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TGD INSPIRED THEORY OF CONSCIOUSNESS Basic Ideas and Concepts Matti Pitkänen http://www.helsinki.fi/~matpitka/conscbooks.html matpitka@rock.helsinki.fi Table of contents • Quantum jump as moment of consciousness • Anatomy of quantum jump • The notion of self • Contents of consciousness of self • Negentropy Maximization Principle • NMP and hyperfinite factors of type II1 • General theory of qualia • New view about time and memory: zero energy ontology • Arrows of experienced and geometric time Table of contents: continuation • p-Adic physics as physics of cognition and intention • Does p-adic physics make itself visible in real physics • Time scales of cognition, intentionality, memory • Fermions and Boolean cognition • Infinite primes, cognition, and intention Quantum jump as moment consciousness • Quantum jump as moment of consciousness. Analogy with elementary particle physics. • New view about the relation of geometric time to experienced time. Quantum jump sequence defines experienced time. Why the locus for contents of consciousness shifts towards geometric future quantum jump by quantum jump? • Resolution of the basic paradox of quantum measurement theory. Also other paradoxes (What was the initial state of universe?). • Hierarchy of Planck constants: fractal hierarchy of quantum jumps with increasing geometric duration= geometric time interval about which conscious experience contains information proportional to the value of Planck constant characterizing the level of dark matter hierarchy. p-Adic time scale hierarchy. Quantum jump as moment consciousness Anatomy of quantum jump. • Quantum jump has complex anatomy. Generation of quantum entanglement by unitary process, state function reduction and state preparation. • Standard quantum measurement theory relies on von Neumann algebras known as factors of type I. They are replaced with hyperfinite factors of type II1 in TGD framework. • Quantum measurement has finite resolution. Only partial reduction of entanglement possible. Characterization in terms of Jones inclusion NM of Neumann algebras. N/M corresponds to the degrees of freedom which are measured at level of selves, N those that are not measured and remain entangled. Also conscious experience has finite resolution. • Interior of space-time surface represents non-quantum fluctuating zero modes representing classical degrees of freedom entangled with quantal degrees of freedom at lightlike partonic 3-surfaces (state of measurement appartus entangled with quantal degrees of freedom). Unitary process regenerates also entanglement between these degrees of freedom. Anatomy of quantum jump • Zero energy ontology states that all quantum states have vaninishing conserved quantum numbers and are creatable from vacuum. • Negative energy states located in geometric future relative to positive energy states. S-matrix as unitary matrix representing time like entanglement between positive and energy components of zero energy states. (Tr(Id)=1 for hyper-finite factors of type II1). Also this kind of entanglement is reduced in quantum jump. • Quantum jump leads to a new state with new S-matrix. Unitary process tend to regenerate this entanglement. The notion of self • Original definition: Self avoids generation of bound state entanglement with environment as long as it stays conscious. Self sequence of several quantum jumps which somehow integrate to a unified experience. Moments of consciousness > elementary particles, self > bound state of them. • Self hierarchy. Entire Universe at the top. Infinite hierarchy of Planck constants characterizes the self hierarchy partially. Self hierarchy identical with dark matter hierarchy? • Everything is conscious but consciousness can be lost by entangling with a larger system. • New definition: Reduction of the notion of self to that of quantum jump. Quantum jump contains sequences of quantum jumps at shorter time scales. Self single quantum jump at highest level of hierarchy of quantum jumps defining self. Bound state of particles is also particle. • Human lifecycle single quantum jump at highest level. We are conscious even during sleep: this allows to know that I existed yesterday. The notion of self Contents of consciousness of self • Subselves experienced as separate mental images. Explains why we can remember a temporal sequence of phone numbers. • Subself a mental image which is a statistical average over mental images of subself. Spatial and subjecto-temporal averaging. The entropy assignable to the mental image increases and mental image ages. Could second law of thermodynamics characterize subjective experience rather than reality? • The sequence of lower level quantum jumps creates the experience about flow of time although there is only single quantum jump at highest level. • Contents of consciousness about the region defined by space- time sheet defining self. Subselves correspond to sub-space- time sheets. • Do sensory selves correspond to partonic 2-surfaces: our visual experience represents world as 2-dimensional! The notion of self • Sharing and fusion of mental images. Generalization notion of entanglement inspired by many-sheeted space-time. Two space-time sheets which are disjoint can have subsheets which are connected by join along boundaries bond. Selves can have subselves which are fused together. Contents of consciousness are not completely private. Pool of shared mental images making possible social behavior and language. • Stereo vision as example: right and left visual fields represent mental images which fuse together to stereo vision. Same happens to the consciousness of us at the level of collective consciousness and gives rise to objective multidimensional view about human condition. • “Length scale dependent” notion of resolution of conscious exerience. The entanglement of sub-selves is not seen in the resolution used by selves. Finite resolution of conscious experience can be described in terms of Jones inclusion NM. For subselves representing the mental images the resolution is better. Selves form abstractions by averaging over subsusbselves. Negentropy Maximization Principle • NMP defines the variational principle for the dynamics of consciousness and is analogous to second law. Information gain in quantum jump is maximized. Reduction of entanglement entropy maximal in quantum jump. • Number theoretic entanglement entropy. Replace the argument of logarithm of rational valued probability in Shannon’s entropy with its p-adic norm. Minimization of the resulting entropy with respect to prime p allows to assign prime p to a system. Prescription generalizes to algebraic extensions. Negative entropy associated with cognitive entanglement between different number fields and correlated for experience of understanding? • The resulting entropy is in general negative! Interpretation as information? Information carrying entanglement as correlate for experience of understanding? Cognitive entanglement involving p- adic numbers necessarily of this kind. What about real-real entanglement? Possible application: quantum computers. • Number theoretic vision: physics essentially algebraic number based (plus simple transcendentals like e). Is entanglement always algebraic so that entanglement entropy would be always non- positive? Or is only entanglement between different number fields algebraic? Negentropy Maximization Principle NMP and hyperfinite factors of type II1 • Single ray in state space has vanishing norm in real context for hyperfinite factors of type II1. What does this mean from the point of view of NMP? • Interpretation in terms of measurement resolution. Quantum Clifford algebra M/N creates the space of states in which state function reduction occurs in the usual manner. • The spinor space associated with M/N can be identified as complex quantum plane. It does not make sense to speak about state function reduction in this space. The moduli squared for components of quantum spinor commute and can be diagonalized simultaneously. The corresponding probabilities have universal spectrum given in terms of rationals. A possible interpretation is in terms of fuzzy logic and fuzzy beliefs. Only for M:N=4 it is possible to have non-fuzzy beliefs and non- fuzzy logic. Negentropy Maximization Principle • What about cognitive measurements? Could p-adic probabilities save the ray? Discretization strongly suggested. Analogy: p- adic and real partonic 3-surfaces have discrete set of common points. • p-Adic integers infinitely large in real sense are finite in p-adic sense and have finite real counterparts obtained by canonical identification of p-adics and reals ( xnpn xnp-n). Probability for single ray infinitesimal as real number could have finite norm in p-adic sense and would be mapped to a finite real number. • For cognitive entanglement rational entanglement probabilitiesvery natural as is also negative entanglement entropy. General theory of qualia • Quantum numbers label quantum states. Qualia correspond to increments of quantum numbers in quantum jump. Also increments of (non-quantum fluctuating) zero modes could correspond to qualia: geometric qualia. • Classification of qualia according to the character of quantum number. • Visual colors as example. Visual color could correspond to QCD color! Increments of color quantum numbers correspond to basic color qualia. Primary colors. Complementary colors. • Quantum model for sensory receptor. Amplification of quantum jump needed. Bose-Einstein condensates at plates of “capacitor”. Discharge gives rise to macroscopic quantum number increment at plates. Does this explain why living matter is full of electrets? Cell membrane basic example? New view about time and memory • The neuroscience view about long term memories not convincing. Four- dimensional archive with same data stored again and again. • New view about time. Experienced time and geometric time two different things as is indeed obvious (irreversibility/reversiliby, subjective future does not exist). Time mirror mechanism allows memory recall as communications with the geometric past. Memories stored in the brain of geometric past. No need to make the the brain now an archive. • Contents of consciousness from 4-dimensional space-time sheet defining highest level in the personal self hierarchy of self. Paradigm of four- dimensional brain. Space-time as four-dimensional organism. • New view about what happens in biological death. The 4-D brain of geometric past continues conscious existence without sensory input. What happens to self: does it find new biological body in geometric future? New view about time and memory • Long term memories by two mechanisms. Episodal memories by sharing mental images of geometric past by time like entanglement: fits nicely with view about S-matrix. • Declarative memories by communication with geometric past. Negative energy signals from magnetic body time reflected from the brain of geometric past as positive energy signals. Possibly amplified if analog of population inverted laser in question. • Libet's findings about neuronal activity preceding experience of volition. Negative energy signals backwards in geometric time initiating neural activity. This should occur in several time scales. Editing of geometric past in time scales of human life possible?! Arrows of geometric and experienced time • Why we can remember geometric past but the information about geometric future is only plans/hopes/expectations… ? • Why geometric past relatively stable and geometric future highly unstable in the sense that our intentional action can affect it? • Arrow of subjective time emerges naturally. How to understand arrow of geometric time in the sense that the space-time sheet representing contents of consciousness seems to drift to geometric future? • Could the geometric future contain a lot of bosonic p-adic space-time sheets representing intentions transformed to negative energy signals propagating into geometric past and generating neural activities there? Geometric past would not contain much p-adic space-time sheets: intentions already realized. • Experienced flow of geometric time as p-adic-to-real phase transition front propagating towards geometric future? Structure of the world of classical worlds as union of those associated with future and past lightcones would explain the arrow of geometric time. Arrows of geometric and experienced time • This does not explain the selections associated with intentional acts. There must be something else involved. • Could geometric future represent a quantum critical phase containing coexisting phases with different values of Planck constants. Could quantum jump would induce phase transition leading to one of these phases? Geometric past would not be quantum critical and relatively stable in time scale characterizing self. • Quantum ethics: choice between phases would mean good deed if it leads to a phase with a larger Planck constant. Evolution would basically mean growth of Planck constant and thus level of consciousness. • At the level of cell the choice of small Planck constant phase (loss of super-conductivity) could lead to cell death. Is this a general mechanism of ageing or does the finite geometric time span of space- time sheets associated with the self of biological body explain finite life span? p-Adic physics , cognition, and intention Basic ideas • p-Adic space-time sheets correlates for cognition and intention. • p-Adic-to-real phase transition for space-time sheet transforms intention to action. Zero energy ontology: everything creatable from vacuum by intentional action. • Most points of p-adic space-time sheets are at infinity if regarded as real points! Our cognitive bodies have size of cosmos! • Rational/algebraic points of H correspond to points common to real and p- adic space-time sheets. If the number of these points large, real space- time sheet reflects via long range correlations the p-adic topology and it makes sense to speak about effective p-adic topology. • Cognitive representations at space-time level always discrete. Explanation for why practical mathematics always discrete. Intention has only discrete grasp on reality. p-Adic physics as physics of cognition and intention Does p-adic physics make itself visible in real physics? • If real partonic space-time sheet is created in intentional action, it obeys effective p-adic topology in some length scale since the number of common points is large. Partonic 3-surfaces possess p-adic topology corresponding to single p-adic prime. • Interior of space-time sheet corresponds to multi-p p-adic topology since partonic 2-surfaces correspond to different p-adic primes. • Short distance physics in p-adic sense determined by p-adic continuity and smoothness and dictates real physics in long length scales and vice versa. Intentionality should manifest itself via p-adic fractality and long range temporal correlations. Short term chaos but predictability in long time scales. • Characteristic p-adic time scales coming in powers of 2 if p-adic length scale hypothesis accepted. For instance, the universal biological time scale .1 seconds corresponds to secondary p-adic time scale associated with Mersenne prime M127 characterizing electron. p-Adic physics as physics of cognition and intention Time scales of cognition, intentionality, memory • Dark matter hierarchy/hierarchy of Planck constants makes possible intentional action in all length and time scales. Preferred time scales of memory and planned action are predicted. • Preferred Planck constants for which which n characterizes n- polygon constructible using compass and ruler number theoretically suggestive since the quantum phase exp(i/n) is expressible using iterated square rooting to rational number and thus very simple : n= 2k s Fs , Fs = 22s +1 , s=0,1,2,3,4, others? Given Fs at most once. Known Fermat primes 3,5,17, 257, 216+1. • n=2k11 , k=0,1,2.. seems to favored in living matter. 211 fundamental constant in TGD. • Also n-multiples of p-adic length and time scales appear and should define important time scales of cognition, intention, and memory. Fermions and Boolean cognition • Fock states in 1-1 correspondence with Boolean statements. Fermion number 0/1 represents bit. Could fermions represent Boolean cognition? • Quantum variant of Boolean algebra. Problem: quantum superpositions of states with different fermion numbers are not consistent with fermion number conservation. • Zero energy ontology comes in rescue. All physical states have vanishing net conserved charges. Positive energy fermion state and its negative energy conjugate as pairs and quantum superposition of Boolean statements possible. Statement and its conjugate appear always pairwise. Somewhat like DNA strand and its conjugate. Infinite primes, cognition, intention Construction of infinite primes • Call the product of all finite primes X. X+1 is not divisible by any finite prime and is infinite prime. Same true for X-1. • Form the number P = n X/s + ms, n and s are coprime, m and n are coprime, and s is square free (contains given prime only once) is also infinite prime. These are simple infinite primes. Much more general infinite primes can be constructed. • Infinite hierarchy of infinite primes. Form the product X of infinite primes at given level and repeat the construction. • Simple infinite primes are in 1-1 correspondence with the states of super- symmetric arithmetic quantum field theory. n and m represent boson states, s represents fermion state. X Dirac sea, division of X by s formation of holes in Dirac sea. Construction of infinite primes repeated second quantization of arithmetic quantum field theory. Do non-simple infinite primes correspond to bound states of this field theory? Infinite primes, cognition, and intention Interpretation of infinite primes • Infinite primes at first level of hierarchy have decomposition to fermionic and bosonic finite primes. Could these primes label fermionic and bosonic partons (3-D lightlike partonic space-times sheets) associated with given space-time sheet? • Infinite prime as decomposition P = A +a into infinite and finite part. Could the primes in the infinite part A characterize multi-p-p-adic effective topology of the real 4-D space-time sheet forced by different topologies of lightlike partonic 3-surfaces with different primes ? • Could the primes in finite part a label the p-adic partons? • Do bosonic primes correspond to bosonic partons which are real (action) or p-adic (intention)? • Fermionic primes correspond always to both real and p-adic space-time sheet. Does p-adic space-time sheet characterized by same algebraic equations represent the real space-time sheet cognitively? Hole- fermion dichotomy corresponds to system-cognitive representation dichotomy. Infinite primes, cognition, and intention • This would define space-time correlates for fermion states identified as correlates of Boolean cognition. Bosons>intentionality, fermions>cognition. • Quantum superposition of Boolean statements requires that every fermion state is accompanied by its antifermion conjugate. Could p- adic fermion have fermion number opposite to that of real fermion so that real-p-adic fermion pair could be created from vacuum. • Could one assign genuine conserved quantum numbers to p-adic space-time sheets? Could one say that the Noether charges defined by C-S action are opposite for the p-adic counterpart of the real space-time sheet? p-Adic conserved charges defined as integrals do not make sense but if p-adic space-time sheet obeys same algebraic equation as real one, p-adic conserved charges can be identified as real ones if they belong to the algebraic extension of p-adics used. • Are sums of p-adic and real conserved charges conserved: do real and p-adic fermionic space-time sheets have opposite energies?

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