angle -
moving
matter. And indeed for him, because of its properties, such a
line will be completely analogous to matter in motion.
If a cube is placed on the plane on which the plane being lives, the whole
cube will not exist for the two-dimensional being, but only the square surface
of it which is in
contact with the plane, that is to say, the cube will exist as a
line with periodical movements. In the same way, all other bodies lying
outside his plane, touching his plane or passing through it, will not exist for
the two-dimensional being. He will be able to sense only their surfaces of
contact or their sections. But if these surfaces
or sections move or change,
quite naturally, the two-dimensional being will think that the
cause of
change
or motion lies in themselves, i.e. is also there, on his plane.
It has already been said that the two-dimensional being will regard only
straight lines as motionless matter, irregular lines or curves will appear to him
to be moving. As regards the
really moving
lines, i.e. those lines
which bind
the sections or the surfaces of contact of the bodies moving through the plane
or along the plane, these will contain something incomprehensible for a two
dimensional being, something
impossible to measure.
They will seem to have
in them something self-existing, self-dependent,
animated.
There are two
reasons for this: the two-dimensional being
can measure
motionless angles
and curves, whose properties he
calls motion, for the very reason that they are
motionless; but he cannot measure moving figures because the changes in
them are outside his control. These changes will depend on the properties of
the
whole body
and its motion, whereas the two-dimensional being knows
only its section, only one side of the whole body. Having no idea of the
existence of that body and regarding its motion as inherent
in the sides and
sections,
he will probably regard them as living beings.
He will credit them
with the possession of something which is absent in ordinary bodies - vital
energy, or even soul. This something will be regarded as unknowable for a
two-dimensional being, since it is the result of an incomprehensible motion of
incomprehensible bodies.
If we imagine a stationary circle lying on the plane, for a two-dimensional
being this circle
will appear as a moving line, possessing very strange and
incomprehensible motion.
The plane being will never see this motion. He may possibly call it
molecular motion,
i.e. the movement of minute, invisible particles of 'matter'.
For a two-dimensional being, a circle rotating round a central axis will, in
some incomprehensible way, appear different from a stationary circle.
Both
will seem to be moving, but moving differently.
Owing to its
double movement, a circle or a square lying on the plane and
rotating round its centre, will be, for a two-dimensional being, an
incomprehensible and unmeasurable phenomenon, somewhat similar to the
phenomenon of life
for the modern physicist.
Thus, for a two-dimensional being, a straight line will be motionless
matter; an irregular line or a curve will be matter in motion; and
a moving
line will be
living
matter.
The centre of a circle or a square will be inaccessible to the plane being,
just as the centre of a sphere or a cube made of solid matter is inaccessible to
us. Moreover, the two-dimensional being will be incapable of even
understanding about a centre, since he will have
no idea of what a centre
means.
It has already been said that, having no conception of any phenomena
occurring outside the plane, i.e. outside his space, the plane being will regard
all phenomena as taking place on his plane. And all these phenomena,
supposedly taking place on his plane, he will regard as being in causal
interdependence
Do'stlaringiz bilan baham: