
 Journal of NonLocality and Remote Mental Interactions Vol. I Nr. 1
TGD inspired theory of consciousness Matti Pitkänen Postal address:
TGD inspired theory of consciousness relies on two identifications. The identification of quantum jump between quantum histories as a moment of consciousness reduces quantum measurement theory to fundamental physics and solves long list of paradoxes of modern physics. The identification of self as a subsystem able to remain unentangled in subsequent quantum jumps provides a quantum theory of observer and one can identify self also as a fundamental statistical ensemble. The generalization of spacetime concept so that it allows both real and padic regions unable to entangle mutually is a crucial prequisite for the notion of self and padic spacetime regions define cognitive representations. In this article these notions are analyzed in more detail. Quantum jump between quantum histories decomposes into three parts corresponding to the unitary U process of Penrose followed by the TGD counterpart of state function reduction in turn followed by a cascade of self measurements giving rise to the TGD counterpart of state preparation. The dynamics of self measurement is determined by the so called Negentropy Maximization Principle (NMP). Selves form a hierarchy and self experiences its subselves as mental images and is in turn a mental image of a higher level self. The experience of self is a statistical average over quantum jumps occurred after the last 'wakeup' and the theory of qualia can be formulated in terms of statistical physics. Self experiences the subselves of subself as a statistical average so that self hierarchy means also an abstraction hierarchy. Self has as its geometric correlate so called mindlike spacetime sheets of finite duration with respect to geometric time (as opposed to subjective time determined by the sequence of quantum jumps) and one can understand how psychological time and its arrow emerge. The new view about time has rather dramatic implications: the civilizations of the geometric past and future exist subjectively now so that one can speak about fourdimensional society. The paradigm of fourdimensional brain in turn provides a completely new view about long term memories. Crucial element behind all these developments is the classical nondeterminism of the fundamental variational principle determining the dynamics of the spacetime surfaces.
1. Introduction 2.Quantum jump as a moment of consciousness 3. Quantum self
I have not been able to avoid totally the use of greek letters and mathematical symbols in the text. I have chosen to represent them in latex code since it is probably familiar to many readers. Thus greek letters are denoted by symbols like \Psi, \alpha, \Delta, \tau. ^n signifies upper index n (say in symbol M^4 for Minkowski space or in n:th power x^n of x). Lower index n is expressed as _n (say x_n or CP_2). Square root of x is expressed as \sqrt{x}. Sum of elements x_n is expressed as SUM_n x_n. x propto y reads x is proportional to y. X times Y denotes Cartesian product of spaces X and Y and x times y denotes the ordinary product of numbers x and y. x \pm y denotes for x plusminus y. x\simeq y can be read as x=about y. and x\sim y can be read as x =roughly about y. \infty denotes infinity.
T(opological)G(eometro)D(ynamics) inspired theory of consciousness can be regarded also as a generalization of the quantum measurement theory. The connection comes from the identification of quantum jump as a moment of consciousness and the replacement of the external observer with the notion of 'self' defined as a subsystem able to remain unentangled during subsequent quantum jumps. This generalization of quantum measurement theory opens the black boxes of of state function reduction and preparation by combining them in the notion of quantum jump between quantum histories. The basic new elements as compared to the standard physics based theories of consciousness are the new view about time and quantum state allowing to resolve the basic paradoxes of modern physics, the notion of manysheeted spacetime; the nondeterminism of the fundamental variational principle determining the dynamics of the spacetime surfaces; and padic numbers. 1. Quantum states as quantum histories General coordinate invariance forces to replace quantum state as time=constant snapshot with entire quantum history with can be regarded as a generalition for the solution of Schrödinger equation describing entire universe. Classical histories correspond to spacetime surfaces. 2. Nondeterminism of quantum jump is outside the realm of spacetime and state space Since quantum jumps occur between quantum histories, the nondeterminism of quantum jump is outside the spacetime and the space of quantum states. This solves the basic paradox of the quantum measurement theory. Time evolution by quantum jumps, subjective time development, corresponds to hopping in the space of solutions of the field equations. 3. Two times, two causalities This view forces to differentiate between subjective time and geometric time. Geometric time is the fourth coordinate for spacetime surfaces whereas subjective time corresponds to a sequence of quantum jumps identified as moments of consciousness. The complete spacetime democracy has most profound implications concerning the interpretation of the theory. The generalization of the spacetime concept involving in an essential manner also the classical nondeterminism of the basic variational principle defining spacetime surface X^4(X^3) associated with a given 3surface X^3, allows to understand how the correspondence between geometric and subjective time emerges. The point is that mindlike spacetime sheets with finite geometric time duration and well defined temporal center of mass coordinate become possible. These mindlike spacetime sheets serve as geometric correlates for conscious selves and one can understand the emergence of the psychological time and its arrow. 4. pAdic physics as physics of cognition pAdic numbers (completions of rationals) is also something essentially new. The very definition of the concept of self as a system able to remain unentangled during subsequent quantum jumps requires padic numbers. The reason is that the unentangled state of two subsystems is unstable unless they correspond to different number fields in which case entanglement is not possible at all. In purely real context the only self would be the entire Universe: subselves inside real self are padic islands in the sea of real numbers. The inherent nondeterminism of the padic field equations is identified as nondeterminism of imagination which is an essential element of cognition. pAdic spacetime regions represent the 'mind stuff', geometric correlate for cognition, they are however not conscious. The transformations of intentions to actions occur in quantum jumps in which padic spacetime region is replaced with a real one whereas sensory input transforms to thought in the reverse transition. This mechanism should apply not only to the ordinary volitional acts but also to various forms of psychokinesis. pAdic spacetime regions are obviously the TGD counterpart for the mind stuff of Descartes and dualism relates material world and cognitive representations which both are Zombies. 5. Connection with statistical physics and selforganization The notion of self as a system able to remain unentangled and able to perform quantum jumps in this state implies also a deep connection with statistical physics. Self corresponds to the sequence of quantum jumps for subsystem and the final states of these quantum jumps define what might be called a fundamental statistical ensemble. The contents of consciousness of self are determined as statistical averages over experiences associated with individual quantum jumps. Self has subselves and expreriences them as mental images. Self experiences also subselves of subself as a statistical ensemble providing kind of abstraction. Selves participate to each quantum jump and thus selforganize. This leads to a quantum level model of selforganization and Darwinian selection can be seen as due to the dissipation accompanying selforganizing systems. 6. The notion of manysheeted spacetime and biosystems as macroscopic quantum systems Concerning the concrete applications of the theory at the level of biosystems and brain, the notion of manysheeted spacetime is of crucial importance since it makes possible to understand how biosystems manage to be macroscopic quantum systems. Also classical color force and Z^0 force play a key role in the new physics associated with the living matter. The implications of the theory are rather farreaching and strongly encourage to give up the cherished belief about brain as a seat of consciousness. In TGD universe our selves involve in an essential manner electromagnetic field structures (topological field quanta) having size measured using Earth size as a unit. Our physical bodies can be seen as kind of sensory and motor organs of these electromagnetic selves. In particular, physical death can be seen only as a death of a mental image about the physical body.
The notions of quantum jump and self are the basic concepts of TGD inspired theory of consciousness. Quantum jump is the microtemporal building block of conscious experience and relates to the theory of consciousness much like physics at Planck length scale relates to the macroscopic physics. Self corresponds to the macrotemporal aspects of conscious experience and statistical ensemble aspect is crucial in the theory of consciousness.
Quantum jump was originally seen as something totally irreducible. Gradually the rich substructure of quantum jump has revealed itself. First of all, quantum jump decomposes into informational time development \Psi_i> U\Psi_i followed by the TGD counterpart of state function reduction realized as a localization in zero modes which correspond to nonquantum fluctuating degrees of freedom of configuration space of 3surfaces (see the first part of [TGD] and of [cbook]): U\Psi_i> \Psi_f^0 . The assumption that the localization occurs in the zero modes of the configuration space poses a very important consistency condition on U. U must effectively correspond to a flow in zero modes such that there is oneone correlation between the quantum numbers \alpha in quantum fluctuating degrees of freedom in some state basis and the values z of the zero modes in state U\Psi_i: \alpha<> z (\alpha) . This together with the fact that zero modes are effectively classical variables, implies that the localization in zero modes can be identified as the TGD counterpart for the state function reduction. The state function reduction is followed by a cascade of self measurements in quantum fluctuating degrees of freedom (the values of the zero modes do not change during this stage) \Psi_f^0> .... > \Psi_f , whose dynamics is governed by the Negentropy Maximization Principle (NMP, see the chapter "NMP" of [cbookI]). At least formally, this process is analogous to analysis at level of cognition leads to a completely unentangled state (apart from entanglement present in bound states) identifiable as a prepared state. It must be emphasized that self measurement is microtemporal aspect of consciousness and does not directly relate to our conscious experience. A good metaphor for quantum jump is as Djinn leaving the bottle (informational time development), fulfilling the wish (quantum jump involving choice) and returning to, possibly new, bottle (localization in zero modes and subsequent state preparation process). One could formally regard each quantum jump as a TGD counterpart of a quantum computation lasting infinitely long time t> \infty followed by a state preparation of the initial state of the next quantum computation.
The dynamics of self measurements is governed by Negentropy Maximization Principle (NMP, see the chapter "NMP" of [cbookI]), which specifies which subsystems of self are subject to quantum measurement in a given self measurement. NMP can be regarded as a basic law for the dynamics of quantum jumps and states that the information content of the conscious experience is maximized. In padic context NMP dictates the dynamics of cognition. a) NMP applies to each self with fixed values of zero modes separately and is therefore in a welldefined sense a local principle. Every self in \Psi_{f}^0 participates in self measurement sequence \Psi_{f}^0> ... \Psi_f, which means that some subsystem of the self is quantum measured. b) A quantum jump for a given irreducible self X corresponds to a measurement of the density matrix for some subsystem Y of X. In this measurement subsystem Y goes to an eigenstate of the density matrix and Y becomes unentangled. Same happens to the complement of Y inside X. The amount of entanglement is measured by entanglement entropy S and S vanishes for the final state of the quantum jump. Thus S can be regarded as negentropy gain having interpretation as some kind of conscious information, or rather, reduction of disinformation. The conscious experience must be assigned with self X. One cannot associate it with the measured subsystem or its complement inside self since they are in a completely symmetric position since diagonalized density matrices are identical. Hence there is no manner to tell which is the measured system and which the measuring subsystem and one must define self measurement as creating an unentangled subsystemcomplement pair inside a self and identify the self as the conscious measurer. In state function reduction zero modes could be regarded as representing dynamical degrees of freedom of measurer. c) NMP states that the entanglement entropy reduction associated with the conscious experience of an irreducible self X is maximal. Interpreting entanglement negentropy gain as a conscious information, on can say that we live in (or create) the best possible world. Only the quantum jumps giving rise to maximum information content of conscious experience occur (it must be noticed however that one can assign several types of information measures with conscious experience). This requirement fixes the quantum measured subsystem Y of given self uniquely unless there are several subsystems giving rise to same maximum negentropy gain: in this case any of the quantum jumps occurs with same probability.
The understanding of the relationship between subjective and geometric time leads to the notion of psychological time involving in an an essential manner the new view about spacetime, in particular the idea about mindlike spacetime sheet (defined as spacetime sheet having finite timeduration) as a geometric correlate of self (see the chapter "Time and Consciousness" of [cbookI]). One can understand psychological time as a temporal center of mass coordinate for the cognitive spacetime sheet. The arrow of psychological time can be understood as resulting from a drift towards the geometric future induced by the the geometry of the future lightcone. The simplest guess is that the average increment of the geometric time per quantum jump is given by \Delta t =k \tau , where k is a numerical constant and \tau some fundamental time scale, most naturally of the order of CP_2 time \tau_{CP_2} about 10^4 Planck times. This means 2^{127}\simeq 10^{38} quantum jumps per .1 seconds so that psychological time is effectively continuous. It must be emphasized, that this identification is based on a dimensional and aesthetic argument and one must keep mind open for the possibility that the duration of the psychological cronon is dynamical and depends on the geometrical size and other properties of self. The notion of psychological time forces to view the entire manysheeted spacetime surface as a living system so that the standard notion of linear time is illusory and reflects the restricted information content of our conscious experience rather than fundamental 4dimensional reality. The paradigm of 4dimensional brain provides completely new understanding of the long term memory. No memory storage of information about the geometric past to the geometric now is needed and one avoids the basic difficulties of neural net models (new memories tend to destroy the old ones). There are two kinds of memories, geometric and subjective. Subjective memory is about real events and its duration is that of subself responsible for the mental image. Geometric memory provides a narrative which changes when geometric past changes in quantum jumps: geometric memory of childhood is about the childhood subjectively now, not the real childhood. There are also two kinds of causalities: the causality of passive events and the causality of active deeds. Various causal anomalies [Deeeke,BR1,BR2} to be discussed in more detail in forthcoming article can be understood from the fact that also the geometric past changes in each quantum jump. A mindboggling possibility is that this effect could occur in a time scale of a year [Peoch] and be testable (see the chapters "Time and Consciousness" and "Quantum Model for Cognition" of [cbookI]).
The notion of self was originally forced by the paradoxes resulting in the attempt to understand consciousness in terms of quantum jumps alone. The concept of self has developed gradually during years and the recent view is probably not be yet the final one. The connection with statistical physics and selforganization theory however encourage to think that basic ideas are sound.
A natural identification of self is as a subUniverse behaving autonomously. Thus subsystems able to remain unentangled are natural candidates for selves. In purely real context the generation of an even slightest entanglement kills self and the subsystems (other than entire Universe) able to remain unentangled under the action of U are extremely rare. As already described, the identification of the geometric correlates of selves as regions of spacetime appearing in the decomposition of spacetime into regions belonging to various number fields solves this problem: entanglement does not simply occur between different number fields. One could critisize this assumption: rational numbers are common to both reals and padics and if entanglement coefficients are rational, entanglement between different number fields might be possible. It is however difficult to understand how the notion of the Hilbert space inner product could make sense unless the whole quantum theory reduces to the field of rationals. The basic prediction is the existence of infinite hierarchy of selves and this has rather dramatic consequences. At the top of the infinite hierarchy is entire Universe, which might be called God. This structure cannot entangled with any larger structure of same kind so that this self can be said to live eternal life. God abstracts all experiences in the infinite hierarchy of subselves to single experience. If infinite primes are allowed, as required by simple physical arguments, God corresponds to infinite padic prime characterizing entire universe and since this prime grows, also God evolves.
In the following basic aspects about how the contents of consciousness of self are determined are discussed. 1. Summation hypothesis, binding, and statistical averaging of experiences Subsystem X possessing self behaves essentially as a separate subUniverse with respect to NMP. Also the subselves of X_i of X have their own experiences. The question is: how the experience of X and experiences of X_i are related? The following basic hypothesis provides a possible answer to this question. a) X experiences the subselves X_i as separate mental images superposed to the pure self experience of X: this is natural since subselves are unentangled and hence behave like separate subUniverses. These subselves are bound in the sense that self experiences them simultaneously. b) The experiences of self X about the experiences of its subselves X_i are abstractions. Subself X_i experiences its subselves X_{ij} as separate mental images. X however experiences them as a single mental image representing what it is to be a subself of X_i, that is the average < X_{ij}> of the mental images X_{ij}. Thus the mental images of subsub...selves of X are smoothed out to an average mental image and become effectively unconcious to X. Averaging hypothesis generalizes quantum statistical determinism to the level of subjective experience and is analogous to the hypothesis about averaging related to temporal binding. When self has no subselves, the experience of self reduces to pure awareness without any mental images. In case of real selves these mental images are padic and thus represent thoughts: thus the empty mind in a state of Oneness means getting rid of thoughts. An interesting question is what kind of experience self decomposing to several subselves, each in state of wholebody consciousness, has: there is no averaging involved so that the mental images of self could be identical with the experiences of subselves. Temporal binding with averaging implies that the experiences of the individual selves are reliable and abstraction brings in the possibility of quantum statistical determinism at the level of ensembles. The inability to perceive the flickering of light when the frequency of the flickering is larger than about 1618 Hz is consistent with the hypothesis that sensory subselves (mental images) have a duration of order .1 seconds and that temporal averaging indeed occurs. Our self can have duration much longer than .1 seconds. For instance, the duration of the ordinary wakeup period could determine the duration of our self. The duration could be even longer: sleep could actually involve awareness and the lack of the sensory memories from sleep period could create the illusion about sleep as an unconscious state. The subjectotemporal sequence of subselves of a finite duration is experienced as a sequence of separate mental images: this makes possible to remember the digits of a phone number despite the presence of the temporal averaging. Summation hypothesis and temporal binding with averaging imply a hierarchy of conscious experiences with increasingly richer but abstracted contents. Also we are mental images of some higher level self. I ended up with padic physics originally as a successful model of elementary particle masses (see the fourth part of "pAdic TGD" of [padTGD]). The only possible interpretation for this success is that this model is a model of a cognitive model so that padic physics and cognition are present already at elementary particle level. This also explains the selection of padic primes corresponding to padic length scale hypothesis as a a result of fight for survival at elementary particle level. Without this selection electron would have practically continuous mass spectrum. 2. Binding of the experiencers by entanglement The binding of experiencers is also possible and this process gives rise to what is usually understood with binding in neuroscience context. a) The simplest assumption is that the binding of selves by quantum entanglement means that they lose their consciousness. In the case of subselves entanglement means binding of separate mental images to single mental image. This process naturally corresponds to the formation of wholes from their parts at the level of conscious experiences. The formation of a mental image (subself) representing word from the mental images representing letters is example of this process. The information about various areas of brain (there are about separate visual areas) could bind by entanglement mechanism. Also the fusion of the left and right visual fields to a single visual field could occur via the entanglement of the corresponding subselves. Rightleft entanglement might occur already at the neuronal level. b) Quantum entanglement could make possible communication between selves belonging to different levels of the self hierarchy: for instance, part of brain representing subself could entangle with a higher level self and mediate communications to those parts of brain which are awake (the semitrance mechanism discussed in the last part of [cbookII]). c) It seems that also subselves of separate selves could entangle. This could make possible shared experiences. Telepathy could be based on this mechanism. Communications might involve entanglement between subselves: classically communication would involve generation of spacetime sheet containing ME serving as a join along boundaries bond connecting the regions representing the subselves of sender and receiver. In the final state this ME would disappear but leave subself which has received the message (during communication stage subself would become unconscious). d) The nondeterminism of Kähler action makes possible timelike entanglement. Long term memories could be seen as shared experiences in which the self at geometric now shares the experience of self in the geometric past. Laser mirrors defined by parallel MEs accompanying magnetic flux tubes could be the realization of this mechanism and present at all levels of the self hierarchy, even at DNA level. The synchronous neuronal firing with the amazing precision of order millisecond [Engel] could be the neural correlate of entanglement between different areas of brain where subselves representing mental images could be located. Z^0 MEs giving rise to ZEG could provide the needed synchronizer at frequency of about one kHz, which corresponds to the duration of the bit of the memetic codeword. In padic state they would define cognitive representations and be passive whereas in the real state they would become active and synchronize neuronal firing (the coupling to Z^0 fields is strongest in cellular length scale). pAdic Z^0 MEs would mimic the neuronal activity and transform to real MEs resonantly when the oscillation frequency is about kHz. Thus synchrony would be generated in phase transition like manner with a neuronal oscillation at kHz frequency serving as a seed. This vision is described in more detail in the chapter "Spectroscopy of consciousness" of [cbookII].
Subjective time development by quantum jumps implies quantum selforganization which can be regarded as a sequence of quantum jumps between quantum histories (see the chapter "Quantum Theory of SelfOrganization" of [cbookI]). This evolution corresponds to a sequence of macroscopic spacetime surfaces associated with the final state quantum histories. Quantum jumps imply dissipation at fundamental level. Dissipation serves as a Darwinian selector of selforganization patterns, which can represent both genes and memes. In particular, one can understand how habits, skills and behavioural patterns are gradually learned. Protein folding occurring to very few final state patterns suggests itself as resulting from selforganization process (proteins would be thus conscious selves).
The notion of self hierarchy, starting from elementary particle level and having entire Universe at the top, is a highly nontrivial prediction of TGD inspired theory of consciousness. Self hierarchy is very much analogous to the hierarchy of subprograms of a computer program and defines a hierarchy of increasingly abstract experiences. Self hierarchy allows to understand computational aspects of brain functioning although connectionistic picture realized as quantum association network seems to work at various levels of the hierarchy (see the chapter "Quantum Model for Intelligent Systems" of [cbookI]). Topological field quanta of em fields (MEs and magnetic flux tube structures) are an part of the self hierarchy and this encourages to give up the view that consciousness is a purely brain centered phenomenon (wavelength of 10 Hz EEG wave has size scale of Earth). Self hierarchy is also crucial for the model of the sensory qualia.
The notion of self means possible fundamental identification of two kinds of ensembles: the subjectotemporal ensemble defined by the quantum jumps occurred after the last 'wakeup' and spatial ensembles defined by the subselves of self defining mental images of self as statistical averages over experiences of subselves of subselves. This leads to the hypothesis that qualia correspond to average increments of quantum numbers and zero modes in quantum jumps. The sharpness of a given quale is determined by the entropy of the distribution for the quantum number increments of given type. At the statistical level qualia correspond to average rates of the change of quantum numbers and zero modes. The rates of change for entropy type variables associated with subselves are assumed to define emotional qualia. This picture is consistent with the assignment of qualia to quantum phase transitions. The sequence of quantum jumps defining self defines also a sequence of maximally unentangled quantum states resulting in the state preparation process governed by NMP. This set of states, which grows in size quantum jump by quantum jump, defines in a natural manner a statistical ensemble identifiable as the fundamental realization of the otherwise fictive notion of statistical ensemble fundamental in the formulation of statistical physics. There are actually two statistical ensembles: the first one being associated with the final states of quantum jump and the second one being associated with the values of zero modes resulting in quantum jump. As far as conscious experience is involved, it however seems that it is the increments of quantum numbers and zero modes which are the relevant statistical variables. This observation anchors the theory of conscious experience to statistical physics (see the chapter "General Theory of Qualia" of [cbookII]). For instance, the increments of zero modes resp. quantum numbers are responsible for geometric resp. nongeometric qualia. More precisely, the gradients with respect to subjective time for the zero modes and for the net quantum numbers associated with selves correspond to qualia. One can classify nongeometric qualia to entropy gradients associated with various increments (emotions in accordance with the fact that peptides are both informational molecules and molecules of emotion); kinestetic qualia (sense of pressure and force and, more generally, gradient of any conserved (with respect to geometric time) quantity associated with self with respect to subjective time); and generalized chemical qualia (rates for the changes of numbers of particles with various quantum numbers). Various entropies associated with self and subselves in turn characterize the sharpness of the mental images, and one can relate concepts like attentiveness, alertness and the level of arousal to these variables. It must be however emphasized that quantum number increments alone need not determine entirely the contents of conscious experience. There is an infinite number of possible quantum jump sequences between two states \Psi_i and \Psi_f. This is also the case for diagonal quantum jumps \Psi_i>.....\Psi_i. The idea that diagonal quantum jumps, and more generally, quantum jump sequences leading from \Psi_i back to \Psi_i, could give all possible conscious information about given quantum history \Psi_i is attractive. The requirement that diagonal quantum jumps give information about \Psi_i suggests that quantum jumps give also other conscious information than the information coded to the quantum number and zero mode increments. For instance, the average over the cascade of self measurements might have interpretation as a counterpart of conscious analysis.
One could argue that the randomness of the quantum jump means that moral choices are impossible. Volition can however be associated with the quantum jumps in which padic spacetime sheet representing intention is transformed to real spacetime sheet representing real action. pAdic evolution defines the fundamental value of the quantum ethics. The selections which tend to increase the value of the padic prime represent good deeds since they mean evolution. The values of this ethics are not in the physical world but in the quantum jumps defining the subjective reality. The padic prime associated with entire universe is literally infinite (for the theory of infinite primes, see the chapter "Infinite primes and consciousness" of [cbookII] was originally motivated by consciousness theory). Infinite primes have however decomposition into finite primes in a welldefined sense and the increase of the infinite prime in a statistical sense implies the increase of finite composite primes and the appearence of new spacetime regions characterized by finite primes. A physical correlate for the increase of finite padic prime is the gradual growth of say cell or biological organism whereas the creation of new organism is a correlate for generation of a spacetime region characterized by padic prime. Selves can make plans since they have 4dimensional geometric memory (conscious experience contains information about a fourdimensional spacetime region, rather than only time=constant snapshot, and gives rise to a "prophecy", a prediction for the future and past, which would be reliable if the world were completely classical). Intentions, plans and anticipations are represented by padic spacetime regions simulating real regions. Selves can make decisions and select between various classical macroscopic time developments. Selves are able to remember their choices since they have subjective memories about the previous quantum jumps. Thus selves are genuine moral agents if they can experience directly that increase of p is good and decrease of p is bad.
I am grateful to Lian Sidorov for a considerable help and encouragement during the preparation of the manuscript as well as for very stimulating discussions.
[BR1] D. J. Bierman and D. I. Radin (1997), Anomalous Anticipatory Response on Randomized Future Conditions, Perceptual and Motor Skills, 84, pp. 689690. [BR2] D.J Bierman and D. I. Radin (1998), Anomalous unconscious emotional responses: Evidence for a reversal of the arrow of time. http://wwwpsy.uva.nl/resedu/pn/PUBS/BIERMAN/1998/tucson/tucson3.html . [Deeke] L. Deeke, B. Götzinger and H. H. Kornhuber (1976), Voluntary finger movements in man: cerebral potentials and theory, Biol. Cybernetics, 23, 99. [Engel] A. K. Engel et al(2000) Temporal Binding, Binocular Rivalry, and Consciousness http://www.phil.vt.edu/ASSC/engel/engel.html. [Peoch] R. Peoch (1995), Network (the journal of Medical Network edited by Peter Fenwick), vol. 62. For a popular article about animalrobot interactions see http://paranormal.se/psi/pk/djur.html . [TGD] M. Pitkänen (1990) Topological Geometrodynamics Internal Report HUTFTIR904 (Helsinki University). The online version of the book is at http://www.physics.helsinki.fi/~matpitka/tgd.html. [padTGD] M. Pitkänen (1995) Topological Geometrodynamics and pAdic Numbers. Internal Report HUTFTIR955 (Helsinki University). The online version of the book is at http://www.physics.helsinki.fi/~matpitka/padtgd.html. [cbookI] M. Pitkänen (1998) TGD inspired theory of consciousness with applications to biosystems. http://www.physics.helsinki.fi/~matpitka/cbookI.html. [cbookII] M. Pitkänen (2001), Genes, Memes, Qualia, and Semitrance . http://www.physics.helsinki.fi/~matpitka/cbookII.html. 
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