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.