Quantum formalism to describe binocular rivalry

arXiv:0709.4516v2 [q-bio.NC] 13 Oct 2009 Quantum formalism to describe binocular rivalry Efstratios Manousakis Department of Physics, Florida State University, Tallahassee, Florida, 32306-4350, USA and Department of Physics, University of Athens, Panepistimioupolis, Zografos, Athens, 157 84, Greece On the basis of the general character and operation of the process of perception, a formalism is sought to mathematically describe the subjective or abstract/mental process of perception. It is shown that the formalism of orthodox quantum theory of measurement, where the observer plays a key role, is a broader mathematical foundation which can be adopted to describe the dynamics of the subjective experience. The mathematical formalism describes the psychophysical dynamics of the subjective or cognitive experience as communicated to us by the subject. Subsequently, the formalism is used to describe simple perception processes and, in particular, to describe the probability distribution of dominance duration obtained from the testimony of subjects experiencing binocular rivalry. Using this theory and parameters based on known values of neuronal oscillation frequencies and firing rates, the calculated probability distribution of dominance duration of rival states in binocular rivalry under various conditions is found to be in good agreement with available experimental data. This theory naturally explains an observed marked increase in dominance duration in binocular rivalry upon periodic interrup- tion of stimulus and yields testable predictions for the distribution of perceptual alteration in time. Keywords: Binocular rivalry, multi-stable perception, temporal perception, psychophysical dy- namics I. INTRODUCTION Several authors (London and Bauer, 1983; Manousakis, 2006; Mavromatos and Nanopoulos, 1998; Penrose, 1989; Schwartz et al., 2005; Stapp, 1980, 2003, 2007) including the founders of quantum mechanics (Jung and Pauli, 2001; Schroedinger, 1967; Von-Neumann, 1955; Wigner, 1983) have discussed the possible relation of consciousness to quantum theory. It has also been argued that the mathematical formu- lation of quantum mechanics is a broader foundation (Manousakis, 2006) which can be adopted to describe the most elementary mental events, i.e., the subjective experience of the process of perception. In the present paper, on the basis of the general character and opera- tion of the process of perception, it is suggested that the formalism of orthodox quantum theory can be adopted to mathematically describe the subjective or mental process of perception. We stress that the mathematical formalism presented here does not aim at describing the brain dynamics of the observer as measured by an observing instrument or by a second external observer observing the brain of the first, but rather its aim is to describe the dynamics of the subjective or mental ex- perience as communicated by the first observer himself. Namely, we seek a formulation to describe the dynamics of the abstract or mental process of the subjective experience or the process of perception, for example, the testimony of observers quantified by the recordings of a time series of events occurring in their experience of binocular rivalry. What is meant by these statements is clarified in the following section by means of a simple example. As described in the following section, an attempt is made to give a precise mathematical description of the character and operational nature of the process of per- ception as experienced by subjects; it is argued and demonstrated in Sec. II by means of examples that the mathematical formalism of standard quantum mechan- ics, as we currently know it, may be sufficient to quanti- tatively describe aspects of our conscious experience and abstract mental processes. The difference between the earlier work on the connection between quantum theory and consciousness and the present work is that, here, we postulate and we present arguments to justify it, that the formalism of quantum theory can be used to describe mathematically the subjective or mental processes, such as the operation of perception in binocular rivalry. The formalism is constructed with the goal to describe em- pirical data which are recordings of the experience of ob- servers to various stimuli, without a need to identify a material system where the function of perception is mani- fested. Namely, the aim is to describe the inner or mental experiences of observers, and, the goal is not to describe an objectively existing physical system. In the present paper, we explore further the quantitative connection of the formalism of quantum theory using the formalism of standard quantum theory (Manousakis, 2006; Stapp, 1980, 2003, 2007; Von-Neumann, 1955) and by apply- ing the formulation to the well-known psycho-physical phenomenon of binocular rivalry (Blake and Logothetis, 2002; Leopold and Logothetis, 1999; Tong et al., 2006). The theory presented here should find applica

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