THE CURVES OF LIFE: A CRITICISM 403 



been written about these deviations ; that it is very easy to 

 overdo them practically can be seen in the cathedral at Tours. 

 And now, where has this collection of examples of spiral 

 formation in nature and art brought us to ? Albrecht Diirer, 

 who also studied spirals and proportion (Jean Goujon said of 

 him, " No one has thoroughly understood the true theory of 

 this volute except Albrecht Diirer"), wrote in the third of his 

 Four Books on Human Proportion as follows : " Therefore 

 regard Nature diligently, order thyself thereby, and depart not 

 from her in thy opinions, neither think that thou canst invent 

 better of thyself, else thou shalt be led astray. For truly Art 

 standeth firmly fixed in Nature, and only he who can tear her 

 forth possesseth her. If thou vanquish her, she will remove 

 many faults for thee from thy work. . . . But the closer thy 

 work is to life in its form so much the better will thy work 

 appear. And this is true : therefore never more imagine that 

 thou either canst or wilt make anything better than God hath 

 given power to his creatures to do, for thy power is impotent as 

 compared with God's creative power. Therefore it is ordained 

 that no man can ever create a beautiful figure out of his own 

 thoughts unless he hath well stored his mind by study." This 

 seems to express the great artist's feeling of the relation of his 

 work to nature, and it implies that if without proper study and 

 observation an artist can achieve nothing, yet there is something- 

 required in the artist that no study or knowledge can give him. 

 In music, for example, many fugues written as degree exercises 

 are as accurate as any of J. S. Bach's, but the latter have some- 

 thing additional, which enables them to live in men's ears and 

 hearts ; but what that something is we have no words for, whose 

 connotation is exact. But in this book, apart from the Leonardo 

 episode, many things are grouped together, but are not fused 

 into a whole. There is the main thesis of spirals, and of their 

 comparison with an ideal spiral of certain properties, with 

 which is connected the very remarkable discovery of Mr. Mark 

 Barr and Mr. Schooling of the </> ratio. Then there are ques- 

 tions of proportion and its mathematical expression. In 

 considering those parts of the book which deal with proportion 

 it is necessary to carefully keep clear in one's mind the difference 

 between symmetry and proportion, remembering that the latter 

 is the connection of unequal quantities with each other, just as 

 the former is the opposition of equal quantities to each other. 



