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Gnostical theory of individual data. (English) Zbl 0575.94005
This paper proposes a new approach to the observation of individual data involving randomness. The main axioms of the modelling are as follows: i) The observation of the variable \(z_ 0\) results in the observed \(z=z_ 0\exp (\Omega)\), ii) z is decomposed into two variables x and y, \(z=x+y\), therefore \(x=z_ 0 ch \Omega\) and \(y=z sh \Omega.\)
The reviewer points out that he also derived the Minkowskian observation model, in his relativistic information theory, but by using the following axioms: a) one observes a pair of variables (x,y) and the result is a linear transformation of x and y, b) there is neither loss nor gain of information, c) when \(x=y\), the observation reduces to the model \(x'=Gx.\)
While the approach of the reviewer is somewhat related to the Yin-Yan Chinese philosophy, one may have some contention on the \(z=x+y\) decomposition as suggested by the author.
Reviewer: G.Jumarie

94A15 Information theory (general)
93E10 Estimation and detection in stochastic control theory