Samstag, 29. September 2007

On the degree of freedom (statistical concept)

Hypothesis1: For every (complex) closed system, the degree of freedom equals 0.

Hypothesis2: Observing any system from within itself (i.e., open system with one subject as the intervening variable), the degree of freedom equals 1.

This in effect means that the degree of freedom depends on the (subjective) epistemological interpretation of reality. It can range from 0 (absolute determinism - the entire complex system can be defined by one finite set of equasions (what kind of matrix?)) to infinity (when interpreting all others as subjects (undeterministic), or objects/god as subjects/actors with 'free will'). Thus, the degree of freedom in the real world depends on the (subjectively interpreted) number of variables that can change independently of each other.

Hypothesis3 (general theory of evolution): The optimal behavior of an actor within a closed system considers the degree of freedom to lie somewhere between 0 and infinity. Either of the extremes are unsustainable from an evolutionary (long-term) point of view.

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