Tertium Organum

on something
or 
in 
something.
So he may call this plane - 'ether' (of course, he will not know that it is 
actually a plane). Then he will say that 'ether' fills all space, but differs in its properties 
from 'matter'. So he will call lines - 'matter'. As a result, the two-dimensional being will 
regard everything that happens as happening in his 'ether', that is, in his space. He will 
not be able to imagine anything as being outside this ether, i.e. outside his plane. If 
something happening outside his plane reaches his consciousness, he will either deny it, 
taking it as subjective, i.e. as a creation of his own imagination, or he will think of it as 
he thinks of all other phenomena, as happening on that very plane, 
in ether. 
Sensing the lines only, the plane being will sense them quite differently from us. 
First of all, he will not sense an angle.
It is very easy to verify this in practice. If we 
hold 
on a level with our eyes
two 

---

matches placed on a horizontal surface at an angle to one another, we will see 
one line. To see the angle we must 
look from above.
The two-dimensional 
being cannot look from above, and therefore cannot see an angle. But by 
measuring the distance between the lines of the different 'solids' of his world, 
the two-dimensional being will be constantly confronted with angles and will 
regard the angle as a strange property of the line which at times appears and 
at others does not appear. In other words, he will refer the angle to time, will 
regard it as a transitory temporal phenomenon - a change in the state of the 
'solid' - or as 
motion.
It is difficult for us to understand this, difficult to 
imagine how an angle can be taken as motion. But it must necessarily be so 
and cannot be otherwise. If we try to visualize how a plane being will study a 
square, we shall see that for a plane being the square must necessarily be a 
moving body.
Let us imagine a plane being faced with one of the angles of the 
square. He does not see the angle - in front of him there is a line, but a line 
possessing very strange properties. As he comes nearer to this line, the two­
dimensional being will see a strange thing happening to the line. One point
will remain in its place, but the other points, on both sides, will 
recede 
backwards.
I repeat: the two-dimensional being has no idea of an angle. 
In its 
outward appearance
the line will remain the same as it was; and yet, 
something will undoubtedly be happening to it. The plane being will say that 
the line moves, but so rapidly that it appears to be motionless. If the plane 
being draws away from the angle and moves along a side of the square, this 
line will become motionless. Reaching an angle, he will again notice 
motion. 
If he makes the circuit of the square several times, he will establish the fact 
that there are regular periodical movements of this line. It is probable that for 
the mind of the plane being, the square will be his conception of a body 
possessing the property of periodical movements, unnoticeable to the eye but 
producing definite physical effects 
(molecular motion),
or the idea of 
periodical 
moments
of rest and motion in one complex line; 
and still more probably the square will appear to him as a 
rotating body. 
Very likely, the plane being will regard the angle as his own subjective 
representation and will doubt whether any objective reality corresponds to 
this subjective representation. But all the same, he will think that so long as 
an 
action 
capable of being measured exists, it must have a cause, and this 
cause must lie in the changing states of the line, i.e. in motion. 
The plane being may call the lines he sees -