Four-Dimensional Vistas | Page 4

asks for his second month's
pay before he is entitled to the first.
THE SUBJECTIVITY OF SPACE
Without going deep into the doctrine of the ideality--that is, the purely
subjective reality--of space, it is easy to show that we have arrived at
our conception of a space of three dimensions by an intellectual process.
The sphere of the senses is two-dimensional: except for the slight aid
afforded by binocular vision, sight gives us moving pictures on a plane,
and touch contacts surfaces only. What circumstances, we may ask,
have compelled our intellect to conceive of solid space? This question
has been answered as follows:
"If a child contemplates his hand, he is conscious of its existence in a
double manner--in the first place by its tangibility, the second by its
image on the retina of his eye. By repeated groping about and touching,
the child knows by experience that his hand retains the same form and
extension through all the variations of distance and position under
which it is observed, notwithstanding that the form and extension of the
image on the retina constantly change with the different position and
distance of his hand in respect to his eye. The problem is thus set to the
child's understanding: how to reconcile to his comprehension the
apparently contradictory facts of the invariableness of the object
together with the variableness of its appearance. This is only possible
within a space of three dimensions, in which, owing to perspective
distortions and changes, these variations of projection can be reconciled
with the constancy of the form of a body."
Thus we have come to the idea of a three-dimensional space in order to
overcome the apparent contradictoriness of facts of sensible experience.
Should we observe in three-dimensional space contradictory facts our

reason would be forced to reconcile these contradictions, also, and if
they could be reconciled by the idea of a four-dimensional space our
reason would accept this idea without cavil. Furthermore, if from our
childhood, phenomena had been of daily occurrence requiring a space
of four or more dimensions for an explanation conformable to reason,
we should feel ourselves native to a space of four or more dimensions.
Poincaré, the great French mathematician and physicist, arrived at these
same conclusions by another route. By a process of mathematical
reasoning of a sort too technical to be appropriately given here, he
discovers an order in which our categories range themselves naturally,
and which corresponds with the points of space; and that this order
presents itself in the form of what he calls a "three circuit distribution
board." "Thus the characteristic property of space," he says, "that of
having three dimensions, is only a property of our distribution board,
_a property residing, so to speak, in human intelligence_." He
concludes that a different association of ideas would result in a
different distribution board, and that might be sufficient to endow space
with a fourth dimension. He concedes that there may be thinking beings,
living in our world, whose distribution board has four dimensions, and
who do consequently think in hyperspace.
THE NEED OF AN ENLARGED SPACE-CONCEPT
It is the contrariety in phenomena already referred to, that is forcing
advanced minds to entertain the idea of higher space. Mathematical
physicists have found that experimental contradictions disappear if,
instead of referring phenomena to a set of three space axes and one
time axis of reference, they be referred to a set of four interchangeable
axes involving four homogeneous co-ordinates. In other words, time is
made the fourth dimension. Psychic phenomena indicate that
occasionally, in some individuals, the will is capable of producing
physical movements for whose geometrico-mathematical definition a
four-dimensional system of co-ordinates is necessary. This is only
another step along the road which the human mind has always travelled:
our conception of the cosmos grows more complete and more just at
the same time that it recedes more and more beneath the surface of
appearances.
Far from the Higher Space Hypothesis complicating thought, it
simplifies by synthesis and co-ordination in a manner analogous to that

by which plane geometry is simplified when solid geometry becomes a
subject of study. By immersing the mind in the idea of many
dimensions, we emancipate it from the idea of dimensionality. But the
mind moves most readily, as has been said, in ordered sequence.
Frankly submitting ourselves to this limitation, even while recognizing
it as such, let us learn such lessons from it as we can, serving the
illusions that master us until we have made them our slaves.

II THE DIMENSIONAL LADDER
LEARNING TO THINK IN TERMS OF SPACES
The Reader who is willing to consider the Higher Space Hypothesis
seriously, who would discover, by its aid, new and profound truths
closely related to life and conduct, should first of all