Space has been defined as "room to move about." Let us accord to
this definition the utmost liberty of interpretation. Let us
conceive of space not alone as room to move ponderable bodies in,
but as room to think, to feel, to strike out in unimaginable
directions, to overtake felicities and knowledges unguessed by
experience and preposterous to common sense. Space is not measurable:
we attribute dimensionality to space because such is the method of
the mind; and that dimensionality we attribute to space is
progressive because progression is a law of the mind. The so-called
dimensions of space are to space itself as the steps that a climber
cuts in the face of a cliff are to the cliff itself. They are not
necessary to the cliff: they are necessary only to the climber.
Dimensionality is the mind's method of mounting to the idea of the
infinity of space. When we speak of the fourth dimension, what we
mean is the fourth stage in the apprehension of that infinity. We
might as legitimately speak of a fifth dimension, but the
profitlessness of any discussion of a fifth and higher stages lies
in the fact that they can be intelligently approached only through
the fourth, which is still largely unintelligible. The case is like
that of a man promised an increase of wages after he had worked a
month, who asks for his second month's pay before he is entitled to
the first.