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.