Length of the cognitive path of iterative reduction of the entropy of binary code sequences from the initial chaos (ideal "white" noise) to the determinism of monotonicity

The purpose of the research is to demonstrate the possibility of assessing the level of cognition by reducing the entropy of the code sequence. In complete chaos there is no order, but evolution, natural intelligence and artificial intelligence are able to counteract disorder, gradually reducing it.

Methods. Shannon entropy is canonized and described in all textbooks, but as a tool for practical application it is flawed due to the enormous computational complexity of its estimates. However, in this century, alternative approaches have been actively developed that significantly simplify calculations. In particular, the entropy in the space of Hamming distances should have a linear computational complexity, and the entropy of the correlation entanglement of code bits should have a quadratic computational complexity. The only problem is that the Hamming entropy and the entropy of the correlation entanglement of bits have their own scales that do not coincide with the Shannon entropy scale.

Results. There should be many entropy metrics, one of such metrics is the length of the cognitive path from the chaos of "white" noise to complete determinism and monotony. The article provides a software implementation of the assessment of such a metric. It is shown that the length of the cognitive path is reduced to both the Hamming distances and the correlation coefficients between the resulting code sequences.

Conclusion. The proposed cognitive path length metric should apparently have its own entropy scale, which does not coincide with the Shannon entropy scale. All this should be considered as a convenient for practical use special case of some simplified evaluation of a computationally complex problem. At least, the program given in the article can be considered as another system of cryptographic key quality tests, which has polynomial computational complexity.

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