is far too early yet to say that the extrusion of this sensitive
substance is an invariable concomitant of insensibility; but at
present the evidence--assuming it to be reliable--does seem to point
that way. When we have made an exhaustive study of what happens to
the "aura" during sleep, in various states of hypnosis, in local and
general anæsthesia and in death we shall be able to draw more definite
conclusions on the subject.

I shall now turn to evidence of a more general type which deals with
the existence of this mysterious substance viewed as a whole rather
than with this or that indication of its presence or properties as did
the previous experiments.

There are many references in Psychic literature which bear on the point
and the general trend of them seems to be that the substance we have
been considering is not, normally, entirely formless and distributed
fortuitously through the body but that it forms an exact counterpart of
the latter or, to be more strictly accurate, of the nervous system.

Lombroso states that Durville has succeeded in separating this
"replica" experimentally from the physical body.

  ("After Death--What?").

He says that it seemed to be connected with the body by a sort of cord
and that the patient under observation was able to see through opaque
objects and to discern events at a distance. The apparent sense organs
of the replica worked, while those of the physical body were put out
of action. When approached, it excited a sensation "like that produced
by cold, by blowing air, by shivering," and if the hand were placed
in it a cold, clammy sensation was experienced. Compare with this
last statement the remarks of Crawford on the sensations produced by
inserting the hand into the midst of the levitating structure.

M. Leon Denis in "Christianity and Spiritualism" quotes experiments
from the "Revue Spirite" for November 1894, and alleges that de Rochas
and Barlemont obtained simultaneous photographs of the body of a medium
and of the exteriorised "double."

A long account of experiments on these lines by Durville appears in the
"Journal de Magnetisme" for 1907 and 1908 but although they tend to
confirm the ideas at which we have already arrived, there is nothing to
be gained by going into their details here.

A very interesting case which has a considerable bearing on the subject
is given in the Proceedings of the Society for Psychical Research, Vol.
VIII, pp. 180-193.

The following is an abbreviated account:

The narrator is a physician and the case seems to have been singularly
well attested and was carefully scrutinised by no less a critic than
Dr. R.H. Hodgson.

 "I passed some four hours in all without pulse or perceptible heart
 beat, as I am informed by Dr. S.H. Raynes, who was the only physician
 present. During a portion of this time several of the bystanders
 thought I was dead, and, such a report being carried outside, the
 village church bell was tolled. Dr. Raynes informs me, however, that
 by bringing his eyes close to my face, he could perceive an occasional
 short gasp, so very light as to be hardly perceptible, and that he was
 several times on the point of saying, 'He is dead,' when a gasp would
 occur in time to check him. He thrust a needle deep into the flesh at
 different points from the feet to the hips, but got no response.[5]
 Although I was pulseless for four hours, the state of apparent death
 lasted only about half an hour. I lost, I believe, all power of
 thought or knowledge of existence in absolute unconsciousness. I came
 again into a state of conscious existence, and discovered that I was
 still in the body, but the body and I had no longer any interests in
 common. I looked with astonishment and joy for the first time upon
 myself--the _me_, the real Ego, while the not-me closed upon all
 sides like a sepulchre of clay. With all the interest of a physician
 I beheld the wonders of my bodily anatomy, intimately interwoven with
 which, even tissue for tissue, was I, the living soul of that dead
 body. I realised my condition and calmly reasoned thus: I have died,
 as man terms death, and yet I am as much a man as ever. I am about
 to get out of the body. I watched the interesting process of the
 separation of soul and body. By some power, apparently not my own, the
 Ego was rocked to and fro, laterally as the cradle is rocked, by which
 process its connection with the tissues of the body was broken up.
 After a little while the lateral motions ceased, and along the soles
 of the feet, beginning at the toes, passing rapidly to the heels, I
 felt and heard, as it seemed the snapping of innumerable small cords.
 When this was accomplished, I began slowly to retreat from the feet,
 toward the head, as a rubber cord shortens. I remember reaching the
 hips and saying to myself, 'Now there is no life below the hips.' I
 can recall no memory of passing through the abdomen and chest, but
 recollect distinctly when my whole self was collected in the head,
 when I reflected thus: 'I am all the head now, and I shall soon be
 free.' I passed around the brain as if it were hollow, compressing it
 and its membranes slightly on all sides towards the centre, and peeped
 out between the sutures of the skull, emerging like the flattened
 edges of a bag of membranes! I recollect distinctly how I appeared to
 myself something like a jelly fish as regards colour and form! As I
 emerged, I saw two ladies sitting at my head. I measured the distance
 between the head of my cot and the knees of the lady opposite the head
 and concluded there was room for me to stand, but felt considerable
 embarrassment as I reflected that I was about to emerge naked before
 her, but comforted myself with the thought that in all probability she
 would not see me with her bodily eyes, as I was a spirit. As I emerged
 from the head I floated up laterally like a soap bubble attached to
 the bowl of a pipe, until I at last broke loose from the body and
 fell lightly to the floor, where I slowly rose and expanded to the
 full stature of a man. I seemed to be translucent, of a bluish cast
 and perfectly naked. With a painful sense of embarrassment, I fled
 toward the partially open door to escape the eyes of the two ladies
 whom I was facing, as well as others who I knew were about me, but
 upon reaching the door I found myself clothed, and satisfied upon that
 point, I turned and faced the company. As I turned, my left elbow came
 in contact with the arm of one of two gentlemen, who were standing
 in the door. To my surprise, his arm passed _through_ mine without
 apparent resistance, the several parts closing again without pain, as
 air reunites. I looked quickly up at his face to see if he had noticed
 the contact, but he gave me no sign--only stood and gazed toward the
 couch I had just left. I directed my gaze in the direction of his,
 and saw my dead body. Suddenly I discovered that I was looking at
 the straight seam down the back of my coat. 'How is this, I thought,
 how do I see my back?' and I looked again, to reassure myself, down
 the back of my coat, or down the back of my legs to the very heels.
 I put my hand to my face and felt for my eyes. They were where they
 should be: I thought 'Am I like an owl that I can turn my head half
 way round' I tried the experiment and failed. No! Then it must be
 that, having been out of the body but a few moments, I have yet the
 power to use the eyes of the body, and I turned about and looked back
 in at the open door where I could see the head of my body in a line
 with me. I discovered then a small cord, like a spider's web, running
 from my shoulders back to my body and attaching to it at the base of
 the neck, in front. I was satisfied with the conclusion that by means
 of that cord, I was using the eyes of the body and, turning, walked
 down the street. A small densely black cloud appeared in front of me
 and advanced towards my face. I knew that I was to be stopped. I felt
 the power to move or to think leaving me. My hands fell powerless
 at my side, my shoulders and my head dropped forward and I knew no
 more. Without previous thought and without effort on my part, my
 eyes opened. I looked at my hands and then at the little white cot
 upon which I was lying, and, realising that I was in the body, in
 astonishment and disappointment, I exclaimed; 'What in the world has
 happened to me? Must I die again?..."

Now, if this case stood alone we should, perhaps, be right to explain
it all as a dream. But it does not stand alone for there are numerous
other cases to be found in the Proceedings of the S.P.R. and in Meyer's
"Human Personality." In my opinion, therefore, it merits the most
careful consideration and contains many points of the greatest interest
and significance.

I think it will be found to work in remarkably well with the whole idea
of the detachable quasi-physical replica, towards which hypothesis the
whole of the observations in this chapter have been tending.

The narrator of the experience seems to think that the vehicle which
he observed to become detached from the body and in which he was
apparently functioning throughout the period in question, was actually
the "Soul" itself, the permanent and immortal post-mortem embodiment of
consciousness.

On the whole this seems to be the view taken by Mr. Carrington,
who quotes the case, and to be that commonly held in France on the
authority of MM. Leon Denis, Delanne and other writers. These latter
refer to the organism in question as the "perisprit" and it is
represented as being the vehicle by virtue of which the Consciousness
persists after Death.

With this view I cannot agree.

I suggest rather, provisionally of course, that the Consciousness
persists embodied in a four-dimensional vehicle to which the word
"physical" as commonly understood cannot be applied at all. The
replica, perisprit or "Etheric Double" as the Theosophists call it,
is only the connecting link between the three and four-dimensional
vehicles which, as we saw at the beginning of this chapter, must be
supposed to exist if the four-dimensional hypothesis is to hold good
at all. It seems likely that it is no more permanent than the physical
body, and that it disintegrates after death in the same way that the
bodily tissues do.

It is interesting to compare and contrast this case with the somewhat
similar one of which a brief resumé was given on page 58. In each case
the consciousness of the narrator was separated from the physical body
but the conditions after separation seem to have been notably different.

In the first case the patient seems to have been independent of space
in that he was able to pay a visit to a friend at a distance of about
a thousand miles and to return in the space of a few minutes; while in
the second he seems to have been tethered to his physical body by the
"cord" to which he refers.

This is perhaps the most important point, but others are easy to
find--notably in the apparent constitution of the temporary vehicle of
consciousness.

It seems probable that in the first case the vehicle was
four-dimensional while in the second it was the "quasi-physical
replica" which we have been discussing.

It is with this supposition in mind that I shall examine the second
case.

First then we notice that the narrator seems to have been in error
in referring to what he saw interwoven, tissue for tissue, with the
physical body, as the Ego. But this error was clearly a very natural
one.

Although the point is not brought out with precision, the record seems
to suggest that the narrator was viewing things with that internal or
four-dimensional vision which I discussed in my remarks on Clairvoyance
in Chapter III.

The process which is described as the separation of soul and body,
I should prefer to describe as the exteriorisation of the "Etheric
Double."[6]

As it happens, this exteriorisation does result in the separation of
the Consciousness from the body, but to say that it _is_ the separation
would be liable to confuse the Consciousness and the four-dimensional
vehicle with the Etheric double.

That exteriorisation should begin at the feet is only what one would
expect from the known fact that the extremities are the first parts of
the body to grow cold at the approach of death.

Throughout the account we notice the extreme plasticity of the vehicle
in which the narrator functioned. It seems to have squeezed out of the
body in a formless condition and then to have recovered its normal
shape as soon as the deforming stresses were removed.

This is entirely in accord with the properties we must postulate for a
substance which can, apparently, be moved and shaped by mere volition
or at least by "mental forces," whatever that may mean, set in motion
by the will. At first, that is to say during the process of extrusion,
the Etheric Double seems to have been under the influence of some
repulsive force acting between it and the body. This is admirably
suggested by the analogy of the soap bubble.

When extrusion was complete, however, the E.D. "fell lightly to the
floor." It was therefore composed of more or less ponderable matter,
which is what we would expect from MacDougal's experiments.

The translucency and bluish colour are entirely consonant with the
observations of Kilner on the aura, which, as already mentioned, I
believe to be closely associated with the E.D.

The part about the clothes is curious and I am not prepared to
hazard any explanation about it, beyond a very tentative proposal of
auto-suggested hallucination.

Scarcely less odd is the apparent ability to use both the physical eyes
and those belonging to the E.D.

But the fact that the latter were in operation is concordant with the
observation of Durville that the sense organs of the exteriorised E.D.
were operative in his experiments.

The small cord connecting the E.D. with the physical body is also in
accordance with his observations.

On the whole then I think it fair to claim that this case fits in
admirably with the experimental work I have quoted.

There is one other source of information which may profitably be
considered here, namely the statements of the clairvoyants and of the
Occultists.

I hope that the criticisms which I have been moved to make about the
Occultists in preceding passages have been sufficiently stringent to
clear me of any suspicion of being unduly credulous or over-ready to
accept their statements as authoritative.

There are many things in their methods and their teachings which
excite my distrust and antipathy.

None the less I think it foolish to ignore every statement which
happens to be supported by, or to form part of, Occult doctrine.

I think it highly probable for instance that clairvoyant descriptions
of facts concerning the Etheric Double are often reliable.

We have seen that the whole question of its study is probably a matter
of observing, directly or indirectly, by ultra-violet light. We also
have reason to suppose that the retina of the eye can be rendered
abnormally sensitive to light of this frequency by artificial means.

But if such abnormal retinal sensibility can be induced artificially,
it is very probable that it may sometimes occur naturally.

Hence, if the E.D. actually exists, as the evidence undeniably
suggests, it is not only possible but probable that certain people will
be able to see it without invoking artificial aid.

It must be remembered that observations of this kind contain, in
themselves, no sort of "supernatural" element, although they may, of
course, receive the most strange and erroneous interpretations at the
hands of the uninformed.

When we turn to Occult literature we find that the theory of the E.D.
is worked out in considerable detail. It is said to be violet-grey
or blue-grey in colour and to interpenetrate the physical body. The
"health aura," _i.e._, the physical aura dealt with by Dr. Kilner, is
said to be that part of the E.D. which projects beyond the physical
body.

It is stated that the physical body and the E.D. are not normally
separated during life, although in certain nervous conditions the E.D.
may be more or less extruded from the physical body. (Compare this with
the diagnostic researches of Kilner.)

 "Anæsthetics drive out the greater part of the E.D., so that
 consciousness cannot either affect or be affected by the dense
 (physical) body. In the abnormally organised persons called mediums,
 dislocation of the etheric and dense bodies easily occurs, and
 the E.D., when extruded, largely supplies the physical basis for
 'materialisations' (and for Crawford's structure. W.W.S.)."

 "In sleep, when the consciousness leaves the physical vehicle which
 it uses during waking life, the dense and etheric bodies remain
 together.... At what is called death the etheric double is drawn away
 from its dense counterpart by the escaping consciousness; the magnetic
 tie existing between them during earth life is snapped asunder...."

 (Taken from "The Ancient Wisdom.")

In other passages it is stated that the E.D. is connected with the
physical body by a filamentary structure, "The silver cord," and that
so long as this is unbroken it is possible for connection between
Consciousness and the physical body to be re-established, but that when
it is broken as occurs in death, the separation is final.

Finally it is definitely stated that this E.D. is a quasi-physical
structure, disintegrates in the same way as the physical body and is
perceived by a mere heightening of the ordinary visual faculty.

Let it be clearly understood that I do not wish one whit more
importance to be attached to this last-quoted evidence than each
individual reader may choose to assign to it and I fully sympathise
with those who prefer to allow it no weight at all.

I have myself a strong penchant in favour of good hard scientific
experiments with apparatus and, if the clairvoyant testimony stood by
itself without any experimental evidence to support it, I should make
no mention of it here. But I think that in common justice we ought
to admit that the statements of the clairvoyants are, in the main,
in close agreement with what we should expect from the indications
afforded us by the experimental work which has at present been done.
In continuing the latter we shall be well advised to keep the former in
our minds as furnishing, at least, useful hints for our guidance.

On the strength of the various considerations discussed above, I am
disposed to extend the four dimensional hypothesis as follows:

 "Connection between the three- and four-dimensional vehicles is
 maintained by means of a substance of peculiar properties, which
 is intimately connected with the nervous system in the conscious
 functioning of which it is an essential factor. States of partial or
 total anæsthesia or insensibility are accompanied and probably caused
 by the extrusion of this substance from the body."

We are now faced by the problem of the constitution of this substance.

To this there would appear to be two possible solutions.

The first of these is that favoured, apparently, by the occultists and
the exponents of the "perisprit" doctrine. The second is that to which
I am personally inclined at present.

According to the former of these two hypotheses, the E.D. is composed
of a sort of "rarified matter" by which, I take it, is meant matter
possessing a smaller complexity of organisation than that with which
we are normally acquainted. This would appear to be more especially
the Occult view; although on technical details of this kind there is
a somewhat unfortunate lack of precision and even of unanimity among
Occult authorities.

A variation on this is the idea that whereas ordinary matter is the
result of vibratory, or other periodic, disturbances in the ether of
a certain frequency, the "matter" of which the E.D. is composed is
the result of similar disturbances of a greater frequency; that it is
matter transposed into a higher key so to speak.

The experiments of Le Bon, who claims to have obtained a temporary
condition of equilibrium in the dissociation products of matter, are
sometimes adduced as supporting this hypothesis.

For my part I have grave doubts as to the correctness of this view.

In the first place, there is nothing in Le Bon's work to indicate
that these dissociation products are capable of being brought into
a state of such very stable equilibrium as must be possessed by the
constituents of the E.D.

In the second, the hypothesis involves us in all the difficulties
which render so unsatisfactory all attempts to account for post-mortem
existence on normal physical lines.

For, on either hypothesis, the E.D. is either the post-mortem vehicle
itself, as held by the French savants, or it is the connecting link
between the two vehicles, as I consider.

If the latter is the case, then in all probability the post-mortem
vehicle is to the E.D. as the E.D. is to the physical body. If the E.D.
is merely rarified matter then the post-mortem vehicle is probably
merely doubly-rarified matter.

For this and other reasons I prefer the idea that the E.D. is composed
of matter having an abnormal four-dimensional complexity.

Indeed, as I pointed out at the beginning of this chapter, this view
seems to be a necessary corollary of the whole four-dimensional
hypothesis I have been advocating.

It is very possible that we shall be compelled to reject the hypothesis
_in toto_ in the light of future research, but until this becomes
necessary I think that my present view of the nature of the E.D. is the
only tenable one.

Whether this abnormal four-dimensional complexity is molecular or
atomic in its nature, or whether it is neither, I am not prepared to
say.

The points in this chapter which I would wish to emphasise are, first,
that if the four-dimensional hypothesis be true, there should exist a
connection between the three- and four-dimensional vehicles.

Secondly, that this link should possess properties of a peculiar nature
distinguishing it from ordinary physical substances.

Thirdly, that there are distinct evidences to be found in very
independent quarters which strongly indicate that such a connecting
link or substance does in fact exist.

Fourthly, that this substance does present unusual features, as for
instance, susceptibility to volitional control and to forces which
appear to be applied from some direction unknown to us (vide my remarks
on the theory of Crawford's structure in Chapter III).

Finally, that, as it appears to be intermediate between the physical
body and the post-mortem vehicle, it is well worthy of the closest
study.

It will be very evident to my readers that this chapter is
"extrapolatory" and speculative in the highest degree. The ideas
discussed are based on experiments which are very far from being
conclusive. I should be sorry indeed to guarantee them all as being of
cast-iron reliability and I have no doubt that comparatively few will
ever receive the amount of confirmation which is necessary before we
can accept such things as proven facts.

Still, tenuous as the evidence is, it all seems to point in the same
sort of direction and I have therefore thought it worth while to give
it the benefit of the doubt and see what could be made of it on the
temporary assumption that it is really reliable.

FOOTNOTES:

[Footnote 5: Note the insensibility.--W.W.S.]

[Footnote 6: NOTE.--In future I shall borrow the term "Etheric Double"
from the Theosophists and use it instead of the rather cumbrous phrase
"Quasi-physical replica." I do not think that the term Etheric Double
is a good one, but it is in common use, and I will adopt it until some
better word is suggested.]




CHAPTER VIII

THE RELIGIOUS ASPECTS OF THE HYPOTHESIS


Although I have no wish to become involved in controversial theology,
I feel it incumbent on me to examine briefly the question of whether a
general acceptance of the four-dimensional hypothesis would be fraught
with any considerable consequences in the sphere of religious thought.

No one venturing to advocate conceptions so far-reaching as those I
have been discussing, would be justified in ignoring their relation to
any important stream of thought with which they might be held liable
to come in contact. And it is evident that any hypothesis formulated,
however tentatively, as a solution to the problems of Survival of Death
and the nature of post-mortem conditions, must inevitably come into
very close contact with Religion.

I shall try to show that it is a matter of contact only and not of
conflict.

Even so, I might have omitted the present discussion had I not found a
tendency, on the part of certain representatives of orthodox theology,
to deprecate any attempt to find an intelligible solution to the
problems involved.

It must be clearly understood that I am not concerned here with the
defence of Psychical Research as a means of investigation, but only
with the legitimacy of the end.

Generally speaking, those with whom I am so unfortunate as to disagree
on this matter accuse me on two counts.

First it is suggested that I am attempting to advance by Reason or
Sight rather than by Faith and, secondly, I am told that to "explain"
such a matter as the Survival of Death or the nature of the connection
between matter and spirit, would tend to reduce everything to terms of
mere mechanism and to leave no place at all in the Cosmos for Divine
Will and Purpose or for the transcendental and mystical aspects of
religion.

I need hardly say that I violently resent both these accusations.

The first charge seems to me to be easy of refutation.

In the first place the idea of "Blind Faith" or "Unreasoning Belief" is
one which involves a contradiction in terms.

As Whately well says in his "Logic":

 "If a man resolves that he will implicitly receive _e.g._, in
 religious points, all the decisions of a certain Pastor, Church or
 Party, he has in doing so performed one act of private judgment
 (_i.e._, the result of reasoning), which includes all the rest."

Hence it is impossible to dissociate Faith and Reason.

Secondly, just as Courage, in its proper sense, does not mean feeling
no fear but the overcoming of it; so Faith consists, not of having no
doubts but of dispelling them, and this involves a deliberate exercise
of the will in choosing between two possible alternatives; that is to
say, an act of reasoning.

Thirdly, I submit that Life is not a sort of crazy competition in which
special awards are to be received for completing the course blindfold,
but a phase in the general upward progress of man--whether considered
collectively or individually--and that consequently any knowledge
is desirable which will enable us consciously and intelligently to
co-operate in the process.

Finally, and I think that this puts the whole matter in one sentence,
however clearly a man can see, he must still be able to believe his
eyes.

However plainly we can see the path, we must still believe that it
leads in the right direction, however conclusively we may demonstrate
a proposition, we are still dependent on our Faith in the validity of
Reason and the veridicity of the observations on which it is based--and
this is equally the case whether the latter be scientific measurements
or spiritual experiences.

The supreme effort of Faith, made by the most material of scientists no
less than by the Saint, is the belief that the Cosmos, of which Reason
is a part, is a coherent whole and not a Chaos.

The second argument appears to me to be equally fissiparous.

In the first place I should never dream of attempting to reduce the
whole Cosmos to terms of mechanism.

Any such idea would be infinitely repugnant to me. Moreover, the
attempt would inevitably be foredoomed to failure since there are
problems which are essentially insoluble. The first and most obvious of
all--the problem of the nature and origin of Consciousness--is one to
which we can never hope to find an answer.

But quite apart from all this I entirely fail to see why the
explanation of mechanism, using the word in its widest sense, should
have any bearing on religion at all.

Religion, by which I mean something more than a mere code of morals, is
concerned rather with motives than with methods.

If a child were to ask one why the sun and moon did not fall on to the
earth, one might reply to the effect that they were prevented from
doing so by the exercise of the Divine Will. Alternatively one might
embark on a disquisition about the law of gravitation and planetary
mechanics.

The two forms of explanation would be by no means mutually exclusive
since the second does no more than expand the first by an exposition of
the means employed.

If, as required by the Christian religion, we believe in the survival
of the individual personality after death, it is evident that this
survival must take place by virtue of certain properties inherent in
the Cosmos and the necessity of Faith in our ultimate destiny will not
be affected by any determination of the nature of those properties.

If our Consciousness does in fact persist after death it must do
so in some state of embodiment, since the idea of pure essence is
inconceivable.

For my part I utterly fail to understand why the study of the nature of
the vehicle in which the consciousness functions after death, or of the
conditions in which it lives, has any more to do with religion, in the
proper sense of the term, than the study of the physical body and the
physical world.

I need hardly say that I do not anticipate that Psychic Research will
confirm the idea of the old-fashioned conventional Heaven and Hell
of harps and crowns on the one hand and fire and brimstone on the
other. But it would be a bold person who would be prepared to maintain
now-a-days that these ideas form an integral part of Christianity.

Modern research on Evolution and the process of natural selection have
somewhat notably discounted the story of Adam and Eve in the garden
of Eden, considered as historical fact. But it would be difficult to
maintain that the Christian religion has suffered as a consequence.

The account of the creation given in Genesis has had to be
re-interpreted in the light of geological and astronomical knowledge,
but Christianity is as vital a force in the world to-day as it was when
that account was taken literally word for word.

Even so, if any specific revelation existed on the subject of the
manner of survival, if, for instance, any of the words of Christ could
be held to contain any precise information on the subject, it might be
contended that no further knowledge was necessary. But this is not the
case.

Immortality is insisted on, but nothing specific is said of the
conditions by virtue of which it obtains. Nor, so far as I am aware, is
any veto laid on endeavours to ascertain those conditions.

I repeat that in my opinion, cosmic mechanism and religion are
distinct, and no knowledge, however full, as to the former can possibly
either impair or replace the latter.

In short I do not see that the necessity for religion as an integral
part of life would be one whit diminished even supposing we knew as
much about the "next world" and conditions of life therein, as we know
of this.

And this contention holds good no matter what results research
may bring to light, no matter how much they may differ from our
preconceived ideas.

For the truth is there all the time although at the moment we may not
have grasped it and the Christian religion, if it be the true religion,
as we believe, was framed, so to speak, to meet the needs of a cosmos
organised in this particular way and in no other.

Unless, therefore, the Christian religion be false, it is impossible
that the results of research, supposing them to be accurate and
reliable,--a matter which can only be ensured by the exercise of
scientific reason,--should in any way conflict with religious truth.

In case any one should feel that I ought to specify more precisely than
I have done, what I mean by the Christian religion, I would refer them
to the Nicene creed. Or if it is a matter of the interpretation of this
in terms of conduct, I should cite "My duty towards God" and "My duty
towards my neighbour" in the Church Catechism. Or in secular writings I
would mention that view of Christianity which is defended by Mr. G.K.
Chesterton in his book "Orthodoxy."

With these I am prepared to stand four-square, although it is
conceivable that I might find myself at variance with some authorities
on the precise interpretation to be given to certain clauses, as for
instance "the resurrection of the dead" in the first mentioned.

But controversies about interpretation have been rife among Christian
theorists from the earliest times and differences of opinion on minor
points do not constitute lack of adherence in fundamentals.

Hitherto in this discussion I have been concerned only with negatives.
That is to say I have been trying to show that there is nothing in the
attempt which has led me to adopt the four-dimensional hypothesis which
is in any way contrary to the essential teachings of Christianity.

There is however a positive side to the question.

I believe that so far from being antagonistic to Christian teaching,
the general acceptance of the hypothesis would be of real value, in
that it would put into the hands of the Church a very powerful weapon
for the repelling of a certain form of attack, that of the scientific
materialist to wit.

I do not mean to claim this as a merit of the four-dimensional
hypothesis as such, for it would equally accrue to any other hypothesis
which might prove to be true.

In the second chapter I gave my reasons for believing that the
establishing of some such hypothesis would be calculated to remove the
principle cause of dissension between religious and materialistically
scientific thinkers. I there pointed out that the chief strength of the
materialist lay in the reluctance or inability of the Church to give
an intelligible explanation of the terms used in speaking of certain
religious and spiritual matters.

I have explained that I see nothing in anyway repugnant to religion in
the attempt to formulate an hypothesis to explain the mechanism of
survival, etc.

Equally it should be observed that religion, considered as something
more than a mere ethical and moral code, would be in no way freed from
the necessity of justifying itself, _qua_ religion, by the acceptance,
however unanimous, of this or any other hypothesis. Such justification
is a matter for an apologetic of quite another order, of which order,
by the way, I regard Mr. Chesterton's "Orthodoxy" mentioned above as a
very admirable example.

What the general acceptance of such an hypothesis would do, would be
finally and for ever to deprive the materialist of the possibility
of maintaining that matter, as he knows it, is the final and only
permanent reality and that Spirit therefore cannot exist.

It is true that this would only involve driving him back one stage. If
we suppose for the sake of argument that we could finally attain to as
complete a knowledge of the "next world" as we at present possess of
this, he could always return to the attack, using with regard to that
state the same arguments as he originally used with regard to this. But
having once broken through the ring fence of matter and demonstrated
that there exist other realities of which he was at one time entirely
ignorant, he could never deny that there might still be realms as yet
unknown to him. He could never catch us again, so to speak.

I admit that the above is a somewhat fantastical supposition and
scarcely within the sphere of practical politics, but the point is,
that until we are prepared to give an intelligible explanation of
things we are pent up in a sort of intellectual _cul-de-sac_ bounded by
matter. We may know, as the result of personal experience, that there
is a way out, that matter is not the only reality; but our knowledge is
a purely personal affair and the scientist is perfectly entitled, if he
wishes, to decline to take the steps that led to the experiences which
have convinced us, to dismiss them as mere hallucinations and to write
off our alleged "revelations" as superstitious myths.

But let us once demonstrate to him, in a manner calculated to appeal
to his intellect, that there may be a non-material reality and the
_cul-de-sac_ is at once broken through and becomes a vista.

It may be one of which we cannot see the end, and we shall certainly
require faith to believe that it leads to the right destination, but
the point is that it _is_ a vista and not a _cul-de-sac_.

This is where I am convinced that the adoption of some hypothesis of
the same general order as that which I have been advocating would
prove of definite value to the Church and that is why I am so strongly
of opinion that the Church, by which term I mean more especially those
whose business it is to concern themselves with the general trend
of Christian policy with regard to contemporary thought, ought to
encourage and not to deprecate or oppose attempts on these lines.

In thus venturing to criticise the Church, I should like to make it
clear that I only do so because I am convinced that the Church is a
vital and indispensable part of human life, and because I wish to see
her influence increased and extended rather than diminished. If I
thought otherwise I should not take the trouble even to criticise.

So far I have said nothing about the religious significance of the
four-dimensional hypothesis as such; considered that is to say as to
its four-dimensionality and not merely in its capacity as a hypothesis.

The reason for this omission is simply that I do not consider that
there is any such significance.

In the main concept of existence in four-dimensional space after death
there is, so far as I can see, nothing either to contradict or to
confirm anything taught by the Church except the bare fact of survival
which both affirm.

I have carefully omitted all reference to the descriptions of
post-mortem existence which have been obtained from time to time
through mediumistic sources. Any such discussion would be both lengthy
and out of place as it would involve a detailed critical examination of
both the authenticity and interpretation of the pronouncements.

The only point about the four-dimensional hypothesis as such which I
think at all likely to be called in question from the religious point
of view, is that involved in the suggestion that Consciousness persists
after death, not in the form of "pure essence" but embodied in some
form of vehicle.

But this is a matter which is fully included under the general
arguments I adduced in favour of the legitimacy of investigating the
"Cosmic mechanism" to the utmost and there seems to be no need for a
separate re-discussion here.

It is interesting to note however that a large number of the early
Christian thinkers adhered to the view that "the soul" had some
sort of material or quasi-material vehicle. A number of quotations
on the subject are given in M. Leon Denis' book "Christianity and
Spiritualism."




CHAPTER IX

SUMMARY AND CONCLUSION


I will bring this work to a close by a brief recapitulation of its more
salient points.

A dimension is defined as "an independent direction in space." A flat
surface is two-dimensional and the space we know is three-dimensional.
The direction of the fourth dimension must be at right angles to every
direction which can be drawn in our space and four-dimensional space is
such that through any point in it, four, and only four, lines can be
drawn mutually at right angles.

From every point in our space a line can be drawn running off in the
direction of four space.

Consequently every point in our space is absolutely accessible from the
direction of the fourth dimension.

The best way of drawing conclusions as to the properties of four space
is by means of the analogy of the two-dimensional world; since four
space is to three space as the latter is to two space.

The fact that we cannot perceive four space, or picture its nature to
ourselves, is no proof that it is non-existent.

I suggest as a working hypothesis that four space is a reality and
that Man possesses at least one other vehicle of Consciousness--a
four-dimensional one--besides his physical body. In this vehicle he is
embodied after discarding the physical vehicle at death and also during
temporary absences from the body during life.

This hypothesis is likely to prove of importance in two respects.
First, it provides Psychic Research with a working hypothesis which may
be essential to its development as a science. Secondly the adoption of
some such hypothesis should go far to remove the principle cause of
recent cleavage between Religious and Scientific thought.

The hypothesis is capable of throwing light on a number of "Psychic"
phenomena which are otherwise very obscure. It affords us a means of
conceiving a mode of existence which is real and yet imperceptible to
our senses, thus surmounting one of the chief difficulties in the way
of conceiving of post-mortem existence.

In the realm of Clairvoyance it enables us to form some idea of the
nature of the faculty of internal vision. With regard to Clairvoyance
in space, it also helps us to some slight extent, although this
phenomenon presents special difficulties of its own.

Other varieties of "out of the body" experiences are much elucidated by
its aid.

The phenomena with which it is most closely connected, however, are
those known under the general title of "apparent penetration of matter
by matter."

To these it affords by far the simplest and probably the only
explanation and, if they are regarded as irrefutably established, it
will be difficult to avoid the conclusion that four space is a reality.

The _locus classicus_ of such phenomena is the Slade-Zöllner
investigation, but this is worthless as evidence. The literature of the
subject abounds with records of similar occurrences.

The hypothesis also seems to offer a possible means of explaining the
paradoxical rigidity of the impalpable structure discovered by Crawford.

The hypothesis may also have a certain significance, even in the realm
of pure Philosophy. It enables us to conceive of the simultaneous
existence of a series of three space simultaneities and, consequently,
is of interest in the consideration of Time and of the possibility of
Prevision.

It also works in well with a certain view of the nature of Vitality.

As regards its relation to ordinary physical science, we find nothing
to conflict with it, but, on the contrary that there are a certain
number of indications that four space is, as I suggest, more than a
mere mathematical concept. It is possible that it may some day come to
be recognised as having some significance in the theory of the nature
of electrons and of ether, while recent views on "Relativity" strongly
indicate that Physicists will soon regard the four-dimensionality of
the Universe as a common place.

       *       *       *       *       *

If the four-dimensional hypothesis is correct there should exist
some sort of connecting link between the physical body and the
four-dimensional vehicle.

The function of this link would be to deflect sensory impressions
out of three space into four space thus enabling them to reach the
Consciousness resident in the latter. Such a link must therefore be,
in some way, intermediate between ordinary matter and four-dimensional
matter.

That is to say, it must possess some degree of four-dimensional
complexity. This may reasonably be supposed to endow it with peculiar
properties.

If such a connecting link be found to exist in practice, it would tend
to confirm the hypothesis.

The experiments of de Rochas, of Joire, of MacDougal, of Baraduc, of
Kilner, and of Crawford seem to indicate that such a connecting link
does, in fact, exist.

This is confirmed by the testimony of clairvoyants, which, though not
of a nature to be rated too highly or accepted lightly, should be
allowed some weight.

The attempt to formulate an hypothesis of this nature is not repugnant
to Religion. Nor is there anything in this particular hypothesis which
can be held to conflict with Religious doctrines.

On the other hand, the acceptance of such an hypothesis would cut the
ground from under the feet of those who seek to maintain that matter is
the only reality and that therefore Spirit and the Spiritual life are
mere illusions.

       *       *       *       *       *

No writer can expect to bring all his readers to his way of thinking.
Indeed it would be unfortunate if he were to do so, as the effect
would be to eliminate that element of critical discussion which is so
fruitful a source of progress.

Consequently, I do not anticipate that every reader will agree with
me. All I venture to hope is that I may have made good my contention
that the four-dimensional concepts, in spite of the scorn poured on
them as a result of the Zöllner fiasco, are worthy of very careful
consideration as a tentative working hypothesis by those who are
seeking to clear up the many obscure problems presented by Psychical
Research.

If this little book is thought worthy of criticism, I shall welcome
it. Its purpose will have been amply served if it succeeds in arousing
interest in what will prove, I believe, a very fruitful field of
speculation and research.




APPENDIX.


To illustrate how the analogy of the relation between two and
three-dimensional space enables us to determine some of the properties
of four-dimensional figures:


(1)

 "Any figure in a space of a given dimensionality generates a
 corresponding figure in the next higher space, by moving in a
 direction at right angles to any direction that can be drawn within
 itself.[7] Or, in general, space of any dimensionality generates, by
 such a movement, the next higher space."

Thus, the lowest sort of space is space of zero dimensions, _i.e._,
a mathematical point. If it moves a distance of one inch, it traces
out a Line one inch long--that is to say a one space "figure." If
this moves at right angles to itself for a distance of one inch, it
traces out a two space figure, viz., a square of side one inch. If this
again moves a distance of one inch in a direction at right angles to
every direction that can be drawn within it, that is, in a direction
perpendicular to itself, it traces out a cube of side one inch, _i.e._,
a three space figure or "solid."

We must, therefore, conclude, from analogy, that if the cube were
itself to move, a distance of one inch, in a direction at right angles
to every direction that can be drawn in our space--in the unknown
direction, that is, of the fourth dimension--it would generate a
"higher solid" of side one inch. The higher solid thus generated is
called a "Tesseract" and its properties are quite well known.


(2)

 "Every figure, in a space of a given dimensionality, contains an
 infinite number of the 'corresponding' figures--see (1)--in the next
 lower space."

Since a point is defined as having "position but no magnitude," it
follows that it would require an infinite number of points to make up a
line.

Similarly a line has length, but no breadth or thickness, and it would
therefore require an infinite number of lines laid side by side to make
up a surface.

Again a surface has, theoretically, no thickness, and it would
therefore require an infinite number of surfaces superimposed on one
another to make up a solid.

We must therefore conclude, by analogy, that it would require an
infinite number of solids to make up a "higher solid."

In particular, a Tesseract must be supposed to contain an infinite
number of cubes, and, in general, four space must be conceived of as
containing an infinite number of three spaces.


(3)

 "The Boundaries of a figure in a space of any dimensionality are
 themselves figures in the next lower space."

Thus a Line (one space) is bounded by Points (zero space).

A surface (two space) is bounded by Lines (one space).

A solid (three space) is bounded by Surfaces (two space).

We must conclude therefore that "higher solids" (four space) are
bounded by Solids (three space).

[Illustration: _Fig. 10_]

To take the special case with which we are already familiar. The line
AB, is bounded by the points A and B. (Fig. 10). The square, A B C D,
is bounded by four lines AB, BC, CD, DA. The cube, A B C D E F G H, is
bounded by six surfaces, namely, ABCD, CDEF, EFGH, GHAB, ADEH, BCFG.

Similarly we must conclude that a tesseract is bounded by cubes.

We shall see later that there are eight of them.


(4)

We may put (3) in a slightly different way, by saying that:

 "Two adjacent portions of space, of any dimensionality, are separated
 by a space of the next lower dimensionality."

The portions AB and BC of the line AC are separated by the point B.
(Fig. 11.) The portions ABEF and BCDE of the fig. ACDF are separated by
the line EB. The portions ABEFGHIM and BCDEMIKL of the solid ACDFGHKL
are separated by the surface BIME.

[Illustration: _Fig. 11_]

Similarly we must suppose that any two adjacent portions of four space
are separated by a three space figure.

Or, again, to alter it slightly, "any space is no more than a boundary
between two adjacent portions of the next higher space." Whence it
follows that the whole of our three space is but the boundary between
two adjacent portions of four space.


(5)

 "A tesseract, which is the four-dimensional analogue of the cube,
 is bounded by Eight cubes. It has Twenty-four plane square faces,
 Thirty-two linear edges, and Sixteen corner points."

This may at first sight seem difficult to grasp.

In reality however, it is quite simple.

We have only to remember that the tesseract is generated by the
movement of a cube, in a direction at right angles to every direction
that can be drawn in the cube, and that whenever a figure of a given
dimensionality moves thus it generates a figure of the next higher
dimensionality.

Thus every point in the cube will trace out a line, every line a
surface, and every surface a solid, and, since the distance moved is
equal to the length of the side of the cube, these surfaces will be
squares and the solids will be cubes.

But let us first consider the analogous case of the generation of the
cube by the movement of a square.

Let A B C D represent the original position of the square. It moves,
a distance equal to one of its sides, in a direction at right angles
to every direction that can be drawn within itself--at right angles,
_i.e._, to every one of its sides--and finally comes to rest in the
position E F G H.

[Illustration: _Fig. 12_]

Every side has traced out another square and we have, in addition, the
old square ABCD, with which we started and the new square EFGH, with
which we end.

Thus even if we had no idea how many sides, edges, and corners a cube
had we could deduce them.

We should say:--

Every side of the original square has traced out a new square--that
makes 4--and we also have the original square and the "final" square
making a total of 6. A cube, therefore, must be bounded by 6 square
surfaces.

Similarly we should reflect that the original square and the final
square have each 4 linear edges, making 8, and that each of the 4
corner points of the original square would trace out a line, making new
lines, and we would therefore conclude that a cube must have 8 + 4 = 12
edges.

Finally, since in a uniform motion no new points will be generated, we
should expect the cube to have a total of 8 corner points, _i.e._, the
four corners of the original square and the four corners of the final
square.

Now let us apply the same methods to the generation of the tesseract by
the movement of a cube.

Observe that just as in the case of the square generating the cube we
had the original square to start with and what I called the "final"
square to end up with, so, in this case, we shall start and end up with
a cube.

In the process of the movement every face of the cube will generate
a new cube--that means 6 new cubes, since the cube must have had 6
faces--and there will also be the original cube and the final cube,
making a total of 8 cubes all told. A tesseract must therefore be
bounded by 8 cubes.

Similarly each line of the original cube will trace out a square.
This, since a cube has 12 edges, gives us 12 new squares plus 6 from
the original and 6 from the final cube, or a total of 24. A tesseract
therefore has 24 plane square faces. Again each point of the original
cube will trace out a line, making 8 new lines, and there will also be
12 lines in the original and 12 in the final cube, making a total of 32.

Finally, there will be 8 points in the original cube and 8 in the final
cube, but none will have been produced on the way. So a tesseract will
therefore have 16 corner points.

There is no reason why this process should not be continued
indefinitely. For a tesseract may be supposed to move, in distance
equal to the length of one of its edges, in a direction not contained
in itself and will generate a _five_ dimensional figure, bounded by
ten tesseracts, and having in it 40 cubes, 80 squares, 80 lines, and
32 corner points. Thus a whole series of Higher Space figures may be
produced. But these are of little practical interest, and I shall not
deal with them here.

FOOTNOTES:

[Footnote 7: NOTE.--The figures thus produced are not necessarily the
strict analogues of the figures which generate them. For instance a
circle, moving in a direction perpendicular to itself, would generate
a cylinder; whereas the three-dimensional analogue of a circle is a
sphere.]


  E. AUSTIN AND SON, LTD.,

  PRINTERS,

  --  CLIFTON, BRISTOL.  --




INDEX


  Anæsthesia, 146, 147

  Apologetics, Christian, 177

  Apport.
    Two-dimensional analogue of, 15, 16
    Discussion of evidence for, 62, 73 sqq.

  Astral plane, 35, 53

  Aura, 142, 143, 161


  Cantilever, Crawford's, 86-91, 145

  Carrington, Hereward, 71, 74, 77, 113-141

  Change--in a two dimensional world, 17, 20

  Clairvoyance, 42, 48

  Crawford, 86, 145, 147


  Death. Loss of weight at, 143

  Dimension. Definition of, 3

  Direct Voice, 62

  Disembodiment, cases of, 58, 150-154

  Dreams, 54, 55

  Electricity. Hinton's theories of, 127

  Etheric double, 35, 62, 147-148

  Energy, conservation of, 117, 120

  Ether. Hinton's analogy, 127

  Exteriorisation of Sensibility, 141


  Faith and Reason, 169

  Fatalism, 107-109

  Flatland, 7


  Geometry. Possible break down of, 124, 126


  Hair-trigger theory, 116, 141

  Hallucination, 50, 51

  Hypothesis. Need of, 24-38
    Valid, 29
    True, 29

  Hyslop, Dr., 77


  Internal Vision, 46-49


  Kilner, Dr., 142-143


  Levitation, 86, 91, 145

  Light. Theories, of 29, 30


  Materialists, 32, 176, 177

  Milan Committee, 83


  Occultists 32, 34

  One-dimensional space, 7


  Palladino, Eusapia, 74, 83

  Parallaxes, Negative, 126

  Peters, Dr., 83

  Phantasms, 52, 55, 57

  Pogorelsky, 84

  Poincaré, 124

  Postvision, 42, 52

  Prevision, 39, 42, 52, 103-107

  Psycho-analysis, 55


  Reason and Faith, 169

  Reichenbach, 140

  Relativity, 133-135

  Religion, 32, 168-180

  Richet, 31

  Rotation in four space, 129


  Sambor, 84

  Secondary personality, 41

  Sensibility. Exteriorisation of, 141

  Slade, 64, 73 sqq.

  Space. Objectivity of, 109-112

  Spectrum, 43

  Symmetry, 131-133


  Telekinesis, 39, 86

  Telepathy, 39, 41

  Television, 46, 48, 111

  Tesseract, 188, 189, 191

  Theologians, 32

  Theosophists, 35, 159, 160

  Time, 92-103
    Measurement of, 94
    Bergson's views on, 96, 98
    Subjective, 99

  Two-dimensional world, analogy of, 7 sqq.


  Ultra-violet light, 43, 144, 160


  Vitality, 113-141

  Vortices. Four-dimensional, 127


  Will, 113-141


  Zero-dimensional space, 7

  Zöllner, 1, 62, 73 sqq.

*** END OF THE PROJECT GUTENBERG EBOOK 64055 ***