SOME OTHER POSSIBLE APPLICATIONS OF THE HYPOTHESIS
In this chapter I propose to deal first with the questions of Time and
prevision and in the next to show how the higher space ideas help us to
clear up certain difficulties in connection with Vitality and Will.
The question of the nature of time is one which brings us into close
contact with Philosophic and Metaphysical thought and one is apt to
find oneself in very deep waters indeed. Still I think it is possible
to show how the higher space ideas come in without involving myself in
controversial statements. I shall leave it to others to decide whether,
as I am inclined to suspect, the acceptance of higher space concepts as
actualities would provide Metaphysicians with a somewhat new field of
speculation or modified methods of expression.
It has been suggested by some writers that "the fourth dimension is
time."
At first sight this definition would seem to conflict with our original
statement that it is an unknown direction in space at right angles
to every direction which we can find. But, as a matter of fact there
is a certain amount to be said for the idea. It might be pointed
out, for instance that for an object to exist at all it must possess
some "extension" in time. It must, that is to say, not only possess
a certain length and breadth and thickness but must also exist for a
certain time. Otherwise it simply does not exist. Then, again, if we
were able to "travel" in time we might fairly claim to be travelling in
a previously unknown direction, different that is from any direction at
present known to us.
Moreover, as I showed at the end of the first chapter, changes in
our space could be accounted for by supposing them to represent
our perception of a series of parallel sections made by our
three-dimensional space cutting an assemblage of suitably shaped and
arranged four-dimensional solids. It is here that I think we find a
clue which may perhaps be relevant to the present discussion.
I am far from being prepared to say that the fourth dimension _is_ time
because I doubt whether time as commonly understood is an "absolute"
thing. It seems to me to be rather a limitation of our finite
consciousness.
In the Divine Consciousness which I take to be alone Absolute there can
be, surely, no Past or Future; all must be comprehended in the Eternal
Now.
But I do think it possible that if we were not limited to three
dimensions in thought and experience we might be able greatly to modify
our present conceptions of time and to understand many things with
regard to it which at present appear obscure.
Let us start by considering for a moment our ordinary idea of "Time."
To start with we associate it with clocks and next, if we go a step
further back, with the movement of the earth relative to the sun and
stars. A clock is merely a mechanical device for subdividing into equal
parts of suitable size the intervals between successive recurrences of
certain astronomical events. In fact our ordinary ideas of time are
determined by a wholly fortuitous arrangement of the component parts of
the Solar System. If the masses etc. were other than they are, our day
and year would be altered accordingly. It is quite conceivable that in
some highly complex system of several "suns" moving under the influence
of their mutual attractions and attended each by its own sub-system
of satellites, there might be a world from which all the observable
astronomical phenomena would be so complicated that its inhabitants
could detect no regularity in them at all.
If, for instance, any given astronomical grouping of the observable
bodies only recurred once in a hundred generations of the inhabitants,
the measurement of time from astronomical data would be scarcely
practicable.
A similar state of things would result if the average life of a man on
earth lasted about ten minutes.
Again we know that the regularity of the changes in our system is
really only apparent, for all the motions by which we habitually
measure time are gradually altering under the influence of tidal
friction.
So we see that all our ordinary ideas of time are based on the
fissiparous assumption that certain distributions of matter will occur
regularly; that is to say in such a manner that if we could observe any
two successive cycles simultaneously they would appear coincident.
The same can be shown to apply to any other system of time measurement
which we can substitute for the observation of astronomical phenomena.
This is so because, apart from all other reasons, every conceivable
method must be based on the assumption that the properties of matter
are invariable. But these seem to be functions of the properties of
ether and since the solar system is certainly, and the whole universe
probably, moving through ether-filled space, this means that our
methods of time measurement must ultimately be based on the assumption
that the ether is homogeneous.
Very probably it is; but there is no reason why it should be--on _a
priori_ grounds.
Now M. Bergson has been at pains to discriminate between this time "of
succession" which we know and true time--the time "of duration." His
view, as I understand it, is that the succession of events or "spatial
simultaneities" by which we _measure_ time no more _is_ time than the
succession of marks on a foot-rule _is_ the material which we measure
with it.
What we actually experience as time does not necessarily correspond
with the spatial recurrences which measure it.
We all of us say, when we are bored, that "the time passed slowly" or,
when we are happy and amused, that "the time flew" and although this
may appear at first sight to be no more than a loose way of speaking I
think that there is more in it than that. It is here, in fact, that we
find what I can only call a "check" on the measurement of time.
It is the apprehension of something capable of undergoing change, of
Psychic states to wit, whose changes are yet totally independent of
the spatial changes by which we ordinarily measure time. A man who is
hanging by a frayed rope over a precipice waiting for someone to come
and rescue him might very likely say that "It seemed hours" although it
might really have been no more than a very few minutes.
Yet in one sense he might be speaking the literal truth. The changes
which took place in his mental states during those few minutes might
well be as complex and extensive as those he would normally experience
in the course of hours.
This should suffice to make clear the difference between the "real time
process" which we measure and the recurrence of spatial simultaneities
by which we measure it.
If we consider the latter alone we soon find that they are difficult
of comprehension. As Mr. Lindsay says in his book "The Philosophy of
Bergson," p. 128.
"If we eliminate real time altogether we get a number of
simultaneities whose relation to each other we cannot understand....
For the relation between the simultaneities is taken to be that of
the parts to the whole, but ... that is itself a simultaneity ...
the relation of the simultaneities which are now taken as in their
aggregate constituting change must be conceived of as necessary, as
somehow all existing at once."
And again:
"We can only understand change by realising that it is incapable of
spatial expression...."
This quotation seems to me to be important because it brings out
clearly the points with regard to which I think that the higher space
hypothesis may be important.
For although I am entirely in accord with the idea that there are, so
to speak, two sorts of time I feel that in the light of the hypothesis
we cannot allow the statement that "change is something which is
incapable of spatial expression" to pass unchallenged.
If it were put in the form, "material change is incapable of expression
in terms of space of three dimensions," I should have nothing to say.
But in the course of my remarks on the phenomena of change in
a two-dimensional world, I pointed out that it is possible to
integrate an infinite number of three-spatial simultaneities into a
four-dimensional whole.
The introduction of this concept seems to me calculated to modify the
whole aspect of the question.
For, by its light, we see that all the three-spatial simultaneities by
which we mark time _can_ exist at once.
They can do so because the arrangement of material particles which
constitutes a given simultaneity may be regarded, if we so wish, as a
thin section of a four dimensional solid.
We can say, then, that there are two sorts of time.
First there is ordinary Physical "time" which is measured by the
recurrence of three-spatial simultaneities and this, if we choose, may
be regarded as produced by the passage across our space of something
which has extension in four dimensions.
Secondly, there is what I am inclined to call Subjective time,
consisting of changes in Psychic states; and which may be regarded,
provisionally, as being perceived by virtue of changes in "objects,"
including the vehicles of our own consciousnesses, in space of four
dimensions, or, at any rate, in space of a dimensionality higher than
three.
I do not mean the foregoing remarks to be taken too literally for I do
not regard three-dimensional change as produced by the passage across
our space of actual four-dimensional solids. This seems to me to be
altogether too crude an idea and was only introduced to bring out my
point that three-dimensional change is _capable of expression_ in terms
of four space.
Whether it is solely a phenomenon of consciousness or whether there may
be something in the nature of four-dimensional "lines of force" which
cut three-dimensional space and determine material distributions I am
not at all prepared even to surmise.
A side light on this matter of the two sorts of time is given by the
phenomena of time in dreams. It is well known that we may be awakened
by a noise and that in the very few seconds between the occurrence
of the noise and our becoming completely conscious we may experience
a long and complicated dream in which we may do and say things which
would take quite a long time in actual life and this without any sense
of hurry.
This seems to show that the "time scale" for the dream state is not
the same as that to which we are accustomed in our waking hours.
The difference should be sought, as Mr. Bragdon points out, in the
differing vehicle of consciousness.
This idea can be pushed much further.
I have suggested that there is a sort of time which is, so to speak,
peculiar to our space and which is expressible in terms of four space;
and that there is another sort of time which appertains to four space
itself, associated, that is, with four space change in the same way
that three space time is associated with three space change.
But if we accept the idea that there are more dimensions of space than
three we cannot refuse to consider the possibility that there are
more than four. If so we must say that four space change is in turn
expressible in terms of five space in just the same way that three
space change is expressible in terms of four space.
Now, it is evident that a being embodied in four space and possessing,
either temporarily or permanently, no three-space vehicle, will be
unaffected by three space change and will, therefore, be independent
of three space time. Four space change would take the place of the
three spatial simultaneities by which we, embodied in three space,
reckon time, and five space change would take the place of the changes
in Psychic states which for us give rise to the second aspect of time
which we have been discussing.
The whole dual nature of time would be repeated but with the difference
of being one dimension higher.
The same may be applied to five space and six space and so on,
indefinitely.
In each case the changes giving rise to the experience of subjective
time would presumably be the resultant of the changes of all spaces
higher than that of the lowest vehicle, but that of the next higher
space would predominate.
Hence Consciousness could never be altogether free of the experience of
time until it was embodied only in the highest space of all, which we
must suppose to possess the attributes of infinitely dimensional space.
And this will only apply to the Divine Consciousness.
All this is admittedly highly speculative but seems to me the natural
deduction if we assume the existence of spaces of dimensionality higher
than four.
The nature of maximally dimensional space is a question which I do not
propose to discuss here as it is somewhat conspicuously outside the
sphere of practical politics. For other observations on this subject,
including some remarks on the concept of "curved time," the interested
reader may profitably refer to Mr. Bragdon's book "Four Dimensional
Vistas."
Mr. Klein treats the question in a rather different, but highly
interesting, manner in his book "Science and the Infinite."
PREVISION.
The subject of prevision is obviously closely allied to that of time,
since the only considerable difficulty lies in the fact that the
incidents forseen are removed in time. They are wrapped in the darkness
of the future and we say that they "have not happened yet."
There are two forms which an attempt to explain the fairly numerous
good cases of prevision may take.
One way is to say that the future is latent in the present in that
it is determined by factors at present in existence. The other is
to say that there is no such thing as Past or Future, but that both
are comprehended in the Now and that it is merely on account of the
limitations of our Consciousness that we cannot apprehend them.
According to the former view the power of prevision is the result of a
mere heightening of the faculties by which we can always foresee the
future to some slight extent. If we see a blind man walking towards the
edge of a cliff it is not difficult to foresee that he will, probably,
fall off it and be smashed at the bottom. Such a sight could easily be
supposed to give rise to a visualisation of the corpse at the bottom of
the cliff, which might pass for a prophetic vision.
In such simple matters it is not difficult to imagine that a suitable
clairvoyant state, combined with unconscious but accurate reasoning and
subsequent visualisation, would enable the percipient to forecast the
future.
But clearly the accuracy of such a forecast would depend on the
perception of _all_ the factors involved, as well as on the precision
of the unconscious reasoning.
Hence, although we might readily accept this explanation in the case of
prevision of events in the immediate future, or in the case of vague
presentiments, it becomes increasingly difficult to do so, as the
event prevised becomes more remote and the number of factors which may
possibly influence the issue are proportionately increased.
I need hardly say that these factors of which I speak must include
Psychic states and so forth.
To use the terminology to which we have by this time become accustomed,
we could, theoretically, forecast the distribution of every particle
of matter in three space, provided we knew present distribution and
velocities; and provided also that no interference could arise from
external, _i.e._, four space, sources. But in order to be certain of
the latter, we must know all about four space dispositions and so on to
the "N"th degree.
Absolute prevision could therefore only result from a complete
knowledge of all the factors in _every_ space combined with absolutely
perfect reasoning powers.
Although, as will be seen, certain of the ideas in the above have
a place in what I believe to be the true theory of prevision, the
explanation as above described does not appear to me to be satisfying.
The heightening of faculty required in all but the very simplest cases
is too great to be accepted except in the last resort.
Now, as regards the other theory, that the future does actually exist
_now_ and that only our own limitations prevent us from apprehending it.
Consider again the crude and metaphorical representation of change as
resulting from the passage across our three space of a congeries of
four space solids which supposes that the distribution of matter at any
moment is simply a very thin cross section of this congeries.
If this were the case it is evident that to anyone who had the power of
moving freely in four dimensions it would be possible to move up the
mass and see what some cross section was like which had not yet arrived
at our space.
This is desperately crude but it gives the general idea.
In order to grasp it better we will transpose it into terms of two-and
three space at the same time altering it slightly. Suppose that a two
space world consists of a colossal soap film. Imagine a thin thread
passing through the film and stretched between two points, one above
the film and one below. If these two points move perpendicularly to
the film the thread will move accordingly. The point where the thread
cuts the film will remain stationary if the thread was perpendicular to
the latter to start with, but will move if the thread was originally
slanting.
To a two space being inhabiting the film, all that will be visible of
the thread will be a minute circle, an atom of two-space matter let us
say.
Now let us imagine an enormous number of such threads, sufficient
to produce all the atoms necessary to make up a complete two space
universe. Suppose also that these are twisted and intertwined in the
most complicated possible manner. Then as they pass across the soap
film they will give rise to the most complex changes in the two space
world.
A three space being, however, could see the filamentary structure as a
whole and would not be limited to the particular section which happened
to be crossing the film at any given moment.
I must again insist that I do not for a moment regard this as being
anything like a true picture of what actually occurs. The point I wish
to make is merely that if, as seems to be the case, three space change
can be represented spatially by the use of four space ideas, then it
is not utterly inconceivable that a consciousness free to move in four
space and independent of three space limitations, should be able in
some obscure way to foresee coming changes.
* * * * *
There is a prevalent notion to the effect that if we admit the
possibility of prevision we are bound to become involved in the slough
of Fatalism.
"If we can foresee what is going to happen," it is urged, "then the
future must be already settled, and we have no power of altering it."
This view appears to me to be fallacious.
Consider again for a moment the filamentary world.
Our forecast of events therein is based on the assumption that the
filamentary structures remain unaltered, that the cross-sections which
will be traversed by the film will not be changed before it gets there.
This is pure assumption and quite unwarranted.
In the first place the two space beings themselves might be able to
alter the arrangement of the threads during their passage across the
film, implying of course the exercise of three space forces, and the
possession of a certain degree of three-dimensionality, on their part.
In the second place all sorts of extraneous three space forces might be
applied.
The argument does not perhaps apply especially felicitously to this
particular analogy, but translated into more general terms it means
that three space change, although expressible in terms of four space,
and perhaps for the very reason that it is thus expressible, is
susceptible to modification under the influence of factors which have
no three-dimensionality.
As stated at the outset, absolute prevision necessitates _every_ factor
being accounted for, and these factors may appear, not merely in three
space or four space, but in N-space too.
In fact, the more accurate prevision is to be, the wider survey must
the percipient take.
In order to attain absolute prevision the precipient must be able to
function consciously in maximally-dimensional space. But this ability
I take to be the exclusive prerogative of the Divine Consciousness.
The purely speculatory character of the foregoing will be evident and I
do not wish it to be taken as more than an attempt to convey a general
impression of ideas which seem somewhat suggestive.
It seems appropriate to end a chapter frankly given over to inchoate
and somewhat formless speculations, with some remarks on the
objectivity or otherwise of space in general.
These remarks have been more especially prompted by Mr. E.L. Gardner's
article on "The Fourth Dimension" which appeared in the _Theosophist_
for October 1916, by a pamphlet for private circulation written by Mr.
T. Olman Todd, 1915, and by Mr. Klein's remarks on Space in his book
"Science and the Infinite."
Throughout this work I have treated four-dimensional space as an
objective reality and, as will appear, I consider that this is
perfectly justifiable.
The general tendency of the above-mentioned writers seems to be to
suggest that this attitude is fallacious and that all space, of
whatever dimensionality, is rather to be regarded as a phenomenon of
consciousness. In saying this I do not pretend to be reflecting with
precision the views expressed by the writers in question. I am merely
giving the general effect produced on my mind by their ideas.
I may say at once that I think that they are probably perfectly right
and that no space of any kind is really objective.
I am, for instance, disposed to agree with Mr. Gardner when he says
that "However willingly we may grant that behind the description
'Fourth Dimension' there stands something that is real, it is of
importance that that reality should be described in terms of Life and
Consciousness and not be regarded as a further extension of Matter or
Form."
Mr. Klein concludes that "our very conception of space is one of the
modes only under which motion or physical phenomena are presented to
our consciousness."
I have neither the knowledge nor the temerity to embark upon a
discussion of the point from the metaphysical point of view and all
I wish to do is to show that I am aware that all our ideas regarding
space are liable to be modified at the hands of the philosophers
and that I have no desire to minimise the importance of their
contributions. On the contrary I think it probable that these may prove
to be of the utmost value. They may, for instance, by interpreting
spatial experience in terms of consciousness, throw light on the very
considerable difficulty to which I drew attention on page 48.
But I submit that for the present purpose we can legitimately disregard
the whole thing. It may well be that the change in passing from
our present state of consciousness to that which I have described
as consciousness in four dimensions is subjective rather than
objective, that the change would be in our consciousness rather than
in spatial conditions. But whatever may be the real nature of our
three-dimensional space from the strictly academic point of view we can
and habitually do treat it as an objective reality and I think it fair
to claim an equal licence in dealing with four-dimensional space.
Pure consciousness is an elusive thing to handle and if we find
evidence to the effect, for example, that the state of consciousness
in which we exist when separated from the body can be accurately
represented by the higher space hypothesis, then surely we had better
say that it is existence in four-dimensional space and have done with
it, just as we say that our normal existence is existence in three
dimensional space.
After all the whole matter is one of "relativity" so to speak. The
final effect with which we are concerned is the reaction of reality
on our minds and, just as we can in dynamics reduce any one member of
a system to rest and treat all motions as relative to that so here it
makes no practical difference whether it is our mind or reality which
changes provided that the changed relation between them is correctly
expressed.