A Mathematical Model of Consciousness

M. Esfahanian

The objective of this paper is to show that non-constructive mathematics is incapable as a framework for research on consciousness. Indeed, we shall discuss how non-constructive mathematics is inconsistent with the physics of consciousness which deals with quantumness. This inconsistency implies the incapability of non-constructive mathematics to represent the free will of a conscious agent. Furthermore, we shall suggest Constructive mathematics (and topos theory which is one of its models) as an alternative framework to study consciousness. The pivotal role of the excluded middle law in our discussion will be addressed in detail.

JOHN M. COWLEY

Michael B. Mensky

We discuss mathematical models describing the action of consciousness and super-consciousness as these phenomena are defined in the Extended Everett's Concept (EEC) proposed by the author. According to the Everett's interpretation of quantum mechanics, the state of the quantum world is a superposition of various classical pictures of the world (classical realities, or alternatives). Humans, due to their ability called consciousness, perceive the alternatives separately: all alternatives are perceived, but subjectively perceiving one of them is accompanied by the sensation of the remaining alternatives as if being invisible. This causes the impression that only one of the alternatives really exists, but this is an illusion of consciousness. When consciousness (separating the alternatives) is turned off (in sleep, trance or meditation) or weakened, another ability arises called super-consciousness. Due to super-consciousness, the human gets access to the set of all alternative realities taken as a whole, selects those alternatives that are favorable, and ensures that just these selected alternatives are experienced after consciousness is turned on again. Thus, EEC explains, on the basis of quantum mechanics, those features of consciousness which are usually treated as mystical. It is shown in the paper how these features of consciousness and super-consciousness can be presented by simple mathematical models.

Henry Pierce Stapp

Henry Pierce Stapp

Xiaoyang Yu

Background/introduction: This study is to discover the nature of consciousness and/or universe. Methods: Comparing the nature to a Game of Life system. Results: Found that the universe and a Game of Life system has the similar mathematical nature. Conclusions: Humans are limited in what they know by the technical limitation of their cortical language network. A reality is a situation model. The universe is a self-driven objective state machine which evolves by itself automatically. Heisenberg’s uncertainty principle can be explained under this situation. If we are happy to accept randomness, it’s obviously possible that all other worlds in the many-worlds interpretation don’t exist objectively. Consciousness is actually the use of a mathematical model by a Turing machine (TM). A TM’s consciousness or decisions shouldn’t be able to alter/impact/change the fated world line of any elementary particle within this world. Except Schrodinger equation (or its counterpart) which is the only actual causality of the objective-reality, any other causality is only a (subjective) Granger causality.