RELATIVITY OF LENGTH 145 



overlooked the fact that he was imagining a world 

 surveyed from outside with standards foreign to it 

 whereas we have to do with a world surveyed from 

 within with standards conformable to it. 



The explanation of the law of gravitation thus lies in 

 the fact that we are dealing with a world surveyed from 

 within. From this broader standpoint the foregoing 

 argument can be generalised so that it applies not only 

 to a survey with metre rods but to a survey by optical 

 methods, which in practice are generally substituted as 

 equivalent. When we recollect that surveying apparatus 

 can have no extension in itself but only in relation to the 

 world, so that a survey of space is virtually a self-com- 

 parison of space, it is perhaps surprising that such a 

 self-comparison should be able to show up any hetero- 

 geneity at all. It can in fact be proved that the metric 

 of a two-dimensional or a three-dimensional world sur- 

 veyed from within is necessarily uniform. With four or 

 more dimensions heterogeneity becomes possible, but it 

 is a heterogeneity limited by a law which imposes some 

 measure of homogeneity. 



I believe that this has a close bearing on the rather 

 heterodox views of Dr. Whitehead on relativity. He 

 breaks away from Einstein because he will not admit 

 the non-uniformity of space-time involved in Einstein's 

 theory. "I deduce that our experience requires and 

 exhibits a basis of uniformity, and that in the case of 

 nature this basis exhibits itself as the uniformity of 

 spatio-temporal relations. This conclusion entirely cuts 

 away the casual heterogeneity of these relations which 

 is the essential of Einstein's later theory."* But we now 

 see that Einstein's theory asserts a casual heterogeneity 



*A. N. Whitehead, The Principle of Relativity, Preface. 



