Civilisation : Its Cause and Cure 



But you say it can be proved by mathematics 

 that the ellipse would be the path under these 

 conditions ; to which I reply that the mathematical 

 proof, though no doubt cogent to the human mind 

 (as at present constituted in most people), is open 

 to the same objection that it does not deal with 

 actual facts. It deals with a mental supposition, 

 i.e.y that there are only two bodies acting on each 

 other a case which never has occurred and never 

 can occur and then, assuming the law of gra- 

 vitation (which is just the thing which has to be 

 proved), it arrives at a mental formula, the ellipse. 

 But to argue from this process that the ellipse is 

 really a thing in Nature, and that the heavenly 

 bodies do move or even tend to move in ellipses, 

 is obviously a most unwarrantable leap in the 

 dark. Finally you argue that the leap is warranted 

 because, by assuming that the moon and planets 

 move in ellipses, you can actually foretell things 

 that happen, as for instance the occurrences of 

 eclipses ; and in reply to that I can only say that 

 Tycho Brahe* foretold eclipses almost as well 

 by assuming that the heavenly bodies moved in 

 epicycles, and that modern astronomers do apply 

 the epicycle theory in their mathematical formulae. 

 The epicycles were an assumption made for a 

 certain purpose, and the ellipses are an assumption 

 made for the same purpose. In some respects 

 the ellipse is a more convenient fiction than the 

 epicycle, but it is no less a fiction. 



In other words with regard to this " path of 

 the moon " (as with regard to any other phenomenon 



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