*Juliana Monachesi *

Nowadays, the relationship between art and mathematics is most visible in computer art which makes use of algorithms in order to develop specific programs for making art. This form of production is also known as “digital art” or “numerical art” because of the binary language used by computers. Mathematics, however, permeates every dimension of life, in forms that are more or less acceptable to our intuition. In Lucia Koch’s solo exhibition at Casa Triângulo (which ends today), the relationships between art and mathematics belong more to the order of froms that are inaccessible through intuition. Thus we find ourselves with in the field of modern mathematics.

“My mother did research in this field, so I learned to think in the language of logic and mathematics. The space I perceive is topological; color is always a relational attribute and element, and my works are sets of sets. This has always been so, but I wanted to make it clearer in the current exhibition,” the artist explains. Topological spaces are a unifying concept that appears in virtually every branch of modern mathematics. Topology is the branch of mathematics that studies topological spaces; it is the study of the topological properties of figures or the geometric properties of a body that are altered by continuous transformation (homeomorphism).

While seeking information on the subject, I come across a text by a scholar [Circe Mary Silva da Silva, “No paraíso dos símbolos: surgimento da lógica e teoria dos conjuntos no Brasil”/ “In the Paradise of Symbols: the rise of set logic and theory in Brazil”] which tells how modern mathematical theory arrived in Brazil. With no expectations, I browse over the text and find an explanation regarding “defined or mentionable sets” and “ideally defined sets” which gives me a broader idea of what it means for an artist to work with sets: “My works are sets of sets…”

The author tells us that, according to mathematician Hélio Gama, “a set is considered defined when a necessary and sufficient condition for an element to belong to that set is known”. However, the idea that there are ideally defined sets is admissible; in this case, “one seeks to admit *a priori* the logical possibility of formulating a criterion for definition, although the criterion cannot be uttered”. Even though the subject here is strictly numbers, I shall allow myself the poetic license of considering Lucia Koch’s works as ideally defined sets.

“Mathematicians diverge with regard to the acceptability –as an element of mathematical logic– of an ideally defined set. The empiricists (Borel and Lebesgue) refute or doubt the existence of a set regarding which defining norms have not been formulated. Some empiricists (Borel and Lusin) go so far as to insist that the definition of a set must imply an effective mode for the construction of its elements. For the idealists (Hadamard, Sierpinski, and R.L. Moore), on the contrary, the existence of unmentionable sets is perfectly legitimate. For Hadamard, the difference between the two points of view is merely psychological” (Gama, 1941, p. 6), quoted by Circe da Silva.

For anyone who has been keeping up with Lucia Koch’s trajectory and arrives at the Casa Triângulo gallery with some norm of definition regarding her groups of works, the exhibition is a surprise. In lieu of the perforated surfaces or the spatial and/or atmospheric photographs of the last few years, we find photographs of collections of tiles. There are elements of known sets: the transparent façade has been covered by perforated adhesives and the exits have been transformed into colored entrances with running acrylic doors – also perforated. The entire series of photographs (of different combinations of tiles) generates a suspension of judgment. What might the artist be dealing with here?

One thing that comes to mind are the ‘tile cemeteries’ that have becoming increasingly rare around town, yet were abundantly present only one or two decades ago. I always considered this to be a very powerful image: unaligned stacks of those old tiles, the memory of a past in which tastes and habits were different – a museum of architectural types and stylistic periods. However, the artist is not interested in the tile’s aesthetic qualities: “The works with images of tiles are directly related to the original walls, creating a sort of mathematical fiction, an order that is parallel to reality”.

I keep wondering whether, in this exhibition, Lucia Koch has not shifted away from the focus of architectural intervention that is so present in her work, taken to its ultimate consequences, it seems to me, in the “Ambient Light” project at Jamac. “My work does not respond only to architecture but to a given situation. Houses, museums and galleries are spaces of different natures for specific uses and events, and are designed and adapted for such. Casa Triângulo’s new space can be traversed, or at least such is the trajectory I imagined: it begins transparently at the façade, where it communicates the most with what is outside it and then goes back inside where it is divided in two all the way to the exits at the rear. The interventions I made with perforated adhesives and at the exits sought to energize this flux. It has more to do with topology, concepts of closed-open, inside-outside”, the artist declares.

She explains the photographic works and the video: “The internal space, self-referential and ostensibly neutral, was used as a place for objects that refer to themselves, a universal set within which other sets communicate. The concrete materials were not constructed according to some aesthetic principle, although the tiles are decorative. They are open systems which may be used to understand mathematical contents, like the materials I handled as a child. And the diversity of the tiles’ patterns creates a certain necessary confusion, generates doubt. At times it suggests an imagination that is more delirious than logical”.

The arrangements that the artist imposes upon this mathematical raw material do, in fact, generate doubt more than they generate logical conclusions (something that is actually a prerogative of art). The computer animation video that was projected onto a wall in a corner of the gallery’s mezzanine during the exhibition, sets in motion that which the photographs only suggest: a succession of images of tiles infinitely recombining themselves in different forms, an undefined set. Once again, the material’s aesthetic power clashes with the project’s most rational intention: the suggestion of an infinite surface decorated with antique patterns is one of unparalleled poetic power.