Sergiy Melnyk

Обсуждается широкий круг проблем взаимоотношения сознания и материи. Особое внимание уделено анализу структуры и свойств сознания в рамках информационной эволюции. А также – анализу роли специфических (невычислительных) свойств сознания в процедуре классических и квантовых измерений. В частности, подробно обсуждается вопрос о «клонировании» сознания (возможности копирования его свойств его на новый материальный носитель). Мы надеемся, что сформулированный нами обобщенный принцип дополнительности откроет новые пути для исследования проблем сознания в рамках фундаментальной физической картины мира.

A wide range of problems of the relationship between consciousness and matter are discussed. Particular attention is paid to the analysis of the structure and properties of consciousness in the framework of information evolution. The role of specific (non-computational) properties of consciousness in the procedure of classical and quantum measurements is analyzed. In particular, the issue of "cloning" of consciousness (the possibility of copying its properties onto a new material carrier) is discussed in detail. We hope that the generalized principle of complementarity formulated by us will open up new ways for studying the problems of consciousness within the framework of the fundamental physical picture of the world.

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 quantummechanical 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.

The paper discusses the possibility of constructing economic models using the methodology of model construction in classical mechanics. At the same time, unlike the "econophysical" approach, the properties of economic models are derived without involvement of any equivalent physical properties, but with account of the types of symmetry existing in the economic system. It has been shown that at this approach practically all known mechanical variables have their "economic twins". The variational principle is formulated on the basis of formal mathematical construction without involving the subjective factor common to the majority of models in economics. The dynamics of interaction of two companies has been studies in details, on the basis of which we can proceed to modeling of more complex and realistic economic systems. Prediction of the possibility of constructing economic theory on the basis of primary principles analogously to physics has been made.

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 present paper discusses the problem of quantum-mechanical properties of a subject’s consciousness. The model of generalized economic measurements is used for the analysis. Two types of such measurements are analyzed – transactions and technologies. Algebraic ratios between the technology-type measurements allow making their analogy with slit experiments in physics. It has been shown that the description of results of such measurements is possible both in classical and in quantum formalism of calculation of probabilities. Thus, the quantum-mechanical formalism of the description of states appears as a result of idealization of the selection mechanism in the proprietor's consciousness.

We propose an axiomatic approach to constructing the dynamics of systems, in which one the main elements 9e8 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.

The algebra of transactions as fundamental measurements is constructed on the basis of the analysis of their properties and represents an expansion of the Boolean algebra. The notion of the generalized economic measurements of the economic “quantity” and “quality” of objects of transactions is introduced. It has been shown that the vector space of economic states constructed on the basis of these measurements is relativistic. The laws of kinematics of economic objects in this space have been analyzed and the stages of constructing the dynamics have been formulated. In particular, the “principle of maximum benefit”, which represents an economic analog of the principle of least action in the classical mechanics, and the principle of relativity as the principle of equality of all possible consumer preferences have been formulated. The notion of economic interval between two economic objects invariant to the selection of the vector of consumer preferences has been introduced. Methods of experimental verification of the principle of relativity in the space of economic states have been proposed.

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 quantummechanical 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.