Limit Geometries of Architectural Filters: Precise Rationality and Poetic Emotion

An architectural filter is a porous material construction that regulates transverse visual relationships, and establishes degrees of connection through the intervention of light and gaze. Filtering boundaries display variable proportions of mass and air, which are instrumental to the production of the spatial experience behind the mediation of matter and geometry. A filter’s structural system synthesizes geometric relations with the capacity to cause architectural atmospheres, as a result of the active border that is technically precise and sensorially ambiguous at the same time. The text sustains that the emerging atmospheres behind the filter cannot take place without a previous, precise geometric production; the poetic dimension of filtering strategies originates from its capacity to transform the concrete geometry of its contour conditions and controlled material execution into an unexpected atmosphere of emotional and incommensurable qualities.

2 The term Limit comes from Latin limes -a real or imaginary line that separates two areas, two countries or two territories; an end reached at a specific time. During the age of the Roman Empire, limes referred to the name given to the no-man's land where borders were imprecise or undefined. Said land remained undefined and without sovereignty, comprising a transitory area between one land and another, between one country and the next. Rome ceded these areas of trade and conflict between barbarians and Romans to peasantsoldiers. Limes had their own legal and civil systems. Marcel Duchamp explored a similar notion in his term inframince, which referred to the space existing between the air and the sea.
3 To dissipate: to cause to spread thin or scatter and gradually vanish.  In his Metaphysics, Aristotle examines that which can be confirmed due to its actual existence and not its potential qualities. The main subject is ens qua ens -being as being.  , appreciated the characteristics of the limit in the autonomy of the subject's will: "The subject does not belong to the world, but is a limit to the world." Wittgenstein, Ludwig: Tractatus Logico-Philosophicus, 5.632. Cited in Paolo Zellini, Op. Cit., 114.
The construction of a filter pulls apart and binds together two contiguous spaces, leading to the distinction between two sides: one interior, containing the observer and the shadows; and one exterior, containing the views and the light source. The border defined by the filter works as much as a connector as it does as a separator in the relationships it creates between the two sides. Therefore, these elements should not be thought of as divisive frontiers but rather in the topologically opposed sense, that is, as a border of connections that becomes clearer as the definition of the filter as a spatial limit becomes more precise.
We could suppose that a filter evolves from an opaque and impenetrable separation in which a progressive opening condition starts to appear, generating a porosity that makes the division permeable to light and gaze. This variable porosity is characterized by the contour conditions that determine the transit of sensory information and, therefore, the atmosphere generated inside. The gaze, lights, and shadows qualify the perception of the new space, while progressively diffusing its contours and reaching the virtuality of the undefined. 2 The effect is that of a space in a continuous process of visual dissipation and mental reconstruction. 3 When establishing the geometric and material limits of a physical space, the filter facilitates the initial definition of the contained space. Aristotle wrote that that which has no limits cannot be comprehensively represented in our thinking, and therefore, cannot be understood. 4 The definition of limits allows for the spatial establishment of a viable and defined reality. Saint Thomas Aquinas wrote that the surface contours and geometric figure of an object are "the edge and confine of the limitless potentiality of all material stratum par excellence, as well as the miraculous balance and meeting point of such potentiality with the fatal contraction performed by the matter of God's perfect form within the limited forms of existence." 5 In a similar manner, a filter forms a physically defined, concrete boundary with the capacity to manifest a transitory potential, establishing a perception of the medium by means of the intersection of the dissipated spaces within the continuum of space and time.
Heidegger wrote in his 1954 text Building, Dwelling, Thinking: "A space is something that has been made room for, something that is cleared and free, namely within a boundary, Greek peras. A boundary is not that at which something stops, but, as the Greeks recognized, the boundary is that from which something begins its presencing…. Space is in essence that for which room has been made, that which is let into its bounds. That for which room is made is always granted and hence is joined, that is, gathered, by virtue of a location…" 6 To form limits means to restrict and control. A space exists based upon the definition of its limits, and it is therefore necessary to mark them out so as to create restrictions on the potential actions and options. Italian author Paolo Zellini explored the value of existence by means of the definition of its limits: "There is nothing more dangerous than the loss of limit and self control: the mistake of the infinite is the loss of the value contained within the relative perfection of that which is specifically determined and formally concluded, causing one to get lost in the nowhere or in an exitless labyrinth.
[…] That which is complete has an end, and the end is a condition that limits, inasmuch as the limitless indicates the absence of any limit under its intrinsic meaning." 7 A permanent dialogue takes place between opposites when a filter configures the limits of architecture. The German Early Romantic poet Novalis (1772-1801) wrote: "All that is visible is locked into the invisible, the audible to the inaudible, the sensible to the insensible. Maybe even the thinkable to the unthinkable." 8 The same idea was explored by Gabriele D'Annunzio (1863-1938, who wrote about music in 1900 through one of his characters, Stelio Efrena in Il Fuoco: "Have you ever thought that the essence of music does not come from sounds? It can be found in the silence that precedes the sounds and in the silence that follows. The rhythm emerges and 9 D'Annunzio cited in Paolo Zellini, Op. Cit., 50. This consideration of silence as a critical component of sound is also explored in the works of composer John Cage, in pieces like 4'33" (1952).
10 The research of Robert Le Ricolais is of particular interest regarding operations with holes as an integral part of structural design operations. See note 24.
lives in these intervals of silence." 9 Similarly, we can assume that the perception behind the filter is a counterposition between freedom and prohibition, between the visible and the invisible, between sound and silence, between light and shadow, between void and matter, between reality and fantasy. As such, these structures have no meaning without this dual, instrumental condition. The experience moves away from the technical aspects that produced it, to become something greater.
The perforated matter acquires the same level of relevance in the perceptive process. The holes collaborate with the geometric configuration of the filter and the resulting interior space. 10 Given this porous quality as formed by geometry, mass, and air, we may understand the holes as another form of matter, compelling us to regard filters as a collection of interstices that facilitate an osmotic and multidirectional flow in a permanent play of dialogues, rhythms, and cadences.
The defining mechanisms of a limit announce the existence of an infinite dimension without revealing a total or overall view or giving direct or full access to a visual truth outside: imagination and memory are always allies in the spatial characterization behind a filter. Filters create timeless effects from the coalescence of light and gaze, and imply a sense of both fugacity and eternity. The physically tangible and concrete avoids any correspondence with a limitless temporal or spatial extension. The limit composed by an architectural filter presents a transcendental order with regards to the space it delimits. Such a limit is created in a technically and constructively exact way, and becomes activated by the intervention of flowing agents through the mediating structure. Like a poem, written with a specific and rigorous meter that takes the reader beyond the physical pages of the book, the permeable limit is built with material contention and geometric discipline, and becomes permeable to the exchange of relationships and participation between both sides. This circumstance blurs the precision of the initial execution, and intentionally attains a state of sensorial instability. involves the structurally and geometrically contained contours that are subsequently superseded, reaching a trance-like emotional state in the process. 11 This changing state of openness determines a visual dissolution of the limits between interior and exterior. It is behind the filter where we experience a delimited but also infinite atmosphere. As the space projects itself beyond its own boundaries, we get a simultaneous perception of proximity and distance that changes depending on the relative position and movement of both the light source and the observer.
The porous separation controls the degree of interaction between one side and the other, bonding both domains together in a process that is constantly evolving. In this place, intuition and memory as constructors of space become fundamental, and any attempt to classify the generated atmosphere is highly complex. This quality of visual dissipation is what allows the perception of a specific architectural atmosphere. In this regard, the filter moves away from stylistic issues, manifesting itself as a timeless invariant in architecture. The atemporality of these architectural filters makes it possible for these mechanisms to achieve certain complexities that are proper to more contemporary architectural realities.

Defining Contour Conditions
"We are approaching a laminar latitude, a place where what we contemplate almost touches transfiguration, taking us beyond, through an interior pathway, to where the aesthetic experience happens in all its magnitude."

Rainer Maria Rilke 12
If the construction of an architectural filter involves the definition of a spatial limit, 13 a filter may be understood as the definition of the geometric contour conditions of a permeable structure that is conceptually extensible to the infinite, and qualifies the character of the space inside, both internally and externally. 14 The internal contour condition configures the filter's distinctly transverse character and the perimetral edge where the filter ends, affecting all relations between one side and the other.
The connections that take place perpendicularly to the predominant filtering plane, that is, between the interior and exterior, define a transit that determines the flow of relationships; hence, the dimension of depth becomes instrumental.
A filter is significantly defined by its transverse permeability, and by its perimetral contour condition, although this component affects the filter's internal definition 11 Simone Weil writes that "Freedom is a limit and that the limit is something in trance at every overcoming stage." See Paolo Zellini, Op. Cit., 22. 14 "A project with an isotropic plan and an infinitely extensive structure meets a chance boundary. An element with a genuine internal structure is cut off by an undefined contour that depends on a perimeter that is foreign to it in the exterior. It is after this precise contour condition that is established outside of its inner pulse that these projects can construct a place." José Antonio Sosa Díaz-Saavedra, "Condiciones de contorno," Arquitectura COAM, 345 (Madrid: COAM, 2006), 32. visually defined in a way that guarantees a relationship between the whole and its parts, making the enclosure function as such. Therefore, the definition of a filter must avoid traditional typographic recommendation in that filters must approach a matter-and-air proportion of equal parts that tends to 0.5. This helps to configure the visual ambiguity that is so characteristic of all filters, leading to the new spatial atmosphere.  Another factor involved in these questions of contours is the relationship between the geometry of the internal mesh and the distance between the observer and the filter. This range establishes a scalar relationship that differentiates some filters from others. When we get considerably close to a facade that was designed as a mesh of assembled elements or a continuous plane of perforated mass, we can see through the interstices to the other side. In this instance, we cannot see the enclosure wall as a filter but rather as a structure that is riddled with openings. If we move away from that enclosure, we can then see a vibrant pattern in which the voids and masses are no longer evident. From an even farther distance, we cannot distinguish any openings, only a continuous plane of matter. Therefore, we can observe that the perception of the filter as such is, to a large extent, due to the scalar relationships between three geometric factors: the internal contour condition or filter mesh -the transverse geometric relation -, the exterior contour condition or filter edge -the longitudinal geometric relation -, and the relative distances between the previous two conditions and the observer. The combined relationships between the internal geometric mesh, the outer edge, and the observer constitutes a critical parameter in the distinction between a filter and simple openings, such as traditional windows, in a blank wall or a wall that is practically opaque. The range of possibilities should shift away from the extremes: far from a continuous plane of matter and far from a single opening. The balance between these three conditions determines the filtering qualities and the atmosphere that such limit comprises.
Spanish architect Juan Navarro Baldeweg proposes a series of lines connecting us with our material environment. "Architecture is the meeting place for all these lines that go diagonally through and perforate the material productions that involve us.

Geometric Rationality and Poetic Emotion
"Order is more than just order: it is organization; organization is more than just organization: it is meaning."

Mies van der Rohe 20
The atmosphere that appears behind a filter embodies the formalization of certain basic topological aspects of the filter's structural organization, such as concentration or dispersion, homogenization or differentiation, opening or closing, continuity or discontinuity, and connection or disconnection. These basic geometric operations refer to the definition of the atmospheres and the relations that emerge within them, instead of the geometric figures that they form. Professor B. H. Arnold states that "the topological properties of a figure are the most basic and fundamental of its geometric properties." 21 We could say that filters are configured from general topological orders that admit the coexistence of several elements. A filter can be formed spontaneously by nature itself, or artificially via the conscious actions of mankind. The former would include arboreal structures, whereas the latter would include constructed filters that enclose architectural atmospheres. Professor and author Carlos Martí referred to trees to illustrate this matter: "A tree has an order of its own, despite the different parts of which it is composed. In this case, order means unity that dominates disparity, a system of rules that gathers together various elements, providing the whole with a new equilibrium." 22 Based on this hypothesis, if we understand a filter as an organized system, we will be able to interpret it as the material result of a specific field condition that admits improvisations that do not alter its essence. The structural configuration of a filter constitutes much more than just a question of form, but a "structural system [that] is capable of maintaining its spatial production even under microscopic variations and changes." 23 The way the filter opens, organizes space, and arranges its parts has to be precise and rigorous, but this is not necessarily so in its external appearance, but in its essence, in the deepest conceptual levels. 24 The quality of the space may be modified but it does not disappear.
The discourse established between geometric rigor and poetic emotion is directly

Conclusions: Filtering Architectural Atmospheres: Phenomena of Interference
We can conclude that a filter exposes organizational systems that synthesize geometric relations with the capacity to cause emotional architectural atmospheres.
Filters perform under a dual function that combines the precision of a crystal and the unpredictable agitation of a flame. A filter is initially built using clear structural and constructive schemes within specific organizational and mechanical constraints, and is later activated phenomenologically through the intervention of light and the gaze. The parallelism between a filter and a poem allows us to illustrate the access to the architectural emotion of the new atmosphere through rigorously scientific and exact operations that involve matter and air. The measurable construction and the intangible experience result in a continuous equilibrium between a technical and a non-technical dimension.