AUGTTST 25, 1922] 



SCIENCE 



229 



But the detection of the early stages, discrim- 

 ination between methods of treatment, and de- 

 termination of the most suitable times and 

 modes of applying these can be adequately pur- 

 sued only in the field. The work of the pro- 

 fessors of entomology and of mycology will be 

 eagerly watched in many parts of the empire, 

 and the men they 'train will have no difficulty 

 in finding useful spheres when the demands of 

 the West Indian islands have been satisfied.- — 

 The London Times. 



SCIENTIFIC BOOKS 



Mathematical Philosophy. A study of fate 

 and freedom. Lectures for educated laymen. 

 By Cassius J. Keyser. Pp. xiv + 466. 

 New York : E. P. Button and Company. 



The common saying, "What man would be 

 a philosopher who might be a mathematician" 

 does not seem to apply to the author of this 

 book, who tells us in the preface that for more 

 than two score years he has "meditated upon 

 the nature of mathematics, upon its significance 

 in thought, and upon its bearing on human 

 life." The book is in the form of twenty-one 

 lectures designed primarilj' for students whose 

 major interest is in philosophy but it aims to 

 appeal to a much wider circle of readers, in- 

 cluding professional mathematicians and the 

 "growing class of those natural-science stu- 

 dents who are interested in the logical struc- 

 ture and the distinctive method of mathematics 

 regarded not only as a powerful instrument 

 for natural science but also and especially as 

 the prototype which every branch of science 

 approximates in proportion as its basal as- 

 sumptions and concepts become clearly de- 

 fined." 



The last lecture of the book is on science and 

 engineering. In this lecture the author con- 

 siders various definitions of engineering and 

 then proposes the following : The science and 

 art of directing the time-binding energies of 

 mankind — the civilizing energies of the ivorld, 

 — to the advancement of the ivelfare of man. 

 The language of this definition portrays the 

 type of language used throughout the volume. 

 The reader may at times feel that the language 

 is too flowery to convey much real information. 



but he will generally find that the words are 

 far from empty. Even in the more mathe- 

 matical parts of the book, where the author 

 speaks of the infinite abelian group of angel 

 flights and discusses the question whether mind 

 IS a group, will frequently disclose much care- 

 ful thought in what might at first appear to be 

 superficial statements. 



Professor Keyser has for a long time been 

 preeminent among American mathematicians 

 as regards a certain type of popularization and 

 the present volume is perhaps, up to the 

 present time, his most successful effort along 

 this line. The scientist who wishes to acquire 

 a knowledge of the nature and bearing of 

 some of the fundamental mathematical con- 

 cepts without going deeply into the subject 

 will find here a unique opportunity. It is true 

 that this knowledge is here presented in a 

 sugar-coated form and that there is a danger 

 that some of the readers may not get within 

 this coating, but it is to be hoped that many 

 others will become really interested in the sub- 

 ject matter and will give it sutficient thought 

 to derive a lasting benefit therefrom. Teach- 

 ei-s of mathematics will probably find here 

 attractive features of their own subject which 

 had escaped their attention. In fact, the 

 present writer found the lecture devoted to 

 the group concept worthy of a second reading 

 although he had given much thought to this 

 particular concept before reading this lecture. 

 The book under review occupies a unique 

 and useful place in the mathematical litera- 

 ture of to-day. It deals with a considerable 

 number of fundamental mathematical con- 

 cepts, including those of transformation, inva- 

 riance, infinity, hyperspace, group, variable 

 and limit. Considerable attention is given to 

 systems of postulates and the properties which 

 are essential to a genuine system. In par- 

 ticular, it is noted that the Hilbert system of 

 postulates for geometry is not intrinsically 

 superior to others. On page 43 our author 

 refers to the system of postulates "devised by 

 the late Professor Hilbert and found in his 

 famous 'Foundations of Geometry,' " which 

 would naturally be construed to mean that Hil- 

 bert died before the publication of this book. 

 This is fortunately not the ease. 



