72 MYSTICISM AND LOGIC 



student must always be liable. In a world so full of evil 

 and suffering, retirement into the cloister of contempla- 

 tion, to the enjoyment of delights which, however noble, 

 must always be for the few only, cannot but appear as a 

 somewhat selfish refusal to share the burden imposed 

 upon others by accidents in which justice plays no part. 

 Have any of us the right, we ask, to withdraw from 

 present evils, to leave our fellow-men unaided, while we 

 live a life which, though arduous and austere, is yet 

 plainly good in its own nature ? When these questions 

 arise, the true answer is, no doubt, that some must keep 

 alive the sacred fire, some must preserve, in every genera- 

 tion, the haunting vision which shadows forth the goal of 

 so much striving. But when, as must sometimes occur, 

 this answer seems too cold, when we are almost maddened 

 by the spectacle of sorrows to which we bring no help, 

 then we may reflect that indirectly the mathematician 

 often does more for human happiness than any of his 

 more practically active contemporaries. The history of 

 science abundantly proves that a body of abstract pro- 

 positions even if, as in the case of conic sections, it 

 remains two thousand years without effect upon daily 

 life may yet, at any moment, be used to cause a revolu- 

 tion in the habitual thoughts and occupations of every 

 citizen. The use of steam and electricity ^to take striking 

 instances is rendered possible only by mathematics. In 

 the results of abstract thought the world possesses a 

 capital of which the employment in enriching the common 

 round has no hitherto discoverable limits. Nor does 

 experience give any means of deciding what parts of 

 mathematics will be found useful. Utility, therefore, 

 can be only a consolation in moments of discouragement, 

 not a guide in directing our studies. 



For the health of the moral life, for ennobling the tone 



