suckerPUNCH: Describe your project.

Pablo LORENZO-EIROA (Eiroa Architects): In the following experimental project for a house several architectural canons are related to computer space and the digital signifiers that emerge from computer codes.

The resulting diagram for House IIb displaces center and corner conditions into a continuous inside/outside relationship that acknowledges its referential system of representation. House IIb develops three topological displacements that affect the stability of each of its three referential Cartesian coordinate planes. These displacements layer information parametrically, combining different source codes through multiple interfaces. Relative displacements are targeted to activate emerging typological instances to overcome the original organizational structure.

Beginning with three centralized nine square grid volumes, the center of one volume is displaced by becoming continuous with the corner of the other—a relationship repeated in the three axes. The relative relationship between the three axes is also displaced activating multiple typologies within a unifying continuous topology. Therefore House II resolves multiple typologies that are first activated and then critiqued through topological displacements. Synthetic complex continuities between centralized courtyards become internalized through the corners; exterior bridge-spaces become internalized; and finally a twofold L-shape space integrates a horizontal XY house, a vertical YZ house and vertical XY house in a continuous topology.

All of these typologies are integrated into a continuous synthesis that displaces their initial set of categories. The displacement of center-corner and interior-exterior relationships through topology is also taken to another level, since the surfaces that actualize these continuities are also delayered. An internalized topo-logos activates a bodily affection by displacing the deterministic binary-based planar condition of the surface into a differentiated field of interstitial spatial delimitations. Architecture has been expanding towards the landscape.

By enfolding this process to displace the architectural container, House II develops an internalized topo-logos that reveal non-deterministic relationships displacing the original referential Cartesian container space through multiple operations. A single topological surface ensures a gradual difference that activates multiple spatial affections.

Cartopological space becomes active as a post-historical manifesto suspension building continuities between structuralism and post-structuralism, acknowledging and displacing the systems of representation including the information processing protocols that are indexed in the constitution of form.

sP: What or who influenced this project?

PLE: Interfaces are spaces of differentiation. Form, as an output of information, becomes independent from the set of variables that have indexed its constitution. Once form is generated, new conditions emerge that may induce relationships further than those which were originally predetermined. This dimension recognizes an affection inherent in form relative to space and inhabitation once it acquires an autonomy.

Today it is critical to acknowledge the structuring of interfaces, the logic of the underlying binary codes that are motivated in the process of representation to transcend their implicit predetermination. Likewise, the superstructures that have dominated the discipline such as typologies, grids, and other underlying structures must be recognized and displaced, in order for the work not to be trapped by predetermination.

The autonomy of the vectorial surface promptly assumed the presence of a different type of space, a “topological” space based on bi-continuous deformation and non linear spatial relationships. Dynamic computer representation has ignored the ground in architecture since XYZ became exchangeable with each other, inducing a groundless vectorial matrix. The now autonomous topological surface promptly assumed a “topological” space-matrix, substituting and also ignoring Cartesian reference. Topology reacted by negating Cartesian order, substituting it but not displacing it. Topology acquires its full potential when it can be contrasted by exploring alternative spatial relationships and dimensions by displacing its three dimensional frame reference. Topological space does not serve as a system of measurement and reference as non-Euclidean geometry is contained within a range (calculus), constructed, structured, regulated, parameterized and measured against a Cartesian coordinate system. Topology deals with self intersecting form that cannot be projected into bi-dimensional planes, resisting representation, while topological surfaces can only be represented in a dynamic three dimensional plot.

The Möbius surface model displaced XY “ground plane”, continuing the first post-structuralist process of reaction to Cartesian order engendered by grounded buildings. The Möbius surface acquired autonomy from the ground informing the architectural envelope. The self intersecting Klein topological model is a combination of two Möbius models integrating XY to YZ adding independency from the ground and acquiring autonomy as an object informing another dimension. The Boy Surface model integrates three Klein topologies and six Möbius models into a continuous sequence, articulating the three coordinate planes XY-YZ-XZ self intersecting each other, providing a continuity between the negative and positive sides of each referential plane and opening up a model that is meant to displace the Cartesian reference.

Spatial organization plays an essential role at a cognitive level, presenting limits to how architects and other disciplines measure and understand different space-time paradigms. There is an emerging necessity to work by layering information in a multi-dimensional space surpassing the constraints of three coordinate space. But this layering of information must be critical of the set of digital parameters that prescribe form. In this sense, progressive parametric topological displacements have to seek for a break in a conceptual differentiation, aiming for a structural change typologically significant to transcend the simple variation of the form of their initial implicit or explicit structures:

THE IMPLICIT PROJECT IN PARAMETRIC VARIATIONS IS TO RESOLVE WITHIN RELATIVE TOPOLOGICAL DISPLACEMENTS SUCH A STRUCTURAL TYPOLOGICAL CHANGE THAT IS ABLE TO CRITIQUE AND TRANSCEND THE DEPARTING STRUCTURE.

sP: What were you reading/listening to/watching while developing this project?:

PLE: Reading: Heinrich Wölfflin, *Renaissance and Baroque*; Manfredo Tafuri, *Theories and History of Architecture*; Enric Miralles with Eva Prats, “How to Lay Out a Croissant”; Bernard Cache, *Earth Moves*; Nader Tehrani, *Material Ultramaterial*; Ciro Najle and Mohsen Mostafavi, *Landscape Urbanism*; Georges Teyssot, “The Membrane and The Fold”; Mario Carpo, *The Alphabet and the Algorithm*; Patrik Schumacher, “Parametricism as Style.” Watching: no TV, resisting Netflix; *La Notte*, Michelangelo Antonioni (dir.); *Pictures From The Surface Of Earth *(NYC), Wim Wenders (dir.). Listening to: Sloth Canon, “Cello Suite No. 1,” J. S. Bach; “Bonnie and Clyde,” Serge Gainsbourg; “Percussion Baby,” Luca Prodan; (maybe) Boys Noize.

sP: Whose work is currently on your radar?:

PLE: Question the question, question these temporary answers, question this media, question this interface; trust no-one 🙂

Additional credits and links:

[eiroaarchitects.com]

Pablo Lorenzo-Eiroa is an associate professor, head professor and coordinator at The Cooper Union in NY and a design principal of eiroa architects new york city and buenos aires. He published Instalaciones: Sobre el Trabajo de Peter Eisenman; and co-chaired and co-edited Life in:formation, ACADIA 2010 and released with Aaron Sprecher Architecture In Formation in 2013.