By a mathematical approach to art it is hardly necessary to say I do
not mean any fanciful ideas for turning out art by some ingenious
system of ready reckoning with the aid of mathematical formulas. So
far as composition is concerned every former school of art can be said
to have had a more or less mathematical basis. There are also many
trends in modern art which rely on the same sort of empirical
calculations. These, together with the artist individual scale of
value, are just part of the ordinary elementary principles of design
for establishing the proper relationship between component volumes;
that is to say for imparting harmony to the whole. Yet it cannot be denied
that the same methods have suffered considerable deterioration since
the time when mathematics was the fundation of all forms of artistic
expression and the covert link between cult and cosmos. Nor have they
seen any progressive development from the days of the ancient Egyptians
until quite recently, if we except the discovery of perspective
during the Renaissance. This is a system which, by means of pure
calculation and artificial reconstruction, enables objects to be
reproduced in what is called "true-to-life" facsimile by
setting them in an illusory field of space. Perspective certainly
represented an entirely new aspect of reality to human consciousness, but
one of its consequences was that the artist's primal image was debased
into mere replica of his subject. Therewith the decadence of
painting, both as a symbolic art and an art of free construction, may
be said to have begun.
Impressionism, and still more Cubism,
brought painting and sculpture much closer to what were the original elements
of each: painting as surface design in colours; sculpture as the
shaping of bodies to be informed by space. It was probably Kandinsky
who gave the immediate impulse towards an entirely fresh conception of
art. As early as 1912, in his book on The Spiritual Harmony in Art, Kandinsky
had indicated the possibility of a new direction which, if
followed to its logical conclusion, would lead to the substitution of a mathematical
approach for improvisations of the artist's imagination. But as he
found other ways of liberating painting from romantic and literary
associations he did not adopt this particular line in his own work.