A series of imminent and necessary breakdowns are inherent to the production of desire: first, because desires connect up to an outside, with something which is always unrecognized, which is totally foreign; next, because desire is brought to turn upon itself, it is seduced into betrayal (by resentment, fear, hate, etc.); finally, because desires are always collective, but the individual makes these collective desire their own, digests and reintegrates them. In each case, there is a kind of fundamental deadlock to any investigation of the unconscious which reflects the essential paradox of psychoanalysis.

We risk not only our feelings and thoughts but even ourselves as beings entirely: the risk of losing not just our habits, our beliefs and our identities, but the very significance, the subjectivity, of our reality. Everything becomes a trajectory, a cosmic machine, a universal process of production. A becoming-nothing which is the essence of consciousness: and in the end will we know which it is — a disease or an experiment? –But what do we matter? For alienation is becoming a stranger; not trading places with a double, nor a diagnosis, but rather this mis-recognition of an alien consciousness always already present within enjoyment, within our desire itself.

The Disaster, the Event, Difference — this is what is always recognized but never known; or rather, you don’t know, you will never know whether this alterity is truly radical or not. We must make a certain wager in order to discover the real, to know our desire, to learn anything at all about ourselves. It is not a question of imitation, but of pure intensities, of movements and singularities and flows. There is always a risk involved in a becoming, a risk which is always recognized and never known to us — a displacement of essence internal to becoming, an infinite capacity which transfigures reality.

Fantasy depends upon an element exterior to the situation itself radically exceeding the space which is gazed upon and yet intricately involved in every detail of its structure: it is not only because the gaze is the fantasy’s only audience that this absolutely alien element is always already the hidden meaning of its excess. But what is ultimately so traumatic is the very fragility and inconsistency not of our fantasy but of reality itself, its ironic vulnerability to sudden and immediate disintegration, our apparent powerlessness in the face of disaster.

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.

A little time warp this time. This extract is from the first ’series’ of scattered early writings, almost two years ago now. I hate looking at old stuff but in practice it can end up teaching you a lot. So here it is:

A personal relationship with the universe is accomplished in the separation which constitutes daily existence. The portion of the universe which is given meaning by my observation and interaction is absolutely separated from the perspective and comprehension of the other. What we speak of is not an absolute reality from which we are separated; our individual perspectives, our relationships–interactions, connections–with external reality constitute appear to constitute a totality. this totality is the self, which we believe to be a unity, that is, to be singular. Common sense suggests that there is only one you. A personal relationship with the universe is the existence of a conscious mind: they are not isolated from one another, but in fact are defined by one another. However, a self-aware creature’s reality is unique, singular unto itself, isolated by an infinite abyss between the realities of other conscious minds, yet the conscious mind is not limited by this separation: a personal relationship with the universe is a linking of finite consciousness with infinity, the absolute, with Being.

Strong but loose. For clarity’s sake, I’ll try to identify two of the major theoretical mistakes I made here. It’s strange indeed to see the resurfacing of themes and examples. Also the way I’d emphasize different aspects of the relation to the other now, like the machinic interfaces and images which mediate the relation between singular beings. I’m now starting to think that the issue of class and money comes into the whole question of ontology much more strongly when you consider the political and sexual connection between systems of knowledge and systems of power. For example, we can’t just say: absolute being is one thing, and processes (natural or human) are different: they have different rhythms, cycles, and so forth. This is because their cycles are all in some sense interdependent even though always seemingly only locally informed–this primal ‘reconnection’ I assumed to be absolute being, but it seems in the light of a more psychoanalytically inclined mindset to be pure narcissism, the desire to assume primary importance in a parasitic modality.

This leads us to the second theoretical mistake: question of ethics remains completely unraised in this text–even as the relation to the other is ceaselessly invoked. It goes implicit, unmediated but ultimately unstated. Perhaps, after all, we cannot state an ethics–but nonetheless, a certain degree of meta-ethics is always required in any project. I would now identify a link within conscious self-reflection to the idea of a bad infinity, a good infinity being represented more clearly in discourse, reason, cooperation, co-evolution. A ‘pure’ meta-ethic would run something like: abuse and addiction are negative forms of infinity; restoration and ethical practice are positive forms of infinity.

This question of being always seems to elude, in one way or another, the traumatic realization that nature’s rhythms are not always sensitive to ours, and likewise that ours are not sensitive to nature’s; but this is no will of a capricious deity, no contradiction– but a fractalized interdependent network of impressions and movements, that is, there’s nothing but different events. And isn’t the ultimate mystery the locus of our own self-difference? The key to this crisis is the relation to the other, and is identified fairly clearly in the text, but still–without any sort of mediation, or modulation of this ‘personal’ relation to the universe.

How is such a relation, after all, not supposed to totalize us, to reduce us to a naked singularity, to quantize us and see us as interchangeable and replacable? It’s only in the rhythm and pulse of the social realm that we are irreplacable–but at the same time, through economy made completely replacable, through politics completely displaced… Society plays a much more complex role in terms of transcendence and sense than can be accounted for merely in the idea of the infinte, or the relation to the other as such… This, then, would mean we need a sort of phenomenology of social forces, or put another way: a meta-psychology of ethics.

Christopher Davia has published an absolutely wild e-book which expands on the systems-cybernetic model of Maturana and Varela. The paper covers autopoesis, fractal catalysis and the ontology of consciousness, and has been made available through Carnegie-Mellon’s psychology department.

Here I’d like to try to make a little more explicit some of the more provocative interrelations between Lacan’s philosophical and psychoanalytic project and the goals of modern artificial intelligence. Let’s start with the “hard problem” of consciousness, which can be phrased: “Why is there a subjective component to experience?” In his seminal article Facing Up to the Problem of Consciousness, Chalmers puts it thus:

It is undeniable that some organisms are subjects of experience. But the question of how it is that these systems are subjects of experience is perplexing. Why is it that when our cognitive systems engage in visual and auditory information-processing, we have visual or auditory experience: the quality of deep blue, the sensation of middle C? How can we explain why there is something it is like to entertain a mental image, or to experience an emotion? It is widely agreed that experience arises from a physical basis, but we have no good explanation of why and how it so arises. Why should physical processing give rise to a rich inner life at all? It seems objectively unreasonable that it should, and yet it does.

This “undeniable” element of experience is the zone of subjectivity proper. It is not, properly speaking, a location, a concept, a word or an object. On the contrary, this zone seems to be the ultimate source of linguistic/gestural ‘reality’; as such, it represents the capacity of a signifier to delay its own signification, the delay being the experience of the signification which depends on future utterances to acquire its meaning. Such a postponement is not technically a concept, a word or an object, but an experience or a temporal mode. There are close ties here to Derrida’s notion of differance here: for Lacan, the self constructs its identity relationally, as signs do.
So, in short, the crisis can be boiled down to a recursion problem: How can we even begin to signify “how the self begins to signify”? This “explanatory impasse” of consciousness, our inability to translate it into schematic, algorithmic or in any sense technical (non-poetic or archetypal description) results, apparently, from the curious self-ownership of experience, from the fractured reflexivity of intentional awareness. Lacan closely analyzes this cut or rupture as the joint or juncture of subjectivity in his 1949 lecture on the mirror stage (which is also the subject of the first paper in Ecrits.)
Lacan’s work on development was of course influenced by Freud, but also very much by Marxist psychoanalyst Henri Wallon, who lectured at the Sorbonne in the first decades of the last century. Wallon’s theory differed from Piaget’s model of development by asserting the possibility of regression (which cannot occur in Piaget’s theory.) For Wallon, from the moment a child is born (and probably much earlier) there already exist impulsive and emotional factors, affective influences from the external environment which are mirrored by internal feelings and a burgeoning subjective awareness. These factors dominate the child’s reality until, by positive and guided interaction, the child differentiates emotional modes and dispenses with “gestural disorder”; the child integrates the external stimuli, allows these to structure their reality (instead of the affective internal sensations which previously dominate.) This second stage (which Wallon called the sensorimotor and projective stage) supports the emergence of two distinct kinds of intelligence: practical intelligence which emerges from the manipulation of real world objects and the child’s own body, and discursive intelligence which can emerge only through structure interaction (imitation, appropriation and correction.) The most important philosophical consequences of Wallon’s views (on Lacan) is the crisis of development. Wallon emphasizes the messy causality, the properly dialectical (in the Hegelian sense) progress of development: the subject is structured by a lack; a positive theory of development is, in a sense, a critical impasse, an anti-synthesis, for an all-too-real crisis of disruption underlies all possible development and progress.
So for Lacan, the crisis at the mirror stage is not the erasure of a previous body composed of “bits and pieces” which are united by a glance in the mirror (“Ah! I am finally unified once and for all!”) To Lacan, the salvation of a unity of consciousness is already a misrecognition and only highlights the ever-present risk of a depersonalization, the traumatic possibility of a real disruption, of regression–one step forward, two steps back. The child has a desire to see himself as an “I,” as a complete entity exterior to the external world. Desire itself, for Lacan, is a desire for wholeness; yet the desire is the hole, desire is the missing piece. The object of desire–the completed self–structures our self-directed activity through maintaining a distance to the desired object. The subject is this division; the object (the symbolic hole within the imaginary whole) is the desire. Lacan, then, is saying that the “recognition” the child experiences when he looks at the mirror is actually a misrecognition, that is, it recognizes a lack: the sense of wholeness emerges from “bits and pieces.” Being doubly outside ourselves: this is what it to be ourselves. So in looking at the mirror, by misrecognizing ourselves, we create a self which is alienated from us, which is structured by a lack which we try forever (impossibly) to close and endlessly fantasize about filling in. Let’s hear from Lacan himself (from Sheridan’s translation of Ecrits):

This act [looking into the mirror], far from exhausting itself, as in the case of the monkey, once the image has been mastered and found empty, immediately rebounds in the case of the child in a series of gestures in which he experiences in play the relation between the movements assumed in the image and the reflected environment, and between this virtual complex and the reality it reduplicates–the child’s own body, and the persons and things, around him. This event can take place, as we have known since Baldwin, from the age of six months, and its repetition has often made me reflect upon the startling spectacle of the infant in front of the mirror. Unable as yet to walk, or even to stand up, and held tightly as he is by some support, human or artificial (what, in France, we call a ‘trotte bébé’), he nevertheless overcomes, in a flutter of jubilant activity, the obstructions of his support, and fixing his attitude in a slightly leaning-forward position, in order to hold it in his gaze, brings back an instantaneous aspect of the image. For me, this activity retains the meaning I have given it up to the age of eighteen months. This meaning discloses a libidinal dynamism, which has hitherto remained problematic, as well as an ontological structure of the human world that accords with my reflections on paranoiac knowledge. We have only to understand the mirror stage as an identification , in the full sense that analysis gives to the term; namely, the transformation that takes place in the subject when he assumes an image–whose predestination to this phase-effect is sufficiently indicated by the use, in analytic theory, of the ancient term imago.

For Lacan, all knowledge is paranoiac because it is built directly upon deception, and in this way he directly opposes himself to Cartesian theories of the subject which derive their power from the reflective axiomatism of the cogito. He can say this because he understands the mirror stage as an identification. In Freudian theory, identification is always identification with another, especially an ideal image of oneself. This assumption of an image is understood to be an ideal mental object from the child’s earliest memories–that we have an imagined ego-ideal which we strive to identify with. In other words, the ego is a fiction:

This form would have to be called the Ideal-I [je-ideal], if we wished to incorporate it into our usual register, in the sense that it will also be the source of secondary identifications, under which term I would place the functions of libidinal normalization. But the important point is that this form situates the agency of the ego [moi], before its social determination, in a fictional direction which will always remain irreducible for the individual alone, or rather, which will only rejoin the coming-into-being (le devenir) of the subject asymptotically, whatever the success of the dialectical syntheses by which he must resolve as I his discordance with his own reality.

The agency of the ego–a phrase which ought to be of some interest to artificial intelligence experts–is identified prior to its social determination as an irreducible fiction, one which cannot be integrated into being-in-the-world by any sort of dialectical synthesis. Yet we are driven towards precisely such a resolution, and this is the rupture in which the ego circulates as a pulse, the cut in which we attempt to resolve our own discordance with ourselves, that is, the break between ourselves and our own reality. Whether or not “Can we model/simulate such a rupture?” is a meaningful question, we shall have to leave for another time.