## Topological Paintings

Topology is the mathematics of distortion. It represents reality through distortions - contracting, stretching, magnifying and also the tearing of form. The topological perspective represents reality in a fluid, chaotic, hybridic, collage-like form, yet simultaneously also realistically.

## Topological Painting Manifesto

In my topological painting distortion is characterized by a simultaneous convergence of three painting styles representing three different perspectives of reality: the innocent eye (impressionism), the thinking eye (cubism) and the painting hand (expressionism). This is a meeting of three epistemological perspectives: the empirical (the innocent eye), the rational (the thinking eye) and the pragmatic (the painting hand), which together create reality as a topological distortion.

Topological painting has roots in the past. Distorted topological paintings were initially drawn by the expressionists who distorted reality in a caricaturistic manner by intensifying emotions in relation to reality. An extreme distortion of reality was presented by Pablo Picasso in his Surrealistic style that in effect was based on his simultaneous Cubism that represented reality from different perspectives concurrently. Topological distortion was also reflected in the futuristic works of Umberto Boccioni, and in Francis Bacon’s painting style. The biomorphic painting style of Juan Miro, Paul Klee and Jean Arp also echoes the topological view of reality. The painter Maurits Cornelis Escher, whose paintings reflected topological thinking by presenting reality in closed circularity according to the structure of the Möbius band and based on a closed sequence of metamorphosis. The style of Salvador Dali’s last paintings was called “the topological painting” and presented a distinctly topological view of reality.

The three perspectives of reality presented above: the innocent eye, the thinking eye and the painting hand, exist together such that one cannot exist without the others. This mutual dependence is characterized by a topological distortion, similar to the Borromean Rings, as presented by the psychoanalyst Jacques Lacan, in a transition from the mathematical field to the psychological field, as well as by the psychologist Kurt Lewin.

In my topological painting reality is shown as a circular transformation of the disarranging of form, in a parallel process of de-construction and re-construction of reality that complement each other. Accordingly this is a representation of the human psyche that functions simultaneously both rationally and irrationally as two complementing opposites. Chaos as a condition for order.