And this relationship of a surface to a solid or of a solid, as we
conjecture, to a higher solid, is one which we often find in nature. A
surface is nothing more nor less than the relation between two things.
Two bodies touch each other. The surface is the relationship of one to
the other.
Again, we see the surface of water.
Thus our solid existence may be the contact of two four-dimensional
existences with each other; and just as sensation of touch is limited to
the surface of the body, so sensation on a larger scale may be limited
to this solid surface.
And it is a fact worthy of notice, that in the surface of a fluid
different laws obtain from those which hold throughout the mass. There
are a whole series of facts which are grouped together under the name of
surface tensions, which are of great importance in physics, and by which
the behaviour of the surfaces of liquids is governed.
And it may well be that the laws of our universe are the surface
tensions of a higher universe.
But these expressions, it is evident, afford us no practical basis for
investigation. We must assume something more definite, and because more
definite (in the absence of details drawn from experience), more
arbitrary.
And we will assume that the conditions under which we human beings are,
exactly resemble those under which the plane-beings are placed, which
have been described.
This forms the basis of our work; and the practical part of it consists
in doing, with regard to higher space, that which a plane-being would do
with regard to our space in order to enable himself to realize what it
was.
If we imagine one of these limited creatures whose life is cramped and
confined studying the facts of space existence, we find that he can do
it in two ways. He can assume another direction in addition to those
which he knows; and he can, by means of abstract reasoning, say what
would take place in an ampler kind of space than his own. All this would
be formal work. The conclusions would be abstract possibilities.
The other mode of study is this. He can take some of these facts of his
higher space and he can ponder over them in his mind, and can make up in
his plane world those different appearances which one and the same solid
body would present to him, and then he may try to realize inwardly what
his higher existence is.
Now, it is evident that if the creature is absolutely confined to a
two-dimensional existence, then anything more than such existence will
always be a mere abstract and formal consideration to him.
But if this higher-space thought becomes real to him, if he finds in his
mind a possibility of rising to it, then indeed he knows that somehow he
is not limited to his apparent world. Everything he sees and comes into
contact with may be two-dimensional; but essentially, somehow, himself
he is not two-dimensional merely.
Public-domain text, read in full here on John Shaqi.
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