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The “Wheel of Samsara” as a Fractal Self-Unfolding Dynamic Crystal — A Construct of Socio-Cognitive Dynamics

Abstract

This work proposes an interpretation of the Buddhist “Wheel of Samsara” (the cycle of birth, growth, decline, and death) not as a flat cyclical scheme, but as a multidimensional fractal self-similar construct that unfolds at any scale — from civilization to the individual personality. Based on a comparative analysis of five levels (civilization, country, community, family, personality), it is shown that each phase of the cycle obeys unified transition operators that depend on the presence or absence of an “external point of observation” and the level of the “sense of one’s own importance” (SOI). The necessity of a transition from probabilistic mathematics to fractal dynamics and the “physics of meanings” — a discipline studying meaning potentials, tensions, and catalytic effects — is substantiated. A simple safeguard mechanism (a three-step reflexive stop-signal) is proposed, applicable at all levels to prevent stagnation and disintegration.

1. Introduction: From a Planar Scheme to a Volumetric Crystal

The classical description of Samsara (four phases: birth – growth – decline – death) is reproduced in dozens of cultural and religious traditions. However, when attempting to apply this scheme to the analysis of real processes (the development of civilizations, the evolution of states, the life cycle of organizations, family dynamics, individual trajectory), an irremovable contradiction arises: the same structure must work at scales differing by millions of times. Either the scheme is trivial (everything always “dies”), or it hides a nontrivial property — fractal self-similarity.

In this work we show that the “Wheel of Samsara” is not a flat cycle, but a multidimensional fractal self-unfolding crystal, where each facet corresponds to a certain level of being (from global to individual), and processes on different facets are connected by recursive operators. Such a view requires abandoning probabilistic description (where disintegration is viewed as a random event) in favor of a deterministic dynamics of meanings — a discipline only now forming at the intersection of nonlinear dynamics, semiotics, and the theory of complex systems.

2. Fractality: Formal Justification

2.1. Self-Similarity and Scale Invariance

A fractal (B. Mandelbrot, 1975) is a structure that looks the same when the scale of consideration changes. In our case, we fix the pattern of phases (unfolding of the future → growth → stagnation / SOI → disintegration) and observe it at levels differing in characteristic time by 4–6 orders of magnitude:

• Civilization: ~10³ years

• Country: ~10² years

• Community: ~10¹ years

• Family: ~10⁰–10¹ years

• Personality: ~10⁻¹–10⁰ years (months–years)

At the same time, the topology of transitions (conditions for phase change) and the set of basic operators (emergence of a construct, institutionalization, growth of SOI, disintegration) remain unchanged. This is the empirical confirmation of fractality.

2.2. Recursive Parameterization

Each level is nested within a higher one (personality → family → community → country → civilization) and simultaneously contains lower ones (civilization includes countries, those — communities, etc.). The phase at a higher level sets boundary conditions for lower ones, while fluctuations at lower levels can initiate a phase transition at a higher one (for example, a critical mass of personalities with third attention changes the trajectory of a community or even a country).

Mathematically, this can be represented as a system of recursive mappings:

F_{L+1} = Φ( F_L , params_L , external_point_L )

where F_L is the vector of phases at level L, Φ is the nonlinear transition operator, and external_point_L is a Boolean variable of the presence of an external observer at that level.

3. The Physics of Meanings: Why Probabilities Are Insufficient

3.1. The Potential of Meaning

Unlike physical particles, meanings do not obey Boltzmann statistics. However, they are capable of performing work: the construct of the “Axial Age” (K. Jaspers) transformed the structure of entire civilizations. Let us introduce the concept of meaning potential U(s) — a measure of the ability of meaning s to initiate transitions in other meanings. The transition from the “growth” phase to the “stagnation” phase occurs when U(construct) is exhausted and replaced by U(SOI) — the potential of self-preservation of the carriers.

3.2. Tension and Catalysis

The difference in potentials between the “idea of life carried beyond the personality” (U_ext) and the “idea of life internalized in SOI” (U_int) creates meaning tension. It is precisely this that drives the process. An external observer (third point, new facade of personality) acts as a catalyst, lowering the activation energy for the transition to a new turn of the spiral (that is, to a repeated unfolding of the future at a new level).

The safeguard (the three-step “stop-signal” algorithm) is a damper that dissipates excess tension and prevents resonant rocking of the system.

3.3. Transition Operators

The probabilistic approach (logistic regression, Markov chains) does not distinguish whether a transition was caused by the growth of SOI or by an external shock. Fractal dynamics requires the introduction of deterministic operators sensitive to structure:

• Operator R (unfolding of the future): activated in the presence of an external point and a deficit of current constructs.

• Operator G (growth): activated with positive feedback between the construct and social energy.

• Operator S (stagnation): activated when U(SOI) > U(construct) and there is no external observer.

• Operator D (disintegration): activated when the stagnant form enters into resonance with external challenges, lacking the ability to adapt.

4. Detailed Unfolding by Levels

Below, each level is described in terms of four phases with concrete historical and empirical examples.

4.1. Civilizational Level (scale: millennia)

1. Unfolding of the future
   New worldview constructs arise: the “Axial Age” (Jaspers) — the emergence of philosophy, religion, science. Prophets, thinkers, discoverers. A person of third attention (or their analog) formulates the “picture of the world” of the next cycle.

2. Growth
   Constructs are institutionalized: church, academies, legal systems, economic formations. The spread of writing, technological modes. Society is restructured under the new ontology.

3. Stagnation / SOI
   Institutions become self-sufficient. Priests, scholars, politicians retreat into SOI: “We are the bearers of truth, the others are barbarians.” Vices: corruption, scholasticism, ritualism instead of living thinking. Form matters more than content. The idea of life turns out to be inside the personality (power, wealth, national superiority).

4. Disintegration
   Civilization loses the ability to respond to challenges. Barbarian invasions, internal collapse, dark ages. The stagnant form collapses under the weight of its own non-viability.
   Example: The Roman Empire (republic → principate → dominate → fall).

4.2. Level of Countries (scale: centuries – decades)

1. Unfolding of the future
   A group of elites / ideologists formulates a national idea, a development strategy. Revolutionary constructs: “catch up and overtake,” “the American dream,” “the Chinese dream.”

2. Growth
   Economic leap, industrialization, infrastructure. Introduction of constructs through education, propaganda, law. New industries and social lifts arise.

3. Stagnation / SOI
   Bureaucratization, oligarchy, cult of personality of the leader or party. SOI of elites: “we are a great power, they must fear/respect us.” Vices: corruption, nepotism, suppression of dissent. Innovation is slowed, imitation of activity begins.

4. Disintegration
   Economic crisis, collapse of the state (USSR), civil war, loss of territories. The construct of “great power” ceases to work, the bardo phase sets in — the search for a new identity.

4.3. Level of Communities (companies, movements, schools, online groups; scale: years – decades)

1. Unfolding of the future
   A leader (a person of third attention or their emissary) creates a construct: a new business, the ideology of a startup, a spiritual teaching. The first enthusiasts appear, “those who see the light.”

2. Growth
   Self-reproduction: hiring, attracting followers, scaling. The community acquires structure, rituals, a common language. Rapid growth of profit / influence / number of participants.

3. Stagnation / SOI
   SOI of founders and old-timers: “we are the pioneers, the newcomers understand nothing.” Clans appear, a division into “us” and “them.” Instead of the cause — management for the sake of management. The construct turns into a dogma. Any new knowledge is perceived as a threat. The idea of life is inside the personality (power, status, recognition).

4. Disintegration
   Key leaders leave or burn out. Turnover, loss of meaning. The community falls apart into factions or quietly disappears. A dead form remains (a legal entity without a soul). Bardo — until the appearance of a new construct.
   Examples: startups after IPO, religious sects after the death of a charismatic, political movements after victory.

4.4. Level of the Family (scale: years – decades)

1. Unfolding of the future
   Creation of a family: a shared image of the future (apartment, children, travel, lifestyle). Young spouses “unfold the construct” of family happiness. Each brings their own expectations.

2. Growth
   Birth of children, accumulation of property, career growth of the spouses. Family rituals, traditions, distribution of roles. Everything works if the construct is living and shared.

3. Stagnation / SOI
   SOI of family members: “I do more,” “I am the mother/father, I decide.” Vices: manipulation, emotional abuse, infidelity, domestic laziness. Form replaces the living relationship. The idea of life is no longer “we build the future together,” but “I am the victim” or “you owe me.”

4. Disintegration
   Divorce, alienation, emotional death of the relationship. People live under one roof as neighbors. Then — a formal break, division of property. Bardo — loneliness or the pain of the past.
   Exceptions: families passing through a crisis via an external point (therapy, change of construct) — an analog of the “second revolution.”

4.5. Level of the Personality (scale: days – years – a whole life)

1. Unfolding of the future
   A person formulates a new image of themselves: “I will become a programmer,” “I will get out of depression,” “I will build a prism.” Insight, epiphany, decision.

2. Growth
   Study, practice, development of skills. First successes, growth of self-esteem. Habits and rituals of support for the new “I” are formed.

3. Stagnation / SOI
   The person retreats into SOI: “I have achieved, I am cool, I know how.” They stop learning and begin to teach others. Vices: pride, judgment, laziness, self-justification. The idea of life is inside the personality (“I am important, not the cause”). Thinking stagnates.

4. Disintegration
   Crisis: loss of job, breakup, depression, illness. The old personality “dies.” Bardo — neither old nor new. If there is an external point (third eye, new facade), reassembly at a new turn is possible. If not — degradation, alcohol, suicide, or quiet survival.
   Example: the creative crisis of an artist, the midlife crisis, the existential crisis after achieving a goal.

5. Comparative Analysis

The discovered regularity: the lower the level, the higher the speed of the cycle and the sharper the disintegration, but also the higher the availability of the external point (at the level of personality, anyone can in principle develop the third eye; at the level of civilization, it is a handful per millennium).

6. Conclusions and Applied Consequences

The “Wheel of Samsara” is nontrivial — it represents a fractal crystal demonstrating self-similarity at all scales of organization.

Probabilistic mathematics is inadequate for describing transitions between phases; what is needed is fractal dynamics supplemented by the physics of meanings — taking into account potentials, tensions, and catalytic effects.

The key control parameter is the presence of an external observer (a third point relative to the plane of the current level). It is precisely this that allows breaking the automatism of the transition “growth → stagnation → disintegration” and exiting to a new turn of the spiral.

The sense of one’s own importance (SOI) is the main poison that turns any construct into a dogma. The only antidote is carrying the idea of life beyond the personality (“there is a cause that requires me,” not “I am important because I am the bearer of the cause”).

The safeguard (the three-step stop-signal: “Am I adequate to myself? Am I adequate to the situation? Am I ready to act?”) has proven its effectiveness at all levels — from personality to community. Its formalization may become the first element of the future “physics of meanings.”

The developed scheme allows diagnosing the phase for any level in real time and taking measures (activating the external point, reducing SOI, launching the safeguard) before stagnation turns into irreversible disintegration.