Automated Architecture; Speculative Reason in the Age of the Algorithm (2)

Automated Architecture Speculative Reason in the Age of the Algorithm Luciana Parisi 2014

In the last forty years, with the algorithmic automation of spatio­ temporal forms and structures, task-specific computer design, based on numerically controlled machines, has been absorbed within a more generic function of computation resulting in custom fabrica­ tion processes, machine control protocols, real time simulations that update live, and interactive models that can be directly tweaked and manipu!ated.1 More radically, the expansion of computational functions in design has Jed to the emergence of computational design thinking, whose focus on material properties, physical forces, pressures and constraints defines dynamic spatio-temporal forms in terms of non-binary and continuously heterogeneous variations of matter. Moving away from computation as a form of symbolic repre­ sentation of physical elements, computational design thinking instead embraces the elemental properties of materials and their gE)nerative rules subtending the dynamic nature of spatio-temporal structures. Instead of following geometrical and mathematical patterns, this form of material computation aims to directly follow the physical emergent patterning and material processes of self-assembly out of the interac­ tion of loose elements. In contrast to the mechanical automation of sequentially linear and assembly systems, this new form of algorith­ mic automation is driven by the physical strategies of materials to compute both architectural form and spatio-temporal performance. 1. For an extensive discussion about this transformation in digital architecture. see N. Leach (ed.). Designing for a Digital World (New York: Wiley, 2001); K. Terzidis, Algorithmic Architecture (Oxford: Architectural Press, 2006); M. Meredith, T. Sakamoto and A. Ferre (eds.). From Control to Design: Parametric/Algorithmic Architecture (Barcelona: Actar, 2008); S. Kwinter, C. Davidson (ed.). Far from Equilibrium: Essays on Technology and Design Culture, (Barcelona: Actar, 2008); L Bullivant. Responsive Environments: Architecture. Art and Design (London: V&A, 2006); L. Bullivant, 4dsocial: Interacti ve Design and Environments. Architectural Design 77:"1 (2007): K. Oosterhuis, Interactive Architecture #1 (Rotterdam: Episode, 2007).

# A C C E L E R A T E But computational design thinking is more importantly a symptom of a more generic acceleration of automation in which algorithmic modelling techniques are now able to select, analyse and evaluate data through the generative evolution of spatio-temporal structures. Paradoxically, the acceleration of automation has pushed forward an anti-digital form of computational design thinking that aims to become one with the fluctuating dynamics of matter. The advance of computational design thinking. and its acute investment in the intelligence of materials. is the result of a major transformation in the digital design of last forty years marked by the advent of interactive computation. and especially in the last fifteen years. since simulations have become consistent with the inherent morphogenesis-or evolutionary capacities-of materials.2 Within digital dE!sign and architecture. this transformation is often associated with the emergence of material computation, an approach to design thinking based on the convergence between evolutionary biology and non-standard geometry or topology. By leaving behind digital model­ ling based on the principles of the Universal Turing Machine. whereby the manipulation of symbols allowed designers to test results and deduce a proof for possible structures. computational design thinking has instead adopted a specific form of inductive reasoning relying on the computational capacity to gather information from the physical world and thereby generate dynamic spatio-temporal structures that are. as it were. empirically derived from matter. From this standpoint. the shift from a form-oriented design, the information-driven manipulation of NURBS (nonuniform rational B-spline) geometry within a computational environment for instance, to a generative-oriented design that integrates material. form and 2. See A. Menges and S. Ahlquist (eds.). Computational Design Thinking (London: John Wiley and Sons. 2011); A. Menges (ed.). Material Computation-Higher Integration in Morphogenetic Design. Architectural Design 82:2.

PAR I S I -AUTOMAT E D ARCH ITECTU R E force a s continuous iterations, has l e d t o an empirically-oriented computation of physical activities which is now central to automated architecture. As opposed to the deductive reasoning of digital archi­ tecture, according to which general and universal rules inform matter, and algorithms aim to produce simulations that match the behaviour of material substrates, the tum towards material computation, in which physical properties are said to be the motor of simulations, marks the adaptation of an inductive mode of reasoning based on the local behaviour of materials from which complex structures emerge. Here design thinking is not based on preestablished truths that have to be proven, but emerges out of the material variations of elements evolving in time through the mutation and adaptation of data. Similarly, with material computation, design thinking is less concerned with the contemplation of truth and more directly geared towards action, operation, and processing in so far as computation becomes a rather practical and intentional-oriented affair in which the ends of matter drive form whilst architectural form becomes one with matter's activities. If mechanical automation-the automaton of the assembly line, for instance-was a manifestation of the functionalist form that shaped matter, the increasing acceleration of automation led by the development of interactive algorithms (including human­ machine and machine-machine interactions) instead reveals the dominance of a practical functionalism whereby form is induced by the movement of matter. Inductive reasoning places the local properties of materials and the varying behaviours of physical elements at the centre of the design process. In particular, by drawing closely on evolutionary biol­ ogy, computation here involves a continual extension of the search space aiming to find novel solutions that emerge as a byproduct of the evolutionary dynamics of selection, mutation, and inheritance. With this form of emergentism in design, algorithms serve to set .!>.. 0 01

# A C C E L E R A T E the range of possibilities, whilst analytical measures establish levels of fitness of specific instances within the set of possibilities.3 Here emergence is not only a property of pattern formation and physical organization. Emergence is also a factor in behaviour, design and computation.� Novel spatio-temporal patterns are said to arise not in formal pre-arrangements, but in the realisation of multiple behavioural capacities not initially determined within the programming. As part of the generic tendency to accelerate automation, the turn to inductive reasoning in computation does not simply aim to instrumentalise or mechanise reason and thus establish the formal condition from which truths can be derived, but more explicitly allows matter to become the motor of truth, to become one with and ultimately constitutive of formal reason, of the rules and the patterns that emerge in the automation of space and time. This matter-driven computational design thinking works not simply to better simulate material behaviour but to produce physically­ induced models, a sort of meta-biological computation based on feedback information scanning of the changing properties of materials. 3. These behaviours are derivatives of simple conditions called agents. An agent holds a simple set of properties; the environment defines a set of rules in which the agents interact. From this standpoint. computational design focuses on the execution of variation methods for the purposeful intent of resolving the complexities that exist in the interrelation and interdependences of material structures and dynamic environments. Computation has the potential to function as a universal application. but the mechanism works only in the processing of specific, non-symbolic conditions relating to materiality, spatiality and context. Whilst the procedures define a vast state space of potentials, the result embodies specific descriptions of the overall system. Computational processes are iterative and recursive but also expansive. They work by growing and specifying the information. which describes form through procedures which recursively generate form. calling variable parameters within the state space. See Menges and Ahlquist (eds.). Computational Design T hinking, 2"1. "1. lbid. CD 0 '1"

PARI S I -AUTOMATED ARCH ITECTU R E But this accelerated computation of matter relying on the efficacy of the physical substrates of matter irremediably misses an ontological question at the core of computation: What and how is algorithmic reason? What is its status vis-a-vis other forms of reason, and how is this manifested? If computation design thinking has rejected the deductive model of universal rules and its top-down method of form finding, then what do solutions simulating the biophysical behavior of matter tell us as to the nature of algorithmic automation itself in this new phase of tech­ nocapital acceleration? Do they mean that the technocapital accelera­ tion of automation has become one with the physical dynamics of matter, defining a dynamic rather than mechanical instrumentalisation of reason? If this is the case. then computational design thinking is perhaps the manifest image of what technocapitalism has been able to achieve by turning the deductive methods of mechanized reason into a multiagent interactive computation whose rules are pre-adapted to physical behavior. Nevertheless. the inclusion of material agency, bio-physical cata­ lysts and temporalities in computational design is also revealing a less tractable tendency of technocapital acceleration: the computational function of algorithms to add new data to processing. This means that, whilst computational design thinking takes inspiration from the material dynamics of the physical world for its generative models, the acceleration of automation ls not simply replacing the organic ends of reason with technical means, but is irremediably constituting a second nature, an algorithmic evolution equipped with its own physical and conceptual levels of order that are not one with matter. One df the most immediate ontological consequences of the acceleration of automation from digital simulations of form-finding to the generation of materially-driven models. is a computational design thinking embracing the seamless fusion of thought and matter.

# A C C E L E R A T E Here the reality of abstraction is suspended and instead explained by and through the concreteness of physical causes determined by the interaction of loose elements. Whilst the acceleration of automation has pushed the formal logic of deductive reason in computation to move beyond the hierarchical top-down simulation of matter-as an instance of a priori reason-it has not stripped computation from its functions of abstraction and quantification. In other words, instead of accounting for the abstract function of algorithmic processes, the material-oriented approach of computational design thinking risks grounding such processes in ideal physical causes, external to algorithmic automation itself. The limit of computational design thinking is its uncritical perpetu­ ation of idealist materialism according to which the relation between computation and reason is mediated or to some extent caused by material data. To put it in another way, the problem of computation as a top-down framework of deductive reasoning rooted in ideal forms or in a thinking subject has been largely circumvented but not overcome by computational design thinking, rooted as the latter is in the aggregate causality of material elements. Within the generic acceleration of automation, this view risks disqualifying rather than explaining the computational process through which physical variables are extracted and abstracted. ln short, this form of design thinking seems to overlook the materiality of computational processing itself, which necessarily goes beyond the appeal to the preexisting complex­ ity of physical causes. To address the specificity of such processing, computational design thinking may need to start from the axiom that abstract data and data abstraction driven by algorithmic agents define the automated function of interaction in online, distributive and parallel systems. Kostas Terzidis, for instance, already envisaged the autonomy of computational processing for automated design when he said: co 0 "1""

PARIS I -AUTOMATED A R C H ITECTU R E Unlike computerization and digitization. the extraction of algorithmic processes is an act of high-level abstraction. [...] Algorithmic struc­ tures represent abstract patterns that are not necessarily associated with experience or perception. [...] In this sense algorithmic processes become a vehicle for exploration that extends beyond the limit of perception.5 But the extension of algorithmic abstraction beyond the limit of perception has also meant that such abstraction corresponds to the intelligible function of rule-based thinking that neither simply matches with the rational faculty of knowing nor with the intuitive capacities of knowing beyond proof. The aim here is not to reject material com­ putation, but to radicalise its implications. As a symptom of a generic acceleration of automation, the generation of spatio-temporal archi­ tectures of a computational order are inconsistent with the physical facts of matter. Similarly, algorithmic automation does not coincide with an abstraction of matter based upon the way in which matter works, but more stubbornly produces axioms-or truths-about what is not yet known and what non-physical or algorithmic agents know. This implies riot the idealisation of the computational capacities of matter (which are continuous with algorithmic automation), but instead a veritable rehabilitation of algorithmic automation in its own right, exposing its own axiomatic thinking or rule-based processing. The rehabilitation of algorithmic automation is also an attempt both to dethrone computation from a closed deductive formalism, based on simple universal rules, and to subtract it from a too imme­ diate merging with bio-physical causality. From this standpoint, the acceleration of automation challenges the paradigm of the mechanical 5. K. Terzidis, Expressive Form: A Conceptual Approach to Computational Design (London and New York: Spon Press, 2003), 71.

# A C C E L E R A T E process determined by discrete steps that are pre-thought and pre-ordered. but also the vitalism according to which material com­ putations are induced by the continuity of physical processes. To put it in another way, the acceleration of automation has entered the uncharted territory of an algorithmic reason that does not simply derive its functions from the local interaction of parts. At the same time. however. algorithmic automation also breaks from the meta­ computational view for which a simple theory can explain complex behaviour or an elegant formula can compress all of its outputs. Far from being an abstraction of physical structures. automated archi­ tecture is instead a manifestation of algorithmic spatio-temporalities that have nothing to do with what already exists in nature (or the relation between rules and randomness that exist in the biological and physical strata). If computational design thinking rejects the representational framework of meta-computation (i.e .. the universe is ultimately made of discrete algorithms). then it also has to admit that what is manifested to us is not the same as what algorithms do-i.e .. their scientific image is intrinsic to them and does not match what is perceivable and cognizable by a subject. But to further clarify how accelerated automation has challenged computational views based on deductive and inductive reasoning. one has to explain the problem of the incomputable. or randomness. that is at the heart of computation today. ACCELERATE RAND O M NESS The acceleration of algorithmic automation cannot be divorced from the problem of the incomputable, and the challenges this posed to the deductive method of logic based on pure reason. In 1931. the logician Kurt Godel took issue with David Hilbert's metamathemati­ cal program and demonstrated that there could not be a complete axiomatic method. nor a pure mathematical formula or universal

PAR I S I -AUTOMATED A R C H ITECTURE truths, according to which the reality of things could be proved to be true or false.6 Godel's 'incompleteness theorems' explained that. even if all the propositions of a system were true. they could not be verified by a complete axiomatic method. Certain propositions were therefore ultimately deemed to be undecidable: they could not be proved by means of the axiomatic method upon which they were hypothesized. In Godel's view, no a priori decision, and thus no finite set of rules. could be used to determine the state of things before things had run their course. Not too long after. the mathematician Alan Turing also encoun­ tered Godel's incompleteness problem whilst attempting to formalize the concepts of algorithm and computation through his famous thought experiment. known as the Turing Machine. In particular. the Turing Machine demonstrated that problems that can be decided according to the axiomatic method were computable problems.7 Conversely, those propositions that could not be decided through the axiomatic method would remain incomputable.8 From this standpoint. 6. See D. Hilbert, "The new grounding of mathematics: First report' in W. B. Ewald (ed.). From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Vol 2 (Oxford: Oxford University Press. 1996). 1115-33; R. Goldstein, Incompleteness: The Proof and Paradox ofKurt Gade/ (New York: Norton. 2005); S. Feferman (ed.). Some basic theorems on the foundations of mathematics and their implications. Collected works of Kurt Godel. Vol. 3 (Oxford: Oxford University Press, 1995). 304-23. 7. A. M. Turing. 'On computable numbers, with an application to the Entscheid­ ungsproblem', Proceedings of the London Mathematica/ Society, 2nd Series, Vol. 42 (1936). For further discussion of the intersections of the works between Hilbert, Godel and Turing. see M. Davis. The Universal Computer. The Rood from Leibniz to Turing (New York & London: Norton, 2000), 83-176. 8. According to Turing, there could not be a complete computational method in which the manipulation of symbols and the rules governing their use would realize Leibniz's dream of a mothesis universo/is. Mothesis Universo/is defines a universal science modeled on mathematics and supported by the co/cu/us rotiocinotor,

# A C C E L E R A T E insofar as any axiomatic method was incomplete, so too were the rules of computation. 9 As Giuseppe Longo explains,10 the problem of the incomputable explained that even closed finite systems (e.g. the pendulum or first order Arithmetic) are undecidable, and inversely, that few and simple deterministic rules or finitary physical or logical structures may give rise to chaotic behaviours or complex logical theories. In other words, a universal calculation described by Leibniz as a universal conceptual language. For first-order cybernetics the calculus ratiocinator refers to the computational machine that could perform differential and integral calculus or the combination of the ratios. As Norbert Wiener pointed out: 'like his predecessor Pascal, [Leibniz] was interested in the construction of computing machines in metal [...] just as the calculus of arithmetic lends itself to a mechanization progressing through the abacus and the desk computing machine to the ultra-rapid computing machines of the present day, so the calculus ratiocinator of Leibniz contains the germs of the machine ratiocinatrix, the reasoning machine.' See N . Wiener, Cybernetics or the Control and Communication in the Animal and the Machine (Cambridge, MA: MIT Press, 1965), 12. For Turing, the incomputable determined the limit of computation: no finite set of rules could predict in advance whether or not the computation of data would halt at a given moment or whether it would reach a zero or one state, as established by initial conditions. This halting problem meant that no finite axiom could constitute the model by which future events could be predicted. Hence, the limit of computation was determined by the existence of those infinite real numbers that could not be counted through the axiomatic method posited at the beginning of the computation. In other words, these numbers were composed of too many elements that could not be ordered into natural numbers (e.g. 1, 2, 3). 9. A clearer explanation of the implications of Godel's theorem of incompleteness for Turing's emphasis on the limit of computation can be found in Gregory Chaitin, MetaMaths: The Quest for Omega (London: Atlantic Books, 2006), 29-32. 10. G. Longo, 'lncomputability in Physics and Biology' available at http://www. di.ens.fr/users/longo (last accessed March 2014). See also G. Longo, "Critique of Computational Reason in the Natural Sciences", In E. Gelenbe and J.-P. Kahane (eds.), Fundamental Concepts in Computer Science (London: Imperial College Press/World Sci., 2008); G. Longo, 'From exact sciences to life phenomena: following Schrodinger and Turing on Programs, Life and Causality', Information and Computation, 207:5 (2009), 543-670.

PAR IS I -AUTOMATED ARCH ITECTURE 'mathematics is an essentially open system of proofs' and 'each real mathematics proof proceeds as an open system'. Hence knowledge does not depend on a predetermined set of axioms insofar as theo­ ries are constantly built, axioms modified and rules amended. From this standpoint, one could extend this view to computation, but explain that knowledge is here produced by means of axioms without n ecessarily passing through the faculty of pure reason or practical reasoning led by the existence of facts. The problem of incomputables for rule-based reasoning, far from proving the fallacy of algorithmic automation in the production of knowledge, rather indicates that there are truths that cannot be proven (by deductive or inductive reasoning) but are nonetheless intelligible within computation and are manifested in the form of an axiom. The problem of the incomputable thus shows that computational axiomatics is inevitably infected with randomness, but also that randomness is each time turned into an axiom by means of rule-based processing, defining algorithmic reason as a nonlinear elabcration of continuous infinities and transformation of its discrete parts. For information theorist Gregory Chaitin, the question of the incomputable reveals that randomness or sensitivity to context or initial conditions is part of even elementary branches of number theory, and that therefore randomness and complexity are intrinsic to the most elemental of particles. In par ticular, Chaitin explains that the halting probability of the Turing Machine, and thus the uncertainty of predicting when-given a certain input-a computation will stop, can nonetheless be computably enumerable despite being infinitely large. Chaitin calls this odd probability Omega: the limit of a computable, increasing, converging sequence of rational numbers. What is new here is that such a limit of computation is also algorithmically random:

# A C C E L E R A T E its binary expansion is an algorithmic random sequence, which is incomputable (or partially computable).11 Chaitin's discovery of Omega clarifies that randomness is intel­ ligible and detectable within the very computational processing in which unpredictable infinities emerge and operate-and yet cannot be synthesised by an a priori program. theory or set of procedures that are smaller in size than it. This means that the incomputable within computational processing can be neither reincorporated into formal deductive logic (since it cannot be proven by means of pure reason), nor explained primarily in terms of those physical causes 11. Chaitin explains that his 0 number is a probability (albeit an infinite number) for a program to halt: First, I must specify how to pick a program at random. A program is simply a series of bits, so flip a coin to determine the value of each bit. How many bits long should the program be? Keep flipping the coin so long as the computer is asking for another bit of input 0 is just the probability that the machine will eventually come to a halt when supplied with a stream of random bits in this fashion. At the same time however. he also points out that Omega is incomputable, and thus the problem of the limit of computation remains unsolvable for a formal axiomatic system: We can be sure that 0 cannot be computed because knowing 0 would let us solve Turing's halting problem, but we know that this problem is unsolvable. In other words: Given any finite program, no matter how many billions of bits long, we have an infinite number of bits that the program cannot compute. Given any finite set of axioms, we have an infinite number of truths that are improvable in that system. Because 0 is irreducible, we can immediately conclude that a theory of everything for all of mathematics cannot exist. An infinite number of bits of 0 constitute mathematical facts (whether each bit is a 0 or a 1) that cannot be derived from any principles simpler than the string of bits itself. Mathematics therefore has infinite complexity. G. Chaitin, 'The Limits of Reason', Scientific American 294:3 ( March 2006), 74-81. On Chaitin, see also R. Brassier, 'Remarks on Subtractive Ontology and Thinking Capital', in P. Hallward (ed.), Think Again: Alain Badiou and the Future of Philosophy (London and New York: Continuum. 2004).

PAR IS I -AUTOMATED A R C H ITECTURE that cannot be computed, thus marking the limit of computation (and hence the necessity to extend computation to the physical world). Instead, the increasing presence of infinite quantities of data (incomputables) within interactive, parallel and online computational systems (including human-machine, but also increasingly algorithm­ algorithm interactions) exceeds totalising mathematical and physical causality, a priori or a posteriori reason alike, by reorienting deductive and inductive methods of computation in counter-intuitive directions. One of the interesting implications of Chaitin's Omega is that it is at once computationally intelligible-and thus physically and conceptually processed by automated systems-yet unsynthesisable by a totalizing theory or practice of knowledge. For computational design thinking, this proposition entails that computation needs to be understood beyond the limits of mathematics, and cannot be easily supplemented by physics. As already mentioned, computational design thinking in particular has embraced this move towards physical causality, demonstrating that material dynamics prove that there are morphogenetic and continuously changing patterns in nature from which a new model of automated architecture can be derived. Instead, Chaitin insists that computation needs to be rethought in terms of an experimental axiomatics for which the incomputable Omega cannot be proven by means of deductive reason, but can nonetheless-although partially and immanently-discretize (i.e., render discrete and intelligible) infinitely large quantities of data. This view is essential to computational design thinking because it importantly reveals that there is a dynamic proper to computation, in which discrete patterns are inevitably accompanied by pattern­ less information. From this standpoint, the accelerated automation of spatio­ temporal structures is not simply attuned to patterns in nature, but instead defines the increasing thickening of a computational stratum, a second nature, whose ends are not compatible with the fluid

# A C C E L E R A T E dynamics of matter. In short, a material computational thinking can­ not overlook the function of incomputable algorithms in automation insofar as incomputable parts are in the majority and can take over the totality of programming .12 The acceleration of automation thus inevitably exposes an acceleration of randomness-patternless data bursting within algorithmic sequencing-and has given way to an experimental axiomatics determined by an immanent discretization of incomputables. Far from determining automation in terms of a Laplacian Universe whose mechanics ensure that outputs can always be deduced from a finite set of inputs or instructions, the accelera­ tion of automation instead reveals that inputs are as big as outputs and that computation can only discover and revise truths through a continuous production of axioms. S PECU LATIVE REASO N I t is now possible to draw some conclusions. The acceleration of automation has led to the emergence of a new form of computational design thinking driven by a close investment in the biophysical dynamics of matter, which are said to produce the most varied patterns out of the infinitesimal relations between their parts. However, this equivalence between the biophysical dynamics 12. As Chaitin hypothesizes, if the program that is used to calculate infinities wm no longer be based on finite sets of algorithms but on infinite sets (or Omega complexity). then programmability will become a far cry from the algorithmic optimization of indetenminate processes actualized through binary probabflities. Programming will instead tum into the calculation of complexity via complexity, chaos via chaos: an immanent doubling infinity or the infinity of the infinite. Contrary to the Laplacian mechanistic universe of pure reason, Chaitin's information theory explains how software programs can include randomness from the start. Thus the incompleteness of axiomatic methods does not define the end point of computation and its inability to engage with dynamical change, but rather its starting condition, through which new axioms. codes, and sets Of instrt.etions have become immanent to non-denumerable reals.

PARI S I -AUTOMATED A R C H ITECTURE of matter and computation mainly assigns to computation the task of revealing or simulating structural variations and spatio-temporal complexities inherent to matter. Hence whilst biophysical patterns are taken to be the principal motor of computation, computation itself tends to recede into the background and remains a mere vehicle for visualizing and proving the indeterminacy of matter. This form of inductive reasoning derives and proves truths by means of empirical measuring, contingent actions, and facts and factors in the world. Computational design thinking thus becomes a mode of doing and practising a thought derived from what already happens in the physical world. From this standpoint, the acceleration of automation perfectly coincides with the technocapitalist illusion that matter can generate infinitesimal variations, an inexhaustible abundance that turns continuously smaller elements into vast resources for the productive eternality of the whole. But the acceleration of automation hardly leads to a blissful bathing in thoughtless matter and instead invades the everyday with the alien reasoning of patternless algorithms which, while they cannot be compressed into a smaller programme or synthesized by a brain, nonetheless lie at the core of all orders of computation (sequential, parallel, distributive, interactive computation). With the acceleration of automation, the explosive advent of algorithmic ran­ domness within computational processing has become inevitable. This means that instead of deriving dynamic patterns of information from matter, patternless data are instead generated within computation itself, and have thus become intrinsic to automated reason. Similarly, incomputables can no longer be explained by the Turing deductive method of reason, whereby all that can be computed is computable. Central to the acceleration of automation today is the profound transformation of formalism triggered by the ingress of incomputa­ bles into axiomatic, which has forced reason (rule-based functions)

# A C C E L E R A T E to become defined in terms of an immanent finality, an experimental final cause or purpose. Just as axioms become experimental truths, so too algorithmic automation exposes its internal inconsistencies: its sequential arrangement of parts becomes the host of random information, an interference that does not disrupt but adds a new order of finality to the programming whole (or the finality of the entire set of instructions). From this standpoint, one needs a theory of speculative reason that not only does away with the dominance of deduction and/or induction in computational design thinking, but that can also add another mode of reason to them that is able to surpass and nonetheless bring forward both truth and fact into an experimental axiomatic. To explain what is meant here by speculative reason, one has to turn to A. N. Whitehead. From his explanation of the function of rea­ son, we immediately learn that reason or the production of concepts implies the addition of new data to the continual chain of cause and effect-the physical laws of nature. In particular, Whitehead claims that the aim of speculative reason is the production of an abstract scheme,13 which he calls 'the concrete arrangement of relations'.14 For reason to be truly speculative, the schemes that are produced 13. According to Whitehead, "[t]he history of modern civilization shows that such schemes fulfill the promise of the dream of Solomon. They first amplify life by satisfying the peculiar claim of the speculative Reason, which is understanding for its own sake. Secondly, they represent the capital of ideas which each age holds in trust for its successors. The ultimate moral claim that civilization lays upon its possessors is that they transmit, and add to, this reserve of potential development by which it has profited." A. N. Whitehead, The Function of Reason (Boston: Beacon Press, 1929), 72. 1LI. 'The true activity of understanding consists in a voyage to abstraction, which is in fact a voyage to the more, fully concrete: to the system in which the fact is enmeshed. The system as conceptualized may be more abstract than the fact itself in that it is more general, but the real systematic context is more concrete, and its elaboration yields more about the existential relations of the fact." Ibid., 76.

PARI S I -AUTOMATED A R C H ITECTU R E and realized must be able t o encounter their finitude and limits: to account for incomputable parts that interfere with the ceaseless mechanisms of the whole.15 In particular, Whitehead warns us against the dominance of two main views as to what the function of reason really is-namely pure and practical reason. In the first, reason is seen as the operation of theoretical realization, whereby the universe is a mere exemplification of a theoretical system. The model of computation that produces complex data through the simplest and most elegant program/formula coincides with this view. Whitehead rejects the meta-computational theory of the universe (e.g. the universe explained by the Leibnizian Principle of Sufficient Reason), as it specifically seeks to capture in the simplest formula the infinity of worlds. The Principle of Sufficient Reason reduces the nexus of actual occasions to conceptual differ­ ences, since the Principle defines how differences can be represented or mediated in a concept.16 According to Whitehead, this one-to-one relation between mental cogitations and actual entities underesti­ mates the speculative power of reason, which is instead an ad�e �ture .JO , 1 : , • •• of ideas that cannot be encompassed by any complete formalism. . 15. 'Abstract speculation has been the salvation of the world-speculations, which made systems and then transcended them, speculations tflat ventured to the furthest limits of abstraction." Ibid. 16. As Whitehead clarifies, '[h]is [Leibniz] monads are best conceived as generalizations of contemporary notions of mentality. The contemporary notions of physical bodies only enter into his philosophy subordinately and derivatively." A.N. Whitehead, Process and Reality: An Essay in Cosmology (New York: Free Press, 1978), 19. Similarly, Deleuze points out that: '[a]ccording to the principle of sufficient reason, there is always one concept per particular thing. According to the reciprocal principle of the identity of indiscernibles. there is one and only one thing per concept. Together, these principles expound a theory of difference as conceptual difference, or develop the account of representation as mediation." G. Deleuze, Difference and Repetition, trans. P. Patton (New York and London: Continuum, 2004), 12.

# A C C E L E R A T E But his notion of speculative reason is also divorced from practical and pragmatic reason, whereby reason is a mere fact or factor in the world, or is explicable as an immediate method of intentional action.17 In algorithmic automation, this notion of practical reason would coincide with the dominance of the interactive paradigm in compu­ tational design thinking that explains it in terms of parts constituting a whole. This view sustains interactive models of automation, where algorithms are correlated to physical data, thereby suggesting that software programs are only one of the factors in the architecture of a responsive system determined by external physical dynamics. Whitehead's study of the function of reason sits comfortably neither with the formal nor practical methods and suggests instead that reason must be re-articulated according to the activity of final causation. and not merely by the law of the efficient cause.18 17. In particular, Whitehead observes, '[w]e have got to remember the two aspects of Reason, the Reason of Plato and the Reason of Ulysses. Reason seeking complete understanding and Reason as seeking an immediate action'. Whitehead, The Function of Reason, 11. 18. Whitehead's efficient cause and final cause can be understood as two modes of prehensions, causal efficacy and presentational immediacy, another parallel level of distinction between the physical and mental poles of an entity. Efficient causes describe the physical chain of continuous causes and effects, whereby the past is inherited by the present. This means that any entity is somehow caused and affected by its inheritable past. As Steven Shaviro explains: ' Efficient cause is a passage, a transmission, an infiuence or a contagion'. Although each actual entity appropriates the past in its own unrepeatable way, it is nonetheless embodied in the material universe that impinges upon it. However, in the process of repeating the patterns of the past there is always a margin of error. a bug in the vector transmission of energy-information from the past to the present. and from cause to effect. The seamless continuity of hereditary patterns is yet again faced with another level of contagion: the contagion of ideas breaking from efficient causality. Shaviro points out that there are at least two reasons for this break in the chain. On the one hand, time is cumulative and therefore irreversible: any actual event adds itself to the past. In other words, the mere addition of facts gives rise to a quantitative effect through which what was there before-Le. A-is 0 N "l""

PARIS I -AUTOMATED A R C H ITECT U R E Final cause explains how concepts are not reflections on material causes, but instead supplement the mere inheritance of past facts with new and often unproven ideas'. Conceptual prehensions, as Whitehead calls them, entail a process of selection and evaluation of facts that not only displaces the fact beyond observation, but also, importantly, recognizes in it another level of reality, an abstraction that is proper to the fact and yet is not determined by it. Final cause, therefore, is rather conceived as a speculative tendency intrinsic to reason and able to drive facts away from recognition so as to come back to them in a transformed fashion. This tendency, according to Whitehead, explains how decisions are carried out, and how the selection of past or existent data becomes the point at which another level of nuance is added to existing things. In other words, reason as a rule-based speculation defines the purpose of a theory and a practice in terms of their ability to add novelty to, and thus to counteract, the causal chain of events. From this standpoint, one cannot explain the universe solely in terms of physical interconnections, as these dangerously omit any counter-agency, any conceptual prehension for which there can be 'no direct observation, intuition or immediate a stubborn fact, which has an objective immortality that is inherited but not fully assimilated by B. The relation between A and B is that of two actual worlds. On the other hand, the repetition of the past is never neutral and undergoes a evaluation on behalf of the receiving entity. by which certain data are selected according to the qualities of joy and distaste of the receiving entity. for instance. The evaluation of inherited data is carried out by conceptual prehensions, which add novelty to what was before, as they are prehensions of eternal objects. It is the mental pole of any actual entity-the conceptual prehensions that do not necessarily involve consciousness-that explains how efficient cause is supplemented by final cause. For Whitehead, a final cause is always adjacent to an efficient cause; the former accompanies and yet supervenes upon the latter. See Whitehead, Process and Reality, on efficient cause, 237-8; on final cause 241; on the transition from efficient to final cause, 210. See also S. Shaviro, Without Criteria. Kant, Oeleuze, Whitehead and Aesthetics (Cambridge, MA: MIT Press 2009), 83; 86-7.

# A C C E L E R A T E experience of real processes.'19 This means that the function of reason serves to unlock possibilities and revise initial conditions within the given order of things. It would however be misleading to equate this notion of final cause or purpose with a teleological explanation of the universe, since for Whitehead the function of reason is 'progressive and never final.'2° This means that the purpose of reason is to revise and change its premises rather than being determined by the essence of who or what does the reasoning. But whilst reason does not stem from matter, it is also attached to the physical decay of things ready to reveal new modes of abstractions from beneath its surface. For Whitehead, speculative reason implies the asymmetrical and non-unified entangle­ ment of efficient and final cause, and must be conceived as a machine of emphasis upon novelty.21 But the finality of speculative reason also explains the autonomy of actual modes of reason. Whitehead claims that speculative reason is reason that only serves itself, rather than being a reason for (and of) something else. In other words, and contrary to the universal principle of sufficient reason, any actuality has its own finality driven by its own mode of reason determined by its own indeterminate partialisation (i.e., discretization) of data, its rendering partially intelligible of infinities. Speculative reason 'is its own dominant interest, and is not deflected by motives derived from other dominant interest which it may be promoting.'22 A tension can be noticed here between a notion of reason 19. Whitehead, The Function of Reason, Ibid., 25 20. Whitehead, Process and Reality, ibid., 9. 21. Whitehead attributes reason to higher forms of biological life, where reason substitutes action. Reason is not a mere organ of response of external stimuli, but rather is an organ of emphasis, able to abstract novelty from repetition. In particular, reason provides the judgment by which novelty passes into realization. intc fact. Ibid., 20. 22. Ibid., 38.

PAR I S I - AUTOMATED A R C H ITECTURE as governed by the purposes of some external dominant interests and those operations of reason that are governed by immediate satisfac­ tions (or self-enjoyment) arising from within.23 But Whitehead sees this tension not as a contradiction between one and many but as a productive contrast within reason, in the same way as the shades of a color maintain their singularity in togetherness. This is to say that speculative reason is internal to all modes of thought, but also that all these modes are infected with their own incomputable data that are each time partially determined and axiomatised.2� From the standpoint of speculative reason, the intelligible capac­ ity of computation must be reconceived in terms of an experimental axiomatic. The acceleration of automation has led computation to confront the increasing power of incomputables at the core of its for­ mal scheme. As much as algorithmic automation is accompanied by an infinite amount of complexities. so have its mechanical functions been transformed into a new source of intelligible operations able to revise axiomatic truths immanently. The acceleration of automation has led not to the reification of deductive formalism for which computation can seamlessly represent all modes of reason, but to the discovery of an intelligible function that lies within (and yet goes beyond) the digital ground of axiomatic. Beneath the social media fa9ade of the interactive paradigm, a new pace in technocapital accelerationism is dictated by the ingress of randomness (incompressible and infinitely large quantities of data) into automation, turning its mechanical function (determined by a steady return to its initial conditions) into a progressive (i.e. forward-inclined) production and transformation of axioms. 23. Ibid., 39. 2�. Whitehead would insist that the speculative function of reason coincides with infinite modes of physical and conceptual prehensions, in which concepts and objects are determined by their own final cause and partial sufficient reason.

# A C C E L E R A T E This also places computational design thinking at the centre of the new order of capitalization of intelligible functions occupied with the axiomatisation of infinitely long and increasingly vast quantities of data. But whilst this has always been the scope of technocapitalism and its instrumentalisation of reason, the acceleration of automated architectures needs to be approached from the standpoint of Chai­ tin's discovery of Omega insofar as this decryption of an infinite number of data are partially (and immanently) axiomatised as such: that is, as probabilities of infinite functions. This speculative computa­ tion requires infinite orders of abstraction that ceaselessly bring truth and fact forward towards new determinations. From this standpoint, the speculative function of reason in com­ putational design thinking corresponds to the algorithmic selection and evaluation of infinite amounts of data, making decisions and generating new solutions. This involves not only the computation of physical data, but more importantly their conceptual prehensions: the capacity of rule-based functions to counteract the physical aggrega­ tion of data by adding new algorithmic patterns to what already exists (i.e. experimental axiomatic). To propose that computational design thinking can be defined in terms of a speculative function of reason is thus to pose the question of whether automated algorithms are able to redirect their own final reason in the computational processing of infinite amounts of data. Whether this can be proven or not, it is hard to dismiss the possibility of a computational design thinking immanent to its own algorithmic reason.