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Underlying principles: the “Paradigm for Viable and Developing Systems” and layered spaces (fiber bundles)


Because it should explain nature, the TFF uses the principles of another Soviet theory, inspired by the laws of nature : the “Paradigm for Viable and Developing Systems” (“PVDS”), with strong, necessary and self-sufficient rules.


The Paradigm answers the following question: what is the essence of the universal law governing Nature, which provides the ability of systems to live and to develop themselves, and what are the mathematical tools which could describe this universal law and which can be used to build the theory ?


As early as in 1946, the Soviet Academician V. Vernadsky felt that the nature-driving Darwin triad “heredity – variability – (natural) selection” should play a central role in the evolution of the elements of the living and non living nature on Earth (he called it all these elements the “noosphere).

Other Russian scientists, as well as the French philosopher P. Teilhard de Chardin have contributed to develop this concept.



At the same time, as the Author underlined, prominent scientist of the 20th century (A. Einstein, L. de Broglie and P. Dirac), all expressed the need to move from the “quantum-relativistic” views of the “modern” physics. 




In today’s modern scientific language, according to Gerlovin, the principles of the “Paradigm for Viable and Developing Systems” (first published in 1988, due to Soviet censure) should be enounced as following:



(1) For a full description of any viable and developing system, it is necessary to consider it being simultaneously in different Sub-Spaces (SS) of an enclosing, comprehensive layered space (also referred to as “Fiber Bundle” in the English version of the book).


The space which includes other layers is called the Enclosing Space, and the sub-spaces (layers) inside are both a base for other layers, and a layer themselves.


It is important to note that such layered spaces are not used as a “convenient mathematical tool” by Gerlovin, but they are seen as real objects in the Nature. An unified, closed theory of the matter cannot be build-up else than in such a layered space.



(2) The structure of space-time of a system of fibers (base) of an enclosing space under any (no matter how cardinal) differences is strongly controlled by a single law valid in all the layers, the Triunity Law (TL) of space – time – matter.

In the TFF, for any viable system, there exists a mechanism of Spatial Metamorphosis (SM) for which this system in the different layers will have mutually coordinated, but different space-time structures. 
In other words, the SM involves the simultaneous existence of              single object in different sub-spaces / fibers, while in each sub-space / fiber this object has very different characteristics and structures.  See Fig. 2, page 8.

This SM is essential in Gerlovin’s work: if some living systems use Time Metamorphosis (like the caterpillar becoming a butterfly), the TM is absolutely neither a rule, nor a necessity in Nature, while SM is an essential and necessary phenomenon for all viable and developing systems.

The SM isn’t possible in the usual 3D + oriented-time, “Euclidian” spaces, but only in layered, multi-dimensional spaces: this scheme is used by the Nature and by the TFF.



(3) With respect to any sub-space (base and / or layer), any other sub-space, part of an enclosing space, is always in the domain of “imaginary”. Here the “imaginary domain” is not a formal mathematical dodge / tool, but it should be understood as a real structural property of all viable and developing systems.



The first 3 principles characterize the stability of systems, their viability.

But for a system to be viable over the time, and not just at the present moment, it should comply with other conditions, providing for their stability in the time, and ability not only to develop, but also to “self-develop”, themselves. The 5 principles hereunder rule over this ability.


Ability to “self-development” is one of the main principles of viable systems. In the process of “self-development”, a system may undergo “Time Metamorphosis” (TM) but, again: unlike the “Spatial Metamorphosis” (SM), the TM is not compulsory for systems which comply with the Paradigm.



(4) Between the sub-spaces  (fibers), and between the basis of the considered layered space (fibration) and its layers (fibers), there exists only an information channel.

This channel bears not only data about the processes taking place in the layer which is the origin of this data, but also signals which are regulating general processes.

Here “information” is taken in its broad sense.



(5) In a stationary regime, the information channels bears a signal which can bring only negative entropy into the sub-space in which it enters.



(6) The development of the viable systems involves a sharp increase in the information debit carrying negative entropy. This information can also contain signals, which regulate the “Darwin Triade”: “heredity – variability – (natural) selection”.

If the debit of negative entropy dominates over the production of positive entropy, then the system is capable of self organization.



(7) Leakage of the channel carrying a positive-entropy signal into the information channel, or the break of the information channel carrying a negative-entropy signal, leads to illness or death of the system.



(8) If the closure and / or the commutability of the reflection / mapping diagram, describing all the information channels of an enclosing space, is broken or violated, then the system loses its viability and is condemned to death.



The eight principles above are significantly restraining the quantity of possible solutions contained in the mathematical equations of the theory.



Note: the principle of the “Darwin Triade” has not been used, however it has been added above, in the definition of the Paradigm.

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