Stapp is using Niels Bohr's "Copenhagen interpretation" in which particles do not have actual visualizable paths. I use David Bohm's "hidden variable" interpretation in which particles have actual visualizable paths and are acted upon not only by ordinary forces, but also by a new kind of "quantum force" that is both nonlocal and state-dependent. State-dependence means that the quantum forces between particles depend on the pattern of information in Hilbert space in addition to the relative distances between the particles. David Chalmers has noted how such patterns of information are essential for a fundamental theory of consciousness. Ordinary classical forces like electromagnetism are not state-dependent. There is no "second process" in Bohm's theory, however, there is an analog to the "selection process" so that whatever can be done in the Copenhagen interpretation can be accounted for in the Bohm interpretation. The superiority of Bohm's theory is that it makes it easier to see how to go beyond current quantum theory to account for consciousness which demands a strong violation of the "irreducible element of chance".

Contemporary quantum mechanical description of nature involves two processes. The first is a dynamical process governed by the equations of local quantum field theory. This process is local and deterministic, but it generates a structure that is not compatible with observed reality. A second process is therefore invoked. This second process somehow analyzes the structure generated by the first process into a collection of possible observable realities, and selects one of these as the actually appearing reality. This selection process is not well understood. It is necessarily nonlocal and, according to orthodox thinking, is governed by an irreducible element of chance.

The occurrence of this irreducible element of chance means that the theory is not naturalistic: the dynamics is controlled in part by something that is not part of the physical universe.

The present work describes a quantum mechanical model of brain dynamics in which the quantum selection process is a causal process governed not by pure chance but rather by a mathematically specified nonlocal physical process identifiable as the conscious process.

1. Introduction.

The orthodox Copenhagen interpretation of quantum theory, as promulgated by Niels Bohr, is pragmatic: the quantum formalism is regarded as merely a set of useful rules for predicting what our classically describable experiences will be under conditions specified by classically describable experiences.

The entry of chance into the theory is regarded as an expression of the brute empirical fact that atomic systems prepared and measured identically, to the best of our experimental capabilities, give nonidentical results that have statistical regularities.

The question of the origin of the element of chance is left unanswered.

Einstein rejected the idea that God plays dice with the universe,

and Bohr concurred in rejecting the idea of a choice on the part of `nature' "[1]. Yet the notion that a definite choice is fixed by nothing at all is even more repugnant to rational thought.

Bohr's interpretation does not cover biological and cosmological systems.

The possibility therefore arises that what appears as pure chance in the restricted domain of atomic phenomena has its roots in a more complete description of nature.

The element of chance normally enters into quantum theory in connection with our observations. In the absence of observations the evolution of the universe is governed by local laws that are natural generalizations of the laws of classical mechanics: the universe is conceived to be an aggregate of localized properties, and the rate of change in each such property is governed exclusively by nearby properties. Observations, however, are associated with a second process" that is logically required to be highly nonlocal [2], and therefore fundamentally different from the first process.

The next issue is what is doing the measuring. All "alive" systems must measure themselves and this requires direct back-action of the objective matter of the system on its subjective quantum wave function. The quantum wavefunction in the presence of back-action is a field of pure qualia or mind.

The aim of the present work is to provide a logical and mathematical framework for a causal theory of brain dynamics in which the controlling element of chance in the quantum selection process is replaced by a nonlocal physical pro- cess identifiable with the conscious aspect of brain process.

In this formulation of quantum dynamics conscious experiences exercise genuine control over brain activity.

Analogous elements should occur in all biological systems, due to the enormous survival advantage they can confer. But in lower life forms, and also in the inanimate part of nature, these elements will, because of the absence in them of the intentional and attentional structure supplied by our brains, be very different from human conscious experiences.

2. Quantum Searching and Survival.

Survival, at least in the animal kingdom, depends on rapidly finding and executing appropriate behaviors. Options are generally available, and the or- ganism must reject those not appropriate in the specific situation in which it finds itself, and pursue one that is appropriate. The process of searching for an appropriate behavior can be likened to a search for the way out of a maze. The classical search procedure is essentially to try, at some mental level, each of the possibilities until a blockage is encountered, and then to back off and try another. This can be very time consuming, and an organism that uses it is likely to be devoured by one that employs a faster process. Massive parallel (and interconnected) processing may offer advantages, but it introduces the compensating problem of keeping the whole system operating in a coherently coordinated way.

For rapid searching the exploitation of the quantum character of brains can confer a huge advantage. Quantum dynamics is essentially hydrodynamics [3]. The contrast between classical and quantum search procedures can be likened to the contrast between the particle and hydrodynamical solutions to the problem of getting out of a maze: in the particle solution the particle bounces randomly around the maze in the hope of finding the small opening; in the hydrodynamical solution the maze is filled with water, which then rushes out through the opening. The essential point is that in classical-particle dynamics what the particle does is completely unaffected by what it would have done if it had been on a nearby trajectory, whereas the flow of water is affected by what is happening nearby: if water rushes out at one place, leaving a void, then nearby water rushes in to fill the void, sucking in water from further away.

This point can be illustrated by considering a circular trough that has also a circular cross section in each radial plane. Suppose this trough is filled with a statistical ensemble representing alternative possibilities for the position and velocity of one particle. Each element of the ensemble oscillates in a radial plane, with no angular motion. Suppose we open a small angular section of the trough so that the particles in that section flow out. The remaining particles, which represent the alternative possibilities, will continue to oscillate forever. But if one fills the trough with water and opens the section then all the water runs out. The quantum probability function for one particle behaves like water, not like the statistical ensemble of independent particles.

A physicist who wants to see this in the equations can consider a wave function for a particle confined to a circle. The time-dependent Schroedinger has on the left the operator i times the derivative with respect to t, and on the right the kinetic energy term. To represent the opening in the maze (i.e., the solution that is not blocked by negative feed-back) add on the right the term b times minus i times a Dirac delta function of the (cyclic) argument x(mod 1). Then the rate of loss of probability in the ring is 2b times the square of the magnitude of the wave function at x=0. This is non-negative, and more detailed calculations show that the probability is rapidly sucked to the point x=0, where it disappears.

A more realistic model would have in place of the Dirac delta function a function with a central plateau bounded on each side by a sharp gaussian fall-off. The rate of flow of probability from the surrounding region into the region of probability loss is controlled by the sharpness of the gaussian walls. This way of searching for an appropriate response should be particularly rapid and effective in a brain organized in the way described in [4], because in that system the unblocked flow out of the maze (of alternatives, most of which are blocked by negative feed-back) creates a template for action, which then automatically evolves into the corresponding action itself. There is no need to convert the solution represented by the unblocked flow into a plan of action, and then to create the corresponding sets of instructions to muscles etc.: the unimpeded flow produces a template for action that, if not blocked, automatically evolves into the appropriate action itself. So the basic problem of rapidly producing an appropriate action is precisely that of rapidly getting all of the probability into an unblocked channel, i.e., of keeping the search process from getting hung up exploring the blocked channels. The hydrodynamical character of the quantum law of evolution provides an efficient way to solve this problem. Notice also that the quantum mechanism does not involve a sudden `all or nothing' leap in phylogenetic development: even a little bit of sucking of the probabilities into unblocked channels will aid survival, and the organism can gradually evolve in a way that tends to enhance the process.

3. Decoherence

It has often been observed that the coupling of a system to its environment has a tendency to make interference phenomena that are present in principle within quantum systems difficult to observe in practice. Phase relationships, which are essential to interference phenomena, get diffused into the environment, and are difficult to retrieve. The net effect of this is to make a large part of the observable phenomena in a quantum universe similar to what would be observed in a world in which certain collective (i.e., macroscopic) variables are governed by classical mechanics. This greatly diminishes the realm of phenomena that require for their understanding the explicit use of quantum theory.

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 single quantum system holds. This will reduce the distances over which the simple hydrodynamical considerations described above will hold. However, the following points must be considered.

a) A calcium ion entering a bouton through a microchannel of diameter x must, by Heisenberg's indeterminacy principle, have a momentum spread of h/&x, and hence a velocity spread of h/m&x, and hence a spatial spread in time t, if the particle were freely moving, of (h/m&x)t. Taking t to be 200 microseconds, the typical time for the ion to diffuse from the microchannel opening to a triggering site for the release of a vesicle of neurotransmitter, and taking x to be one nanometer, one finds the diameter of the wave function to be about 0:04 centimeters, which is huge compared to the 1/100000000 centimeter size of the calcium ion. There is, therefore, in brain dynamics a powerful counter-force to the mechanisms that tend to diminish quantum coherence effects.

b) The normal process that induces decoherence arises from the fact that a collision of a state represented by a broad wave function with a state represented by a narrow wave packet effectively reduces the coherence length in the first state to a distance proportional to the width of the second state. But in an aqueous medium in which all the states of the individual systems have broad packets this mechanism is no longer effective: coherence lengths can remain long.

c) Even if the coherence length were only a factor of ten times the diameter of the atom or ion involved in some process, the cross section involved would be a hundred times larger. The search processes under consideration here involves huge numbers of atoms and ions acting together, and the cross-section factors multiply. Thus even a small effect at the level of the individual atoms and ions could give, by virtue of the hydrodynamical effect, a large quantum enhancement of the efficiency of an essentially aqueous macroscopic search process.

4. Quantum Theory and Experience

The core problem in quantum theory is perhaps best illustrated by Einstein's example [5] of a radioactive atom placed in a Geiger counter that is hooked up to a pen that is drawing a line on a moving strip of paper: when the atom decays the Geiger counter fires, and this causes a blip to be drawn on the moving strip of paper. Since all the parts of the apparatus are made up of atoms and electrons, etc., one should be able to apply quantum theory. But if one simply applies the Schroedinger equation, or the equations of local field theory, one finds that the moving strip will evolve into a continuous superposition of possibilities, with every possible time of decay represented by a correspondingly placed blip. No single decay time is singled out as the actual decay time. But what is observed if one looks at the strip is a blip appearing in one place, rather than a smeared out superposition of all the possibilities. So quantum theory, if left in this stage where only the Schroedinger equation (or the corresponding equation of local quantum field theory) is considered, is incomplete: some ex- planation of the mismatch between what we experience and what is generated by the Schroedinger equation is needed. Some account is needed for the process that selects, from the continuum of possibilities generated by Schroedinger equation, the particular thing that we actually see.

Physicists have proposed a number of possible ways of completing the theory. I do not wish to describe them here in detail. The chief contenders can be tied to the names of Bohr, Bohm, Everett, Heisenberg, and Wigner. Very briefly, the essence of each position is as follows: Bohr [6]: Quantum theory is a set of useful rules that scientists can use to compute statistical predictions about whether or not certain conceivable classically describable experiences will appear under various conditions specified by classical describable experiences. Defect: The theory formulated in this way admittedly does not cover biological and cosmological systems, hence a putative theoretical description of nature herself might be useful for the further development of science.

Bohm [7]: There is in addition to the quantum wave function also a real clas- sical world whose motion is controlled by the wave function.

As in classical mechanics the entire course of history is fixed at the moment of the creation of the universe.

Defects: This formulation is very non parsimonious because the Schroedinger equation must grind out forever the infinitudes of "empty branches" of the wave function that will never have any effect on the classical world, which is the only part of reality that we experience.

Also, the statistical aspects of quantum theory enter though the obscure idea of a preferred statistical ensemble of universes.

Finally, consciousness can play no causal role in the dynamics.

Everett [8]: The wave function of the universe is continually separating into "branches" that are "decoherent" in the sense that if one restricts the set observables to certain localizable collective (macroscopic) properties then the state of the universe is approximately equivalent to a statistical mixture of these branches. It is assumed that there are separate mental states associated with these separate branches, and that they can be treated as members of a statistical ensemble with weights specified by the weights of the corresponding statistical ensemble of branches. All of the mental states in this ensemble are assumed to really exist, even though each such state contains no awareness of the others. Defects: This formulation is very non parsimonious: only one of the infinitude of mental universes is ever experienced by us.

Also, the treatment of the mental states does not follow from the physics: the state of the universe is a "conjunction" of the branches (it consists of branch 1 and branch 2 and ...) whereas in order to apply statistics the set of mental worlds must be "disjunctive" (it consists of mind 1 or mind 2 or ...). The notion that a single mental state can evolve into either mental state 1 or mental state 2, with specified probabilities, seems incompatible with the idea that the two alternatives are simultaneously present and really existing. At the very least, these ideas constitute a radical departure from normal ideas about the relationship between conjunctions and disjunctions. Furthermore, the notion that the wave function separates into well defined distinct "branches" is not always applicable: the normal evolution of a wave is an amorphous spreading out. This creates a serious technical problem, not yet resolved, of how to define the decomposition of an amorphous quantum structure into a disjunction of classically describable observable realities in such a way that a probability can be coherently assigned to each of the associated overlapping mind/brain states, if there is no physical process that picks out and actualizes one of these overlapping states, and rejects the others. Finally, consciousness can play no causal role in the dynamics.

Heisenberg [9]: Heisenberg is a co-creator of the Copenhagen interpretation that I have associated with Bohr. But he also proposed a picture of nature herself in which there are two kinds of realities: potentialities and actualities. It is possible to regard the wave function as a representation of "potentialities" for "actual events": the potentialities evolve according to the Schroedinger equation until the conditions for a possible `event' are created, and then this event either occurs or does not occur, according to a prescribed statistical rule. If the event occurs then the wave function changes to a new form that reflects the fact that this event has occurred, and then it (the new wave function) proceeds again to evolve according to the Schroedinger equation. The events are supposed to occur in connection with "measuring devices". Defects: The definition of "measuring device" is not specified, and hence the theory is not well defined. And, again, mind plays no role in the dynamics.

Wigner [10]: Wigner, giving credit to von Neumann, suggests that what characterizes a "measuring device" is the occurrence of an "experience" in connection with the measurement. Specifically, the "measuring devices" of the Heisenberg interpretation are identified with the aspects of brain dynamics directly associated with the occurrence of a conscious experience.

Each of these general approaches has its contemporary proponents. Thus the works of Ghirardi, Rimini, Weber, and Pearle [11] are in the Heisenberg spirit. The works of Gell-Mann and Hartle [12] are in the Everett framework. The works of Omnes [13] are, apparently, in the Bohr spirit. The present work is in the Heisenberg-Wigner-von Neumann spirit: I accept the general idea of Heisenberg that the wave function specifies propensities for events to occur, and the idea of Wigner (or von Neumann) that these events are associated with experiential qualities, in some very generic sense, but allow events to occur in both inanimate and animate systems. However, I focus first on those particular events that are identifiable with human conscious events, since we have direct information about these. 5. Choice and Consciousness

William James concludes from a study "of the particulars of the distribution of consciousness" (as contrasted with our perhaps misleading intuition) that "consciousness is at all times primarily a selecting agency". He says also: "It is to my mind utterly inconceivable that consciousness should have nothing to do with a business to which it so fathfully attends". But why should he, or anyone else, even imagine that consciousness has nothing to do with the choices we make? The reason, of course, is that this is what classical physics tells us.

Let me explain. The infant learns, early on, through concordance of impressions gleaned from the five senses, including reports of others, to think that things like apples and toys, etc. continue to exist even when no one is sensing or actively thinking about them. Classical physics extends this idea of objective existence to the whole world of inanimate objects: all such things, large and small, are conceived to be mere aggregates of simple localizable properties that evolve according to local deterministic laws. Functional structures, such as pistons and drive shafts, though usefully conceived by us as whole functional entities, are considered to be fundamentally nothing but the aggregates of the interacting local parts of which they are formed. According to classical thinking, no extra property not explainable in terms of the aggregrate of simple localized properties is needed to explain, at least in principle, the behavior of even the most complex physical structure. This is the basic idea of classical physics. If we extend that idea to the bodies of human beings then their behaviors should, in principle, be completely explainable in terms of their localizable components. Conscious thoughts do not appear in the classical-physics description, and hence, in principle, no reference to such things should be needed to explain human behavior. Any notion that certain functional features or aspects of brain dynamics have an experiential "beingness as a whole" that goes beyond the elemental beingness of the interacting local properties is alien to classical thinking, and directly con- tradicts it if any dynamical role is given to such entities that is not completely reducible to the local dynamics of the local parts. Thus, according to the ideas of classical mechanics, our conscious thoughts are excess baggage: all physical behavior would be just the same if the functional structure of the brain were just what it is, but no conscious thoughts were present.

It is difficult to believe that thoughts do nothing: that they are pure excess baggage. Yet how is one to make sense of the alternative idea that they, them- selves, do something that their parts are not doing? How can a "whole" have an effect that is not ultimately just the effect of its parts acting in unison? Our point of departure is the fact that in (Heisenberg-von Neumann-Wigner) quantum field theory there are two distinct dynamical processes. They are most clearly displayed in the so-called Heisenberg picture, or representation. There the local operators of the theory evolve according to the Heisenberg equations of motion, which are the Heisenberg-picture counterparts of the Schroedinger equation. These equations generate from the operators located along any space- like surface (or constant-time slice) the operators at all spacetime points, i.e., at all points, from the infinite past to the infinite future. This is analogous to the situation in classical mechanics, where the classical equations of motion generate, from values on one spacelike surface, the values of all quantities at all times and places. But this part of the dynamics is, in the quantum case, only half the story, and the relatively trivial kinematic part at that. The nontrivial part of the dynamics is the part that controls the evolution of the (Heisenberg picture) state of the universe. This part consists of selections that are not determined by the local deterministic aspects of the quantum dynamics. Orthodox quantum theory says that these selections are determined by pure chance, but the simplest naturalistic possibility is that they are controlled by some nonlocal aspect of the physical universe. If, in the case of brain process, this aspect can be identified with our conscious thoughts, then consciousness would be a bona fide selecting agency. Because the selection events are events they do not have separate parts: each quantum event is a selection and actualization, all at once, of a spatially extended structure of propensities.

How could such a quantum process of selection and actualization work? 6. General Description of Brain/Mind Dynamics Before going into the mathematical details of the model, I give a brief general description of my conception of how the quantum brain/mind works. For a more detailed description see reference [4]. Each conscious event is the felt event that actualizes a certain "executive" pattern of brain activity. This pattern endures long enough for it to become "facilitated": i.e., to become etched into the physical structure of the neurons in such away that a subsequent excitation of part of the pattern tends to spread to the whole pattern.

The sequence of conscious thoughts associated with a given brain is represented by a sequence of actualizations of such patterns. The patterns in such a sequence have, in general, a large carry-over of components from one pattern to the next. Thus the sequence of executive patterns has the structure of a "marching band" that marches into and out of existence, with new parts coming into being at each step, and older parts fading out.

The Duke of Plaza Toro

Gondoliers, Gilbert and Sullivan

Enter subjective "qualia":

The "feel" of each thought expresses the intentional and attentional content of the associated actualized executive pattern. The pervading experience of the presence of an enduring "I" is the felt process of continually re-actualizing the slowly changing peripheral part of the executive pattern. This part provides the over-all orientation for the executively controlled part of the mind/brain process. The sequence of felt events that actualize the executive patterns constitutes a tiny part of the brain activity: it rides on a vast substrate of unconscious brain activity that is controlled by the local deterministic process governed by the equations of local quantum field theory.

Each executive pattern consists of a template for action that is constructed largely from components of earlier templates, and it issues its directives to the lower-level processes simply by the automatic spreading of the neural patterns of excitations that comprise it. The processing is analog, not digital, with a continual inflow of information from the environment, to which the body and brain adapt. Although the analog process can be simulated, at great expense, by a digital computer, the issue here pertains to how real brain tissues and aqueous ionic solutions, etc. function in real time. Due to the quantum nature of the brain, and in particular to point a) mentioned in section 3 above, the brain state must evolve, via the local deterministic process determined by the equations of local quantum field theory, into a superposition of states each of which contains at the executive level a different alternative possible template for action. Each alternative is represented, during some brief time interval, by a relative stable enduring pattern of neural activity, and this stability constitutes the condition required for an event to occur. The "second process" now enters. It is represented in the physical realm (i.e., in Hilbert space) by a selection of one of these alternative possible states, each of which specifies a distinct template for action.

According to orthodox quantum ideas, this selection event is controlled by pure chance. The use of "pure chance" in a pragmatic context is completely acceptable. But it is not acceptable at the level of ontology. In the context of a naturalistic science some explanation in terms of physical quantities is needed, at least in principle, for how the particular reality that actually appears is picked out from the collection of alternative possibilities that are created by the local deterministic part of the dynamics.

The simplest naturalistic possibility is that the selection is controlled by the state vector itself, since this vector, and its changes, represent the physical reality. A most natural possibility would be for the choice to be controlled by the aspect of the state vector that specifies the environment that defines the possible states between which the selection event must choose. In our case that aspect would be the state of the brain itself, or, perhaps, even the aspect of the brain associated with the "I" mentioned above. In this latter case it would be the "I", as it is represented in the quantum dynamics, that selects the sequence of templates for action that controls the behavior of the organism. But how could such a quantum process work?

7. Mathematical Formulation

My aim here to provide a mathematical model of causal quantum brain dynamics in which the quantum selection process is governed by our conscious thoughts, rather than by pure chance; i.e., where the notorious stochastic selection process of quantum mechanics, called the "irrational" element by Pauli, is replaced by a causal process in which our conscious thoughts, acting as whole entities not reducible to aggregates of local properties, become the bona fide selecting agents.

Quantum electrodynamics (extended to cover the magnetic properties of nuclei) is the theory that controls, as far as we know, the properties of the tissues and the aqueous (ionic) solutions that constitute our brains. This theory is our paradigm basic physical theory, and the one best understood by physicists. It describes accurately, as far as we know, the huge range of actual physical phenomena involving the materials encountered in daily life. It is also related to classical electrodynamics in a particularly beautiful and useful way. I take it as the basis of this work.

In this section I assume the reader to have some knowledge of the principles of quantum electrodynamics, and the notations used to describe it. I draw particularly on references [14] and [15], which describe in detail the natural connection between quantum electrodynamics and classical electrodynamics. In the low-energy regime of interest here it should be sufficient to consider just the classical part of the photon interaction defined in [14].

Then the explicit expression for the unitary operator that describes the evolution from time t1 to time t2 of the quantum electromagnetic field in the presence of a set of specified classical charged-particle trajectories, with trajectory Li......with each element of the superposition accompanied by the coherent-state electromagnetic field that this set of trajectories generates. Let the state of the electromagnetic field restricted to the modes that represent consciousness be called .... Using the decomposition of unity one can write ...... Hence the state at time t can be represented by the function ....., which is a complex-valued function over the set of arguments .... where n is the number of modes associated with.... Thus in this model the contents of the consciousness associated with a brain is represented in terms of this function defined over a 2n dimensional phase space. To construct a causal dynamics in which the state of consciousness itself controls the selection of the next state of consciousness one must specify a rule that determines, in terms of the evolving state ... both the time ti+1 when the next selection event occurs, and the state .... that is selected and actualized by that event. In the absence of interactions, and under certain ideal conditions of confinement, the deterministic normal law of evolution entails that in each mode k there is an independent rotation in the (qk; pk) plane with a characteristic angular velocity .... Due to the effects of the motions of the particles there will be, added to this, a flow of probability that will tend to concentrate the probability in the neighborhoods of a certain set of "optimal" classical states | q; p >. The reason is that the function of brain dynamics is to produce some single template for action, and to be effective this template must be a "classical" state, because, according to orthodox ideas, only these can be dynamically robust in the room temperature brain [16]. According to the semi-classical description of the brain dynamics, only one of these classical-type states will be present, but according to quantum theory there must be a superposition of many such classical-type states, unless collapses occurs at lower (i.e., microscopic) levels. The assumption here is that no collapses occur at the lower brain levels: there is absolutely no empirical evidence, or theoretical reason, for the occurrence of such lower-level brain events.

So in this model the probability will begin to concentrate around various locally optimal coherent states, and hence around the various (generally) isolated points (q; p) in the 2n phase space of the fact that the template for action actualized by the quantum brain event is represented as a projected body-world schema, i.e., as the brains projected representation of the body that it is controlling and the environment in which it is situated. Let a certain time ti+1 > ti be defined by an (urgency) energy factor ... is to assuage the classical intuition that the action-potential pulse along each nerve "ought to be classically describable even when it is not observed", instead of being controlled, when unobserved, by the local deterministic equations of quantum field theory. But the validity of this classical intuition is questionable if it severely curtails the ability of the brain to function optimally.

A second important feature of this selection process is that the actualized state ... is the state of the entire aspect of the brain that is connected to consciousness. So the feel of the conscious event will involve that aspect of the brain, taken as a whole. The "I" part of the state ... is its slowly changing part. This part is being continually re-actualized by the sequence of events, and hence specifies the slowly changing background part of the felt experience. It is this persisting stable background part of the sequence of templates for action that is providing the over-all guidance for the entire sequence of selection events that is controlling the on-going brain process itself.

A somewhat more sophisticated search procedure would be to find the state ... , as before, but to identify it as merely a candidate that is to be examined for its concordance with the objectives imbedded in the current template. This is what a good search procedure ought to do: first pick out the top candidate by means of a mechanical process, but then evaluate this candidate by a more refined procedure that could block its acceptance if it does not meet specified criteria.

It may at first seem strange to imagine that nature could operate in such a sophisticated way. But it must be remembered that the generation of a truly random sequence is itself a very sophisticated (and indeed physically impossible) process, and that what the physical sciences have understood, so far, is only the mechanical part of nature's two-part process. Here it is the not-well-understood selection process that is under consideration. I have imposed on this attempt to understand the selection process the naturalistic requirement that the whole process be expressible in natural terms, i.e., that the universal process be a causal self-controlling evolution of the Hilbert-space state vector in which all aspects of nature, including our conscious experiences, are efficacious. No attempt is made here to show that the quantum statistical laws will hold for the aspects of the brain's internal dynamics controlled by conscious thoughts. No such result has been empirically verified. The v>

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