124 ANIMAL BEHAVIOUR 



Obviously the actual space of our intuition is non-isotropic. 

 A man always walks (that is ordinarily) ahead in the direction 

 o — > + X, that is, is where he starts from and he walks in the 

 direction of the relaxed axes of his eyes. He does not " skid " 

 from side to side as a rule but turns his body so that he still 

 walks ahead. He can only move up and down with difficulty 

 (say by jumping) and then his range of movement is very limited. 

 Right and left are, in actuality, different, partly because of his 

 bodily asymmetry and partly because right-handed and left- 

 handed things (such as gloves, cyclones and anticyclones, etc.) 

 are not the same and cannot be superposed. Thus his space- 

 dimensions are anisotropic. 



Duration has only one dimension — past and future. Time, 

 to the mathematician, is the same in the past as in the future, 

 the formal difference being — / and + t. Eclipses can be cal- 

 culated in past time by the same expressions as in future time. 

 Duration is thus extension and in the mathematics of relativity 

 it is only the fourth extensional dimension (being made so by a 

 mathematical artifice involving the " imaginary," i). 



But the fundamental thing in life is duration that is one- 

 directional and irreversible. Time has " an arrow " given by 

 the entropy-law. An animal continually grows old and never 

 grows young again. Mathematical time (says Oliver Lodge) is 

 as a roadway, but duration is as a river. We can turn back along 

 the road, but we can only turn back on the river when we oppose 

 the resistance of the current. 



The multi-dimensional geometries and the apparent paradoxes 

 of relativity-theory have become conceivable because we can now 

 imagine, and partly realize velocities of motion that transcend 

 those of the Newtonian period. To the old-fashioned biology, 

 based on Newtonian mechanics, there are still three dimensions 

 of anisotropic space and a single dimension of irreversible time. 

 But it must be most clearly realized by the student that space and 

 time intuitions are not unchangeable hut evolve. As our domina- 

 tion over nature, and our powers of moving more and more 

 quickly increase, so our intuitions of space and time must change. 

 The complexities of relativity-theory come from the potential 

 increase of such powers indicated by the equations of the newer 

 physics. 



