Tertium Organum

It variability
is a 
sign of the three-dimensional world, we must seek for that which is 
constant, 
and in this way we may come closer to an understanding of the four­
dimensional world. Moreover, we are accustomed to regard as really existing
only that which can be measured in length, breadth and height. But, as has 
been pointed out already, it is necessary to widen the boundaries of the 
really
existing. Mensurability
is too crude a criterion of existence, because 
mensurability itself is too conditioned a concept. So we may say that any 
approach to an exact investigation of the domain of higher dimensions 
probably requires the conviction, derived from direct sensation, that many
things that 
cannot be measured
have a real existence, more real indeed than 
many things that can be measured. 

---

CHAPTER 6 
Methods of investigating the problem of higher dimensions. Analogy between 
imaginary worlds of different dimensions. One-dimensional world on a line. 'Space' 
and 'time' of a one-dimensional being. Two-dimensional world on a plane. 'Space' 
and 'time', 'ether', 'matter' and 'motion' of a two-dimensional being. Reality and 
illusion on a plane. Impossibility of seeing an 'angle'. An 'angle' as motion. 
Incomprehensibility, for a two-dimensional being, of the functions of the objects of 
our world. Phenomena and noumena of a two-dimensional being. How could a plane 
being understand the third dimension? 
In order to determine what the domain of higher dimensions could be and 
what it 
could not
be, a series of analogies and comparisons are generally 
used. 
The usual way is to imagine 'worlds' of one and two dimensions and, from
the relationship between the lower worlds and the higher worlds to deduce
the possible relation of our world to the four-dimensional world in the same
way as from the relations of points to line, of lines to surfaces, of surfaces to
solids, we deduce the relationship of our solids to four-dimensional bodies. 
Let us examine all that this method of analogies has to offer. 
Let us imagine a 
one-dimensional world.
It will be a line. On this line let us imagine living beings. They will only be
able to move backwards and forwards along this line which represents their 
universe, and they themselves will have the aspect of points or sections of the
line. Nothing outside this line will exist for them, neither will they be 
conscious of the line itself on which they live and move. Only two points will
exist for them - ahead and behind; or maybe only one point, ahead. Observing
changes in the state of these points the one-dimensional being will call these 
changes 
phenomena. 
If we suppose that the line on which the one­
dimensional being lives, passes through various objects of our world, then, in
all these objects the one-dimensional being will see only one point. If his line 
is intersected by different bodies, the one-dimensional being will sense them 
only as the appearance, the more or less prolonged existence and the
disappearance of a point. This appearance, existence and disappearance of a
point will be a 

---

phenomenon.
For the one-dimensional being phenomena will be constant or variable, of 
long or short duration, periodical or not periodical, according to the character and 
qualities and the rate and nature of the motion of objects passing through the line. But 
the one-dimensional being will be totally unable to explain the constancy or variability, 
the long or short duration, the periodicity or non-periodicity of the phenomena of his 
world, and will simply regard these as attributes inherent in the phenomena. Bodies 
intersecting the line may be very different, but for the one-dimensional being all 
phenomena will be absolutely