(…) Animals see two dimensions. They constantly sense the third dimension but do not see it. They sense it as something transient, as we sense time. The surfaces which animals see possess for them many strange properties; these are, first of all numerous and varied movements. It has been said already that all illusory movements must be perfectly real for them. These movements seem real to us also, but we know them to be illusory, as for instance the turning round of a house as we drive past, the springing up of a tree from round the corner, the movement of the moon among the clouds and so on.
(…) In addition, many other movements will exist for animals which we do not suspect. Actually a great many objects, completely motionless for us - indeed all objects - must appear to animals as moving. And it is precisely in these movements that the third dimension of solids will be manifested for them, i.e. the third dimension of solids will appear to them as motion.
(...) Let us try to imagine how an animal perceives objects of the external world. Let us suppose that a 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.
} Which these ‘cosmonauts’ (read ‘aquanauts’) are,” they said.
