PHILOSOPHY OF PHYSICS MILNE 233 



nebulae. In that case the velocity-distance proportionality would 

 be an altogether ephemeral thing. There is, however, no observa- 

 tional evidence that the nebulae are being accelerated. I have given 

 reasons elsewhere for supposing that the velocity of each nebula is a 

 constant, apart from effect of irregularities in distribution leading to 

 residual gravitational iields. We may consider a smoothed out 

 model of the universe in which the velocity of each is actually con- 

 stant, the distance increasing accordingly with the time. Observa- 

 tion and all theories agree in showing that the nebulae were all very 

 close together about 2,000,000,000 years ago, reckoned by clocks at 

 ourselves. The nebulae may then be likened to an army of objects 

 which all parted company at a definite epoch in our own past, and 

 since then have moved each with its own constant velocity. 



Now, in all schemes so far proposed for the universe, every particle 

 or nebula in the ideal scheme is equivalent to every other. The 

 relation between itself and the rest of the universe is the same 

 whatever nebula is chosen. The reason that this condition is im- 

 posed ° on w^orld models is that we have only actually observed a 

 very small portion of the universe and we want to build up a model 

 of the whole which will not endow the observed portion with sjDecial 

 properties. Removing the last vestige of an anthropocentric view 

 of the universe, we refuse to consider our own viewpoint as special, 

 and we regard any other viewpoint as equally good. If you like, 

 we are extrapolating the observed portion of the universe in the 

 fairest possible way, first by constructing round the edges of the 

 observed portion adjacent portions as similar as possible, then build- 

 ing on to those, and so on, meaning always by " as similar as pos- 

 sible " the possession of the same features as viewed from the view- 

 point to which the extrapolation is extended. Distance and epochs 

 of events on the nebulae can then be assigned in principle by the 

 methods given. The space in which they are embedded is a purely 

 constructed entity. 



It may seem at first sight that if we construct a world model 

 with the same relation of each particle to the rest, then it must 

 extend indefinitely through infinite space. For the possession of 

 an experienced boundary is impossible. Yet it can be shown that 

 on the procedure we have outlined, in view of any observer the sys- 

 tem is of finite radius and the distance of the remotest members of 

 the system cannot exceed a finite length. The apparent paradox 

 is removed by noting that the nebulae form what is called an " open " 

 set of points, infinite in number, having the surface of a sphere for 

 the set of limiting points. The limiting points themselves are not 



* In most current prcseutatioiis of relntivlstic cosmology this condition is not imposed, 

 but is verified a posteriori. In my own presentation it Ij imposed a priori. 



