234 THEORIES AND MODELS 



sophisticated formalism. As an example, consider that since Mendel's 

 time we have learned to concei\'e genes as incompletely independent. 

 We think now of groups of genes associated in linear arrays of some 

 stability (chromosomes). Gi\'en this model, Gamow brings to the 

 study of genetic "coding" a very refined formalism already known to 

 permit determination of the statistical distribution of length in the 

 pieces obtained by repeated random breakage of, say, a great many 

 sticks. 



Concei\dng analogy between two systems, we found on the more 

 familiar a model for the less familiar. So doing, we promptly apply 

 to the second the formalism our previous experience shows success- 

 fully applicable to the first. Often we cannot simply adopt that for- 

 malism unchanged: instead we purposively adapt it, to allow for the 

 difference ( s ) that distinguish the problem system from the model 

 system. We meet this situation in the theory Torricelli constitutes by 

 suggesting that the atmosphere be conceived on the model of a "sea 

 of the air." We then conceive the possibility of explaining certain 

 puzzling observations as aerostatic phenomena, analogous to simple 

 hydrostatic phenomena already amply familiar. But now in construct- 

 ing the axioms of our new theory we take care to modifij the axioms 

 of hydrostatics— to render account of that ready compressibility of 

 the atmospheric fluid which so markedly distinguishes it from fluids 

 treated in hydrostatics. 



MODELS AND SEMANTIC RULES 



A scientific theory may be constituted by affiliating model and for- 

 malism in any of three rather different fashions. Without insisting on 

 their absolute distinctness, I think it useful to distinguish these three 

 cases, which are characterized by the different ways in which "mean- 

 ing" is attached to the primitive concepts, i.e., those that figure in the 

 axioms of the theory. 



First case: Direct denotations and simple models. Consider New- 

 tonian mechanics in its most familiar applications to medium-sized 

 terrestrial systems. Like Euclid before him, Newton gave his system 

 a notably formal development. His primitive concepts include 

 "force," "mass," "time," and "space." In medium-magnitude terres- 

 trial applications we ordinarily attach to "space" denotations estab- 

 lished with the aid of meter sticks, systematic triangulation, and the 

 like; to "time," denotations established around clocks of one sort or 



