The fourth dimension, so-called, has been drawn to the public
attention, of late, by reason of the wide publicity given to Prof.
Einstein’s theory of Relativity. What _is_ the fourth dimension? How
can it be conceived?
The world in which we live is a three-dimensional world. It has length,
breadth and height, (Combinations of these). Starting at a given point,
draw a line. This is one dimension--length. Move this line at right
angles to itself, on a flat surface, and you generate a square--length
and breadth. Move this square at right angles to itself, and you
generate a cube--adding height. Theoretically, it should be possible
to move this cube at right angles to itself, in some direction,
and generate a “tesseract” or “hypersolid.” That would be a fourth
dimensional figure.
Or again, take a point. Two lines can be drawn through this point at
right angles to one another, on a sheet of paper; but if you want to
draw a third line through the point, at right angles to the first two,
you have to draw it at right angles to the paper itself, as though it
were standing up in the air. How can a fourth line be drawn through
that point, at right angles to the other three? That would be the
fourth dimension.
Theoretically, a fourth dimension is provable, and a great deal is
known concerning fourth dimensional geometrical figures. Dr. Manning
has written a whole book on the subject: “Geometry of Four Dimensions.”
But it is practically impossible for us to conceive the fourth
dimension in our minds. We can only arrive at it by analogy.
For instance, a right-hand glove cannot be turned into a left-hand
glove; but if it is turned inside out, it becomes one. Similarly, it
has been proved that a hollow rubber ball can be turned inside out in
the fourth dimension without tearing the ball!
It is impossible to tie a true knot in a piece of string in two
dimensions; one end has to be lifted over the other (into the third
dimension). And, in our three dimensional space, it is impossible to
tie a knot in a piece of string both ends of which have been held or
sealed. But Prof. Zollner obtained such knots in the presence of the
medium Slade, and this made him believe in the fourth dimension, and
caused him to write his famous book “Transcendental Physics.”
Einstein has proposed that time is the fourth dimension, as we know;
but this is not a dimension, strictly speaking. This idea has been
worked out in some detail, from an original point of view by P. D.
Ouspensky, in his ingenious book “Tertium Organum.”
It has been contended that “clairvoyance” is fourth dimensional sight.
It is certainly true that, by adding another dimension, we are enabled
to see things which would otherwise be invisible. Thus, if you have
a box containing some rings, you cannot see the rings so long as the
box is kept on a level with the eyes--that is, in two dimensions. But
if you elevate your eyes (or lower the box) and look into it from
above, you can see the rings inside. That is, by adding another (third)
dimension, you are enabled to see what you could not see before, in a
“closed” space. Similarly, it has been contended, by adding a fourth
dimension, it is possible for clairvoyants to see into what is to us
a “closed” room, or closed box, and describe its contents. Of course,
this is merely an analogy, which cannot be pressed too far.
While the fourth dimension cannot be visualized by the mind, therefore,
a good deal has been learned concerning it, from the theoretical
point of view, and mathematically it can be shown to be possible.
Its geometry is also well known. The interested reader may find the
subject exhaustively treated in Hinton’s books; in the books of Claude
Bragdon, and in “The Fourth Dimension Simply Explained,” issued by Munn
and Co., New York.