176 SCIENCE AND ART AND EDUCATION vii 



Now, it is a very remarkable fact but it is 

 true of most things in this world that there is 

 hardly anything one-sided, or of one nature ; and 

 it is not immediately obvious what of the things 

 that interest us may be regarded as pure science, 

 and what may be regarded as pure art. It may 

 be that there are some peculiarly constituted 

 persons who, before they have advanced far into 

 the depths of geometry, find artistic beauty about 

 it ; but, taking the generality of mankind, I think 

 it may be said that, when they begin to learn 

 mathematics, their whole souls are absorbed in 

 tracing the connection between the premisses and 

 the conclusion, and that to them geometry is pure 

 science. So I think it may be said that mechanics 

 and osteology are pure science. On the other 

 hand, melody in music is pure art. You cannot 

 reason about it ; there is no proposition involved 

 in it. So, again, in the pictorial art, an arabesque, 

 or a " harmony in grey," touches none but the 

 aesthetic faculty. But a great mathematician, 

 and even many persons who are not great mathe- 

 maticians, will tell you that they derive immense 

 pleasure from geometrical reasonings. Everybody 

 knows mathematicians speak of solutions and 

 problems as " elegant," and they tell you that a 

 certain mass of mystic symbols is " beautiful, 

 quite lovely." Well, you do not see it. They do 

 see it, because the intellectual process, the process 

 of comprehending the reasons symbolised by these 



