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TGD Inspired Theory of Consciousness

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Year 2010

The arrow of time and self referentiality of consciousness

The understanding of the relationship between experienced time whose chronon is identified as quantum and geometric time has remained one of the most difficult challenges of TGD inspired theory of consciousness. Second difficult problem is self referentiablity of consciouness.

One should understand the asymmetry between positive and negative energies and between two directions of geometric time at the level of conscious experience, the correspondence between experienced and geometric time, and the emergence of the arrow of time. One should explain why human sensory experience is about a rather narrow time interval of about .1 seconds and why memories are about the interior of much larger CD with time scale of order life time. One should have a vision about the evolution of consciousness: how quantum leaps leading to an expansion of consciousness occur.

Negative energy signals to geometric past - about which phase conjugate laser light represents an example - provide an attractive tool to realize intentional action as a signal inducing neural activities in the geometric past (this would explain Libet's classical findings), a mechanism of remote metabolism, and the mechanism of declarative memory as communications with geometric past. One should understand how these signals are realized in zero energy ontology and why their occurrence is so rare.

In the following I try to demonstrate that TGD inspired theory of consciousness and quantum TGD proper indeed are in tune. I have talked about these problems already earlier and the motivation for this posting is that the discussions with Stephen Paul King in Time discussion group led to a further progress in the understanding of this issues. What I understand now much better is how the self referentiality of consciousness is realized.

Space-time and imbedding space correlates for selves

Quantum jump as a moment of consciousness, self as a sequence of quantum jumps integrating to self, and self hierarchy with sub-selves experienced as mental images, are the basic notions of TGD inspired theory of consciousness. In the most ambitious vision self hierarchy reduces to a fractal hierarchy of quantum jumps within quantum jumps. Quantum classical correspondence demands selves to have space-time correlates both at the level of space-time and imbedding space.

At the level of space-time the first guess for the correlates is as light-like or space-like 3-surfaces. If one believes on effective 2-dimensionality and quantum holography, partonic 2-surfaces plus their 4-D tangent space distribution would code the information about the space-time correlates. By quantum classical correspondence one can also identify space-time sheets as the correlates modulo the gauge degeneracy implied by super-conformal symmetries.

It is natural to interpret CDs as correlates of selves at the level of the imbedding space. CDs can be interpreted either as subsets of the generalized imbedding space or as sectors of WCW. Accordingly, selves correspond to CDs of the generalized imbedding space or sectors of WCW, literally separate interacting quantum Universes. The spiritually oriented reader might speak of Gods. Sub-selves correspond to sub-CDs geometrically. The contents of consciousness of self is about the interior of the corresponding CD at the level of imbedding space. For sub-selves the wave function for the position of tip of CD brings in the delocalization of sub-WCW.

The fractal hierarchy of CDs within CDs is the geometric counterpart for the hierarchy of selves: the quantization of the time scale of planned action and memory as T(k)= 2kT0 suggest an interpretation for the fact that we experience octaves as equivalent in music experience.

Why sensory experience is about so short time interval?

CD picture implies automatically the 4-D character of conscious experience and memories form part of conscious experience even at elementary particle level. Amazingly, the secondary p-adic time scale of electron is T=0.1 seconds defining a fundamental time scale in living matter. The problem is to understand why the sensory experience is about a short time interval of geometric time rather than about the entire personal CD with temporal size of order life-time. The explanation would be that sensory input corresponds to subselves (mental images) with T≈ .1 s at the upper light-like boundary of CD in question. This requires a strong asymmetry between upper and lower light-like boundaries of CDs.

The localization of the contents of the sensory experience to the upper light-cone boundary and local arrow of time could emerge as a consequence of self-organization process involving conscious intentional action. Sub-CDs would be in the interior of CD and self-organization process would lead to a distribution of CDs concentrated near the upper or lower boundary of CD. The local arrow of geometric time would depend on CD and even differ for CD and sub-CDs.

  1. The localization of contents of sensory experience to a narrow time interval would be due to the concentration of sub-CDs representing mental images near the either boundary of CD representing self.

  2. Phase conjugate signals identifiable as negative energy signals to geometric past are important when the arrow of time differs from the standard one in some time scale. If the arrow of time establishes itself as a phase transition, this kind of situations are rare. Negative energy signals as a basic mechanism of intentional action and transfer of metabolic energy would explain why living matter is so special.

  3. Geometric memories would correspond to subselves in the interior of CD, the oldest of them to the regions near "lower" boundaries of CD. Since the density of sub-CDs is small there geometric memories would be rare and not sharp. A temporal sequence of mental images, say the sequence of digits of a phone number, would correspond to a temporal sequence of sub-CDs.

  4. Sharing of mental images corresponds to a fusion of sub-selves/mental images to single sub-self by quantum entanglement: the space-time correlate could be flux tubes connecting space-time sheets associated with sub-selves represented also by space-time sheets inside their CDs.

Arrow of time

TGD forces a new view about the relationship between experienced and geometric time. Although the basic paradox of quantum measurement theory disappears the question about the arrow of geometric time remains. There are actually two times involved. The geometric time assignable to the space-time sheets and the M4 time assignable to the imbedding space.

Consider first the the geometric time assignable to the space-time sheets.

  1. Selves correspond to CDs. The CDs and their projections to the imbedding space do not move anywhere. Therefore the standard explanation for the arrow of geometric time cannot work.

  2. The only plausible interpretation at classical level relies on quantum classical correspondence and the fact that space-times are 4-surfaces of the imbedding space. If quantum jump corresponds to a shift for a quantum superposition of space-time sheets towards geometric past in the first approximation (as quantum classical correspondence suggests), one can understand the arrow of time. Space-time surfaces simply shift backwards with respect to the geometric time of the imbedding space and therefore to the 8-D perceptive field defined by the CD. This creates in the materialistic mind a temporal variant of train illusion. Space-time as 4-surface and macroscopic and macro-temporal quantum coherence are absolutely essential for this interpretation to make sense.

Why this shifting should always take place to the direction of geometric past of the imbedding space? Does it so always? The proposed mechanism for the localization of sensory experience to a short time interval suggests an explanation in terms of intentional action.

  1. CD defines the perceptive field for self. Negentropy Maximization Principle (NMP) or its strenghtened form could be used to justify the hypothesis that selves quite universally love to gain information about the un-known. In other words, they are curious to know about the space-time sheets outside their perceptive field (the future). Therefore they perform quantum jumps tending to shift the superposition of the space-time sheets so that unknown regions of space-time sheets emerge to the perceptive field. Either the upper or lower boundary of CD wins in the competition and the arrow of time results as a spontaneous symmetry breaking. The arrow of time can depend on CD but tends to be the same for CD and its sub-CDs. Global arrow of time could establish itself by a phase transitions establishing the same arrow of time globally by a mechanism analogous to percolation phase transition.

  2. Since the news come from the upper boundary of CD, self concentrates its attention to this region and improves the resolution of sensory experience. The sub-CDs generated in this manner correspond to mental images with contents about this region. Hence the contents of conscious experience, in particular sensory experience, tends to be about the region near the upper boundary.
  3. Note that the space-time sheets need not to continue outside the CD of self but self does not know this and believes that there is something there to be curious about. The quantum jumps inducing what reduces to a shift in region sufficiently far from upper boundary of CD creates a new piece of space-time surface! The non-continuation of the space-time sheet outside CD would be a correlate for the fact that subjective future does not exist.

The emergence of the arrow of time at the level of imbedding space reduces to a modification of the oldest TGD based argument for the arrow of time which is wrong as such. If physical objects correspond to 3-surfaces inside future directed light-cone then the sequence of quantum jumps implies a diffusion to the direction of increasing value of light-cone propert time. The modification of the argument goes as follows.

  1. CDs are characterized by their moduli. In particular, the relative coordinate for the tips of CD has values in past light cone M4- if the future tip is taken as the reference point. An attractive interpretation for the proper time of M4- is as cosmic time having quantized values. Quantum states correspond to wave functions in the modular degrees of freedom and each U process creates a non-localized wave function of this kind. Suppose that state function reduction implies a localization in the modular degrees of freedom so that CD is fixed completely apart from its center of mass position to which zero four-momentum constant plane wave is assigned. One can expect that in average sense diffuction occurs in M4- so that the size of CD tends to increase and that the most distant geometric past defined by the past boundary of CD recedes. This is nothing but cosmic expansion. This provides a formulation for the flow of time in terms of a cosmic redshift. This argument applies also to the positions of the sub-CDs inside CD. Also their proper time distance from the tip of CD is expected to increase.

  2. One can argue that one ends up with contradiction by changing the roles of upper and lower tips. In the case of CD itself is only the proper time distance between the tips which increases and speaking about "future" and "past" tips is only a convention. For sub-CDs of CD the argument would imply that the sub-CDs drifting from the opposite tips tend to concentrate in the middle region of CD unless either tip is in a preferred position. This requires a spontaneous selection of the arrow of time. One could say that the cosmic expansion implied by the drift in M4- "draws" the space-time sheet with it to the geometric past. The spontaneous generation of the asymmetry between the tips might require the "curious" conscious entities.

The mechanism of self reference

Self reference is perhaps the most mysterious aspect of conscious experience. When formulated in somewhat loose manner self reference states that self can be conscious about being conscious of something. When trying to model this ability in say computer paradigm one is easily led to infinite regress. In TGD framework a weaker form of self referentiality holds true: self can become conscious that it was conscious of something in previous quantum jump(s). Self reference therefore reduces to memory. Infinite regress is replaced with evolution recreating Universe again and again and adding new reflective levels of consciousness. It is however essential to have also the experience that memory is in question in order to have self reference. This knowledge implies that a reflective level is in question.

The mechanism of self reference would reduce to the ability to code information about quantum jump into the geometry and topology of the space-time surface. This representation defines an analog of written text which can be read if needed: memory recall is this reading process. The existence of this kind of representations means quantum classical correspondence in a generalized sense: not only quantum states but also quantum jump sequences responsible for conscious experience can be coded to the space-time geometry. The reading of this text induces self-organization process re-generating the original conscious experience or at least some aspects of it (say verbal representation of it). The failure of strict classical determinism for Kähler action is absolutely essential for the possibility to realize quantum classical correspondence in this sense.

Consider now the problem of coding conscious experience to space-time geometry and topology so that it can be read again in memory recall. Let us first list what I believe to know about memories.

  1. In TGD framework memories corresponds to sub-CDs inside CDs (causal diamonds defined as intersections of future and past directed light-cones) and are located in geometric past. This means fundamental difference from neuroscience view according to which memories are in the geometric now. Note that standard physicist would argue that this does not make sense: by the determinism of field equations one cannot think 4-dimensionally. In TGD however field equations fail to be deterministic in the standard sense: this actually led to the introduction of zero energy ontology.

  2. The reading wakes up mental images which are essentially 4-D self-organization patterns inside sub-CDs in the geometric past. Metabolic energy is needed to achieve this wake up. What is needed is generation of space-time sheets representing the potential images making possible memories.

This picture combined with the mechanism for generating the arrow of phychological time and explaining why sensory experience is located to so short time interval as it is (.1 second, the time scale of CD associated with electron by p-adic length scale hypothesis) allows to understand the mechanism of self reference. It deserves to be mentioned that the discussion with Stephen Paul King in Time discussion group served as the midwife for this step of progress.

  1. When the film makes a shift to the direction of geometric past in quantum jump subselves representing mental images representing the reaction to the "news" are generated. These correspond to sub-CDs contains space-time surfaces as correlates of subselves created and the information contents of immediate conscious experiences is about this region of space-time and imbedding space. They are like additional comment marks on the film giving information about what feelings the news from the geometric future stimulated.

  2. In subsequent quantum jumps film moves downwards towards geometric past and markings defined in terms of space-time correlates for mental images are shifted backwards with the film and define the coding of information about previous conscious experience. In memory recall metabolic energy is feeded to these subsystems and they wake up and regenerate the mental images about the remembered aspect sof the previous conscious experience. This would not be possible in positive energy ontology and if determinism in strict sense of the world would hold true.

  3. Something must bring in the essential information that these experiences are memories rather than genuine sensory experiences (say). Something must distinguish between genuine experiences and memories about them. The space-time sheets representing self reference define cognitive representations. If the space-time sheets representing the correlates for self-referential mental images are p-adic, this distinction emerges naturally. That these space-time sheets are in the intersection of real and p-adic worlds is actually enough and also makes possible negentropic entanglement carrying the conscious information. In TGD inspired quantum biology this property is indeed the defining characteristic of life.

  4. There is quite concrete mechanism for the realization of memories in terms of braidings of magnetic flux tubes discussed here.

Background material can be found in the chapter About the Nature of Time.

Does harmonic complexity reduce to 3-adicity?

I have been updating the chapter Self and Binding of TGD inspired theory of consciousness. The goal is to base the theory from the beginning on ideas like zero energy ontology, hierarchy of Planck constants aand its connection with dark matter, p-adic physics as physics of cognition and intentionality -and in in particular, life as something residing in the interection real and p-adic worlds. The notion of number theoretic entropy makes it possible to assign to rational or even algebraic entanglement probabilities a positive negentropy and this has meant a breakthrough in the understanding of TGD inspired theory of consciousness and life. These updatings are extremely fruitful -not only because they force to throw away the ancient and obsolete stuff- but because the interaction of new ideas with old ones produces something completely unexpected new ideas.

The understanding of music experience is especially fascinating challenge for a consciousness theorists. In TGD framework quite nice vision about the basic aspects of music experience emerges. Octave phenomenon can be reduced to p-adic length scale hypothesis implied if the causal diamonds defined as intersections of future and past directed lightcones and playing key role in quantum TGD have discrete size spectrum coming as octaves of CP2 length. Also the preferred role of certain rational frequencies can be understood in the p-adic context from the fact that sine waves in p-adic context can be defined only by introducing an algebraic extension of p-adic numbers allowing the needed roots of unity. Plane waves are defined p-adically only in discrete subset of points and for harmonics of the fundamental frequency. This implies automatically the preferred role of a limited set of rational valued multiples of the fundamental.

The following little excerpt from the updated chapter provides a inspired vision about one particular aspect of music experience, namely the harmony and allows to interpret Pythagorean vision about music scale in terms of 3-adicity, to deduce a measure for a harmonic measure of the chord, and to replace the Pythagorean tuning of 12-tone system based on perfect fifths with a unique tuning based on 3-adicity.

An interesting question relates to the conditions guaranteing that a chord is experienced as harmonious in the Pythagorean sense. Pythagorean tuning is based on the notion of perfect fifths identified as a scaling by 3/2 producing the sequence C,G,D,A,E,.. In this tuning major-C scale corresponds to ratios C= 1/1, D=9/8, E=81/64, F=4/3, G= 3/2, A=27/16, B= 243/128, C=2/1. Eb and F# correspond to ratios 25/33 and 36/29. All notes are expressible as powers of two and three. Since the multiplication of any note by a power of two does not affect the harmony it should be to drop the powers of two from the integers characterizing the notes in the ratio of three notes. For instance, C-E-G reduces 3:34:1, C-Eb-G to 34:1:33, and tritonus C-Eb-F# to 39:1:33.

The problem of Pythagorean tuning is that one cannot represent 2 as an exact integer power of 3/2 and the scalings give infinite number of tones. If the construction starts from Gb then F# and Gb correspond to frequencies, which are not quite identical in Pythagorean tuning. One could make compromize by introducing the geometric mean of F# and Gb but this would bring in 31/2 and would force to leave the world of pure rationals. For string instruments and electronic instruments the Pythagorean tuning is practical but for instruments like piano the transposition of the scale is impossible.

One should be able to characterize a given chord harmonically by a function F(a,b,c), which is symmetric under the permutations of the reduced pitches a, b and c obtained by dropping powers of two and is invariant under over all scaling of the reduce frequencies. The elementary symmetric functions F(a,b,c)=[a2(b+c)+b2(a+c)+c2(a+b)]/abc and G(a,b,c)=[a3+b3+c3]/abc are the simplest functions of this kind. Either of these functions or their product or ratio could be considered as a measure for the harmonic complexity. The value of the denominator abc equals to 3n, n=3,7,12 in the cases considered. The numerator has in all cases 3-adic norm equal to one for both F and G. This suggests that the 3-based logarithm of the 3-adic norm 1/|abc|3=|F|3=|G|3 having the values 3,7, and 12 for C-major, C-minor, and tritonus could serve as the measure for the complexity. It is indeed smallest for major and largest for tritonus. 3-adic norm for the product 1/a1a2...an of n tones of the chord defines a measure of complexity in more general case. A good guess is that the 3-adic norms of the elementary symmetric functions give rise to the same measure.

For the chords C-E-G, F-A-C, and G-H-D appearing as basic chords in C- major scale the values of the harmonic measure are 3, 2, and 8. This means that the basic chords are not harmonically equivalent in Pythagorean system whereas in equally tempered system they would be. One might think that this explains why the tonic is remembered. The anomalously low value for F-A-C relates to the fact that it is only tone for which the power of 3 is negative. Situation changes of F is identified as a minimal power of 3 giving F equivalent with Pythagorean F within the resolution of ear to pitch which is about |Δ f/f|= 4.3 per cent . F=35/28 gives |Δ f/f|= 4.8 per cent. This F would give for F-A-C the harmonic measure 8 which equals to that for G. This looks more reasonable than the purely Pythagorean value. This definition would also allow to find a unique choice of powers of three for 12-chord system. For instance, F# is favored over Gb since it corresponds to a positive power of 3.

To sum up, music seems to provide a possible manifestations of 3-adicity, and the proposed measure of harmonic complexity might provide a manner to construct also a theory of aesthetically pleasing harmonic progressions.

For details and background see the updated chapter Self and Binding of "TGD Inspired Theory of Consciousness".

Negentropy Maximization Principle updated

Conscious existence is continual recreation of the Universe. My own humble contribution to this magnificent activity is endless updating of the chapters of the books about TGD. During this particular cascade of quantum jumps I updated the chapter Negentropy Maximization Principle of "TGD Inspired Theory of Consciousness" so that zero energy ontology and causal diamonds, hierarchy of Planck constants, and the vision about life as something in the intersection of real and p-adic worlds - which is nothing but number theoretical criticality- are taken into account from the beginning. I managed to build a vision about what it means mathematically to be in this intersection and what it means for U-matrix. I also found an expression for U-matrix as a collection of M-matrices so that these two matrices are not independent of each other as I had erratically thought. Unitarity of U states the orthogonality for the zero energy states defined by M-matrices. Very beautiful.

Number theory enters into game strongly: for instance, different algebraic extensions of rationals are regarded formally as quantum states and there is unitary dispersion in this space. Also the notion about leakage between different number fields at the level of partonic 2-surfaces leads to amplitudes expressible in terms of points of partonic 2-surface belonging to the algebraic extension of rationals. Kind of number theoretic QFT emerges naturally. For the first time I encountered really naturally infinite collection of commutative diagrams, which mathematicians have used since the days of Adam and Eve. We theoretical physicists are rather slow in our reactions. I attach the abstract of the updated chapter below.

In TGD Universe the moments of consciousness are associated with quantum jumps between quantum histories. The proposal is that the dynamics of consciousness is governed by Negentropy Maximization Principle, which states the information content of conscious experience is maximal. The formulation of NMP is the basic topic of this chapter.

Negentropy Maximization Principle (NMP) codes for the dynamics of standard state function reduction and states that the state function reduction process following U-process gives rise to a maximal reduction of entanglement entropy at each step. In the generic case this implies at each step a decomposition of the system to unique unentangled subsystems and the process repeats itself for these subsystems. The process stops when the resulting subsystem cannot be decomposed to a pair of free systems since energy conservation makes the reduction of entanglement kinematically impossible in the case of bound states. The natural assumption is that self loses consciousness when it entangles via bound state entanglement.

There is an important exception to this vision based on ordinary Shannon entropy. There exists an infinite hierarchy of number theoretical entropies making sense for rational or even algebraic entanglement probabilities. In this case the entanglement negentropy can be negative so that NMP favors the generation of negentropic entanglement, which need not be bound state entanglement in standard sense. Negentropic entanglement might serve as a correlate for emotions like love and experience of understanding. The reduction of ordinary entanglement entropy to random final state implies second law at the level of ensemble. For the generation of negentropic entanglement the outcome of the reduction is not random: the prediction is that second law is not a universal truth holding true in all scales. Since number theoretic entropies are natural in the intersection of real and p-adic worlds, this suggests that life resides in this intersection. The existence effectively bound states with no binding energy might have important implications for the understanding the stability of basic bio-polymers and the key aspects of metabolism. A natural assumption is that self experiences expansion of consciousness as it entangles in this manner. Quite generally, an infinite self hierarchy with the entire Universe at the top is predicted.

The identification of life as a number theoretically critical phenomenon is also consistent with the idea that the transformation of intention to action corresponds to a U-process inducing leakage between different sectors. This leakage makes sense in the intersection where same mathematical expression defines both real and p-adic partonic 2-surfaces which are the fundamental objects in TGD framework. What these statements really mean requires a construction of number theoretical variant of quantum theory applying in the intersection of real and p-adic worlds.

Besides number theoretic negentropies there are also other new elements as compared to the earlier formulation of NMP. Zero energy ontology modifies dramatically the formulation of NMP since U-matrix acts between zero energy states and can be regarded as a collection of M-matrices, which generalize the ordinary S-matrix and define what might be called a complex square root of density matrix so that kind of a square root of thermodynamics at single particle level justifying also p-adic mass calculations based on p-adic thermodynamics is in question. The hierarchy of Planck constants is a further new element having important implications for conciousness and biology. Hyper-finite factors of type II1 represent an additional technical complication requiring separate treatment of NMP taking into account finite measurement resolution realized in terms of inclusions of these factors.

NMP has important implications for thermodynamics. In particular, one must give up the standard view about second law and replace it with a formulation taking into accoung the hierarchy of causal diamonds assigned with zero energy ontology and dark matter hierarchy labeled partially by the values of Planck constants, as well as the effects due to negentropic entanglement. In particular, in the case of living matter breaking of second law in standard sense is expected to take place and be crucial for the understanding of evolution. Self hierarchy having the hierarchy of causal diamonds as imbedding space correlate leads naturally to a thermodynamical description of the contents of consciousness and quantum jumps is very much analogous to quantum computation. This leads to a vision about the role of bound state entanglement and negentropic entanglement in the generation of sensory qualia. Negentropic entanglement leads to a vision about cognition. Negentropically entangled state consisting of a superposition of pairs can be interpreted as a conscious abstraction or rule: negentropically entangled Schrödinger cat knows that it is better to keep the bottle closed. A connection with fuzzy qubits and quantum groups with negentropic entanglement is highly suggestive. The implications are highly non-trivial also for quantum computation, which allows three different variants in TGD context. The negentropic variant would correspond to conscious quantum computation like process.

For details see the chapter Negentropy Maximization Principle.

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