March 23, 1922J 



NA TURE 



381 



new methods of medical treatment for infected man. 

 (2) Systematic instruction and tactful control of the 

 peoples affected. This will be the duty of the medical 

 and teaching professions of the stricken countries. 

 Anyone who has watched the increase of well-taught 

 and capable physicians in such a country as India 

 during the last twenty years will base great hopes on 



the growth of this influence. (3) And most important, 

 a common and indignant consciousness that these 

 plagues are not inevitable, that by combined effort they 

 can be cast off, and that it is a disgrace to humanity that 

 one-half of its members should be harbouring these 

 loathsome parasites. 



The Theory of Relativity in Relation to Scientific Method.^ 



By Dr. Dorothy Wrinch, Fellow of Girton College, Cambridge. 



SOME interesting criticisms of the theory of rela- 

 tivity have been advanced recently by M. Paul 

 'ainleve, in two papers in the Comptes rendus de 

 Academic des Sciences de Paris.^ M. Painleve attacks 

 the theory as it at present stands, on grounds which 

 are of general scientific interest. He criticises the 

 expression for ds, the element of length adopted by 

 l^instein, 



ds^ = dt^i - air) - r^{d9'' + sin'' dd<p^) - dr^l{i - air). 



on the ground that it is one of a very large number 

 of forms which satisfy the Einstein conditions. He 

 cites some of the other possible forms for the relation 

 between the length element and the four co-ordinates 

 ir, 0, </>, t), and indicates the various consequences which 

 ensue according to the particular form adopted. 



At this point we encounter, as M. Painleve points 

 out, a serious difficulty ; but it is a difficulty which 

 is present in all scientific investigations. The botanist 

 plotting on paper the results of experiments which 

 were designed to discover the relation between two 

 variables, :!C and y, is faced by the same problem when 

 he decides on the method to be adopted in interpolation. 

 For his experiments merely tell him that, whatever 

 the relation between the variables may be, the function 

 connecting them must be such that when x = x,-, we also 

 have y=yn where (x^, y^), (x2,y2) • • • (xr,yr) • • • 

 (xn,yn) represent, roughly speaking, the results of his 

 experiments. But the number of his observations is 

 necessarily finite ; and it is evident that there are at 

 least as many functions satisfying these conditions as 

 there are points in the mathematical continuum. This 

 difficulty of choosing between a set of functions all of 

 which satisfy the data of the problem presents itself 



It several critical points of the Einstein theory. It is 

 iitirely plain that if science is to be possible, some 



turther principle is required. 



The Simplicity Postulate. 



In the face of this difficulty, it has been the practice 

 Mt" scientific writers to choose the simplest function 

 I \ailable. The question of what constitutes simplicity, 

 or rather the question of when one function is simpler 

 than another, is a difficult one, but in ordinary scientific 

 work, and especially in biology, the term is considered 

 to be well understood. In selecting the simplest alter- 

 native, no one, of course, would hold that the other 

 alternatives are impossible. Indeed, the simplicity 



' Paper read before the Congress of Philosophy in Paris on December 29, 

 1921. 



• " La Mecanique classique et la thferie de la relativity," October 24, 

 igzi ; " La Gravitation dans la mecanique de Newton et dans la mecanique 

 d'Einstein," November 14, 1921. 



criterion arranges the various possibilities in serial 

 order. If the first of this set afterwards proves un- 

 suitable, the next one is taken, and so on. Thus, in 

 outline, we may say that the procedure of science is 

 to attach probabilities to the various functions in such 

 a way that the probabilities of functions arranged in 

 order of simplicity decrease rapidly to zero, so that 

 there is little probability of any of the more complicated 

 functions which could be devised being the correct one. 

 In criticising this procedure from a logical point of 

 view, it will be of no avail to demand, at the outset, a 

 definition of the relation involved in the proposition 

 that one function is simpler than another. Common 

 sense uses the notion of simplicity, and we cannot go 

 behind common sense. The business of the logician is 

 to interpret it and relate its various beliefs inter se, 

 eliminating when necessary the less fundamental beliefs 

 in favour of those which are held more firmly and the . 

 deductions which can be drawn from these beliefs. 

 But this absence of definition makes it important to 

 consider the way in which the simplicity postulate is 

 used in relativity theory. M. Painleve discusses some 

 of the alternative forms for the length element, to 

 which he sees no objection. He shows that some of 

 them carry with them consequences as to the change 

 in dimensions of a moving body which are mutually 

 inconsistent and in direct contradiction to the Einstein 

 theory. It may therefore be possible to make a choice 

 between some of them by means of data of this kind, 

 and consequently to settle the controversy as to the 

 form of ds, at least to the extent of eliminating those 

 forms which give certain types of change in the dimen- 

 sions of bodies in motion. M. Painleve states that he 

 considers some of his forms to be as simple as the 

 form adopted by Einstein. In the absence of a de- 

 cision being reached by means of further data, the 

 objection of M. Painleve will fall to the ground only if 

 it is established that the form which Einstein has 

 used for the length element is the simplest one which 

 fits the facts of the external world. 



The Value of Comprehensiveness. 



There is another logical property which enables us 

 to assign a value to rival scientific theories. In 

 choosing between various ways of relating facts inter 

 se, we shall evidently prefer theories which group 

 together the largest number of facts under one set of 

 assumptions. Comprehensiveness is, indeed, an im- 

 portant test of the value of a theory, for as the 

 number of facts which are linked together by a theory 

 increases, the theory grows in importance as a 



NO. 2734, VOL. 109] 



