Abstract An attempt to mathematically formalize the problem of intelligence causes difficulties, if only because there is no single definition for intelligence adopted by all psychologists. In this work, this problem is addressed in the following way: through highlighting the essential features of the informal definitions of human intelligence that have been given by expert psychologists it is conducive to put forward an abstract mathematical description of intelligence. Analogies between the problem of intelligence and the problem of quantum mechanical measurements are found, and then the solution to a model problem on the influence of observations on a process of quantum tunneling of particles through a potential barrier is given. Within the framework of the quantum mechanical approach with a non-Hermitian Hamiltonian, a system of differential equations, which formally reflect the concept of intelligence, is formulated, and its analytical solution is presented. On the basis of the obtained solution of the model problem, this paper discusses the question of what phenomena and processes can accompany a process of the realization of intelligence.
Abstract An attempt to mathematically formalize the problem of intelligence causes difficulties, if only because there is no single definition for intelligence adopted by all psychologists. In this work, this problem is addressed in the following way: through highlighting the essential features of the informal definitions of human intelligence that have been given by expert psychologists it is conducive to put forward an abstract mathematical description of intelligence. Analogies between the problem of intelligence and the problem of quantum mechanical measurements are found, and then the solution to a model problem on the influence of observations on a process of quantum tunneling of particles through a potential barrier is given. Within the framework of the quantum mechanical approach with a non-Hermitian Hamiltonian, a system of differential equations, which formally reflect the concept of intelligence, is formulated, and its analytical solution is presented. On the basis of the obtained solution of the model problem, this paper discusses the question of what phenomena and processes can accompany a process of the realization of intelligence.
The challenge of this work is to connect quantum mechanics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e. in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self- supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of an information force that represents a bridge to intelligent particle. It has been suggested that quantum mechanics should be complemented by the intelligent particle as an independent entity, and that will be the necessary step to physics of Life. At this stage, the intelligent particle is introduced as an abstract mathematical concept that is satisfied only mathematical rules and assumptions, and its physical representation is still an open problem.
The challenge of this work is to connect physics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e. in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self- supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of the information force that represents a bridge to intelligent particle. As a follow-up of the proposed concept, the following question is addressed: can artificial intelligence (AI) system composed only of physical components compete with a human? The answer is proven to be negative if the AI system is based only on simulations, and positive if digital devices are included. It has been demonstrated that there exists such a quantum neural net that performs simulations combined with digital punctuations. The universality of this quantum-classical hybrid is in capability to violate the second law of thermodynamics by moving from disorder to order without external resources. This advanced capability is illustrated by examples. In conclusion, a mathematical machinery of the perception that is the fundamental part of a cognition process as well as intelligence is introduced and discussed. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the purpose of Life.
This article examines some experimental conditions that invite and possibly require recourse to quantum-mechanical-like mathematical models (QMLMs), models based on the key mathematical features of quantum mechanics, in scientific fields outside physics, such as biology, cognitive psychology, or economics. In particular, I consider whether the following two correlative features of quantum phenomena that were decisive for establishing the mathematical formalism of quantum mechanics play similarly important roles in QMLMs elsewhere. The first is the individuality and discreteness of quantum phenomena, and the second is the irreducibly probabilistic nature of our predictions concerning them, coupled to the particular character of the probabilities involved, as different from the character of probabilities found in classical physics. I also argue that these features could be interpreted in terms of a particular form of epistemology that suspends and even precludes a causal and, in the first place, realist description of quantum objects and processes. This epistemology limits the descriptive capacity of quantum theory to the description, classical in nature, of the observed quantum phenomena manifested in measuring instruments. Quantum mechanics itself only provides descriptions, probabilistic in nature, concerning numerical data pertaining to such phenomena, without offering a physical description of quantum objects and processes. While QMLMs share their use of the quantum-mechanical or analogous mathematical formalism, they may differ by the roles, if any, the two features in question play in them and by different ways of interpreting the phenomena they considered and this formalism itself. This article will address those differences as well.
The article provides a critique of atomistic ontology and reductionism in explaining the nature of life and consciousness. As an alternative direction based on organic ontology, fundamental psychophysical principles and quantum-information approach, the concept of quantum monadology is proposed, the metaphysical foundations of which are given in the works of G. Leibniz and N. Lossky. A model of «elementary intelligence» in complementary unity with the elementary body is proposed. The premise of this representation is the mathematical formalism of quantum mechanics. The wave function is interpreted as a prototype of consciousness, and the observed physical quantities are interpreted as a prototype of the material body of the monad given in its phenomenal experience. The probabilistic nature of the behavior of quantum particles is explained by the objective existence of chance and the activity of quantum objects, which, perhaps, should be considered as a potential basis for the formation of the psyche. To characterize the internal state of the monad, the concept of a color charge is introduced, which has the meaning of a binary information code, and the principle of dynamic complementarity is formulated. A model of the elementary «life cycle» of a quantum monad is constructed. Elementary intelligence is understood as the ability for intellectual activity, including the processing of information significant for life, as a result of which the existence of quantum monads is maintained and reproduced. A substantial justification of quantum Darwinism is given, and a hypothesis about the genesis and co-evolutionary development of the «elementary psyche» and physical body of monads in the process of global evolution is put forward. A conclusion is made about the possibility of constructing a model of quantum behavior and the synergetic interaction of monads that form more complex systems, as well as about the prospect of developing a quantum ontology of matter and consciousness. The construction of a model of «elementary natural intelligence» will contribute to the identification of fundamental ontological limitations in the development of strong artificial intelligence.
The present article explores the modeling of human cognitive activity in response to external informational stimuli of varying modalities. The mathematical foundation of the proposed model is based on elements of the mathematical apparatus of quantum mechanics, the theory of information images/representations, as well as a new approach to the description of information objects using. The theory of informational images/representations is employed to describe the mechanisms of information transmission, processing, and generation. A brief overview of this theoretical framework is provided in the article. The cognitive activity under investigation is modeled using a one-dimensional potential well with walls of differing heights. Within this interpretation, the internal barrier symbolizes the boundary between the conscious and subconscious levels of the mind. The proposed theoretical approach was then utilized to parametrize the studied cognitive systems. A mathematical model was subsequently formulated, using the principles of self-oscillatory quantum mechanics, leading to the formulation of an equation that describes the state function of an informational image during cognitive processes. In order to investigate various scenarios of informational influence, computer-based simulations were conducted. Consequently, characteristic patterns were identified, including the oscillatory nature of changes in the state function of informational images and the emergence of distinct threshold effects. These findings are in agreement with existing experimental data.
This paper examines the structural discrepancy between the mathematical formulations of physics—particularly those of quantum mechanics—and the conditions under which human beings recognize existence and establish observation. The fundamental equations of quantum mechanics do not require sensory distinctions such as whether a particle is “moving” or “at rest”; the same formalism allows both dynamic and static states. In contrast, human perceptual structures presuppose continuous change or motion for the recognition of existence and the establishment of observation. A completely unchanging entity does not readily emerge within the sensory world. Focusing on this discrepancy, this paper argues that mathematical equations describe the consistency of states rather than the conditions of existential recognition or generative processes. Furthermore, concepts such as “will” and “choice” do not belong to the third-person domain described by mathematical formalism, but instead function as first-person preconditions. Accordingly, this paper does not claim that there exist phenomena that cannot be expressed mathematically; rather, it clarifies that there are layers of reality that mathematics does not, by design, attempt to describe. This distinction does not indicate a limitation of mathematics, but instead reveals a layered structure of world-description, offering a new perspective for connecting physics, cognitive science, and philosophy.