Tertium Organum

matter,
and the angles ­
motion. 
Thus, the plane being will call an irregular line with an 

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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. 

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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