As a follow up to the previous post on Vermeer's Allegory of Painting, I have been thinking about the importance of geometrical relationships in the organisation of pictorial space. Interest in science flourished in the 17th century and Vermeer was fascinated by optical devices like the camera obscura. I wonder if the very notion of the rational organisation of his compositions according to various geometrical relationships amounted to an idea? A quick analysis like the one above seems to suggest that the artist was very conscious of mathematics, like many artists before him. Rules of proportion and harmony had been passed down through the centuries and were to be enshrined in academic approaches to art making in the 18th century. The ancient Greeks were fascinated by the mathematical laws they observed in nature. They enjoyed optical illusions and other visual phenomena that can be represented by mathematical formulae. Artists in the Renaissance, in their study of classical civilisation, began to employ some of these rules to create ever more illusionistic representations of space.

In this painting, Vermeer creates a totally believable illusion of three dimensions through the use of linear perspective. This is the stage on which the action of the painting (the artist painting his model) takes place. This sense of illusionistic space is further enhanced by the way he depicts light, from the window behind the curtain to the left of the composition, falling across various objects to reveal their forms.

However, Vermer is also interested in the arrangement of shapes across the two dimensional picture plane. The main central triangle creates a very stable composition. A regularly spaced network of horizontals further anchors the important objects in harmonious relationships. The whole arrangement appears almost completely symmetrical. This allows the artist to create a series of more organic shapes - the folds of the curtain, the billowing cloth of the model's blue sleeve and the network of lines and creases on the wall map - to compliment and soften the geometrical organisation.

Vermeer belongs to a long tradition of artists who have exploited this method of pictorial composition. Look carefully at this example:

Piero della Francesca The Baptism of Christ, 1442 Tempera on panel 167 x 116 cm National Gallery, London

Try drawing a version of the painting that concentrates on its composition. Pay particular attention to the geometrical organisation of space, both in terms of the illusion of three dimensions (using perspective and the diminution of scale) and the arrangement of forms across the picture plane. See if you can work out how the artist set about placing the main elements of the composition.

Once you've done this, try to suggest what this kind of geometrical arrangement suggests about the artist's view of the universe.


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