Quantum Brain Dynamics:
Henry Stapp in two excellent articles (Stapp 1997a and b) reviews the development of quantum theory and outlines how it is essential to understanding the mind/brain relationship. Stapp sets up the issue as follows. “Brain process is essentially a search process: the brain, conditioned by earlier experience, searches for a satisfactory response to the new situation that the organism faces. It is reasonable to suppose that a satisfactory response will be programmed by a template for action that will be implemented by a carefully tuned pattern of firings of some collection of neurons. The executive pattern would be a quasi-stable vibration that would commandeer certain energy resources, and then dissipate its energy into the initiation of the action that it represents.” Patterns of firings and quasi-stable vibrations are, what I have termed the surface and deep structures of processing that are represented by Llinas' Tensor and my Holonomic Theories respectively.
Stapp goes on to note that “If the programmed action is complex and refined then this executive pattern must contain a great deal of information and must, accordingly, be confined to a small region of phase space.” Holonomic theory indicates that spread functions such as those that compose holography, do indeed make it possible to contain a great deal of information within a small region (patches of dendritic receptive fields) of phase space. Stapp further notes that “the relative timing of the impulses moving along the various neurons, or groups of neurons, will have to conform to certain ideals to within very fine levels of tolerance. How does the hot, wet brain, which is being buffeted around by all sorts of thermal and chaotic disturbances find its way to such a tiny region in a timely manner?” Llinas' Tensor Theory deals with the timing issue.
Further: “How in 3n dimensional space (where n represents some huge number of degrees of freedom of the brain) does a point that is moving in a potential well that blocks out those brain states that are not good solutions to the problem --- but does not block the way to good solutions find its way in a short time to a good solution under chaotic initial conditions?“ Stapp notes that classical solutions to this problem won't work and that “the quantum system [will work as it] has the advantage of being able to explore simultaneously (because the quantum state corresponds to a superposition of) all allowed possibilities.” Stapp provides a viable metaphor in a glob or cloud of water acting together rather than as a collection of independently moving droplets. “The motion of each point in the cloud is influenced by its neighbors.”
However classical holography will also do just this. But the advantage of holonomy, that is quantum holography, is that it windows the holographic space providing a “cellular” phase space structure, in patches of dendritic fields thus enhancing the alternatives and speed with which the process can operate. In short, though the information within a patch is entangled, cooperative processing between patches can continue to cohere or de-coherence can “localize” the process.
With regard to evidence regarding the scale at which quantum processes are actually occurring, a number of publications have reported that quantum coherence characterizes the oscillations of ions within neural tissue channels. (e.g. See Stapp 1997; and Jibu et al 1994; Jibu and Yasue in this volume). The question immediately arises as to whether decoherence occurs when the channels communicate with each other and if so, how. Stapp notes that “phase relationships, which are essential to interference phenomena, get diffused into the environment, and are difficult to retrieve. These decoherence effects will have a tendency to reduce, in a system such as the brain, the distances over which the idea of a simple quantum system holds. ”
Hameroff and Penrose (1995) have also dealt with the limited range over which quantum coherence can operate. These authors suggest that excitation at the microtubular scale follows quantum principles but that decoherence self-organizes towards the end of an axon or dendrite. Davydoff (see Jibu, this Vol.) Ross Adey (1987) and I (1991) have independently proposed that microtubular quantum coherence provides saltatory coupling between dendritic spines and saltatory conduction in between nodes of Ranvier in axons via soliton waves. (See also, Jibu and Yasue, this volume). Soliton waves would thus provide a longer range over which coherence can be maintained.
An additional mechanism for coherent channel interaction has been proposed by Jibu, Pribram and Yasue (1996). This proposal focuses on the phospholipd bilayer that composes the membrane within which the channels occur. The phosphate parts of the molecule are hydrophilic capturing water as in a swamp. The water in such a region can become ordered into a super-liquid form that, by way of boson condensation, can act as a superconductor. Channels become connected over a limited distance by a transitional process that is quantum-like at a somewhat larger scale than the channels per se.
Thus, at the neural systems scale, there are two quantum-like fields, one pre-synaptic composed by the fine branching of axons as they approach the synapse; the other post-synaptic composed of the fine branches of dendrites. Hiroomi Umezawa and his collaborators (Stuart, Takahashi and Umezawa 1979) pointed out that not only quantum but “classical” processing can be derived from quantum field theory. The relevance of all this to the brain/mind issue is that both Umezawa and Giuseppe Vitiello (2004) have, on the basis of mathematical insights, proposed that interactions among these two quantum brain fields is necessary for self-reflective consciousness to occur. Hiley notes: “this is part of a bigger mathematical structure of bi-algebras that Umezawa and Vitiello are exploring. The doubling arises from a natural duality.” I add, could this doubling arise from the nature of the Fourier relationship? The Fourier transformation results in a complex number that represents both a real and a virtual line, a built-in duality.
My question is not an idle one. Our optical system performs a Fourier transform that results in the dual of real and virtual. One of these must be repressed in getting about in the space-time world. But the repression is incomplete. Experiments using glasses that invert the optical image to make the world look upside down, have shown that actively moving about re-inverts the image so that the world again looks “normal”. Re-reversal takes place over time when the glasses are removed. Vitiello's “double” is thus twice unveiled.
To return to the topic of “scale”: In the brain, at what scale does decoherence initially occur? There are two types of processes that are excellent candidates. The local chemical activities, constituted of neuro-transmitters, neuro-modulators and neuro-regulators appear, at present, not to share properties that are best described in quantum terms. Their operation transforms the entangled quantum processes into larger scale influences on neural circuitry especially at synaptic sites. A second locus for decoherence is the region of the axon hillock. It is here that the passive conduction of dendritic activity influences the spontaneous generation of the discrete impulses that transmit the results of processing at one location to another location via neural circuitry.
FORMALISMS:
The Quantum formalism:
The initial quotation introducing this essay is from the ending of an excellent paper by George Chapline (1999) entitled “Is theoretical physics the same thing as mathematics”. Chapline's provocative title employs a bit of poetic license. Nonetheless the paper provides considerable insight as to the applicability of the quantum formalism to other scales of inquiry. Chapline shows that quantum theory “can be interpreted as a canonical method for solving pattern recognition problems” (p95). In the paper he relates pattern recognition to the Wigner-Moyal formulation of quantum theory stating that this “would be a good place to start looking for a far reaching interpretation of quantum mechanics as a theory of pattern recognition” (p97). In a generalization of the Wigner- Moyal phase space he gives the physical dimensions as the Weyl quantization of a complete holographic representation of the surface. He replaces the classical variable of position within an electromagnetic field with ordinary creation and annihilation operators. He shows that “representing a Riemann surface holographically amounts to a pedestrian version of a mathematically elegant characterization of a Riemann surface in terms of its Jacobian variety and associated theta functions” (p.98). This representation is equivalent “to using the well known generalized coherent states for an SU(n) Lie algebra” (p.98). This is the formalism employed in “Brain and Percption” (Pribram, 1991) to handle the formation of invariances that describe entities and objects.
There is much more in Chaplin's paper that resonates with the holonomic, quantum holographic formulations that describe the data presented in “Brain and Perception”. These formulations are based on quantum-like wavelets, Gabor and Wigner phase spaces. Whether these particular formulations will be found to be the most accurate is not the issue: rather it is that such formalisms can be attempted due to the fact that the “fundamental connecting link between mathematics and physics is the pattern recognition of the human brain” (p.104).
As an example of the utility of these insights, Chapline indicates how we might map the co-ordination of processing in the central nervous system. He notes that “the general idea [is] that a quantum mechanical theory of information flow can be looked upon as a model for the type of distributed information processing carried out in the brain.” He continues, “one of the fundamental heuristics of distributed information processing networks is that minimization of energy consumption requires the use of time division multiplexing for communication between processors, and it would be natural to identify the local internal time in such networks as quantum phase” (p.104). The caveat is, as noted, that quantum phase is fragile in extent and must be supplemented by the processes described in comparing holonomic (quantum holographic) theory with the tensor theory of Llinas (which applies to neural circuitry rather than to the fine fibered quantum holographic processing per se).
Bohm and Hiley (1981) had also undertaken a topological approach to quantum mechanics based on a Wigner-Moyal cellular structure of phase space. In the current volume, Hiley (this volume) carries the approach further by relating it to Gabor's handling of signal transmission (communication) with what we now call a Gabor function (he called it a quantum of information) which is the centerpiece of the Holonomic Brain theory presented in “Brain and Perception” (1991). Hiley is able to introduce a phase space distribution function that allows calculation of quantum probabilities without having to resort to non-commuting dynamic variables. This makes easier the transition to the commuting aspects of groups.
It thus shows the intimate connection with the Heisenberg group as used by Schempp in describing the fMRI process.
Hiley goes on to note that underlying the Wigner-Moyal distribution is the simplectic group. (Note that Chapline has focused on an SU(n) Lie group. The simplectic group is mathematically the more general). “The simplectic group is in turn covered by a metaplectic group that underlies Schroedinger's equation, as well as Hamilton's equation of motion and the classical ray formulation of optics. The metaplectic ‘double' covers the symplectic group in the same way that the spin group SU(2) double covers the rotation group SU(3).
The importance of these insights is that “we have a mathematical structure that is basic to both classical mechanics and quantum mechanics. At this level there is no basic difference between the dynamical equations of classical and quantum mechanics. The difference arises once one asserts there is a minimum value for this action and equates this value to Planck's constant h. “ (Hiley, this volume)
“What this means is that certain results --- may look as if they are quantum in origin but in fact have nothing to do with quantum mechanics per se but arise from the group structure that is common to both forms of mechanics. For example the Fourier transformation is common to both classical and quantum situations. Indeed the Fourier transformation is at the heart of of Gabor's discussion of information transfer. Thus any results that emerge from an analysis of either the Wigner-Moyal approach or the Bohm approach may not necessarily have to do with quantum phenomena per se, and for that reason I would like to call the emerging dynamics that I will discuss below ‘information dynamics'.” (Hiley, this volume)
Observables, Observations, and Measurement:
Just what is the specific role of the brain in helping to organize our conscious relatedness? A historical approach helps sort out the issues. The Matter/Mind relationship has been formulated in terms of cuts. In the 17 th century the initial cut was made by Renee Descartes (1662/1972) who argued for a basic difference in kind between the material substance composing the body and its brain and conscious processes such as thinking. With the advent of quantum physics in the 20 th century Descartes' cut became untenable. Werner Heisenberg (1930) noted a limitation in simultaneously measuring the moment (rotational momentum) and location of a (material) mass. Dennis Gabor (1946) found a similar limit to our understanding of communication, that is, minding, because of a limitation in simultaneously measuring the spectral composition of the communication and its duration.
These indeterminacies place limits to our observations of both matter and mind and thus the location of the matter/mind cut. Heisenberg (1930) and also Wigner (1972) argued that the cut should come between our conscious observations and the elusive “matter” we are trying to observe. Niels Bohr (1961) argued more practically that the cut should come between the instruments of observations and the data that result from their use.
In keeping with Bohr's view, these differences in interpretion come about as a consequence of differences in focus provided by instrumentation (telescopes, microscopes, atom smashers, and chemical analyzers). Measurements made with these instruments render a synopsis of aspects of our experience as we observe the world we live in.
The Fourier Relationship:
The formalisms found to be important in quantum measurement as it relates to the brain/mind issue is the Fourier (1802 ) relationship. This relationship states that any space-time pattern can be transformed into the spectral domain characterized by a set of waveforms that encode amplitude, frequency and phase. Inverting the transform realizes the original space-time configuration. The transform domain is “spectral” not just “frequency” because the Fourier transformation encodes both the cosine and sine of a waveform allowing the interference between the 90 degree phase separation to be encoded discretely as coefficients.
The advantage gained by transforming into the spectral domain is that a great variety of transformed patterns can be readily convolved (multiplied) so that by performing the inverse transform the patterns have become correlated. This advantage is enhanced in quantum holography (which I have called Holonomy). Chapline (2002) in a paper entitled: “Entangled states, holography, and quantum surfaces” argues that the simplest way to encode “fundamental objects --- may be as multi-qubit entangled states” (p. 809). I suggest that, impractical as it may currently seem, it would be more productive to encode “qulets”, wavelet transformations, to preserve phase. As noted, Lie group theory can be used to describe how, by way of co-variation, various perspectives (images) of an object can form an invariant entity. (Pribram 1991) Image processing as in tomography such as PET scans and fMRI are prime examples of the utility of such encoding.
The diagram below provides one summary of what these measurements indicate both at the quantum and cosmic scale. The diagram is based on a presentation made by Jeff Chew at a conference sponsored by a Buddhist enclave in the San Francisco Bay area. I had known about the Fourier transformation in terms of its role in holography. But I had never appreciated the Fourier-based fundamental conceptualizations portrayed below. I asked Chew where I might find more about this and he noted that he'd got it from his colleague Henry Stapp who in turn had obtained it from Dirac. (Eloise Carlton a mathematician working with me and I had had monthly meetings with Chew and Stapp for almost a decade and I am indebted to them and to David Bohm and Basil Hiley for guiding me through the labyrinth of quantum thinking.)
The diagram has two axes, a top-down and a right-left. The top-down axis distinguishes change from inertia. Change is defined in terms of energy and entropy. Energy is measured as the amount of actual or potential work necessary to change a structured system and entropy is a measure of how efficiently that change is brought about. Classically, these measurements are made in terms of numbers. Inertia is defined as moment, the rotational analogue of mass. Location is indicated by its spatial coordinates in terms of their geometry.
The right-left axis distinguishes between measurements made in the spectral domain and those made in spacetime. Spectra are composed of interference patterns where fluctuations intersect to reinforce or cancel. Holograms are examples of the spectral domain. I have called this pre-spacetime domain a potential reality because we navigate the actually experienced reality in spacetime.
The up-down axis relates mind to matter by way of sampling theory (Barrett 1993). Choices need to be made as to what aspect of matter we are to “attend”. The brain systems coordinate with sampling have been delineated and brain systems that impose contextual constraints on sampling have been identified (Pribram 1959; 1971). The down-up relationship describes the emergence of mental patterns of from material patterns.
My claim is that the basis function from which both matter and mind are “formed“ is the potential reality, the flux (or holo-flux, see Hiley 1996). This flux provides the ontological roots from which conscious experiences regarding matter as well as mind (psychological processes) become actualized in spacetime. To Illuminate this claim, let me begin with a story I experienced: Once, Eugene Wigner remarked that in quantum physics we no longer have observables, (invariants) but only observations. Tongue in cheek I asked whether that meant that quantum physics is really psychology, expecting a gruff reply to my sassiness. Instead, Wigner beamed a happy smile of understanding and replied, “yes, yes, that's exactly correct”. If indeed one wants to take the reductive path, one ends up with psychology, not particles. In fact, it is a psychological process, mathematics, that describes the relationships that organize matter. In a non-trivial sense current physics is rooted in both matter and mind. (Chapline 2000, “Is physics and mathematics the same thing?”).
Conversely, communication ordinarily occurs by way of a material medium Bertrand Russell (1948) addressed the issue that the form of the medium is largely irrelevant to the form of the communication. In terms of today's functionalism it is the communicated sample of a pattern that is of concern, not whether it is conveyed by a cell phone, a computer or a brain and human body. But not to be ignored is the fact that communication depends on being embodied, instantiated in some sort of material medium. This convergence of matter on mind, and of mind on matter, gives credence to their common ontological root. (Pribram 1986; 1998). My claim is that this root, though constrained by measures in spacetime, needs a more fundamental order, a potential that underlies and transcends spacetime. The spectral basis of the quantal nature of both matter and of communication portray this claim.
