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                          SCIENTIFIC ROMANCES.


                                   BY
                           C. H. HINTON, B.A.

  What is the Fourth Dimension?
  The Persian King.
  A Plane World.
  A Picture of Our Universe.
  Casting Out the Self.

  [Illustration: _FIRST SERIES._]

                               _London._
                     SWAN SONNENSCHEIN & CO., LIM.,
                          Paternoster Square.
                                 1886.




                     What is the Fourth Dimension?


                               CHAPTER I.

At the present time our actions are largely influenced by our theories.
We have abandoned the simple and instinctive mode of life of the earlier
civilisations for one regulated by the assumptions of our knowledge and
supplemented by all the devices of intelligence. In such a state it is
possible to conceive that a danger may arise, not only from a want of
knowledge and practical skill, but even from the very presence and
possession of them in any one department, if there is a lack of
information in other departments. If, for instance, with our present
knowledge of physical laws and mechanical skill, we were to build houses
without regard to the conditions laid down by physiology, we should
probably—to suit an apparent convenience—make them perfectly
draught-tight, and the best-constructed mansions would be full of
suffocating chambers. The knowledge of the construction of the body and
the conditions of its health prevent it from suffering injury by the
development of our powers over nature.

In no dissimilar way the mental balance is saved from the dangers
attending an attention concentrated on the laws of mechanical science by
a just consideration of the constitution of the knowing faculty, and the
conditions of knowledge. Whatever pursuit we are engaged in, we are
acting consciously or unconsciously upon some theory, some view of
things. And when the limits of daily routine are continually narrowed by
the ever-increasing complication of our civilisation, it becomes doubly
important that not one only but every kind of thought should be shared
in.

There are two ways of passing beyond the domain of practical certainty,
and of looking into the vast range of possibility. One is by asking,
“What is knowledge? What constitutes experience?” If we adopt this
course we are plunged into a sea of speculation. Were it not that the
highest faculties of the mind find therein so ample a range, we should
return to the solid ground of facts, with simply a feeling of relief at
escaping from so great a confusion and contradictoriness.

The other path which leads us beyond the horizon of actual experience is
that of questioning whatever seems arbitrary and irrationally limited in
the domain of knowledge. Such a questioning has often been successfully
applied in the search for new facts. For a long time four gases were
considered incapable of being reduced to the liquid state. It is but
lately that a physicist has succeeded in showing that there is no such
arbitrary distinction among gases. Recently again the question has been
raised, “Is there not a fourth state of matter?” Solid, liquid, and
gaseous states are known. Mr. Crookes attempts to demonstrate the
existence of a state differing from all of these. It is the object of
these pages to show that, by supposing away certain limitations of the
fundamental conditions of existence as we know it, a state of being can
be conceived with powers far transcending our own. When this is made
clear it will not be out of place to investigate what relations would
subsist between our mode of existence and that which will be seen to be
a possible one.

In the first place, what is the limitation that we must suppose away?

An observer standing in the corner of a room has three directions
naturally marked out for him; one is upwards along the line of meeting
of the two walls; another is forwards where the floor meets one of the
walls; a third is sideways where the floor meets the other wall. He can
proceed to any part of the floor of the room by moving first the right
distance along one wall, and then by turning at right angles and walking
parallel to the other wall. He walks in this case first of all in the
direction of one of the straight lines that meet in the corner of the
floor, afterwards in the direction of the other. By going more or less
in one direction or the other, he can reach any point on the floor, and
any movement, however circuitous, can be resolved into simple movements
in these two directions.

But by moving in these two directions he is unable to raise himself in
the room. If he wished to touch a point in the ceiling, he would have to
move in the direction of the line in which the two walls meet. There are
three directions then, each at right angles to both the other, and
entirely independent of one another. By moving in these three directions
or combinations of them, it is possible to arrive at any point in a
room. And if we suppose the straight lines which meet in the corner of
the room to be prolonged indefinitely, it would be possible by moving in
the direction of those three lines, to arrive at any point in space.
Thus in space there are three independent directions, and only three;
every other direction is compounded of these three. The question that
comes before us then is this. “Why should there be three and only three
directions?” Space, as we know it, is subject to a limitation.

In order to obtain an adequate conception of what this limitation is, it
is necessary to first imagine beings existing in a space more limited
than that in which we move. Thus we may conceive a being who has been
throughout all the range of his experience confined to a single straight
line. Such a being would know what it was to move to and fro, but no
more. The whole of space would be to him but the extension in both
directions of the straight line to an infinite distance. It is evident
that two such creatures could never pass one another. We can conceive
their coming out of the straight line and entering it again, but they
having moved always in one straight line, would have no conception of
any other direction of motion by which such a result could be effected.
The only shape which could exist in a one-dimensional existence of this
kind would be a finite straight line. There would be no difference in
the shapes of figures; all that could exist would simply be longer or
shorter straight lines.

Again, to go a step higher in the domain of a conceivable existence.
Suppose a being confined to a plane superficies, and throughout all the
range of its experience never to have moved up or down, but simply to
have kept to this one plane. Suppose, that is, some figure, such as a
circle or rectangle, to be endowed with the power of perception; such a
being if it moves in the plane superficies in which it is drawn, will
move in a multitude of directions; but, however varied they may seem to
be, these directions will all be compounded of two, at right angles to
each other. By no movement so long as the plane superficies remains
perfectly horizontal, will this being move in the direction we call up
and down. And it is important to notice that the plane would be
different, to a creature confined to it, from what it is to us. We think
of a plane habitually as having an upper and a lower side, because it is
only by the contact of solids that we realize a plane. But a creature
which had been confined to a plane during its whole existence would have
no idea of there being two sides to the plane he lived in. In a plane
there is simply length and breadth. If a creature in it be supposed to
know of an up or down he must already have gone out of the plane.

Is it possible, then, that a creature so circumstanced would arrive at
the notion of there being an up and down, a direction different from
those to which he had been accustomed, and having nothing in common with
them? Obviously nothing in the creature’s circumstances would tell him
of it. It could only be by a process of reasoning on his part that he
could arrive at such a conception. If he were to imagine a being
confined to a single straight line, he might realise that he himself
could move in two directions, while the creature in a straight line
could only move in one. Having made this reflection he might ask, “But
why is the number of directions limited to two? Why should there not be
three?”

A creature (if such existed), which moves in a plane would be much more
fortunately circumstanced than one which can only move in a straight
line. For, in a plane, there is a possibility of an infinite variety of
shapes, and the being we have supposed could come into contact with an
indefinite number of other beings. He would not be limited, as in the
case of the creature in a straight line, to one only on each side of
him.

It is obvious that it would be possible to play curious tricks with a
being confined to a plane. If, for instance, we suppose such a being to
be inside a square, the only way out that he could conceive would be
through one of the sides of the square. If the sides were impenetrable,
he would be a fast prisoner, and would have no way out.

What his case would be we may understand, if we reflect what a similar
case would be in our own existence. The creature is shut in in all the
directions he knows of. If a man is shut in in all the directions he
knows of, he must be surrounded by four walls, a roof and a floor. A
two-dimensional being inside a square would be exactly in the same
predicament that a man would be, if he were in a room with no opening on
any side. Now it would be possible to us to take up such a being from
the inside of the square, and to set him down outside it. A being to
whom this had happened would find himself outside the place he had been
confined in, and he would not have passed through any of the boundaries
by which he was shut in. The astonishment of such a being can only be
imagined by comparing it to that which a man would feel, if he were
suddenly to find himself outside a room in which he had been, without
having passed through the window, doors, chimney or any opening in the
walls, ceiling or floor.

Another curious thing that could be effected with a two-dimensional
being, is the following. Conceive two beings at a great distance from
one another on a plane surface. If the plane surface is bent so that
they are brought close to one another, they would have no conception of
their proximity, because to each the only possible movements would seem
to be movements in the surface. The two beings might be conceived as so
placed, by a proper bending of the plane, that they should be absolutely
in juxtaposition, and yet to all the reasoning faculties of either of
them a great distance could be proved to intervene. The bending might be
carried so far as to make one being suddenly appear in the plane by the
side of the other. If these beings were ignorant of the existence of a
third dimension, this result would be as marvellous to them, as it would
be for a human being who was at a great distance—it might be at the
other side of the world—to suddenly appear and really be by our side,
and during the whole time he not to have left the place in which he was.


                              CHAPTER II.

The foregoing examples make it clear that beings can be conceived as
living in a more limited space than ours. Is there a similar limitation
in the space we know?

At the very threshold of arithmetic an indication of such a limitation
meets us.

If there is a straight line before us two inches long, its length is
expressed by the number 2. Suppose a square to be described on the line,
the number of square inches in this figure is expressed by the number 4,
_i.e._, 2 × 2. This 2 × 2 is generally written 2², and named “2 square.”

Now, of course, the arithmetical process of multiplication is in no
sense identical with that process