ENGINEERING AND PURE SCIENCE — SWANN 207 



Now, frequently, the rule-of-thumb procedure, while deficient in 

 the obviousness of its relation to fundamentals, is apt to take care 

 of complications in circumstances which might be almost infinitely 

 difficult for any mathematician to take care of by trying to solve 

 for the consequences of the fundamentals. Thus, if an authority on 

 acoustics should endeavor to construct a violin without collaboration 

 with an exponent of that craft, I doubt that he would produce as 

 good a violin as Stradivari. Moreover, I rather surmise that if 

 Antonio Stradivari and Nicolo Amati came to life today and held 

 a discussion with the great violinmakers of our epoch, the discussion 

 would be much more harmonious than would one between engineers of 

 these periods. 



When the physicist is presented with a complex situation, where 

 the complexity has not grown under his own guiding hand, he may feel 

 temporarily at a loss to know where to begin the attack upon his prob- 

 lem. His standard method of procedure is to take the simple, under- 

 stand it thoroughly, and build up from it the complex. When he 

 cannot start with the simple, his natural desire would be to peer 

 through the complex in the hope of finding the simple as the origin 

 of it all in the background, as one might suppose a person, suddenly 

 coming upon a television apparatus, seeking to peer through the com- 

 plexity of operation down to those fundamentals which constituted 

 the experiment of 40 years ago. Having found the fundamentals in 

 this way, he would like to watch the offspring of these fundamentals 

 develop through themselves, their children, and their grandchildren, 

 to the television set which is before him. In this way, he would feel 

 that he could understand the operation of the set and be in a position 

 to keep it in order and possibly improve it. 



However, when the complex is presented to the physicist, he is faced 

 with several difficulties. In the first place, the complex is apt to be 

 made up of a heterogeneous mixture of methods and principles, some 

 of dubious relevance and some even inconsistent. Or even, if irrel- 

 evancy and inconsistency are absent, the complexity of the situation 

 may be such that it is very difficult, if not humanly impossible, to trace 

 matters back to their fundamentals. One then has to deal with em- 

 pirically discovered laws which one must believe to have their origin 

 in more fundamental laws, although he may not be able to trace that 

 origin. Such empirical laws are represented in perhaps their nearest 

 approach to their fundamentals by the ordinary laws of stress and 

 strain applicable in the theory of elasticity. In a vein farther re- 

 moved from the fundamentals one has such empirical regularities as 

 have dictated the general shape and method of construction of a violin. 



The fact is that the solution of a problem involves two parts, the 

 fundamental laws which control all problems of the class studied, 

 and the features (boundary conditions) which determine the particu- 



