THE FOURTH DIMENSION. 



93 



possesses for the physicist. Still more convincing than these cos- 

 mological reasons to the majority of men is the physio-psychologica] 

 reason drawn from the phenomena of vision which Z6llner adduces. 

 Into this main argument we will enter in more detail. 



When we " see " an object, as we all know, the light which pro- 

 ceeds or is reflected therefrom produces an image on the retina of 

 our eye ; this image is conducted to our consciousness by means of 

 the optic nerve, and our reason draws therefrom an inference re- 

 specting the object. When, now, we look at a square whose sides 

 are a decimetre in length, and whose centre is situated at the distance 

 of a metre from the pupil of our eye, an image is produced on the 

 retina. But exactly the same image will be produced there if we 

 look at a square whose sides are parallel to the sides of the first 

 square but two decimetres in length, and whose centre is situated 

 at a distance of two metres from the pupil of the eye. Proceeding 

 thus further, we readily discover that an eye can perceive in any 

 length or line only the ratio of its magnitude to the distance at which 

 it is situated from it, and that generally a three-dimensional world 

 must appear to the eye two-dimensional, because all points which 

 lie behind each other in the direction outwards from the eye pro- 

 duce on the retina only one image. This is due to the fact that the 

 retinal images are themselves two-dimensional ; for which reason, 

 Zollner says, the world must appear to a child as two-dimensional, 

 if it be supposed to live in a primitive condition of unconscious men- 

 tal activity. To such a child two objects which are moving the one 

 behind the other, must appear as suffering displacement on a sur 

 face, which we conceive behind the objects, and on which the latter 

 are projected. In all these apparent displacements, coincidences 

 and changes of form also are effected. All these things must appear 

 puzzling to a human being in the first stages of its development, 

 and the mind thus finds itself, as Zollner further argues, in the first 

 years of childhood forced to adopt a hypothesis concerning the con- 

 stitution of space and to assume that the world is three-dimensional, 

 although the eye can really perceive it as omy two-dimensional. 

 Zollner then further says, that in the explanation of the effects of 

 the external world, man constantly finds this hypothesis of his chi l d- 



