THE FOURTH DIMENSION 123 



definite conclusions in regard to what would be the condi- 

 tion of things if the universe really exists in a fourth, or 

 even in some higher dimension. Professor W. W. R. Ball 

 tells us that 



" the conception of a world of more than three dimensions 

 is facilitated by the fact that there is no difficulty in imagin- 

 ing a world confined to only two dimensions which we 

 may take for simplicity to be plane though equally 

 well it might be a spherical or other surface. We may 

 picture the inhabitants of flatland as moving either on the 

 surface of a plane or between two parallel and adjacent 

 planes. They could move in any direction along the 

 plane, but they could not move perpendicularly to it, and 

 would have no consciousness that such a motion was 

 possible. We may suppose them to have no thickness, 

 in which case they would be mere geometrical abstractions ; 

 or we may think of them as having a small but uniform 

 thickness, in which case they would be realities." 



" If an inhabitant of flatland was able to move in three 

 dimensions, he would be credited with supernatural powers 

 by those who were unable so to move ; for he could appear 

 or disappear at will ; could (so far as they could tell) create 

 matter or destroy it, and would be free from so many con- 

 straints to which the other inhabitants were subject that his 

 actions would be inexplicable to them." 



" Our conscious life is in three dimensions, and natur- 

 ally the idea occurs whether there may not be a fourth 

 dimension. No inhabitant of flatland could realize what 

 life in three dimensions would mean, though, if he evolved 

 an analytical geometry applicable to the world in which 

 he lived, he might be able to extend it so as to obtain results 

 true of that world in three dimensions which would be to 

 him unknown and inconceivable. Similarly we cannot 

 realize what life in four dimensions is like, though we can 

 use analytical geometry to obtain results true of that world, 

 or even of worlds of higher dimensions. Moreover, the 

 analogy of our position to the inhabitants of flatland en- 



