100 THE MECHANISM OF LIFE 



can be exactly compensated by the opposite kinds of motions of 

 our own body.* 



That means that our three-dimensional space is merely al 

 description of our three degrees of freedom of mobility. If we were ' 

 immovable both in body and eyes, fitted tightly into a solid, 

 transparent universe, we could not have the conception of space,! 

 although we could perceive phenomena to succeed each other 

 there might, for instance, be successive light and darkness. If 

 we imagine ourselves fitted closely into an indefinitely long 

 drain-pipe, we should have freedom of mobility in our dimen- 

 sion (xox) ; if we had to crawl wedged in between two immensely l 

 stretched out plates of glass, we should have freedom of mobility 

 in two dimensions (xox and yoy). If we could move everywhere 

 between the two plates of glass, the latter w r ould be parallel to 

 each other ; note, however, that we need not think about the 

 drain-pipe being straight, nor of the plates of glass being flat 

 both might be curved, and still our space would have one or twoj 

 dimensions. Now remove the plates of glass so that while we 

 are still able to move backwards and forwards, and from side 'to 

 side, we can also gravitate upwards or downwards. 



In the latter case we have three degrees of mobility, and our 

 space becomes three-dimensional (xox, yoy y and zoz). As yet 

 our freedom of mobility is not quite the same in all three dimen- 

 sions. We can move forwards and backwards and from side to 

 side on smooth ice with equal facility, though we always have 

 the " pure intuition " of backwards and forwards (because w 

 can only see in front), and we always have that of right and left 

 (because the functioning of the nervous system is bilaterally 

 asymmetrical). But we can with difficulty raise ourselves above 

 the level of the ice, and we do not usually fall through it. There- 

 fore the intuition of movement up and down is not nearly so 

 intense as are those of movement in the other dimensions. So, 

 also, we judge distances on the horizontal more accurately than 

 we do in the vertical dimensions, and we are afraid to look down 

 through " empty space " from a height that is, we have little 

 control of our mobility in that way, and so we are afraid to fall. 

 And so also non-Euclidean geometries are less familiar and 

 more difficult to us because they express less easily our intuitions 

 of freedom of movement. The four-dimensional geometry is still 

 more difficult, because most people do not appear yet to have 



* That is to say, all motions would be relative if we did not have the 

 absolute intuition of motion of our own body. 



