A MODEL OE NATURE. 173 



of them we can forsee the results of combinations of causes which 

 would otherwise elude us. We can predict future events, and can 

 even attempt to argue hack from the present to the unknown past. 



But it is possible that these advantages might be attained by means 

 of axioms, assumptions, and theories based on very false ideas. A 

 person who thought that a river was really a streak of blue paint might 

 learn as much about its direction from a map as one who knew it as it 

 is. It is thus conceivable that we might be able, not indeed to con- 

 struct, but to imagine, something more than a mere map or diagram, 

 something which might even be called a working model of inanimate 

 objects, which was, nevertheless, very unlike the realities of nature. Of 

 course the agreement between the action of the model and the behavior 

 of the things it was designed to represent would probably be imperfect, 

 unless the one were a facsimile of the other; but it is conceivable that 

 the correlation of natural phenomena could be imitated, with a large 

 measure of success, by means of an imaginary machine which shared 

 with a map or diagram the characteristic that it was in many ways 

 unlike the things it represented, but might be compared to a model in 

 that the behavior of the things represented could be predicted from 

 that of the corresponding parts of the machine. 



We might even go a step farther. If the laws of the working of the 

 model could be expressed by abstractions, as, for example, by mathe- 

 matical formulas, then, when the formulae were obtained, the model 

 might be discarded, as probably unlike that which it was made to 

 imitate, as a mere aid in the construction of equations, to be thrown 

 aside when the perfect structure of mathematical symbols was erected. 



If this course were adopted we should have given up the attempt to 

 know more of the nature of the objects which surround us than can be 

 gained b}^ direct observation, but might nevertheless have learned 

 how these objects would behave under given circumstances. 



We should have abandoned the hope of a physical explanation of 

 the properties of inanimate nature, but should have secured a mathe- 

 matical description of her operations. 



There is no doubt that this is the easiest path to follow. Criticism 

 is avoided if we admit from the first that we can not go below the sur- 

 face; can not know anything about the constitution of material bodies, 

 but must be content with formulating a description of their behavior 

 by means of laws of nature expressed by equations. 



But if this is to be the end of the study of nature, it is evident that 

 the construction of the model is not an essential part of the process. 

 The model is used merely as an aid to thinking, and if the relations of 

 phenomena can be investigated without it, so much the better. The 

 highest form of theory — it may be said — the widest kind of generali- 

 zation, is that which has given up the attempt to form clear mental 

 pictures of the constitution of matter, which expresses the facts and 



