The Asymptote of Consciousness and the Law of the Quarter
M.D., Ph.D. Professor Valeriy Revo
Author Information[1]
Statements and Declarations Funding.
The author has not received support from any organization for the submitted work.
Competing Interests. The author declares that he has no conflict of interest.
The author declares that he does not use AI or AI-based technologies.
Acknowledgment. The author thanks his wife, Zoya Revo, for all possible support in the author’s work when writing this article.
ISBN 978-1-990242-26-7
URL
1.Abstract
Humans' primary resource is consciousness. Interest in its nature and the limits of its development stems from its existential significance. However, according to K. Gödel's second theorem, consciousness cannot be fully and consistently formalized. This requires a language and conceptual apparatus at a higher level than consciousness itself. The purpose of this paper is to identify the limit of consciousness's development, circumventing Gödel's limitation. The author's goal is to demonstrate the theoretical and practical significance of this limit. The results obtained are of interest to psychiatry, psychology, pedagogy, biology, artificial intelligence, and the philosophy of science.
Key words: consciousness, asymptote, biological constant, law of the quarter.
In this paper, the author develops his previously obtained results from studying the systemic nature and systemic patterns of development of life to its highest level of organization, namely, the level of developed consciousness. He demonstrated for the first time its systemic insufficiency and also for the first time defined the limits of its systemic development.[2] It is represented by the asymptote of consciousness that he discovered – a fundamental biological constant.
According to V. Revo (2006), consciousness is a systemic category expressing the highest form of reflection through subject-object and subject-subject relations[3]. It provides a volitional, figurative, and symbolic reflection of oneself and the environment within oneself, as well as oneself within the environment, occurring in the active and dynamic systemic synthesis of a developed brain and the social form of external memory. J. W. von Goethe expressed it this way: "Man knows himself only insofar as he knows the world, which he knows only in himself, and himself in himself."[4] After all, he himself is a part of this world.
Consciousness is capable of reflecting the real world at all levels of its systemic organization, creating images of representation. The creation of imaginative and conceptual images is essentially the work of probabilistic and multivariate models in consciousness, which is consistent with the quantum concept of superposition of states.
The systemic organization of consciousness involves information processing in the quantum dimension, while its virtual component represents religious consciousness.
Consciousness is incapable of a complete and self-consistent formalization of itself, as follows from the second incompleteness theorem (Gödel, 1931).
This is a special case of the universal limitation of a quantum observer. This understanding is provided by the unification of formal logic, quantum physics, and neurobiology. Its formal consistency follows from Gödel's second incompleteness theorem (1931), from the second law of thermodynamics through the increase in entropy of Clausius (1865), from quantum physics through Heisenberg's uncertainty principle (1927), and from the impossibility of self-measurement.
At the same time, religious consciousness functions as a unique meta-level of consciousness, the systemic representation of which is conditioned by the illusion of the ability to control oneself from a higher level of systemic organization (HLSO). Since this virtual higher level is represented in the structure of developed consciousness as part of it, by definition, it cannot have a higher level of systemic organization than consciousness itself..[5]
In reality, consciousness reflects the surrounding reality and itself within itself, whereas religious consciousness serves merely as a generator and repository of ethical and moral principles and norms. The ability to follow them or consciously ignore them constitutes the main difference between the bearer of a developed consciousness and the rest of the living world. Since ethical principles and norms are subjective, they lack expected content. Moreover, at each historical stage and in different circumstances, they change, sometimes radically. Therefore, ethical norms, like morality, have many isomers.
Another function of the virtual component of consciousness is to block the system's accidental transition to a phylogenetically new level of systemic organization. However, this component only provides a simulation of such a possibility. In accordance with its status, albeit virtual, religious consciousness claims to control the formation, development, and activity of developed consciousness, conditioned by the social environment.
In contrast to the interpretation of the concept of psychophysical parallelism by Hartley, Leibniz and others, in which consciousness was considered only through its relation to intra-corporeal processes, the author’s systemic concept (Revo, 1986) presents consciousness as a systemic unity of the developed brain and the social form of external memory.[6]
In this regard, the ongoing attempts in modern neuro- and psychophysiology to express consciousness through sensations and reflexes, dating back to Locke and Descartes, are anachronistic.
Since the operating principle of consciousness is quantum, realized on a macroscale, the only stable systemic carrier of this consciousness in living beings is a water-protein matrix. This protein is functionally prion-like in its properties, ensuring conformational stability, template induction (templating), and state transfer. To date, no other protein structures have been identified that are capable of performing the function of quantum-wave integration. The neuron, therefore, is both an anatomical-functional and systemic superstructure over protein nodes organized in a prion-like manner.
In one of his works, the author showed (see Fig. 1) that in the systemic model of living, the proportion of elements that form consciousness asymptotically tends to 25% of the total number of systemic elements of the organism..[7] This may be due to the limited nature of its resources, insufficient to satisfy the needs of consciousness at this level of development.
This limit is an invariant of phylogenesis and defines the boundaries of cognitive capabilities and biological stability. These circumstances allow the author to present them as a manifestation of the biological law of proportions he discovered, in the form of the law of a quarter for consciousness. With the continued, infinite systemic complication of living during phylogeny, consciousness cannot encompass the entire system; it is limited to a quarter of the organism's systemic resources.
With excessive cognitive load on consciousness, it begins to consume more resources than is possible for a given living system, and the system loses stability. This may explain a number of mental and psychosomatic conditions as a breakdown in systemic proportions.
Therefore, any approaches based on "strengthening or expanding consciousness" (cognitive practices, psychotherapy, brain stimulation) will be effective only within the natural quota. Beyond this, defense mechanisms will kick in, and further growth will be impossible.
The asymptote of consciousness shows us the limits of neuroengineering. Indeed, no neurotechnology or brain stimulation will transform an entire organism into consciousness. Its resource base cannot exceed its asymptote for a given conscious state. This is a natural barrier to AI based on biological systems.
Let us consider the systems model of human (V. V. Revo, 1986, 2003, 2024). See Fig. 1.
Legend:
I.n = 16
II. n = 8
III. n = 4
IV. n = 2
V. n = 1
Σn = 31
Left-hand side Right-hand side
(system input) (system output)
– Single-color circle is a basic system element
– First-order subsystem
– Second-order subsystem
– Third-order subsystem
– Fourth-order subsystem
Roman numerals indicate the levels of systemic organization (LSO) of the basic information biomechanisms of the living; n = number of subsystems of this LSO in the system of V LSO; Σn = total number of subsystems in the system. The basic systemic biomechanism of the I LSO is a system of living protein in a reversible ultra-high-frequency conformational dynamic (hydration ⇄ dehydration), II LSO – Genetic system, III LSO – Pre-cephalic nervous system (only single neurons, as well as networks, and ganglia), IV LSO – A highly evolved brain system, V LSO – Highly evolved consciousness system in systemic unity with the social form of external memory. The elements on the right side of the model represent the system output (system shell), while the elements on the left side represent the system input (system base). The open book at the base of the model represents the social form of external memory. The protein systemic elements of the inner pyramid represent consciousness.
Figure 1. Human Systemic Information Model (V. Revo, 1986, 2003, 2024)
It consists of two pyramidal structures, one within the other. The inner pyramid of the model includes six elements, three on each side. These elements first appeared in animals with a developed brain. The systemic model of these animals has one such element on each side. Animals with this level of systemic organization were the first in the history of living beings to possess a self-awareness apparatus.
Since these systemic elements are proteinaceous in nature, it can be assumed that they play a crucial role in the functioning of consciousness. This model represents a human who has undergone socialization. Among other things, it illustrates the violation of the law of conservation of parity in living systems due to the violation of mirror symmetry. This law, which is the same for both inert and living matter, is expressed in living matter as a violation of mirror symmetry at the level of the systemic organization of living.
In the systemic organization of humans, consciousness plays a unique role. Today, one can only marvel at the foresight of Socrates, who, according to Plato (Phaedrus), considered writing a product of consciousness. After all, writing is one of the leading symbolic-sign forms of external memory. Therefore, it should not be considered outside the human spirit, as it is possible only as a product of consciousness.
The further development of life during the stages of phylogenesis will not change this situation. The asymptote of consciousness demonstrates this.
We will never be able to imagine a new basic information mechanism for organisms that will emerge at the sixth and subsequent stages of phylogeny. However, since the organizing principle of the systemic structure of future life forms will remain the same, we can construct systemic models of life at any level of systemic organization. See Fig. 2. After all, the general systemic principle has remained unchanged throughout the history of life.
Figure 2. Systemic information model of a hypothetical living being of VI LSO (V. Revo, 2024).[8]
In the systemic model of living beings, from IV LSO to humans (V LSO), as the total number of elements increases, so does the number of systemic elements representing consciousness.
This series constitutes a recursive sequence of pairs of numbers: 15 and 2, 31 and 6. The systemic metamorphosis of subsequent generations of life at the stages of phylogenesis will yield the following pairs: 63 and 14 (organisms of VI LSO), 127 and 30 (organisms of VII LSO), 255 and 62 (organisms of VIII LSO), 511 and 126 (organisms of IX LSO), and so on.[9]. The number of system elements representing consciousness in IV LSO living organisms accounts for 13.3% of the total number of all system elements in the organism. Empirical data on the development of consciousness in IV LSO animals has been confirmed. This level of consciousness is exhibited by higher primates, dolphins, and crows. This indicates the emergence of consciousness, but this is not yet a mature form of it.
For V LSO living organisms, this figure is 19.35%. For living organisms of each subsequent LSO, it is: for VI LSO ≈ 22.22%, for VII LSO ≈ 23.62%, for VIII LSO ≈ 24.31%, for IX LSO ≈ 24.66%, for X LSO ≈ 24.88%, for XI LSO ≈ 24.94%, for XII LSO ≈ 24.97%, for XIII LSO ≈ 24.9987%, for XIV LSO ≈ 24.9993%, for XV LSO ≈ 24.9997%, etc. Since there have always been long time intervals between phylogenetic stages, this series encompasses a duration that is orders of magnitude greater than the existence of the physical world known to us. But it is precisely this circumstance that determines the reality of the open pattern of development of consciousness – its asymptote.
These circumstances allow us to derive the law of a quarter (a model invariant). The proportion of systemic elements that form consciousness increases monotonically from stage to stage of phylogenesis and asymptotically approaches 25% of the total number of elements (with equal weights and a binary architecture of levels). At subsequent stages of phylogenesis, this proportion approaches 25% with increasingly smaller increments.
The systemic power of consciousness will continually increase according to the stages of phylogenesis, but its asymptote will prevent it from reaching a quarter of the total number of systemic elements in the structure of life. A quarter is understood as a systemic boundary beyond which consciousness cannot transcend, regardless of its increasing complexity.
We should expect a development in which, according to the systemic law of phylogeny, what we define as consciousness will be replaced by something with a fundamentally different, higher form of life organization. However, according to the same law, the development of consciousness will not cease. Nevertheless, at each subsequent stage of phylogeny, the systemic status of each element of consciousness will decrease by one systemic order. It will become a subsystem of a new basic systemic mechanism of life, the characteristics of which are transcendental to humans. At the same time, the systemic elements represented by the prion-like protein in LSO IV and V will persist, but in a new configuration, they will create something that replaces consciousness as we understand it. The quantum mechanism of this new, higher form of systemic organization of life will be preserved.
At the same time, the systemic peculiarity of the structure of the elements forming the inner pyramid is noteworthy. These are elements of an exclusively protein nature of basic rank, with the exception of the first-order subsystemic element in the right half of the model, representing the systemic output. The structure of consciousness contains an ethical component, which is also developing. Therefore, for living organisms from previous stages of phylogeny, the future under new conditions may not be so dramatic. However, by definition, the food chain cannot change its nature and role in the system of relationships between living organisms.
One can only speculate about what the living organism of the new VI LSO will be like, since K. Gödel's second incompleteness theorem defines fundamental limitations. It can be said that a certain first metastage in the development of living organisms, the hierarchy of which is represented by levels I through V of the LSO, is approaching its completion.[10].
Since the number of new forms and species of living organisms that emerged at each stage of phylogeny decreased exponentially, creating only Homo sapiens L. at the fifth stage, further development presupposes the onset of the first stage of the second metastage of phylogeny.
At this stage, a new basic information element will appear in the systemic structure of the new living organism of the sixth metastage of phylogeny. For humans, its nature is transcendental. However, we know the principle of its systemic structure, determined by the fundamental characteristics of the preceding metastages of the first metastage of phylogeny of living organisms. This allows us to predict the systemic structure of all phylogenetically subsequent life forms.
Since the moment of self-awareness as a bearer of consciousness, humans have attempted not only to comprehend their nature but also to find opportunities for its development. One such attempt is presented here. It is based on the systemic information paradigm proposed by the author. It functions as a generator of hypotheses that biologists and physicians can test in practice. These could include calculations of phylogenetic limits, for example, for consciousness, immunity, disease programs, and cognitive plasticity. This could help determine the limits of tumor growth, the stability of the immune response, or the effectiveness of therapy, as they may have similar asymptotes within the framework of the author's proposed model. Such asymptotes are well known in fundamental sciences, for example, the speed of light and absolute zero. Unlike physical constants, measurable quantities with a finite limit (electron charge, Planck's constant, the gravitational constant), asymptotes are unattainable fundamental limits (the speed of light, absolute zero, the limit of consciousness).
Biological constants are also known, but they are not finite values, but rather a finite range representing a plateau. Several examples of asymptotic behavior are given here. For example, in the Michaelis-Menten model, the reaction rate increases with substrate concentration but does not exceed Vmax.[11] For a fixed amount of enzyme, this is the upper limit. Mortality and tumor growth are described by the Gompertz curve (1825), which shows an initial rapid rise, then a slowdown and a plateau.[12] In neurophysiology, in the passive membrane model, the potential exponentially tends to a stationary level.[13] In pharmacodynamics, "the dose-effect" curve saturates, and additional doses produce ever smaller increases.[14] In psychophysics, sensory systems exhibit a decrease in sensitivity and exit at a plateau.[15], [16]
Unlike the examples given, the asymptote of consciousness (1/4) is derived from the architecture of a human systemic model, in which the systemic elements that form consciousness have equal weights in a binary hierarchy. They are all proteinaceous in nature. There are no parameter variations in this model. By its nature, it is comparable to the Shannon limit in communication theory, the speed of light, or the temperature of absolute zero in physics. The asymptote of consciousness demonstrates a mathematically determined ceiling, not an empirically determined plateau.
In total, the author proposed and substantiated five fundamental biological invariants: three specific systemic elements of living (protein, genetic, and neural); phylogenetic memory, which is inaccessible to editing; the duration of each systemic metamorphosis not exceeding the Planck time; the constancy of the number of systemic elements in the structure of living organisms at each level of systemic organization; and the asymptote of consciousness, which he calculated. This allowed them to be classified as biological constants. Their introduction into scientific discourse, along with the rejection of the natural-philosophical paradigm and the adoption of a systems-informational one, provides, for the first time, a solid basis for recognizing biology and medicine as fundamental sciences.
Unlike measurable constant parameters, asymptotes define the boundaries of the possible – the fundamental limit of the organization of living systems.
The author's use of the classical systems approach allowed him to create systems models of phylogeny and systems models of living organisms that emerged at each stage. Having understood the principles of systemogenesis in living things, the author discovered measurable fundamental patterns within them. This enabled him to understand their content.
This, in turn, allowed him to uncover the universal principle of the systemic organization of living things at the stages of their phylogeny and develop a methodology for searching for fundamental systemic biological constants.
Among the five fundamental biological invariants (including constants and asymptotes) discovered by the author, one is the asymptote of consciousness. The theoretical and practical significance of this achievement is particularly great. The author demonstrated the potential for constructing adequate systemic models not only in biology and medicine, but also in other domains of knowledge where systemic organization is fundamental.
Gentet, L. J., Stuart, G. J. & Clements, J. D. (2000). Direct Measurement of Specific Membrane Capacitance in Neurons. Biophysical Journal, 79(1): 314-320. DOI: 10.1016/S0006-3495(00)76293-X.
Goethe, Johann Wolfgang von. “Studie nach Spinoza.” Berliner Ausgabe. Kunsttheoretische Schriften und Übersetzungen [Band 17-22], Band 18, Berlin: Aufbau-Verlag, 1960. http://www.zeno.org/nid/20004855817. Accessed July 8, 2025.
Gompertz Benjamin (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, Vol. 115, pp. 513–583. DOI: 10.1098/rstl.1825.0026.
Fechner, Gustav Theodor. Elemente der Psychophysik. Leipzig: Breitkopf und Härtel, 1860. T. 1. S. 55-65.
Holford, Nick. Holford N. H. G. and Sheiner L. B. "Understanding the Dose-Effect Relationship-Clinical Application of Pharmacokinetic-Pharmacodynamic Models," Clin Pharmacokin 6:429-453 (1981)-The Backstory. December 2011. The AAPS Journal 13(4):662-4. DOI: 10.1208/s12248-011-9306-5
Michaelis, L.; Menten, M. (1913). Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333–369.
Revo, Valeriy V. Ot kristalla k soznaniiu [From Crystal to Consciousness], Preprint no. 867 (Moscow: RTI of the Academy of Sciences of the USSR, 1986), Russian State Library, Record no. 001319445; storage codes FB 2 86‑13/1948. [In Russian].
Revo, Valeriy V. Stokhasticheskoe i determinsticheskoe v ierarkhicheskikh sistemakh [Stochastic and Deterministic in Hierarchical Systems], Preprint no. 908 (Moscow: Radiotechnical Institute of the USSR Academy of Sciences, 1990). [In Russian].
Revo, Valeriy. Encyclopedia of Systemic Knowledge. Moscow: Folium. 2006, 259. ISBN 5938810477. [In Russian]. LC Control Number 2007443229.
Revo, Valeriy. General Theory of Relativity and Systemic Insufficiency of Consciousness.
Preprint. 2023. ISBN 978-1-990242-04-5. http://dx.doi.org/10.2139/ssrn.4635603
Revo, Valeriy. Systemic Features of Living before and after Human. Preprint. Oct 2024. ISBN 9781990242151. http://dx.doi.org/10.2139/ssrn.4977181 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977181
Revo, Valeriy. Systemic Features of Living before and after Human. Preprint. Oct 2024. ISBN 9781990242151. http://dx.doi.org/10.2139/ssrn.4977181 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977181
Revo, Valeriy. Systemic Model of Phylogenesis and the Future of Humanity.
Preprint. 2025. ISBN 978-1-990242-14-4. http://dx.doi.org/10.2139/ssrn.5020100. https://bac-lac.on.worldcat.org/search?queryString=no:1504501505
Weber, Ernst Heinrich. De pulsù, resorptione, auditu et tactu: Annotationes anatomicae et physiologicae. Leipzig: C. F. Koehler, 1834. S. 111–113.
[1] Retired. Independent. Canada. Correspondence should be sent to [email protected]
[2] Valeriy Revo. General Theory of Relativity and Systemic Insufficiency of Consciousness.
Preprint. 2023. ISBN 978-1-990242-04-5. http://dx.doi.org/10.2139/ssrn.4635603
[3] Valeriy Revo. Encyclopedia of Systemic Knowledge. Moscow: Folium. 2006, 259. ISBN 5938810477. LC Control Number 2007443229. [In Russian].
[4] Goethe, Johann Wolfgang von. “Studie nach Spinoza.” Berliner Ausgabe. Kunsttheoretische Schriften und Übersetzungen [Band 17-22], Band 18, Berlin: Aufbau-Verlag, 1960. http://www.zeno.org/nid/20004855817. Accessed July 8, 2025.
[5] V. V. Revo, Stokhasticheskoe i determinsticheskoe v ierarkhicheskikh sistemakh [Stochastic and Deterministic in Hierarchical Systems], Preprint no. 908 (Moscow: Radiotechnical Institute of the USSR Academy of Sciences, 1990), 6. [In Russian].
[6] Revo, Valeriy V. Ot kristalla k soznaniiu [From Crystal to Consciousness], Preprint no. 867 (Moscow: RTI of the Academy of Sciences of the USSR, 1986), Russian State Library, Record no. 001319445; storage codes FB 2 86‑13/1948. [In Russian].
[7] Systemic Features of Living before and after Human. Preprint. Oct 2024. ISBN 9781990242151. http://dx.doi.org/10.2139/ssrn.4977181 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977181
[8] V. V. Revo, Systemic Model of Phylogenesis and the Future of Humanity (Preprint, Jan 3, 2025), DOI 10.2139/ssrn.5020100; ISBN 978‑1‑990242‑14‑4.
[9] Valeriy Revo. Systemic Model of Phylogenesis and the Future of Humanity.
Preprint. 2025. ISBN 978-1-990242-14-4. http://dx.doi.org/10.2139/ssrn.5020100. https://bac-lac.on.worldcat.org/search?queryString=no:1504501505
[10] Ibid.
[11] Michaelis, L.; Menten, M. (1913). Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333–369.
[12] Benjamin Gompertz (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, Vol. 115, pp. 513–583. DOI: 10.1098/rstl.1825.0026.
[13] Gentet, L. J., Stuart, G. J. & Clements, J. D. (2000). Direct Measurement of Specific Membrane Capacitance in Neurons. Biophysical Journal, 79(1): 314-320. DOI: 10.1016/S0006-3495(00)76293-X.
[14] Holford, Nick. Holford N. H. G. and Sheiner L. B. "Understanding the Dose-Effect Relationship-Clinical Application of Pharmacokinetic-Pharmacodynamic Models", Clin Pharmacokin 6:429-453 (1981)-The Backstory. December 2011. The AAPS Journal 13(4):662-4. DOI: 10.1208/s12248-011-9306-5
[15] Fechner, Gustav Theodor. Elemente der Psychophysik. Leipzig: Breitkopf und Härtel, 1860. T. 1. S. 55-65.
[16] Weber, Ernst Heinrich. De pulsù, resorptione, auditu et tactu: Annotationes anatomicae et physiologicae. Leipzig: C. F. Koehler, 1834. S. 111–113.
M.D., Ph.D. Professor Valeriy Revo
Author Information[1]
Statements and Declarations Funding.
The author has not received support from any organization for the submitted work.
Competing Interests. The author declares that he has no conflict of interest.
The author declares that he does not use AI or AI-based technologies.
Acknowledgment. The author thanks his wife, Zoya Revo, for all possible support in the author’s work when writing this article.
ISBN 978-1-990242-26-7
URL
1.Abstract
Humans' primary resource is consciousness. Interest in its nature and the limits of its development stems from its existential significance. However, according to K. Gödel's second theorem, consciousness cannot be fully and consistently formalized. This requires a language and conceptual apparatus at a higher level than consciousness itself. The purpose of this paper is to identify the limit of consciousness's development, circumventing Gödel's limitation. The author's goal is to demonstrate the theoretical and practical significance of this limit. The results obtained are of interest to psychiatry, psychology, pedagogy, biology, artificial intelligence, and the philosophy of science.
Key words: consciousness, asymptote, biological constant, law of the quarter.
- Summary statement
In this paper, the author develops his previously obtained results from studying the systemic nature and systemic patterns of development of life to its highest level of organization, namely, the level of developed consciousness. He demonstrated for the first time its systemic insufficiency and also for the first time defined the limits of its systemic development.[2] It is represented by the asymptote of consciousness that he discovered – a fundamental biological constant.
- Introduction
According to V. Revo (2006), consciousness is a systemic category expressing the highest form of reflection through subject-object and subject-subject relations[3]. It provides a volitional, figurative, and symbolic reflection of oneself and the environment within oneself, as well as oneself within the environment, occurring in the active and dynamic systemic synthesis of a developed brain and the social form of external memory. J. W. von Goethe expressed it this way: "Man knows himself only insofar as he knows the world, which he knows only in himself, and himself in himself."[4] After all, he himself is a part of this world.
Consciousness is capable of reflecting the real world at all levels of its systemic organization, creating images of representation. The creation of imaginative and conceptual images is essentially the work of probabilistic and multivariate models in consciousness, which is consistent with the quantum concept of superposition of states.
The systemic organization of consciousness involves information processing in the quantum dimension, while its virtual component represents religious consciousness.
Consciousness is incapable of a complete and self-consistent formalization of itself, as follows from the second incompleteness theorem (Gödel, 1931).
This is a special case of the universal limitation of a quantum observer. This understanding is provided by the unification of formal logic, quantum physics, and neurobiology. Its formal consistency follows from Gödel's second incompleteness theorem (1931), from the second law of thermodynamics through the increase in entropy of Clausius (1865), from quantum physics through Heisenberg's uncertainty principle (1927), and from the impossibility of self-measurement.
At the same time, religious consciousness functions as a unique meta-level of consciousness, the systemic representation of which is conditioned by the illusion of the ability to control oneself from a higher level of systemic organization (HLSO). Since this virtual higher level is represented in the structure of developed consciousness as part of it, by definition, it cannot have a higher level of systemic organization than consciousness itself..[5]
In reality, consciousness reflects the surrounding reality and itself within itself, whereas religious consciousness serves merely as a generator and repository of ethical and moral principles and norms. The ability to follow them or consciously ignore them constitutes the main difference between the bearer of a developed consciousness and the rest of the living world. Since ethical principles and norms are subjective, they lack expected content. Moreover, at each historical stage and in different circumstances, they change, sometimes radically. Therefore, ethical norms, like morality, have many isomers.
Another function of the virtual component of consciousness is to block the system's accidental transition to a phylogenetically new level of systemic organization. However, this component only provides a simulation of such a possibility. In accordance with its status, albeit virtual, religious consciousness claims to control the formation, development, and activity of developed consciousness, conditioned by the social environment.
In contrast to the interpretation of the concept of psychophysical parallelism by Hartley, Leibniz and others, in which consciousness was considered only through its relation to intra-corporeal processes, the author’s systemic concept (Revo, 1986) presents consciousness as a systemic unity of the developed brain and the social form of external memory.[6]
In this regard, the ongoing attempts in modern neuro- and psychophysiology to express consciousness through sensations and reflexes, dating back to Locke and Descartes, are anachronistic.
Since the operating principle of consciousness is quantum, realized on a macroscale, the only stable systemic carrier of this consciousness in living beings is a water-protein matrix. This protein is functionally prion-like in its properties, ensuring conformational stability, template induction (templating), and state transfer. To date, no other protein structures have been identified that are capable of performing the function of quantum-wave integration. The neuron, therefore, is both an anatomical-functional and systemic superstructure over protein nodes organized in a prion-like manner.
- Results
In one of his works, the author showed (see Fig. 1) that in the systemic model of living, the proportion of elements that form consciousness asymptotically tends to 25% of the total number of systemic elements of the organism..[7] This may be due to the limited nature of its resources, insufficient to satisfy the needs of consciousness at this level of development.
This limit is an invariant of phylogenesis and defines the boundaries of cognitive capabilities and biological stability. These circumstances allow the author to present them as a manifestation of the biological law of proportions he discovered, in the form of the law of a quarter for consciousness. With the continued, infinite systemic complication of living during phylogeny, consciousness cannot encompass the entire system; it is limited to a quarter of the organism's systemic resources.
With excessive cognitive load on consciousness, it begins to consume more resources than is possible for a given living system, and the system loses stability. This may explain a number of mental and psychosomatic conditions as a breakdown in systemic proportions.
Therefore, any approaches based on "strengthening or expanding consciousness" (cognitive practices, psychotherapy, brain stimulation) will be effective only within the natural quota. Beyond this, defense mechanisms will kick in, and further growth will be impossible.
The asymptote of consciousness shows us the limits of neuroengineering. Indeed, no neurotechnology or brain stimulation will transform an entire organism into consciousness. Its resource base cannot exceed its asymptote for a given conscious state. This is a natural barrier to AI based on biological systems.
Let us consider the systems model of human (V. V. Revo, 1986, 2003, 2024). See Fig. 1.
Legend:
I.n = 16
II. n = 8
III. n = 4
IV. n = 2
V. n = 1
Σn = 31
Left-hand side Right-hand side
(system input) (system output)
– Single-color circle is a basic system element
– First-order subsystem
– Second-order subsystem
– Third-order subsystem
– Fourth-order subsystem
Roman numerals indicate the levels of systemic organization (LSO) of the basic information biomechanisms of the living; n = number of subsystems of this LSO in the system of V LSO; Σn = total number of subsystems in the system. The basic systemic biomechanism of the I LSO is a system of living protein in a reversible ultra-high-frequency conformational dynamic (hydration ⇄ dehydration), II LSO – Genetic system, III LSO – Pre-cephalic nervous system (only single neurons, as well as networks, and ganglia), IV LSO – A highly evolved brain system, V LSO – Highly evolved consciousness system in systemic unity with the social form of external memory. The elements on the right side of the model represent the system output (system shell), while the elements on the left side represent the system input (system base). The open book at the base of the model represents the social form of external memory. The protein systemic elements of the inner pyramid represent consciousness.
Figure 1. Human Systemic Information Model (V. Revo, 1986, 2003, 2024)
It consists of two pyramidal structures, one within the other. The inner pyramid of the model includes six elements, three on each side. These elements first appeared in animals with a developed brain. The systemic model of these animals has one such element on each side. Animals with this level of systemic organization were the first in the history of living beings to possess a self-awareness apparatus.
Since these systemic elements are proteinaceous in nature, it can be assumed that they play a crucial role in the functioning of consciousness. This model represents a human who has undergone socialization. Among other things, it illustrates the violation of the law of conservation of parity in living systems due to the violation of mirror symmetry. This law, which is the same for both inert and living matter, is expressed in living matter as a violation of mirror symmetry at the level of the systemic organization of living.
In the systemic organization of humans, consciousness plays a unique role. Today, one can only marvel at the foresight of Socrates, who, according to Plato (Phaedrus), considered writing a product of consciousness. After all, writing is one of the leading symbolic-sign forms of external memory. Therefore, it should not be considered outside the human spirit, as it is possible only as a product of consciousness.
The further development of life during the stages of phylogenesis will not change this situation. The asymptote of consciousness demonstrates this.
- Systemic features of the asymptote of consciousness
We will never be able to imagine a new basic information mechanism for organisms that will emerge at the sixth and subsequent stages of phylogeny. However, since the organizing principle of the systemic structure of future life forms will remain the same, we can construct systemic models of life at any level of systemic organization. See Fig. 2. After all, the general systemic principle has remained unchanged throughout the history of life.
Figure 2. Systemic information model of a hypothetical living being of VI LSO (V. Revo, 2024).[8]
In the systemic model of living beings, from IV LSO to humans (V LSO), as the total number of elements increases, so does the number of systemic elements representing consciousness.
This series constitutes a recursive sequence of pairs of numbers: 15 and 2, 31 and 6. The systemic metamorphosis of subsequent generations of life at the stages of phylogenesis will yield the following pairs: 63 and 14 (organisms of VI LSO), 127 and 30 (organisms of VII LSO), 255 and 62 (organisms of VIII LSO), 511 and 126 (organisms of IX LSO), and so on.[9]. The number of system elements representing consciousness in IV LSO living organisms accounts for 13.3% of the total number of all system elements in the organism. Empirical data on the development of consciousness in IV LSO animals has been confirmed. This level of consciousness is exhibited by higher primates, dolphins, and crows. This indicates the emergence of consciousness, but this is not yet a mature form of it.
For V LSO living organisms, this figure is 19.35%. For living organisms of each subsequent LSO, it is: for VI LSO ≈ 22.22%, for VII LSO ≈ 23.62%, for VIII LSO ≈ 24.31%, for IX LSO ≈ 24.66%, for X LSO ≈ 24.88%, for XI LSO ≈ 24.94%, for XII LSO ≈ 24.97%, for XIII LSO ≈ 24.9987%, for XIV LSO ≈ 24.9993%, for XV LSO ≈ 24.9997%, etc. Since there have always been long time intervals between phylogenetic stages, this series encompasses a duration that is orders of magnitude greater than the existence of the physical world known to us. But it is precisely this circumstance that determines the reality of the open pattern of development of consciousness – its asymptote.
These circumstances allow us to derive the law of a quarter (a model invariant). The proportion of systemic elements that form consciousness increases monotonically from stage to stage of phylogenesis and asymptotically approaches 25% of the total number of elements (with equal weights and a binary architecture of levels). At subsequent stages of phylogenesis, this proportion approaches 25% with increasingly smaller increments.
The systemic power of consciousness will continually increase according to the stages of phylogenesis, but its asymptote will prevent it from reaching a quarter of the total number of systemic elements in the structure of life. A quarter is understood as a systemic boundary beyond which consciousness cannot transcend, regardless of its increasing complexity.
We should expect a development in which, according to the systemic law of phylogeny, what we define as consciousness will be replaced by something with a fundamentally different, higher form of life organization. However, according to the same law, the development of consciousness will not cease. Nevertheless, at each subsequent stage of phylogeny, the systemic status of each element of consciousness will decrease by one systemic order. It will become a subsystem of a new basic systemic mechanism of life, the characteristics of which are transcendental to humans. At the same time, the systemic elements represented by the prion-like protein in LSO IV and V will persist, but in a new configuration, they will create something that replaces consciousness as we understand it. The quantum mechanism of this new, higher form of systemic organization of life will be preserved.
At the same time, the systemic peculiarity of the structure of the elements forming the inner pyramid is noteworthy. These are elements of an exclusively protein nature of basic rank, with the exception of the first-order subsystemic element in the right half of the model, representing the systemic output. The structure of consciousness contains an ethical component, which is also developing. Therefore, for living organisms from previous stages of phylogeny, the future under new conditions may not be so dramatic. However, by definition, the food chain cannot change its nature and role in the system of relationships between living organisms.
One can only speculate about what the living organism of the new VI LSO will be like, since K. Gödel's second incompleteness theorem defines fundamental limitations. It can be said that a certain first metastage in the development of living organisms, the hierarchy of which is represented by levels I through V of the LSO, is approaching its completion.[10].
Since the number of new forms and species of living organisms that emerged at each stage of phylogeny decreased exponentially, creating only Homo sapiens L. at the fifth stage, further development presupposes the onset of the first stage of the second metastage of phylogeny.
At this stage, a new basic information element will appear in the systemic structure of the new living organism of the sixth metastage of phylogeny. For humans, its nature is transcendental. However, we know the principle of its systemic structure, determined by the fundamental characteristics of the preceding metastages of the first metastage of phylogeny of living organisms. This allows us to predict the systemic structure of all phylogenetically subsequent life forms.
- Discussion
Since the moment of self-awareness as a bearer of consciousness, humans have attempted not only to comprehend their nature but also to find opportunities for its development. One such attempt is presented here. It is based on the systemic information paradigm proposed by the author. It functions as a generator of hypotheses that biologists and physicians can test in practice. These could include calculations of phylogenetic limits, for example, for consciousness, immunity, disease programs, and cognitive plasticity. This could help determine the limits of tumor growth, the stability of the immune response, or the effectiveness of therapy, as they may have similar asymptotes within the framework of the author's proposed model. Such asymptotes are well known in fundamental sciences, for example, the speed of light and absolute zero. Unlike physical constants, measurable quantities with a finite limit (electron charge, Planck's constant, the gravitational constant), asymptotes are unattainable fundamental limits (the speed of light, absolute zero, the limit of consciousness).
Biological constants are also known, but they are not finite values, but rather a finite range representing a plateau. Several examples of asymptotic behavior are given here. For example, in the Michaelis-Menten model, the reaction rate increases with substrate concentration but does not exceed Vmax.[11] For a fixed amount of enzyme, this is the upper limit. Mortality and tumor growth are described by the Gompertz curve (1825), which shows an initial rapid rise, then a slowdown and a plateau.[12] In neurophysiology, in the passive membrane model, the potential exponentially tends to a stationary level.[13] In pharmacodynamics, "the dose-effect" curve saturates, and additional doses produce ever smaller increases.[14] In psychophysics, sensory systems exhibit a decrease in sensitivity and exit at a plateau.[15], [16]
Unlike the examples given, the asymptote of consciousness (1/4) is derived from the architecture of a human systemic model, in which the systemic elements that form consciousness have equal weights in a binary hierarchy. They are all proteinaceous in nature. There are no parameter variations in this model. By its nature, it is comparable to the Shannon limit in communication theory, the speed of light, or the temperature of absolute zero in physics. The asymptote of consciousness demonstrates a mathematically determined ceiling, not an empirically determined plateau.
In total, the author proposed and substantiated five fundamental biological invariants: three specific systemic elements of living (protein, genetic, and neural); phylogenetic memory, which is inaccessible to editing; the duration of each systemic metamorphosis not exceeding the Planck time; the constancy of the number of systemic elements in the structure of living organisms at each level of systemic organization; and the asymptote of consciousness, which he calculated. This allowed them to be classified as biological constants. Their introduction into scientific discourse, along with the rejection of the natural-philosophical paradigm and the adoption of a systems-informational one, provides, for the first time, a solid basis for recognizing biology and medicine as fundamental sciences.
Unlike measurable constant parameters, asymptotes define the boundaries of the possible – the fundamental limit of the organization of living systems.
- Conclusion
The author's use of the classical systems approach allowed him to create systems models of phylogeny and systems models of living organisms that emerged at each stage. Having understood the principles of systemogenesis in living things, the author discovered measurable fundamental patterns within them. This enabled him to understand their content.
This, in turn, allowed him to uncover the universal principle of the systemic organization of living things at the stages of their phylogeny and develop a methodology for searching for fundamental systemic biological constants.
Among the five fundamental biological invariants (including constants and asymptotes) discovered by the author, one is the asymptote of consciousness. The theoretical and practical significance of this achievement is particularly great. The author demonstrated the potential for constructing adequate systemic models not only in biology and medicine, but also in other domains of knowledge where systemic organization is fundamental.
- References
Gentet, L. J., Stuart, G. J. & Clements, J. D. (2000). Direct Measurement of Specific Membrane Capacitance in Neurons. Biophysical Journal, 79(1): 314-320. DOI: 10.1016/S0006-3495(00)76293-X.
Goethe, Johann Wolfgang von. “Studie nach Spinoza.” Berliner Ausgabe. Kunsttheoretische Schriften und Übersetzungen [Band 17-22], Band 18, Berlin: Aufbau-Verlag, 1960. http://www.zeno.org/nid/20004855817. Accessed July 8, 2025.
Gompertz Benjamin (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, Vol. 115, pp. 513–583. DOI: 10.1098/rstl.1825.0026.
Fechner, Gustav Theodor. Elemente der Psychophysik. Leipzig: Breitkopf und Härtel, 1860. T. 1. S. 55-65.
Holford, Nick. Holford N. H. G. and Sheiner L. B. "Understanding the Dose-Effect Relationship-Clinical Application of Pharmacokinetic-Pharmacodynamic Models," Clin Pharmacokin 6:429-453 (1981)-The Backstory. December 2011. The AAPS Journal 13(4):662-4. DOI: 10.1208/s12248-011-9306-5
Michaelis, L.; Menten, M. (1913). Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333–369.
Revo, Valeriy V. Ot kristalla k soznaniiu [From Crystal to Consciousness], Preprint no. 867 (Moscow: RTI of the Academy of Sciences of the USSR, 1986), Russian State Library, Record no. 001319445; storage codes FB 2 86‑13/1948. [In Russian].
Revo, Valeriy V. Stokhasticheskoe i determinsticheskoe v ierarkhicheskikh sistemakh [Stochastic and Deterministic in Hierarchical Systems], Preprint no. 908 (Moscow: Radiotechnical Institute of the USSR Academy of Sciences, 1990). [In Russian].
Revo, Valeriy. Encyclopedia of Systemic Knowledge. Moscow: Folium. 2006, 259. ISBN 5938810477. [In Russian]. LC Control Number 2007443229.
Revo, Valeriy. General Theory of Relativity and Systemic Insufficiency of Consciousness.
Preprint. 2023. ISBN 978-1-990242-04-5. http://dx.doi.org/10.2139/ssrn.4635603
Revo, Valeriy. Systemic Features of Living before and after Human. Preprint. Oct 2024. ISBN 9781990242151. http://dx.doi.org/10.2139/ssrn.4977181 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977181
Revo, Valeriy. Systemic Features of Living before and after Human. Preprint. Oct 2024. ISBN 9781990242151. http://dx.doi.org/10.2139/ssrn.4977181 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977181
Revo, Valeriy. Systemic Model of Phylogenesis and the Future of Humanity.
Preprint. 2025. ISBN 978-1-990242-14-4. http://dx.doi.org/10.2139/ssrn.5020100. https://bac-lac.on.worldcat.org/search?queryString=no:1504501505
Weber, Ernst Heinrich. De pulsù, resorptione, auditu et tactu: Annotationes anatomicae et physiologicae. Leipzig: C. F. Koehler, 1834. S. 111–113.
[1] Retired. Independent. Canada. Correspondence should be sent to [email protected]
[2] Valeriy Revo. General Theory of Relativity and Systemic Insufficiency of Consciousness.
Preprint. 2023. ISBN 978-1-990242-04-5. http://dx.doi.org/10.2139/ssrn.4635603
[3] Valeriy Revo. Encyclopedia of Systemic Knowledge. Moscow: Folium. 2006, 259. ISBN 5938810477. LC Control Number 2007443229. [In Russian].
[4] Goethe, Johann Wolfgang von. “Studie nach Spinoza.” Berliner Ausgabe. Kunsttheoretische Schriften und Übersetzungen [Band 17-22], Band 18, Berlin: Aufbau-Verlag, 1960. http://www.zeno.org/nid/20004855817. Accessed July 8, 2025.
[5] V. V. Revo, Stokhasticheskoe i determinsticheskoe v ierarkhicheskikh sistemakh [Stochastic and Deterministic in Hierarchical Systems], Preprint no. 908 (Moscow: Radiotechnical Institute of the USSR Academy of Sciences, 1990), 6. [In Russian].
[6] Revo, Valeriy V. Ot kristalla k soznaniiu [From Crystal to Consciousness], Preprint no. 867 (Moscow: RTI of the Academy of Sciences of the USSR, 1986), Russian State Library, Record no. 001319445; storage codes FB 2 86‑13/1948. [In Russian].
[7] Systemic Features of Living before and after Human. Preprint. Oct 2024. ISBN 9781990242151. http://dx.doi.org/10.2139/ssrn.4977181 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4977181
[8] V. V. Revo, Systemic Model of Phylogenesis and the Future of Humanity (Preprint, Jan 3, 2025), DOI 10.2139/ssrn.5020100; ISBN 978‑1‑990242‑14‑4.
[9] Valeriy Revo. Systemic Model of Phylogenesis and the Future of Humanity.
Preprint. 2025. ISBN 978-1-990242-14-4. http://dx.doi.org/10.2139/ssrn.5020100. https://bac-lac.on.worldcat.org/search?queryString=no:1504501505
[10] Ibid.
[11] Michaelis, L.; Menten, M. (1913). Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333–369.
[12] Benjamin Gompertz (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London, Vol. 115, pp. 513–583. DOI: 10.1098/rstl.1825.0026.
[13] Gentet, L. J., Stuart, G. J. & Clements, J. D. (2000). Direct Measurement of Specific Membrane Capacitance in Neurons. Biophysical Journal, 79(1): 314-320. DOI: 10.1016/S0006-3495(00)76293-X.
[14] Holford, Nick. Holford N. H. G. and Sheiner L. B. "Understanding the Dose-Effect Relationship-Clinical Application of Pharmacokinetic-Pharmacodynamic Models", Clin Pharmacokin 6:429-453 (1981)-The Backstory. December 2011. The AAPS Journal 13(4):662-4. DOI: 10.1208/s12248-011-9306-5
[15] Fechner, Gustav Theodor. Elemente der Psychophysik. Leipzig: Breitkopf und Härtel, 1860. T. 1. S. 55-65.
[16] Weber, Ernst Heinrich. De pulsù, resorptione, auditu et tactu: Annotationes anatomicae et physiologicae. Leipzig: C. F. Koehler, 1834. S. 111–113.
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