32 SECTIONAL ADDRESSES 



connection with, semi-permeable membranes, but on the whole does 

 not get far with it. As in much of Gibbs's work, it is the idea itself, 

 rather than what he does with it, that is important. This idea of the grand 

 ensemble is not yet incorporated in the new physics. In the quantum 

 theory we take a number of electrons and nuclei and, allowing for their 

 interactions, we construct something that is practically the canonical 

 ensemble. But we take fixed numbers of them — this is partly reflected 

 in the technical process of using normalised wave-functions. Now in 

 an experiment dealing with a large number of particles we are never 

 really sure exactly how many there are, and to assume this number is 

 much like assuming a constant energy for them. If the canonical ensemble 

 is a better idea than the micro-canonical, then the grand ensemble is 

 superior to the petty ensemble. In the new mechanics nobody has yet 

 succeeded in making anything of it, or has made any proposal how to do 

 so, but I will venture the forecast that when some of our present difficulties 

 in the quantum theory are cleared up, it will be found that we shall be 

 using the grand ensemble with its indefinite number of atoms. 



Reverting to my main theme, what is the moral of all this ? It is 

 that the new physics has definitely shown that nature has no sharp 

 edges, and if there is a slight fuzziness inherent in absolutely all the 

 facts of the world, then we must be wrong if we attempt to draw a picture 

 in hard outline. In the old days it looked as if the world had hard 

 outlines, and the old logic was the appropriate machinery for its dis- 

 cussion. Things went wrong when it was found necessary to call in 

 the help of the principle of probability ; this appeared first as an alien, 

 but there was hope in the old days that the alien might be naturalised. 

 It has resisted the process and we now recognise that it cannot be as- 

 similated, because it provides the necessary step to a wider reason, 

 that of the new fuzzy world of the quantum theory, a world which is 

 not contained in the old. How far it will be possible to make a full 

 synthesis of the new and the old I do not know, but I like to think there 

 is something in my analogy from the history of the quantum theory, 

 and to suppose that we are still in the condition corresponding to the 

 Old Quantum Theory, and that some day a real synthesis will be made 

 like that of the New Quantum Theory, so that there will be only one 

 thing in the world that has not indefinite outlines, and that will be a new 

 reformed principle of reasoning. 



I may fitly conclude this part of my subject by returning to the point 

 from which I started. As an example of what the ordinary man regards 

 as correct reasoning I quoted some words of Sherlock Holmes. I must 

 now confess that I was not quite sincere in my quotation ; the impres- 

 sion I gave was the impression the reader carries away, but on examining 

 the text I was interested to find that the great detective had himself 

 arrived at the ideas I have been putting forward. In the sentence before 

 he said ' No, no ; I never guess. It is a shocking habit, destructive of 

 the logical faculty,' he had said : ' I could only say what was the balance of 

 probability — I did not expect to be at all accurate.' The master-mind 

 uses the word logic in its modern sense. 



There inay be a feeling among some that the very general suggestions 



