Valentin F Turchin - Collected Quotes

"Cybernetics is based above all on the concept of the system, a certain material object which consists of other objects which are called subsystems of the given system. The subsystem of a certain system may, in its turn, be viewed as a system consisting of other subsystems. To be precise, therefore, the meaning of the concept we have introduced does not lie in the term ‘system’ by itself, that is, not in ascribing the property of ‘being a system’ to a certain object (this is quite meaningless, for any object may be considered a system), but rather in the connection between the terms ‘system’ and ‘subsystem’, which reflects definite relationship among objects." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"Cybernetics studies the organization of systems in space and time, that is, it studies how subsystems are connected into a system and how change in the state of some subsystems influences the state of other subsystems." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"In modern mathematics set theory plays the role of the frame, the skeleton which joins all its parts into a single whole but cannot be seen from the outside and does not come in direct contact with the external world. This situation can be truly understood and the formal and contentual aspects of mathematics combined only from the 'linguistic' point of view regarding mathematics." (Valentin F Turchin, "The Phenomenon of Science: a cybernetic approach to human evolution", 1977)

"In the process of the evolution of life, as far as we know, the total mass of living matter has always been and is now increasing and growing more complex in its organization. To increase the complexity of the organization of biological forms, nature operates by trial and error. Existing forms are reproduced in many copies, but these are not identical to the original. Instead they differ from it by the presence of small random variations."  (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"Principles so general that they are applicable both to the evolution of science and to biological evolution require equally general concepts for their expression. Such concepts are offered by cybernetics, the science of relationships, control, and organization in all types of objects." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"The branch of modern science called cybernetics gives us concepts that describe the evolutionary process at both the level of intracellular structures and the level of social phenomena. The fundamental unity of the evolutionary process at all levels of organization is transformed from a philosophical view to a scientifically substantiated fact." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"[…] the cybernetic approach brings us to another point of view according to which the analogy between society and the organism has a profound meaning, testifying to the existence of extraordinarily general laws of evolution that exist at all levels of the organization of matter and pointing out to us the direction of society's development." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"To master a concept means to be able to recognize it, that is, to be able to determine whether or not any given situation belongs to the set that characterizes this concept." (Valentin F Turchin, "The Phenomenon of Science: A cybernetic approach to human evolution", 1977)

"To use set theory in the way it is used by modern mathematics, however, it is not at all necessary to force one's imagination and try to picture actual infinity. The 'sets' which are used in mathematics are simply symbols, linguistic objects used to construct models of reality. The postulated attributes of these objects correspond partially to intuitive concepts of aggregateness and potential infinity; therefore intuition helps to some extent in the development of set theory, but sometimes it also deceives. Each new mathematical (linguistic) object is defined as a 'set' constructed in some particular way. This definition has no significance for relating the object to the external world, that is for interpreting it: it is needed only to coordinate it with the frame of mathematics, to mesh the internal wheels of mathematical models. So the language of set theory is in fact a metalanguage in relation to the language of contentual mathematics, and in this respect it is similar to the language of logic. If logic is the theory of proving mathematical statements, then set theory is the theory of constructing mathematical linguistic objects." (Valentin F Turchin, "The Phenomenon of Science: a cybernetic approach to human evolution", 1977)