Basic Ideas of TGD inspired Theory of Consciousness
- Matti Pitkänen
- Alkutie 56, 00660, Helsinki, FINLAND
- Department of Physics, Theoretical Physics Division,
- P.O. Box 9 Fin-00014, University of Helsinki, Finland
- Previous level
1. A brief summary of Quantum TGD
1.1. TGD as a generalization of the string model
1.2 The concept of configuration space
1.3 äGeneral coordinate invariance and the definition of the Khler function
1.4 Quantum states as spinor fields in CH
1.5 State function reduction as quantum jump between deterministic quantum histories
1.6. TGD inspired measurement theory
1.7. The concept of effective spacetime
- 2. TGD inspired theory of consciousness
2.1 The problem of subjective time as key to a theory of consciousness
2.2 Some consequences
- 3. Application to human consciousness
3.1 How to stay conscious?
3.2 Brain as a macroscopic quantum system
3.3 Jumps between quantum histories at the level of brain
3.4 Two kinds of quantum jumps and mystic experiences
- 4. About cognitive aspects of consciousness
4.1 Thoughts as simulations
4.2 äVacuum degeneracy of the Khler action
4.3 Nonuniqueness of the classical spacetime due to vacuum degeneracy
4.4. Vacuum degeneracy and the problem of subjective time
4.5 Comparison with Penrose-Hameroff theory
- 5. Summary
- The basic ideas of a TGD inspired theory consciousness are described briefly. The first element is a TGD-based description of quantum states as deterministic quantum histories and the description of the state function reduction as a jump between two deterministic quantum histories. The second element is the identification of quantum jumps as acts of free will/conscious experience. The contents of the conscious experience are assumed to be determined by the region of 3-space to which the nondetermism of the quantum jump is localized. The definition of concept of energy momentum in TGD provides a natural identification of subjective time. Also the duration of subjective time is naturally associated with quantum jump and the arrow of time follows from the basic structure of TGD. The third element is the generalization of quantum measurement theory so that it applies to all systems in interaction with the surrounding world. There are basically two kinds of quantum jumps. Quantum jumps of the first kind change the value of subjective time and there is no subject-object distinction. These quantum jumps perhaps correspond to the higher states of consciousness described by mysticians. Quantum jumps of second kind do not change the value of the subjective time, are associated with subystems and governed by the principle of negentropy maximation. These jumps could correspond to ordinary sensory perception understood as measurement of the density matrix of subsystem. Conscious experience has also cognitive aspects and classical nondeterminism at the level of the effective action might explain these aspects.
- 1. Quantum TGD very briefly
- In the following only those aspects of TGD relevant to the TGD inspired theory of consciousness are reviewed. The interested reader can get more detailed information from my personal homepage, where the books 'Topological Geometrodynamics' and 'p-Adic numbers and Topological Geometrodynamics' can be found as ps-files. Also hypertext representation of the basic ideas of TGD and p-adic TGD can be found in this homepage. The illustrations related to the TGD-based concept of spacetimeand TGD-based model of biosystemsare recommended.
- 1.1 TGD as a generalization of the string model
- Quantum TGD [TGD, padTGD] can be regarded as a generalization of string model in the sense that point like particles are replaced with 3-dimensional surfaces (rather than one-dimensional strings) of certain 8-dimensional space H=M^4_+ x CP_2. The orbits of 3-surfaces are 4-dimensional surfaces. A radical generalization of the spacetime concept is involved. Macroscopic spacetime is regarded as a macroscopic 4-surface in H and elementary particles correspond to 'small' 3-surfaces with size of the order of the Planck length. By gluing small 3-surfaces by topological sum operation to macroscopic 3-surface one obtains macroscopic spacetime containing particles as topological inhomogenities. Macroscopic objects are also regarded as 3-surfaces having outer boundaries and glued by topological sum contacts to the larger background 3-surface. TGD thus means a completely new manner to interpret even the everyday world around us. Needless to say, TGD has nontrivial applications at all length scales.
- 1.2 Configuration space concept
- The construction of quantum theory relies on the concept of configuration space CH [TGD]. CH consists of all possible 3-surfaces in H=M^4_+ x CP_2. All topologies are allowed: in particular surfaces with several disjoint components are also possible. Quantum theory reduces to the construction of spinor geometry for CH. This necessitates the construction of metric and spinor structure. Physical states correspond to some basis of spinor fields in CH. Physical requirements force Kähler geometry, which means that the tangent space of CH allows complexification and the representation of the imaginary unit by the antisymmetric tensor J satisfying JJ =-G, where G is the metric tensor. K ähler geometry can be coded into the Kähler function K and the task is to identify K ähler function.
- 1. 3 General coordinate invariance and the definition of K ähler function
- In the definition of the K ähler function the basic ingredient is the requirement of General Coordinate Invariance, which is also the cornestone of General Relativity. 4-dimensional diffeomorphism group Diff^4 rather than 3-dimensional Diff^3 is in question and one encounters a problem since the points of CH correspond to 3-surfaces rather than 4-surfaces. Somehow the definition of K ähler function should associate a unique 4-dimensional surface to a given 3-surface for Diff^4 to act on. The connection with ordinary quantum field theories and string models can be made here. One can define variational principle in the set of 4-surfaces of H in terms of so called K ähler action, which is Diff^4 invariant. It is defined in terms of an imbedding space geometry and can be regarded as the nonlinear counterpart of Maxwell action for K ähler form, which can in turn be regarded as Maxwell field. The extremals of the K ähler action satisfy Euler Lagrange equations, which would define classical theory if ordinary QFT were in question. The idea is to define Kähler function K(X^3) as an absolute minimum of the Kähler action for all 4-surfaces containing X^3 as submanifold (boundary of X^3 belongs to the boundary of X^4). This means that one constructs all extremals of K ähler action going through X^3 and seeks from this set the extremal X^4(X^3) with the minimum value of K ähler action. There is an obvious temptation to identify X^4(X^3) as classical spacetime so that classical physics becomes part of configuration space geometry.
- The absolute minimum spacetime surface X^4(X^3) need not be unique, which means nondeterminism already at classical level. In fact, the properties of Kähler action suggest that for certain critical 3-surfaces this is the case. In present of N-fold degeneracy one can replace the critical 3-surface X^3 with N-fold replica of X^3. This degeneracy and related classical nondeterminism might play important role in biosystems and might imply the picture proposed by Penrose.
- 1.4 Quantum states as spinor fields in CH
- Quantum states correspond to spinor fields in CH. It turns out that spinor components span the Fock-space associated with second quantized free spinor fields of H on spacetime surface. Diff^4 invariance implies that the value of the CH spinor field is same for all diffeorelated 3-surfaces on X^4(X^3). Diff^4 invariance with respect to time translations implies deterministic time-evolution so that there is no need to postulate any Schrödinger equation for configuration space spinor fields. What is important is that quantum states correspond to entire deterministic quantum histories rather than an equal time snapshot of single deterministic history. This implies deep difference between TGD and standard quantum field theories. The problem of defining the concept of subjective time, when physical states are regarded as quantum histories, will be considered later and leads to the TGD inspired theory of consciousness.
- 1.5 State function reduction as quantum jump between deterministic quantum histories
- Quantum jumps are an essential element in the interpretation of the standard quantum theory. Unless one is willing to adopt the Many Universe interpretation quantum jump (state function reduction) must be regarded as a spontaneous nondeterminism at the level of Schr ödinger equation. This kind of behaviour is extremely awkward mathematically. In TGD quantum jumps occur between between deterministic quantum histories and are completely outside the realm of the geometric spacetime so that determinism at the level of solutions of Schr ödinger equation is not lost. The paradoxes related with concept-pairs subjective/objective disappear. Determinism is realized at the level of geometric spacetime and nondeterminism at the level of state space. Objective worlds correspond to determistic quantum evolutions and, according to the theory of consciousness to be formulated, subjective experience corresponds to the quantum jump between two objective worlds.
- An especially unpleasant paradox for theoretician is that conventional determinism makes theoretician useless! If only single deterministic history is actually realized then the mental constructs of theoretician are in principle not testable since it is not possible to compare different time evolutions. If quantum jumps between different deterministic histories are possible it becomes possible to genuinely test theories. In the proposed picture one also avoids the question about the initial values of dynamic variables at the moment of big bang.
- 1.6 TGD inspired measurement theory
- TGD also suggests a generalization of the standard quantum measurement theory and this generalization adds additional elements to the TGD inspired theory of consciousness.
- The standard measurement theory postulates that quantum subsystem in interaction with the measuring system goes to the eigenstate of the measured observables. If the experiment is repeated (the measurement interaction does not change in time), no further quantum jumps occur.
- The TGD-based generalization is following. Quantum measurement theory applies to any subsystem in interaction with its environment. The fundamental observable is the density matrix of the subsystem obtained by integrating over the degrees of freedom associated with the environment. The negentropy associated with this density matrix could be regarded as a measure for the amount of selfknowledge obtained via the interaction with the environment. When a subsystem measures its own density matrix it goes to an eigenstate of the density matrix. Since the eigenstates of the density maximize the negentropy one can say that subsystem tends to maximize its self knowledge.
- The ordinary entropy maximation principle of thermodynamics seems to be closely related to the negentropy maximation principle. Ordinary thermodynamic negentropy measures the observer's knowledge of the external world. Assume for simplicity that external world consists of an ensemble of quantum systems in interaction. The interaction implies that these systems are continually performing quantum jumps in order to maximize their self knowledge. The nondeterminism of the quantum jump implies, however, that the knowledge of the observer decreases gradually implying the increase of thermodynamical entropy.
- 1.7 The concept of effective spacetime
- CH spinor fields cannot be localized to single 3-surface so that in TGD quantum states can be regarded as superpositions of infinitely many 3-surfaces, or equivalently, classical spacetimes, which are absolute minima of K ähler action. The general structure of quantum field theories suggests that it should be possible to define quantum average spacetime as an absolute minimum of so called effective action. It seems natural to identify this effective spacetime as the counterpart of the observed classical spacetime. In fact, the symmetries of Kähler action dictate the form of the effective action to very high degree. The properties of Kähler action, in particular the analogy with the spin glass phase, motivate the hypothesis that effective spacetime obeys p-adic rather than real topology below certain length scale L(p) [padTGD]. Effective spacetime is assumed to consist of regions with different p-adic prime p glued together along their boundaries. p-Adic hypothesis leads to highly succesful predictions for elementary particle masses and simple argument shows that p-adic QFT should be free of ultraviolet divergences. p-Adic concepts may also have highly nontrivial applications to biosystems [padTGD,~homepage].
- 2. TGD inspired theory of consciousness
- TGD inspired theory of consciousness contains 3 basic elements.
a) The interpretation of quantum jump as the act of free will or equivalently as a moment of consciousness. Consciousness is here defined as 'pure alertness': no cognitive abilities such as memory and thinking need be involved;
b) The generalization of the ordinary quantum measurement theory (already described) so that it applies to the interaction of any subsystem with the surrounding world;
c) The properties of K ähler function, in particular its vacuum degeneracy, suggest a more concrete description of thinking systems as macroscopic quantum systems.
Details about various developments can be found from my homepage.
- 2.1 The problem of subjective time as key to the theory of consciousness
- The replacement of quantum state with quantum history raises a problem. If states are quantum histories how it is possible to define the concept of subjective time at all? The concept of the quantum jump suggests a solution of the problem. Assume that any quantum system is conscious only during the quantum jump and that the contents of consciousness are determined by the properties of the initial and final quantum histories. Identify the conscious 'I' as the region the configuration space CH, where the nondeterminism of the quantum jump is located. Assuming that this region corresponds to some finite region of space M^4_+ the value of the subjective time could perhaps be defined as average value of the time variable in this region.
- There is however difficulty associated with this definition. Diff^4 invariance implies that there is nondeterminism involved with all 3-surfaces on the orbit of given X^3 so that non-determinism cannot be located in time like direction whereas spatially the location is possible. It will be later found that the vacuum degeneracy of the Kähler action implying classical nondeterminism might make possible localization in the time direction and the coding of the information about the past to the concious experience.
- There is a more formal approach for identifying subjective time [TGD,padTGD ] described in detail in my homepage. Imbedding space is cartesian product of future light cone M^4_+ with CP_2 and M^4_+ globally breaks exact Poincare invariance. Poincare transformations do not commute with Diff^4 transformations since Poincare transform of the absolute minimum spacetime surface is in general not an absolute minimum spacetime surface. One can however define Diff^4 invariant Poincare transformations so that infinitesimal Poincare transformations act as ordinary infinitesimal Poincare transformations on 3-surfaces, which are intersections of the spacetime surface with M^4_+ proper time=constant hyperboloid (denote proper time by a in the sequel). Outside the hyperboloid the transformations induce deformation of the absolute minimum spacetime. One can select the value of a freely resulting in a one-parameter family of unitarily related energy momentum eigenstate basis. A non-trivial S-matrix for these state basis a_1 and a_2 can be defined in obvious manner. The identification of a as subjective time is suggestive. This definition also associates in a natural manner time duration with the conscious experience as the difference a_2-a_1.
- The arrow of time can easily be understood in this picture. Imbedding space is the cartesian product of thge future light cone M^4_+ (empty Robertson-Walker type cosmology) and CP_2. The boundary of the future light cone corresponds to the moment of big bang and for a given value of the light cone proper time a there is much more room in the future than in the past so that in the long run the subjective time associated with the quantum jump is bound to increase.
- One can critisize this definition of the subjective time as purely formal. The assumption of a preferred state basis is also somewhat questionable. Furthermore, one would expect that the contents of consciousness for quantum jump is determined by the comparison of the entire histories so that quantum jumps with a definite value of subjective time should be possible only for some special quantum systems and involve higher cognitive abilities.
- The quantum jumps changing the value of subjective time are trivial in the limit, when subjective time is not changed. Also, ordinary state function reductions associated with subsystems and not changing the value of subjective time must be allowed. Negentropy maximation principle is assumed to govern these quantum jumps. It is essential to notice that quantum jumps changing the value of subjective time are necessary: otherwise the Universe would end up to a state of maximum negentropy and nothing would happen after this.
- 2.2 Some consequences
- The proposed identification for the act of free will as quantum jump or equivalently as a moment of consciousness resolves many paradoxes related to the phenomenon of consciousness.
- \noindent a) Moments of consciousness form a discrete sequence and there is only single universal consciousness. 'You' is 'Me' at different moment. There is obvious parallel with the Brahman=Atman identity of Eastern religions and also with the experience of oneness associated with mystic experiences. The reason why I cannot remember of being 'You' for a moment ago is that the memories are coded into the quantum state and the memories are expected to correspond to that region of 3-space, where nondeterminism is located.
b) The idea of parallel streams of consciousness is simply wrong in this picture. This removes several problems related to consciousness. It is easy to understand why separate units of consciousness cannot communicate directly: they do not exist simultaneously. A solution to the conceptual problems raised by the study of split brain patients emerges. For split brain patients either left of right half of the brain is conscious at time but not both. Different brain halves seem to have even different plans of future and the transition between two different 'Me':s takes place instantaneously. If both brain halves are assumed to correspond to continuous streams of consciousness one ends up with a hopeless mess. Which of these halves corresponds to the 'actual Me'. Does the nondominating half correspond to a second 'Me'? What happens, when second half begins to dominate as the 'actual Me'?
c) The possibility that lower units of consciousness form larger units of consciousness (without knowing it!) is not excluded. The two brain halves of a healthy person obviously do so. The collective behaviour of an ant society might have an explanation in terms of higher consciousness associated with the society. Similarly, our own consciousness could be regarded as that associated with a society of cells. The formation of higher states of consciousness might occur even at the level of human society and could be even crucial for the development of civilization and the formation of language.
d) The basic assumption is that the content of the experience is determined from the properties of the initial and final states in the region of CH where the nondeterminism is located. This implies that sensory experience measures always changes rather than static properties. Sensory experience seems to have this kind of nature. In principle, all sensory qualia should be related to the properties of the initial and final states in the quantum jump. In some instances, the quantum jumps cause negligible change in the properties of the external world (consider vision as an example) so that sensory experience can be said to give rather faithful picture of some aspects of the objective world.
e) Clearly, the quantum jumps which do not change subjective time and are governed by negentropy maximation principle must correspond to ordinary sensory perception. Negentropy maximation principle poses restrictions on free will: the interaction with environment gives the alternatives (eigenstates of the density matrix), from which subsystem can select one. For ensembles, various alternatives have different probabilities given by standard quantum theory. The quantum jumps with no subsystem-external world division perhaps correspond to the states of conciousness described by mysticians: absence of subject-object division, the experience of oneness, the extension of 'I' to Self identified as something larger than that limited within boundaries of body, etc ..
- 3. Application to human consciousness
- 3.1 How to stay conscious?
- Quantum measurement theory states that if the interaction between subsystem and environment does not change with time the system performs just quantum jump and remains in the resulting state after that. Since consciousness is associated with quantum jumps subsystem must fall into an nonconsious state unless the interaction with enviroment changes in time. This is just what seems to occur. When we want to sleep we find some peaceful place and minimize the interaction with the environment. We get sleepy, when hearing boring lecturer. Constant sensory stimulation leads rapidly to the disappearence of the sensory experience, and our eyes make small continuous movements to avoid the disappearence of the visual field. Insects can see only a moving object. The brain can however stay conscious by generating nerve pulses leading to hallucinatory experiences. Similar phenomenon seems to occur at the level of nerve cells: when sensory stimulation stays constant, nerve cells stop firing.
- 3.2 Brain as a macroscopic quantum system
- The idea of Penrose and Hameroff about brain as macroscopic quantum system fits nicely with previous ideas. For instance, one could understand mental illness quantum mechanically as a loss of quantum coherence in brain, in other words, that some regions of brain lose their ability to be in quantum coherent states. This loss of coherence could be perhaps detected in the EEG as a loss of spatial coherence. The phenomenon of multi-personality disorder could also be understood from this point of view: single personality corresponds to some part of the brain being conscious while the remaining parts are nonconscious. The splitting into separate personalities could also understood as a partial loss of macroscopic quantum coherence: for split brain patients this splitting is caused artificially. The ability of, say, actors to create temporally new side personalities might have explanation as the ability of the brain to form new quantum subsystems.
- One can understand some other peculiarities of neurophysiology. One puzzling phenomenon pointed to me by Stan Klein and described also by Penrose in Shadows of the Mind is that cerebellum seems to be unconscious whereas cerebrum is conscious. There is some plausibility in the idea that the small number of acts of free will per unit time in cerebellum might explain it's apparent unconsiousness. Automaton like behaviour is certainly desirable in the control of motion (hardly any one would buy a car with free will). There is however also a counterargument. If the idea about quantum criticality of biosystems (to be discussed in later section) is correct at the level of tubulins then the basic difference between cerebrum and cerebellum would be that cerebellar tubulin dimers are far from Maxwell line and unable to perform phase transition like quantum jumps. For instance, narcotics could push tubulins too far from Maxwell line. Hameroff has suggested in quantum-D web page that the quantum jumps associated with postsynaptic microtubules are part of nerve pulse propagation. If however cerebral tubulins are too far from the Maxwell line, postsynaptic potentials cannot push cerebellar tubulins to the Maxwell line anymore. This would mean that in cerebellar nerve pulses propagate very differently. This looks somewhat odd. On the other hand, microtubular quantum jumps may not be essential for nerve pulse propagation.
- In any case, this leads to consider the possibility that cerebellum is conscious after all but our measurements somehow fail to detect this. Suppose that cerebellum and cerebrum do not form larger quantum system cerebrum+cerebellum but are most of the time in the same relation to each other as different brain halves of split brain patient. Or Me and You. If we perform 'consiousness measurement' by stimulating the cells of cerebellum electrically and ask subject person what he feels he answers 'Nothing' and we conclude that cerebellum is unconscious. This conclusion could be wrong since the 'I' of the subject person with which we talk corresponds very probably to some part of the brain containing speech centers but not the cerebellum since cerebellum does not possess any linguistic abilities. We address our question to the wrong person!
- This line of though would explain also the peculiar blind sight phenomenon. Person believes to be blind but it is obvious that this is not the case. In this case visual cortex and speech centers do not form larger quantum system Vision+ Speech anymore. When we as Mr. Speech 'Do You See' we get the answer 'No'. We should ask Mr. See but he cannot talk. There is also the case in which right half of the brain has suffered damage leading to paralysis of the left half of the body but the patient does not know it. Perhaps one could actually construct a map of the brain by finding what regions combine with Speech region to form a single quantum system and use this kind of map to detect pathological conditions. Perhaps one could someday fix the situation by simple quantum medicine!
- 3.3 Jumps between quantum histories at the level of brain
- In quantum jump between histories, the past of the system, defined in terms of the effective quantum average space time, also changes. There is evidence for this kind of change. In experiments in which the subject person decides to do something, say to take pencil from the table, neurological activity begins about one second before the conscious decision. The materialistic interpretation is that consciousness is a passive spectator and conscious experience is a by-product of a deterministic time evolution. The alternative interpretation is based on the assumption that the process of taking pencil into the hand is a macroscopic quantum jump between two widely different spatial configurations and the corresponding histories. The new history necessarily leads in a deterministic manner to a final state, where person has the pencil in his hand. Since this process must occur smoothly, the new history must differ from the old one already before the moment of decision so that the neurological processes begin before the moment of decision. This interpretation allows to deduce that brain is able to change its past in the time scale of order one second. A stronger conclusion is that the dimension for the region of nondeterminism is typically of order one second in time like direction and therefore corresponds to the subjective duration associated with a typical conscious experience. The interested reader can find a discussion of Libet and Kornhuber experiments in my homepage [padTGD]. The Ping-Pong example of Penrose is also discussed in terms of TGD-based concept of quantum jump.
- Note that in all situations, where free will actually occurs, one can argue that free will is just an illusion since the deterministic time development in the final state history indeed leads continuosly from initial to the final state. This observation perhaps explains why the concept of free will has turned out to be apparently unnecessary element in objective science.
- 3.4 Two kinds of quantum jumps and mystic experiences
- As already noticed one can clearly distinguish between two kinds of quantum jumps.
a) The ordinary state function reduction corresponds to a quantum jump which does not change the value of the subjective time. This quantum jump is associated with subsystem-external world interaction and subsystem goes to an eigenstate of the density matrix maximizing its negentropy interpreted as the amount of self knowledge. It is essential to notice that the quantum jump is not random since a preferred state basis is involved. Note also that the measurement interaction of the classical theory of state function reduction is generalized so that it applies to all quantum subsystems and state function reduction is by no means restricted to macroscopic systems.
b) In the second type of reduction, the value of subjective time changes and the preferred state basis for this quantum jump are energy momentum eigen state basis associated with the initial moment a_1 and final moment a_2. These quantum jumps are necessary since the quantum jumps of the first kind would sooner or later lead to a situation, where there is no entanglement between various subsystems and nothing happens.
- The basic distinction between these quantum jumps is that in the first quantum there is division of the Universe into subsystem and external world and negentropy maximation principle governs the quantum jump. Sensory perceptions whixh involve always subject-object division should correspond to this kind of quantum jumps. In the second type of quantum jump there is no division: entire universe performs the quantum jump although 'I' can be localized still. This is very reminiscent of the states of consciousness described by mystics. For instance, Krishnamurti again and again emphasizes the disappearence of the distinction between observer and observed in these states of consciousness. Since subjective time flows everyone of us is in fact performing quantum jumps of second type and what is needed is to cease quantum jumping of the first kind. Indeed, the practical method to achieve englightment is to make mind empty by minimizing mental activity and sensory perceptions: these activities indeed involve the division of world to subject and object and can be identified as quantum measurements. Also one must avoid attachment, the quantal counterpart for attachment is clearly quantum entanglement. One method to get rid of sensory entanglement is to perform sensory quantum measurement: indeed the exercises used to achieve the state of empty mind involve repeated scanning of the entire body paying attention to each part of body separately. The second method is to perform extension of subsystem defining the 'I' so that reduction becomes unnecessary: one feature of personal development of mystics is the gradual extension of self to include objects of external world. The ultimate extension of self over the boundaries of 'I' to Self is in accordance with the possibility that quantum jumps of second type can involve arbitrary large regions of spacetime. Mystics associate the feeling of 'emptiness' and 'timelessness' with the enlighted states. Perhaps this is what should be experienced, when nothing changes in the quantum jump. This state of pure consciousness might perhaps correspond to the limiting case of quantum jump for which the change of subjective time approaches zero and S-matrix describing transition amplitudes becomes unit matrix so that only 'forward scattering' is possible.
- To me the gradual realization of these rather precise analogies have been a rather shattering experience. As a theoretical physicist I have strong tendency to trust on rational thinking as a unique way to understand Nature. It is amazing meditative practice has produced essentially the same theory of consciousness, which seem to forced by Quantum Theory. To mention one amusing example, buddhist tradition has emphasized the momentary nature of consciouss experience and there is even estimate for the number of moments of consciousness per unit time: the estimate is of same order of magnitude than obtained from Penrose-Hameroff theory!
- 4. About cognitive aspects of consciousness
- Only some kind of elementary awareness should be associated with the quantum jumps occurring at elementary particle level. Very probably electron cannot remember its past experiences whereas memory and thinking are crucial aspects of the ordinary human consciousness. Quantum jumps described previously might well be all what is needed to explain also the cognitive aspects of consciousness since time duration is in general involved with the quantum jump and the contents of consciousness are determined by initial and final quantum histories so that past and future are in principle present in the contents of consciousness. This means that memory, future plans and also thoughts might well be describable in this picture. TGD suggest the possibility of quantum states and quantum jumps for which cognitive aspects are quite explicitely present as a simulation of classical history. Rather remarkably, several very general ideas combine together in natural manner in TGD-based framework:
a) the idea of Penrose about biosystem as a quantum superposition of macroscopically different classical spacetimes.
b) the description of thinking system as a quantum critical system.
c) the escription of macroscopic quantum jump as quantum analog of phase transition.
d) the catastrophe theory of Thom.
- 4.1 Thoughts as simulations
- The basic feature of cognitive functions seems to be the simulation of possible histories. Memory corresponds to a simulation of past and future plans and predictions to the simulation of the future. The arrow of time probably explains why the simulation of past is so reliable that we speak of actual memories rather than predictions of the past. The possible nonuniqueness of the classical spacetime and related classical nondeterminism suggest a possible origin for the simulatory aspects of consciousness. The basic idea is following. If the classical spacetime associated with a given 3-surface X^3 is nonunique, one must also specify, besides X^3, some minimum number of other 3-surfaces at the selected orbit X^4(X^3) of X^3 in order to specify classical spacetime completely. This minimal set of 3-surfaces could be regarded as a discrete simulation for the time development of X^3 and thus as an elementary thought. In the following this argument is developed in more detail.
- 4.2 Vacuum degeneracy of the K ähler action
- Perhaps the most fundamental property of Kähler action is its vacuum degeneracy. K ähler action allows enormous numbers of vacuum extremals. Any 4-surface with CP_2 projection for which the induced Kähler form of CP_2 vanishes has a vanishing Kähler field and Kähler action (which is nonlinear counterpart of the Maxwell action) and is therefore a vacuum extremal. The submanifolds of CP_2 for which the induced K ähler form vanishes are called Lagrange manifolds and in general they are two-dimensional submanifolds of CP_2. A more familiar example is provided by the n-dimensional Lagrange manifold of phase space spanned by the coordinates (q_i,p_i), i=1,..,n. For instance, p_i= const submanifolds and any manifolds obtained from these manifolds by applying canonical transformations are Lagrange manifolds.
- Vacuum extremals allow the diffeomorphisms of M^4 and canonical transformations of CP_2 as symmetries. All possible topologies allowed by the imbeddability requirement are possible so that the vacuum degeneracy is enormous. The vacuum degeneracy suggests strongly that for some critical 3-surfaces, the absolute minimum spacetime is not unique as the following arguments intend to show.
- 4.3 Nonuniqueness of the classical spacetime from vacuum degeneracy
- Absolute minimum spacetimes is in general not vacuum extremal but one can expect that, in some cases, it could be regarded as a small deformation of some vacuum extremal. It can however happen that for some critical 3-surface there are two or more topologies giving the same value of Kähler action (also several minima with same topology could occur). Critical surfaces are just those 3-surfaces, where the topological or some other characteristics of the absolute minimum spacetime surface change discontinuously. In this kind of situation one encounters the problem of selecting between several alternatives and there seems to be no manner to fix uniquely the correct classical spacetime. The only way out of difficulty is the extension of configuration space so that it becomes N-sheeted in the points X^3 for which absolute minimum is N-fold degenerate. At quantum level this classical nondeterminism corresponds to additional discrete degrees of freedom labeled by integer n=1,..,N.
- The nonuniqueness of the classical spacetime induces the nonuniqueness of the effective spacetime since one can define the average spacetime in many manners by fixing in some continuous manner the classical spacetime associated with the critical 3-surfaces X^3. In general quantum states can be regarded as superpositions over these different effective spacetimes. Following Penrose it is tempting to identify this quantum superposition for effective spacetime geometries as a fundamental property of biosystems. Stating it differently: evolution would favour the formation of macroscopic quantum critical systems.
- There is close analogy with phase transitions and catastrophe theory. K ähler function is completely analogous with thermodynamical free energy. Typically, free energy depends on state variables x,.. and external parameters (a,b,..). Simplest situation corresponds to van der Waals equation of state with one state variable x and two external parameters (a,b). The minimization is performed with respect to state variables x keeping (a,b) constant. The 2-dimensional surface of minima is many sheeted in some region of (x,a,b)-space and looks locally like a cusp catastrophe. For cusp catastrophe 3 solutions to the extremization conditions exist in the cusp region. For generic x only one of these is an absolute minimum. The situation changes however on the Maxwell line, where two branches have the same value of the free energy and where phase transitions occur. This simple picture generalizes to the higher dimensional situation and as Thom has shown that the description of cusp catastroph can always be reduced to the canonical description using only 3 coordinates. More complicated catastrophes can be constructed from cusps but as far as discontinous jumps in x are considered, cusps are the basic catastrophes.
- In the present infinite-dimensional context, the external parameters are the configuration space coordinates specifying the 3-surface X^3. These are held constant in the minimization of Kähler action. The state variables correspond to the coordinates specifying 4-surface X^4 going through X^3. For vacuum surfaces X^3, which have vanishing induced Kähler field, there exist an infinite number of vacuum surfaces with varying topologies going through X^3 and the deformations of these surfaces give good candidates for the absolute minima. At critical 3-surfaces the nature of the absolute minimum surface changes: for instance, the topology of this surface can change. The preceiding argument applies to vacuum X^3:s but also for X^3 sufficiently close to vacuums situation is expected to be same by continuity.
- The cusp catastrophe implies that there are two different effective spacetimes associated with X^3 so that the point of the extended configuration space is completely described by associating a binary digit with the critical surface. For multicatastrophes (say one catastrophe per tubulin dimer in microtubule) a sequence of binary digits describes the situation. One can easily imagine that a thinking system could perform quantum computation using the quantum states specified by these binary sequences. This binary structure should somehow reflect itself in the properties of the effective spacetime and it is very tempting to speculate that the binary structure of the microtubules (tubulin dimers have two possible conformations) is related to these binary sequences. This argument suggests that biosystems should correspond to 3-surfaces near vacuum extremals. One can generate negative Kähler action by deforming vacuum extremal so that Kähler electric fields are generated: this leads to the generation of ordinary electric fields, too. Perhaps the the important role of electric fields in biosystems is closely related to the minimization of Kähler action. Possible applications along these lines are considered on my homepage.
- A further plausible looking assumption is that the nonuniqueness of the absolute minimum spacetime corresponds to the branching of the absolute minimum 3-surface at certain value a=a(cr) of the proper time coordinate a so that 3-space is unique before this time. This kind of branching is analogous to the development of hydrodynamic shock wave and the field equations of TGD indeed are indeed conservation laws analogous to hydrodynamic equations. The action for the different branches is same only in codimension one subset of CH and clearly one has an analog of Maxwell line (shock wave corresponds also to cusp catastrophe). In order to specify the branch uniquely one must specify at least two 3-surfaces: the first one must have a< a(cr)and the second one must have a> a(cr) . For this kind of quantum jump, a natural definition for subjective time is as the average value of the a(cr) over all critical 3-surfaces and really corresponds to a real choice occurring at this moment of time.
- There are some unsatisfactory features in this picture and it is difficult to decide whether or not to take quantum criticality seriously.
a) The concept of effective spacetime and quantum superposition which occurs for effective spacetimes in quantum critical case could be regarded perhaps somewhat artificial since they are derived concepts in the proposed formulation of Quantum TGD. The idea of Penrose about superpositions of spacetime geometries is contained in the general theory automatically since quantum state can be regarded as a superposition of spacetime surfaces. It might be that the general theory is capable of explaining also the cognitive aspects of consciousness since states are identified as quantum histories so that memories, plans and other cognitive aspects could be contained in the description.
b) The construction of quantum computer model in terms of the effective space time concept may not be possible. One should define effective spacetime concept for quantum subsystems in order to define quantum entanglement: physical intuition tells that this should be possible. It seems however impossible to construct time evolution for effective 3-surfaces changing continuously the coefficients of various branches in the superposition. What can happen is that effective 3-surface is unique up to moment a_ 1 and after that it is superposition of, say 2 branches, with constant coefficients, after a_2 it is superposition of, say 4, branches, etc... The fact that this Schrödinger type time evolution is piecewise constant gives rather strong, perhaps too strong, limitations on quantum computations.
c) The idea that quantum average spacetime is not unique is not quite in accordance with the idea that quantum average is in question! On the other hand, the concept of quantum average in infinite dimensional context is not what naive expectations suggest, and already in statistical mechanics the quantum average defined in terms of free energy becomes non-unique at the critical line. It might also be that effective spacetime is essential part of the definition of the theory and states what is the observed spacetime in a given quantum state.
d) The assumption that thinking system is localized on Maxwell line is unsatisfactory unless the coordinate transversal to the cusp is discrete. Otherwise one must assume that the state function of the quantum critical system has deltafunction type singularity on Maxwell line. On the other hand, biosystems are certainly very rare occurrences in Nature and quantum criticality is therefore an attractive idea. Furthermore, since the effective spacetime surface is obtained as an absolute minimum of theeffective action by minimizing also with respect to the degrees of freedom associated with the 3-surface X^3 (whereas X^3 is fixed in the variations, whose minimum gives X^4(X^3)), the localization effective spacetime on Maxwell line might result from the dynamics associated with the effective action. In particular, the time development of the effective 3-space could well involve branchings at critical moments of time in analogy of the development of shock waves.
- An interesting possibility is that vacuum extremals correspond to subregions of actual absolute minimum spacetimes. For example, at elementary particle level, quantum super position for CP_2 type extremals, the infinitely degenerate effective spacetimes associated with elementary particles, leads to the mathematical structure of super string model and to succesfull predictions for particle masses. Furthermore, the fact that vacuum extremals have vanishing action and are absolute minima of p-adic (!) Kähler action suggests that infinite degeneracy might be encountered even in macroscopic quantum systems and it might be worth of pondering the possible interpretation of this degeneracy in case of biosystems.
- 4.4 Vacuum degeneracy and the problem of subjective time
- One can argue that the proposed formal identification of the time parameter a in the definition of energy momentum basis as subjective time is correct but that the conscious experience associated with the quantum jump a_1--> a_2 contains information on the change of entire quantum history rather than about snapshot for a simeq (a_1+a_2)/2. Also one could argue that quantum system capable of experiencing subjective time must have higher cognitive abilities and the problem is to understand how these abilities could arise in the Universe predicted by TGD.
- A possible solution to the problem of understanding how quantum jump can contain information about the past associated with a definite value of time is suggested by the following argument. In the shock wave analog, the region V^4 of nonuniqueness for the effective spacetime was assumed to begin at definite time t_0 and extend to all times t>t_0. This makes it difficult to associate definite value of subjective time to the quantum jump selecting one spacetime branch. Assume, however, that the nondeterministic region V^4 (with finite duration) is finite and that spacetime is unique outside this region. Inside V^4 effective spacetimes are obtained from appropriate vacuum extremals by a small deformation and this replacement results from the interaction with the external spacetime. Since the interaction with the external world is causal the interaction codes some information about the past of the external world to each spacetime branch inside V^4. This information is read consciously in a quantum jump selecting unique branch inside V^4. There is a more or less definite value of subjective time associated with these kind of quantum jumps. The duration of conscious experience is identifiable as the extension of V^4 in time direction.
- 4.5. Comparison with Penrose-Hameroff theory
- It is interesting to compare the TGD-based picture with the O(bjective) R(eduction) scenario of Penrose and Hameroff. OR is regarded as distinct from the ordinary S(ubjective) R(eduction). OR is assumed to take place for a state, which is superposition of different 3-space geometries (say, two conformations of tubulin dimer) and Penrose proposes in his book an estimate for the reduction time in terms of quantity having interpretation as gravitational interaction energy. The question whether actual nondeterminism is involved with OR is left open. The flow of the subjective time and consciousness is associated with OR or rather Orch OR, orchestrated OR occurring in microtubules.
- Quantum superposition for spacetimes, which is only a heuristic concept in Hameroff-Penrose theory, is strictly defined concept in TGD (modulo uncertainties related to the precise definition of the configuration space geometry). The counterpart of OR in TGD can be regarded as a quantum jump performed by the entire Universe and changing the value of the subjective time, possibly having an identification also as a 'enlightened' state of consciousness involving no subject-object splitting. If one takes quantum criticality seriously, then also classical nondeterminism would be involved. It is however hard to see how gravitational interaction might force OR to occur in some time scale depending on the system's size and mass.
- Penrose-Hameroff theory provides an estimate for the reduction time and quite reasonable estimates are obtained in case of biosystems. In TGD context the p-adicity of the effective spacetime might provide a natural estimate for the reduction time as the p-adic time scale L(p) simeq 10^4 *sqrt(p) sqrt(G) is in accordance with the assumption that below this length scale p-adic QFT applies and at longer length scales real topology is a good approximation. This kind of time scale appears also number theoretically: the operator exp(i* int(Vdt)) (int denotes integral) generating unitary time evolution in the p-adic case exists, when the p-adic norm N_p(int(Vdt)) of the exponent satisfies N_p(int(Vdt))<1. A tempting possibility is that state function reduction must take place before this condition ceases to be satisfied. The real counter part for the reduction time t(red) is of order sqrt (p)^n*L(p), where the integer n depends on the strength of the interaction. The unexpected feature is that reduction time increases with the increasing typical size of the p-adic quantum system: just the opposite happens in the real context if one takes seriously the estimate of Penrose! The possibility of quantum systems with arbitrary large size would mean that the states of cosmic consciousness described by mystics are perhaps possible. For a system of cell size p is about 2^ (169) and the time is of order t(red) sim 2^ (169n/2)10^ (-14) seconds. n=1 would give a time scale of order 10^3 years as an upper bound for t(red). This suggests that the characteristic feature of p-adic biosystems is perhaps the extreme weakness of the p-adic interaction Hamiltonian. For microtubules with p-adic length scale of order 10^(-8) meters one obtains upper bound of 10 years for t(red).
- 5. Summary
- This brief essay gives only the basic ideas of the TGD inspired theory of conscious and intelligent systems, as they have gradually developed during last 10 years or so. The interested reader can find more detailed discussions on my homepage, where applications of TGD to the description of biosystems can also be found. Of course, all these developments are highly speculative and I would be happy if these ideas can serve as an inspiration for others, who has been caught by the fascinating problem problem of consciousness.
- I am grateful for Joe Brenner for kindly making grammatical corrections to the text as well as pointing out many typing errors and missing words in the text.
- [TGD] M. Pitkänen (1990). Topological Geometrodynamics . Internal Report HU-TFT-IR-95-4 (Helsinki University). Summary of Topological Geometrodynamics in book form. Book contains construction of Quantum TGD, 'classical' TGD and applications to various branches of physics.
- [padTGD] M. Pitkänen (1995). Topological Geometrodynamics and p-Adic Numbers. Internal Report HU-TFT-IR-95-5 (Helsinki University). Report on application of p-adic numbers in attempts to understand quantum field theory limit of TGD. Chapters 4-9 are especially interesting as far as this paper is considered.
- The updated versions of both reports are available as ps-files from my personal ~homepage. Homepage contains also a hypertext representation of the basic ideas and concepts of TGD.
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