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TGD Inspired Theory of Consciousness
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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.
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.
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.
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".
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.For details see the chapter Negentropy Maximization Principle.