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arXiv:0705.1617 · NeuroQuantology

Non-Computability of Consciousness

Daegene Song

Published Sep 20, 2007• 9 citations
arXivHTMLPDF

Abstract

With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes.In this paper, the answer to this question is shown to be no.A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer.Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element.The concept that this is solely a quantum effect and does not work for a classical case is also discussed.

DOI
10.14704/nq.2007.5.4.146

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With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes.In this paper, the answer to this question is shown to be no.A certain phenomenon of consciousness is demonstrated to be fully represented as a computational process using a quantum computer.Based on the computability criterion discussed with Turing machines, the model constructed is shown to necessarily involve a non-computable element.The concept that this is solely a quantum effect and does not work for a classical case is also discussed.
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Information is a part of the physical universe as matter and energy. Today first small quantum computers begin to appear. A quantum computer represents information by qubits. In quantum computation there are two principles (algorithms) that speed up the computation, Fourier Transform and Grover's amplification algorithm. Quantum artificial intelligence is introduced by linear algebra-based quantum machine learning and symbolical quantum artificial intelligence. The initial motivation for relating quantum theory to consciousness was related to free free will in a deterministic world, since the quantum world is nondeterministic. The dualism of mind and matter involves the unresolved problem of how the mind and brain could interact. The relationship of union between the mind and the body of a person is resolved by quantum measurement. Sir Roger Penrose argues that elementary acts of consciousness cannot be described by a Turing machine. Such non-countable elementary acts of conscious ness are only present in the wave function collapse (measurement). Penrose assumes that the wave function collapse is not random, it represents an objective reduction.
Pioneering work into Very Large Scale Integration (VLSI) and the theory of computation reveals a new revolution. Quantum physics is essential to the understanding of deuces with two stable states and to how theoretically, classical Turing computation is physically possible. Furthermore, completely novel quantum‐mechanical computational devices utilizing dimensional confinement can be made; similar mechanisms may well exist in natural biological systems and brains. Shows that this new quantum‐mechanical perspective yields the basis for a model of conscious machinery, with correspondingly well defined processes specifying the nature of perception, cognition and information, for which as yet computer science has no agreed definitions.
Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as a quantum computer. The physical processes represent computations of the quantum computer. Quantum information is the real fundament of the world. The conception of quantum computer unifies physics and mathematics and thus the material and the ideal world. Quantum computer is a non-Turing machine in principle. Any quantum computing can be interpreted as an infinite classical computational process of a Turing machine. Quantum computer introduces the notion of “actually infinite computational process”. The discussed hypothesis is consistent with all quantum mechanics. The conclusions address a form of neo-Pythagoreanism: Unifying the mathematical and physical, quantum computer is situated in an intermediate domain of their mutual transformation.
According to the Church-Turing Thesis (CTT), effective formal behaviours can be simulated by Turing machines; this has naturally led to speculation that physical systems can also be simulated computationally. But is this wider claim true, or do behaviours exist which are strictly hypercomputational? Several idealised computational models are known which suggest the possibility of hypercomputation, some Newtonian, some based on cosmology, some on quantum theory. While these models' physicality is debatable, they nonetheless throw into question the validity of extending CTT to include all physical systems. We consider the physicality of hypercomputational behaviour from first principles, by showing that quantum theory can be reformulated in a way that explains why physical behaviours can be regarded as 'computing something' in the standard computational state-machine sense. While this does not rule out the physicality of hypercomputation, it strongly limits the forms it can take. Our model also has physical consequences; in particular, the continuity of motion and arrow of time become theorems within the basic model.