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       Basic Ideas and Concepts

                Matti Pitkänen

              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 NM 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

•   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
                                                     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

•   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

•   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 NM. 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
                                                  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

• 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
             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

•   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
                                                     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

• 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

• 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

•   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,

• 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
                                        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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