X Kavya

| Karl S. Chu (*1950)


The Turing Dimension


The following article delineates a philosophical interpretation of computation by situating it as an existential quest of humanity propelled by the metaphysics of desire. As such, it goes beyond the mere celebration of computers to generate virtual reality or cyberspace by disclosing a certain complicity in the use of instrumental reason to achieve what is essentially a gnostic quest for fulfillment. This quest, which is inevitably implicated within the context of an evolutionary cosmology, may eventually be recognized as a machinic philosophy of the tragic effect: a phenomenology of the spirit of universal information processing made possible by the advent of the Universal Turing Machine.

"Science is a differential equation. Religion a boundary condition".(Alan Turing)

If tragedy, or a certain philosophical interpretation of tragedy, is the origin and matrix of speculative thought in general, and dialectical thought in particular, the emerging phenomena that is about to explode into the virtual universe of possible worlds will not escape the resonance of the tragic effect that accompanies and haunts speculative endeavors. The philosophical impulse behind tragedy, according to Philippe Lacoue-Labarthe (PLL), is a dialectic of tones that schematizes, through a general system of combination or the calculable, the opposition of the ideal tone (the subjective aspiration toward the absolute) and the heroic artistic tone of discord or agon in order to arrive at a higher unity or resolution in the One-All through the spirit of the poetic genre. The poetic genre, in the current situation, is about to become the only genre based on an algorithmic conception of the world where everything enters into an extended wandering under the unthinkable while being sustained by the elusive umbrella of the intractable. It would eventually unfold itself into a drama of appearances and disappearances implicated within a virtual cloud, or labyrinth, that is the work of the infinite itself. For those who are eager to achieve communion, the virtual membrane of space would be more than adequate since it provides an immersive arena within which such a fusion can take hold of and thereby permeate into the imaginary and ecstatic soul of the subject. Whereas for those who remain in tension toward that which cannot be encapsulated or embodied, the green membrane of space is merely a global cockpit of architecture directed toward the absolute infinite beyond the threshold of representation. Nonetheless, the emerging drama signifies the coming of age of the Pythagorean premonition of the world as numbers, and the permutation of numbers in the form of bits would provide the new materiality necessary for a cosmopolitical drama to stage itself on the new plane of immanence destined to rise to the level of an epic proportion.

Seen from this light, the recurrence of tragedy has been in the making for the last two thousand years beginning with Euclid's axiomatic treatment of geometry, Leibniz's quest for a symbolic logic, and Russell's and Whitehead's monumental Principia Mathematica in the early part of the twentieth century. It is a consequence of the manifest destiny of instrumental reason whose aim, on the one hand, is to verify and control knowledge by means of a mechanization of mathematics that finds concrete expression in the Universal Turing Machine (UTM), and on the other, to enter into communion with the substance of affects engendered by the instrumental use of reason in the first place. The tragic effect is a dialectic of fusion of numbers and beings driven by a utopic impulse that channels and transports the spirit of universal information processing into an epic dramatology of transubstantiation.

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In this echo of tragedy, the subject is mediated by the Universal Turing Machine, which will, in due time, prove to be a gnostic medium that operates on the logic of functional synthesis. It is a machinic alchemy of subjectivation that enfolds both the subject and the object of architecture into this instrumental medium by generating a universal surface upon which a mutant reality can exfoliate into a possible world. This tragic dimension is the scene of a transfusion where the Subject of speculative Idealism finds him/herself immersed into the manifold cockpit of the topological surface now being engendered by the Universal Turing Machine. It is a trajectory, or a tragic transport, that becomes infused with the medium by steering from within the infinite movements of thought and lines of flight in order to overcome, through a dialectics of transgression, the fabric of mimetology brought on by the machine of the double bind. It is simultaneously a catharsis of the subject and of the medium that represents both the substance of Aristotelian mimesis as a mode of poesis and mimesis in the sense of mimetism or imitation. It is this aspiration for overcoming through sublimation that turns into a play of mourning, which lies behind every metaphysical desire, that induces a philosophy of the tragic effect, or tragic pleasure of the sublime, by situating the subject of architecture in an in-between space of melancholy, or, to use Plato's designation, metaxy. Even though it is at once the nearest and yet the farthest from absolute fulfillment, it may require the intrusion of the caesura so that what appears is not the alternation of representations or simulations but the limits of representation itself.

With the publication of the paper On Computable Numbers, with an Application to the Entscheidungsproblem in 1936, Alan Turing launched the specification for an abstract machine that would ultimately engender a new world by laying out a new plane of immanence specific to its mode of formal implementation. This plane is the virtual arena upon which diagrammatic flows and constructions are instantiated by the abstract machine. The birth of the Universal Turing Machine (UTM) marks the inauguration of the Hyperzoic Era (the artificial life of self-organizing systems) by redefining the projective content of the plane of immanence as information-theoretic in origin. It is the harbinger of a new breed of biomechanical species and carries with it the germ of a Brave New World more fantastic and hyperbolic than anything we have seen in the history of human civilization. In its most significant form, the UTM is not merely another instrument in the history of technical inventions ; it is a computational monad that redefines a new plane of immanence as the spectacle of a second order nature transposed onto the cultural universe of humanity that is founded upon the first order nature. As a generative mechanism, the UTM has brought to the foreground a universe of counterfactual possibilities by showing that these potential states of affairs are inextricably woven into the invisible fabric of reality itself. Its latent ambition is to exfoliate this reality in all its manifestations through the inner workings of the Turing Dimension : a linear sequence of cells that function as the channel through which information is processed to form the digital economy of the Universal Turing Machine.

The UTM is a logical counterpart of Leibniz's idea of the metaphysical monad. It is a computational monad that is founded upon the classical model of computation due its reliance on the mechanism of classical logic for its operation. As such, the UTM is an abstract machine composed of a linear tape, that is potentially infinite in length and is divided into squares or cells, and a device called a head which reads and re-writes binary digits registered on each cell according to the instruction set of the program. The tape serves as a receptacle for storing as well as for processing binary information.(…)

The notion of universality derives from the fact that every UTM can compute, according to the Church/Turing Thesis, anything that is logically computable and can therefore model and nest within itself any model of computation, classical or otherwise. As such, it is a simple conceptual mechanism capable of perpetually inducing an internal model, or perception (Leibniz's term for the same feature within a monad), of the world by means of an internal principle that continually modifies its internal state to arrive at a more comprehensive version of the model or perception of the world. In other words, the UTM is a logical subset that can compute the potential content of the larger set that is the universe itself. Consequently, by the nature of its embeddedness, it is capable of altering the content of the universe by further computing the numerical substance of the cosmos and staging it onto the plane of immanence as diverse modalities of possible existence. According to Rolf Landauer of IBM, who has done fundamental research into the material and energetic aspect of computation, not only does physics determine what computers can do, but what computers can do, in turn, will define the ultimate nature of physical laws. This is a profound and radical idea that necessitate a new paradigm concerning the nature of computation and, consequently, of our role as active participants, or agents, in the evolution and transformation of the universe at large.

The Universal Turing Machine therefore is a machinic idea of a perpetual computing system, or an abstract evolutionary machine, that processes information through sequential iteration of bits by registering them on the linear tape of the machine that is potentially infinite in length. As such, it is endowed with the latent capacity to self-organize and transforms its internal states, at least in principle, into all possible states of a monad without end. Even though its initial design is predicated by the need to delineate the consistency of the sequence of steps necessary in the formation of a mathematical proof, a response made by Alan Turing to David Hilbert's call (1900) for resolution to the so-called decision problem, the UTM has transcended its original function by overcoming its task as an instrument of representation. It has now entered into the domain of self-organizing systems with the ambition to assert its autonomy as a mode of existentiation, or auto-projection. This is an ontological status distinct from a condition that is dependent, as a prime mover, solely on external forces that instantiate its will to action. In other words, the UTM is a primitive precursor of a biomechanical species with the metaphysical ambition to embody a machinic form of artificial life and neural intelligence. Since the UTM is the simplest and the most general type of computing system, its internal principle or program can be made to accommodate a generalized form of genetic algorithm that could evolve through self-modification and optimization of its internal states. It could, in principle, evolve through self-replication and mutation into ever more complex states of monadic encoding by incorporating new axioms into its existing matrix of axioms. In the process, it would bifurcate into other self-replicating UTMs, each of which in turn would bifurcate and nest other self-replicating UTMs to form an epigenetic landscape of computational monads or a machinic phylum of Universal Turing Machines. Even though the Leibnizian monad continually engages in simultaneous, albeit non-linear, modification of multiplicities as it develops into higher levels of complexity, the UTM is a one-dimensional cellular automata that self-organizes and transforms itself by incessantly rewriting the binary digits registered on the tape that constitutes the Turing Dimension. It is a one-dimensional universe of monadic states generated by the perpetually evolving code of the machine.

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The Turing Dimension, together with the arrow of time, establishes the plane of reference necessary for the mapping and projection of the Turing Surface into the plane of expression. Each UTM is a monadic agent that enters into autocatalytic reactions with other UTMs to weave a multi-layered tapestry of surfaces which subsequently coalesce by forming into a Universal Turing Surface as the virtual membrane of the mechanosphere. The Surface oscillates according to the dynamic flow of information outputted by each scanning particle as it scans and rewrites bits along the linear sequence of cells marked on the tape of the Turing Dimension of each machine. (…) Such a perpetual Turing Machine is an abstract biological engine made to sustain itself through self-modification and self-maintenance within the intertextual networks of machinic phylums generated by Universal Turing Machines. Each Turing Dimension therefore is an aperiodic time machine that weaves a fractal surface with inflections and perturbations that amplify to form holes and vortices on various regions of the membrane that constitutes the Universal Turing Surface. These are the caesurae of the Turing Dimension that interrupt the crazed oscillations of the tragic effect induced by the dialectics of fusion operating in complicity with the synthetic logic of the Universal Turing Machines.

(…) Herein lies the supreme irony of a gnostic quest that may well be usurped by the very instrument that promises to deliver. The internal principle and the internal complexity contained within each computational monad is dependent on the universe of computable functions drawn from the universe of mathematics that has proven to be irreducibly random and incomplete in its organization. As a consequence, any algorithmic compression that reflects the matrix of the internal complexity would be a code that is also irreducibly random, a specific kind of randomness that is qualitatively different from any random scrambling of bits.(…) If the totality of all possible worlds is a mirror of the infinity of possible effects engendered by the absolute infinite cause, there are, in all likelihood, no binary strings that can encapsulate the hidden logic of the absolute infinite in its entirety. However, if there do exist such a Metacode, it would, by definition, pertain to all possible worlds including those that exist outside the domain of the laws of physics that underlies the present state of the universe. Yet Seth Lloyd of MIT has suggested a suprising proposal stating that in a universe in which local variables support universal computation, a quantum theory of Everything can be simultaneously correct and fundamentally incomplete.

(…) Let it suffice for the moment to say that, the Turing Dimension is the potential infinite interspersed with breaks or interruptions that lie between overlapping dimensions of the tragic effect. The Universal Turing Surface is the instrumental medium that exfoliates into a topo-dramatology of the virtual cockpit of architecture infused with an ambivalent mixture of exultation and despair. It is a theatre where the very excess of the speculative switches into the very excess of submission to finitude (PLL), as defined, in this context, by the logic and limits of computability. It is at once a tragic comedy and a machinic philosophy of the tragic effect. Nothing symbolizes the emergence of the Hyperzoic Era more clearly and explicitly than the emergence of the Universal Turing Surface that lays out a virtual cartography of a possible world among an infinite number of possible worlds. Architecture is implicated in the folds of this cartography that has become the green membrane of space suspended essentially in a twilight zone that is everywhere and nowhere. The Universal Turing Surface is the phase space topology engendered by the cyclothmic oscillations of the Universal Turing Machine. It is saturated with the stuff of information out of which unheard of dreams and dramas emanate to form a part of the living texture of the evolving universe. The Surface is nonetheless permeated with the Caesura of the Turing Dimension, which allows each interruption to sustain a pause or the empty moment, the absence of moment that, if luck is with it, may allow for the intrusion of the prophetic word (PLL). The Universal Turing Surface is the new plane of immanence that is, above all else, a cosmopolitical orchestration, an onto-organology constituted by an autopoeisis : a self-generated organ of a self-synthesized information system (John Wheeler) within demiurgic space.

Karl S. Chu

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X Phylum, version 3.0



La fin du deuxième millénaire sera finalement reconnue comme l'ère évolutionnaire de la convergence. Une convergence, due, en grande partie, à l'émergence et à la complicité, au vingtième siècle, de la computation et de la biogénétique, qui vont progressivement transformer la communauté globale en une économie démiurgique, jusqu'à présent contrôlée et limitée par un capitalisme normatif. Il y a des raisons de croire qu'un Brave New World est déjà en train de se créer; je l'ai évoqué ailleurs sous le terme d'ère Hyperzoïque, ère à la fois très prometteuse et pleine d'incertitude. Elle s'avérera, sans aucun doute, beaucoup plus incrédule et perfide que toutes les ères qu'a connues l'histoire de la planète. Si l'ère Cambrienne marque l'explosion soudaine de la diversité et de la complexité des animaux multicellulaires dont les descendants occupent le monde aujourd'hui, l'émergence de l'ère Hyperzoïque annonce la profusion d'un nouveau type de vie ; la vie artificielle des machines abstraites et de l'architecture, qui se manifestera par un nouveau type d'économie bionique de la mécanosphère, en coïncidence avec la biosphère. Une telle condition transformera le comportement du capitalisme normatif, passant d'une logique basée sur la production de produits statiques à une économie démiurgique qui engendrera la vie artificielle de systèmes globaux intelligents. C'est dans la sphère de la virtualité que la matrice globale de systèmes computationels évolutionnaires produira et peuplera la planète de formes diverses de vie et d'êtres artificiels.

C'est dans ce contexte d'une cosmologie évolutionnaire que le projet X PHYLUM s'inscrit pour élaborer une nouvelle forme d'architecture proto-bionique. Son mode de devenir est basé sur la logique auto-génétique du système-L (Système de Lindenmayer) qui est un

des types les plus simples de systèmes arborescents récursifs. L'infrastructure axiomatique qui gouverne sa génération requiert un ensemble de fonctions mathématiques afin de déterminer ses manifestations morphologiques viables en tant qu'expression architecturale. En plus d'engager des mécanismes auto-reproductifs et auto-organisateurs,

X PHYLUM tente également de conceptualiser une théorie computation-nelle de l'architecture basée sur le modèle classique de la computation, "l'Universal Turing Machine", inventée par Alan Turing dans un article fondateur publié en 1936 sur les nombres quantiques. Le nouveau paradigme de la cosmologie évolutionnaire nécessiterait, en fin de compte, un calcul des quanta comme infrastructure ; calcul cependant qui, aujourd'hui, est encore à

l'état embryonnaire en terme de recherche et de développement. X PHYLUM est toutefois un index marquant la formation d'une espèce d'architecture génétique basée sur une conception algorithmique du monde.

En tant que système auto-génétique, X PHYLUM est une monade computationnelle qui est un équivalent logique de la notion de monade métaphysique de Leibniz. C'est une singularité, ou une totalité incomplète, dont la morphologie est générée par un principe interne et provisoirement fermé afin de se qualifier elle-même comme forme de proto-espèce. Les monades leibniziennes sont des entités modales qu'on peut caractériser comme espèces métaphysiques. Une reconceptualisation des monades du point de vue de la computation nécessite une redéfinition et une généralisation du concept biologique "d'espèce" afin qu'il puisse englober un cadre de référence catégorielle plus vaste. Une différence fondamentale entre la notion d'espèce et la typologie réside dans le fait que les espèces requièrent des processus morphogénétiques pour le développement et l'évolution des ensembles individués ou des singularités, alors que la typologie est basée sur une classification statique d'arrangements typographiques dérivés de la conjonction de l'iconographie et des programmes utilitaires influencés par des valeurs culturelles. Partant de cette notion généralisée de l'espèce, un système auto-organisé, un robot ou une infrastructure logique dynamique seraient considérés à la fois comme de nouveaux types d'espèces et comme des formations diachroniques de processus épigénétiques, évoluant en "espèces épistémiques" ou des hyperstructures qui résident dans quelque domaine de configurations virtuelles. L'univers de la virtualité est donc une constellation dynamique composée de sphères indiscernables en constante mutation, de forces, d'information et de particules virtuelles qui s'autoreproduisent continuellement et s'auto-synthétisent en matrices de plus en plus complexes d'auto-organisations monadiques.

Les mouvements internes des monades computationnelles sont propulsés par la dynamique de mécanismes auto-génératifs dont les désirs abstraits, tels que les compulsions, les propensions ou les tendances innées sont déjà implicites au sein de l'espace de configuration des axiomes. Le déploiement d'une monade computationnelle génère une profondeur logique similaire à la complexité de temps nécessaire pour générer et produire une espèce. Même s'il s'agit essentiellement d'une procédure diachronique, le processus n'épuise pas l'excédent d'information qui rentre en jeu dans la modulation non linéaire des séquences génératives. L'émergence d'une monade est un événement dérivé de la formation algorithmique. Pourtant, des intrusions inexplicables ou des implications virtuelles parviennent à pénétrer dans ces processus non linéaires, qui s'opposent à toute appropriation simpliste d'analyse ou de prédiction quantitative même dans le contexte d'une procédure strictement déterministe. Les événements qui déterminent la constitution des monades sont véritablement complexes en ce sens qu'ils constituent des effets émergents générés par l'énorme complicité de relations causales qui entrent inévitablement en collision et en interaction avec les particules virtuelles qui accompagnent et entourent un ensemble donné d'explications axiomatiques. La diachronie, en tant que procédure phylogénétique, est également soumise à des interventions synchroniques de la part de particules virtuelles et à des co-implications dérivées de conditions se trouvant aussi bien à l'intérieur qu'à l'extérieur d'un ensemble donné de formations axiomatiques. Elles contiennent un excédent de méconnaissable et d'indéterminé en raison du fait que les chaînes algorithmiques extrêmement complexes sont imprégnées de degrés variables de hasard quant à leur composition interne. Enfin, la computation est un phénomène physique et logique et, à ce titre, il est circonscrit par la théorie de l'inachèvement et de l'indécision de Gödel. La construction de la vie artificielle de l'architecture, d'une nouvelle forme d'architecture bionique sera également inévitablement limitée et délimitée par la logique et les limitations physiques du computable. La constructibilité est une fonction de la computabilité.

Karl S. Chu

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Karl S. Chu (1950)

1977 – Bachelor of Architecture, University of Houston, Texas
1984 – Master of Architecture, Cranbrook Academy of Art, Bloomfield Hills, Michigan
2000 – Lefever Fellowship, Ohio State University


2000 / 1990 – Southern Design Institute of Architecture (SCI-Arc) Los Angeles
2000 – Columbia University, New York

Principaux projets et réalisations

2000 – "Jungle" recherche théorique sur le développement des systèmes génératifs ; proposition architecturale et urbaine.
1999 – "X Phylum"

Bibliographie sélective de Karl S. Chu

2000 – "The Caesura of the Turing Dimension" (version abrégée) Natural Born CAADesigners, Birkhaüser, Bâle ; "The Cone of Immanenscendence" ANY, Issue of Diagram Works, New York, NY ; "X Phylum" Domus, n° 822, Italie ; "Genosphere" développement autour du concept des "mondes possibles" leibnizien (à paraître)
1998 – "Hourglass of the Demiurge" Architectural Design, Issue on Architects in Cyberspace, n°136, Londres ; Architektur & Bauforum, n°196, Autriche
1996 – "The Virtual Anatomy of Hyperstructures" Architectural Design, Issue on Architects in Cyberspace, No. 118, Londres
1995 – SPACE, n°334, Séoul, Corée