Fractal Ontology

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.
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Science, Information and Time

There are no whole truths: all truths are half-truths. It is trying to treat them as whole truths that plays the devil.

Alfred North Whitehead

It is necessary to go beyond all the pieces of spoken information; to extract from them a pure speech-act, creative story-telling which is as it were the obverse side of the dominant myths, of current words and their supporters.
It is also necessary to go beyond all the visual layers; to set up a pure informed person capable of emerging from the debris, of surviving the end of the world, hence capable of receiving into the body the pure act of speech.

Gilles Deleuze (The Time-Image)

Becoming unfolds along spatial and temporal symmetries. Biogenesis is the slow process of isolating extensive differences (from a million intensive differences) and making its form hard, becoming like a diamond or like a stone in the river — so that the difference become invisible to the stream, to the flow, but resists and therefore modifies the flow imperceptibly. (more…)

Part One: Criticism and Untruth-Machines

A. Neurosis and Transcendence: the Algebra of Bad Conscience

We are healed of a suffering only by experiencing it in full.  Marcel Proust

For Nietzsche, uncovering the peculiar logic of the unconscious, revealing the function of this or that unobserved striving, would only form part of the analysts’ role. A rich, analytic transformation of the real space of mental (political) activity is the full meaning of diagnostic criticism. Any real diagnosis contains a hard criticism of declining mental (social) habits. Criticism moves towards a healthier biopolitics. Diagnosis isolates cycles, reaction-patterns, irresponsible and neurotic aspects of mental and social processes.

This selective isolation, the method of genealogical deconstruction may seem purely negative and critical; and indeed, it amounts to a profound negation of conventional modes of thinking and feeling. But there is also always a powerfully positive sense of diagnosis: to indicate and affirm the pathways which return us to health, which unhinge our bodies from habit, which bring us to a new earth.
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Symmetric Relations

A scientific theory classifies phenomena based on a universal set of structural relationships. Experiments and theories which deserve the name scientific thus share a coherent set of properties. First, they are systematic, meaning that phenomena as presented possess certain structural or virtual unities despite actual or potential diversities. A fully systematic theory is also complete in that nothing is arbitrarily left out of the universe of discourse.

Events, spaces and processes are presented as approximating a mode of relation which is in every case either symmetrical or complementary, and possibly even transitive (symmetrical and complementary.) Consider the relation between two inter-connected processes A and B. A symmetric relationship could be as follows: A exhibits behavior x when B exhibits behavior x, and A exhibits behavior y when B exhibits behavior y. Complementary relations, on the other hand, could be (for example): A exhibits x when B exhibits y, and A exhibits y when B exhibits x. Complementary relations are characterized by a disjoint or heterogeneous symmetry which distinguishes them from the smooth or homogenous symmetries of the first type of relation.
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The following is the first half of chapter 1 from Jean-Hugues Barthélémy’s book Penser l’individuation: Simondon et la philosophie de la nature. Paris: L’Harmattan, 2005. p. 37-48. Original translation by Taylor Adkins on 10/22/07.

Chapter 1

The concept of object and the concept of subject, in the same virtue of their origin, are limits that philosophical thought must overcome. –Gilbert Simondon

1. Ontology and ontogenesis: from Bergson to Simondon

The philosophically fundamental watchword of all Simondian thought undoubtedly resides in the idea according to: the process of individuation cannot be ob-jectified by knowledge, since the former is produced by the latter if the knowledge of individuation is itself the individuation of knowledge. This is why the principal introduction of his thesis ends with these lines:

We cannot, in the usual sense of the term, know the individuation; we can only individuate, individuate ourselves, and individuate in ourselves; this seizure is thus, in the margin of knowledge properly stated, an analogy between two operations, which is a certain mode of communication. The individuation of the real exterior to the subject is seized by the subject thanks to the analogical individuation of knowledge in the subject; but it is through the individuation of knowledge and not by knowledge alone that the individuation of (non-subject) beings is seized. Beings can be known by the knowledge of the subject, but the individuation of beings can be seized only by the individuation of the knowledge of the subject.[1]

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In the first place, singularities-events correspond to heterogeneous series which are organized into a system which is neither stable nor unstable, but rather ‘metastable,’ endowed with a potential energy wherein the differences between series are distributed. (Potential energy is the energy of the pure event, whereas forms of actualization correspond to the realization of the event). In the second place, singularities posses a process of auto-unification, always mobile and displaced to the extent that a paradoxical element traverses the series and makes them resonate, enveloping the corresponding singular points in a single aleatory point and all the emissions, all dice throws, in a single cast. In the third place, singularities or potentials haunt the surface. Everything happens at the surface in a crystal which develops only on the edges. Undoubtedly, an organism is not developed in the same manner. An organism does not cease to contract in an interior space and to expand in an exterior space–to assimilate and to externalize. But membranes are no less important, for they carry potentials and regenerate polarities. They place internal and external spaces into contact without regard to distance. The internal and external, depth and height, have biological value only through this topological surface of contact. Thus, even biologically, it is necessary to understand that ‘the deepest is the skin.’ The skin has as its disposal a vital and properly superficial potential energy. And just as events do not occupy the surface but rather frequent it, superficial energy is not localized at the surface, but is rather bound to its formation. Gilbert Simondon has expressed this very well: the living lives at the limit of itself, on its limit… The characteristic polarity of life is at the level of the membrane; it is here that life exists in an essential manner, as an aspect of a dynamic topology which itself maintains the metastability by which it exists… The entire content of internal space is topologically in contact with the content of external space at the limits of the living; there is, in fact, no distance in topology; the entire mass of living matter contained in the internal space is actively present to the external world at the limit of the living… To belong to interiority does not mean only to ‘be inside,’ but to be on the ‘in-side’ of the limit… At the level of the polarized membrane, internal past and external future face one another. [Gilles Deleuze, Logic of Sense. Trans. Mark Lester with Charles Stivale. New York: Columbia, 1990. p. 103-104.]

Gilbert Simondon, L’individu et sa genese physico-biologique (Paris: P.U.F., 1964), pp. 260-264. This entire book, it seems to us, has special importance, since it p (more…)

Cellular automata

The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty. D’arcy Thompson

All organisms are modular: life always consists of sub-organisms which are involved together in a biological network. The interrelations between organ and organism form a series of feedback loops, forming a cascading and complex surface. Each organ parasites off the next, but this segmentation is not spontaneous. Rather, it is development itself, the decoupling of non-communicating spaces for the organization of divergent series. Creative evolution, self-organization and modularity are the same idea.

The theory of the development of metabolic modularity is called morphogenesis. ‘Morphogenesis’ in its literal sense means the creation of shapes or forms. But in the (relatively) narrow sense we intend it here, morphogenesis is a self-symmetry of the biological structure (onto itself) which allows it to develop in such a way as to divide while remaining unseparated, that is: to ‘individuate,’ or split apart into fused symmetrical segments.
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The following is Michel Serres’s essay “Eternal Return” in Hermes IV: Distribution. Paris: Les Editions de Minuit, 1977. pp. 115-124. Original translation by Taylor Adkins on 10/10/07

Philosophers glorify Nietzsche for having suddenly rejoined the Greeks through their fulgurating intuition of the Eternal Return. Either from an ignorance of ethics or incomprehension of the general figure that this thesis takes in his philosophy, I reduce this to a vision of the world. Vision with the meaning of sight, and world with the sense of the world. All simply.

If time is considered in geometrical figures by optical interceptions and a mechanism of movements, the Eternal Return is cosmological. In that case, the solar system (and it only) has been calculated by Laplace. Celestial Mechanics and the Exposition of the System of the World established rigorously, for the first time, the mechanical invariability of the large axes for the planetary orbits. The stars turn forever. This eternal return reduces the world to the exclusion of the universe, and reduces mechanism to the exclusion of other sciences. Neither the Greeks nor the classical age ever obtained this demonstration. Conversely, the time that we consider is reversible.

If the time that one endorses is that of a formation, of bodies as spheres, and with which one tries to surpass mechanical reversibility, then, if there is return, it is cosmogonic. However, cosmogony enters science little by little around the middle of the 18^th century, with Thomas Wright and Buffon. If Laplace has erased the latter in the seventh note of the Exposition, the former has inspired Kant. Natural History and the Theory of the Sky marks the appearance of the Eternal Return in scientific cosmogony.

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It is characteristic of our age that we no longer remember how to feel utopia. To experience the absence of place, a break in the flow of time. But the utopian vision is not merely a smooth or well-organized space outside of history, beyond danger and death. It is also a powerful impulse, a primary affect of sociality. The aporetic flash of insight which is glimpsed in the symphonic vision of an actual utopia is so overpowering it actually exerts an unbinding force upon thought, deforming and deconceptualizing, breaking truth down into its rhythms. Utopia as commonly conceived is above all a logical place, a space where things make sense. But what if they don’t make sense to us anymore? A utopian thought imagines radical transformation, and accordingly is a thought which transforms thought, an image taken for a radical act. But there is no act, only images of free subjects. Only endless contradictions. But we forget they are more than contradictions. They are indications. The utopian thought is above all a directed thought, a thought of direction. We can’t remember how to point to ‘nowhere’. We should not allow ourselves to forget how to feel the irony of the utopian thought. We can only sketch the subtle complexity of this ancient impulse, noting this or that feature. A general utopian political project is a false ideal; it makes utopia an act, something hard, inert, dangerous. Futurism is false; we must be against the generic utopia. We must try always to see the more subtle, and political sense of nowhere.
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Artificial intelligence stands in need of a fresh thought: a new thinking of complexity, of the virtual, and of machines. Instead of a virtual founded upon forms which remain forever the same, we need an idea of the virtual founded upon difference itself. We need a creative virtuality.

The task of building a robot demands a lucid and algorithmic way of grasping the frame problem. An adaptive principle of distinguishing problem spaces, some genetic evolution culminating in the capacity to mark a difference. So how do the sense organs evolve? Which is another way of asking: how does experience form?

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