Polymetric Analysis: Retrospective and Perspective

Question

Referee this paper: ijritcc.v4i1.1729 by Petro P. Trokhimchuck

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

(Is this your paper?)

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The concept of polymetric analysis is analyzed. The necessity of creation, basic peculiarities of development and some application of this science are discussed. Bonds of polymetric analysis and other sciences, including mathematics, computer science and theory of information, are shown. Problem of century in cybernetics by S. Beer and way of their resolution with help of polymetric analysis is analyzed too.

Comments

This paper is about a problem-solving methodology called "polymetric analysis", to which physics ideas have made a significant contribution, e.g. "The polymetric method may be represented as functional expansion of the optical interpretation of the quantum mechanics on all knowledge." This optical interpretation is described in the paper and is the work of the same author. 

Polymetric analysis came to my attention via a paper in the cs.AI category at arxiv, https://arxiv.org/abs/2111.09762 ;

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I have returned to this paper several times since requesting a review, but it's still rather baffling. 

For example, mathematically, special importance is attached to quadratic forms (i.e. polynomials in which every term has degree two). Various kinds of functions are to be built up. A notion of duality (between what Trokhimchuck calls "straight" and "opposite" objects) is also there. Also important is "optimal calculation", which seems to mean, performing calculations as efficiently as possible, given their computational complexity. 

So some kind of mathematical toolkit is assembled, but I don't see the reason why these particular tools are regarded as ideal for all purposes. 

Then there's a typology of systems ("theory of hybrid systems") that I don't understand at all. But we are told that classical mechanics is a "simple system", quantum mechanics in the Heisenberg picture is a "parametric simple system", quantum mechanics in the Schrodinger picture is a "functional simple system", and quantum mechanics in the interaction picture is a "semisimple system". 

There is also a general theory of measurement according to which a measurement has a "logic region" and a "chaotic region".