178 THE PRINCIPLES OF SCIENCE 



to be prized beyond all other possibilities of explanation. In our own 

 age this spirit still moved in Einstein, who expressed a very deep- 

 seated conviction in writing that: 



I feel sure that pure mathematical construction allows us to discover 

 the concepts, and the laws connecting them, which supply the key to 

 the understanding of natural phenomena. ... In a certain sense, 

 therefore, I hold it to be true that pure thought can comprehend 

 reality, as the ancients dreamed. 



Those who share this conviction find explanation in the mathematical 

 form of a physical theory. Of course, not all scientists share this con- 

 viction, and not all accepted scientific theories have this form. More- 

 over, we shall find in the next chapter that a theory cannot be purely 

 mathematical if it is to function at all as a physical theory. We must 

 be able to find in its abstract postulates something more than the epit- 

 ome of clarity: in them we must find also some sense of analogy. 



Analogy. "Explain" laws by derivations from theoretical postulates 

 unexplained and inexplicable in the context of the theory they con- 

 stitute? To wield the dieory eflFectively, clearly we must somehow 

 learn to grasp its postulates— and this we always seek to do by relat- 

 ing them analogically to things or situations that serve us as "models." 

 Thus, Bridgman observes, 



. . . the model is a useful and indeed unescapable tool of thought, 

 in that it enables us to think about the unfamiliar in terais of the 

 familiar. 



The lonians perforce sought models outside the science they were 

 first to create— and found them everywhere, e.g., in the action of the 

 winnower's sieve, and the operation of felting. However, by the 

 middle of the 19th century, one particular privileged class of scien- 

 tific models was established by the rise of classical mechanics. The 

 major scientific synthesis extant, it was thoroughly familiar, ap- 

 parently simple, and superbly competent to give a convincing ac- 

 count of just those purely mechanical systems of which man had had 

 the longest and widest experience, and now felt the deepest under- 

 standing. A Kelvin might then understandably assert: 



I never satisfy myself until I can make a mechanical model of a 

 thing. If I can make a mechanical model I can understand it. As 

 long as I cannot make a mechanical model all the way through I 



