xxxvlJ perception. 131 



NOTE. 



As stated in the foregoing chapter, an intelligent being, which Case"of a 

 should derive its knowledge of space from sight alone, could j^emg 

 have no idea of more than two dimensions in space. The eye knowfecl"e 

 sees surface only ; and if knowledge of space came exclusively °^ ®P^°^ 

 through the eye, it would be of superficial extension alone, sio-ht only. 

 And further : the superficial extension thus cognised would not 

 be that of a plane surface, but that of the interior surface of a cognise 

 sphere ; for, as previously stated, the eye really sees all things, °"ly 

 as it sees the stars, projected on the interior surface of a sphere, and that 

 It would consequently be impossible for such a being to have *^^'' snrface 

 any knowledge of the properties of a plane surface, or of any 

 surface except a spherical one ; and as a straight line cannot be 

 drawn on a sphere, it could have no idea of a straight liae. 

 All plane surfaces would appear to it as portions of the surface it wonkl 

 of the sphere, and all straight lines would appear as arcs of ^°^ . 

 great circles drawn on the sphere. The propositions of solid lin'es'as 

 geometry would be unmeaning to such a being : the propositions ^^''^^ °^ 



f FGilt 



of plane geometry would appear to be true only on an infinitely circles. 

 small scale ; and a race of such beings would perhaps make the -plane 

 first great improvement in their methods of studying geometry, geometry 

 by introducing the conception of infinitely small portions of ggem^rue 

 surface, in order thereon to study the properties of lines and to it only 



%--• . . n^ly ■ 



There is nothing hypothetical in all this ; it is simple mathe- small 



matical truth. It is mathematically impossible for the eye to see ' ^ ^' 



a plane surface or a straight line. Plane surfaces, and indeed '^^^ ^J^ 



CtlUllOt SG6 



all surfaces whatever, are see^i as portions of the surface of a a plane 



lere : straight lines are see7i as arcs of great circles on the •'*"i"'^'^.'' "'" 

 sphere. Every one who understands enough of geometry to line, 

 perceive the absurdity of asking whether the moon appears straight 

 bigger or less than a cheese, is aware that this is true of the lines are 

 heavens ; and every one who has studied the theory of perspec- ^,.^!! ^^ 

 tive knows that it is true of what we see on the earth. When great 

 we 2^<'rceive plane surfaces and straight lines by sight, we do not ''"° '^^' 

 see them ; we infer them from what we see. Perception is only 



K 2 



