Algebraic Concepts Characterized / Architectonic Articulations / Projective Theory of Technology / Thinking as an Algebraic Mechanist / Uncategorized

Architectonic disposition: ichnography, scenography, orthography

 by Vera Bühlmann

author’s manuscript.

In his Ten Books on Architecture, the Roman architect Vitruvius gathered all the existent knowledge on architecture in one comprehensive treaty including the building of temples, of course, but also the construction of clocks (gnomon, sun-dials) and the fabrication of machinery. The dedicated aim of gathering all the distributed knowledge in architecture has been to generalize from local customs and the ethical/religious meanings attributed to the built works, and to propose rules and conceptual distinctions for addressing and critically evaluating „the establishment of public order“[1] in a manner that can preserve the built environment’s „worth“. Vitruv proposed three categories – utilitas, firmitas, and venustas –, and introduced six elementary concepts by which an architectural object can be qualified according to these categories.[2] None of these concepts is self-standing, like a separate metrics, but rather must be brought to work together by the architect in singular manners; the planning of this interplay – this is the work in which an architect can be more or less professed. Vitruvius’ conceptual apparatus is to provide critical assessment of such professionalism, such that the „worth“ of architecture can be preserved over generations and regions. It includes practical aspects as well as theoretical ones, which he distinguished as fabrica and ratiocination. The six elementary concepts are (1) ordinatio: centering in selecting one module from which the metrical unit for the overall taxation is to be derived in order to the establish a singular work’s „ordination“ by articulating and proportioning the members of the work; this idea of ordination is analogous to Vitruv’s suggestion that rather than ideas of the magnitudes and scales impersonated by a particular God, the human body can be referent to proportionate metrics in architecture;, (2) dispositio: regarding the conception and disposition of all the work’s elements in plans, (3) eurythmia: the well-proportioned overall appearance of the work, (4) symmetria: for the harmony of the order with regard to the module from which its metrics is derived, (5) decor or propriety: for customization of the work according to established customs, and (6) distributio (in Greek oikonomia): for a distribution of building materials and expenses adequate to the wealth and status of the customer.

The generalization from local customs and the ethical/religious meanings attempted by Vitruv is so interesting because it proceeds in a manner of which I claim here that it parallels rather than imitates or reproduces philosophical methods of generalization and classification. Against this postulate of parallelism (—> equation), there is a long tradition of Vitruv’s reception; according to this reception, architecture, especially the public order it articulates in cities, was thought of as realizing an ideal of a cosmic order in the here and now of the world. The predominant critique on Vitruv since the Renaissance is that his proposed methods operate with proportion, without ever specifying the attributes of the proportions with precise ratios.[3] If, however, we return to his interest in the preservation of architecture’s worth not through the discourse of aesthetics, regarding architecture as an art, but through an approach informed by physical conservation, Vitruv’s apparent failure reveals itself as its very mark of distinction and excellence: whatever the value this worth preserves may be – beauty, harmony, the good, etc – such an approach at systematization lives from not specifying the nature of this value in any determinate manner (—> negentropy, —> invariance). The preservation of this value would be achievable only as a state of entropy, in which all of its articulations would be equally „likely“ – meaning in the architectonic context which is concerned with criteria of adequacy rather than of happening – equally „adequatable“. Such an entropic state provides an atomism of value like the thermodynamic state of entropy (of the universe) provides an axiomatism of forces. We can think of the disposition of a work, its plan-ability, as such an entropic state, and we can call this ‘architectonic disposition’, picking up on Alberti and Serlio, an architectonic model. According to Vitruv, the elements of this disposition – quasi its vertices – must comprehend the full combinatorial space of the totality of possibilities the six elementary concepts are capable of determining. “Planning” or “design” – to use todays concepts – can be read as a reduction of the combinatorial potentiabilities, by configuring the potential elements in an objective way.[4] Vitruv foresees three dimensions of conception which we know today as ground plan, elevation and perspective. He calls these three dimensions of conception orthographia (the natural, potential elements, in renaissance: elevation), ichnographia (the contraction of the potentiabilities of these elements, in renaissance: floorplan) and scenographia (the operation of contracting, in renaissance: perspective or 3 dimensional plan).

If Vitruv’s triad of architectonic disposition could be demonstrated in a generalized form, then his architectural theory might lend itself for developing an information architectonics. It might provide orientation in how to generalize again from the numerous spreading out of disciplines that fall victim to increasing local seclusion, hermeticism, and what could be called a certain banality of highly technical specialization without systemic overview. Might the conceptual apparatus that constitutes architecture as a profession (rather than as an art or as a science) provide a model of how to preserve the „worth“ of the public order that is embodied in knowledge? This, of course, is but a biased and speculative outlook. But here are some indexes of how such a re-interpretation of architectonic disposition could be started.

The notion of architectonic disposition has recently been picked up by Michel Serres, who argues exactly along these lines. Ichnography, scaenography, orthography are terms that allow him to theorize a notion of system which contracts the first and the second laws of thermodynamics: its invariant conservation (1st Law) and its drift towards dissolution (2nd law). „Physics describes a system,“ he argues, „but not one that is hierarchic, deductive, or tightly ordered, as in the series of the Stoics: it is a set, a general equilibrium, a balance sheet that takes account of the stochastic“[5], as he puts it in The Birth of Physics (1977), where he develops his notion of the foedera naturae, the natural contract, in distinction to what he calls the foedera fati, the contract of destiny. Serres interest in the contract, here and in other texts, must be understood as translating the dimension of architectonic „orthography.“ Like this, one can decipher the same notion of system, always contracted to mathematical models and never self-evident, which he explored perhaps most prominently in his book Le Système de Leibniz et ses Modèles Mathématiques (1968). The introduction here is entitled „Ensembles théorique“ and Serres begins with the subchapter „Scénographie, Ichnographie.“ Scholars interested in Leibniz share a kind of embarassment, he begins. It concerns the irreconcilability of Leibniz’s rigorously systematic thought, while this very systematicity doesn’t cease to refuse itself to rigorous understanding. Leibniz presents his reader, as Serres puts it,

„a potential ordonnance which lets itself be divined and which refuses itself ceaselessly, a vague idea of a perceived coherence seen a thousand times in the mode of cavalier, and which hides its géometral, the sense of progressing in a labyrinth of which one holds the thread but has no map. Offered perspectives, multiplied points of view, infinitely iterated possibilities: it never seems that one could actually arrive at the exhaustive limits of a synoptic, spread out, complete and actual plan“.[6]

Serres here argues for a notion of the system which comprehends and organizes all that obeys the principle of identity, yet as an invariant of which he assumes nothing else except that it be capable of absorbing and integrating all the variations that can actually be attributed to it; one can refer to such a notion of system only via mathematical models, he maintains. Such models are not addressed as representing a reality (or ideality), they must be fashioned in profile to each other rather than to a frame of reference. Their profiles are to be worked out under the criteria of isomorphism (equality with regard to their formality) between all of them, rather than correlation (linear hierarchies of consequentiality) or representation between model and modeled reality. In Serres’ notion of a mathematical system „there is a plurality of possible paths of deduction;“[7] it is thus a notion of system which is „an irreversible order,“ which „like a ladder“ is made up of a plurality of „orders, derived from an infinitely replicated infinity of infinities (par „infinité d’ infinités infiniment répliquée’)“.[8] Within such a sheaf of orders, „my enunciations are universal and they conserve the analogy [a „discrete multiplicity“, which Serres contrasts with a function as „a continued variation“]“[9]. This is why mathematical modeling of the system, conceived as a ladder where different orders, each infinite, are leading from one to the other, progresses indefinitely. Its steps are governed by „laws of binding one–multiple, finite– infinite, which are of value in multivalent manner for perception, liberty, knowing, creativity, remembering etc, which all are at work also in the mathematical model.“ Hence, to Serres it is not mathematics which governs all these aspects of reality (perception, liberty, consciousness, creation, remembering etc) rather, he assumes, „there is no relation of cause and effect here, there is a parallelism of structure“. Serres’ notion of a system which contracts the invariant conservation (1st law, orthographia) and its drift towards dissolution (2nd law, ichnographia) is alway integrated, bound together (scenographia) mathematically, in models. The system, thereby, is never represented by its models. The relation between them is a contract that formulates their mutually implicative cordiality, the orthographic politeness that makes up the foedera naturae, the Natural Contract: „the model of the system, this is the system of the model“.


[1] cf. the preface by Vitruv, dedicated to his Ceasar.

[2] I understand these concepts as elementary in a quasi-material, quasi-pre-socratic sense: all of them factor in all of the architectonic work, like the material elements in the Timeaus factor in all of the sensible bodies (all things are made up fire, water, earth and air, and between them we can assume the lawfulness of a proportionality: fire is to earth as air is to water).

[3] Günther Fischer, Vitruv NEU, oder was ist Architektur? Birkhäuser, Basel 2009.

[4] One can say that Vitruvius introduced models in „space“, the renaissance, with Alberti, introduced the models we are used to today (lineamenta), as models of motion in „time“, and that in today’s discrete (digital) geometric paradigm we are discovering models in „life“ (—> invariance)

[5] Michel Serres, The Birth of Physics, Clinamen Press, Manchester 2000, p. 128.

[6] Michel Serres, Le Système de Leibniz et ses Modèles Mathématiques (1968), here cited from the kindle edition, position 162. My own translation, from French: „[…] une ordonnance potentielle qui se laisse toujours entrevoir et qui sans cesse se refuse, l’ idée vague d’ une cohérence perçu mille fois en vue cavalière et qui dérobe son géometral, la sensation de progresser dans un labyrinthe dont il tiendrait le fil sans en avoir la carte. Perspectives offertes, points the vue multipliés, possibilitiées infiniment itérées: il ne parait jamais qu’on puisse parvenir aux limites exhaustives d’un plan synoptique, étalé, complet, actuel.“

[7] ibid., position 190.

[8] ibid., position 487.

[9] ibid., position 492.

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