(Matt Dixon)

Thinking Cybernetics:
Mapping the Intersections between Metaphysics, Technology, Biopolitics

(abstract for panel)

The purpose of this panel is to gather together ideas, perspectives, and questions from a diverse variety of thinkers and disciplines relating to the theory and practice of cybernetics. Our goal is to raise a series of critical questions concerning the intersection between biopolitics, metaphysics, and technology.

While each paper is devoted to a specific author or authors and is generally focused on a particular theme or aspect of cybernetics, all of us in some way are arguing for a larger transformation of philosophical, political, social, and technological categories. There are many urgent questions posed by cybernetics; and moreover, its development has so far tended to furnish many other fields of investigation with new tools for studying new problems. As St-Exupery wrote in 1939: “The machine does not isolate man from the great problems of nature, but plunges him more deeply into them.” What does philosophy have to tell us today about our relationship to technology? What does cybernetics imply for metaphysics, ethics and epistemology — or even for the future of writing?

Finally, how do we think the relationship between cybernetics and bio-politics? Perhaps the most troubling question raised by cybernetics concerns the relationship between autonomy and authority. It would appear that everything hinges on the inflection placed upon the word “control”! Cybernetics is derived from a Greek word meaning “governance,” from which an apparently simple question arises: Are we controlling — or controlled by — the systems of machines “we” have built?

When Einstein wrote that it has become “appallingly obvious” our technology “has exceeded our humanity,” he was voicing his concern about the disastrous effects of unimpeded technological growth without a corresponding growth in social responsibility. Certainly, at the very least, technology plays more than a purely mediatory role in society.

Thus another important problem brought to the fore by cybernetics is the role of language itself as a socio-political machine. We assert that thinking our relationship to language and technology today demands a wholesale reformulation of old ways of thinking, in order to explore new cybernetic and philosophical problems. The point is that we need more than a new philosophy of cybernetics, we need a “cybernetic philosophy” (though this also requires a transformative reading of the contemporary philosophy of technology.)

Our first hope is that by gathering together concepts which allow a new understanding of our relationship to technology, we can trace original lines of questioning and resistance. Our second hope is that, through these intersections, there may perhaps result new methods of traversing and escaping systems of control. As B.F. Skinner wrote in Contingencies of Reinforcement in 1969, “The real problem is not whether machines think, but whether men do.”

Panel Members: Joseph Weissman, Taylor

Notes on Derrida and Cybernetics

Let us conjecture that the invention of the transistor — an auto-controllable circuit — indicates the attainment of a critical level of development in cybernetics, a “tipping point.” Then for writing the corresponding moment is the invention of the video camera, perhaps more precisely the photograph: now seeing is writing, literally marking. Visio-literature is the only kind that can ever exists for us today — even ancient literature is post-modern for 21st-century readers. We cannot simply forget the history of writing, which is also the history of humanity — a spirit which is more like a ghost successively inhabiting our bodies, then our writing-instruments, then our machines, and next…?

Driven by a new kind of virtue, cybernetics questions the character or essence of humanity. It ungrounds our classical assumptions, our metaphysical coordinates. It has an uncanny tendency to dissolve rigorous divisions between human beings and animals, and then in turn the holy division between animals and machines. Ontological collapse. Becoming-machine is always a becoming-animal, but the dissolution goes even further than this.

In its fullest and strangest sense — as both a theory of systems and a theory of control — cybernetics blurs the division between information and noise, between chaos and organization. Cybernetics extrudes not only a difference at the heart of hominid unicity, in the specific identity of the human — the closure of a certain conservative metaphysic — but also the awakening of a new kind of multiplicity — cybernetics, in its own way just like writing, a new kind of writing: a massive, convivial and tool-generating science of social technology.

There are no universal codes. Automation demands a new philosophy of writing, writing beyond codes, surpassing the regime of pure and mixed order-signs. Cybernetics is co-extensive with a spontaneous revival of humanity, waiting in a sense upon the closure of certain ‘closed’ metaphysics, and the gentle re-opening of smooth spaces for thought — the illumination of ‘in-between’ spaces for new experiments, new explorers. In a profound sense, the practice of cybernetics has a vital connection to the future of the human struggle for freedom — a future, whether of absolute violence or unequalled pity, which seems almost precluded by the ravenous shadows of colossal war machines.

Our languages, our religions, our economies, our political groups and rules, even our sciences and philosophies, are violent swarms of machines (waging wars for peace) — and this catastrophe which is erupting, which is already here, is of the order of true “event,” but also enigmatically is of another order entirely — a futural order — indicaticating an entirely new position with regard to the tangled mazes of classical ontology. Cybernetics is already a position beyond thought, even in a sense beyond cybernetics — a movement beyond motion, telecommunication, uncannily points beyond the bloody quagmires characteristic of contemporary political and economic culture — indeed beyond all the tiny slaveries of “civic” society.

Within the networked folds of communicating devices, a new aspect of humanity is awakening, a new kind of struggle for enlightenment and freedom across the globe. A revolution between people, a revival of human society, a dynamic, even exuberant regeneration through interconnection and multiplicity. Cybernetics provokes an apparent and disturbing contradiction: it is a purely immanent, historical intervention, itself a kind of abstract social ‘machine’ which transforms all manner of social practices.

Yet, within this operation, a completely new dimension intrudes, guiding these transformations unconsciously, like a shadow or precursor — a glimmer of pure exteriority. An intimation of closure, not of an ending but of vast, chaotic and potentially dangerous transformations occuring all aspects of society. Decentralization and reintegration on a massive scale. An out of joint time, indeed.

One of Derrida’s most important projects in the Grammatology is to show the essential necessity of writing, of the “trace,” in (‘classical’) philosophical discourse — especially in those discourses which had always believed it possible to do without them! For example, Hegel — the first cybernetician — rehabilitates thought on the basis of a memory which is productive of signs.

The trace is a disjunction before it is a decision — an oversight which completely overturns the metaphysical machinery of classical philosophy. In this sense, Derrida’s overall critique of metaphysics resonates not only with cybernetics as a world-historical system of deterritorialization, but perhaps even more curiously, with certain rupturous developments in abstract algebra and pure mathematics.

In particular, the cautious critique of the signifier, and the advocation of a more primordial logic of the mark, trace, differentiation or distinction, functions in a quite similar way in relation to the philosophy of writing as does Herbert Spencer-Brown’s groundbreaking work in metamathematics — in particular his development of a ‘primary algebra’ or mathematical logic of “distinction”2 — to the philosophy of mathematics.

Spencer-Brown constructs his system presuming only the existence of two asymmetrical states — a marked state (a cross) and an unmarked state (a void) — upon which two asymmetrical operations can be performed. Namely, marks can be repeated — placed alongside another, or ‘called’ — and marks can be reversed — embedded within another, or ‘crossed.’

Here is an example of possible notation, as well as the identities for the two basic operations:

Mark                 ( ).
Un-mark             .

Calling:             ( ) ( ) = ( ).
Crossing:         ( ( ) ) = .

[For those wishing a brief demonstration on the primary arithmetic and algebra, as well as further information on connections to other areas of mathematics and science, you will find some wonderful resources here.]

Astoundingly, using this minimal system, Spencer-Brown was able to derive a majority of the results of mathematical logic, arithmetic, and set theory; and in this way he resolved many formerly irresolvable difficulties. In fact, many results from all of these fundamental branches of mathematics can be derived without difficulty — and sometimes in easier ways! — from Spencer-Brown’s primary algebra.

Godel writes in his proof (on unprovable statements in fundamental arithmetic) about the ‘possibility’ that there may indeed be a proof of completeness — however, it will necessarily be one which is not in the language of set theory or arithmetic. Spencer-Brown’s logic is a candidate for a rehabilitation of just this kind — a ‘primary’ arithmetic which grounds logic itself — illustrating that even the notion of proof itself depends not (only) upon a formal system, but even upon a pre-systematic logic of distinction, a marking in some form or another.

Another way to express the same logic: writing comes before mathematical intuition, even before speech — it provides the ground, the possibility for intellection, the virtual field in which intuition can be set free. Writing supplants formal systems, reinvents them, plays with them, comprehends and surpasses them. The notion of “supplanting” is, for Derrida, an adequate definition of the art of writing itself.

We wish to ask in turn how the mark itself is supplanted by a pure machinic operation, by ‘parasitic’ systems of control — how the logic of writing finally becomes curious and makes an experiment of itself, overturning and tearing itself apart, decentralizing and reintegrating the quantized pieces, in a wild and Dionysian burst of radical self-transformation.

Is a whole new kind of “writing” beginning to seem closer to reality than ever before? — a question which itself may also be a symptom that writing is always already unfolding a new dimension from within itself. But it seems like today a new kind of possibility is becoming visible. While the question of technology is not the substance of Derrida’s analysis, but rather a peripheral inquiry or marginal case, it serves as a useful interruption which causes a coherence at a higher structural level of writing. Such twists and rearrangements are all over Derrida’s work — they are practically a signature — but especially in this case they have more than a rhetorical import.

Derrida is reminding us that cybernetics, in some sense, also points to the closure of a certain metaphysical and historical age — not merely that it is a new science of writing equally as “deep” as philosophy, but on the contrary, that cybernetics has a tendency to precisely supplant philosophy, as writing had already done to images.

(notes for an abstract)

If the theory of cybernetics is by itself to oust all metaphysical concepts — including the concepts of soul, of life, of value, of choice, of memory — which until recently served to separate the machine from man, it must conserve the notion of writing, trace, written mark, or grapheme, until its own historico-metaphysical character is also exposed.

[...[E]ven before being determined as human… or nonhuman, the gramme — or the grapheme — would thus name the element. An element without simplicity. An element, whether it is understood as the medium or irreducible atom, of the arche-synthesis in general, of what one must forbid oneself to define within the system of oppositions in metaphysics, of what consequently one should not even call experience in general, that is to say the origin of meaning in general.]

(Jacques Derrida, Of Grammatology 9)

Norbert Weiner introduced the neologism ‘cybernetics’ — in connection with the ancient Greek root meaning ‘governance’ — to denote a new science of systems of control. Cybernetics studies real complex systems and their automatic management, but it is also a rigorous science of energetics and pure information. The most essential expression of cybernetics itself and its own working ontology can perhaps be traced to Von Neumann, who conceived of a swarm of networked machines which could also function together as a kind of generic factory, and so would be able to reproduce all of its own component elements (and hence itself.) In this image we perhaps witness a glimpse of an “adult” cybernetics — the closure of metaphysics, the end of writing, the convergence of biology and cybernetics — a “transubstantiation” of flesh into the virtual.

This image is not without its poignancy. Is cybernetics a symptom, even of the horizon of a metaphysical — and not only a historical — era? A new dawn which has not even struck the horizon: we catch glimpses, a blurring of boundaries, an impression of lightening. Interfaces become depths while automation whirrs smoothly. Computational ease produces enormous, vivid and completely new spaces for thought. Cybernetics in its fuller historical sense has revolutionized not only production but the way we process information itself — in many ways transforming the face of the earth — and promises only to accelerate this bizarre interpenetration of systems of control.

This is perhaps the reason why the question of cybernetics is such an uncanny one: it questions us in return. Cybernetics is deconstruction, an historical equivalent. We experience this revolution simultaneously as integration and decentralization, a dramatic leap in both intelligence and automatization.
In a profound sense we experience cybernetics only in anticipation — that is neither as a subject or an object, but as a pure interface, producing various integrated systems of control. In this sense we can speak of a cybernetics which itself is in control of a system of metaphors and can therefore be taken apart and re-assembled; such a re-assembly is underway and must even be pushed forward. This science of information, of managing non-linear systems, is an anticipation of a historical and metaphysical era which has not yet arrived, and which still depends on the intensification of writing to a new plateau of celerity.

Today the question of cybernetics has begun to pose itself with some urgency. How do we “decentralize” and “reintegrate” a science of control driven by a virtual presence — an exterior or futural presence — and which opens itself up in terms of a new dimension of time, an immanent rupture of history?

Other Possible Paper Titles for Cybernetics Panel:

“Transforming Technology: Simondon and Deleuze”

“Noise, Interface, Information: Serres and Levinas on Communication”

“The Software of Desiring-Machines: Guattari, Cybernetics and Politics”

Insofar as it tends towards a studied negation (or counter-actualization) of our numb existence, endlessly dramatizing the existential narrative of escape, contemporary cinema conveys an intense and disturbing truth about modern reality. It is not just the easy and everyday dissociation that life is a movie, but more surprisingly, that movies have become indistinguishable from our real lives. Drama is not merely a terrifying absence, simply the dissolution of the synchrony of the One, but an enigma even more puzzling still– the cinematographic interface is already an incontrovertible diachrony, a renegade communication across an abyss of broken myth. Cinema: the art of time turned in upon itself. The surface story splits the world in Two, by drawing a sacred circle (or rectangle) in which larval intensities can escape from their segmented order of time (or space.) Images transcend history.

Drama, in its fiery and stormy heart, is the story of the becoming-One, the becoming-Image, the imaginary One whose becoming exceeds the “legal” or “logical” boundaries of the story world. Above all the telling draws together the one who can answer a profound question, that is, the one who tells responds to a specific call. While a matter may hold terrifying secrets, and suddenly seem to overflow the encircled space with dark and terrible visions of other worlds, nonetheless, like a vampire, the storyteller would not have come without being asked inside. Who knows, it may even be that the real story cannot even begin without a pre-original apology, a gift or other crude offering of gratitude, on the part of the interlocutor. For drama is not recitation, it is spoken reverie.

Only original impressions are magical. Only if God were a playwright, could existence be so profoundly miserable and magnificent at once; and in such a delicate symmetry! Who must be convinced the universe expresses themes which are by turn unfathomable or tragic or transfiguring? We feel becoming as dramatization, already “actualization.” Now what is needed is to digitize creativity, to automate the playwright, to quantify writing. For becoming is the body upon which the author, the artist, the cinematographer play, these mad directors of active and reactive forces of intensity. All elemental and narrative forces are available at their palette. The complete artist — who is thus in absolute hell, for he knows a little about horizons. Now it is revealed: God writes straight in crooked lines, or put another way: being is indifferent.

And becoming is a black hole. Yes, the movie is our life. Why deny it? It is already over and the story hasn’t even begun. The medium itself is fluid, full of noise. Yet, despite its transience, cinema is still richly traversed by pure elemental forms. There are sublime moments of crystallization in cinema that rival or exceed anything I have ever experienced.

For the space of the drama, the screen functions as a turbulent transparence.

Preface (Emergence from Noise)

This study seeks to explore the relation between dramatic theory and artificial intelligence. The goal is to shed light on a broader and more difficult question: how do we reconcile authorship with autonomy? In terms of this deeper question of creativity, it will suffice for the purposes to investigate only peripherally the question of human expressivity. Indeed, almost our entire concern will be with a-linguistic feedback systems, and in particular, systems of non-human communication. The first goal of this study will be to develop a theory of “autonomous” interfaces. This model is then applied to several particular examples of interactive systems, followed by a description of the computational as well as phenomelogical features of ‘deeply generic’ interactivity.

Consider the problem of dynamically generating a dramatic story. Since playable characters would be to some degree autonomous to the plot, how do we achieve dynamic interweaving with the plot? The future parts of the story must be actively rewritten, the world must be warped about the active characters, entities in the game-universe controlled from somewhere outside. The space of user behavior is precisely the critical gap of narrative control between the plot and the characters.

In terms of developing interactive drama, we are still awaiting some legitimate cybernetic interconnection across disciplines. In short, we have need for generic representations of plots and characters and then rules of mixing them up, arranging and transforming them to respond to user interaction. In terms of design, then, we need to create a machinic interface between the author and the story space. Even though the fields are abstract, a real engineering is required here. We need to build literary machines which can resolve this break between plot and autonomous characters.

Efforts similar to our study have in the past produced conceptions of drama-managers (micro-agents who arrange plot-atoms combinatorically to conform to certain desired dramatic functions.) Eventually most studies have concluded that the problem lies in the authorial interface. You don’t want to have to program a thousand different variables to describe a character, but on the other hand, you don’t want very few variables. In fact, you want a natural interface which develops a full character based on a partial description, with a lot of creative guessing and inventing in between. That is, you want to be able to describe in natural language what a character is going to act like.

This behavioral dimension of activity is difficult to characterize; certain languages (like ABL) even make behaviors the elemental basis of programs. Again, we run into similar problems, if almost all the drama and narrative is being generated by the plot subsystem, how do you account for the uniqueness of new users? How do we dynamically generate characters without simply scripting behaviors? The answer is to have many layers of evaluation, and more complex levels for more complex interweavings characters and plots. The key is pragmatic variation: it is a tool which can be used at the lowest level of language generation as well as at the highest level of overall dramatic management.

Let us briefly anticipate our results in order that the situation be made clear. There is an inescapable gap in the philosophical and computational discourse on interactivity, the explicit question of bridging this gap together narratively. Now, in many ways, the problem of natural language understanding is strictly beyond the scope of this study, though obviously the theoretical apparatus we develop is intended to be generic enough to effectively model certain interesting features of human languages and stories. Examples of such models will be sketched out in the final section.

(sorry, more on this soon)

Remarks on Turing and Spencer-Brown

(Joseph Weissman)

Introduction

Computation is holographic. Information processing is a formal operation made abstract only by a reduction in the number of free variables, a projective recording which analyzes from all angles the entropy or information contained in the space. Thus, basing my results partly on Hooft’s holographic conjecture for physics (regarding the equivalence of string theory and quantum theory,) and by extending Spencer-Brown’s work on algebras of distinction (developed in his Laws of Form,) I will sketch the outlines of a new theory of universal computation, based not on system-cybernetic models but on holographic transformations (encoding and projection, or more precisely, fractal differentiation and homogeneous integration.)

Hooft’s conjecture allows us to extend the Laws of Form with an “interface” model where computation doesn’t require an observer, only the potentiality of being observed. In other words, all we need is the construction of a interface (positive feedback system, i.e., an iterative calculation or mutual holographic projection) in order to process information. Light itself can be thought of as encoding information, and in particular, electromagnetic waves form a necessary part of holographically recorded information. In other words, to operate in a formal system is to derive information only from interfaces, simpler than but in some way equivalent to the “real” objects.

This abstraction is at the heart of Spencer-Brown’s The Laws of Form which describes the fundamental features of any formal system. These formal operations are also representable as holographic operations. Furthermore, since a description of the holographic structure of a process is equivalent to a description of its original form, we ought to be able to understand computation exclusively in terms of holographic operations. We can represent a region of space by a projection onto a holographic surface. The key point is that we lose a dimension, but owing to a fractal mapping, we lose no information. This projective holographic process can continue until we reach a representation (reality?) with no dimensions at all, i.e., pure or manifest information itself (a holomorphic field.) This stepwise or iterative movement towards pure information is holographic in essence.

Claude Shannon has defined information processing as the conversion of latent, implicit information into manifest information; we will add, into its (dimension-zero) holographic representation. Information processing occurs through holographic projection and encoding: any presented multiplicity can be converted into pure information through some n-dimensional holographic “cascade”. An observer distinguishes spaces, an interface encodes these distinctions, thereby extruding the holographic sub-structure of the universe (the “virtual” information processing occuring in distinguished regions of space.) It is in this context that Spencer-Brown provides a unique insight to cybernetics with his analysis of the operation of distinction. In combination with the holographic paradigm for the physical structure of the universe, a correspondingly extended algebra of distinction for the structure of formal systems provides the basis for our claim that information processing can be thought of, at the limit of abstraction, as consisting fundamentally of holographic operations.

Holographic Space and Information Processing
(How to move from n to n-1 dimensions.)

All our knowledge is symbolic.

Goethe

A holographic surface is a two-dimensional representation of a three-dimensional volume of space. It is composed of heterogeneous “perspectives” where any piece of the surface encodes a complete construction of the entire volume from its given vantage point. The importance of this structure is that it is fractal: a hologram reduces the number of dimensions isometrically while leaving the presented information intact. Some recent results in quantum physics and string theory suggest that the structure of a hologram, a system which can be extrapolated from its surface, is very much like the structure of the universe. For instance, the AdS/CFT correspondence [1] suggests that the string theory and quantum field theory are in fact equivalent languages for describing the same underlying reality. More precisely, a string theory on a given space is equivalent to a quantum field theory without gravity defined on the conformal boundary of that space. Maybe not so surprisingly, the dimension of the quantum theory is lower by one or more than the dimension of the string theory. For example, there is a duality between Type IIB string theory on a five-dimensional space and a supersymmetric Yang-Mills gauge theory on the four-dimensional boundary. The theories are equivalent, but one is simpler: it has less dimensions and doesn’t need to discuss gravity.

Hoof’t has shown even more explicitly that the limit of any gauge theory (with a large enough number of colors) is a version of string theory — despite the fact that string theory doesn’t appear to be a theory of quantum gravity! Hooft’s holographic principle states that all of the information contained in a volume of space can be represented by a theory which “lives” only in the n-1 dimensional boundary of that region. Information (entropy) is proportional to the surface area of a region, not to its volume. By a theory ‘just on the edge’ of a formal space, we can get every bit of the information contained within the entire deep volume of the space. A two-dimensional boundary is all we need, it’s equivalent to what’s inside the three-dimensional region.

What is a hologram? A hologram maps a volume onto a surface. A holographic surface ‘completely’ contains the volume it describes; the information it encodes is fractally distributed upon its surface. Any piece of the hologram stores information about the entire scene at a fidelity equal to its optical sensitivity. Essentially, each point on the holographic material records a photograph of the scene. In a hologram, one entire space (the scene or situation) is the projection of another space topologically equivalent to its n-1 dimensional surface (the holographic representation.) The operation of recording a hologram requires a coherent light source which is split by a mirror. The first beam is meant to bounce off the scene. The interference patterns of this signal beam and the second reference beam is recorded onto the holographic plate. The second beam is later used in the reconstructing the scene. When the processed hologram is illuminated by the reference beam, the diffraction patterns reconstructs the original signal beam.

So there is at least one particular ‘theory-space’ operating over the surface of any given volume which is equivalent (a dual theory) to the ‘theory-space’ operating over the volume itself. The holographic ‘crust’ of a system is a complete mapping; the strong holographic principle suggests that the system itself is an illusion, a projection of the simpler system onto a ‘bigger’ space. They are equivalent descriptions of an underlying reality. ‘Truth’ is not in the hologram or its projection, but in the operation which maps between. It is an immanent theorizing which allows these hidden dualisms to surface, through a logical revolt to structures of knowledge and power. Holograms are a model of the universe and consciousness only insofar as we recognize their status, like any structure, as metaphors. Nonetheless, it certainly seems true that some metaphors are remarkably more descriptive, apt and succint than others. Some even capture essential structural and technical unities, tracing the intricate diachrony of machinic interaction. I think we still have new things to learn from holograms.

My question here is the genealogy of computation, the nature of information-processing. My conjecture is that we can understand information-processing in terms of the holographic paradigm in such a way as to realize that it is possible to ground a model, or reduce a constellation of particular complex problems to simpler, equivalent problems. In particular, ordinary logical computation can be easily modeled by the laws of form which can then be realized by holographic transformations. My point is that the holographic transformations themselves are a much simpler and “reduced” language for discussing the exact same theoretical series of problems. Specifically, computation can be understood using a single, unary operation: holographic transformation.

Therefore my main task here is to show that a holographic model for information processing is equivalent to a universal Turing machine. In other words, the capacity for holographic projection (which is inherent in any selected region of space, for all physical processes and relationships) embodies the essence of what constitutes an information-processing machine.

The second task is to show how the Laws of Form constitute a detailed logic of holographic transformation, the creation (projection) of (parts of) the universe by the division of space. (Interestingly, though we shall not consider this too deeply, the Laws of Form also exhibit an isomorphism to electrical circuits.) Our specific concern with the laws of Form will be to show their unique applicability to holography, as an algebraic model to show how holographic transformations could in fact embody the essential operation of computation.)

What is Computation?

Astonishing! Everything is intelligent.

Pythagoras

We will begin with a brief analysis of the holonomic model and sketch some key isomorphisms to models of computation. First, a hologram is nothing more a flat map of a region of space (conforming informationally to the boundary of the space.) Every ‘difference’ in that volume of space is conserved, recorded upon the holographic surface whose projection, when illuminated by the signal beam, is this volume.

A hologram is a fractal map of a region of regular space. It is a particularly interesting structure for us because we find in it two different scales persisting unresolved. On the one hand, there are the micro-photographs which collectively constitute the surface, whereas on the other hand, we have the macro-holograph which singularly represent the volume. In a holographic structure we subtract a dimension while conserving information: the operation of passage between spaces of different dimension is certainly transversal, the hologram results from a complex transduction.

To record a hologram is to transfer the information contained in a volume of space (a scene) onto a surface (the holographic material.) Ontologically we are dealing with different kinds of information. This transference has only practical limits. Theoretically we can take this process infinitely, packing a surface full of holograms, then micro-holograms, then micro-micro-holograms… This recursive operation is the metamathematical operator of abstraction (embodied as ‘transposition’ in LoF); it is a transformation which takes a given concrete space to the zero-dimension ‘extrusion’ of the entire volume onto a single point. Here there is a turning point: the legitimately ontological transformation which connects us to Spencer-Brown. From the space to a single point, but the process can even be continued: from the single point (which maps an entire volume in n dimensions with a micro-hologram cascade) with a positive dimension less than one. From these inter-dimensional mappings, it becomes clear we are interested not in positioning but in topology: information is being written directly into the structure of the space. These mixed topological structures are not arbitrary, but they are also not regular or continuous. They conform to new kinds of spaces with alternate symmetries. There are an infinite number of these in-between spaces, any particular layer would but another step in an infinite fractal recursion.)

There are not really two inverse operations: recording a volume onto a surface and projecting a volume from a surface. Holographic space is a generalization of both of these, allowing the operations to become continuous. This brings us to 1936, when Emil Post described a model of computation which is extremely interesting to me for several reasons. First, because it represents a move beyond Turing towards a simpler model, which is still formally equivalent. Post’s system is extremely simple, but complex enough to be formally equivalent to recursion — that is, it describes a universal computer. Second, Post-Turing machines are structurally isomorphic to Spencer-Brown’s Laws of Form extended to n-dimensions. [2]

However, while Post-Turing machines may be fundamental models in some senses, it is clear we need a second-order model of computation to account for emergent properties of distinction. In other words, we need to assume a user, programming the machine with methods and posing to it problem-spaces of various kinds. But if we presume the user, we leave his desires (enfolded within his programs) unexplained, we leave them as the musician leaves the composition: we perform it precisely as we are enjoined by the quasi-linguistic flow of instructions. A universal machine also performs without deviation or flourish. But how, then, are creative deviations to methods and problem-spaces generated? So far, we have not consciously conjoined cybernetics with psychoanalysis on this particular point. We have assumed that only the mysterious users with their magical organic brains can ‘outrun’ the infinite logical loop computation cannot overcome. Godel’s general recursive function — the method of representing formulas by numbers, a program by a series of instructions — appears to be the cognitive limit, the asymptotic horizon of computation complexity. But already to give a complete and formal deductive theory (symbol logic) we would have to find an equivalent predicate in recursive form, which is the key observation from which Godel’s theorem immediately follows.

The existence of provably unprovable statements is difficult to reconcile, but Spencer-Brown’s Laws of Form do precisely this. By showing that containing a space is to make a distinction, recursivity is introduced prior to symbolic reduction. Indeed, we can outline an equally fundamental (though considerably more complex) mode of computation where creative responses arise through feedback and transformation. Interfaces themselves should be intelligently generated for a given problem space, through analyzing its holographic structure, ‘deducing’ the underlying program, or technical schematic. How are the forms of programs generated? But after all, what is the shape of desire? How do we connect the forms we imagine to digital forms? Interfaces must become porous membranes, they must be designed to be broken through and overcome.

The interface itself must be the site of the transformation of the problem space and therefore of the underlying representation of the problem. Abstract computation is embodied by this process of generating new interfaces for problem spaces. In other words, we extrude from the surface/image of the problem information about its projected space. We move from a series of distinctions which bound the space of the problem to an interface which functions to transform the problem, if you like, from the Form to the anti-Form (quasi-distinctions, on the boundaries of distinct forms.) Programs ultimately do nothing more than operate over a series of marked and unmarked spaces in order to simplify and transform them according to rules based on the state of the machine. Post’s machine is a formalization of this insight, representing an ‘atomization’ of Turing instructions; but is further reduction in the complexity of the machine is possible?

The smallest universal Turing machine was described by Stephen Wolfram, who suggested that a 2-state, 3-symbol Turing machine was the smallest universal possible. This year, a 20-year old cybernetics student, Alex Smith, proved that this machine was indeed the smallest universal machine possible. The machine is similar in its simplicity to a Post machine. However, the recursive step must still be made. In fact, the machine must be able to simulate itself, it’s entire field of operational decision-making. The program which would perform this would amount to a meta-operating system. Simply it is able to create virtual machines; each of these obviously contain a similar program capable of virtualizing another series of machines… However, we are getting ahead of ourselves. Again, our basic project here is simply to show that holographic transformations are equivalent to the operations of a universal computer. How do you build a holographic computer? Storing information with light is really a very old idea. But holography is quite different from photography, for enough information to reconstruct the entire scene is distributed throughout the entire surface of the holographic material — whereas in a photograph only a single light ray is recorded at any particular point, so cutting the photograph destroys half the information. Cutting holographic material, on the other hand, merely dulls the resolution of the encoded information, causing distinctions to become blurred.

Holography and Distinction

It’s been known for more than a hundred years, ever since Maxwell, that all physical systems register and process information.

Seth Lloyd

David Bohm has argued that the structure of the universe itself is holographic [3]; I am saying the same thing about computation. The holographic paradigm has had a recent successful implementation in multidimensional associative memory [4]. Interestingly, the model seems to naturally reproduce many characteristics of organic memory: dynamically localizable attention, making it effective for generalization and pattern recognition with changeable focus [5]. These results are compelling, but not enough to make our case. It is necessary to point out in addition several aspects of the holographic paradigm that are important to computation.

(1) A hologram is a complete map of a volume which fits on the conformal boundary of that volume. The surface is a fractal representation of this volume which reproduces the optical (electromagnetic) properties of the volume when decoded or projected. Thus a hologram is an encoded map of a complex region which it represents in its micro-structure (it cannot be reconstructed without the recording signal which produced it.) The operations of recording and projection are not just analogies to the metamathematical operations of abstraction and instantiation, but in fact the pure model and wholly commensurate with the ontological split evinced between pure and computationally-oriented, recursive mathematics (as in Godel, who closes his proof by writing that there might still be proofs of completeness — but which simply cannot be stated in set theory or arithmetic.)

(2) A hologram then is a complete system (of calculation.) It is formed by the gathering and hardening of electrons into light or dark areas, into marked and unmarked spaces. This bonding of electrons is not without tensions, but they are relatively stable allowing for the formation of the micro-images. A hologram is a formally operational space, every portion of the space reproduces the entire scene from a given perspective. A hologram is a functionally complete system, a calculus.

(3) Every point on a hologram is an optical algorithm (or lambda expression,) encoding a functional mapping of a series of higher dimensional points onto a single, lower-dimensional point. This fractal mapping binds parameters into expressions, each micro-scene is a non-linear function of the interference of optical signals, the excitation slowly hardening into regions of light and dark, visible and invisible.

The Laws of Form represent the horizon of metamathematical abstraction. In his simple calculus we find the fundaments of set theory, arithmetic and logic. (In particular, Bricken and Kauffman have shown there is a simple mapping from the laws of form to mathematical logic.) What is important to remember is that the laws of form are a reduced image of the more complex logical axiom-systems (which can still be derived from the simpler image.) In fact, the more complex system is again a projection of the simpler. The Laws of Form encode holographically the generic features of computation, or reasoning within the boundaries a formal system. What is critical is that we are dealing with a meta-formalization (not wholly unlike the Godel numbers) where transformations in the Laws of Form can be interpreted as systems of mathematics. The Laws of Form can be seen also the logical basis for electronic circuits. Every circuit has a form, a pattern of decisions or distinctions it makes. A circuit is a recognition-machine, whose responses vary predictably on the basis of the information with which it is presented, trained to recognize information that appears in a certain form. All mathematical formulations are encoded in a logical language whose structure is not arborescent but holographic — characterized by progressive abstraction of projective and integrative operations. Holograms represent not only the basis of formal computation but in many ways are an apt paradigm for formal and informal process of all kind, of information processing at the most abstract limit.

A final key comparison to make here would be to the Einstein field equations, where particular solutions correspond to specific space-time topologies. A hologram models the concept of operation, not only formalization but projection. The recursive aspect that makes a holographic surface ‘coded’ and therefore the origin of computability is that holographic representation involves an mapping across a dimensional break accomplished through multiple perspectives, or fractal transpositions of the original space.

(notes)

1. See Witten, Anti-de Sitter Space and Holography, or Gubser, Klebanov and Polyakov, Gauge Theory Correlators from Non-Critical String Theory

2. I Grattan-Guinness, The manuscripts of Emil L Post, Hist. Philos. Logic 11 (1) (1990), 77-83.

3. Bohm, David (1980) Wholeness and the Implicate Order, Routledge, London.

4. K. I. Khan and D. Y. Yun. Characteristics of Multidimensional Holographic Associative Memory in Retrieval with Dynamically Localizable Attention. IEEE Transactions on Neural Networks, 9(3):389–406, May 1998.

5. ibid

(see also)

Claude E. Shannon: A Mathematical Theory of Communication, Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, 1948. (online here)

Taylor, R. Gregory (1998). Models of Computation and Formal Languages. New York: Oxford University Press

G.Japaridze, The logic of interactive Turing reduction. Journal of Symbolic Logic 72 (2007), No.1, pp. 243-276.

Fractal Effervescence (2006), David April

Simondon and the Theory of Individuation

There is something eternal in a technical scheme… and it is that which is always present, and can be conserved in a thing.

Gilbert Simondon

Gilbert Simondon’s reformulation of information theory on the basis of a new philosophy of technology has, in comparison to earlier attempts, at least the following major advantages to its credit:

- His thought introduces us to an entirely new way of understanding technology. His earliest work investigates the intrinsic nature of the machine. He asks about the conditions of the genesis of machines in the world, the essential nature of their concrescence from an abstract model.

- Maybe more importantly, he gives us a new conceptual model for understanding reality, in terms of the process of individuation, or as he would put it, transduction in a metastable environment. It is a model which has isomorphisms in nearly every branch of science, from physics (turbulence, quantum field theory,) chemisty (crystals, superfusion,) psychology (perception, affection, the unconscious,) mathematics (chaos,) and biology (transduction, individuation.)

- By discussing the orientation of perception and action in terms of metastable relationships (instead of pure relations, concepts, species, etc.) we are able to move beyond the hylemorphic model of perception and reality (which hypostasizes “individuals” from what is really, and before anything else, a process of individuation.)

- In short, Simondon’s philosophy attempts to work its way beyond, and underneath, categories like association and representation towards a non-hylemorphic program for science in general.

Simondon outlines no less than the lineaments of a new physics, a new chemistry, a new biology, a new psychology, and perhaps a new philosophy – all now re-organized by an individuation of our scientific knowledge.

One of the most interesting aspect of his philosophy is that we are drawn, in Bachelardian fashion, to consider the ‘poetic’ or nonverbal knowledge articulated, for example, by the hands of the craftsman or of the musician. He introduces us philosophically to this harmonious dialogue between self and other which occurs in technical creativity (and perhaps in creating abstract and philosophical machines most especially.) There resound throughout Simondon the praises of technical creativity. Van Lie even considers that Simondon’s thought suggests a new kind of humanism — a sort of technological humanism, on the basis of a new model of perception.

I would probably agree: Simondon writes that perception is always the resolution of a conflict. Not to mention that the historical replacement of the human hand by the machine, the perception that the machine was superior to men in this or that aspect, in terms of value – this comprises no less than the essence of alienation in Marxian theory.

Suffice it to say Simondon’s political importance today also cannot be understated. In short, we should understand our political systems in terms of individuation, instead of thinking the individuation of political systems in terms of particular systems, whether historical regimes or eternal ‘substances’ or ‘forms’. By in this way comprehending the incompatibility within every system which produces individuation, we approach a middle path beyond Plato and Aristotle, towards a new political ontology, a political onto-geny.

But Simondon’s real project is the radical critique of autopoesis. Simondon takes on the cyberneticists at their very foundation, in the very idea of a system. He reminds us that even though we may unravel the series of temporal sequences and structures in an individual system, there will always be something left over. In particular, there will be what Simondon calls a pre-individual field of singularities — a heterogeneous manifold of potential differences.

Without this milieu, this field of tensions, there could not come to exist a system of relations, or a machine, an organism, a body, a crystal, or an individual of any sort. The process of individuation requires a field of singularities, it plays upon these intensities; individuation is the transformation of these tensions into structures, and necessarily produces a new differential milieu in this doubling and unfolding of structures and series. The pre-individual field is called “pregnant” in its intensity with the potential for individuation. Relationships are always relative, never pre-existent. Rather, they emerge transductively through differentiation . An individual is always within the pre-individual field which was the condition for its genesis which precedes it ontologically.

Simondon’s realization of the continuity between the technical and the cultural has the power to transform our scientific worldview, because we can recognize there is no opposition between “man” and “machine.” What is in question is this very relationship, which is misunderstood because we have for so long misunderstood the nature of the machine.

Process

In Mechanism and Biological Explanation [Maturana 1970], Humberto Maturana and Francisco Varela argue that machines and biological forms are very closely related — so closely, in fact, that biologists can reasonably claim living systems are machines. This is not meant merely as a pedagogical metaphor, but rather as a rigorous analogy, which emphasizes important symmetries, and even better, expresses concisely specific experimental and theoretical aims. In what sense, then, are living systems machines?

A machine is defined by a group of abstract operations, satisfying certain specific conditions. An abstract machine is this system of inter-relations which is itself independent of the actual components which ‘realize’ the machine. A fishing boat can be made from many kinds of wood, sailed on many bodies of water, used to store many species of fish; a game of tag can be played with an arbitrary number of arbitrary people in any suitable space. What matters is not the specificity of a given component but the specificity of its relationships. We can define living systems as specific groups of components and their inter-relations, according to both abstract structure and specific functionalities. But insofar as we are only considering their structure, living beings are isomorphic to collections of finite groups of abstract machines: biology considers micro- and macro-structure, whereas systems theory studies inter- and intra-relations.

In short even the two styles of theorizing are quite closely related. Maturana and Varela are arguing that, just like abstract machines and actual living systems, our theories of living systems and our theories of machines are isomorphic. The two explanatory modes are, in some way, the same thought expressed twice, spoken in different languages and at different rhythms, for different people altogether. Yet the generic series of interrelations which they both describe have essential structural symmetries. A change in location just varies our perceptive horizon of possible actualizations, but not their underlying rule. It is precisely this ‘synthetic’ level of biological analysis which must invoke the immaterial plane of inter-relations. Whereas to analyze in terms of a machine is to identify rules of inter-dependence, modes of producing inter-activity which already imply a potential materiality. Either theoretical analysis produces a structural definition, independent from any particular material reality.

Machine

This abstract-machinic level of analysis seems quite distinct from what we consider the engaged and active analysis in biology, observing and experimenting with living systems. But this indicates that we do not yet have a general theory of living machines of sufficient explanatory power. It is clear, at any rate, that we need both layers of analysis in order to understand living processes. Despite their apparent unity, we must examine the machine and the organism in both their concrete difference and abstract structure, both the concept model and the material instance. Indeed, these are the simultaneous and irreducible aspects of scientific explanation: “The structures of living systems and their actual (material) components are complementary yet distinct aspects of any biological explanation: they complement each other reciprocally but cannot be reduced to one another.”2 Whether biology or cybernetics, we find an inherent double-articulation of inter-relations and intra-relations, of ontological rules and actual instances. The question in either case is not how the information is embodied or a specific component realized. Rather, the cybernetic or biological question is how these abstract bodies of information are correlated, not the specific operation content (form) but the specification of operation (in-formation.) The two sciences are the same, their problem spaces are isometric.

Order

Our question is how to use theory to build new machines. Let’s sketch out a potential theoretical apparatus capable of properly posing our question. We have considered that the concept of machinic autopoesis in Maturana and Varela has a function in both biology and cybernetics. The important idea here was that it really had the same function in both disciplines, just on different scales. After all, autopoesis is the raw material of individuation itself. Autopoesis conditions possible modes of inter-relation and orderings of sub-developments. It regulates its own development, it is self-different and yet identical; it constitutes a turbulent yet stable flux which maintains a complex and well-adapted cycle of behavior, carefully “managing” the roles and inter-relations of components.

Cybernetics is about developing systems of control; the idealized abstract machine is more or less a perfectly decentralized machinic awareness, an image of the human mind itself, it would be a perfectly nebulous rhizomatic network, and would be aware as a swarm of submachines, even perhaps “alive” through this emergent consciousness within the algebraic balance of computational sub-components. As Raymond Ruyer wryly notes, we might fall into the dualistic fallacy less if there weren’t any mirrors around! Sure, nature and our brains and society are a rhizomatic network; and there’s really no reason to think we can’t eventualy develop computers exceeding human intelligence. Remember: the computer is really just a further evolution of mnemotechnics, memory technology. Computers are ideal symbolic manipulators, precisely because they are unaware of what they are manipulating. They promise to “forget” what the message is about, to transmit the signal innocently. We value this about computers now; but it may not be true in the future!

For now, at least, computers are without the human bias of caring about the information they are processing. Humans, of course, imagine they have an opinion about the world; and we imagine computers do not form such opinions, or anyway, that we haven’t found any evidence yet that they do. They do not remember something unless told to; they have no autonomy, no desire. But how is human desire, human automony produced, at bottom? What are the machines of the unconscious which produce the strongest or most subtle desires, passions, impulses? The delicate chemistry of our instincts is the most sensitive and credible sense we possess. The question underneath all of this is the production of subjectivity; how do we regulate and preserve life and awareness? How do we measure the principle of difference, how do we calculate the origin of exteriority? How do we transform a theoretical inversion into an intervention into real situations, to actual new formations? A few notes, for now: (1) Life is structural, but it depends upons an a-structural ‘reserve’ of energy, or chtonic milieu. 2) Life is structured becoming, pulls itself out from an inner space. (3) Life produces scale, ordering, introduces zones and grids and metric planes into the universe, into itself, by mapping its local environment onto itself.

Our first conclusion here is that all measuring has to be brought down to a vital scale; more precisely, all scales are biological, they are produced and constrained by biology. They are formed and deformed by sensation and imagination. (We cannot measure what we cannot imagine, what we are not clever enough to think up a way to measure.) The other point to notice is that our abstract model here is topological at root. The concrete model must be considered as a purely materialist, immanent conception. Life is time, light, energy, space — life is em-bodied. Cybernetics seeks to describe and produce systems of “control”; it is ‘information-architecture’ without ontology. What exists is energy embodied in a specific system; what doesn’t exist per se is the machinic form which is ‘clearly embodied. The immaterial is our theory of machines, the becoming-invisble. Both technological and biological systems ‘embody’ a specific immaterial form, and condition the production of new (sociotechnical, theoretical) formations. But each formation is always at risk of arising (or collapsing) due to a spontaneous, asymmetrical pulse.

[1] – Francisco Varela; Humberto Maturana. Mechanism and Biological Explanation. Philosophy of Science, Vol. 39, No. 3. (Sep., 1972), pp. 378-382.

A machinic assemblage, through its diverse components, extracts its consistency by crossing ontological thresholds, non-linear thresholds of irreversibility, ontological and phylogenetic thresholds, creative thresholds of heterogenesis and autopoiesis. The notion of scale needs to be expanded to consider fractal symmetries in ontological terms… What fractal machines traverse are substantial scales. They traverse them in engendering them. But, and this should be noted, the existential coordinates that they ‘invent’ were always already there… we need to rediscover a manner of being of Being — before, after, here and everywhere else — without being, however, identical to itself; a processual, polyphonic Being singularisable by infinitely complexifiable textures, according to the infinite speeds which animate its virtual compositions. – Felix Guattari, Chaosmosis

0
Where can we find an abstract machine? But they have no single position in space: only a series of instructions, for plugging other machines together.

1
They come in swarms: a family relation between machines, a family of spaces for operation. The operation is survival: using energy creatively to intensity and prolong function.

1.1
Specifically and generally, machines transform energy; similarly, formal transitivity is the source of the abstract machines’ genetic relation.

1.2
Abstract machines can themselves be divided into equivalent classes of sub-species which are all isomorphic to one another.

1.3
But the most fundamental family of machine, the one to which all the species belong, is the abstract machine, or simple agent.

2
A machine is a libidinal, alchemical abstraction made concrete, where the abstract machine is distinguished by its formality.

2.1
An abstract machine embodies a purely discursive distinction. It is a shift in viewpoint, a transgression of a limit up to a complete transference of energy. A pure transformation of lead into gold without waste or remainder.

2.2
The abstract machine is incorporeal, because it operates between within and without, by distinguishing within from without.

3
The ontological question is entirely the question of the appropriate schema for this strangely mixed topology, the logic of discrete abstract space.

3.1
The abstract machine arranges distinctions. It is a thought gloriously vanquished by its own triumph.

3.2
The machine is not only noise, but relation: it moves and eats. The machine coordinates spaces to transform energy; the abstract machine distinguishes species from the spaces it operates over, evolving new paths over the energy fields it transforms.

3.3
A war machine on the outside, a state machine on the inside. And an abstract machine within both.

4
The abstract machine opens the ontological question by reorganizing the space.

4.1
Technology is not equivalent to the abstract machine. We never produce without becoming: what matters is, as always, whether the machine works, or even, how the machines break down.

4.2
Technology marks time today, and perhaps even tomorrow. It seems there will always be the need for new machines which bond instead of break, which liberate time from the cage of repetition, which inspire our thoughts, which motivate our actions and stir our beliefs beyond any limits we knew were possible. The abstract machine — is hope.

5
The abstract machine is a symbol which symbolizes the act of making a symbol: it is a count.

5.1
The terrifying importance of the abstract machine is of course political. But the machine is the overman: are we afraid to say it?

5.2
By transposing a tangled hierarchy of intensities, the abstract machine can create a new agency, it can breathe life into a new social excitation, it can exploit secret well-springs of desire, it can even motivate the unconscious group subjectivity towards higher goals in a controlled but effective way.

5.3
God is dead only because we needed better machines — healthier machines.

6
What are we but dividers and re-combiners of genetic flows? What is thought, what even is life, but a self-organizing machine which distinguishes spaces?

6.1
A rule transformed of obscurity into clarity. It is the symbol or signifier, an absolute image.

6.2
A trial always follows retroactively from a ruling, our first key to the curiously machinic logic of decision-making. A sensitive machine, with a head possessed of a sequence of complex probes, is able to stand up and face the problem.

6.3
To judge is to not fail to distinguish between minimally different spaces, to sediment one’s perspective into a fundamental rule. Thus justice insofar as it applies to rendering verdicts is always negative, even if the ruling is innocence/made innocently.

6.4
Trials always begin with the mapping of the interconnected series of spaces, with a customary presentation of the divergent viewpoints on the behavior. But in reality all we have is a noisy crowd all shouting their impressions at once — until the judge must finally shout: silence! For unless there opens up a space in the crowd for the marking of privilege of one set over another set, the mapping, and therefore, the trial, cannot even begin.

6.5
In fact, the rule must be in place before a mapping of the spaces can even occur.

7
There are three distinct aspects of the abstract machine which we can describe qualitatively. First, it provides a mapping between an interconnected sequence of spaces. Second, it marks the privilege of one set over another set in these transactions. Third, it uses these distinctions as new models to create an arbitrary number of new problem spaces including its own.

7.1
We can imagine a swarm of agents populated over an open problem space. The agents live in the space: their outside is another agent’s inside. This fractal recursivity allows the creation of potentially limitless interfaces between various species of problem-spaces.

7.2
A well-selected sequence of transactions arises evolutionary, not by chance. Paths encode distinctions on a field, maps encode fields onto distinctions.

7.3
Abstract machines trace new maps, experiment with new paths. Algorithms embody formal distinctions (of complexity-family); in other words, abstract machines compute new interfaces from genetic operations.