
NATURE 

THURSDAY, AUGUST ‘12, 1915. 

THE PROBLEMS OF SCIENCE, 
Problems of Science. By Prof. F. Enriques. 
Authorised Translation by K. Royce. Pp. 
Xvi+392. (Chicago and London: The Open 
Court Publishing Co., 1914.) Price ros. net. 
ESIDES two introductory chapters of a more 
or less metaphysical kind, this work con- 
tains four others dealing respectively with logic, 
geometry, mechanics, and the extension of 
mechanics; the last concluding with a section on 
the phenomena of life. This range of subjects 
is so great that, as might be expected, the treat- 
ment of them is unequal; but the fact that they are 
all discussed by a mathematician is significant, 
and for at least two of the main topics (geometry 
and physics) the author’s special knowledge is 
of great value. 
Naturally, a reader will be inclined to attach 
most weight to the section on geometry; in some 
respects he will be right. In this domain 
Prof. Enriques is a leading authority, and 
as he is treating of a subject with which he is 
thoroughly familiar, the result is very lucid and 
informing. We have a valuable historical account 
of -the development of geometrical concepts, 
culminating with projective geometry in its 
modern form, and the different non-Euclidean 
theories, including the non-Archimedean geometry 
of Veronese; a good discussion of postulates; 
and a certain amount of psychological criticism, 
which is of a more controversial kind. One 
remark may be noticed as being (in English, at 
any rate) rather misleading. Before discussing 
Veronese’s geometry, the author says :—‘In the 
preceding examples the postulates that correspond 
to the various geometries express different 
physical hypotheses.” As it stands, this 1s 
incorrect; any geometry, as such, is independent 
of physics altogether. What is probably meant 
is that each of the three Archimedean geometries 
is conceivably admissible as the “real”? geometry 
most suitable for the physicist to assume in con- 
structing his hypotheses. For instance, certain 
observations might make it simpler to assume a 
Riemann geometry than to modify the laws of 
motion. There is, on the other hand, no 
possibility of detecting by observation the exist- 
ence of a non-Archimedean space, and there does 
not seem to be any possible development of 
physics which would naturally require the 
assumption of such a space. 
To us the most interesting part of the book 
is that which deals with time. The author makes 


639 

and physical time which is likely to be really 
valuable, if used with the proper reservations; 
and he makes several useful remarks which 
illustrate the difference between a mathematician 
and an unmathematical metaphysician. For 
instance, it is pointed out that “the notion of 
before and after does not furnish any criterion for 
comparing two intervals of time which have not a 
common beginning (or end)’—or, we may add, 
are derived from a succession A, B, C, D, which 
involves that BC<AD. For instance, yesterday 
and to-day together are longer than to-day; but 
from this we cannot infer anything about the 
length of to-day as compared with that of yester- 
day. The importance of having a ciear concept 
of time has been recently emphasised by the 
theory of relativity (discussed pp. 349-63), and 
hypotheses in elasticity and thermodynamics where 
the influence of “heredity” is assumed (pp. 
316-17). 
The sections on physics are very interesting, 
and, so far as we can judge, give a sound and 
clear view of its main principles, as at present 
understood. The author’s general attitude is stated 
on p. 366 in a passage too long to print here. 
Briefly, it is that in any physical science we form 
a set of concepts and hypotheses by abstraction 
from a set of experiments; we thus have a 
provisional “scheme of relations” which we test 
by more refined experiments. The latter may 
refute one or more of our hypotheses; as a matter 
of fact, the more usual result nowadays, at least 
in physics, is to suggest corrections or modifica- 
tions in our formule, by which they become more 
concordant with the results of observation. This 
summary, of course, does not do justice to the 
author; it is in the way he shows historically 
how these tendencies have been at work that one 
great merit of his work consists. In this respect 
he may be compared with Mach, by whom he has 
evidently been much influenced. 
The section on biology might well have been 
omitted; the time has not come for making any 
such general statements about the principles of 
biology as we can make about those of mathe- 
matics and physics. We are glad to find, 
however, that on p. 201 he does protest (all too 
mildly) against some of the absurdities of the 
experimental psychologists, when they wander 
from their proper sphere. That Wundt, for 
instance, should attempt “to derive the planary 
structure of intuitive space from the fact that the 
arrangement of the bones is such as to favour 
rectilinear movement” is one of the most extra- 
ordinary examples of begging the question we 
have ever seen. As Prof. Enriques points out, 
(like Bergson) a distinction between psychological | the arrangement of the bones is not in favour of 
NO. 2389, VOL. 95] 
BB 
