182 
HINTON. 
the facts of four-dimensional movement and apprehend the 
consequences of these conceptions. 
Without the formation of an experience of four-dimen¬ 
sional bodies, their shapes and motions, the subject can be 
but formal—logically conclusive, not intuitively evident. 
It is to this logical apprehension that I must appeal. 
It is perfectly simple to form an experiential familiarity 
with the facts of four-dimensional movement. The method 
is analogous to that which a plane being would have to 
adopt to form an experiential familiarity with three-dimen¬ 
sional movements, and may be briefly summed up as the for¬ 
mation of a compound sense by means of which duration 
is regarded as equivalent to extension. 
Consider a being confined to a plane. A square enclosed 
by four lines will be to him a solid, the interior of which can 
only be examined by breaking through the lines. If such 
a square were to pass transverse to his plane, it would im¬ 
mediately disappear. It would vanish, going in no direction 
to which he could point. 
If, now, a cube be placed in contact with his plane, its sur¬ 
face of contact would appear like the square which we have 
just mentioned. But if it were to pass transverse to his 
plane, breaking through it, it would appear as a lasting 
square. The three-dimensional matter will give a lasting ap¬ 
pearance in circumstances under which two-dimensional mat¬ 
ter will at once disappear. 
Similarly, a four-dimensional cube, or, as we may call it, 
a tesseract, w T hich is generated from a cube by a movement 
of every part of the cube in a fourth direction at right 
angles to each of the three visible directions in the cube, if 
it moved transverse to our space, would appear as a lasting 
cube. 
A cube of three-dimensional matter, since it extends to no 
distance at all in the fourth dimension, could instantly dis¬ 
appear if subjected to a motion transverse to our space. It 
would disappear and be gone without it being possible to 
point to any direction in which it had moved. 
