Tertium Organum


parts, and they appear to us variable. But if we look more closely, we shall



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Tertium-Organum-by-P-D-Ouspensky


parts, and they appear to us variable. But if we look more closely, we shall 
see that this is an illusion. It is three-dimensional things that are unreal and 
variable. And they cannot be real, because, in actual fact, they do not exist, 
just as 
imaginary sections of
a solid do not exist. Only four-dimensional 
bodies are real. 
In one of his lectures collected in the book
A Pluralistic Universe, 
Professor James draws attention to an observation by Professor Bergson that 
science always studies only the 
t of the universe,
i.e. not the universe as a 
whole, but only the 
moment, 
the 'time-section' of the universe. 
The properties of four-dimensional space will become clearer for us if we 
make a detailed comparison of three-dimensional space with a surface and 
find out the differences that exist between them. 
In his book, 
A New Era of Thought,
Hinton examines these differences 
carefully. He imagines two equal right-angle triangles cut out of paper and 
placed on a plane surface with the right angles pointing in different 
directions. These triangles are exactly equal but, 
for some reason,
they are 
quite different. One has its right angle pointing to the right, the other points to 
the left. If anyone wishes to make these triangles 
absolutely identical,
it can 
only be done with the help of three-dimensional space. This means that one 
of the triangles must be picked up, turned over and replaced on the plane. 
Then they will be two equal and 
absolutely identical
triangles. But to do this, 
it is necessary to lift one triangle from the plane into three-dimensional space
and turn it over in that space. If this triangle is left on the plane, it can never 
be made identical with the other if, at the same time, the relation between the 
angles of the two triangles is to be kept. If the triangle is merely turned round 
on the plane, this relation will not be maintained. In our world there are 
figures completely analogous to these two triangles. 
We know certain shapes which are equal the one to the other, which are exactly 
similar, and yet which we cannot make fit into the same portion of space, either 
practically or by imagination. 


If we look at our hands we see quite clearly that our two hands are a very 
complicated case of non-symmetrical likeness. They are at the same time alike and 
quite different. One is 
right,
the other is 
left. 
We can imagine only one way in which 
the two hands may be brought into complete likeness. 
If we take the right-hand glove and the left-hand glove, they will not fit any more than 
the right hand will coincide with the left hand. But if we turn one glove inside out, 
then it will fit. Now, to suppose the same thing done with the solid hand as is done 
with the glove when it is turned inside out, we must suppose it, so to speak pulled 
through itself. ... If such an operation were possible, the right hand would be turned 
into an exact model of the left hand.* 
But such an operation would be possible only in higher-dimensional space, just as 
the turning over of the triangle is possible only in a space higher than the plane. It is 
possible that, even granting the existence of four-dimensional space, a hand cannot be 
turned inside out and pulled through itself for reasons not dependent on geometrical 
conditions. But the example still holds good. Theoretically, things in the nature of the 
turning of a hand inside out should be possible in four-dimensional space, for in that 
space different, even very far removed points of our space 

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