CHAOSOPHY 1993-22
An ASKLEPIA FOUNDATION Journal
ODE TO WHITE NOISE AND STRANGE LOOPS
The Concepts of Form and Intentionality in Information Theory
by Iona Miller, ©1993
ABSTRACT: Physics deals with the energetic aspect of the world. Information theory deals with the communicational aspect, the message from the external world (universe) to the individual and his reactions. Information is a quantity whose value depends on its usability, what it adds to a representation--its originality, unforeseeability. The general study of information theory can be applied to perception in the human receptor.
The emergence of imagery from white noise--the figure/ground distinction of Gestalt--is one implication relevant to process-oriented therapy and certain philosophical considerations about the nature of chaos and order in reality. Wave fronts exhibit a fractal nature, including sound waves. Meaningful sound, such as music and speech lies in between total white noise and the monotone of indefinitely held pure notes.
We tend to take the constant imaginal flux of the stream of consciousness for granted, rarely focusing our conscious awareness in that direction. But we can experientially "decode" the universal "message" it contains for us in terms of potential holistic repatterning. No universal message is really "transmitted" because it is a nonlocal quantum phenomenon of consciousness. There is no channel or receiver, but the classical ego interprets it that way--as incoming information.
"...Any metaphysics, any reflection of the individual on the world, implies a theory of perception, and any consideration of the latter will react on the former, whether or not one accepts the esse est percipi of Berkeley. Thus, a closed circuit of knowing exists; our concept of the universe depends on the knowledge that we have of the process of perceiving it."
--Abraham Moles, INFORMATION THEORY AND ESTHERIC PERCEPTION
INFORMATION THEORY
The succession of levels of perception reflects the concept of Gestalt, of form perceived as whole. Each sensory channel has several levels of perception which correspond to a distinct message and each possess symbolic repertoires which differ widely in extent and structure. Repertoires grow smaller as they appeal to higher functions.
The most original message is that composed in a system such that all the symbols are equiprobable, where uniform distribution of the occurence of symbols gives the maximum possible choice in constructing the message. This maximum information is equivalent to maximum entropy--thus chaotic.
Thus, a message of maximum information may appear senseless if the individual cannot decode it in order to make it intelligible. Coding means translating the message into a special language adapted to the channel to increase the flow rate of information.
Redundancy furnishes a guarantee against errors in transmission, since it permits the receptor to reconstruct the message even if some of its elements are lacking on the basis of a priori knowledge of the structure of the language. A situation of communication is defined by choosing a channel and level of observation adapted to transmitter and receiver.
Information theory sheds light on the concept of form. Form, or Gestalt, is a group of elements perceived as a whole and not the product of a random collection. Form is thus a message which appears to the observer as not being the result of random events.
Adaptation to the environment and learning results from being able to select from complex and redundant messages of the environment a few elements assembled to provide constant control over the external world.
Therefore, to perceive is to select; to apprehend the world is to learn the rules of perceptual selection. Any form, Gestalt, is the first element of a structure and as such expresses the ascendancy of the intelligible over the perceptible.
The message carrying the most information is also the one most difficult to tranmit because it reduces its symbols to the elements just perceptible by the receptor (subliminal, unconscious); that is it adapts to the channel. On a television screen it appears as "snow," a gray, perpetually agitated, foggy undulation with little, capricious, constantly changing outlines.
We can conjecture that a similar phenomenon occurs in dreamhealing where participants report uniformly gray or mottled imagery, often in the form of clouds or mists.
In over-all appearance, it is indistinguishable from background noise, with a uniform probability distribution for its elements. It loses all interest because it lacks intelligible meaning. The message contains too much information, and exceeds our capacity for understanding. It therefore creates boredom. When it is learned, the signal becomes automated and is consigned for subliminal response only--a change in state of consciousness of its informational content. They remain below the awareness threshold in the stream of consciousness.
The message of maximum information has no redundancy, and we have no a priori knowledge about its evanescent structure. It is easy to render approximately, but virtually impossible to duplicate--ever. It is most fragile, and we cannot guess, practically, what will follow on the basis of what has preceded.
It's only interesting if we know how to organize it. Otherwise it doesn't capture our attention spontaneously. It lacks esthetic value completely, because it does not appear at all to the natural capacities of the receiving individual. Absence of structure or internal organization is connected with too large a flow of information. In fact, the absence of structure, of apparent organization, is equivalent to too large a rate of original information.
Therapy provides a temporary channel, or structure for the stream of consciousness. It closes the circuit on the self-recursive loop which gets us out of the unregenerate egoic state of consciousness.
Maximum information capacity of a channel is a limit attained only for a receptor who is totally ignorant of what might be transmitted to him, for whom all symbols are equiprobable. (Ref. Babe of the Abyss).
A symbol is a constant mode of grouping subelements which (may be or) is known a priori. The sets of collections follow an inherent rule which marks their intelligibility along the continuums of foreseeability/unforeseeability, intelligibility, and originality.
Thus, the concept of symbol is intimately connected to that of form. The concept of intelligibility or signification becomes explicit through this connection. The study of signification is essentially a study of symbolism. To create an elementary form is to assure in the message a redundancy, an at least statistical foreseeability.
Foreseeability is the receptor's capacity to know, as the message unfolds in time or space, what will follow on the basis of what has been transmitted; it is the capacity to extrapolate the temporal or spatial series of message elements, to imagine the future of phenomenon on the basis of its past.
Foreseeing via awareness of archetypal patterns; in holograms or fractals, the whole is inherent within the part. Emergence in terms of symbolism could mean extruding a form from undifferentiated consciousness. It is the panoply of images (symbols in context) that form the stream of consciousness.
The degree of predictability is equivalent to a message's degree of coherence, the proportion of regularity. Foreseeability is a statistical liason between past and future, through autocorrelation--a recursive function related to memory. It is a function of the interval over which the considered foreseeability extends.
Mean autocorrelation expresses their internal coherence, hence their tendency to become structures. The autocorrelation function is zero for a perfectly disordered phenomenon (chaos) and tends to either +1 or -1 for a perfectly ordered, that is, indefinitely foreseeable, phenomenon. If the form of a phenomenon is related to its autocorrelation, reciprocally the information content of the message must be a function of autocorrelation.
All our senses function through Fourier transforms. In Fourier analysis, there exist "components" and negative frequencies; in extending Fourier's integral to nonperiodic phenomena, there are harmonic "components" which precede in time the phenomenon itself (precursor waves). These creations of the mind suddenly congeal to become material entities which can be measured by experiment.
Phenomena perceptible on the human scale suggest the concept of periodicity, which when it is regular leads to the concept of rhythm via repetition--cyclic or reflexive time--chronicity, recurrence, retiteration. Repetition opposes multiplicity to unicity; it impresses on the mind the possibility of multiple occurences without suggesting the concept of periodicity. A completely irregular repetition provokes no expectation. Expectation is essential to foreseeability. Rhythm provokes expectation. The amount of periodicity is the degree of order in temporal organization.
The human individual's perception of periodicity (order) is most sensitive around one second. Below around 0.1 second, the phenomenon of repetition dissolves into continuity and the concept of periodicity vanishes. In vision and hearing after five to ten seconds, the mind doesn't expect the return of events, and the perception of periodicity wanes. Yet, as few a four ticks of a clock will lead to expectation quickly followed by boredom.
Within the length of the present, we can only integrally apprehend a limited, maximum number of information elements as a form. If the message is denser in informational content, either we neglect it or proceed to scan the field.
One of the fundamental characteristics of the human receptor is the existence of a maximum limit to the flow of perceptible information. When this maximum flow is exceeded, we select based on our previous experience, forms from the message presented to us. Forms are abstractions, elementary stages of intelligible. If this criteria fails us, we are overwhelmed, left behind by the originality of the message, and generally lose interest.
The message most difficult to transmit is that without redundancy (with maximum information), hence without any a priori form. It is both easiest to give an approximate picture of it and most difficult to give an exact picture of it. It is the most fragile of messages. Interestingly, this message is most devoid of esthetic value (it isn't art)--and of a priori meaning (it doesn't need interpretation).
Structures are equivalent to mental forms. The more structured a message is, the more intelligible it is, the more redundant it is, and the less originality it has. The psychology of form posits a figure-ground opposition. The figure (form) is defined completely only by its opposition to the background: Its organization detaches it from the disorganized. Differentiation is established between an amorphous background and contrasting, symmetrical, negative, complementary forms.
The meaningful signal emerges from the amorphous background. General lack of interest defines backgrounds against which interesting phenomena are to stand. Within the message are perturbations or errors, which also do not interest the receptor. This is the ubiquitous appearance of chaos at the most fundamental level.
WHITE NOISE: THE VOICE OF CHAOS
A certain amount of noise occurs because of the structure and spontaneous activity in the brain. Added noise is another possible link between neural nets and chaos, in addition to attractors. Adding 'noise' or 'temperature' to a system resets the connection weights by some random amount in simulations. In a top-down epistemology, it is neural nets "all the way down", biased by chaotic noise.
J.R. Eiser (1993-Chaopsych) has suggested that, "Perhaps chaos theory could help by offering a view of such fluctuations as an integral feature of any dynamic systems, and not just 'noise' or 'error', or an ad hoc correction mechanism. "
Goertzel points out that in chaos-based learning "noise" is not artificially added to the system, but "pseudo-noise" is inherent to the neural network's nonlinear dynamics. It can be automatically controlled by adding an additional level of feedback to the dynamics.
There is absolutely no structural difference between noise and signal, but noise is generally an undesirable perturbation in a transmission--interference by a chaotic agent perturbing an essentially ordered phenomenon. Perturbations make a signal deteriorate.
In reality, this morphological distinction is logically inadequate; they share the same nature, other than the intent of the transmitter. A noise is a signal that the sender does not want to transmit, or one we do not want to perceive, or receive, and try to eliminate. (repression, denial, tuning out others or aspects of reality, selective filtering, etc.)
By analogy with light, white noise is the prototype of perfect, ideal noise. It has no other characteristics than its perfect disorder; white noise is the expression of perfect disorder. In white noise any element of the repertoire can occur within any interval. It is a perfectly formless message.
This message is identical to the message most difficult to transmit since it uses simultaneously and randomly all the available elements of the repertoire. Optimal coding makes the most extensive use of all available elements of the repertoire, eliminating redundancy. Naturally, the receptor will have to decode this message and recast it in an intelligible form.
White noise is fragile; one white noise looks like any other. The only possible difference may be in the over-all intensity. Although the absence of intent more than the absence of form distinguishes a noise from a message, the limiting morphological case, perfect noise, is important. Form emerges from noise through temporal and material organization.
White noise is a perfect perturbation, a noise of practically infinite spectrum. To mask perception, a perturbation must be much stronger than the phenomenon. The receptor can perceive an organized phenomenon hidden inside an amorphous phenomenon. This may seem paradoxical since we might assume that a signal is masked when a more intense one is superimposed.
Within a channel, every message may be expressed as a temporal form, a function of time. Every alteration of the signal's form is reflected by an alteration of its spectrum, and reciprocality.
Einstein discovered that background noise is due to the agitation of electrons in conductors. He established that this noise is inherent in the nature of things and proportional to absolute temperature--just like the molecular agitation causing Brownian movement.
The only way, therefore, to reduce perturbation which drowns a signal in any channel is to diminish the range of frequencies it transmits--reducing its capacity, the extent of the repertoire of elements it can convey (archetype vs. complex). The choice of elements is reduced, particularizing a priori the nature of the signal which we want to amplify or receive, which is unknown.
Information gained in one direction is lost in another, according to the very nature of things as expressed in the uncertainty principle. In order to increase sensitivity indefinitely, we must know more and more about the nature (frequency) of the message to be received.
NOISE THUS APPEARS AS THE BACKDROP OF THE UNIVERSE, due to the nature of things. The Gestalt universal sound current is generated by chaotic perturbations. Any signal must stand out from noise. There is no signal without noise, no matter how little.
Signal emerges from noise, as order from chaos, and figure from ground. Noise is the factor of disorder (chaos) contingent on the intent of the message, which is characterized by some kind of order. It introduces a dialectic, figure-ground, connected with the dialectic, order-disorder, which constitutes the second law of thermodynamics.
Noise can only degrade the orderliness of the message; it cannot increase the particularized information because it destroys intent. Amplifying noise dissolves signal. The message disapppears into the background noise. Holding at the perceptual threshold is how subliminal audio/visual messages are constructed.
Disappearance is not a simple deficiency, a "drowning" of the interesting, meaningful phenomenon in the uninteresting background noise. Rather, for the human receptor this dissappearance is an "intellectual" operation, or more exactly, the failure of this operation. For the human receptor, it depends directly on the psychology of perception--a filtering process.
We can extract the signal only on the condition that we have an increasing amount of time, tending to infinity as the phenomenon is more deeply drowned in noise. In altered states of consciousness, such as Cosmic Consciousness, such an operation may become theoretically possible at the fractal "edge of infinity," the chaotic boundary, or twilight zone of imagination.
The limits of perception come up against the inevitable uncertainty principle, which determines the basic elements of sensation itself--the "texture," the "grain," of the message. From the dynamic elements we must draw the symbols which serve to construct the repertoire of fundamental elements. They can still be characterized by the qualities of the ancient elements fire, air, water, and earth--and ether, plasma, quintessence.
The length of presence is a sort of scintillation or "phosphorescence" from immediate perceptions, ranging from a fraction of a second to several seconds. This instantaneous memory is a reflex repeated indefinitely at ultra short intervals. Memory brings about the perception of duration connected with the sensation which fills up time. It dates events in our consciousness while the phosphorescence of perception lasts.
Memory makes it possible to perceive form in the course of scanning, in the environment and imagination. In a message too complex to be apprehended instantaneously, it represents the elementary memory necessary to the perception of autocorrelation. For example, it conditions the perception of temporal forms of rhythm and melody.
Memory affects mental structure based on the messages received. This structuring is education, and is facilitated symbolically, not photographically.
To summarize, the boundary of a form is an internal coherence which remains equivocal if it is not opposed to a ground having a different degree of coherence. An organizational signal always emerges against a disorganized ground, noise. Noise can only be logically defined on the basis of intent.
When the receptor is an individual and the transmitter the external world, the concept of intent gives way to that of choice, that is, of value judgement. In the absence of other operational indications, perceptual choice favors structured forms over amorphous messages. Thus, from a statistical viewpoint alone, this choice introduces a morphological distinction between forms and noises.
The perfect morphological type of noise is white noise. Noises of this sort (elementary erratic shocks) compose the backdrop against which the events of the universe must stand out if they are to be perceived. An intelligible, organized perception cannot be masked by an erratic phenomenon such as a white noise until the latter has a much higher level. The amplification of phenomena is limited by the uncertainty principle.
We use the delay required to perceive a phenomenon drowned in a noise in order to integrate the ordered phenomenon and discriminate it from contingent, erratic phenomena. Redundancy allows perception of a phenomenon drowned in formless noise with a much higher level. Redundancy can be insured by repeating signals for a time much longer than strictly necessary to identify the message in isolation. This might be analogous to chronicity in archetypal psychology-chronic re-emergence in physiognomy, behavior, emotions, beliefs, etc.
The rate of information flow of a message is determined by the structures that the receptor perceives in the message. These structures are created by memory, which summarizes the set of messages the individual has already received in statistical rules or in symbols. The receptor is thus a developing (learning) system. Each message modifies the receptor's capacity to receive succeeding messages.
Memory spontaneously creates emergent symbols by associating the set of elementary perceptions coming from a set of elementary sensations with only one or a reduced number of these sensations. The latter become the symbol. Symbolization is thus a reduction in the number of elements which results from frequent repetition of a microgroup of elementary sensations.
Memory is a statistical phenomenon resulting from a statistical destruction of the recorded elements of perception.
THE VORTEX OF WAVE MOTION
Recursive, reflexive, refluxive dynamics is reflected in the self-referencing properties in patterns. The edge of waves display fractal self-similarity. The study of reflexive topology and geometry of the process of self-reference echoes consciousness looking at itself, or self-consciousness. In similar fashion fractal patterns of self-similarity form and re-enter themselves at different levels of their own pattern.
The universal "message" is self-teaching and self-unfolding to minds of a particular level of consciousness. Never the same yet always the same. It is dynamic and holographically encrypted within the essence of our being. At each level of the tangled hierarchy, there is at least a minimal-resolution complete picture of the archetype of the hierarchy. This minimal-resolution images displays perhaps only the "outline," and the topological and/or geometrical invariants of the detailed picture.
Nature always takes the most efficient route in any process. Her intentionality emerges along the path of least action, least resistence. Therefore her voice is that of maximum information flow: white noise. The medium is the message.
Forms, patterns, geometries, and consciousness tend to recursively bend back upon themselves in reflection space. We are in the realm of the looking-glass universe. We find this tendency in spontaneous regression through personal history and transpersonal evolutionary development. The "cosmic download" is a recapitulation of the entire organic and inorganic evolutionary history, phylogeny, and ontology.
We find the principle of reflex in the symmetry of organic forms. It is the cosmological and microcosmic basis of physical phenomena in String Theory--cosmic strings and subquantum strings, that sometimes bend back and "bite their own tail" in circular fashion, like the Ourobourous serpent of creation.
REFERENCES
Moles, Abraham; INFORMATION THEORY AND ESTHETIC PERCEPTION; University of Illinois Press; Urbana, Chicago, London, 1968.
Webb, Burt and Goertzel, Ben; Chaopsych, October, 1993 discussion.
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