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Orders of the Real


Alan Sondheim

Writers Forum

Copyright © Alan Sondheim, 2005. The right of Alan Sondheim to be identified as author of "Orders of the Real" has been asserted generally in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988.

Cover image Copyright © Alan Sondheim, 2005

ISBN 1 84254 601 5
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Aphoristic Essay on Analog and Digital Orders


2 Filtering and Analog Digital


3 On Code and Codework


4 Coding, encoding, confusion


The Abacus, Infinite and Otherwise


The Laying-Out (infinite abacus)


Plain and Heap


Infinitely Small


Infinite abacus, accountancy, culture


What remains after the deluge


Implementation of Infinite Abacus

Towards A Primary Differentiation Between Film and Video


Presence of Future Presence of Video: Thing II




Video II


Postmodern Checklist


Writing for the Return of It




The Defuge Rhyme


Defuge ii


Defuge iii: the impasse


Defuge iv


defuge, fifth and final section, explanations:


Future Culture


Aphoristic Essay on Analog and Digital Orders

The digital: by digital I mean discrete. By digital I mean systemic, characterized by systematization, parameterization.

The analog appears continuous; the digital appears discrete, broken.

In everyday life, the digital is the result of an intervention.

An intervention is a mapping. Every mapping, unless a mapping of itself (ikonic), leaves something out.

The intervention requires the setting of a standard raster. A raster is a filtering of a quantity, almost always with discrete steps. Think of a raster as a screening, creating elements out of a continuous bandwidth, then quantifying those elements.

The elements are ordered. The raster sorts the continuous fabric of the real into separable categories.

The raster is standardized so that information may be transmitted and received through coherent channels, by means of a coherent transmitter and receiver.

The standardization of the raster is a protocol. The protocol must be agreed upon by both sender and receiver.

In everyday life, the establishment of a raster and protocol requires energy and communication. Raster and protocol must be communicated.

After raster and protocol are established, the parceled semantic content, coded by raster, may be communicated.

Coding and community establishes raster and protocol. Encoding codes an object from analog to digital.

From the viewpoint of the digital, the analog is forgotten; the process is irreversible.

A digital parcelling is accurate only to the limits of a particular and conventionally-established tolerance. The tolerance, more often than not, is tied to economy. In general, the greater the capital available, the lesser the tolerance.

The analog possesses no tolerance. The analog is there.

The digital is never there. The digital is always process, in-process.

If the digital is indexical, "pointing towards" a mapping of the continuum, the analog is that scale. The analog is ikonic, the digital is indexical.

The distinction between the digital and its referents or domains is ontological; the distinction between analog and its domain is epistemological.

At zero tolerance - "no room for error" - and an infinitely-fine raster, the digital is equivalent to the analog. The map, in other words, is exactly equivalent to the thing itself.

The thing itself is equivalent to the thing itself; this is identity.

At infinite tolerance - infinite error permitted - and infinitely-coarse raster, the digital is equivalent to a kind of mark.

A mark totalizes its demarcated.

A mark is an instance.

There are numerous "real worlds" of nearly-decomposable systems. (Herbert Simon) The world of everyday life appears continuous; it is only in dreams, for example, one encounters jump-cuts - sudden shifts of place and time. This continuous world appears analogic.

The world of symbols and signs - the world of languaging and inscription - appears discontinuous, syntactic, and digital, characterized by discrete moments and entities.

The filmworld (Christian Metz) appears an entanglement of languaging and continuities. Because film is an operable subject (i.e. a subject whose discursive field is somewhat definable), the entanglement tends towards polarities, interpretations, interpenetrations, etc. Frames are digital; the diegesis is analog (continuous story), and digital (semiotics of narrative); the psychoanalytics are digital (continuous processing of the subject-viewer).

Neurophysiology implies, not only entanglements of digital (neural firings) and analog (potentials), but the problematizing of the analog / digital split on ontological / epistemic grounds. The domains are both inseparable and problematized; the distinction is useless.

The same is true on the level of fundamental physics, at least as far as current research goes; there are quantum processes that involve discrete levels, and there are continuums; there is the breakdown of space-time at small distances / times, and so forth. If the world is information "all the way down," the coding at this level is again neither analog nor digital.

In other words, mental and fundamental physical events and processes abjure any clear distinction between analog and digital, to the extent that the phenomenology of both is inappropriate. If there is a "book of nature," its syntax is as yet unknown; perhaps the idea of syntax itself is inappropriate as well.

One is always searching for the syntactics, however; it is by means of coding and encoding that the universe is grasped.

The analog slips through the fingers. The world slips through the fingers.

Any element of a raster is independent of any other element. Any element may be transformed without transforming any other element. Truth values within the digital are problematic. The digital is cleanly separable, breakable. The digital is clean.

Any element of the analogic real is interconnected and inseparable. The transformation of any element alters any other element. Truth values are inherent. The application of truth values is digital. The analogic is a membrane. The analogic is dirty, inseparable, unbreakable.

The dirty analogic problematizes its symbolic. The clean digital is already symbolic.

The digital object is analogic.

The analogic representation is digital.

Ghosts are embedded within the analogic. Ghosts are excluded from the digital.

Absence or exclusion from the digital is equivalent to non-existence from the viewpoint of the digital. Ghosts are existence and existents within the analogic.

The digital envelops the act of differentiation; the analog envelops integration. The analog smoothes what the digital disrupts.

The digital requires a place to stand. The digital requires an origin. The analog of Cartesian coordinates is countermanded by the discrete and arbitrary location of the origin.

The digital draws a distinction; the analog erases it.

To draw a distinction is the construct a potential well, within which the distinction functions, in spite of the corrosion of the world.

To erase a distinction is to corrode it, to sublimate it to the analogic real, the plasmatic world.

The plasmatic world is the heated world in which distinctions last less time than the processes required to convey information. The plasmatic world, a theoretical construct, is necessarily inoperable. The world of the landscape - without a preferred viewpoint - is such a world.

The cold-world is the world of the permanence and transformations of distinctions. The cold-world is a world of potential wells, in which signs convey, remain - in which structures remain intact, in which semantic content flows through structures.

The digital quantifies the analog.

The digital carries a price-tag.

Coding, by its very nature, is digital, that is to say, discrete.

Never, "above", as "below", but "as above, "apparent" as below. Metaphor and metonymy are always already tropes, within the digital.

The signifier does not reference the signified; it creates it from the analogic. The creation of a signifier re-inscribes the signified elsewhere; as in Saussure's example, the signifier never operates "within" the real, but within a chain of signifiers, a hermeneutics on the plane of the Other, which inauthentically appears to create the "Originary" plane, i.e. Creation.

To create by speech ("and the Lord said") is always already to embody the creation as inscription. Inscription separates the inscribed and thereby created entity from its complement, the inscribed world external to the inscribed and created entity.

The totality of inscriptions necessarily forms a coherent and closed system, since the system is, after all, created by humans or other organisms, and their cultures.

Somewhere von Foerster characterizes organism by negation. Negation is the first speech act. Negation is the primary speech act, "not this, not that" - "avoid that - that is dangerous" - "do not go there."

To negate is to inscribe. To negate is to create. The creation of an entity is always a carving-away. The creation of an entity implies a reduction relative to that entity.

The digital is the carving-away of what is deemed extraneous. The digital saws into the extraneous, which is its residue.

The residue is the residue of the analog; the residue is parasitic, noise.

The digital is noiseless, absolute silence.

The analog is absolute noise.

The circle of signifiers washes against mental impressions. The image of something is always already a construct (Sartre), rule-bound, but the image of the image is analogic.

If something is an analog of something else, both suffer from similar noise. Both suffer from similarity.

If something is a representation of something else, both draw structures from each other.

The analog is unstructured; the digital is structured.

The analog is communality, use-value. The digital is community, exchange-value. Exchange may be direct or indirect, transitive. Exchange may be based on apparent equivalence, on agreement, on contract. Exchange binds entity to entity. Exchange defines entity. Exchange defines entity in relation to (by virtue of) entity.

Analogic use-value is imminent and immanent. Digital exchange-value is distanced, defined. Analog is subject; digital is object. The object of digital is subject to analog. Exchange replaces use. The subject of analog is object to digital. Exchange replaces use.

Digital is always already a presumed contamination of the real. The presumption is always already false.

The analog is always already a presumed healing or suturing of the real. The presumption is always already false.

Without the digital, communication would be impossible. The ideality of the feral world is equivalent to the world under erasure.

To throw away the scaffold is to retain it. To retain everything, releases everything.

"Wovon man nicht sprechen kann, darueber muss man schweigen." (Wittgenstein) - is already lost.

2 Filtering and Analog Digital

Reworked from a 1978 Toronto Notebook, "On the successive eliminations of the entity in transformations" or rather all that is necessary from the diagram

a a' a"

f f'
The function f moves a to a'; f' moves a' to a'' and of course there is a composition f'f(a)  a' or some such. a disappears as an entity, and one might generalize, considering a series of functions f, f', f'', f''' ... such that (ff'f''f'''(z)) is a filter over z. In the lifeworld, f^n extends in either direction, i.e. n ranges over the integers at the least.

In reality, n ranges over the continuum. Every entity z carries its filter and a filter is non-existent without an entity. The continuous transformation of the entity is defined by the filter and vice-versa. Since z may split in the process, the filter may split. The series of f need not define any particular entity, but may be considered split from a previous entity, i.e. one out of an almost infinite number of processes, infinite in relation to the continuum. In this fashion, the worlding process is visible, the entity disappears, as entities do. Entities are named in any case in relation to space-time; too great a dispersion, and entity disappears qua entity; the background microwave radiation of the universe is an example. Too small a dispersion, virtual particles for example, and entity entity is ontologically problematic. Within everyday life, water and other liquids, as well as gases, are not considered entities, while glass, also liquid, is. It's a question of a family of usages in relation to viscosity for example. There is also a notion of intrinsic identity based on communality and communication; humans are entities, although rapidly undergoing decomposition. Reichenbach's genidentity may be of value here; it references the actual material substrate of a coherent object, held together over a substantial period of time, and undergoing change qua object. Such an object brings human phenomenology with it; objects out- gas, wear, dissolve, split, from what might temporarily be considered an origin. All origins and all endpoints are subject to filtering, which dissolves them as such. One is left with continuous birthing, continuous languaging and worlding, something related to Bohm's implicate order on one hand and maya on the other. Of course the filtering itself is filtered, there is no end to it. To be human is to attempt to halt such, impede what is identified as dissolution, death, permanent impediment.

Ownership arises out of this, as does the urge to collect, related to the urge to hunt, to permanently annihilate, absorb, be reborn in the blood of the other. To stay with the filter is to remain analogic, deeply human, chthonic; to impede is to construct the digital, build, aerate, delude. The digital is always already inauthentic, Vaihinger's as-if which resides for and in the moment. Culture veers among the various orders, as if the world and its history is ordered and orderly; it is the sympathetic, not empathetic, magic of this that allows us to survive.

3 On Code and Codework

Consider a well-defined entity x, and its complement -x. Then x^-x = N, the null set. Consider a second entity y and -y, y^-y = N. Think Nx and Ny, the null set relativized to x and y. Consider three entities x, y, z, and take pairs xy, yz, zx. These are symmetrical yx, zy, xz. Let ab stand for a^b. Then xy, yz, zx are equivalent to null. Let x, y, z divide a planar region into three regions bordering on each other. Let x@y represent a line equidistant from the entities x and y. Then x@y, y@z, z@x all meet at a single point. Divide the plane so that all entities are grouped in triads; each triad meets in a single point. Divide the plane so that these single points are grouped in triads and so forth. What branches are available? Is a single point reached? To operate with x and -x such that x^-x = N is to operate with discrete entities common to distributive Aristotelian logic.

Now consider a second set, X, Y, etc., mapped onto the first; the mapping may be one-to-one, one-to-many, many-to-one. If the first, the resulting mapping is reversible. If the second, it is reversible but the coding itself is not reversible. If the third, the mapping is not reversible; the result is a set of possibilities, not a single one.

Codes are mappings. There are two types of codes, declarative and performative. An example of the former is Morse; it is one-to-one, but all that is produced is equivalence. An example of the second is Perl; Perl codes procedure. If procedure is coded, then the contents of the procedure are doubly coded. If a Perl program parses {A} to produce {B}. Then the primary coding is the program which constructs and orders procedures. The secondary coding is {A} -> {B} which may be considered the semantic plane of the code.

In Eco's A Theory of Semiotics, only a rule "may properly be called a code," and a rule couples items from one system with some from another. Eco extends the possibility of code to "a set of possible behavioral responses on the part of the destination." This is performativity. In codework, primary and secondary coding are entangled. Entanglement may be considered noise in the system. With noise, the null set N is blurred across fuzzy sets with parasitic inputs; x^-x and x^y may be and usually are ill-defined. It is this ill-definition - which functions for example in current definitions of words like freedom - that tends towards political economy. Political, because culture and the social are at stake in relation to the definition which is always already under contestation, and economy, because there are limited resources and examples for any particular definition.

With codework, meaning itself is problematized as a result of entanglement. In Eco, it is the code which reaches a destination, not the message. The decoding of the message may or may not be equivalent to the source. Noise is always already present and is considered within the channel. This is the T-model of the parasite described by Serres. Eco states "When a code apportions the elements of a conveying system to the elements of a conveyed system, the former becomes the expression of the latter, and the latter becomes the content of the former. A sign-function arises when an expression is correlated to a content, both the correlated elements being the functives of such a correlation." Code is a collocation or system (not necessarily the same) of processes; processes are performative; both are temporally-embedded. A mapping f(x) = y is not temporally-embedded; thus the mapping of the even numbers onto the number system may be considered an ideality which is, regardless of temporal processes. The structure is given all-at-once within the formula (and its proof); its proof is a carrying-out of the truth-value, or a revealing of the truth-value, of the structure.

There are mappings which are systemic, i.e. structure-dependent, and there are mappings which are non-systemic or purely heuristic, such as randomly assigning letters in a message to a triple number (page / line / letter-position) originating from a particular edition of a particular book. In all of these instances, of course, terms like "system" and "assign" are themselves fuzzy; nevertheless there's a tremendous difference between the anecdotal and the structural, and there are practical differences in the ensuing codes and their employment. Peter Gardenfors, in Conceptual Space, The Geometry of Thought, considers "conceptual spaces" which are related to tessellation of the plane. This reminds one of Peirce's simplest mathematics, which is also related to Venn diagrams; in all of these, sets of entities and concepts in the life-world are mapped into other spaces which may or may not reflect thinking processes. Geometry is always bound by its spatial representations; there is no reason to think, at all, that the mind necessarily works through spatial or any representation for that matter. Representation is always coded; Sebeok, in Approaches to Animal Communication, "Semiotics and Ethology," points out that the "model suggested here entails a communication unit in which a relatively small amount of energy or matter in an animal (a) the source, brings about a relatively large redistribution of energy or matter in another animal (or in another part of the same animal), (b) the destination, and postulates (c) a channel through which the participants are capable of establishing and sustaining contact." Maturana somewhere talks about such communication as the mutual orienting of cognitive domains. Sebeok states that "Every source requires a transmitter which serves to reorganize, by a process called encoding, the messages it produces into a form that can be understood by the destination. The source and the destination are therefore said to fully, or at least partially, share (d) a code, which may be defined as that set of transformation rules whereby messages can be converted from one representation to another." As long as one sticks to transformation rules, code is always procedural. Sebeok states that "The string generated by an application of a set of such rules is (e) a message, which may thus be considered an ordered selection from a conventional set of signs."

I think that ordered is problematic as well, since there is clearly a qualitative difference between book-ordering as described above, and a set of rules based on mathesis. Where does the arbitrary come in? One might say - and this is an important principle - that the content of a code itself is directly correlated to its arbitrariness. In this sense, the measure of a code is related to the entropy of information within the process of encoding. The greater the degree of the arbitrary, the more difficult to break, the greater the entropy and therefore the greater the degree of information within it. This is not on the level of the double-level of the code, i.e. the content it operates upon, if there is such content (as in the Perl example above), but within encoding itself. Every encoding is an encoding of encoding; if the encoding is fully realized by the product of the code, then its semantic content / information is low. If Morse encodes a message, more than likely the message may be decoded based only on the distribution of letters. The Morse content is low. If a book is used, the decoding is increasingly difficult and the content of the code is high.

This is also related to issues of redundancy vis-à-vis Shannon and Weaver. Note that a message and its destination are irrevocably ruptured; there is no guarantee that an equivalence is attained on any level. Code operates more often than not on an ontological plane disassociated, or associated by intention only, with both its source and its decoding; there is no guarantee that the source and the message-at-its-destination have anything in common. There is no guarantee of the coherency of the practice of coding in a particular case, no guarantee of one-to-one or one-to-many or many-to-one, no guarantee of a zero-parasite-demographics - no guarantee that the channel, in fact, has not been derailed altogether, as often happens with bacteriophages. Bateson, in Bateson and Ruesch, Communication, The Social Matrix of Psychiatry, states "codification must, in the nature of the case, be systematic. Whatever objects or events or ideas internal to the individual represent certain external objects or events, there must be a systematic relationship between the internal and the external, otherwise the information would not be useful." Today one can say, "otherwise the information might not be useful," since it is precisely in the breakdown of systematic relationships that innovation emerges.

But meaning may be produced even out of tautology. For example, propositional logic may be derived from the Sheffer stroke, "not both A and B"; it can also be derived from its dual, "neither A nor B." What can we say about these? Only that they represent, as processes or cullings of particular bounded universes, an unbinding / unbounding - "neither A nor B" points elsewhere altogether, and "not both A and B" points either elsewhere or towards an underpinning of union. At the heart of this reduction of propositional logic, is a tendency towards dispersion, towards wandering, the nomadic, even though the symbols within the calculus proper are completely mute. The Sheffer stroke and its dual, by the way, are related as well to the processes of inscription with which this essay began - for what is x^-x, than an inscription of an entity, a process of coding (and all coding is inscription of one form or another) the real for the purposes of comprehension, a process that produces, not only meaning, but all the meaning there is. There is no outside to the sememe, just as there is no landscape without a viewpoint. In this sense we are bounded, and bound to be bounded.

I want to acknowledge and take responsibility for interpretations here which are necessarily shallow and possibly misrepresentations as well; this is true in particular of Gardenfors' book which is complex, and which I have just begun. I have found the concept of conceptual spaces of use here, as a way of thinking through code, process, representation, sememe, Eco's planes of expression and content, etc.; but I do not yet understand it within Gardenfors' theory. I have also completely neglected what I think is most necessary, a detailed typology of codes, taking for example temporality into and out of account in various ways. I cannot see how one can proceed without a deep reading of Eco's "Theory of Codes" which is the major section of A Theory of Semiotics. In the same book, Eco develops a typology of sign production which is quite useful. Other references might be Barthes' S/Z (although I constantly find his poeticizing beautiful and problematic), and a quite useful early book, Symbol Formation, An Organismic-Developmental Approach to Language and the Expression of Thought, Werner and Kaplan, Wiley, 1963.

Finally, it is clear from all of the above that at best one can sketch a discursive field, complete with intensifications themselves representing concepts; this is similar to a loosely-structured Wittgensteinian family of usages. "Code," like "game," is always a strategy and a wager from a theoretical viewpoint, and like much such viewpoints, everything and nothing is at stake. One would hope for a future of usefulness, politics, and aesthetics to emerge; the danger, in relation to codework itself, is that a style develops, and that the uneasy underpinnings - which at least for me are the most interesting aspects of it - eventually disappear, absorbed back into issues of genre, etc.

Code, like the processes of postmodernity, is always in a state of renewal, whether or not the type or concept remains, and at stake within this renewal is our interpretation of the world itself - our actions and our reading of being and beings. Wittgenstein's "silence" at the end of the Tractatus is code's success, not failure; it is the always already of the always already, but not its foundation.

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