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arXiv:1110.5283

Fundamental Measurements in Economics and in the Theory of Consciousness

Sergiy Melnyk, Игорь Георгиевич Тулузов

Published Oct 21, 2011• 1 citation
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Abstract

A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. Elementary (indivisible) technology, in which the object's consumer values are variable, in this case can be formalized as a generalized economic measurement. The algebra of such measurements has been constructed. It has been shown that in the general case the quantum-mechanical formalism of the theory of selective measurements is required for description of such conditions. The economic analogs of the elementary slit experiments in physics have been created. The proposed approach can be also used for consciousness modeling.

DOI
10.48550/arxiv.1110.5283

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A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. Elementary (indivisible) technology, in which the object's consumer values are variable, in this case can be formalized as a generalized economic measurement. The algebra of such measurements has been constructed. It has been shown that in the general case the quantum-mechanical formalism of the theory of selective measurements is required for description of such conditions. The economic analogs of the elementary slit experiments in physics have been created. The proposed approach can be also used for consciousness modeling.
A new constructivist approach to modeling in economics and theory of consciousness is proposed. The state of elementary object is defined as a set of its measurable consumer properties. A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement. We were also able to obtain the classical interpretation of the quantum-mechanical law of addition of probabilities by introducing a number of new notions. The principle of "local equity" assumes the transaction completed (regardless of the result) of the states of transaction partners are not changed in connection with the reception of new information on proposed offers or adopted decisions (consent or refusal of the transaction). However it has no relation to the paradoxes of quantum theory connected with non-local interaction of entangled states. In the economic systems the mechanism of entangling has a classical interpretation, while the quantum-mechanical formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness.
A new constructivist approach to modeling in economics and theory of consciousness is proposed.The state of elementary object is defined as a set of its measurable consumer properties.A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement.We were also able to obtain the classical interpretation of the quantum-mechanical law of addition of probabilities by introducing a number of new notions.The principle of "local equity" assumes the transaction completed (regardless of the result) of the states of transaction partners are not changed in connection with the reception of new information on proposed offers or adopted decisions (consent or refusal of the transaction).However it has no relation to the paradoxes of quantum theory connected with non-local interaction of entangled states.In the economic systems the mechanism of entangling has a classical interpretation, while the quantum-mechanical formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness.
The standard approach to modeling of systems involving subjects (economic subjects, in particular) is based both on the information on their structure and the phenomenological assumptions on their properties.The alternative approach used in the physical theory is based on the analysis of group properties of a set of measurements of the observed system.The aim of the present paper was to study the possibilities of its use for modeling in economics.It has been shown that in the general case the quantum mechanical formalism of the theory of selective measurements is required for that.A proprietor's refusal or consent for the offered transaction is considered as a result of elementary economic measurement.The algebra of such measurements has been constructed.The economic analogs of the elementary slit experiments in physics have been created.The proposed approach can be also used for consciousness modeling.
We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements is the consciousness of a subject. The main axiom is the statements that the state of consciousness is completely determined by the results of measurements performed on it. In case of economic systems we propose to consider an offer of transaction as a fundamental measurement. Transactions with delayed choice, discussed in this paper, represent a logical generalization of incomplete transactions and allow for a more rigorous approach to studying the properties of the algebra of economic measurements. Considering the behavior of an object as a sequence of actions and choices allows extending the obtained results to random systems, which include the subject's consciousness as one of its elements. The specifics, on which the description of fundamental measurements is based, allows easily transferring the formalism of Schwinger's theory of selective measurements (and the consequent quantum-mechanical formalism) to the economic and social systems.
A physical model for phenomenological proto-consciousness as an intrinsic, primary property of matter is introduced. A fundamental particle is characterized as a classic-like system in physical space supplemented with an information space that endows the particle with the capacity of storing and processing incoming information which has causal power on the behaviour of the particle. These features transform the postulated initial random particles into information-theoretic Darwinian physical systems controlled by algorithms susceptible of evolution under natural selection. Consciousness is then defined as the elementary microscopic sentient process of subjectively experiencing a representation of the locations of the surrounding systems that is induced on matter by the irreversible erasure of dynamically superfluous stored information when the particle is measured. A physical description of the possible emergence of both quantum behaviour of matter in accordance with the conventional quantum formalism and consciousness in complex biological systems as a quantum coherence phenomenon is explored.
The problem of measurement in economic models and the possibility of their quantum-mechanical description are considered. It is revealed that the apparent paradox of such a description is associated with a priori requirement of conformity of the model to all the alternatives of free choice of the observer. The measurement of the state of a trader on a stock exchange is formally defined as his responses to the proposals of sale at a fixed price. It is shown that an analogue of Bell's inequalities for this measurement model is violated at the most general assumptions related to the strategy of the trader and requires a quantum-mechanical description of the dynamics of his condition. In the framework of the theory of weak continuous quantum measurements, the equation of stock price dynamics and the quantum-mechanical generalization of the F. Black and M. Scholes model for pricing options are obtained. The fundamental distinctions between the obtained model and the classical one are discussed.