Decembek 5, 1913] 



SCIENCE 



793 



planet would quickly assume the aspect of 

 a ruined and bankrupt world. 



As our lecturer has been constrained by 

 circumstances to back into his subject, as 

 he has, that is, been compelled to treat 

 first of the service that mathematics has 

 rendered engineering, he will probably 

 next speak of the applications of mathe- 

 matics to the so-called natural sciences — 

 the more properly called experimental sci- 

 ences — of physics, chemistry, biology, econ- 

 omics, psychology, and the like. Here his 

 task, if it is to be, as it ought to be, exposi- 

 tory as well as narrative, will be exceed- 

 ingly hard. For how can he weave into 

 his narrative an intelligible exposition of 

 Newton's "Principia," Laplace's "Meca- 

 nique Celeste," Lagrange's "Mecanique 

 Analytique," Gauss's "Theoria Motus 

 Corporum Coelestium," Fourier's "Theorie 

 de la Chaleur," Maxwell's "Electricity 

 and Magnetism," not to mention scores of 

 other equally difficult and hardly less im- 

 portant works of a mathematical-physical 

 character? Even if our speaker knew it 

 all, which no man can, he could not tell it 

 all intelligibly to his hearers. These will 

 have to be content with a rather general and 

 superficial view, with a somewhat vague 

 intuition of the truth, with fragmentary 

 and analogical insights gained through 

 settings-f orth of great things by small ; and 

 they will have to help themselves and their 

 speaker, too, by much pertinent reading. 

 No doubt the speaker will require his hear- 

 ers, in order that they may thus gain a 

 tolerable perspective, to read well not only 

 the two volumes of the magnificent work of 

 John Theodore Merz dealing with the his- 

 tory of European thought in the nine- 

 teenth century, but also many selected por- 

 tions of the kindred literature there cited 

 in richest profusion. The work treats 

 mainly of natural science, but it deals 

 with it philosophically, under the larger 



aspect, that is, of science regarded as 

 thought. By the help of such literature in 

 the hands of his auditors, our lecturer will 

 be able to give them a pretty vivid sense of 

 the great and increasing role of mathe- 

 matics in suggesting, formulating and solv- 

 ing problems in all branches of natural sci- 

 ence. Whether it be with "the astronom- 

 ical view of nature" that he is dealing, or 

 "the atomic view" or "the mechanical 

 view" or "the physical view" or "the 

 morphological view" or "the genetic view" 

 or "the vitalistic view" or "the psycho- 

 physical view" or "the statistical view," in 

 every case, in all these great attempts of 

 reason to create or to find a cosmos amid 

 the chaos of the external world, the pres- 

 ence of mathematics and its manifold serv- 

 ice, both as instrument and as norm, illus- 

 trate and confirm the Kantian and Eie- 

 mannian conception of natural science as 

 "the attempt to understand nature by 

 means of exact concepts." 



In connection with this division of his 

 subject, our speaker will find it easy to 

 enter more deeply into the spirit and mar- 

 row of it. He will be able to make it clear 

 that there is a sense, a just and important 

 sense, in which all thinkers and especially 

 students of natural science, though their 

 thinking is for the most part not rigorous, 

 are yet themselves contributors to mathe- 

 matics. I do not refer to the powerful 

 stimulation of mathematics by natural 

 science in furnishing it with many of its 

 problems and in constantly seeking its aid. 

 What I mean is that all thinkers and espe- 

 cially students of natural science are en- 

 gaged, both consciously and unconsciously, 

 both intentionally and unintentionally, in 

 the mathematieization of concepts — that is 

 to say, in so transforming and refining 

 concepts as to fit them finally for the amen- 

 ities of logic and the austerities of rigorous 

 thinking. We are dealing here, our speaker 



