EinStein: An Exercise in Spatial Composition

This text comes from a game that Aimar Perez Galí proposed to me a few weeks ago, that is, to consider spatial composition by introducing a constraint in the rules of its own language. Inspired by minimalist choreographer Lucinda Childs’ statement nothing personal, the game already contained a first exercise in abstraction, suggesting a spatial reading through the syntax of its geometric relationships. However, space… is quite personal. Detaching Euclidean space (x, y, z) from time and matter, and their interrelationships, is in itself an exercise in restriction and of speculative fiction.

It is difficult to put a limit on space. There are multiple interdependencies and it is as diverse as the very physics that constitutes it. As Karen Barad, physicist and feminist theorist, proposes, adding to the fact that space is inseparable from time, as the physicist Albert Einstein elucidated at the beginning of the 20th century in the Theory of Relativity, what we call Space is, in reality, spacetimemattering. Space is not detached from time nor from matter. Therefore, when we talk about Space we are also always talking about Time and Matter. When we talk about Time, Matter and Space are entangled in it. When we talk about Matter, this is Time and Space, too. Space is emergent, a system that cannot be reduced to its parts without dismembering the whole.

Spacetime curve

When composing space, not only do the Euclidean axes (x,y,z) and geometric bodies (point, line, plane, volume) intervene, but so too all the relationships, creatures, particles, events, materials, politics and matter that compose it, whether they are atmospheric, biological, geological, hydrological, quantum, chemical or geometrical (and many others). In fact, it is when one puts a limit on or tries to outline space that all the politics, frictions, interdependencies and ideologies that coexist and converge in it become visible. Geometry and mathematics are often considered as detached from political or ideological constructions, as even these carry in their structure specific inscriptions designed and elaborated in a specific space-time, with their respective decisions, obliterations and specific interests.

Regarding the composition of architectures, simply the force of gravity and the chemistry of materials are already determining restrictions for its design. As well as the traces left in the process and the future of any construction, be it spatial, temporal, social or ecological, and the interrelations between the inhabitants that this architecture will host^[1]Multiple interrelationships between multiple inhabitants, human, more than human, electromagnetic (e.g. sun light) or even the water that comes out of the tap connected to an infrastructure that in … Continue reading.

Architecture is a creator of restrictions but also of possibilities. Drawing such apparently innocuous elements as a wall, door, or window as geometric figures on paper or on a screen are decisions that produce a lasting effect on materiality. From the graphite on the paper or the lines of computer bits, a future tangible composition is outlined that will produce a chain of events from the moment it is drawn until it materializes and is sustained over time. These lines, even if they are simply lines on a plane, as for example in Lars Von Trier’s film Dogville or the markings on a road, already affect movement, restrictions and the relationships that develop within them.

Drawing a line is already an act that per-forms and pre-forms future relationships and exclusions in the spacetimattering in which we are all entangled. The etymology of the Greek word graphia, translated as ‘writing,’ means inscribing a trace on earth/clay that forever changes the state of that matter, whether it is a line, language, or an abstract/administrative division between lands. Geography, calligraphy, cartography, orthography, scenography, choreography, phonography, musicography. Drawing in architecture is a spatiotemporal composition, like a musical score or writing, with its own codes and its own rules and restrictions embedded. By drawing a line, matter and time accumulate in it in a dense present^[2]Haraway, Donna (2016). Staying with the Trouble. Making Kin in the Chthulucene. Durham: Duke University Press., a past modified from a present that projects a future and transforms it. An expanded temporality, which develops in time but is not progressive, like a relentless arrow of time headed towards the future, but rather accumulates past and future events from that present act of graphing.

During the architecture degree we receive several maxims about restriction: ‘Form follows function’ (Louis Sullivan), ‘Less is more’ (Mies van der Rohe), ‘Limitation makes the creative mind inventive’ (Walter Gropius), ‘Ornament and Crime’ (Adolf Loos), and Firmitas, utilitas, and venustas (Vitruvio). This is true for the design tools, as well, such as the Neufert Architect’s Data, which standardizes and indicates the optimal measurements in the use of spatial design, and in which bodies are magically exchanged by limiting the pre-defined uses of that space^[3]In addition, Anthropometry, the science of the standardization of bodies used in the design of spaces, has its origin in the criminology sciences of the 19th century that differentiated the abject … Continue reading:

Neufert Architects’ Data. Bathroom measurements

Around the 1960s, coinciding with the North American Minimalist movement, the architect John Hejduk proposed the Nine Square Problem, right at the time George Perec joined the Oulipo group and Lucinda Childs began her interest in creating choreographies with geometric space patterns. For the Nine Square Problem, Hejduk designed an introductory pedagogical exercise to his students in schools of architecture in the United States in which he abstracted architecture from a diagram and its syntactic elements to focus on the spatial relationships between points and lines, pillars and walls, disassociating them from the relationships that emerge through the program’s needs and uses.

‘The Nine Square Problem’, John Hejduk (1954-1963-1985). Conceptual drawing with notes. John Hejduk fonds Collection Centre Canadien d’Architecture/ Canadian Centre for Architecture, Montréal

‘The Nine Square Problem’, John Hejduk (1954-1963-1985). Conceptual drawing with notes. John Hejduk fonds Collection Centre Canadien d’Architecture/ Canadian Centre for Architecture, Montréal

The aim of this exercise, conceptually connected to scientific thought and to the Western ontoepistemological tools of separation and differentiation and analysis by parts, was that students forget and get rid of the cultural and personal preconceptions with which they arrived to architecture school and to learn to design and compose space with, and from, geometric relationships on a grid in a uniform plane, considered the language of spatial composition.

However, Hejduk, after his geometry exercises, developed projects like Victims, which he described as “a construction of time.” In these projects he worked with another type of restriction, that is, precisely the inseparable link between geometry, the life it hosts and the place in which it unfolds, designing spaces for specific ways of inhabiting, such as ‘The House of the Suicide’ or ‘The House of the Mother of the Suicide.’

‘Victims’, John Hejduk. AA publication 1986

Spatial restrictions and considerations tend to be tied to their time. Material crises, social crises, ecological crises, even the delirious days of Starchitects when the possibilities introduced by digital design programs and unequally distributed wealth gave (and continue to give) rise to unnecessary extravagances. Time is a fundamental condition of architecture, its durability, also of a text or music, whose traces remain as technofossils for generations.

Given the conflicts of spatial composition in architecture, for the game of geometric restriction I would like to propose the aperiodic patterns^[4]These structures are important for Material Sciences. For example, to understand the Quasicrystals, used in the development of sustainable energies and which, unlike their ‘noble’ … Continue reading used in mathematics, forms that can cover infinite surfaces without their patterns repeating.

The shape hobbyist (as he describes himself) David Smith^[5]David Smith, seeing that he might have discovered the EinStein, contacted Craig S. Kaplan, an associate professor of computer science at the University of Waterloo in Canada, and later Dr. Chaim … Continue reading, recently found an aperiodic pattern, sought for years, that can be solved with a single piece, the EinStein (which despite sharing the name of the theoretical physicist Albert Einstein, mentioned at the beginning of this text, in this case means ‘a stone’).

EinStein

This 13-sided polygonal outline generates an aperiodic pattern, which means it never repeats a form, no matter how far it is extended in space and time, creating aperiodicity simply by its geometry.

Aperiodic monotile. © Smith et al. / arXiv 2023

EinStein can be thought as a two-dimensional geometric spatial composition. A pattern that ceases to be a pattern when adding pieces, which by being able to assemble infinitely without repeating the pattern, it also incorporates variation over time, by generating movement through a non-static, non-symmetrical and aperiodic geometry. A pattern for a movement that never repeats.

It’s your turn now, Aimar. Perhaps you can try to introduce the EinStein in a choreographic composition to keep the game going.

All illustrations are from the Canadian Centre for Architecture (CCA), Montréal, available here.