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Second-order cybernetics, also known as the cybernetics of cybernetics, is the recursive application of cybernetics to itself and the reflexive practice of cybernetics according to such a critique. It is cybernetics where "the role of the observer is appreciated and acknowledged rather than disguised, as had become traditional in western ...
Second-order cybernetics: Also known as the cybernetics of cybernetics, second-order cybernetics is the recursive application of cybernetics to itself and the practice of cybernetics according to such a critique. Schismogenesis; Self-organisation; Social systems theory; Syntegrity; Variety and Requisite Variety; Viable system model
Cybernetics is a transdisciplinary approach for exploring regulatory systems with feedback, their structures, constraints, and possibilities. Cybernetics is relevant to the study of systems, such as mechanical, physical, biological, cognitive, and social .
Cybernetics, according to Wiener's definition, is the science of "control and communication in the animal and the machine". Heinz von Foerster went on to distinguish a first order cybernetics, "the study of observed systems", and a second order cybernetics, "the study of observing systems".
For a relational signature X, FO[PFP](X) is the set of formulas formed from X using first-order connectives and predicates, second-order variables as well as a partial fixed point operator used to form formulas of the form [, ], where is a second-order variable, a tuple of first-order variables, a tuple of terms and the lengths of and coincide with the arity of .
In contrast to the frequency domain analysis of the classical control theory, modern control theory utilizes the time-domain state space representation, [citation needed] a mathematical model of a physical system as a set of input, output and state variables related by first-order differential equations. To abstract from the number of inputs ...
As a result, second-order logic has greater expressive power than first-order logic. For example, there is no way in first-order logic to identify the set of all cubes and tetrahedrons. But the existence of this set can be asserted in second-order logic as: ∃P ∀x (Px ↔ (Cube(x) ∨ Tet(x))). We can then assert properties of this set.
It is the first public usage of the term "cybernetics" to refer to self-regulating mechanisms. The book laid the theoretical foundation for servomechanisms (whether electrical, mechanical or hydraulic), automatic navigation , analog computing , artificial intelligence , neuroscience , and reliable communications .