T(opological)G(eometro)D(ynamics) inspired theory of consciousness

Matti Pitkänen

Postal address:
Department of Physical Sciences, High Energy Physics Division, PL 64, FIN-00014, University of Helsinki, Finland.
Home address:
Puutarhurinkatu 9, 10960, Hanko, Finland


1. Introduction

2.TGD in nutshell
2.1 Space-times as a 4-D surfaces in 8-D imbedding space
2.2 The notion of manysheeted space-time
2.3 Quantum TGD
2.4 p-Adic physics as physics of cognition, intention, and anticipation

3. TGD inspired theory of consciousness
3.1 Quantum jump between histories as moment of consciousness and self as a subsystem able to remain unentangled
3.2 What is the most general structure of the self hierarchy?
3.3General view about psychological time

4. Quantum brain
4.1 Basic new physics effects
4.2 A possible vision about quantum brain

About notation

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~= y can be read as x=about y. and x~y can be read as x =roughly about y. infty denotes infinity.

1. Introduction

In this introductory article I summarize briefly what Topological Geometrodynamics (TGD) and TGD inspired theory of consciousness are and describe the speculative picture about biosystems and discuss briefly the TGD view about quantum brain.

The identification of quantum jump between quantum histories as a moment of consciousness reduces quantum measurement theory to fundamental physics. Quantum entanglement is the central quantum notion and Schrödinger cat able to be living and dead simultaneously is the classical manner to 'illlustrate' the notion ( illustration ) 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 entanglement of subselves of same or of two separate selves means fusion of mental images to a more complex mental image ( illustration ). In the latter case it means sharing of mental images crucial, not only for remote mental interactions, but also for genuine communications.

The notion of manysheeted space-time ( illustration ) allows to understand how biosystems manage to be macroscopic quantum systems. Topological field quantization implies that also classical fields have particle like aspects: these particle like aspects are crucial for the models of sensory qualia, sensory representations and long term memory as well as for the general model of control and coordination in living matter. One can fairly say that any living system has besides the ordinary physical body also a field body ( illustration ), as a matter fact a hierarchy of bodies.

A further generalization of the space-time concept involves the introduction of p-adic topologies besides the real topology ( illustration ). p-Adic space-time regions are identified as cognitive representations for the real regions and thus correspond to the 'mind stuff' of Descartes. The transformation of intention to action correspond to a quantum jump in which p-adic space-time regions is replaced with a real one.

The realization of the sensory representations at the field body outside the brain represents the most radical departure from the views of standard neuroscience and a rather detailed theory for both 'personal' sensory representations and magnetospheric sensory representations presumably responsible for the third person aspects of consciousness results.

More detailed representations can be found from the online books "TGD inspired theory of consciousness with applications to biosystems" [3] and "Genes, Memes, Qualia, and Semitrance" [4] at my homepage. The online books "Topological Geometrodynamics" [1] and "TGD and p-Adic numbers" [2] represent the recent view about TGD as a unification of fundamental interactions.

To the beginning

2. TGD in nutshell

The reader can probably skip this section in the first reading if she/he feels it too technical and start directly from the section devoted to the general theory of consciousness which I have tried to formulate with minimal reference to TGD based physics.

2.1 Space-times as a 4-D surfaces in 8-D imbedding space

Topological Geometro-Dynamics (TGD) can be regarded as a unified theory of fundamental interactions. TGD was originally an attempt to construct a Poincare invariant theory of gravitation [1,2,3,4]. Space-time, rather than being an abstract manifold endowed with a pseudo-Riemannian structure, is regarded as a 4-surface in the 8-dimensional space H=M^4_+times CP_2, where M^4_+ denotes the interior of the future light cone of the Minkowski space (to be referred as light cone in the sequel, see the illustration) and CP_2= SU(3)/U(2) is the complex projective space of 4 real dimensions [1]. CP_2 is obtained also by identifying the points of complex 3-dimensional space differing by a complex scaling ( illustration. The size of CP_2 which is about 10^4 Planck lengths replaces Planck length as a fundamental length scale in TGD Universe. For details about CP_2 see the appendix of [1].

The identification of the space-times as submanifolds of M^4_+ times CP_2 leads to Poincare (translations, rotations, Lorentz transformations) invariance broken only in cosmological scales and solves the conceptual difficulties related to the definition of the energy-momentum in General Relativity. Even more, sub-manifold geometry, being considerably richer in structure than the abstract manifold geometry behind General Relativity, leads to a geometrization of all basic interactions and elementary particle quantum numbers. In particular, classical electroweak gauge fields are obtained by inducing the spinor curvature of CP_2 to the space-time surface. One can say, that the mere hypothesis that space-times are representable as 4-surfaces of M^4_+times CP_2 realizes Einstein's great dream in a very elegant and economical manner: very concisely, submanifold geometry brings in the notion of shape besides the notions of distance, angle, and curvature.

2.2 The notion of manysheeted space-time

TGD approach forces a generalization of the conventional space-time concept to what might be called manysheeted space-time. The topologically trivial 3-space of General Relativity is replaced with a manysheeted space-time containing matter as particle like 3-surfaces "glued" to the topologically trivial background space-time sheet by extremely tiny connected sum (wormhole) contacts having CP_2 size connecting the space-time sheets. Space-time sheets can be connected to each other also by join along boundaries bonds (illustration).

Space-time sheets have outer boundaries and form a hierarchical structure. Macroscopic material bodies are identified as 3-surfaces with boundary identified as the outer surface of the macroscopic body. For instance, my physical body is a space-time sheet with my skin representing its outer boundary whereas external world is represented by a larger space-time sheet at which the space-time sheet representing my body is 'topologically condensed'. This generalization implies a radical reformulation of the condensed matter physics. Space-time sheets are connected to each other by wormhole contacts and join along boundaries bonds. Various new physics effects related to the manysheeted space-time concept are discussed in the four books about TGD: see for instance, the chapters "TGD and Nuclear Physics" and "Anomalies Explainable by TGD Based Space-time Concept" of [2].

Manysheeted space-time concept is especially important in TGD inspired theory of consciousness and its applications to biosystems [3,4] since it makes possible macroscopic quantum systems. The reason is simply that the large non-atomic space-time sheets contain very few elementary particles so that the temperature at these space-time sheets can be extremely low and therefore various kinds of macroscopic quantum phases are possible.

The basic prediction of TGD is that the sign of energy depends on the time orientation of the space-time surface so that energy can be also negative as opposed to situation in standard physics. For instance, pairs of space-time sheets with opposite energies can be generated from vacuum. This makes possible an effective overunity production of energy, a mechanism of coherent locomotion, classical signalling to the direction of the geometric past and many other exotic effects which could be important in living matter.

Absolute minimization of so called Kähler action is the fundamental variational principle of TGD and assigns to a given 3-surface X^3 a classical space-time surface X^4(X^3) which is much like a field-theory counterpart of Bohr orbit of particle going through a fixed point (now 3-surface). Another useful analogy is four-dimensional soap film spanned by a 3-dimensional frame which minimizes instead of area a non-linear counterpart of the Maxwell action. The variational principle is characterized by classical non-determinism caused by enormous vacuum degeneracy and this forces a generalization of the notion of 3-surface in order to achieve classical determinism in a more general sense. In soap film analogy this means that single frame does not fix the soap film uniquely and auxiliary frames are needed. 3-surfaces are in general unions of disjoint 3-surfaces with timelike separations ('association sequences' ( illustration) playing the role of auxiliary frames) rather than single time=constant snapshots of the space-time surface. In particular, space-time sheets with a finite time duration, 'mindlike' space-time sheets, are possible and are good candidates for the geometric correlates of selves in TGD inspired theory of consciousness ( illustration).

Perhaps the most plausible identification for the classical non-determinism is as a physical correlate of language understood in a very general sense: the sequences of spacelike three-surfaces with timelike separations ('association sequences'( illustration)) are like sequences of the basic units of language. The identification of the 'association sequences' as classical correlates of thoughts has been also considered. It seems however that p-adic space-time regions are more natural in this respect, and that association sequeces are symbolic representations of thoughts rather than thoughts: cognition transformed to sensory experience.

2.3 Quantum TGD

The basic manifesto behind quantum TGD is the geometrization of not only classical physics but also of quantum theory. 'Quantization without quantization' means that only the notion of quantum jump remains outside the geometrization program.

a) The arena of quantum dynamics is the infinite-dimensional space CH of all possible 3-surfaces of H=M^4_+times CP_2. Since one can assign to a given 3-surface X^2 a unique space-time surface X^4(X^3), one could equivalently speak of the space of four-surfaces satisfying the field equations defined by the fundamental variational principle. This space is geometrized by providing it with a metric and spinor structure crucial providing geometrization of distance measurement and spin. The infinite-dimensionality of the space CH has dramatic implications: the mere requirement that the metric exists and allows Riemann geometry fixes the metric essentially uniquely. Also the choice of the imbedding space H is fixed to H=M^4_+times CP_2 since maximal symmetries are required in order that the configuration space geometry exists mathematically.

b) There is no quantization involved: physical states correspond to classical spinor fields in the configuration space of 3-surfaces and fermionic oscillator operators have purely geometric interpretation. Configuration space spinors (as opposed to spinor field) correspond to the states of ordinary quantum field theories. The limit when 3-surfaces are reduced to points gives ordinary quantum field theory.

As far as theory of consciousness is considered, the fundamental feature of the configuration space is that it has two kinds of degrees of freedom.
a) The degrees of freedom in which metric is nonvanishing correspond to quantum fluctuating, non-classical degrees of freedom. Sensory qualia, for instance colors, correspond to direct conscious information about these degrees of freedom.
b) The degrees of freedom in which metric vanishes (points are at zero distances) correspond to what I call zero modes and are purely TGD based prediction basically due to the non-point like character of particles identified as 3-surfaces. Zero modes are the counterparts of the classical macroscopic variables and in every quantum jump a localization in zero modes occurs: this process mathematisizes the phenomenological notion of state function reduction. For instance, particle spin corresponds to a quantum variable whereas the configuration of the needle of the measurement apparatus representing spin direction corresponds to a zero mode. Geometric aspects of conscious experience (shapes, sizes,...) are determined by zero modes.

The replacement of point like particle with 3-surface means giving up the locality of the physics at space-time level: physics is however local at the level of configuration space containing 3-surfaces as its points. For instance, classical EPR nonlocality is purely local phenomenon at the level of configuration space. Besides allowing to get rid of the standard infinities of the interacting local field theories, the non-locality explains topologically the generation of structures, in particular biological structures which correspond to space-time sheets behaving as autonomous units.

2.4 p-Adic physics as physics of cognition, intention, and anticipation

p-Adic number fields R_p are labelled by primes p=2,3,5,... and, just like real numbers, they can be regarded as completions of rational numbers q=m/n, m,n integers to contain the p-adic counterparts of algebraic and transcendental numbers. p-Adic numbers emerged to TGD first only as an effective mathematical tool but it has turned out that p-adic physics is fundamental element of TGD.

TGD space-time decomposes into regions obeying real and p-adic topologies ( illustration). p-Adic regions obey the same field equations as the real regions but are characterized by p-adic non-determinism since the functions having vanishing p-adic derivative appearing as integration constants of differential equations are piecewise constant functions. Therefore one cannot fix the solutions of dynamical equations by giving the initial values of dynamical variables for fixed value of time (for instance, initial positions and velocities are integration constants for Newton's equations and fix the solution). Pseudo constant depends on a finite number of positive pinary digits of its arguments (x= SUM_n x_np^n in f(x) is replaced by x_N= SUM_{n< N}x_np^n). This means that p-adic space-time regions are obtained by glueing together regions for which integration constants are genuine constants.

The interpretation of the p-adic regions is as cognitive representations of the real physics occurring in real regions. The freedom of imagination is due to the p-adic non-determinism. p-Adic regions perform mimicry and make possible for the Universe to form cognitive representations about itself. In this vision real/p-adic mindlike space-time sheets are interpreted as geometric correlates of sensory/imagined experiences. p-Adic regions provide also geometric correlates for intentionality.

To the beginning

3.TGD inspired theory of consciousness

In the following I summarize basic aspects of TGD inspired theory of consciousness relevant to the paranormal phenomena. The basic philosophy behind TGD inspired theory of consciousness is crucial for the model but I discuss it only bfiefly here. Material about the underlying philosophy (neither monistic nor dualistic but 'tripartistic') can be found in the chapter "Matter, Mind, Quantum" of [3].

3.1 Quantum jump between histories as moment of consciousness and self as a subsystem able to remain unentangled

The basic notions of TGD inspired theory of consciousness are quantum jump between quantum histories (rather than time=constant snapshots of single quantum history) as moment of consciousness, and the notion of self as subsystem able to remain unentangled in subsequent quantum jumps (see for instance the chapters "Matter, Mind, Quantum" and "Self and Binding" of [3]). There is a deep structural analogy with physics: quantum jump is the elementary particle of consciousness and selves are atoms, molecules,.... of consciousness.

1. Quamtum jump as a moment of consciousness

Each quantum jump replaces the solution of field equations (universe) with a new one. Quantum jump involves three steps:
a) the unitary time development U giving rise to the S-matrix summarizing quantum physics as it is understood by particle physicist,
b) the counterpart of state function reduction,
c) and state preparation involving a sequence of self measurements.

U can be said to generate multiverse, quantum superposition of potentialities, a state of oneness in which everything is entangled with everything. State function reduction and preparation in turn mean gradual decomposition of the universe to maximally disentangled subsystems interpretable as a conscious analysis, a process giving rise to distinctions and separations. Thus oneness and separation are both basic aspects of consciousness. The sequence of quantum jumps defines subjective time whereas geometric (or physicist's) time corresponds to the fourth spatial coordinate. The distinction between these times allows to resolve the basic paradoxes of modern physics and philosophy of mind.

2. Self

Self is by definition a subsystem able to remain unentangled in subsequent quantum jumps. Only bound state entanglement is stable in quantum jump and selves correspond to regions of the space-time surface having local topology in a given number field (real or p-adic number fields labelled by primes). p-Adic space-time regions are interpreted as physical (nonconscious as such) correlates for imagination, intention and cognition, whereas real regions correspond to matter. The unitary operator U could in principle generate entanglement even between p-adic and real regions (rational entanglement coefficients make sense in any number field), which is destroyed in self measurement. This is crucial for the generation of cognitive maps assigning to the states of matter (say reading of physical measurement apparatus) cognitive states (say the cognitive mental image about the reading of the measurement apparatus).

The contents of consciousness of self are determined as the average over the quantum jumps occurred after it was created (the real or p-adic space-time region corresponding to self appearing in quantum jump). Selves can have subselves and self experiences them as mental images. Self itself represents a mental image of a higher level self. Self experiences only the average of subselves of given subself. Thus statistical averaging is involved in both subjectotemporal sense and spatially and is of central importance in the theory of qualia. Qualia are identified as averages of quantum number and zero mode increments over quantum jump sequence defining subself (mental image) (see the chapters "General Theory of Qualia" and "Spectroscopy of consciousness" of [4].) It seems that the foundations of, not only quantum measurement theory, but also statistical physics, reduce to the theory of consciousness.

Quantum entanglement between subselves means fusion of mental images. Entangling self loses its consciousness. The subselves of two separate selves can entangle and this corresponds to a fusion and sharing of mental images so that consciousness is not so private as usually thought. Sharing of mental images is not possible if one uses elementary notion of subsystem. TGD (as also quantum field theory) however forces length scale dependent characterization of the subsystem allowing subsystems of disentangled systems to entangle (the entanglement between the subsystems is not 'visible' in the length scale of the systems containing them). The generalization of the subsystem concept is forced by the fact that the space-time sheets representing subsystems are information theoretically blackhole like systems. Blackhole like property derives from the fact that smaller space-time sheets are glued to the larger space-time sheet by wormhole contacts for which the induced metric has Euclidian signature. As a consequence, the throats of the wormhole contact are surrounded by causal horizons at which the signature of the induced metric transforms from Minkowskian to Euclidian (since the induced metric becomes degenerate at the horizon, the topologically 3-dimensional horizon is metrically 2-dimensional and gives rise to conformal invariance absolutely crucial for the theory). Blackhole like property implies that the description in the length scale associated with the larger space-time sheet contains only very rough information about the smaller space-time sheets (this is the space-time correlate for the averaging of the conscious experiences of subselves of subself).

3.2 What is the most general structure of the self hierarchy?

Selves form a hierarchy ( illustration ). This hierarchy need not be a simple nested hierarchy represented by a tree or a union of disjoint trees. On the other hand, arbitrary connections between the levels of the hierarchy imply paradoxal situations. Simple questions help to get a grasp on the problem. What happens if the branches of a given tree or separate trees are connected? What kind of connections are allowed without ending up with a paradoxical situation in which one cannot tell which one of the two selves is the subself of another self. The appearence of loops in the self hierarchy certainly leads to this kind of paradoxal situations since self can become its own subself.

This kind of paradoxal situations are avoided if only those selves which belong to the same level of the self hierarchy can fuse so that one has a collection of trees which can have horizontal connections (both intra- and inter-tree) between the nodes belonging to the same hierarchy level ( illustration). The presence of a horizontal connection means that two separate selves share the mental image resulting in the fusion. Of course, the same mental images could be shared by an arbitrary number of selves, and this could be one of the mechanisms making possible both social behaviour and the propagation of memes. Also a genuine communication might necessitate sharing of the mental images rather than being only active sending and passive receival. Sharing of mental images might occur also in hypnosis and various remote mental interactions and identification phenomena. Long term memory could also involve the sharing of the same mental image by the selves of the geometric past and geometric now.

The paradox-free situation is achieved if the selves are arranged according to the local space-time topology so that all p-adic selves with given prime are at the same level in the hierarchy and real selves (p=infinity formally) are at the top of the hierarchy. Subselves must always have smaller p than self and real selves are at the top. Quantum entanglement allows only fusion of selves at the same level of the hierarchy and thus having the same local topology labelled by the p-adic prime p. Algebraic extensions of p-adic numbers presumably bring in more refined sub-hierarchies for a given value of p and they could correspond to various levels of mathematical cognition. This hierarchy is represented by a collection of trees which can have horizontal connections joining nodes at the same level. The sharing of mental images by the fusion of subselves is thus possible. The level of the self in the hierarchy can change and is induced by a quantum jump in which the local number field (p-adic or real) associated with the space-time sheet representing self changes from R_{p_1} to R_{p_2}. Also a given real space-time sheet can be characterized by the p-adic prime defining the p-adic length scale characterizing its size. It is yet not clear whether real space-time sheets with different values of p-adic prime can have bound state entanglement.

3.3 General view about psychological time

A natural resolution of the problems related to the preferred role of single moment of time for conscious experience is based on the idea that biological growth and self-organization is a 4-dimensional phase transition proceeding in the direction of the geometric future quantum jump by quantum jump. And, in particular, that the dominating contribution to the conscious experience comes from the front of the phase transition where the volition is.

What is then this fundamental phase transition giving rise to what we call life? We know that the front of phase transition corresponds to volitional consciousness. We also know that volition as a transformation of intention to action in TGD universe corresponds to the p-adic-to-real phase transitions of space-time space-time sheets taking place in quantum jumps ( illustration). Thus the natural conclusion is that p-adic-to-real phase transition is the fundamental phase transition inducing the biological self-organization and determining the value of psychological time and inducing its arrow (( illustration). This phase transition could occur for massless extremals (MEs) and perhaps also for the flux tubes of wormhole magnetic fields (and thus for magnetic mirrors) representing the plan for the evolution of the biological system and induce biological self-organization of matter around the resulting electromagnetic hologram like templates.

At least the selves at the same level of self hierarchy possess same value of psychological time. It might even be that the entire living biosphere (with magnetosphere included) could be seen as a phase transition front proceeding to the direction of the geometric future. This conclusion is of utmost importance since it leaves no other possibility that to accept that even biosphere defines conscious self and we correspond to only single level in the self hierarchy. In particular, the notion of collective consciousness is more or less 'a must' in this framework.

Physical death means that the 4-dimensional body becomes mature and could survive at least for some time in a state in which conscious experience does not contain the dominating input from the phase transition zone. Some kind of a meditative, timeless form of consciousness should be in question. This vision conforms with the idea that physical life is only one stage in much longer lasting process of conscious evolution. These 4-dimensional bodies can in principle communicate with the living ones and long term memories about the deceased might represent one form of this communication. The communications would be based on the same mechanism as long term memories in general: by looking at magnetic mirror with length of order lightlife or more I can see, not only me of the past, but also my fellow (not only) human beings ( illustration). At quantum level this means timelike quantum entanglement making possible to share experiences.

To the beginning

4. Quantum brain

The crucial elements in the theory of quantum brain are quantum criticality of TGD Universe and the notions of manysheeted space-time and topological field quantization leading to the notion of field body.

4.1 Basic new physics effects

Concerning concrete application of the theory at level of biosystems and brain, the notion of manysheeted space-time is of crucial importance since it makes possible to understand how biosystems manage to be macroscopic quantum systems.

1. Generation of structures, topological field quantization, and quantum-classical correspondence

Manysheeted space-time allows to understand topologically the generation of structures( illustration ). Even the macroscopic objects of every day world correspond to space-time sheets. The replacement of pointlike particles with 3-surfaces of arbitrarily large implies the crucial non-locality at space-time level. Concerning the undestanding of bio-superconductivity the basic observation is that the space sheets which are much larger than atomic space-time sheets contain very low densities of ordinary particles so that the temperature can be extremely low and macroscopic quantum phases are possible ( illustration ). Manysheeted space-time leads also to a radically new view about metabolism, homeostatis and biocontrol allowing to understand several findings challenging the basic dogmas of biology.

Topological field quantization implied both by topological reasons and by the absolute minimization of the Kähler action implies that space-time surfaces are field theory counterparts of Bohr orbits and have complex topology. This means that topologically relatively featureless linear Maxwell fields are replaced by extremely complex topological structures. Quantum-classical correspondence has been a basic guide line in the construction of the theory and states that classical space-time physics provides classical correlates for various quantum aspects of physical system leads to the view that the topological field quanta accompanying a given material system provide a representation for its quantum structure, kind of a manual.

This topological self referentiality generalizes further to the idea that the inherent non-determinism of the p-adic dynamics makes possible space-time representation of quantum jump sequences and classical non-determinism of Kähler action the non-determinism inherent to the linguistic representations for the contents of consciousness of self. This in turn implies feedback loop to the configuration space level: configuration space spinor fields can represent (not faithfully) quantum jump sequences and thus the contents of consciousness associated with a sequence of quantum jumps (self), so that the ability to become conscious about being conscious about something can be understood. As also noticed, one can also speak about 'field body' (or actually hierarchy of them) as being associated with the material system. This field body, which is much larger than material system, serves as a sensory canvas at which sensory representations are realized and performs motor control ( illustration).

2. Magnetic flux tubes, electric flux quanta, and MEs as basic topological field quanta

Magnetic flux tubes are the simplest topological field quanta of magnetic fields and familiar already from superconductivity. By the quantization of the magnetic flux the thickness of the magnetic flux tubes of Earth's magnetic field is of order cell size (few microns) and the superconducting magnetic flux tubes are ideal seats for one-dimensional ionic and atomic superconductors. Magnetic flux tube structures define what might be called magnetic body in TGD based model for brain consciousness. Plasmons consisting of closed toruslike flux tube structures accompanied by ionized matter represent the simplest magnetic lifeforms and should serve as templates for various biostructures from DNA to neural circuits to blood circulation and also the field body associated with living system. The flow of ions between atomic space-time sheet and magnetic flux tubes represents the fundamental realization of metabolism (see the chapter "Macroscopic quantum coherence and quantum metabolism as different sides of the same coin" of [4]).

The attempt to understand the non-Hertzian scalar waves of Tesla led to the realization that by the electric-magnetic duality of quantum TGD magnetic flux tube structures have as their duals topological field quanta of electric field carrying essentially constant energy density (see the chapter "Model for quantum control and coordination" of [3]). Biosystems are full liquid crystal electrets and electric flux quanta are ideal for their modelling. Also non-Hertzian scalar waves representing a space-time sheet moving with light velocity and carrying an essentially constant electric field in the direction of propagation are predicted. The non-Hertzian waves could be emitted in the generation of nerve pulses in directions transversal to the parallel axons and negative energy non-Hertzian waves could provide a mechanism of bound state formation between identical nerve pulse patterns representing symbolically thoughts as 'association sequences', that is temporal sequences of spacelike 3-surfaces with timelike separations (made possible by classical non-determinism of the Kähler action).

The so called massless extremals (MEs) define an extremely general class of solutions of field equantions ( illustration ). MEs can be regarded as topological field quanta of radiation fields, 'topological light rays'. MEs are ideal for classical communications for several reasons. They carry lightlike vacuum em and/or Z^0 currents propagating with light velocity without dispersion. MEs with a cylindrical geometry represent high precision classical signalling possible over arbitrary long distances. The lightlike vacuum current at given transversal section of ME is non-deterministic and thus optimal for coding classical information.

MEs are also ideal for quantum communication and the lightlike boundaries of MEs act in a well-defined sense as quantum holograms. The lightlike em current associated with ME generates also patterns of coherent photons. MEs carry also so called supercanonical representations which are genuinely quantum gravitational states: state functionals in the set of 3-surfaces ('world of worlds') and thus represent higher abstraction level than ordinary matter.

For these reasons MEs have taken the main role in TGD inspired theory of consciousness. MEs and magnetic flux serve also as field bridges acting as correlates of bound state entanglement making possible the fusion of subselves of different selves to form more complex shared mental images. In partcular, the mirror model of memories relies on MEs.

3. Also classical color and Z^0 fields are important

Also the classical color force and Z^0 force, which becomes strong in cellular length scale, play a key role in the new physics associated with the living matter. For instance, the classical Z^0 force explains the chiral selection occuring in living matter: in the standard model this phenonenon is a mystery since the weak interactions mediated by the quanta of Z^0 field are extremely weak. EEG MEs responsible for sensory representations at magnetic sensory canvas should be able to penetrate the Faraday cage defined by the ionosphere (and any Faraday cage) somehow. It is not clear whether em MEs can penetrate Faraday cages as such whereas Z^0 MEs (which are also gravitational MEs) certainly can. The transformation of Z^0 ME to em ME by a color rotation after it has penetrated through the Faraday cage defined by Earth's ionosphere could be a key element of the sensory representations. The simplest model consistent with this view is that Z^0 MEs (ZEG) mediate motor control from magnetic sensory canvas and the em MEs (EEG) obtained from them by color rotation mediate sensory input as a feedback.

4. Quantum spin glass property of TGD universe and macrotemporal quantum coherence

Penrose and Hameroff have proposed that microtubules could act as quantum computers and that macroscopic and macrotemporal quantum coherence is due to some yet unkown quantum gravitational effect [5]. The quantum states involved would be quantum superpositions of tubulin conformations and quantum gravitation would somehow make these quantum superpositions stable. There are however strong objections againsts macrotemporal quantum coherence in standard physics framework [6].

4.1 Spin glass degeneracy lengthens the lifetimes of bound states

Penrose-Hameroff hypothesis is highly interesting from TGD point of view since TGD Universe is quantum spin glass in the sense that there is an infinite number of different configurations of space-time sheets whose energies differ only by the gravitational interaction energy. Also the generation of coherent gravitons by MEs might have a role to play in the quantum physics of living matter. Especially so because genuine quantum gravitational states are state functionals in the space of 3-surfaces, that is in the world of worlds: therefore they should correspond to higher abstraction level of consciousness than ordinary elementary particles. Furthermore, the gravitational constant associated with the energy of the induced gauge fields is by a factor \sim 10^7 larger than the gravitational constant associated with elementary particles. The task is to put these pieces together.

A detailed study of Penrose-Hameroff hypothesis shows that it indeed has a TGD counterpart.

a) TGD Universe allows quantum computing under natural assumptions and the huge quantum spin glass degeneracy broken only by classical gravitation is crucial for the preservation of quantum coherence.

b) Quantum computation occurs optimally for irreducible selves for which all subselves have fused to single subself in state of 'oneness' so that there are no dissipating subsystems. Second prequisite is that all but center of mass zero modes of 3-surface representing say join along boundaries condensate of tubulin molecules (microtubule) transmute to quantum fluctuating degrees of freedom when 3-surfaces topologically condenses to a larger space-time sheet. Otherwise a complete localization in zero modes equivalent with state function reduction would occur in each quantum jump and quantum computation would not be possible in time scales longer than CP_2 time about 10^{-39} seconds defining the average duration of a single quantum jump (quantum jump corresponds to 'elementary particle of consciousness' having duration of CP_2 time). Bound state lifetime defines the duration of the non-decohering state.

c) The problem is that standard physics predicts too short life times for the bound states so that quantum computations would still last for too short time. The huge spin glass degeneracy associated with the join along boundaries bonds connecting space-time sheets representing bound systems however implies that there is an immense number of bound states with almost degenerate energy. This means that the branching ratio for the decay to unbound states is reduced dramatically and bound state lifetime increases.

4.2 Sex everywhere?

There are good reasons to expect that the temporary transformation of the zero modes to quantum fluctuating degrees of freedom fundamental process in living matter. The formation of bound states is a generic mechanism for generating new quantum fluctuating degrees of freedom and could make possible quantum computation like processes and multiverse states of consciousness containing large amounts of conscious information. This process liberates also binding energy as usable metabolic energy (buy now- pay later mechanism).

a) At macrolevel sexual organism could be basic example of multiverse state involving experience of oneness generated by the formation of quantum bound state between partners. Neuroscientists use to talk about rewards and punishments and one might argue that life involves kind of sexual pleasure as a reward for the formation of bound states at all levels of hierarchy. Spiritual experiences would represent a more abstract experiences of this kind involving the formation of bound states of the field bodies by MEs serving as field bridges.

b) One could see information molecules and receptors as representatives of opposite molecular sexes: information molecules being active quantum binders free to move from flower to flower whereas receptors would be the passive party attached to some structure. The binding of the information molecule to the receptor would be the analog of sexual intercourse. Usually the receptors are bound to larger structures such as cell membrane and also the zero modes for some parts of these larger structures could become quantum fluctuating in the process.

c) The binding of molecules by lock and key mechanism is a fundamental process in living matter and could generate large number of quantum fluctuating degrees of freedom and generate conscious intelligence. This could explain why long linear macromolecules are so important for life. From the viewpoint of classical chemistry it is not obvious why DNA is arranged into long chromosomes rather than separate short threads. In TGD universe the reason why would be that for chromosomes the number of quantum fluctuating degrees of freedom and thus the amount of conscious intelligence is maximized.

d) The Ca^{++} ions binding to microtubules and molecules like calmodulin could act as switch like bridges between water clusters and microtubules and thus able to dramatically increase the number of quantum fluctuating degrees of freedom and initiate quantum computation like process. The de-attachment of Ca^{++} ions would halt the process.

e) The temporal transformation of zero modes to quantum fluctuating degrees of freedom allows quantum jumping from a potential well of spin glass energy landscape to another well. These wells could represent almost everything from protein conformations to habit routines. Ca^{++} ions and catalysts could be involved with the control of these processes.

f) The binding of the information molecules to receptors is a universal control mechanism in living matter. In TGD universe information molecule would initiate genuine quantum information processing lasting for the lifetime of the information molecule-receptor complex. In particular, neurotransmitters could induce molecular states of oneness in receptor-neurotransmitter complex or perhaps even in larger-sized structures. If neurotransmitters have join along boundaries bonds to other neurons mediated by magnetic flux tube structures, they could act as conscious quantum links in quantum web and induce quantum computation like processes involving distant neurons just as link links in the web induce classical computations involving distance computers. Could excitatory neurotransmitters and modulators wake up neurons, that is encourage the decay of neuronal bound states and self organization by dissipation whereas inhibitory transmitters would favour the generation of neuronal bound states? Synchronously firing neuron groups acting as single self seem to be an exception to this rule. Interestingly, the role of inhibition is most prominent in human brain.

4.2 A possible vision about quantum brain

TGD framework encourages strongly to give up the cherished belief about brain as a seat of consciousness. The following working vision looks the most plausible one.

1. Brain and body as sensory organs of electromagnetic selves

In TGD framework life is self-organization phenomenon involving in essential manner Earth's magnetic field serving as template for the condensation of biomatter. In TGD universe our selves involve in an essential manner electromagnetic field structures (topological field quanta) having size measured using Earth size as a natural unit. Our physical bodies can be seen as kind of sensory and motor organs of these electromagnetic selves. My personal magnetic (or field) body ( illustration ) is one particular self of this kind and partially generated by magnetic crystals in brain as well as magnetic haemoglobin molecules.

In this framework physical death can be seen only as a death of a mental image about the physical body. Besides my personal magnetic body there are also other field bodies: these higher levels selves are multibrained organism analogous to multicellulars and could use our brains (in particular during sleep) for their own purposes. The entire magnetosphere forms can be regarded as a magnetic organism of this kind and we play the role of sensory receptors and motor organs of this magnetic Mother Gaia. It is quite possible that during sleep our selves entangle to form larger subselves (mental images) of the magnetic Mother Gaia: this fusion of mental images is much like the fusion of the left and right visual fields to a single visual field giving rise to stereovision (see chapter "Magnetospheric sensory representations" of [4]).

2. Model of sensory representations

The TGD based model for sensory representations relies on some very simple counter arguments against the standard view.
a) Any computer scientist would argue that the processing of data and its representation must be separated completely: this requires that sensory representations are realized outside brain.
b) If head rotates also sensory representations inside brain should rotate and we should experience this rotation. We however do not experience this rotation which suggests that the sensory representations occur in a fixed inertial frame, perhaps outside brain.
c) EEG frequencies correspond to wavelengths or order Earth size, which suggest that sensory representations are realized on structures of this size: that is personal magnetic body, magnetosphere of Earth, and even large magnetic structures. The sensory representations at the magnetosphere of Earth would naturally correspond to the third person aspect of our consciousness (see the chapter "Magnetospheric sensory representations" of [4]).

'Me as a computer sitting at is own terminal' metaphor leads to the idea that magnetic flux tube structures associated with brain serve as the personal magnetic body to which 'sensory data files' in brain are projected ( illustration ). This sensory canvas is outside of brain and has size which can be as large as Earth's size and even larger (lightlife seems to provide a reasonable estimate for the size). MEs serve as projectors and frequency-place coding induces magnetic quantum phase transition at some distance along magnetic flux tube having slowly varying thickness: the distance is determined by the frequency. In this manner it is possible to assign, not only simple sensory qualia (presumably at 40 Hz frequency band) to the points of the perceptive field but also more complex features. At quantum level sharing of mental images (feature in brain and 'feeling of existence' at some point of magnetic body) by entanglement is in question and EEG ME is a necessary prequisite for the generation of entanglement.

Also the projection of data at EEG frequencies to manybrained magnetospheric selves (magnetic flux tubes of Earth's magnetic field) representing higher collective levels of consciousness must be considered seriously. This idea has obviously far-reaching implications concerning various paranormal phenomena.

The simplest assumption is that MEs and magnetic flux tubes form parellel pairs acting effectively as laser mirrors ( illustration ): in this manner two amplification mechanism can be utilized since ME acts as resonant wave cavities interacting resonantly with the Alfven waves representing oscillations of magnetic flux tubes. Resonance condition fixes the distance at which a feature associated with a given frequency is assigned, and the requirement that magnetic transition frequency corresponds to this frequency leads to very stringent constraints on the representation and a close correspondence between EEG bands, brain structures, and magnetospheric structures emerges (see the chapters "Magnetic sensory canvas hypothesis" and "Magnetospheric sensory representations" of [4]). Cavity resonances (in particular Schumann resonances) associated with space-time sheet complex of Earth make possible horizontal communications between personal magnetic sensory canvases by sharing of mental images and could be responsible for the strange experiences associated with hypnagogy (experiencing directly what it is to be quite another person, say).

3. Mirror model of long term memories

The realization about how macrotemporal quantum coherence is realized in TGD framework led to a concrete model long term memories. The quantum spin glass degeneracy crucial for macrotemporal quantum coherence is caused by the differences in classical gravitational energy between spin glass states. Therefore the transitions between different configurations are expected to involve the generation of gravitonic MEs which can be regarded also as em or Z^0 MEs or both, most naturally Z^0 MEs.

This suggests a realization of the mirror model of memory. It is the topological correlates of gravitons which are mirrored from curved almost vacuum space-time sheet and allow the self of geometric now to see self of geometric past in mirror. In quantum context the light ray reflected in mirror need not carry classical information but because of the possibility of time like entanglement can serve only as an entangler of the mental images in geometric past and geometric now. The reason why for gravitons is that they have so weak interaction with background. What is fascinating is that classical gravitational binding energies in the range spanned by the cell membrane thickness and cell length scale (all p-adic length scales in this range correspond to Gaussian Mersennes (see the chapter "Macroscopic quantum coherence and quantum metabolism as different sides of the same coin" of [4]) correspond to time range 1 millisecond- 32 years, roughly the span of human memories. In particular, microtubule conformations could code for declarative long term memories. Also a connection with the idea that so called 1/f noise (now gravitonic) is crucial for consciousness and long term memory emerges.

By combining basic facts about the role of hippocampus and temporal lobes in long term memory with this picture, one ends up with a rather concrete model of long term declarative memory in terms of memory representations (see the chapter "Quantum model of memory" of [3]).) allowing re-interpretation of concepts like memory consolidation, long term potentiation, and hippocampal theta. For instance, hippocampal theta can be identified as the correlate for the binding of various mental images to single memory mental image.

4. p-Adic physics as physics of cognition and intention and frontal lobes

p-Adic bound state entanglement is possible only in fermionic degrees of freedom since all p-adic configuration space degrees of freedom are zero modes. Bound state entanglement corresponds to positive entanglement negentropy not possible in real context (see the chapter "Negentropy Maximization Principle" of [3]).). These states must have identical entanglement propabilities for any subsystem-complement pair to guarantee that the density matrix is completely degenerate: this is very quantum computerish feature. For a positive negentropy entanglement stable against self measurements the entanglement probabilities must be identical and the number of the entangled states must be divisible by a power of p^N of p. The real counterpart of the entanglement negentropy is Nlog(p). The interpretation of these cognitive subselves is as cognitive mental images carrying genuine information. p-Adic bound state of cognitive mental images with positive entanglement negentropy gives rise to the experience of understanding.

Frontal lobes are believed to be the seat of higher mental functions like cognition, intention, planning, and volition and thus p-adic physics should be especially important in the understanding of frontal lobes.

Since long term memories and intentions differ from each other only by real--> p-adic and geometric past --> geometric future replacement, it is rather straightforward to generalize the mirror model of long term memories to a mirror model of intentionality and goal structures (see the chapter "Quantum model for cognition and intention" of [3]).)

One of the nice outcomes is a model for comparison type emotions reducing the comparison process to a formation of bound state of subselves representing the mental images to be compared. For bound state self entanglement entropy does not increase and this gives rise to positive emotion. For unbound state entanglement entropy increases and gives rise to negative emotion. If nearly identical subselves bound state entangle, the emotion is positive or negative depending on whether the goal was realized or not.

The new view about memory allows to interpret working memory in a new manner. Working memory can be seen as a mechanism in which habit routines are initiated, modified, and replaced by new ones. Paper, pencil, and eraser metaphor provides a vision about how this process occurs and explains classical poorly understood findings about some effects of frontal lobe damage. Quantum spin glass model of brain describes habit routine as a point of a fractal spin glass energy landscape. The replacement of the habit routine with a new one means a formation of a bound state in which some zero modes become temporarily quantum fluctuating degrees of freedom so that a state completely localized at the bottom of a potential well in spin glass landscape is delocalized (eraser action). The state localizes at the bottom of new potential well representing new habit routine when the bound state decays. Therefore the generation of macrotemporally coherent quantum states representing superpositions of, say, firing entangled multineuron states, is absolutely essential for cognition and intentionality.

The realization of the memetic code in terms of temporal sequences of zero energy cognitive neutrino pairs with a duration of about millisecond and the direction of the neutrino spin representing binary digit (see the chapter "Genes and Memes" of [4]).) leads to a concrete model for quantum cognition and the temporary binding of two p-adic memetic codewords allows also quantum computation type process at neuronal level (see the chapter ( "Quantum model of cognition" of [3]).). The p-adic-to-real tranformation for cognitive neutrino pairs gives rise to a symbolic representation of thoughts generating automatically a nerve pulse pattern since the spin flip of a real neutrino to the direction of the background Z^0 magnetic field (Z^0 magnetization) generates nerve pulse.

5. EEG patterns as correlates for features

Sensory canvas model splits sensory representations nicely from their production (the same occurs in computers!) and one of the remaining big challenges is to understand something about the general principles involved with the construction of the features assigned to the points of the sensory canvas. TGD leads to a quantum model of nerve pulse generation based on Sine-Gordon soliton sequences associated with Josephson junctions between interior and exterior of axon and in this model electrochemical aspects of the nerve pulse reflect deeper quantum dynamics. (see the chapter "Quantum model of EEG and nerve pulse" of [4]). Perhaps Sine-Gordon soliton sequences should be assignable to nerve pulse patterns coding sensory experience and memetic code words to the nerve pulse patterns translating cognition to symbolic representations.

Quite generally, synchronous EEG patterns are correlates for bound state entanglement between neurons and even brain structures representing 'features' [7]. The idea that mesoscopic EEG patters associated with the 1-2 cm sized regions of cortex and having average duration of order .1 seconds, might correspond to MEs providing electromagnetic representation of 126-bit memetic code suggested by generalization of the genetic code and predicting correctly the time scale of nerve pulse (millisecond) and temporal resolution of sensory experience (.1 seconds) (see the chapter "Genes and Memes" of [4]) by rapid amplitude modulations of waves in alpha band by multiples of alpha frequency, is very attractive. This kind of patterns could be associated with other larger regions and EEG rhytms in theta and delta range and represent information usually not conscious-to-us.

6. Z^0 MEs as synchronizers?

Syncronized regions of brain define excellent candidates for subselves representing mental images: different sychronized brain areas could represent entangled subselves. Neuronal synchrony occurs in millisecond time scale [8]. It is difficult to understand how this could occur if only neural circuits are involved. Rather, Z^0 MEs which are not visible in EEG directly should provide kHz rhytm serving as a pacemaker (note that kHz corresponds to the duration of the bit of the memetic code!). The idea is natural since classical Z^0 force is strongest in cell length scale. Z^0 MEs are in passive and active states and passive state would be most be represented by p-adic Z^0 MEs related to the representation of thought/intention/plan.... When synchronization occurs seed stimulus at resonant frequency generates p-adic ME as a simulation of the oscillation and p-adic ME is resonantly transformed to real ME re-inforcing the seed of resonant oscillation so that syncronous regions are generated in phase transition like manner when syncronized region syncronizes region to which it send excitatory nerve pulse patterns. This same mechanism could be quite general and also behind some psychokinetic phenomena.

To the beginning


[1] M. Pitkänen (1990), Topological Geometrodynamics. Internal Report HU-TFT-IR-95-4 (Helsinki University).

[2] M. Pitkänen (1995), Topological Geometrodynamics and p-Adic Numbers. Internal Report HU-TFT-IR-95-5 (Helsinki University). http://www.physics. helsinki.fi/~matpitka/padtgd.html .

[3] M. Pitkänen (1998), TGD inspired theory of consciousness with applications to biosystems.

[4] M. Pitkänen (2001), Genes, Memes, Qualia, and Semitrance.

[5] S. R. Hameroff and R. Penrose (1996), Orchestrated reduction of quantum coherence in brain microtubules: A model for consciousness. In: Toward a Science of Consciousness - The First Tuscon Discussions and Debates , S. R. Hameroff, A. Kaszniak and A. C. Scott (eds.), MIT Press, Cambridge, MA. pp. 507-540.

[6]M. Tegmark (1999), The importance of quantum decoherence in brain processes, arXiv: quant-ph/9907009.

[7] W. J. Freeman (2001), Making sense of brain waves: the most baffling frontier in neuroscience , http://sulcus.berkeley.edu .

[8] A. K. Engel et al (2000), Temporal Binding, Binocular Rivalry, and Consciousness, http://www.phil.vt.edu/ASSC/engel/engel.html .