Academic journal article Cosmos and History: The Journal of Natural and Social Philosophy

Fundamental Mathematics of Consciousness

Academic journal article Cosmos and History: The Journal of Natural and Social Philosophy

Fundamental Mathematics of Consciousness

Article excerpt


The problem of measurement in quantum mechanics (QM) and the role of the observer have been part of quantum theory from the very beginning of its founding but have still not been resolved and remain the central reason for having so many different interpretations of quantum theory, how to take into account measurement and the so-called "collapse of the wave function". The standard von Neumann (1955) interpretation of orthodox quantum theory, is that the unitary time evolution of the quantum state is interrupted upon measurement and a particular value emerges, given by theoretical quantum probability. What specific value will emerge though, quantum theory cannot predict. Observational choice in the laboratory determines the context of what is to be observed, and we may even presume (as Richard Feynman and John A. Wheeler would hold) that without observation, quantum systems don't even have any properties. As Wheeler (1981) stated, "no phenomenon is a phenomenon until it is an observed phenomenon". As such, the observer's choices play a fundamental role in the "external" reality that one observes. The observer is an integral part of the process of what is to be observed. Quantum theory opened the door to consciousness but did not provide a solution (Kafatos and Nadeau, 2000; Kafatos, Tanzi, and Chopra, 2011).

Building upon the quantum framework, we realize today that quantum theory has many profound implications for understanding the nature of consciousness. Consciousness continues to challenge all of science even though science has made tremendous strides, e.g. in brain science. Nevertheless, not much progress has been achieved in understanding or even accounting for the most elementary subjective experiences. In fact, many neuroscientists even hold the view that the brain has nothing to do with quantum mechanics, even though they would tacitly agree that quantum mechanics is the foundation of all (physical) reality, including the brain! Today, scientists in several polls when they are asked what are the top two most important and unsolved topics facing science, they respond, the nature of the universe, and the nature of conscious experience. Upon reflection, these two profound issues might in fact be closely related to each other.

As such, what used to be in the domain of philosophy and metaphysics, the origin of the mind and in more general terms examining the nature of consciousness and how consciousness arises, can now be approached by science.

However, the issue of consciousness still presents a clear embarrassment to modern science. Despite the great successes of theoretical physics, cosmology and quantum field theory, the advances in molecular biology, brain science, neuroscience and associated phenomena such as memory, anesthesia and quantum brain processes (cf. Pribram, 1966, 1991; Libet et al., 1983; Kafatos and Nadeau, 1991/2000; Hameroff and Penrose, 1995; Roy and Kafatos, 1999; Roy and Kafatos, 2004; Bernroider and Roy, 2005) to just mention a few of the most successful modern scientific fields, we still don't have a comprehensive theory of consciousness that accounts for conscious experience. We even don't seem to agree on a common framework of consciousness-related terms. Yet, any theoretical advance will have to involve an understanding and development of a suitable set of mathematical languages (Kato and Struppa 1999; Kato 2001; Struppa et al. 2002; Kafatos, 2014).

What is lacking is a true dialogue between science and philosophy and the merging of the two. Although science is always based on ontological assumptions (i.e. its foundations are philosophical) most scientists are reluctant to consider the metaphysical assumptions of what they do professionally (Kafatos and Nadeau, 1991/2000). Yet, the role of consciousness has been a central part of the philosophical discourse not just in the monistic schools of the East, particularly Advaita Vedanta, Shaivism and Buddhism (SwamlPrabhavananda and Isherwood, 1975; Chatterji, 1986; Kafatos and Kafatou, 1991; Dyczkowski, 1992, 1994; Pandit, 1997; Swami Shantananda, 2003; Swami Vimuktananda, 2005; Singh, 2006; SenSharma, 2007; Swami Laksmanjoo, 2012), as well in the great western philosophical systems of Spinoza, Kant, Hegel, and Whitehead and others; and in the ancient philosophies of Heraclitus, Plato, the Neo-Platonists and in the philosophy of the father of philosophy, Socrates himself. …

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