AA Cavia

Decrypting the Event

2015-03-26T00:00:00+01:00

Decrypting the Event

Notes on Seminar 4 of Computation as Capital @ The New Centre

March 2015

“Between the secret and communication there only exist determinative relationships that are unilateral, asymmetrical, or irreversible.”

- François Laruelle, ‘The Truth According To hermes: Theorems on the Secret And Communication’

The contemporary concern with tactics of opacity stems from a networked gaze of panoptic fibre now global in reach. Laruelle provides us with a set of conceptual procedures attuned to the task of elaborating a cryptography of being, via a non-performative mode of inquiry that goes beyond negation. This challenge to relational thought should be brought to bear on computation itself, signalling an exit from the bind of total addressability.

What does it mean to encrypt? Encryption inscribes the irreversible into computation, activating a mathematical asymmetry performed by way of a cipher. The irreversible function implies a unilateral determination with the evental quality of a decision. As a calculation that admits no reflection, the encrypted hash contains a claim to radical immanence.

Encryption suggests itself as an informational correlate to the Laruellian secret, an uninterpretable kernel which does not give itself to appearance – there is no hermeneutics of the One, just as the encrypted confers no meaning – but on closer inspection this resemblance is merely a surface effect.

If the digital is the “division of the one into two” (Galloway), the notion of a dark crypt of data seems incompatible with the immanence of the Laruellian object, hindered as it is by its fundamental relationality. A datum, from the Latin, is always ‘something given’, data cannot but appear.

The dyadic mode of the digital seems to preclude pure immanence. Laruelle considers it “doubtful” that philosophy’s “auto-speculative kernel” is reducible “to numerical combination”, the secret is “numerically invulnerable”. He outright rejects a dichotomy of thought and computing, just as he dismisses a cognitivist conception of philosophy. Even though artificial intelligence may surpass human capacities, it won’t do so in terms of an analogous performance.

For Laruelle, philosophy is that which effectuates for the first time, a “radical commencement” which is not equivalent to a “performance” of consciousness. Non-philosophy “radicalizes” this irreducibility as it foregoes the decision altogether, avoids performance as such — it remains defiantly incomputable.

Similarly Negarestani, in his call for a revisionary humanism, highlights the epistemic limits of the algorithm by characterising human rationality in terms of a non-monotonic logic engaged in abductive reason, a sapience beyond the scope of algorithmic modes of inference. The distinction with Laruelle is in a commitment to the inhuman as the basis for a constructive “vector of reason” in the face of an artificial general intelligence.

At stake in tracing an artificially computable determination – the inhuman capacity for an irreversible decision or spontaneous event – is an elaboration of a politics and ethics of the inhuman, as part of a wider project of inhumanism. Pure immanence in this regime amounts not simply to a withdrawal, negation or refusal to compute, but to a complete abstention from the problem of calculation as such.

The digital is governed by what we might call the principle of sufficient metadata – that all data necessarily entails the existence of metadata which reflects upon it. This follows from the definition of digital data as simultaneously addressable and quantifiable, as its two intrinsic properties – the fact that data “must conjoin givenness and relation” (Galloway).

Therein lies the limit of cryptography as a claim to pure immanence in the digital – there will always exist metadata, itself a form of data, precipitating a recursive relation of unending reflection that both locates (addresses) and measures (quantifies) the secret. Even as the encrypted declares itself uninterpretable, it does so within a regime of cascading relation, set within a broader binarism.

The asymmetry that allows an individual to encrypt a message such that the entire computational power of the NSA will toil to decrypt it is undermined by the principle of sufficient metadata, which admits metadata as a necessary condition, revealing the secret on a different scale of abstraction.

Likewise a dark web possesses no pure immanence, there is no end to the depths of metadata, no matter how far you obfuscate up the stack. There is always another layer to the onion skin of relation – an IP address exposing an entry to the gates of the hidden realm – a residual is always to be found.

The digital regime is a domain rooted in difference, in the primary distinction enacted by the binary, the cleaving of the one into two. Any attempt at withdrawal is reassimilated, leaving us with a tyranny of relation — the addressability of any gesture.

There can be no evental site (Badiou) in digital computation, as there can be no excluded part due to the principle of sufficient metadata. A computer may produce unpredictable results, but these are grounded by determinate functions, they are calculable. Indeterminacy may be artificially seeded via an external source of entropy, but to locate an immanent undecidability in computing, one that mirrors Badiou’s incalculable event, one has to trace computation to its limit state.

Parisi’s claim of a speculative computing aims to fold the halting probability, Omega (Ω) – a computably enumerable sequence that is nevertheless infinite and algorithmically random – into the “core” of computation. It seeks to transform the limit of a system into its intrinsic property, to render a threshold into a constitutive condition. This movement, proceeding via Whitehead, admits indeterminacy into the heart of computation, but only at the cost of a coherent definition of what it is to compute.

Randomness within computation is only ever encountered as a limit condition, just as the probabilities embodied by Ω are only enumerable in infinite time. At these thresholds computing collapses into indeterminacy. To state that “the immanence of infinities” (Parisi) present as “random actualities” (Ibid) in incomputable algorithms is in some sense constitutive of “programming cultures” (Ibid) is a provocative but hyperbolic claim.

We might consider instead an indeterminacy present in the very definition of computation, in the form of the undecidability of the halting problem, as a symptom of an incomplete axiomatics. Computing suffers from an indeterminate relation to time.

The infinite probabilities of Ω cast a virtual shadow over computation, marking out the boundaries of its determinacy, unactualised but nevertheless present as real objects with real effects. The figure of the incomputable is immanent to the regime, necessitated by the incompleteness of computation, but cannot simply be reduced to an “intrinsic randomness” (Ibid) embedded in the algorithm.

Ultimately the irreversible cipher that encrypts, while possessing the determinacy of a decision and producing the qualities of a secret, fails to attain the status of either radical immanence or evental site by virtue of its grounding in the digital. The age old dualism of the discrete (quanta) and the continuous (continua) appears intact. But we may look to the root of quanta, its very constitution, for an exit.

Quantum computing (Deutsch) presents a flight from this dualism, the promise of a computing faithful to the indeterminacy of physical matter. It suggests the capacity for the incalculable event to emerge as a spontaneous decision in computation. Quantum cryptography contains the potential to constitute a Laruellian secret, to apriorize the a priori.

Quantum information theory is the domain in which a non-computation could be effectuated as correlate to Laruelle’s method. It’s unit, the qubit, lays claim to being an uninterpretable kernel – an unreadable, indivisible form that can nevertheless be transported (entanglement) and computed (quantum logic gates).

The quantum bit is a continuously valued superposition of states, it is of the domain of continua rather than the digital, or more precisely, a figment of the “rupture of the discontinuous” (Barad), the unraveling of the duality. At no point is it both fully addressable and quantifiable, as stated by the uncertainty principle. It never reveals itself, admits no reflection – measurement precipitates its collapse – and only comes into relation during quantum computation. As such only its results (calculations) are apparent. Encryption in this scheme produces secrets that cannot be preserved during observation.

Laruelle asserts the need for “a theory of the event that leans towards quantum theory by way of the generic”. The qubit could be the foundation for both the theory of a computable event (as spontaneous decision) and a speculative theory of non-computation, suggesting a kernel possessing a radical immanence located within the realm of computation, a secret that evades calculability, present at the origin of the discrete.

_{Image: Bloch Sphere depicting the manipulation of a qubit (Credit: Xin Wang)}

Sources

Alain Badiou, 2013, ‘Logics of Worlds: Being and Event II’, Bloomsbury Academic
Karen Barad, 2014, ‘Re-membering the Future, Re(con)figuring the Past’, Duke University Keynote
David Deutsch, 1985, ‘The Church-Turing principle and the universal quantum computer’, The Royal Society of London A 400, pp. 97-117
Alexander R. Galloway, 2014, ‘Laruelle: Against the Digital’, University of Minesota Press
François Laruelle, 2013, The Transcendental Computer: A Non-Philosophical Utopia, translated by Taylor Adkins & Chris Eby
François Laruelle, 2010, ‘The Truth According To hermes: Theorems on the Secret And Communication’, Parrhesia, Number 9, 18-22
Reza Negarestani, 2014, Labour of the Inhuman, e-flux
Reza Negarestani, 2014, Intelligence and Spirit, Urbanomic
Luciana Parisi, 2013, Contagious Architecture (p14-21), MIT Press

Volatility Smile

2015-03-14T00:00:00+01:00

Volatility Smile

Notes on Seminar 2 of Capital as Computation @ The New Centre

March 2015

The informational commodity asserts itself as the dominant commodity form. The circulation of capital through financial derivatives outstrips that consumed in the exchange of real commodites at a ratio of 10:1 (BIS), while a third of global GDP is now tied up in financial products (BIS: Table 19).

The medium of contingency embodied by the market locates value in the relation risk ~ volatility, encoded in derivative pricing mechanisms. Endless bifurcation is our fate in a regime that capitalizes risk by manifesting volatility in price differentials, asserting an ontology based on what Lucretius called clinamen, a deep indeterminacy of being.

Bifurcation summons contingency – there is no cause, or sufficient reason, for a system to adopt one equlibrium state over another during a symmetry-breaking bifurcation. With no natural law to ground it, state itself becomes contingent. Bifurcation is this very process of contingency taking place in phase space.

Wiener’s cybernetic vision of stability via feedback has been supplanted by a continual pricing of a radical contingency that is neither probabilistic nor predictable. In an ironic twist, Wienerian dynamics are embedded in the pricing of derivatives (Black-Scholes-Merton), which abdicate all predictive duties to instead represent market movement as a random walk, a non-deterministic trajectory without memory.

The pricing mechanism of finance is a mode of capital accumulation oriented around power asymmetry in the market (Nitzan & Bichler). In this “power theory of finance” (Malik), capital is “a dynamic power-ordering organized through price as its measure/medium” (Ibid). Labour is absent, the commodity withdraws to reveal a regime grounded in pure difference.

In this interpretation, price itself writes the contingent reality of the market (Ayache). In concord with Bifo’s observation that finance is “the emancipation of the sign from all referents”, the underlying asset vanishes from view, rendering finance an “engine, not a camera” (Mackenzie), an ontological force of little representational value, nothing but a volatility smile beaming back at you.

The risk ~ volatility relation is a measure of exposure to future contingency. A power theory of value bases capital on a projection in time, namely a discounted capacity for future earnings (Nitzan & Bichler). In the form of futures and options, derivatives continually inscribe contingency into the present by the pricing mechanism (Ayache). This is an apt definition of total hegemony – to have hedged your future against all contingencies, to call this hedge the present.

Here cybernetics is cast aside for a catastrophe theory of history, volatility as an agent of accumulation, perpetual crisis administering the shocks needed to bifurcate the price surface, singularities acting as engines of risk. As proposed by Rene Thom, catastrophe may be generated by a system from within, rather than imposed as an exogenous shock, leading us towards an autopoietic theory of finance, capable of regenerating itself while on the cusp of self-induced collapse.

The once hyperbolic claim that capital has transformed into “abstract positive feedback” (Plant & Land) to a threshold where “divergence has reached critical proportions” (Ibid) begins to ring true. The failure of cybernetics to act as “a defence against the cyberpathology of markets” (Ibid) has allowed the bifurcating angel of finance free reign.

Like Abaddon – the exterminating angel – finance casts its own plague, but on the emergence of what Badiou calls an event. The circumscription of contingency, its complete absorption into the scheme of capital accumulation, attempts a suppression of the evental by adopting its very undecidability as the basis of value, by pre-emptively rendering it calculable.

Meillassoux’s metaphysics – which asserts, through the principle of unreason, the only necessary absolute as contingency – appears resonant with an ontology of finance, a mode whose only productive function is the generation of difference, whose limit condition is that of the chaotic orbit.

But contingency is itself of the order of Number. Chaos is by definition a parametric phenomenon, topologically identifiable by a dynamics which eludes basins of attraction. This is the ultimate undoing of Meillassoux’s proposal, the fact that Number never disappears as an entity underpinning an absolute category which should admit no grounding.

We might say, rather, that contingency is the trajectory of Number through time (entropy), constituted as event, as “something that finally happens” (Meillassoux: 108), the very condition of the market, which in turn enacts a temporal indexing of differentials via pricing, as a means of harnessing contingency as risk.

The deferred difference of the derivative pricing mechanism, the pricing differantial (Malik), echoes the recurrence relation embedded in computation. Cascading bifurcations are likewise recursive phenomena, producing recurrent sequences of states (De Landa: 20). One might say the pathology of the market is the recursion of difference manifest in pricing, producing “ineliminable volatility” (Malik) endogenously, self-reflexively perturbing the trajectory of the derivative price.

A parametric spectre of catastrophe haunts finance, which proliferates bifurcations in the intensive realm of the virtual (Deleuze). It is the circumscription of potential actualities that is at play in the pricing surface (Roff), a dynamic terrain that continually destabilizes its own constitution (implied volatility).

Finance emerges as a hegemonic apparatus busy mastering time as a medium of contingency. Undermining finance power may involve parametric strategies, attractors with which to lure it into other orbits, in a bid to reclaim the constitution of the present. Contingency, from contingere, may ‘befall’ us (Meillassoux: 108), but our economic inscription of it remains an open practice.

Sources

Eliye Ayache, 2014, The Writing of the Market, Urbanomic Press
David W. Bates, 2014, “Unity, Plasticity, Catastrophe: Order and Pathology in the Cybernetic Era” (Catastrophes, Lebovic, Nitzan, Killen, Andreas Ed.), De Gruyter
Franco ‘Bifo’ Berardi, 2012, Emancipation of the Sign: Poetry and Finance During the Twentieth Century, e-flux
Bank of International Settlements (BIS), ‘Table 23A: Derivative financial instruments traded on organised exchanges’ and ‘Table 19: Amounts outstanding of over the counter (OTC) derivatives’, May/June 2013
Manuel De Landa, 2002, Intensive Science & Virtual Philosophy, Continuum
Gilles Deleuze, 2001, Difference & Repetition, Chapter 4, Continuum
Donald Mackenze, 2008, An engine, not a Camera, MIT Press
Suhail Malik, 2014, Ontology of Finance, Urbanomic Press
Quentin Meillassoux, 2008, After Finitude, Continuum
Nitzan & Bichler, 2009, Capital as Power, Routledge
Jon Roffe, 2014, From a restricted towards a general theory of the pricing surface, Urbanomic Press
Sadie Plant & Nick Land, 1994, Cyberpositive (Unnatural, Matthew Fuller Ed.), Underground

Capital as Computation

2015-03-05T00:00:00+01:00

Capital as Computation

Notes on Seminar 1 of Capital as Computation @ The New Centre

March 2015

_{Al Karaji, inductive proof of the binomial theorem (1007 AD)}

The conceptual schema of computation developed in the mid 19th Century harnessed a form of mathematical relation known as recurrence. This mapping of the function, the act of bringing functions into relation – a mapping of a map – brought reflexivity to relation. It can be traced back as far as the Fibonnaci sequence (1202), Al-Karaji’s inductive proofs (1000 AD), and beyond that to Euclidean division and the origins of induction (Parmenides).

The difference equations underpinning the ‘difference engine’ (Babbage) relate functions to themselves. Iteration is a form of self composition, a special case of recursion – each term of a sequence defined as a function of the preceding terms.

Iteration, and its parent recursion, are the means by which computation achieves efficacy in calculation. As the primary techniques of computing, they allow a lossy compression of the laws of nature in the form of algorithms (Negarestani).

The difference engine (Babbage) uses a finite difference method (divided differences) to compute values of polynomial functions solely by a series of addition operations, embodied in mechanical ‘adders’. It reduces the entire problem of calculating the polynomials to a matter of difference.

The computer is rooted in an interplay of difference and repetition, within an unbounded recursive relation, consigned to a task of eternal recurrence.

“The eternal return does not cause the same and the similar to return, but is itself derived from a world of pure difference. Each series returns, not only in the others which imply it, but for itself, since it is not implied by the others without being in turn fully restored as that which implies them.

The eternal return has no other sense but this: the absence of any assignable origin - in other words, the assignation of difference as the origin.” (Deleuze)

Within the wider task of thinking capital as computation, the self-referential mode of production defined by capital can be considered to rest on a recurrence relation – accumulation as a hermetic, circular relation of value that refers only to itself in terms of a monotonic growth function.

The black box of capital admits no bounds, possesses no origin but difference through value. It suffers from its own halting problem. In the vocabulary of Luhmann, it exists as an operationally closed system. The environment it defines is the hostile landscape of the market.

It’s tempting to see the algorithm as the thought image of capital –– a sealed black box of monotonic logic, a recursive regime with no limit but Number. Everything within it quantized and discretized as value.

For Badiou, following the definition of ordinal numbers within set theory, the entirety of Number emerges from a recurrence relation, in the form of succession, as the axiomatisation develops by induction. The only set to escape the succession relation is the empty set (void), or zero.

There is on the surface an ironic sense in which zero partakes in the digital regime, caught within a relation of recurrence it cannot escape. But it is precisely the void that acts as the grounding for the whole field of computation – located firmly within the regime of Number – out of which difference can arise. A double irony which should not escape us – the void serves as ground.

Lagrange was a key figure in the ‘decimalisation’ of France from 1800. The French government owned the prototype metre and kilogram till 1875, and can be viewed as a critical actor in the quantification of everyday life. Computation, in postulating an entirely discrete, quantized world, is the inheritor of this Lagrangian legacy.

Lagrangian optimality - a method for locating stationary points in functions - exposes the limits of computation, which is often instrumentalised to locate maxima. Discretization limits the optimality of the result (Longo), as the method is based on a differential calculus - it is “sensitive to encoding” (Negarestani). Nevertheless optimisation is the primary task of software.

It’s no coincidence that the difference engine arrives just as the theory of the division of labour for mass production, outlined by Babbage himself, culminating in Taylorism, is born. Iteration and recursion are techniques of efficacy, complementary to the management of production, leading what Marx saw as a decentering of labour power by fixed capital (machines).

In the notion of the ‘automaton’ as “a moving power that moves itself”, Marx intuited the evolution of machinery to universal computation, the reduction of labour to “merely conscious linkages”. The ‘analytical engine’ (Babbage) used punchcards borrowed from the Jacquard loom to formally outline this concept of the general purpose computer.

Computing is a means of calculating the values of a function, and so determining whether a function is effectively calculable (Church-Turing). It takes the form of a procedure or effective method, an enactment of difference.

Recursion ensures the universality of the turing machine is not limited by the fact a computable function must be describable in a finite number of instructions. It is instead the material limits of finite time and a finite length of tape needed to store the input and output which bound it.

“It is this substitution of the infinity of time for the infinity of space which I have made use of, to limit the size of the engine and yet to retain its unlimited power.” (Babbage)

In practice the infinite potential of the analytical engine is thus based on a recourse to infinite time, giving rise to what Turing later showed to be the undecidability of the halting problem. In this manner eternal recurrence is embedded as the labour of the machine from inception. Like capital it calculates without reference to an origin, unanchored in a world of pure difference, knowing not if it will ever halt.

Sources

Charles Babbage, 1864, Passages from the Life of a Philosopher
Alain Badiou, 2008, Number & Numbers, ch. 10: Recurrence, or Induction, Polity Press
Gilles Deleuze, 2001, Difference & Repetition, p. 125, Continuum
Al Karaji, (c. 953 – c. 1029), Al-Fakhri fi’l-jabr wa’l-muqabala (Glorious on algebra)
Giuseppe Longo, 2009, Critique of Computational Reason in the Natural Sciences, CNRS
Niklas Luhmann, 2012, Introduction to Systems Theory, Polity Press
Karl Marx, 1858, Grundrisse (Fragment on Machines), pp. 690-712
Reza Negarestani, 2012, Abducting the Outside, Urbanomic

Parametric Objects

2014-12-10T00:00:00+01:00

Parametric Objects

December 2014

“For each work of art that becomes physical there are many variations that do not.”

- Sol LeWitt, Sentences on Conceptual Art (1967)

What of the lowly parameter? Endlessly mistaken for number, deemed too trivial, passive, inert or otherwise incidental to merit proper scrutiny. And yet all around us entities are simulated, modelled, rendered, ranked, quantized, financialized – subject to an ever expanding array of parametric operations. From voice compression to parametric architecture, cascading style sheets to CGI, high frequency trading to climate modeling, the parameter reveals itself as a key mediator, an unsung hero of relation, warden of that “radical commencement” (Laruelle) we call creativity - for what is the creative act if not singular, and what is a mathematical singularity (nothing) without a parameter.

Seen as the agent of a means of production – of the informational commodity – the parameter forms a new regime of representation. If the digital “divides one into two” (Galloway), the parameter is a collateral of this cleaving – constituted in relation, summoned by the condition of the multiple. The parameter is not simply number, but an actor engaged in a structuring. Not simply a bystander, a paralytic measure, but the paramour of relation. The parameter is number cast as active agent and brought into relation. Its “deep relationality” (Parisi: 103) evokes the notion of an operationally closed system (Luhmann) bounding relations in the form of functions.

These functions define an environment we might refer to as the virtual. For Deleuze, the virtual forms part of reality; it is real but not actual. Unlike the purely negative category of the possible, the virtual is productive, it makes ontological claims – less a virtual reality than a real virtuality (De Landa: 33). The virtual not simply as a passive domain of simulation, a mere model, but a complementary field of potentials continuously circumscribing the actual. The virtual as a site for the dynamic structuring of state spaces – the tracing of orbits, limit cycles, singularities – that define relations.

As Levy Bryant notes, this conception of the virtual presupposes a form of structuring – the constraining of relations to trajectories – albeit a structuring so radically fluid as to absorb chaos within its schema. The ontological status of the virtual is evoked by the collapse wave function interpretation of quantum mechanics. If reality is a continual collapse of superposed multiplicities (waves) into actual singularities (matter), the virtual is the domain multiplicities inhabit as real potential, the medium of becoming.Matter itself can be speculated as the process of collapse rendered as entanglement – a “mattering” (Barad) – implying relation as the basis for the formation of substance. In this ontology, relation, founded on the numeric concept of the multiple, proposes the parameter as an agent constitutive of matter.

Parameters within the virtual act in a similar capacity to Whitehead’s eternal objects (Whitehead: 13). These are “potentials for the process of becoming” (29), contributing to the “definiteness” (23) of an actual entity. They imply “alternatives, contingencies, situations that could have been otherwise” in an entity (Shaviro). Whitehead’s recourse to metaphysics can be avoided by folding the notion of eternal objects as potentials into the virtual, in the guise of the parameter. In this gesture we shed the transcendental guarantor of God, but we must be wary of simply replacing it with Number.

Production in the regime of the parameter involves the instantiation of a relation within a state space. Instantiation is the process of making actual a potential within a field of multiplicities. Computational interactions continually produce instances, individual points on trajectories within parameter surfaces. Computation, as a means of constructing topologies, provides an environment for speculations in state space - a medium conferring plasticity on parameters. Parametric systems “contain a tension between their laconic definitions, within a symbolic language, and their instantiation. The one is finite while the other is potentially endless.” (Borevitz)

The means of production enabled by the universal Turing machine does not simply conjure the image of the Borgesian library. It summons infinity interactively at the very site of production, creating a problematic for the digital artist – creation becomes an unresolvable act of discrimination and negation without finitude. Within parametric production, a shadow is cast over each concrete instance by “the bundle of possibilities, mutually consistent or alternative, provided by the multiplicity of eternal objects” (Whitehead: 102). These potentials “abduct the actual relations of data” and “expose parametric aesthetics to… infinite quantities” (Parisi: 103).

This burden, this excess of the virtual, a surplus of becoming over substance, weighs heavily on parametric objects. For art after finitude, the combined effect of these potentials induces the parametric sublime (Borevitz) as affect – one integral to the conditions of production as such. The parametric sublime develops from access to vast parameter surfaces facilitated by digital computation. As a specific case of the mathematical sublime (Kant), it is induced by the inability of a finite mind to prehend a magnitude. High dimensional state spaces create a vertigo of instantiation in an expansive field. Whereas earlier forms of the sublime operate in the geographic domain of landscape, or else the spiritual realm of the divine, the parametric sublime presents a boundlessness within the intensive domain of the virtual. It evades optics.

The sublime expresses a fearful response to boundlessness – terror gives way to awe only when prompted by the recognition that an authority, originally in the form of Nature, “has no dominion over us” (Kant). The parametric sublime invokes an authority we could call Number. The tyranny of number is the conflation of quanta with being. If the digital denotes the reduction of substance to discrete enumeration, a quantized world, then Number occupies a central ontological position in this regime.

Within software, instances acquire an aura of equivalence – instantly interchangeable points on a parameter surface, locked in a process of exchange and interaction, a continual becoming mediated by computation. Number is the trusted authority that enables this equivalence. For Frege, equivalence is the property that allows number to emerge from thought – number consists in “marking equinumeracy” (Badiou: 16). Prior to set theory, thought presupposes number via the concept of equinumeracy. Cardinality is the construct that allows equivalence to instead follow Number, grounded by a summoning of the empty set, ∅ (Halmos: 42).

In the wake of Cantor, we can only assume the sum of potentials for any given parametric relation, underpinned by Number, to be transfinite, and as such uncountable and incomputable. The limits of computability are above all material. The materialism grounding the infinite potential of the computer was originally “an unlimited memory capacity obtained in the form of an infinite tape” (Turing), today posited in the form of unlimited silicon memory.

Babbage sought to circumvent this limitation of the difference engine by a “substitution of the infinity of time for the infinity of space” in order “to limit the size of the engine and yet to retain its unlimited power”. Replacing infinite matter with the eternal is a manoeuvre intended to reinstate a transcendental status to the machine, of rendering it an eternal object, leading directly to a conceptual bind – the undecidability of the halting problem (Turing).

The materialist basis of computation instead draws us towards an “energetics” (Mackay) of virtuality, the recognition that to hold entropy at bay demands a source of energy. It is to recognize that information systems, biological or inorganic, are black boxes of negative entropy (Wark), Maxwell’s Demons busy acting in defiance of the wider universe, but only at a cost – their exhaust coming in the form of an entropic pollution of the environment.

This is the basis of the illusory nature of the sublime in the parametric domain of production – the incomputable transfinite offers no more than a mirage of sublimity. Number retains a transcendental authority over the limited field of the computable. To express the parametric condition is to resist the authoritarian impulse of the sublime, to not yield to Number, but instead endow the parameter with a form of its own, raising the question of practice within a parametric regime of representation – a plastic art of the parameter.

While instances follow trajectories constrained by parametric relations, the summation of trajectories compose a phase portrait. A phase portrait presents the paths, bounds and limits that describe a given system. It exposes basins of attraction, bifurcations, catastrophes, criticalities, singularities – all the topological features immanent to a set of relations. The phase portrait depicts the parametric as always actively engaged in this circumscription of the actual. It articulates the condition of continual becoming instigated by the parameter in computation.

_{On the occasion of Thomas Locher, Post-Information @ Galerie Silberkuppe.}
_{Image: Thomas Locher, A - H, 2002/2015. A - G, 2002/2015.}

Sources

Alain Badiou, 2008, Number and Numbers, Polity Press
Karen Barad, 2007, Meeting the Universe Halfway: Quantum Physics and the Entanglement of Matter and Meaning, Duke University Press
Brad Borevitz, 2006, Sublime, http://not-it.onetwothree.net/text/2006/07/13/sublime
Levy Bryant, 2006, Deleuze’s Two Conceptions of the Virtual
Manuel De Landa, 2002, Intensive Science & Virtual Philosophy, Bloomsbury Academic
Gilles Deleuze, 2001, Difference & Repetition, Chapter 4, “Continuum”
Alexander R. Galloway, 2014, Laruelle: Against the Digital, University of Minnesota Press
Peter Halmos, 2001, Naive Set Theory, 1974 Edition, Springer
Immanuel Kant, Critique of Judgement, #26, 260
François Laruelle, 2013, The Transcendental Computer: A Non-Philosophical Utopia, translated by Taylor Adkins & Chris Eby
Niklas Luhmann, 2012, Introduction to Systems Theory, Polity Press
Robin Mackay, 2012, Slade Contemporary Art Lecture Series 2012-13
Quentin Meillassoux, 2009, After Finitude: An Essay on the Necessity of Contingency, Continuum
Luciana Parisi, 2013, Contagious Architecture, MIT Press
Steven Shaviro, 2007, Eternal Objects
Alan Turing, 1948, “Intelligent Machinery.” Reprinted in “Cybernetics: Key Papers.” Ed. C.R. Evans and A.D.J. Robertson. Baltimore: University Park Press, 1968. p. 31.
Mckenzie Wark, 2014, #Theory21c
Alfred North Whitehead, 1979, Process & Reality, Macmillan USA

Perlin Fields

2013-12-02T00:00:00+01:00

Perlin Fields

Notes on the production of Perlin Field (2013)

“The fact that noise doesn’t repeat makes it useful the way a paint brush is useful when painting. You use a particular paint brush because the bristles have a particular statistical quality - because of the size and spacing and stiffness of the bristles. You don’t know, or want to know, about the arrangement of each particular bristle. In effect, oil painters use a controlled random process.”

- Ken Perlin, 1999

1994. Parametric production matures to the point where clouds in the backdrop of a Lion King landscape are entangled with mechanisms of encryption, war, financial derivatives trading.

Noise emerges as a cloaking device for information in the 20th Century. Its status as unwelcome perturbance to early tele-communication signals gives way to strategic deployment.

SIGSALY, the World War II secure speech system, uses white noise masking as part of its encryption scheme. Nicknamed ‘Green Hornet’, the buzzing signal is indecipherable to the human ear.

The moderns rush to claim noise as their own. Russolo booms the loudest, announcing “the variety of noises is infinite”.

Man made noise develops from industrial waste product to a subversive gesture with a claim to political agency (Attali). With the advent of computation it mutates into a mimetic actor, both reactionary and legible.

Noise, not as a subversion of signal, but rather as duplicitous agent, active as both veil and mime, cynically acting out the semiotics of nature on one hand, while cloaking information on the other.

Ken Perlin wins an academy award for an algorithm (TRON, 1982).

Supplanting texture mapping, procedural terragens imbued with noise generate the landscape of video gaming. Character loci appear more human in all their stuttering, indecisive glory.

Algorithmic trading floods markets with noise, rendering them illegible to all but the most adept analysts. The noisy trader acts as a straw man designed to distract from the true noise in the system - sophisticated attempts at masking high-frequency trading strategies.

Noise as an object that precedes us. Ancestral noise in the form of stochastic gene expression inducing phenotype variation. Developmental noise and its role in processes collectively known as evolution. Biological multiplicity itself entailed by cellular noise.

Noise is a pseud. Its posturing as random and complex is exposed only through wilful decomposition. The additive synthesis of periodic functions organised into octaves generate a mimesis of fractal form.

Noise destabilises Platonic idealism. Its ontological affinity lies with contingency. Noise denounces, as Meillasoux does, “the ‘stabilist’ illusion of sensible becoming —the illusion that there are invariants or immutable laws of becoming”.

All those modern attempts to politicise noise run counter to an admission of agency to the object behind the phenomenon. The algorithm, as both actor and medium, should be afforded its own representation.

To let noise be manifest is the aim (and struggle) of the work.

_{Image: Water Vase, Ken Perlin (1985)}

Markov Walks

2012-06-19T00:00:00+02:00

Markov Walks

June 2012

“Every thought emits a throw of the dice.”

- Mallarmé, A Throw of the Dice Never will Abolish Chance (1897)

“The true subject of art is unity.”

- Theo Van Doesburg, Against Imitative Artists (1922)

“Every appeal to the One is theological.”

- Alain Badiou, Being and Event (1988)

I’ve been studying the works of De Stijl (1917-1924) - that moment in abstract painting and architecture in which the two entered an intimate, coordinated and prolonged liaison. Whilst trying to unpack my own thoughts on the output of the group, I’ve increasingly been drawn to the schematics of founder Theo Van Doesburg, which have become a departure point for some of my recent work.

In the essays of De Stijl a strict anti-individualism is the basis for an appeal to aesthetic unity in the arts. The essays talk of a “new plasticism” (Mondrian, No Axiom but the Plastic), the importance of diagonal lines (Van Doesburg, Elementarism), colour as a physical material (Van Doesburg, The New Aesthetic), and other principles often guided by a naive notion of unity.

Van Doesburg, Architecture Analysis (1923)

“A: But I still don’t understand why you favour the straight line and have come entirely to exclude the curved.

B: In searching for an expression of vastness, I was led to seek the greatest tension: the straight line, because all curvature resolves into the straight, no place remains for the curved.”

Mondrian, Dialogue on Neo-Plasticism (1918)

In some ways, the graphical sensibility of De Stijl outran its conceptual positioning, in that I can see an interest in stochastic composition within the work of Mondrian and Van Doesburg that undermines their repeated claims to universalism (cf. Komposition Weiss, Komposition IX, Pier and Ocean). It’s interesting to take a trajectory from De Stijl to early computer art to see how aesthetic unity as a paradigm breaks down during the decades that follow.

Manfred Mohr, Random Walk (1969)

Take the pioneering stochastic works of Manfred Mohr, whose Random Walks, printed on an ink plotter in the 1960s, I was fortunate enough to see at DAM during a trip to Berlin. Their graphical resemblance to De Stijl only serves to further enmesh these works, which I see as part of a wider path taken by the Century on its way to uncovering first multiplicity, then complexity. Computation only served to unmask the full potential of aleatory composition — which pre-dates the computer algorithm through so much modernist work — turning it from an anti-motif to an embedded technique ever-present in cultural production, latent in everything from auto-tune and granular synthesis to photography filters and film cgi.

The demise of the whole — as articulated by Deleuze (assemblages) and Badiou (being as inconsistent multiple) — could be considered the foundation of computer art. Computers, ever adept at exploring parameter spaces, are engines of multiplicity - they can’t help but explore parametric multiples.

Van Doesburg, Contra Construction. Maison Particulaire (1923)

If Van Doesburg was probing how architecture and visual abstraction could intertwine (a path culminating in parametric design), Mohr was making explicit how computers could express a new understanding of order through art. The decades that followed ‘Random Walks’ were dominated culturally by the twin paradigms of fragmentation and multiplicity, leading to a climate in which a benign visual complexity has emerged as a cliché of both the abstract (digital) arts and parametric architecture.

I began creating sketches using De Stijl principles at some stage along my readings, as both documentation and an exercise in encoding aesthetic knowledge, and these became a trigger for the production of a piece I call ‘Markov Walks’.

I’ve been producing alterbots. They combine mimetic and stochastic tendencies. I feed them artworks, some my own, some from the history of art. These ‘alterbots’ draw for me. Their brains are based on markov chains: a probabilistic, memoryless scheme trained on input graphics. The bots use these chains to conduct graphical ‘walks’ on a canvas. They forget where they’ve been. They wander. They absorb aesthetic knowledge, encoded digitally, producing original work as they go along. They exhibit a markov uncanny redolent of twitterbots. I’m in a prolonged collaboration with them.

In Markov Walks I’ve produced a documentation of this trajectory from De Stijl to Random Walks, taking the axonometric schematics of the former, producing my own hand-drawn sketches and feeding them to my alterbot to produce a modern variant of the latter. I think of it as artist and algorithm working closely in a joint wandering, a form of 21st Century dérive through a period that shaped our present aesthetic sensibilities.

You can see various outputs over at STD-IO 012.

_{Image: AA Cavia, Markov Walk 012-01 (2012)}