International Encyclopedia of Systems and Cybernetics

"The application of a function to its own value to generate a series of similar values" (JOHANSEN BERTOGLIO – 1985).

Recursivity is a constructive process, not merely a structural embedment feature, as would be for example a set of wood carved Russian dolls.

The mathematical concept has been transferred into the autopoiesis theory and experimentally explored by M. EIGEN et al (1975, 1979 and 1992).

A. ZELEZNIKAR comments on recursivity in the following way: "Processes in an autopoietic system are organized circularly, as they depend recursively on each other; they form a recursive closure. Production processes are synthetizing, transforming or destroying various components which appear in an autopoietic system. For instance, destruction of components produces substrate on which processes of production can act. A unity assembles its components" (1988, p.208).

According to F. BAILLY, F. GAILL and R. MUSSERI: "Recursivity corresponds to a principle of information economy by the use of one and only one reiterated formal law for each stage of development. Such a simplicity is perfectly compatible with a very rich combinatory and morphological power and its intrinsic uniqueness harmonizes well with the representation of an integrated and determined individuality" (1991, p.58).

Recursivity is also a crosslevel process, in which case it may be self-similar in a fractal sense. Reproduction of the elements (or subsystems and their characteristic interrelations is a global process, which operates, for example:

- in a living being, by the multiple action of its genetic code;

- in a society, by way of a set of values, norms and knowledge, transmitted through processes of education and instruction.

Recursivity makes the system's behavior more or less predictable, because it implies a limited (while sometimes gigantic) repertoire of possible states, given in sequences acceptable for the system.

Moreover, from level to level, some measure of self-similarity can be observed. Organizational closure is a crosslevel isomorphy.

In reference to human systems, J. JOHANNESSEN makes an interesting comment: "At every level of recursivity, there will be two conflicting tendencies:

1. The tendency to function as part of the larger system

2. The tendency to maintain individual autonomy" (1991, p.44-5).

Thus, recursivity seems to be a result of a peculiar class of individual response to interactions (Those which are – or seem -useful to the components) and of a constraint favoring systemic cyclical or catalytic self-reproductive processes, through a kind of reciprocal conditioning. This could well emerge as a basic law of sociogenesis.

As observed by J.C. LUGAN, "The idea of recursivity breaks off from the cause-effect linear concept… It introduces a self-constitutive, self-producing and self-organizing cycle" (1993, p.92).

A similar opinion is G. BATESON's who considered cybernetics as "dealing with problems of control, recursiveness and information" (1979, p.227)