A.— MATHEMATICAL AND PHYSICAL SCIENCES 29 



pulsory causality of the old mechanics, and there seemed no loophole 

 allowing us to do so until the Uncertainty Principle. Knowing what we 

 now know we may ask why no one discovered the loophole by applying 

 a strict analysis, for example by the use of symbolic logic. Such an 

 analysis would presumably have revealed the fault, but the trouble is 

 that it would also have revealed other unwarranted assumptions which 

 we have made but which we do not in the least want to doubt, so that it 

 would not really have helped in pinning down the exact point of error. 

 It is invention, not criticism, that leads to the advance of knowledge. 



Following up the later history of the subject, the success of Heisenberg 

 in exploiting the idea of observables for atoms seemed to repeat the 

 brilliant success of Einstein twenty years earlier in using the same idea 

 over relativity. It seemed to imply that what was wanted in physics 

 was to free ourselves of all abstractions and only make theories about 

 real things. There grew up a great cult of doubting the reality of 

 unobserved things, and then a curious thing was found ; the charm 

 did not work again, and only a few minor things have come out of it. 

 The work of the New Quantum Theory has in fact run most surprisingly 

 in the opposite direction. The technique is largely concerned with 

 wave-functions, which are quantities much more abstract than anything 

 in classical mechanics. There is certainly nothing observable, or even 

 picturable, about waves propagating themselves in many-dimensional 

 space with absolutely unknowable phase, and with intensity controlled 

 by the curious extraneous rule of normalisation. Largely by the use 

 of these wave-functions the whole of atomic physics has been reduced 

 to order, and so has molecular physics, except that it yields problems in 

 which so many electrons are interacting that a full discussion is not 

 feasible. So the doctrine of theorising only about observables was not 

 really a useful doctrine ; it merely provided a germinating idea. In 

 fact we may well ask what an observable is, and if we go at all beyond 

 direct sensations, which as physicists we certainly intend to do, the 

 answer becomes perfectly indefinite. This opinion I heard admirably 

 expressed a few years ago by the late Prof. Ehrenfest. It was in a 

 physics meeting in Copenhagen and someone was proposing a way out 

 of certain difficulties which involved, as he maintained, a reversion to 

 the cult of the observable. Prof. Ehrenfest said : ' To believe that one 

 can make physical theories without rnetaphysics and without unobserv- 

 able quantities, that is one of the diseases of childhood — das ist eine 

 Kinder krankheit. ' 



I have dwelt at some length on the history of the quantum theory 

 because I think it serves as an analogy to the deeper question of what is 

 wrong with the old logical processes. Just as we used to feel the all- 

 pervading compulsive force of causality, so we feel the all-pervading 

 force of pure logic. Just as we felt that classical mechanics provided no 

 room for anything beyond itself, so we feel that the old logic is the only 

 admissible kind of reasoning. We knew that certain things led to the 

 Old Quantum Theory and obstinately refused to fit into mechanics, and 

 we know that the principle of probability can cover many things outside 

 the old logic. Many men tried to force the quantum into the classical 



