SPACE 23 



local signs ; and secondly, through the innervation of our 

 muscular activity. In both cases, these sensations show the 

 same very important property of reversibility, which is made 

 possible by reciprocal cancelling of the direction-sensations. 

 From this we conclude that both kinds of direction-signs, in 

 spite of their different origin, are united in one and the same 

 central sense-organ. This central sense-organ for the direc- 

 tion-signs is in close connection with the semicircular canals 

 of the inner ear. 



POINT AND ATOM 



Having brought the analysis of the basal elements of 

 biology thus far, we are in a position to explain some prob- 

 lems of fundamental importance. It was Helmholtz, as we 

 know, who pointed out that in a world of human beings 

 having cylindrical lenses, the axiom of plane geometry, in 

 accordance with which the shortest distance between two 

 points must be a straight line, would not hold good. We 

 can now explain this paradox, for we can show that there 

 are two sorts of straight lines, one of which invariably obeys 

 the axiom, while the other does not. 



If we understand by " line " a series of direction-signs, 

 then undoubtedly the straight line (i.e. the sequence one after 

 the other of all the similar direction-signs) is the shortest 

 course, i.e. the one that requires the smallest number of 

 direction-signs to get from one point to another. Every 

 deviation from the straight course by bringing in direction- 

 signs of other kinds, will sooner or later lead to the interpola- 

 tion of the opposed sign ; and such a course must be reversed 

 again if the goal is not to be missed. Each detour, by this 

 interpolation of other signs and then their correction, in- 

 creases the number of direction-signs employed. 



If, on the other hand, we understand by " line " a series 



