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a concept in differential geometry associated with the concept of parallel displacement. A connection is a particular type of relation—a comparison relation—between geometric objects associated with distinct points of a given space. A connection is characterized by the geometric properties of transformations of tangent spaces from point to point. For example, what is known as an affine connection is defined by an affine mapping of tangent spaces; here, the geometric objects are compared in terms of their affine properties. By generalizing the concept of an affine connection, we arrive at the concept of a space with a connection with respect to any Lie group (seeTOPOLOGICAL GROUP).
REFERENCESRashevskii, P. K. Rimanova geometriia i tenzornyi analiz, 3rd ed. Moscow, 1967.
Norden, A. P. Prostranstva affinnoi sviaznosti. Moscow-Leningrad, 1950.
the interdependence in the existence of phenomena separated in space and/or time. The concept of connection is one of the most important scientific concepts: human cognition begins with the discovery of persistent, necessary connections, and science is based on the analysis of the connection between cause and effect—the universal interconnection of the phenomena of reality, the existence of which makes possible the laws of science.
In the history of cognition the principle of a universal interconnection among objects and phenomena has been one of the basic principles of dialectics. Until the 20th century, however, the main subject of discussion was not the concept and logical structure of connection itself but the principle of interconnectedness. To some extent, this was because science used a relatively narrow selection of types of connections. The focus was on the division of connections into internal and external, necessary and fortuitous, and essential and inessential.
An important step in the development of the idea of connection is associated with the 19th century. On the basis of the critique of mechanism, which had reduced all connections to mechanical ones, the characteristics of the connections inherent in various forms of the movement of matter were elucidated. The factual basis for this advance was provided by the achievements in chemistry and biology, which proved the profoundly unique character of chemical and biological connections and showed that they are not reducible to the connections of mechanical movement. On a philosophical and methodological level, the problem of connection was formulated in German classical philosophy and was subjected to a detailed analysis from the standpoint of the materialist dialectic by F. Engels and V. I. Lenin. Since then, the principle of the universal interconnection of objects and phenomena has been affirmed as one of the leading principles in the methodology of scientific knowledge.
The development of science in the 20th century has been accompanied by the constant, significant expansion of the typology of connections under study. As a result, the problem of connection is subjected to concrete scientific analysis, as well as philosophical analysis. The analysis of new types of connection has become an extremely important factor in the development of new methodological trends in science. The discovery of information links and control links, both direct-link and feedback types, has led to the emergence of cybernetics. The methodology of structuralism originated as a result of the recognition of the independent role of the structural connections between language and a number of other objects. The systems approach grew out of the necessity of simultaneously taking into account several types of connections.
The diversity of contemporary concepts about connections is reflected in the diversity of approaches to classifying them. From a philosophical and methodological standpoint, the classification of connections in terms of forms of the movement of matter has definitive significance. The differentiation of connections according to the forms of determinism is important. Classical science operated primarily with univocal connections of rigid determinism, but in a number of modern disciplines the study of statistical aggregates depends on connections of probability and correlation.
Connections are also classified according to their strength. When a particular phenomenon is strictly linked with some other phenomenon (body organs, for example), the connection is described as rigid. When the connection between two phenomena in a totality can be established statistically (for example, the connection between individuals in a population), it is described as corpuscular. Connections may be differentiated by the character of the result they yield (the connection of result, when one phenomenon is the direct cause of another, and the connection of transformation), the direction of action (direct-link and feedback), the type of processes defined (function, development, and control connections), or the substratum or content serving as an object (connections maintaining the transfer of matter, energy, or information).
The concept of connection plays an important constructive role in the initial analysis of an object of study, in the methodological justification of a new object of study, and in the process of re-creating this object in an integral theoretical model.
REFERENCESEngels, F. Dialektika prirody. In K. Marx and F. Engels, Sock, 2nd ed., vol.20.
Lenin, V. I. “K voprosu o dialektike.” Poln. sobr. soch., 5th ed., vol. 29.
Zinov’ev, A. A. “K opredeleniiu poniatiia sviazi.” Voprosy filosofii, 1960, no. 8.
Novinskii, I.I. Poniatie sviazi v marksistskoi filosofii. Moscow, 1961.
Shchedrovitskii, G. P. Problemy metodologii sistemnogo issledovaniia. Moscow, 1964.
Blauberg, I. V., and E. G. Iudin. Stanovlenie i sushchnost’ sistemnogo podkhoda. Moscow, 1973.
E. G. IUDIN