Page 36 - Studio International - April 1966

Mathematical models
The term covers a wide range of objects. Here it
refers to three-dimensional models first made in the
nineteenth century to help in visualizing abstract
formulae in space. These range from string models to
plaster surfaces. The former have their origins in the
work of Monge (the founder of descriptive geometry)
and were probably first made after 1850. An example
of the latter is the Surface of Kummer (1864). This
was shown to the art world in 1936—the Surrealists
had 'discovered' the mathematical models in the
Institut Poincaré which they called 'mathematical
objects' (a class of 'objets trouvés') praising them for
their 'disconcerting elegance'.
Around this time certain works of Gabo and Pevsner
showed affinities with mathematical models.
Although he always denied it Pevsner based his
Developable Surfaces on a concept found in certain
mathematical models.
The Russian Constructivists were interested in
mathematical models from the beginning as the
technical demands of their work encouraged a basic
knowledge in the engineering field just as the old art
was dependant on optics, anatomy, etc. The isolated
work of Gabo (illustrated) was an experiment on a
given theme, a model in the Institut Poincaré
demonstrating a mathematical space formula (similar
to the one illustrated).
Gabo has explained that his idea was to take this Right Gabo Construction. 1936
complicated formula and change its realization to
prove that what was basically a fantasy (the intuition
of the mathematician) could be seen through the
intuition of an artist, Gabo says he was attracted to He then devised the 'spheric' theme, an invention Gabo has never made use of formulae but
this model as it was totally asymmetric and that few which he has used more or less consistently ever Vantongerloo, in the thirties, employed equations in a
other models have interested him. since. (The English scientist L. L. Whyte has written number of paintings and sculptures (to judge by
Gabo's Heads of 1916 were partly based on an . . some dates are interesting, though they should their titles) although the works in no way resembled
interest in stereometrics, and the stereometric cube not be overstressed. Gabo took up his spheric theme mathematical models or diagrams. In certain
became the principal theme for a new conception of around 1936, Fejes began his systematic sculptures of Vantongerloo, a Construction in the
sculpture, a consistent development in his works up mathematical study of spherical point arrangements Sphere of 1917, and Plane and Space of 1945, he was
to 1936. in Hungary in 1942 without knowing of earlier work, intuitively dealing with topological themes.
In 1936 he decided that the cube (cornered) concept tentative attempts by J. J. Thomson from 1904 The first artist to deliberately use a topological
of space was restrictive and looked for something in onwards . . .' see his article The unity of visual notion was Max Bill; these were the Endless Ribbon
science that could be considered a basic space experience in the Bulletin of the Atomic Scientists sculptures that date from 1935 based on Mobius'
model, but found it non-existent. Vol XV no. 21959) discovery of 1858.

In Moholy's Bauhaus address, constructivism and con- physics, the creative construction which the artist ther
structive art are presumably to be taken as one and the presents to the world is not scientific, but poetic. It is th(
same. poetry of space, the poetry of time, of universal harmony
`Constructive art is processual, forever open in all direc- of physical unity.' 4
tions. It is a builder of man's abilities to perceive, to react Read's is the Romantic interpretation where the overal
emotionally and to reason logically.' vision is accounted more important than the question o
We can compare this to Gabo (1959) : its relationship to 'theory' and 'principles' or a discus
`To be constructive means to me to be guided by the sion of the real 'elements' used. Read clears the way fo
pattern of our consciousness and to create our images the widest interpretation when he says, 'The acceptance
according to the structure of our consciousness itself, for of such a philosophical basis for art still leaves a consider
only in this way shall we be able to fulfil the task of keep- able latitude in the manipulation of such elements.'
ing the state of mind of the human being, including our Although these quotations date from 1948 they imply
own, in balance and in harmony with the laws of life, that constructive art is the same, fundamentally, a
thus enhancing its growth.'3 abstract art. This is both a throw back to Circle and some
Finally only Gabo remained as a spokesman for con- thing that can be seen again in developments after 194!
structivism, and although he no longer projected a in England and the Continent.
collectivist programme, his ideas continued to retain To understand this we have to go back to Circle (1937
much of the basis of The Realistic Manifesto. Progressively whose most important contributors were Mondrian (wh(
Gabo's views became a philosophy of art, rather than a arrived in London a year later and left in 1940), Moholy
technical/ideological programme, and one open to wide Nagy who left for the U.S. in the year of its publication
interpretations. (having arrived two years earlier), and Gabo, who arrive(
One of the foremost interpreters has been our own Herb- in 1935 and stayed till 1946. Of this period Mondrian
ert Read. wrote, 'Later, constructivism was continued in Paris am
3 Of Diverse Arts, Faber, 1962. `The best preparation for a true appreciation of con- London where it became homogeneous with neo-plasti
structive art is a study of Whitehead and Schrodinger. cism; however, there always remained differences in
4 Read : Gabo and Pevsner, But it must again be emphasized that though the intel-
Museum of Modern Art, viewpoint.'
New York, 1948. lectual vision of the artist is derived from modern The reference to Paris is of course to the importan