Tertium Organum

large disc 
is placed before an animal and, beside it, a 
large sphere of
the same diameter. 
Facing them directly at a certain distance, the animal will see two circles. If 
it starts walking round them, the animal will notice that the sphere remains a 
circle but the disc gradually narrows and becomes a narrow strip. As the 
animal continues to move round it, the strip begins to widen and gradually
becomes again a circle. The sphere will not change its form as the animal 
moves round it, but strange phenomena will begin to occur in it as the animal 
draws near. 
Let us try to understand how the animal will perceive the surface of the 
sphere as distinct from the surface of the disc. 
One thing is certain - it will perceive a spherical surface 
differently from us. 
We perceive convexity or sphericity as a 
property common to 
many surfaces. 
Owing to the nature of its mental apparatus, the animal should perceive 
sphericity as an 
individual property 
of the given sphere. What should 
sphericity look like, taken as an individual property of a given sphere?
We can say with the utmost conviction that sphericity will appear to the 
animal as a movement of the surface it sees. 
When the animal comes near to the sphere, in all probability what happens 
is something like this: the surface the animal sees springs into rapid motion; 
its centre projects forward, and all the other points begin to recede from the 
centre with a velocity proportionate to their distance from the centre (or the 
square of their distance from the centre). 
This is the way in which the animal must sense a spherical surface. 
It is reminiscent of the way we sense sound. 
At a certain distance from the sphere the animal sees it as a plane. 
Approaching it and touching some point of the sphere, it sees that the relation 
of all the other points to that point 
has changed 
as compared with what it 
should be on a plane, as if all the other points have moved, have drawn aside. 
Touching another point it again sees all the other points withdrawing from it. 
This property of the sphere will appear as its 
motion,
as 'vibration'. And 
indeed the sphere will resemble a vibrating, undulating surface. In the same 
way 
any angle
of a motionless object must appear as 
motion
to the animal. 

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The animal can see an angle of a three-dimensional object only if it moves past it, 
and in that case the object will seem to have turned - a new side has appeared, and the 
old side has receded or moved aside. An 
angle
will be perceived as a turning, a 
movement of the object, i.e. as something transient, 
temporal,
i.e. as a change in the 
state of the object. Remembering the angles met with before - which the animal has 
seen 
as the motion of bodies - it will regard them as gone, finished, vanished, 
belonging to the 
past. 
Of course, the animal cannot 
reason
thus, but it will act as though this was its 
reasoning. 
If the animal could think of phenomena (i.e. angles and curved surfaces) which have 
not yet entered its life, it would no doubt represent them to itself 
only in time.
In other 
words, the animal could not allow them any real existence at the present moment when 
they have not yet appeared.
If it could express an opinion about them, it would say that 
these angles 
exist as a potentiality,
that they 
will be, 
but that 
at present they are not. 
For a horse, the comer of a house past which it runs every day, is a