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Re-examination of the basic notions of TGD inspired theory of consciousness

Matti Pitkänen

Published Jan 1, 2017• 0 citations
Publisher

Abstract

TGD inspired theory of consciousness is based on certain basic assumptions such as the identification of state function reduction as a measurement of universal observable identified density matrix characterizing entanglement and Negentropy Maximization Principle (NMP) as fundamental principle. Both the adelic approach and the notion of World of Classical Worlds (WCW) force to challenge these assumptions. Adelic approach strongly suggests the reduction of NMP to number theoretic physics somewhat like second law reduces to probability theory: there would be no need to postulate NMP as a separate principle and NMP would hold true only in statistical sense so that we would not live in the best possible world as strongest form of NMP would imply. The dimension of the extension rationals characterizing the hierarchy level of physics and defined an observable measured in state function reductions is positive and can only increase in statistical sense. Therefore the maximal value of entanglement negentropy increases as new entangling number theoretic degrees of freedom emerge. h eff / h = n identifiable as factor of Galois group of extension characterizes the number of these degrees of freedom for given space-time surfaces as number of its sheets. State function reduction is hitherto assumed to correspond always to a measurement of density matrix which can be seen as a reaction of subsystem to its environment. This makes perfect sense at space-time level. Higher level measurements occur however at the level of WCW and correspond to a localization to some sector of WCW determining for instance the quantization axes of various quantum numbers. Even the measurement of h eff / h = n would measure the dimension of Galois group and force a localization to an extension with Galois group with this dimension. These measurements cannot correspond to measurements of density matrix since different WCW sectors cannot entangle by WCW locality.

DOI
10.13140/rg.2.2.34758.83521

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TGD inspired theory of consciousness is based on certain basic assumptions such as the identification of state function reduction as a measurement of universal observable identified density matrix characterizing entanglement and Negentropy Maximization Principle (NMP) as fundamental principle. Both the adelic approach and the notion of World of Classical Worlds (WCW) force to challenge these assumptions. Adelic approach strongly suggests the reduction of NMP to number theoretic physics somewhat like second law reduces to probability theory: there would be no need to postulate NMP as a separate principle and NMP would hold true only in statistical sense so that we would not live in the best possible world as strongest form of NMP would imply. The dimension of the extension rationals characterizing the hierarchy level of physics and defined an observable measured in state function reductions is positive and can only increase in statistical sense. Therefore the maximal value of entanglement negentropy increases as new entangling number theoretic degrees of freedom emerge. h eff / h = n identifiable as factor of Galois group of extension characterizes the number of these degrees of freedom for given space-time surfaces as number of its sheets. State function reduction is hitherto assumed to correspond always to a measurement of density matrix which can be seen as a reaction of subsystem to its environment. This makes perfect sense at space-time level. Higher level measurements occur however at the level of WCW and correspond to a localization to some sector of WCW determining for instance the quantization axes of various quantum numbers. Even the measurement of h eff / h = n would measure the dimension of Galois group and force a localization to an extension with Galois group with this dimension. These measurements cannot correspond to measurements of density matrix since different WCW sectors cannot entangle by WCW locality.
TGD inspired theory of consciousness relies on two fundamental identifications. The identification of quantum jump between quantum histories as a moment of consciousness reduces quantum measurement theory to fundamental physics and solves long list of paradoxes of modern physics. The identification of self as a subsystem able to remain unentangled in subsequent quantum jumps provides a quantum theory of observer and one can identify self also as a fundamental statistical ensemble. The generalization of spacetime concept so that it allows both real and p-adic regions, is a crucial prequisite for the notion of self. Quantum jump between quantum histories decomposes into three parts corresponding to the unitary U process of Penrose followed by the TGD counterpart of state function reduction in turn followed by a cascade of self-measurements giving rise to the TGD counterpart of state preparation. The dynamics of self-measurement is determined by the so-called Negentropy Maximization Principle (NMP). Selves form a hierarchy and self experiences its subselves as mental images and is in turn a mental image of a higher-level self. Selves can have common subselves and this makes possible fusion and sharing of mental images. The experience of self is a statistical average over quantum jumps occurred after the last 'wake-up' and the theory of qualia can be formulated in terms of statistical physics. Self experiences the subselves of subself as a statistical average so that self-hierarchy means also an abstraction hierarchy. Self has as its geometric correlate so called mindlike spacetime sheets of finite duration with respect to the geometric time (as opposed to subjective time determined by the sequence of quantum jumps) and one can understand how psychological time and its arrow emerge. The paradigm of four-dimensional brain provides a completely new view about long-term memories and intentionality. Crucial element behind all these developments are both the classical non-determinism of the fundamental variational principle determining the dynamics of the spacetime surfaces making possible nondeterminism of symbolic representations and the inherent nondeterminism of p-adic differential equations making possible cognitive representations. Together with the nondeterminism of quantum jump these nondeterminisms make possible the self-referentiality of consciousness. Combining this general theory with the notion of manysheeted spacetime one ends up to a vision about biosystems as macroscopic quantum systems and to a rather detailed view about quantum brain.
The basic difficulties and challenges of Quantum Mind program are analyzed. The conclusion is that the recent form of quantum theory is not enough to overcome the challenges posed by the philosophical problems of quantum physics and quantum mind theories, and the puzzles of quantum biology and quantum neuroscience. Certain anomalies of recent day biology giving hints about how quantum theory should be generalized serve as an introduction to the summary of the aspects of quantum TGD especially relevant to the notion of Quantum Mind. These include the notions of many- sheeted space-time and field (magnetic) body, zero energy ontology, the identification dark matter as a hierarchy of phases with large value of Planck constant, and p-adic physics proposed to define physical correlates for cognition and intentionality. Especially relevant is the number theoretic generalization of Shannon entropy: this entropy is well defined for rational or even algebraic entanglement probabilities and its minimum as a function of the prime defining p-adic norm appearing in the definition of the entropy is negative. Therefore the notion of negentropic entanglement makes sense in the intersection of real and p-adic worlds and is negative: this motivates the proposal that living matter resides in this intersection. TGD inspired theory of consciousness is introduced as a generalization of quantum measurement theory. The notions of quantum jump and self de_ning the generalization of the notion of observer are introduced and it is argued that the notion of self reduces to that for quantum jump. Negentropy Maximization Principle reproduces standard quantum measurement theory for ordinary entanglement but respects negentropic entanglement so that the outcome of state function reduction is not random for negentropic entanglement. The new view about the relationship of experienced time and geometric time combined with zero energy ontology is claimed to solve the basic philosophical difficulties of quantum measurement theory and consciousness theory. The identi_cation of the quantum correlates of sensory qualia and Boolean cognition, emotions, cognition and intentionality and self-referentiality of consciousness is discussed.
Negentropic entanglement for which number theoretic entropy characterized by p-adic prime is negative so that entanglement carries information, is in key role in TGD inspired theory of consciousness and quantum biology. The key feature of negentropic entanglement is that density matrix is proportional to unit matrix so that assumption that state function reduction corresponds to measurement of density matrix does not imply state function reduction to one-dimensional sub-space. This special kind of degenerate density matrix emerges naturally for hierarchy heff=nh interpreted in terms of a hierarchy of dark matter phases. I have already earlier considered explicit realizations of negentropic entanglement assuming that E is invariant under group of unitary or orthogonal transformations (also subgroups of unitary group can be considered - say symplectic group). One can however consider much more general options and this leads to a connection with topological quantum computation (TQC). Entanglement matrix E equal to 1/n1/2 factor times unitary matrix U (as a special case orthogonal matrix O) defines a density matrix given by ρ=UU†/n= Idn/n, which is group invariant. One has NE respected by state function reduction if NMP is assumed. This would give huge number of negentropically entangled states providing a representation for some unitary group or its subgroup (such as symplectic group). In principle any unitary representation of any Lie group would allow representation in terms of NE. In principle any unitary representation of any Lie group would allow a representation in terms of NE. In as generalized number theory vision, a natural condition is that matrix elements of E belong to algebraic extension of p-adic numbers used so that discreted algebraic subgroups of unitary or orthogonal group are selected. This realizes evolutionary hierarchy as a hierarchy of p-adic number fields and their algebraic extensions, and one can imagine that evolution of cognition proceeds by generation of negentropically entangled systems with increasing algebraic dimensions and increasing dimension reflecting itself as an increase of largest prime power dividing n and defining p-adic prime in question. One fascinating implication is ability of TGD Universe to emulate itself like Turing machine: unitary S-matrix codes for scattering amplitudes and therefore for and negentropically entangled subsystem could represent sub-matrix for S-matrix as rules representing the laws of physics in approximation that world corresponds to n-dimension Hilbert space. Also limit n→ ∞ makes sense, especially so in p-adic context where real infinity can correspond to finite number in sense of p-adic norm. Here also dimensions n given as products of powers of infinite primes can be formally considered.
The basic ideas and implications of TGD inspired theory of consciousness are briefly summarized. The notions of quantum jump and self can be unified in the recent formulation of TGD relying on dark matter hierarchy characterized by increasing values of Planck constant. Negentropy Maximization Principle serves as a basic variational principle for the dynamics of quantum jump. The new view about the relation of geometric and subjective time leads to a new view about memory and intentional action. The quantum measurement theory based on finite measurement resolution and realized in terms of hyper-finite factors of type II1 justifies the notions of sharing of mental images and stereo-consciousness deduced earlier on basis of quantum classical correspondence. Qualia reduce to quantum number increments associated with quantum jump. Self-referentiality of consciousness can be understood from quantum classical correspondence implying a symbolic representation of contents of consciousness at space-time level updated in each quantum jump. p-Adic physics provides space-time correlates for cognition and intentionality.
This article is a summary of TGD inspired theory of consciousness as it is towards the end of 2025 and of its applications to biology. This article gives a summary of TGD inspired theory of consciousness as it is towards the end of 2025. In the TGD framework, it is not possible to discuss consciousness without the TGD view of space-time and quantum. Also the applications to quantum biology and neuroscience have been essential in the development of ideas. The basic inspiration has come from the deep philosophical problems of recent day physics and philosophy of consciousness. The TGD view of consciousness can be seen as a generalization of quantum measurement theory: the observer as an outsider becomes a part of the system. The basic new elements are zero energy ontology (ZEO) as a new quantum ontology forced by the new view of space-time as 4-surfaces analogous to Bohr orbits of particles as 3-D surfaces. The dynamics of the classical space-time obeys holography = holomorphy principle. The failure of a strict classical determinism provides geometric correlates of intention and cognition. ZEO allows us to solve the basic problem of quantum measurement theory, allows free will, and provides a new view of the relation between geometric time and subjective time. Physical existence, identified as the mathematical existence of quantum states: one can speak of quantum Platonia. Conscious existence is identified as quantum jumps between them and can be seen as two different kinds of existence. The classical non-determinism gives rise to quantum jumps giving rise to conscious entities, selves, and the ordinary quantum jumps are predicted to change the arrow of time. This means death and reincarnation of self with an opposite arrow of time. Also the number theoretic visions of TGD is central. A key implication of the number theoretic vision is a hierarchy of Planck constants heff making possible quantum coherence in arbitrarily long scales crucial for the coherence of living matter. p-Adic length scale hierarchy is the second number theoretic prediction. The applications to quantum biology and neuroscience rely on these hierarchies. In this article, the key notions and ideas of TGD, especially those relevant to consciousness and quantum biology, are summarized. The TGD view of consciousness emphasizing recent progress is summarized. The basic ideas and applications to quantum biology are also described.
This article has been inspired by two books. The first book "On intelligence" is by Jeff Hawkins. The second book "Consciousness: the science of subjectivity" is by Antti Revonsuo. Jeff Hawkins has developed a highly interesting and inspiring vision about neo-cortex, one of the few serious attempts to build a unified view about what brain does and how it does it. Since key ideas of Hawkins have quantum analogs in TGD framework, there is high motivation for developing a quantum variant of this vision. The vision of Hawkins is very general in the sense that all parts of neo-cortex would run the same fundamental algorithm, which is essentially checking whether the sensory input can be interpreted in terms of standard mental images stored as memories. This process occurs at several abstraction levels and involve massive feedback. If it succeeds at all these levels the sensory input is fully understood. TGD suggests a generalization of this process. Quantum jump defining moment of consciousness would be the fundamental algorithm realized in all scales defining an abstraction hierarchy. Negentropy Maximization Principle (NMP) would be the variational principle driving this process and in optimal case lead to an experience of understanding at all levels of the scale hierarchy realized in terms of generation of negentropic entanglement. The analogy of NMP with second law suggests strongly thermodynamical analogy and p-adic thermodynamics used in particle mass calculations might be also seen as effective thermodynamics assignable to NMP. In Part II of this two-part article, I will first finish discussion of a more detailed quantum model for association and abstraction processes. I will then compare various theories and philosophies of consciousness with TGD approach following the beautifully organized representation of Revonsuo. Also anomalies of consciousness are briefly discussed. My hope is that this comparison would make explicit that TGD based ontology of consciousness indeed circumvents the difficulties against monistic and dualistic approaches and also survives the basic objections that I have been able to invent hitherto.