THE FOURTH DIMENSION. 



95 



tions of the heavenly bodies by means of a three-dimensional mo- 

 tion has been. 



Zollner's arguments from the phenomena of vision may be re- 

 futed as follows : In the first place it is incorrect to say that we see 

 the things of the external world by means of two-dimensional retinal 

 images. The light which penetrates the eye causes an irritation 

 of the optic nerves, and any such effect which, though it be not 

 powerful, is, nevertheless, a mechanical one, can only take place on 

 things which are material. But material things are always three- 

 dimensional. The effect of light on the sensitive plates of photog- 

 raphy can with just as little justice be regarded as two-dimensional. 

 Our senses can have perception of nothing but three-dimensional 

 things, and this perception is effected by forces which in their turn 

 act on three-dimensional things, namely our sensory nerves. It is 

 wrong to call an image two-dimensional, for it is only by abstraction 

 that we can conceive of a thickness so growing constantly smaller 

 and smaller as to admit of our regarding a three-dimensional picture 

 as two-dimensional, by giving it in mind a vanishingly small thick- 

 ness. It is also wrong to say, as Zollner says, that when we see the 

 shadow of a hand which is cast upon a wall we see something two- 

 dimensional. What we really perceive is that no light falls upon 

 our eye from the region included by the shadow, while from the 

 entire surrounding region light does fall on our eye. But this light 

 is reflected from the material particles which form the surface of the 

 wall, that is, from three-dimensional particles of matter. We must 

 always remember that our eye communicates to us only three-dimen- 

 sional knowledge, and that for the comprehension of any thing which 

 has two, one, or no dimensions, a purely intellectual act of abstraction 

 must be added to the act of perception. When we imagine we have 

 made a lead-pencil mark on paper, we have, exactly viewed, simply 

 heaped alongside of each other little particles of graphite in such a 

 manner that there are by far fewer graphite particles in the lateral 

 and upward directions than there are in the longitudinal direction, 

 and thus our reason arrives by abstraction at the notion of a straight 

 line. When we look at an object, say a cube of wood, we recognise 

 the object as three-dimensional, and it is only by abstraction that 



