* This is the draft version of my article for a book edited by José Aragüez: The Building (Lars Müller publishers, forthcoming).
“A computational approach enables architecture to be embedded with an extraordinary degree of information.“
(Michael Hansmeyer: www.michaelhansmeyer.com)
The Contract of the Architect
by Vera Bühlmann
I would like to discuss three of Michael Hansmeyer’s recent experiments in computational architecture (Platonic Solids (2009), Subdivided Columns (2010), Digital Grotesque (together with Benjamin Dillenburger 2013))in relation to what Peter Eisenman has recently foregrounded as the plot in which architecture, be it digital or not, should situate itself: architecture alone among all other disciplines, Eisenman maintained, is capable of such miraculous deeds as saving a void from the negative by making it positive, or doubling and dividing volumes (cubes).[1]
The acts captured in the deeds of which Eisenman claims the architect alone to be capable of are related to a set of classical problems in mathematics that has arguably propelled the development of mathematics as the »technics/art of learning« (mathematics literally means all that pertains to mathema, Greek for learning) at large: doubling the cube, angle trisection, and squaring a circle. These problems have often raised mistrust because manners of resolving them are not rooted in »elementary« mathematics (the Euclidean axioms) but involve so-called »superior« mathematics – which means that any resolution to these problems manifests in geometrical constructions that cannot be achieved with compass and ruler alone. They involve operations on symbols that are pure place-holders, substitutes one draws upon on entirely speculative grounds because what these »superior« symbols claim to stand in for counts, according to all established common sense and knowledge, at best as genuinely unsettled; case items of such symbols are the zero, the imaginary unit i, the natural base e, but in pre-modern times also numbers for negative or infinitary values etc. These symbols may operate on speculative grounds, but they nevertheless act with a certain an agency (when organized in technical form, they can operate and trigger real effects); but when they do, the »rationality« and »reason« that is applied in this agency is not necessarily homogenous and uniform in nature. Hence, to determine the reference of these abstract place-holders (by legitimization or characterization) falls out of the scope of mathematics properly, and into the responsibility of domains like metaphysics, cosmology, ontology or politics. Our current technology (based on electricity and information) largely trusts in the use of the likes of such symbols; but their »character« and »nature« is no less disputed today than ever – a situation which features in the »abstract problems« at stake in much of the diverse discourses that seek to address »the digital« in distinction to »the analog«, e.g. between favoring axiomatics (measuring) over algorithms (calculating) (or reversely), set-theory over category theory (or reversely), bottom-up methods over top-down methodologies (or reversely), object-oriented over process-based programming (or reversely).
This is indeed why I want to speak of Eisenman’s »plot« for architecture in the poetic sense of this word as the »arrangement of events that happen in a story«, that is triggered by tensions and attractions, conflicts and resolutions between characters that are disparate, comically or sometimes tragically so, because they are symbolically encrypted and may well belong to different contexts that are not, in any immediate way, smoothly configurable within one setting. Thereby, I suggest to view »the building« as »the story«, and its poetic plot as the prism through which we can regard a building as an actual and active form of knowledge. A prism in optics is a diligently cut and polished solid figure, which breaks the rays of color and light that shine through it according to particular patterns. A building then is a form of knowledge because it realizes a »promise« as it appears through a particular prism. What is at stake in a promise becomes fixed as the promise is formulated in a building’s plot, it cannot be regarded as settled outside of its formulation. The idea I want to pursue here, in a certain modulation of the Vitruvian interplay between »fabrica« and »ratiocination« that characterizes architecture as a profession (both artistic and technical), is that a building needs »a plot« to present itself in the light that is »adequate« to it with regard to its »principles«. We can think of this plot as a quantum-optical device, an architectonic crystal of broken and configured symmetries that establishes a particular spectrum of possible terms (ichnographia) over which a particular partition scheme can be erected (orthographia) that allows for the articulation of the terms in desirable and agreeable form (scaenographia) as a contract. Architectural modeling then depends not on intention or plan, design or objective requirement alone, but also on what I suggest could be called »the impersonal agency« that is at work in »technical form« with which an architect »partners« when he formulates the promise a building is going to realize. Such a contract will always produce certain (architectural) qualities (e.g. in Vitruv: solidity, utility, beauty), this is the commitment of architecture as a profession (rather than as an art or as a science); but it does so in manners that may range anywhere between poor and excellent. This challenges both architects and civil societies, because the »character« of these qualities in a fabricated whole is symbolical.
This has two important aspects:
- With regard to itself, such contractual quality is always perfect, fulfilled (because symbols are self-referential, they build on what they assume is given and then record the givenness of what they have assumed to be there in the first place).
- With regard to the stakes that are being contracted in the formulation of a promise, of which the contractual qualities are an effect, such quality is never perfect or fulfilled – because it is the very character of a promise to be overdetermined with meaning, oversaturated with attractiveness (or repulsion), and to sparkle in its formulations with more or less brilliance.
So how can we look within this context at Michael Hansmeyer’s experiments in computational architecture? One: All three of his works explore how an architect can »partner« with this »impersonal agency« that is at work in technical form. And two: all three works explore and seek getting used to symbolic self-referentiality. Each one articulates a symbolic form that contracts an actuality, a dramatic plot at work within particular »elements«.
Platonic Solids (2009) attends to the most primitive forms, the platonic solids, and repeatedly employs one single operation – the division of a form’s faces into smaller faces – until a symbolic form is articulated in »agreeable« manner.
Subdivided Columns (2010) focuses on the Doric Column and subdivides it iteratively eight times according to its own order, thereby producing 5,8 million faces. One such pre-specific typicality of this order is elected here and plotted into a cardboard model (1 mm sheets).
The Digital Grotesque (2013, [together with Benjamin Dillenburger]) is a walkable room produced by 3-D printing. A simple input form is recursively refined and enriched, culminating in a geometric mesh of 260 million individually specified facets. Every detail of the architecture in this project is generated through customized algorithms, without any manual intervention. And yet it is not only that during the computation every point (spatial or temporal) is latently connected to all the other points; rather, each one actively reflects them all at once at every instant, and this in an individual manner that in each case responds to and communicates with all the others – the actuality of this happening, this is what the architects settles.
Copyrights of the images by courtesy of Michael Hansmeyer and Benjamin Dillenburger
[1] „The Foundations of Digital Architecture: Peter Eisenman,“ in conversation with Gregg Lynn on the opening day of the Archaeology of the Digital exhibition at the Canadian Center for Architecture (CCA). Available online: https://www.youtube.com/watch?v=hKCrepgOix4
