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Back to Fractal Neurodyamics and Quantum Chaos Part 1

5 The Fractal Link between Chaos and Quantum Mechanics.

5.1 The Scale Link between Neurosystems and Cellular Dynamics. The occurrence of chaos in neurosystem dynamics suggests that the brain may also utilize the fractal aspect of chaos as an intrinsic aspect of its processing, in combination with the natural scale transformations from organism to cell to molecule. The architecture of the central nervous system includes specific linkages between the level of whole neurosystems and the single cell. One is illustrated in fig 3(d) where a single hippocampal CA1 pyramidal cell has inputs from distinct brain regions, the sensoria and the reticular activating system via distinct neurotransmitters and distinct anatomical regions of the cell.

Such architecture permits a two-way relation between large-scale neurosystems dynamics and that of single cells, which both enables large-scale bifurcations to alter the stability of single cells and for single cells to precipitate bifurcations at the neurosystems level. The utilization of instability to provide responsiveness pinpoints the unstable aspects of the dynamics at the centre of processing demands, because these are the unresolved aspects of the internal model. The occurrence of either chaotic sensitivity or self-organized criticality at the neurosystems level could then enable a small subpopulation or even a single critical cell to precipitate global bifurcation.

The brain may utilize sensitive instability to deal with computationally difficult situations by mapping parallel representations on a fractal basis similar to Penrose's (1989) fractal algorithms for parallel computation (Dewdney 1989), with the added feature that continuous dynamical instability is used in addition to resolve ambiguous situations which remain intractable digitally.

5.2 The Complexity of Form of the Eucaryote Excitable Cell. Such reasoning places an additional emphasis on the neuron (Stevens 1989) as an integrated field processing unit, thus replacing the trivial formal neurons of McCulloch-Pitts, or optimizing analogue models such as the Hopfield net (Tank & Hopfield 1987) with a sophisticated integrated unit capable of chaos and unstable bifurcations. This is supported by the obvious complexity of typical central nervous neurons, with up to 100,000 synaptic junctions having a variety of anatomical forms fig 10(c), unstable bifurcations across threshold, and other non-linear features, (a). On a descending series of scales, the cell is itself a physical fractal both structurally and functionally in terms of its dendritic and axonic trees, (b) and in terms of subcellular processing both across dendrites (d) and synapto-synaptic junctions (e). Despite the approximate conformity to linearity of neuronal conduction over a restricted range above threshold (a), the neuron also has pivotal features of self-organized criticality in the form of tuning to its threshold, sigmoid limit-cycle bifurcation at threshold, and chaotic dynamics as depicted by the Chay-Rinzel model. The sensitivity of sensory modules such as pressure organelles also displays non-linear [quadratic] dynamics.

The fractal nature of dendritic and axonal trees provides the neuron with its second outstanding complex systems feature, which is that of a fractal integral transform. The capacity of the neuron to use its fractal structure to form many-to-many synaptic contacts lies at the foundation of its traditional role as a summation module. When organized in layers this permits a global integral transform, leading to the formation of complex fields from simple ones in sensory processing. The combination of this architecture with oscillatory signals could generate a Fourier-type invertible transform which would permit the retrieval of previous structures in a form comparable to a hologram, consistent with phase decoherence dynamics in experimental studies of the cortex and hippocampus.

Two characteristics of the neuron pivotal to a reassessment of its function are thus:

Fig 9: Morphogenic and contact fields and bifurcations: (a) impact of position within primary morphogenic tissue bifurcations on the development of brain regions, (b) cell-adhesion properties of proteins such as CAMs enable migration of specific neuron types, both along the glial scaffold and to specific cell layers or target types, (c) Specificity of ascending optic fibres may be limited to a general affinity for cortex suggesting the form of cortical sensory architecture may be organized by input from sense organs and stimulation in early life, rather than genetic specificity alone (Blakemore 1991).

5.3 The Non-linear Synapse. The fractal geometry of the neuron leads to an examination of the way cell organelles can provide a similar bridge between cellular and molecular dynamics. A variety of cell organelles provide a non-linear basis for sub-cellular dynamics. The concentration dynamics of the synapse fig 10(e) involves a rich diversity of feedbacks with non-linear characteristics. Concentration dynamics is linear only for single molecule interactions, but critical ion channels such as the acetyl-choline channel require two molecules for activation, thus having quadratic dynamics. Synapto-synaptic junctions display bilinear dynamics. Both of these can lead to chaos. Membrane dynamics also involve piezo-electric interactions. Microtubules have also been proposed as functional cellular automata (Hameroff 1987).

Such non-linearities make it possible for unstable fluctuation at the synaptic vesicle or ion channel level, within a critically poised neuron, to precipitate cellular instability and subsequent global neurosystem bifurcation. In cortical synapses, there is no need for the large number of vesicles seen in the neuro-muscular junction, and it has been proposed that in some synapses, the release of contents of a single vesicle is sufficient to traverse the threshold and elicit a post-synaptic response. A single vesicle, releases around 10,000 acetyl-choline molecules, activating 2000 ion channels, causing discrete micro-potentials even at the neuro-muscular junction, which depolarize the membrane by about 1 mV, sufficient to result in an action potential if a cell is already at threshold.

Eddington (1935) and Eccles (1970) discussed the possibility of quantum-mechanical action of the vesicle and pointed out that the uncertainty of position of a vesicle of 400 oA diameter and mass 3 x 10^-17g is about 30oA, comparable with the thickness of the membrane. Because of this, the vesicle can be regarded as a quantum object, which is at the same time capable of triggering cellular and hence global instability. The topological closure of the vesicle membrane results in the amplification of quantal instabilities from the level of the molecule to the larger level of the vesicle. The kinetics of vesicle association with the pre-synaptic membrane is determined by binding to one, or a few proteins, making vesicle release a function of the kinetics of one or a few molecules. The precise mechanism of vesicle exocytosis is not yet elucidated, but may involve the vesicle membrane protein synapsin I.

5.4 The Molecular Level. Activation of a single ion channel requires one or two neurotransmitter molecules. While the ion flux resulting from a single open ion channel will not generally elicit an action potential, if the channel happens to command a critical site on the two-dimensional dendritic surface, for example close to the cell body where the action potential begins, and the cell is at or near threshold, then the single quantal encounter of a neurotransmitter binding to an ion channel could be capable of evoking an action potential. The fractal nature of ion channel kinetics finally allows for the interaction of molecular quantum excitations on a variety of fractal scales, constituting the quantum chaotic level of expression. Long-term potentiation associated with a receptor-kinase-membrane feedback (Alkon 1989, Winson 1990) is another kinetic process at the molecular level which permits a molecular change to trigger a distinct global history, however the determinate nature of memory makes it one of the less likely aspects of brain function to be subject to quantum instability.

The four levels of instability link in stages, making it possible for the fractal aspect of chaotic dynamics at the global, cellular, synaptic and molecular levels to combine to provide a fractal model in which global and quantum instabilities are linked by mutual interactions of scale. Global instabilities in brain dynamics may be dynamically-linked to fluctuation of a critical neuron. Threshold instability similarly makes the neuron a potentially unstable dynamical system which is open to synaptic perturbations. Quantization at the level of the synaptic vesicle allows for amplification of quantum fluctuations in binding proteins into vesicle rupture that is capable of eliciting micropotentials at the neuronal level. Sensitive dependence and quantum amplification thus give the brain the capacity to detect fluctuation at the quantum level. This is consistent with the sensitivity of sensory apparati which are all capable of detections at or close to the level of single quanta [see 7.1].

Fig 10: Non-linear and fractal aspects of the neuron. (a) Non-linearities occur in formation of a limit cycle and excitation threshold (ii), despite approximate linear relation between depolarization current and firing rate in a limited range (i). Sigmoid transmission curve (iii) and mechanoreceptive bulbs also have a non-linear response. (b) Fractal structures of dendrites of two cell types and their electrodynamics (Schierwagen 1986). (c) The anatomical complexity of the neuron is illustrated by the structural variety of synaptic junctions, which also utilize distinct neurotransmitters. (d) Dendritic microcircuits and synapto-synaptic junctions (e) place the level of net organization one or two levels below the neuron. Synaptic conduction involves many feedbacks (e), some of which, including the two-molecule activation of the acetyl-choline ion channel have quadratic rather than linear concentration dynamics.

6 The Evolutionary Origins of Fractal Processing

It is one thing to establish the possibility that fluctuations at the quantum level could in principle become amplified into global instabilities in the brain, but quite another thing to explain why the brain should find it advantageous to allow such disordered processes to intervene in its functioning. Normally noise in a system is regarded as the anathema of computational precision, so an explanation is in order.

6.1 The Computational Intractability of Survival in the Open Environment. The principal task of the brain of is to compute the survival strategy most likely to enable the organism to evade death and produce viable offspring. A computational problem is intractable if the number of computational steps required grows super-exponentially with the complexity of the problem. The travelling salesman problem (Bern & Graham 1989), finding the shortest route round n cities illustrates this, growing with (n-1)! A problem may also be formally undecidable in the sense of Gödel. Many adaption-survival problems in the open environment share the characteristics of intractable problems, because each strategy tends to be matched by a competing strategy in another organism and the number of options rapidly exponentiates. An active organism must also complete a processing task within 0.1-1 second if it is going to have survival utility, regardless of its complexity. Such arguments make it clear why parallel processing is an integral feature of vertebrate nervous systems.

The fractal algorithm (Penrose 1989, Dewdney 1989), which in addition to parallelism, features fractal task assignment, shares significant features with biological processing. Including attractor dynamics with chaotic regimes in such a scheme provides additional features of sensitive dependence, phase space exploration, continuous resolution of instabilities, and the capacity to form new symbolic structures through bifurcation. It also provides a dynamic model for cognition in which bifurcation generates a series of symbolic structures, which become stable representations forming the successfully-modelled aspects of a problem. The complementary unstable component may continue to hunt through chaotic states, either bifurcating to stability, or forming a fractal instability which could in turn be perturbed by quantum instabilities.

6.2 Chaotic Excitability as a founding Eucaryote Characteristic. Chaotic excitability may originate deeper in evolutionary history, representing one of the oldest features of eucaryote cells (King 1978, 1990). The Piezo-electric nature and high voltage gradient of the excitable membrane provides an excitable single cell with a generalized sense organ. Sensitive dependence would enable such a cell to gain feedback about the external environment, rather than becoming locked in a particular oscillatory mode. Excitation could be perturbed mechanically and chemically through acoustic or molecular interaction, and electromagnetically through photon absorption and the perturbations of the fluctuating fields generated by the excitations themselves. Such excitability would predate the computational role of neural nets, making chaos fundamental to the evolution of neuronal computing rather than vice versa. The chemical modifiers may have been precursors of the amine-based neurotransmitters which span acetyl-choline, serotonin, catecholamines and the amino acids such as glutamate and GABA, several of which have a primal status chemically. The use of positive amines may have chemically complemented the negatively charged phosphate-based lipids, fig 11, in modulating membrane excitability without requiring complex proteins. It is thus possible that chaotic excitation dates from as early a period as the genetic code itself and that the first eucaryote cells may have been excitable via direct electrochemical transfer from light energy, before enzyme-based metabolic pathways had developed.

Fig 11 : Primal chemical aspects of neurotransmitters. (a) Primal uv-bridge between catecholamines and indoles. (b) Serotonin, Nor-adrenalin (R=OH) & Dopamine (R=H) and (c) their psychoactive variants are monoamines. (d) Acetyl-choline and (e) Phosphatidyl-choline demonstrate a common tertiary amine involvement.

6.3 Consciousness as an Evolutionary Manifestation of Chaotic Neurodynamics. From this perspective it is natural to postulate that, far from being an epiphenomenon, consciousness is a feature which as been elaborated and conserved by nervous systems because it has had unique survival value for the organism. We are thus led to an examination of how chaotic excitation may have evolved from single-celled animals through the early stages represented by Hydra to the complex nervous systems of metazoa. We have seen how chaotic excitation provides for exploration of phase space and sensitivity to internal and external fluctuations. However the conservation of consciousness may also involve features expressed only by chaotic systems which are fractal to the quantum level.

It is a logical conclusion that the conscious brain has been selected by evolution because its biophysical properties provide access to an additional principle of predicitivity not possessed by formal computational systems. One of the key strategies of survival is anticipation and prediction of events (King 1978, Llinás (1987). Computational systems achieve this by a combination of deductive logic and heuristic calculation of contingent probabilities. However quantum non-locality may also provide another avenue for anticipation which might be effective even across the membrane of a single cell, if wave reductions are correlated in a non-local manner in space-time.

7 Quantum Models in the Central Nervous System

7.1 Quantum Sensitivity in the Senses. The limits to the sensitivity of nervous systems are constrained only by the physics of quanta rather than biological limits. This is exemplified in fig 1(a) by the capacity of retinal cells to record single quanta, and by the fact that membranes of cochlear cells oscillate by only about one H atom radius at the threshold of hearing, far below the level of thermodynamic fluctuations. Moth pheromones are similarly effective at concentrations consistent with one molecule being active, as are the sensitivities of some olfactory mammals. The quantum uncertainty of the vesicle in relation to the membrane has also been noted above as a source of sensitivity of the synapse to quantum fluctuation.

7.2 Sense Modes as Quantum Modes. The very distinct qualitative differences between vision, hearing, touch and smell do not appear to be parallelled in the similar patterns of electrical excitation evoked in their cortical areas. It is thus hard to see how the internal model of reality generates such different subjective modalities as the experiences of vision smell and hearing from common electrochemical dynamics. One possibility is the senses are generated in the internal model by the same quantum modes of sensory excitation, namely photons, phonons, membrane solitons and weak bonding interactions. If all these excitations can occur simultaneously in the membrane, its quantum-chaotic excitation could represent a form of cellular synesthesia, which is subsequently specialized in representing each individual sense mode.

Fig 12: (a) Excitations of single rod cells shows peaks with 0, 1, or 2 photons being registered, consistent with quantum statistics of photons being released very slowly at a rate corresponding to the marks below (Bailer & Lamb ex Blakemore 1991). Dereferencing of a perceived stimulus back to the original time (Libet 1979).

7.3 Quantum Mechanics and Wave Packet Reduction. Quantum systems differ fundamentally from the classical case, in which in principle conforms to a deterministic description. While the evolution of the system proceeds according to a deterministic Hamiltonian equation :


the measurement process, results in causality violations in which the probability interpretation


constitutes the limits on our knowledge of the system, resulting in a stochastic-causal model, in which measurement collapses the wave function from a superposition of possible states into one of these states. While quantum-mechanics predicts each event only as a probability, the universe appears to have a means to resolve each reduction of the wave-packet uniquely, which I will call the principle of choice, the subject of Schrödinger's famous cat paradox, in which quantum mechanics predicts a cat killed as a result of a quantum fluctuation is both alive and dead with certain probabilities, while we find it is only one : alive, or dead! The stochastic-causal processes of quantum mechanics violate causality because Heisenberg uncertainty


prevents a complete causal description of quantum dynamics, which can predict future [or past] states only as probabilities in each instance of reduction of the wave packet.

It is one thing to suggest that quantum fluctuations could in principle evoke global bifurcations of brain function, but quite another to determine what advantage might accrue from such seemingly stochastic activity. The possibility of a connection between quantum mechanics and brain function has been a source of interest since the discovery of the uncertainty principle, because of its implications for consciousness & free-will, and several interesting models have been developed. The connection between the observer's mind and quantum mechanics is pivotal in some interpretations of wave function collapse.

7.4 Quantum Chaos versus Uncertainty as Substrates for Classical Chaos. Repeated attempts to model a variety of quantum analogues of classical chaotic systems have revealed significant differences which may prevent the full display of chaotic dynamics in the quantum analogues. Two theoretical approaches have been mounted on a variety of transition systems. In the semi-classical approach, fig 13(b) point particles are replaced by wave packets whose trajectories are calculated to provide a simulation of the wave function (Tomsovic & Heller 1991). Complementing this are quantum wave function approaches, such as quenched quantum mechanics, and studies of the so-called scarring of some chaotic wave functions around the periodic orbits (Gutzwiller 1992), which are necessarily embedded in any chaotic system (a). A variety of systems have been explored experimentally from hydrogen atom in a magnetic field to particles such as electrons traversing a molecule or molecular medium (c).

The spreading of wave fronts results in some smoothing of the classical picture of chaotic mixing, including tunnelling between trajectories, non-diffusive or time reversible dynamics, and the level repulsion between eigenvalues characteristic of the many-body dynamics of atomic nuclei. At the time of writing, verdicts on the capacity of quantum systems to fully exhibit chaos is still in flux, with some quantum systems, including magnetically excited atoms and electrons traversing molecular media appearing to display key features of chaos (Schuster 1986, Casati 1986, Giesel 1989, Wintgen & Honig 1989, Zhang et. al. 1990, Berry 1991, Peterson 1991, Uzer 1991). The electron traversing a molecule (Gutzwiller 1992) gives a simplified picture of chaos in molecular dynamics displaying chaotic variation in transition time [phase]. Sensitive dependence of molecular kinetics follows.

However it is the stochastic wave-reduction aspect of quantum mechanics which ultimately underpins the unpredictabilities found in chaotic physical systems. Statistical mechanics ultimately derives its random variation from Heisenberg uncertainty [7.3.3] in the form of wave-packet reduction. For example the positional statistics of molecular kinetics is made uncertain through diffraction of the wave aspect of a molecule by other molecules. An amino acid at room temperature has a self-diffraction angle of about 5o (King 1989), contributing initial condition uncertainty to each successive chaotic encounter, fig 13(c) when traversing a molecular medium. One of the important roles of classical chaos may thus be the amplification of quantum uncertainty into macroscopic indeterminacy. Sensitive-dependence in physical systems may thus result in quantum inflation, the amplification of quantum fluctuation into global perturbations of the dynamic. The distributed nature of wave reduction over the eigenspace may thus link to the ergodicity of chaotic systems.

Fig 13: The quantum stadium represented (a) by quantum wave functions displays scarring of several wave functions around embedded periodic solutions (Gutzwiller 1992), (b) semi-classical approach provides a close approximation using a finite number of periodic solutions at least for some stages (Tomsovic & Heller 1991), (c) electron traversing a molecule has continuous variation of time [phase] with chaotic irregularity (Gutzwiller 1992).

7.5 Quantum Concepts in Brain Function. Bohm's work on the Einstein-Podolsky-Rosen conjecture, Bell's theorem and the Aspect experiments (Clauser & Shimony 1978, Aspect et. al. 1982) which display spin-correlations between a split photon pair over space-like intervals have demonstrated that hidden variable theories cannot be locally causal, leading several researchers to postulate the idea of non-local states correlating the activity of various parts of the brain (Penrose 1987).

Interest in quantum concepts in brain function has had a considerable history starting from Eddington (1935), and continuing with Eccles (1970). Basar (1983) has suggested matrix theory and Feynman diagram approaches (Stowell et. al. 1989) to resonances at the neurosystems level. Popper and Eccles (1977) and Margenau (1984) have also discussed the possibility of quantum reduction being dependent on the mind of the observer, leading to the paradox of Wigner's friend in which an observer's friend splits the wave function, and reports on the result. Multiple minds thus lead to ambiguities of splitting. One way around this paradox is to require mind to be a unity rather than a multiplicity removing the ambiguity of the reduction point, another is that the first conscious observer in the chain collapses the wave function. Recent studies using down-converters demonstrate that the possibility of gaining information about a photon's path collapses the wave function and that such knowledge can be erased to regenerate a coherent wave (Horgan 1992). Although such istinctions ultimate reach the conscious observer, collapse appears to occur with the loss of ambiguity, whether or not immediately manifest in conscious experience.

Deutch (1985) has analysed the potentialities of a quantum computer, which has a fuzzy logic representing quantum superposition of states to form a probability function in the interval [0,1] in place of the usual {0,1} = {T,F} of formal logic. Although the algorithmic capacity of such a quantum computer does not extend the class of functions computable by a conventional Turing machine, several specific instances have been given in which a quantum computer might solve special tasks more efficiently, (Lockwood 1989). These do not appear to provide significant advantages over parallel distributed processing. Both these authors adhere to the Everett many-worlds interpretation of quantum mechanics in which the collapse of the wave function never occurs, and all histories having a non-zero probability under the quantum prediction are presumed to co-exist as parallel aspects of a cosmic wave function. This bypasses the Schrödinger cat paradox, however it contradicts the evidence of our conscious sensory processes, which in common with physical measuring apparati, experience a single historical process. Collapse of the wave function also appears to be the aspect of quantum mechanics which underlies the indeterminacy of chaotic systems.

The mathematician Roger Penrose (1986,1989) has also studied the relation between the conscious brain and quantum physics and attempted to combine quantum theoretic and relativistic ideas. He has suggested that collapse of the wave function may be a deterministic process based on the interaction of the superimposed wave function with the gravitational field at the level of one graviton, thus having parallels to decoherence theories (Zurek 1991).

7.6 The Supercausal Model. A final model (King 1989), which also combines quantum theory and relativity, develops a supercausal hidden-variable theory which is consistent with conventional quantum mechanics, but allows for correlations between quantum events over both space and time, replacing the stochasticity of the quantum model with a transcausal description, which is non-local in space-time. The temporal ordering of causal events is thus violated below the quantum level by space-time symmetric interactions. This description prevents determination of a system from initial conditions, because the non-local correlations include future states of the system. It is based on the transactional interpretation of special-relativistic quantum mechanics.

The relativistic energy-momentum equation [7.6.1]

has dual energy solutions   [7.6.2]

in which the negative energy solution has reversed temporal behaviour in space-time.

This is consistent with Feynman diagrams in which a particle travelling in the usual (retarded) direction can be equated with its anti-particle in the time-reversed (advanced) state. This fact allowed Dirac to predict the existence of the positron from the negative energy solutions to the electron wave equation.

As a simple example, the Hamiltonian equation [5.3.1] for a zero spin particle with mass m has elementary solutions:



where   [7.6.4]

One solution travels in each direction in space-time, forming distinct retarded and advanced solutions. For a photon which is its own anti-particle, these reduce to the offer and confirmation waves of the emission and absorption foci.

Fig 14: (a) Feynman diagram of exchange of a photon, (b) higher-order diagram. (c) One-photon transaction involves interfering offer and confirmation waves. (d) Electron deflection and positron creation and annihilation. The time-reversed electron is a positron. (e) contingent emitters and absorbers as boundary of collapse. (f) Spliced reduction interactions.

In the Feynman diagram Fig 14(a), the force between electrons is determined by integrating all possible virtual photon and higher-order interactions (b). The photon is virtual because it exists only for an interval consistent with the uncertainty relations [7.3.3], and is detected only by its secondary effects in the electric field. While in virtual exchange, all possible exchanged photons are summed, in the case of a real exchanged photon, the boundary condition that only one real photon is exchanged, forces reduction of the packet of all possible such exchanges to one real exchange. Time reversal is standard in Feynman diagrams, a time-reversed electron being equivalent to a positron (d).

Such time-reversal is used in the transactional interpretation of quantum mechanics (Cramer 1986) fig 14(c), a mutual encounter between emitter and absorber is modelled by the release of crossed-phase advanced and retarded waves, each having zero-energy, the offer wave of the emitter and the confirmation wave of the absorber. While the retarded offer wave travels with elapsing time in the usual manner, the advanced confirmation wave, back-propagates in a time-reversing manner from the absorber to the earlier emission event. The mutual interference of these advanced and retarded waves produces a real superposition (the photon) between the emission and absorption events in space-time.

Modelling reduction of the wave packet now depends on the mutual interaction of all contingent emitters and absorbers as in (e), on the basis that a photon can only be created linking the two events and cannot simply disappear into space, following Feynman's absorber theory (Davies 1974). This means that the probability distribution is determined by boundary conditions which include all contingent absorbers which could have alternatively participated in the emission event (f). However, because these include future states which have not been causally determined, a logical regress results, leading to paradox in terms of temporal determinism. Transactions can also link contingent foci across both time-like and space-like intervals by linking confirmation waves at any particular emission vertex, regardless of the proper time interval to the contingent absorbers, e.g. cA1 and cA2 in fig 14(e), explaining the pair-splitting experiments of Aspect et. al. (1982).

One way of modelling transactional collapse is via a bifurcation of a non-linear interaction between all contingent foci, however the time parameter in any such bifurcation has to be handled very carefully. Whether or not collapse results from a non-linearity in gravitation as suggested by Penrose (1989), the space-time boundary constraints are inconsistent with the usual idea of temporal causality defined by initial conditions and Laplacian determinism.

Transactional collapse is also consistent with quantum decoherence models, which include incidental collapse caused by field and thermal excitations (Zurek 1991). Although decoherence has the effect of breaking a transactional contingent set into a class of smaller sets linked by emission and absorption foci, similar to higher-order Feynman diagrams, it does not alter the supercausal properties of transactional reduction, enfolding the implicate order of quantum non-locality without disruption. Thus similar space-time properties apply to kinetic molecular systems with many thermodynamic and other quantum interactions between production of an intermediate and its reaction.

8 Supercausality and the Conscious Brain

8.1 Superset Correlations and the Evolution of Chaotic Neurosystems Dual-time supercausality results in pseudorandom behaviour consistent with the probability interpretation, which is non-local not only in space, but also in time. This could enable a neural net to become internally interconnected through sub-quantum effects which were non-local in time, and hence enable a form of predictivity unavailable through classical computation. The mutual exchange of quanta between such units would make them a contingent transactional set of emitters and absorbers. Such linkage could arise via excitons, or photon or phonon exchange. The cell membrane topology forms a global link between its quanta of excitability, making such linkages possible also in the single cell. A variety of excitons, including the major oscillations of the EEG could also form a basis for neurosystems linkage in the brain. The many-to-many transform nature of the neuron may provide a basis for this effect through the connection of any given state to a large population of neurons in the cortex.

An excitable cell or neurosystem which evolved initially to achieve constrained optimization through chaotic fluctuation, could thus also display a new type of predictive modelling through non-local quantum interactions. Predictive optimization may thus have driven the evolution of the excitable cell and subsequently a structurally-unstable chaotic brain in which consciousness and free-will become direct manifestations of the quantum non-locality underlying membrane and brain-function.

This view combines a reductionist approach, in which biological phenomena are reduced to chemical and finally physical models (Skinner 1989), with a new emphasis on quantum physics as the limit of a fractal process. A component of panpsychism is included in the physical description, in which consciousness can be associated with a real quantum by virtue of the uncertainty arising from its wave-particle duality. Sentience is the capacity of the emitter to utilize the confirmation waves of contingent absorbers in wave-packet reduction, while free-will or intent is the uniqueness implied by the principle of choice. Emergentism, the capacity of a system to be more than the sum of its parts, is also present, because the time-symmetric subquantum associations in the model are developed as a result of the large number of units in a parallel net which can become transactionally related as mutual conditional emitters and absorbers. This gives the brain a degree of cooperative uncertainty which is lacking in a single quantum. Free-will raises possibilities that the mind can at least in some ways alter the future states of the universe. The limits of such possibilities remain to be established.

8.2 Anomalies of Time Perception Since Grey-Walter first made subjects witness movement of slide show via a motor cortex probe and found they witnessed the slide change before they pressed a dummy button, the time properties of conscious experience have remained a conceptual challenge.

Two experiments outline some of the puzzling temporal properties of consciousness. In the first, (Kolers & von Grunau 1976) alternate lights of different colour flash for 150 ms with an intervening gap of 50 ms. Subjects report a single moving light which changes colour at the mid point, even on a first exposure, or random colour change. This creates an apparent paradox because the colour change apparently occurs before the second light has come on.

In a second class of experiment (Libet et. al. 1979), which has been the subject of repeated discussion (Libet 1985a,b,1987,1989, Churchland 1981 a,b, Honderich 1984, Snyder 1988) involves the subjective timing of stimulation of one hand [say the left, which excites the right somatosensory area] at the same time as direct stimulation of the opposite [left] finger somatosensory area. The genuine hand-tingle is perceived before the cortically induced one even if it actually occurred afterwards. Because of the considerable delay for the development of neuronal adequacy for the conscious experience [200 - 500ms] the time of the experience appears to be referred back to the primary evoked potential [10-20ms after stimulus], fig 12(b).

Although this referral can be explained as a construct of the internal model, similar to spatial representations which are subjectively "out there", temporal projection comes close to causal paradox. Libet suggests "a dissociation between the timings of the corresponding mental' and 'physical' events would seem to raise serious though not insurmountable difficulties for the ... theory of psychoneural identity". Penrose (1989) "suggested that a materialistic explanation of Libet's phenomena would require a revolution in fundamental physics" (Dennett 1991). "This antedating procedure does not seem to be explicable by any neurophysiological process... [but is] attributable to the ability of the self-conscious mind to make slight temporal adjustments, i.e. to play tricks with time." (Popper & Eccles 1977).

Dennett (1991) explains such features by looping of the subjective time sequence out of the physical sequence. The order of consciously perceived events does not have to be coincident with the physical or apparent physiological order when parallel processing builds up a global model of a time sequence. The order in which constructs become established may be arbitrary, within the space-time constraints of a large parallel device, but the completed construct will nevertheless represent the sequence of the original, perhaps modified by simplifying assumptions of the internal model. This approach suggests however that the completed representation cannot be formed until after the sequence ends, [e.g. until both the red and green lights have flashed and not half-way across], and may require editing of the partial constructs of the model either prior or subsequently to their registration.

Further experiments are required. The supercausal model was constructed to deal with the causal paradox of free-will but could apply also to these examples. Observational difficulties make the issue similar to the problems of quantum measurement. One difficulty is pinpointing the time of subconscious origin of a response which results in a button press or a verbal signal. Another is that comparing the absolute times of stimuli and neurophysiological events with those of perceived conscious events ['it happened when the hand was at 2'] involves comparing the 'representing and represented' states (Dennett 1991).

8.3 Supercausality and the Representation of Time in the Cortex

One particularly interesting idea is that time is represented in the same distributed and holographic manner that other modalities are. The relationship between the frontal lobes and the rest of the cortex appears to involve representations of activities integrating future states [intentions] into time-directed actions based on past experiences [memories]. The frontal lobes generalize motor acts into associations in a similar manner to the sensory association areas in the rest of the cortex. Thus the frontal cortex may generate a spatially distributed representation of time in terms of the organization of both remembered and planned actions spanning the past and future, utilizing oscillatory phase relations as seen in EEG and evoked potential studies, possibly in the 40Hz mode suggested by Crick & Koch (1990). Coherent oscillations would link by Hebbian coincidentality. Both short-term working memory and the long-term consolidation of the limbic system may thus form part of a transform representation of time.

Subjective time may thus be an internal model whose basis is quite different from mechanical notions of linear time, partly because it requires integrated representation of past memorizations and learning with future plans and survival strategies. It is easy to see that visual perception constructs an external spatial reality but more difficult to accept the possibility that time is similarly an internal construct. What may be even more difficult to accept is that the subjective notion of free-will or intent arises because the function of consciousness is to anticipate, forming an "ill posed" problem in time.

A holographic representation of time generated by the frontal cortex and limbic system thus provides a possible realization of the supercausal model. The central task of the brain is the representation of the activity of the organism in terms of both past and future temporal dynamics. While the past is based predominantly on memory, the future, representing the organism's survival strategy, may be based on complementary principles of computation and predictivity, utilizing both attractor-based computation and access to quantum non-locality. The modal oscillations in such a holographic representation are time-symmetric in the sense that the beats of phase coherence measure only a circular phase-shift and not a direction. This is exactly the same act that is required in quantum measurement to determine the uncertainty relations, since counting beats to determine frequency and wavelength requires a time or distance determined by the uncertainty relations [5.3.3]. It thus raises the rather odd spectre that cortical oscillations and their corresponding mental states may be inflated quanta reverberating through the brain. It also suggests that the subjective notion of the present may be an extended quantum of the present, forming a reverberating envelope of past and future states.

Solving the problem of temporal representation is central to understanding the nature of attention, consciousness, and will, both because of the causal paradox implied by will, and because the problem of the 'ghost in the machine' is essentially a problem of how the temporal dynamics of attention are organised. Enclosing this ghost of attention within the quantum of the present carries the paradox into the causality-violating arena of sub-quantum physics.

8.4 The Experiencing Totality

Although normal waking experience has a reasonable correspondence to our concept of physical reality, the experiences of dreaming and other reflexive states such as hypnogogic and meditative trance, psychotropic hallucinations and near-death experiences, which transcend correspondence to the physical world, raise fundamental questions concerning the relation between the mind and the physical world. Dreaming is one of the most outstanding of these non-collective conscious states. It is one which we are all aware of, and one whose intensity, in cases of good recollection, parallels, or even exceeds that of sense experience of the 'real world'. Dreaming has definite correlates in central nervous activity in the REM phases of sleep, originally called paradoxical because of the appearance of internal waking arousal, illustrated in the EEG's and PET scans of fig 4, contrasting with the slow wave activity of deep sleep. The unusual properties of such states suggest that the more esoteric aspects of mind, which I will term dreaming, may contain deeper clues to its underlying nature beyond physical correspondence. In such a dual model, mind is more fundamental to reality than merely a physical internal model, a complementary principle to physical reality, emerging physically through indeterminacy.

The concept of a dual totality in which mind and universe are primary components raises further deep issues. While it may not be possible to describe mind from the point of view of physical world constructs alone, it is possible to describe the physical world as stability properties of conscious experience. Similarly, although our model of the physical world is inferential, our conscious experience from birth to death is direct and undeniable. It is thus possible to mount an alternative description of reality in which mind is primary and fundamental and the physical world is merely a stability structure of mind, as is central to the Indian philosophy of mind. The link between chance, living organisms and consciousness is also central to the Chinese oracle I Ching (Wilhelm 1951) in which these three are regarded as joint manifestations of a unifying predictive cosmic principle.

The status of such reflexive conscious states as dreaming may thus represent one of the greatest enigmas of scientific enquiry, because it is here that the temporal paradoxes described enter into unstable self-feedback without direct input from the external world. Dreaming is traditionally viewed as an illusory or hallucinatory invention of the mind, functioning either in the release of psychological tensions, or as a subjective manifestation of neural processing during sleep, possibly in the consolidation of long-term memories (Koukkou & Lehmann 1983, Winson 1990), or even to forget as Francis Crick has suggested. Although true REM sleep appears to be a mammalian trait, there is evidence for a paralysis phase of sleep in animals spanning the arthropods and vertebrates. Although dreams presumably do serve a physiological function, as evidenced by metabolic compensation after periods of deprivation, the origin of the content of dreaming remains obscure.

Complementing physiological studies of dreaming is a parallel stream of literature addressing the possibility that dreaming has unusual space-time properties, associated as much with future as with past experiences (Dunne c1935). Although the significance of dreaming in western culture has concentrated on the symbolism of dreaming as an expression of fears and aspirations in daily life and its analysis as a means of therapy, reference to dreaming in other cultures, such as Australian aborigines, and the Senoi of Malaysia includes the use of dreams to anticipate future problems and events, and is based on the concept that the dreaming state is another level of conscious reality, which is not an illusory representation of the 'real world', but is rather a mode of conscious existence in its own right. I have had many personal dreaming experiences with attest to such temporal properties of dreaming, including having a double dream of being stung, reporting the dream to my wife and an hour later being stung wide awake in bed.

Similar accounts occur in societies, such as the Huichols and Mazatecs of Mexico and the Amazonian Cashinahua, Shipibo, Jivaro, etc. where plants or fungi are taken to induce hallucinatory trance states during shamanic rites. Five aspects of these states have been noted by anthropologists; geometrical illusions, visions of animals and demons, the separation of the mind from the physical body, clairvoyant visions of distant places, and divination of past or future events (Harner 1973)."On the day following one ayahuasca party, six of nine men informed me of seeing the death of my 'chai', my mother's father. This occurred two days before I was informed by radio of his death".

The apparent capacity of people, in near-death experiences to have perceptions of their surroundings from another physical position [out of their body] invites further questions concerning the physical location of consciousness, particularly when they [occasionally] report accurate details they could not have witnessed from their physical position, such as the patient who correctly perceived a discarded shoe on a ledge three floors above the room where she had cardiac arrest (Groff S. 1988).

In what I would loosely describe the Sorcerer's Explanation, the dreaming aspect of reality underlies the physical so that the waking experience of the physical world is just one manifestation of a wider dreaming totality, rather than vice versa. Castenada (1976) in his many allegories, discusses the technique of dreaming in which the dreaming and waking state are connected by intent so that dreamer can gain control. The technique involves picking some simple action that the dreamer will perform as an act of volition to assume temporary command of their will, and check the onrush of dreaming attention. For example the act of looking at the backs of one's hands while in the dream. This technique is parallelled in Stephen LaBerge's (1985,1990) research into lucid dreaming (Blackmore 1990), in which the subject learns to make a variety of reality tests of the dreaming state by combining waking practice tests with setting intent during the sleep phase. These are complemented by waking techniques such as looking for the gaps (see 1.4.3) in conscious experience, stopping the internal dialogue and stalking (Abelar 1992).

The empirical investigation of such reflexive conscious states constitutes the best hope we have for discovering the foundations of the mind-brain relationship. While research is dominated by clinical tinkering with the brain from outside, a comprehensive description will continue to elude society. Thus balancing the pictures gained by brain lesions, EEG studies and PET scans should be an emphasis on pure consciousness research, combining scientific techniques with the traditional means used by societies throughout history, namely meditative and shamanic trance, the use of power plants and dreaming techniques. Several of these have been largely ignored as unscientific, or prohibited as dangerous to consumer society because of their very capacity to induce fractal or chaotic conscious states, thus setting back by decades society's development of an understanding of the mind-brain relationship. Complementing such traditional techniques are new devices emerging from brain research laboratories. One valuable such device is the Dream Light developed by LaBerge (1990) from research studies on dreaming EEGs, which detects REM periods and alerts the subject by a flashing light or acoustic signal. Such devices can help to bring the relatively uncharted and inaccessible realms of consciousness into the scientific arena.

9 The Cosmological Perspective

The brain may be one of the few places where the supercausal aspect of wave-packet reduction can be clearly manifest, as a result of its unique capacity to utilize correlations in its dynamics. Although other unstable systems such as the weather may also display such features of non-locality, it is difficult to think of a physical experiment which could in any way match the brain as a detector of correlations within the stochastic model of quantum mechanics. In this respect it should be noted that cosmology is not simply a matter of vast energies, but also quantum rules. The diversity of wave-particles resulting from symmetry-breaking of the fundamental forces finds its final interactional complexity, in which all forces have a common asymmetric mode of expression, in complex molecular systems. It is thus natural that fundamental principles of their quantum interaction may be ultimately realized in the most delicate and complex molecular systems known - those of brain dynamics.

10 Conclusion

The importance of developing a model of brain function which gives a consistent description of mind, consciousness and free-will, is profound. The model described links the structural instability of brain dynamics, quantum uncertainty and the dual-time model. The quantum-physical brain may thus be more than just an interface between sensory input and decision-making. It may in fact be a doorway between complementary aspects of the physical universe, the time-directed nature of real-particle symmetry-breaking and the time-symmetric aspect of the sub-quantum domain (King 1989). If so, the role of consciousness and mind-brain duality may be central to cosmology.


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NOTE: All diagrams are digitally processed by the author. All original sources are indicated in the text or captions.