Septembee 10, 1920] 



SCIENCE 



239 



may be too narrow a view and lead progress 

 into a cul-de-sac; the second may be so broad 

 that it is useless as a guide, and diverges 

 indefinitely from experimental knowledge. 

 When this last case happens, it must be con- 

 cluded that the knowledge is not yet ripe for 

 theoretical treatment and speculation is pre- 

 mature. The time when speculative theory 

 and observational research may profitably go 

 hand in hand is when the possibilities, or at 

 any rate the probabilities, can be narrowed 

 down by experiment, and the theory can in- 

 dicate the tests by which the remaining wrong 

 paths may be blocked up one by one. 



The mathematical physicist is in a position 

 of peculiar difficulty. He may work out the 

 behavior of an ideal model of material with 

 specifically defined properties, obeying mathe- 

 matically exact laws, and so far his work is 

 unimpeachable. It is no more speculative 

 than the binomial theorem. But when he 

 claims a serious interest for his toy, when he 

 suggests that his model is like something 

 going on in Nature, he inevitably begins to 

 speculate. Is the actual body really like the 

 ideal model? May not other unknown condi- 

 tions intervene? He can not be sure, but he 

 can not suppress the comparison; for it is by 

 looking continually to Nature that he is 

 guided in his choice of a subject. A common 

 fault, to which he must often plead guilty, 

 is to use for the comparison data over which 

 the more experienced observer shakes his 

 head; they are too insecure to build exten- 

 sively upon. Yet even in this, theory may 

 help observation by showing the kind of data 

 which it is especially important to improve. 



I think that the more idle kinds of specula- 

 tion will be avoided if the investigation is 

 conducted from the right iwint of view. 

 "When the properties of an ideal model have 

 been worked out by rigorous mathematics, all 

 the underlying assumptions being clearly 

 understood, then it becomes possible to say 

 that such properties and laws lead precisely 

 to such and such effects. If any other dis- 

 regarded factors are present, they should now 

 betray themselves when a comparison is made 

 with Nature. There is no need for 



pointment at the failure of the model to give 

 perfect agreement with observation; it has 

 served its purpose, for it has distinguished 

 what are the features of the actual phe- 

 nomena which require new conditions for 

 their explanation. A general preliminary 

 agreement with observation is necessary, 

 otherwise the model is hopeless; not that it is 

 necessarily wrong so far as it goes, but it has 

 evidently put the less essential properties fore- 

 most. We have been pulling at the wrong end 

 of the tangle, which has to be unravelled by 

 a different approach. But after a general 

 agreement with observation it established, 

 and the tangle begins to loosen, we should 

 always make ready for the next knot. I sui)- 

 pose that the applied mathematician whose 

 theory has just passed one still more stringent 

 test by observation ought not to feel satis- 

 faction, but rather disappointment — " Foiled 

 again! This time I had hoped to find a dis- 

 cordance which would throw light on the 

 points where my model could be improved." 

 Perhaps that is a counsel of perfection; I own 

 that I have never felt very keenly a disap- 

 pointment of this kind. 



Our model of Nature should not be like a 

 building — a handsome structure for the popu- 

 lace to admire, until in the course of time 

 some one takes away a corner stone and the 

 edifice comes toppling down. It should be 

 like an engine with movable parts. We need 

 not fix the position of any one lever; that is 

 to be adjusted from time to time as the latest 

 observations indicate. The aim of the 

 theorist is to know the train of wheels which 

 the lever sets in motion — that binding of the 

 parts which is the soul of the engine. 



In ancient days two aviators procured 

 to themselves wings. Dsedalus flew safely 

 through the middle air across the sea, and 

 was duly honored on his landing. Youag 

 Icarus soared upwards towards the sun till the 

 wax melted which bound hs wings, and his 

 flight ended in fiasco. In weighing their 

 achievements perhaps there is something to 

 be said for Icarus. The classic authorities 

 tell us that he was only " doing a stunt," but 

 I prefer to think of him as the man who 



