Vol. 9 pp. 27-49

F.I. Mavrikidi, S.A. Khorkov

NUMERICAL ASYMMETRY FOR THEORETICAL ECOLOGY: BIOLOGICAL PROBLEMATIZATION OF MATHEMATICS

People obey the laws of nature,

even when they act against them. I.W. Goethe

Annotation. It is noted that modern ecological and humanitarian problems of humanity have raised the question of the need to change the style of thinking and, on this basis, to revise the scientific methods of cognition of Nature. As it turned out, many purely mathematical, but non-physical facts remained in the shadow of physical and mathematical science, which could form the basis of integrative or biological mathematics. The main message of the work lies in the identity of the mathematical content of the fractal geometry of Nature, objects of thought, and those objects that are created by man in the process of practical and theoretical activity. Philosophically, this is the unity of opposites, elevated into biodiversity as a multiplicity of paired opposites. The empirical basis of the work is the idea of systemic potentialities of fractals. Fractals make it possible to unite previously disparate theories, facts, and generalizations that theoretical ecology has absorbed. Their formal embodiment is numerical asymmetry, connecting real and p-adic numbers. It significantly expands the arsenal of mathematical modeling of theoretical ecology and creates the possibility of developing a formal mathematical theory with ecological content.

Keywords: system, fractal, duality, numerical asymmetry, theoretical ecology, biomathematics.

For citation: Mavrikidi F.I., Khorkov S.A. [Numerical asymmetry for Theoretical Ecology: biological problematization of mathematics]. Upravlenie tekhnosferoi, 2026, vol. 9, issue 1, рр. 27–49. DOI: 10.35634/UdSU.2026.81.80.003. (In Russ.).

REFERENCES

Reimers N.F. Ecology. Teorii, zakony, pravila, printsipy i gipotezy [Theories, Laws, Rules, Principles, and Hypotheses]. Moscow: Rossiya molodaya, 1994, 367 p. (In Russ.).
Weizsäcker E., Wijkman A. Come On! A Report to the Club of Rome. Springer, 2018, 220
Moskovkin V.M. Doklad rimskogo kluba: orgii samokritiki [The Report of the Club of Rome: Orgies of Self-Criticism]. Nauka, Iskusstvo, Kul'tura [Science, Art, and Culture]. 2018, Issue 2(8), pp. 126 – 145. (In Russ.).
Ignat'ev M.B. Kiberneticheskaya kartina mira [Cybernetic Picture of the World]. SPb: GUAP, 2010, 416 p. (In Russ.).
Colyvan M., Ginzburg L.R. Laws of nature and Laws of ecology, Oikos 101:3 (2013), pp.649 – 653.
Frame M., Urry A. Fractal Worlds Grown, Built, and Imagined. Yale Univ. Press, 2016, 515 p.
Mavrikidi F.I. Chislovaya asimmetriya v prikladnoi matematike [Numerical asymmetry in applied mathematics]. Moscow: Del'fis, 2015, 414 p. (In Russ.).
Khor'kov S.A. Problema rascheta ehlektropotrebleniya mnogonomenklaturnogo tsekha promyshlennogo predpriyatiya, modeli i metodiki dlya ee resheniya [The problem of calculating the electricity consumption of a multi-nomenclature workshop of an industrial enterprise, models and methods for its solution]. Izhevsk: Publ., IZHGTU im. M.T. Kalashnikova, 2019, 123 p. (In Russ.).
Khor'kov S.A., Mavrikidi F.I. Tekhnotsenozy, sistemy i ikh modeli. [Technocenoses, Systems, and Their Models]. Izhevsk: Institut komp'yuternykh issledovanii, 2025, 310 p. (In Russ.).
Selivanova V.I. Ehtyudy ob ehkstrapolyatsii [Etudes on extrapolation]. Moscow: VZPI, 1991, 223 p. (In Russ.).
Rosenberg G.S., Ryansky F.N. Teoreticheskaya i prikladnaya ehkologiya: Uchebnoe posobie. – 2-e izd. [Theoretical and applied ecology: textbook. – 2nd ed]. Nizhny Novgorod: Publ., Izd-vo Nizhnevart. ped. in-ta. 2005, 292 p. (In Russ.).
Tkacheva L.O. Vozdeistvie fraktal'nykh dinamicheskikh izobrazhenii na funktsional'noe sostoyanie cheloveka [The Effect of Fractal Dynamic Images on Human Functional State] Vestnik SPBGU [Bulletin of St. Petersburg State University]. 2010, Ser. 12, issue 2, pp. 378 – 387. (In Russ.).
Werner G. Fractals in the nervous system: conceptual implication for theoretical neuroscience, Frontiers in Physiology 2010, vol.1, art.15 p.1 – 28.
Gisiger T. Scale invariance in biology, Biol.Rev. 76, 2001, pp, 161 – 209.
Tutubalin V.N., Barbasheva Y.M., Grigoryan A.A. Devyatkova G.N., Uger E.G. Matematicheskoe modelirovanie v ehkologii [Mathematical modeling in ecology]. Moscow: Yazyki Russkoi kul'tury, 1999, 134 p. (In Russ.).
Gartle S., Marshall P., Kauffman S. The Reasonable Ineffectiveness of Mathematics in the Biological Sciences, Entropy, 2025, 27, 280. Available at: https://doi.org/10.3390/e27030280.
Rosenberg G.S. Vvedenie v teoreticheskuyu ehkologiyu [Introduction to theoretical ecology]. In 2 vol., Tol'yatti: Kassandra, 2013, 565 p. (In Russ.).
Ganea O.E. Hyperbolic Neural network, arXiv:1805.09112v2 [cs. LG] 2018.
Gerasimova I.A. Priroda zhivogo i chuvstvennyi opyt [The nature of living and sensory experience], Voprosy filosofii [Voprosy Filosofii], 1997, no. 8, pp. 123 – 134. (In Russ.).
Panov V.G. Razum [Myths. Emotions. Reason]. Moscow: Vysshaya Shkola, 1992, 252 p. (In Russ.).
Auehrbakh F. Tsaritsa mira i ee ten' [The Queen of the World and Her Shadow]. Odessa: MATHESIS, 1913, 50 p. (In Russ.).
Winslow C.F. Force and Nature. Attraction and Repulsion. McMillan, 1869/483 p.

About the Authors

Mavrikidi Fyodor Ivanovich

Candidate of Technical Sciences, senior researcher, Institute of oil and gas problems of the Russian Academy of Sciences, Moscow, Russia.

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Khorkov Sergey Alekseevich

Associate Professor of the Department of Thermal Power Engineering, Institute of Oil and Gas named after M.S. Gutseriev, Federal State Budgetary Educational Institution of Higher Education "Udmurt State University", 426034, University st., 1, Izhevsk, Russia.

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