THE FINITE UNIVERSE 



THE first steps towards a rational conception of the 

 world were taken by the astronomers, and all their 

 work tended towards the idea of a universe whose 

 extent could only be expressed by the vague notion 

 of infinity. From Galileo to the Herschels and our 

 own time the steady improvement of the telescope 

 has meant the steady recession of meets and bounds, 

 until the distances of space have become unthink- 

 ably vast. The result is reflected in popular speech, 

 and in much popular writing. The idea of a uni- 

 verse infinite in extent, infinitely varied in char- 

 acter, is a commonplace. 



Yet, if we consider it closely, there has been very 

 little to justify this belief. On the contrary, per- 

 haps the most remarkable thing in the advance- 

 ment of knowledge has been the fixing of limits in 

 natural phenomena. There is, in fact, much to 

 suggest that there are in nature boundaries beyond 

 which there is nothing, ultimate units of matter 

 which cannot be subdivided, speeds which cannot 

 be exceeded. All this is in direct contradiction to 



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