The mathematical fictions of Lucia Koch, by Juliana MonachesiAn imagination more delirious than logical...Juliana Monachesi

Material Concreto (4 x 4), by Lucia Koch

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.

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“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

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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

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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.

Published by Juliana Monachesi at canalcontemporaneo.com.br, in 2005

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