That a scientific theory is, in some sense, a personal achievement,
becomes evident when we study a number of theories lying within the
same branch of science. The ordinary belief that science is completely
impersonal is certainly not true. And yet it is not easy to see how
a scientific theory can express the personality of its author; it is
difficult, that is to say, to understand in what way a scientific
theory can resemble a work of art. It seems that the fact that a
scientific theory must have “objective truth” renders it an altogether
different thing from a work of art. It would be more just to say that
the element of objective truth radically differentiates a scientific
theory from those works of art which are independent of all experience
of life--as certain musical compositions may be, for instance. But
it is not clear that, in general, works of art are independent of
objective truth; all those works of art which assume experience claim
assent--they do, in their intention, claim universal assent--to the
truth of their assumptions. The serious artist believes his personal
vision to be true; he will not, probably, claim “absolute” truth for
it, but neither does a scientific theory profess to be absolutely true.
And, further, works of art and scientific theories exist to serve the
same purpose--to aid _comprehension_. An artist’s chief title to
consideration is to be found in the depth and extent of his vision,
in the profundity and range, that is to say, of the comprehension he
makes possible. The value of a scientific theory is judged by the same
criteria. So far, therefore, it would appear that the chief difference
between a work of art and a scientific theory is to be found in their
subject-matter. It cannot even be said that the subject-matter is
arranged to serve different ends in the two cases, for in each case the
end which is aimed at is æsthetic satisfaction. Comprehension is one of
the elements of what is loosely termed the æsthetic emotion, and it is
the most important element. Even when we descend to particulars, and
study the quality of similes in poetry, and, indeed, “ornamentation”
generally, we shall find the criterion we employ is still the degree
of comprehension afforded by the device. But we cannot here work out
the analogy in detail. It is sufficient to show that works of art that
have a reference to experience, to an external world, in short, are, in
important respects, similar to scientific theories.
Since, then, a work of art, although conditioned by experience,
may nevertheless be a personal achievement, we need have no _a
priori_ objection to conceding personality to a scientific theory.
In each case it is the method of transformation from what we may
call the raw material to the finished product which is the personal
thing. The artist’s raw material, whether it be the Thames in a fog,
a number of incidents from Holinshed, or the lives of the inhabitants
of a Russian village, is no more and no less common property than are
the _données_ from which a scientific man constructs a theory;
the end product, also, in each case, claims universal assent and
bestows comprehension. What is personal is the law of transformation
by which the one objective thing is changed into the other objective
thing. The law of transformation is different for each individual
mind, and this is as true of scientific men as of any other sort of
men. In this sense, then, both works of art and scientific theories
are personal achievements. A history of science written from this
point of view would be instructive. It would be interesting to trace
the personal element in each great scientific achievement, to show
what kinds of personalities have dominated us, to see what meaning
_eccentricity_ can have as applied to the thought of a scientific
man. But although a detailed history of this kind has not yet been
written, certain _national_ differences have long been recognised.
There is almost as marked a difference between English and French
science as between English and French literature. The English
scientific mind is, on the whole, intuitive, mobile, illogical, and
very prone to imagery of a curiously practical kind. The French
scientific mind, on the other hand, likes to simplify the complicated
reality to as few terms as possible, and then to build up an impeccable
logical edifice. Maxwell was a very fine type of the great English
man of science, but we have Poincaré’s authority for saying that the
great _Treatise on Electricity and Magnetism_ awakens in the
French reader feelings of distrust. So far from finding an impeccable
logical structure, he finds that different parts of the book are
written from different points of view, and that these points of
view are even irreconcilable with one another. Maxwell’s liking for
immensely complicated mechanical models, designed to illustrate some
abstruse equation, is also a stumbling-block to the French reader.
What are such models supposed to prove? Surely Maxwell did not suppose
that the æther contained trains of geared wheels with “idle wheels”
in between? What mysterious satisfaction did he derive from such
unnecessary and irrelevant pictures? But this curious liking for models
is characteristic of the English school, and it is a characteristic
that Continental physicists have never been able to understand. It is
doubtless a manifestation of the English reluctance to get out of touch
with experience. The English man of science trusts logic much less
than he trusts experience. The Frenchman has much less respect for
experience. He is willing to simplify in a way which, to the English
mind, is almost outrageous--to see the Universe as a collection of
little billiard balls with forces varying inversely as the square of
the distance. And on such assumptions he is willing to proceed as far
as logic can take him. There is, indeed, a school in France which
asserts that all we can ever know of the Universe is its equations;
we can never know what they “mean” in the English sense. From the
æsthetic point of view there is no doubt that the French method is to
be preferred. We can all share Lagrange’s satisfaction when he says,
in the Avertissement to his _Mécanique Analytique_: “Je me suis
proposé de réduire la théorie de cette Science, et l’art de résoudre
les problèmes qui s’y rapportent, à des formules générales, dont le
simple développement donne toutes les équations nécessaires pour la
solution de chaque problème.” But we must remember that when the
interest is chiefly in the “développement” the assumptions may remain
uncriticised. The English way is to hold the assumptions tentatively,
and to be always open to the suggestions of experience. The German way,
which, if we are to judge by the work of Riemann and Einstein, seems
to be to concentrate an immense critical apparatus on the assumptions,
is equally interesting. The “philosophic” tendency which is supposed
to characterise German thought in other departments, is certainly
apparent in its science. The three tendencies are sufficiently marked
to constitute national differences and suggest that a detailed analysis
of individual achievements would yield equally interesting results.