A.— MATHEMATICAL AND PHYSICAL SCIENCES 33 



I have been making are open to every sort of criticism. Perhaps they 

 are right ; as I have said, it is part of my doctrine that the details of a 

 physicist's philosophy do not matter much. But whether it is wrong or 

 right, my next point is one on which I do very much hope that there 

 may be a consensus of agreement. This is that the subject of probabiHty 

 ought to play an enormously greater part in our mathematical-physical 

 education. I do not merely mean that everyone should attend a course 

 on the subject at the university, but that it should be made to permeate 

 the whole of the mathematical and scientific teaching not only at the 

 university but also at school. To the best of my recollection in my own 

 education I first met the subject of probability at about the age of 13 

 in connection with problems of drawing black and white balls out of 

 bags, and my next encounter was not till the age of 23, when I read a book 

 — ^I think it was on the advice of Rutherford — on the kinetic theory of 

 gases. Things are better now, but mathematicians are still so interested 

 in the study of rigorous proof, that all the emphasis goes against the study 

 of probability. 



Its elements should be part of a general education also, as may be 

 illustrated by an example. Every month the Ministry of Transport 

 publishes a report giving the number of fatal road accidents. Whenever 

 the number goes up there is an outcry against the motorists, and when- 

 ever down, of congratulation for the increased efficiency of the police. 

 No journalist ever seems to consider what should be the natural fluctuations 

 of this number. A statistician answers at once that the natural fluctuation 

 will be the square root of the total number, and apart from obvious 

 seasonal effects that is in fact about what the accidents show ; the number 

 is roughly 500 ± 25. The proof of this does not call for any difficult 

 mathematics, neither the error function nor even Stirling's formula, 

 but can be done completely by the simple use of the binomial theorem. 

 There is no mathematical difficulty that should trouble a clever boy of 

 15 ; it is only the train of thought that is unfamiliar, and it is just this 

 unfamiliarity that is the fault of our education. The ideas and processes 

 connected with the inaccuracy of all physical quantities are much easier 

 to understand than many ideas that a boy has to acquire in the course 

 of his studies ; it is only that at present they are not taught, and so when 

 met they are found difficult. 



This is not the place to describe a revised scheme of education. I would 

 only say that it is not special new courses that are needed, but rather a 

 change in the spirit of our old courses. When a boy learns about the 

 weighing machine, emphasise its sensitivity, and consider the length of 

 time that must be taken for the weighing. When he has a problem on 

 projectiles, make him consider the zone of danger and not merely the 

 point of fall. At a rather higher level, but still I should hope at school, 

 introduce the idea of a distribution law ; for example, in doing central 

 orbits work out Rutherford's law of scattering. Calculate the fluctuations 

 of density of a gas, or the groupings in time of the scintillations of «- 

 particles. All these things ought to be examples of a familiar train of 

 thought, and not merely a highly specialised side branch of mathematics 

 first met at the university. It is the incorporation of probability in the 

 other subjects on which I want to insist, but there will of course remain 



