328 



SCIENCE 



[N. S. Vol. XLII. No. 1080 



above title, publislied in the April, 1915, ntun- 

 ber of the Revue du Mots. As this article was 

 written by a Frenchman after the beginning 

 of the great European War, it has naturally- 

 been very much influenced by feelings aroused 

 by events connected with this war. 



The central thought of the article is that 

 there is a great tendency to lay too much stress 

 on quantity and too little on quality in speak- 

 ing about scientific achievements. It is per- 

 haps natural, under the conditions existing 

 while the article was written, that the author 

 concluded that the Germans had done most 

 during the last forty years to acclimatize in 

 Europe the conception which makes quantity 

 the sole criterion for the social, intellectual 

 and moral values of the people. Many Ameri- 

 can readers may however regret to find that 

 this conception is said to be of American 

 origin, even if this statement is modified by 

 the fact that the most cultured Americans are 

 striving to habituate their countrymen to 

 judgments based on quality. 



Among the illustrations given by Professor 

 Borel in support of his contention that the 

 Germans have in recent years unduly empha- 

 sized quantity is the following small table, 

 which aims to give the approximate number of 

 letters in an average volume of certain im- 

 portant mathematical periodicals: 



Mathematische Annalen . . 1,680,000 



American Journal 1,014,000 



Journal de MatMmatiques. .1,012,000 



Acta Mathematica 980,000 



Journal fur Matliematik . . . 875,000 

 Annali di Maiematica .... 825,000 



This table was first published at the end of 

 the " Generalregister " to the first fifty 

 volumes of the Mathematische Annalen. About 

 two years after its publication the Transac- 

 tions of the American Mathematical Society 

 began to appear in volumes involving a much 

 larger number of letters than the American 

 Journal, which occupies the second place in 

 the given list. While it may be questioned 

 whether it is desirable to direct special atten- 

 tion to the mere size of the volumes of a 

 periodical the given table has at least an indi- 

 rect value, since it furnishes an interesting 



concrete illustration of the meaning of a 

 million. 



As questions relating to quantity are much 

 more easily treated by statistical methods than 

 those relating to quality, the growing popular- 

 ity of statistical methods, even in educational 

 matters, seems to be a sign that we are at 

 present placing too much emphasis on quan- 

 tity at the expense of quality. Mental inert- 

 ness naturally leads to considerations of quan- 

 tity rather than of quality. It is much easier 

 to enumerate the books and articles v^ritten 

 by a certain man than to exhibit the value and 

 influence of these publications. It is easier 

 to estimate a man's wealth in dollars than to 

 determine the merits of his inteUeetual con- 

 tributions or his moral influence on his fellows. 

 It is easier to give the number of students at 

 a university and the size of the budget than 

 to estimate the value of the work done at the 

 institution. 



In view of the fact that questions of quan- 

 tity are usually much easier than those re- 

 lating to quality, it is perhaps the more sur- 

 prising to find that Professor Borel attributes 

 to America the origin of the conception which 

 makes quantity the unique criterion for social, 

 intellectual and moral values of the people. 

 If this criticism is not deserved it should cer- 

 tainly not pass unanswered, for the implica- 

 tions which it involves are fundamental and 

 far-reaching. The fact that the criticism was 

 made by a man of very high scientific standing, 

 who recently spent some time in our midst 

 and in company with some of our leading men, 

 makes it all the more noteworthy. 



It is perhaps especially interesting that the 

 tendency to make quantity the sole criterion 

 for intellectual values should be regarded as 

 being of American origin. Intellectual leader- 

 ship even along somewhat baneful lines im- 

 plies vigorous inteUeetual life, and it is of 

 some interest to find that we are credited 

 with such life by a competent observer. As 

 Professor Borel is a mathematician it would 

 appear probable that his conclusions in regard 

 to the intellectual activities of a people would 

 be largely influenced by their mathematical 

 productiveness. It can, however, not be said 



