September 20, 1901.] 



SCIENCE. 



429 



order by codifying the observed facts and 

 laws in accordance with an artificial sys- 

 tem, and thus arranging our knowledge 

 under a comparatively small number of 

 heads. The simplification introduced by a 

 scheme which, however imperfect it may 

 be, enables us to argue from a few first 

 principles, makes theories of practical use. 

 By means of them we can foresee the re- 

 sults of combinations of causes which would 

 otherwise elude us. We can predict future 

 events, and can even attempt to argue back 

 from the present to the unknown past. 



But it is possible that these advantages 

 might be attained by means of axioms, as- 

 sumptions 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 in- 

 deed to construct, but to imagine, some- 

 thing 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 be- 

 tween the action of the model and the be- 

 havior 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 rep- 

 resented, but might be compared to a model 

 in that the behavior of the things repre- 

 sented could be predicted from that of the 

 corresponding parts of the machine. 



We might even go a step further. If the 

 laws of the working of the model could be 

 expressed by abstractions, as, for example, 

 by mathematical formulae, 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 mathe- 

 matical 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 by direct observation, 

 but might nevertheless have learned how 

 these objects would behave under given cir- 

 cumstances. 



We should have abandoned the hope of a 

 physical explanation of the properties of 

 inanimate nature, but should have secured 

 a mathematical description of her opera- 

 tions. 



There is no doubt that this is the easiest 

 path to follow. Criticism is avoided if we 

 admit from the first that we cannot go be- 

 low the surface ; cannot 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 construc- 

 tion 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 

 generalization, is that which has given up 

 the attempt to form clear mental pictures 

 of the constitution of matter, which ex- 

 presses the facts and the laws by language 

 and symbols which lead to results that are 

 true, whatever be our view as to the real 

 nature of the objects with which we deal. 

 From this point of view the atomic theory 

 becomes not so much false as unnecessary ; 

 it may be regarded as an attempt to give an 

 unnatural precision to ideas which are and 

 must be vague. 



Thus, when Eumford found that the 



