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1) a set of variables selected by an observer. (Ashby, 1960)

2) Usually three distinctions are made: 1. An observed object. 2. A perception of an observed object. This will be different for different observers. 3. A model or representation of a perceived object. A single observer can construct more than one model or representation of a single object. Some people assume that 1. and 2. are the same. This assumption can lead to difficulties in communication. Usually the term "system" is used to refer to either 1. or 2. "Model" usually refers to 3. Ashby used the terms machine," "system," and "model" in that order for the three distinctions. (Umpleby)

3) a set or arrangement of entities so related or connected so as to form a unity or organic whole. (Iberall)

4) Any definable set of components. (Maturana and Varela, 1979)

Any portion of the material universe which we choose to separate in thought from the rest of the universe for the purpose of considering and discussing the various changes which may occur within it under various conditions is called a system. (J. W. Gibbs, from his biography by Muriel Rukeyser, page 445)
(1) A set of variables selected by an observer (Ashby) together with the constraints across variables he either discovers, hypothesises or prefers. Inasmuch as the variables of a system may represent (see representation) the components of a complex machine, an organism or a social institution and a constraint is the logical complement of a relation, an equivalent definition of system is that (2) it represents a set of components together with the relations connecting them to form a whole unity. Unlikee in general systems theory, in cybernetics, a system is an observer's construct. If it describes, simulates or predicts a portion of his environments it may be regarded as a model of that portion (see reconstructability). The model and the modelled "world" share the same organization but because of their different material realizations they are likely to differ in structure. Cybernetics starts with investigating all possible systems and then inquires why certain systems are not materially realized, or it asks why certain conceivable behaviors are not followed. Systems neither exist independent of an observer nor imply a purpose. (Krippendorff)
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