Environment as Configuration

Environment as Configuration

Through the Lens of Observer-Dependent Theory of Everything (ODTOE) “The environment is not a separate object, but a mode of organization of accumulated results. It is not an entity. It is a configuration.”

1.1 Mathematical Formalization through ODTOE Pankratov Anton Sergeevich • February 2026

1.2 1. CENTRAL THESIS Environment is a fundamental category requiring precise definition: Environment ≠ simply sum of results. Environment = structured system of mutual action of these results. And further — definition: Environment is not a separate object, but a mode of organization of accumulated results. It is not an entity. It is a configuration. In reducing environment to “sum of results” five properties are lost: • Inertia — environmental resistance to changes • Density — saturation of environment with interactions • Selective Pressure — environment’s ability to select compatible elements • Self-Replication — environment’s ability to reproduce itself • Second Order — environment’s ability to generate new environments Each of these statements is direct consequence of ODTOE mathematical apparatus.

1.3 2. ENVIRONMENT = CONFIGURATION: CORRESPONDENCE WITH ODTOE 1.3.1

2.1. “It is not an entity. It is a configuration.”

This statement has precise formal equivalent in ODTOE.

In section 4.1 of theory, configuration space C is defined — complete metric space of all possible states of reality: C = {c1 , c2 , . . .},

d : C × C → R+

(formula 4.1)

Space C plays role of formal substrate — set of potential configurations, none of which is “actual” until act of observation. Correspondence: Environment Thesis

ODTOE Formalization

Environment is not entity

Configuration C ∈ C has no ontological status until act of observation Environment = point C in space C, realized by operator Ô R = Ô(Ψ) — reality generated by act of observation (Axiom A) C has metric d and structure — topological space C determined by potential U (C) and dynamics dC/dt (eq. 4.4)

Environment is configuration Environment derived from processes Environment ≠ sum of results Environment = mode of organization

Statement “environment is configuration” coincides with ontology of ODTOE, where reality R is configuration C ∈ C generated by collective observation.

1.4 3. FIVE PROPERTIES OF ENVIRONMENT: DERIVATION FROM ODTOE Reduction of environment to “sum of results” loses five properties. Each is formal consequence of ODTOE. 1.4.1

3.1. INERTIA

Inertia — environmental resistance to changes ODTOE introduces inertia of configuration I(C) as central quantity (Postulate P2): I(C) =

wj · Bj (C)

(formula P2.2)

Inertia is total cognitive coherence (belief) of all observers “invested” in current configuration. More people believe in current reality state, harder to change it. Reconfiguration speed inversely proportional to inertia:

v(C → C ′ ) =

α I(C)

(formula P2.1)

Environment with high I(C) resists changes: reconfiguration requires overcoming collective belief of observers in current state. Environmental inertia is not metaphor, but measurable quantity, proportional to sum wj · Bj . 1.4.2

3.2. DENSITY

Density — saturation of environment with interactions In ODTOE environmental density determined by two factors: (a) Number of observers N (t): by Postulate P1, multiverse cardinality |M | = K N (t) . More observers interact in environment, “denser” configuration space. (b) Coherence level S: by formula 4.5: S =1−

|Bi − Bj | n(n − 1)

High S with large n means group of observers tightly connected — their “beliefs” are close. Environmental density in ODTOE terms: Density = N (t) × S Product of observer count by coherence. Environment of 1000 coherent observers “denser” than 10,000 desynchronized. In dynamics equation (4.4): α dC =− · ∇U (C) + η(t) I(C) density determines steepness of potential ∇U (C) — denser environment “attracts” observers more strongly to specific configuration. 1.4.3

3.3. SELECTIVE PRESSURE

Selective Pressure — environment’s ability to select compatible elements In ODTOE selective pressure formalized through collective observation mechanism (Postulate P5): Pcoll (E) = 1 −

(1 − Bik )

(formula P5.1)

Observer with Bi incompatible with general configuration (Bi ≈ 0 regarding current R) contributes factor (1 − 0k ) = 1 to product — environment “does not notice” them.

Observer with high Bi compatible with configuration contributes factor (1 − Bik ) < 1, strengthening Pcoll . Environment “pulls them in.” Selective pressure operates automatically: environment amplifies coherent observers and weakens incoherent ones not through conscious selection but through structure of collective probability itself. Second mechanism — belief dynamics (D1.3). Observer whose expectations diverge from collective reality (sgn = −1) loses B over time. Environment “washes out” incompatible observers through negative feedback. 1.4.4

3.4. SELF-REPLICATION

Self-Replication — environment’s ability to reproduce itself In ODTOE self-replication follows from feedback between R and B (section 4.5 of theory): • By axiom (A): R = Ô(Ψ) — reality determined through B (through observation operator) • By equation (D1.3): dB = γ · sgn ·d · B(1 − B) — belief determined through R (observed reality) Self-consistent system: R → B → R → B → . . . Observer sees configuration R — their Bi adjusts (sgn = +1 when matching expectation). Adjusted Bi reinforces same configuration R. Environment reproduces itself through “reality ↔ belief” loop. = G(B, R(B)), where R(B) = F [Ô(B), S(B), I], generates attractors Nonlinear system dB — stable configurations toward which environment returns after perturbations. Self-replication is attractor pull. Logistic multiplier B(1 − B) in equation D1.3 makes B = 0 and B = 1 absorbing states. Environment with B ≈ 1 for all participants “locks up”: continuously reproduces itself, and exit is impossible without external intervention. 1.4.5

3.5. SECOND ORDER

Second Order — environment’s ability to generate new environments Property corresponds to Statement 3 of ODTOE (self-reference of theory): ODTOE contains itself as special case — it serves as one of Ntheories theories of everything and simultaneously describes conditions of its own existence. Environment is configuration C ∈ C. “Second-order environment” is configuration containing operators creating new configurations. Meta-configuration C ∗ : C ∗ = {C1 , C2 , . . . , Cn , Ô∗ } where Ô∗ is operator generating new configurations from Ψ.

Meta-environment (type 9 in classification of environments) — practical embodiment of this principle. By Postulate P6: Ntheories (t, S) = N0 (t) · (1 − S)m + 1 Second-order environment manages the parameter S itself, determining number of coexisting configurations. Meta-environment not merely exists in C — it projects new regions of C.

1.5 4. CONFIGURATION vs. ENTITY: WHY THIS DISTINCTION IS FUNDAMENTAL 1.5.1

4.1. Ontological Distinction

“Entity” presumes ontological independence — something existing regardless of observer. This contradicts Axiom (A): “Reality does not exist in definite state before act of observation.” “Configuration” is point in space C, realized by specific collective observation act. Depends on observers (their B, A, H), on coherence (S) and on history of previous observations (Λ). It is derivative. But configuration possesses its own dynamics. Equation (4.4) describes configuration evolution as movement in potential field with inertia and stochastic term. Configuration “resists” (through I(C)), “attracts” (through ∇U (C)) and “noises” (through η(t)). Derivative — but not passive. 1.5.2

4.2. Mode of Organization = Potential of Configuration

Environment is “mode of organization of accumulated results.” organization” is potential U (C):

In ODTOE “mode of

• Same “results” (observers, resources, knowledge) form different configurations C1 , C2 , . . . with different potentials U (C1 ) ̸= U (C2 ) • Potential determines which transitions “profitable”: system tends to minimum U (C), most stable organization • “Mode” is region of attraction (basin of attractor) in space C Environment ≠ sum of results: same results, organized differently (different potential U ), give different configuration, different environment, different reality. 1.5.3

4.3. Causal Logic

Environment has no independent source. Completely derived from observation processes. Causal chain in ODTOE:

Step

Process

Formalization

Observers

Act of observation

Configuration

Feedback

Self-Maintenance

Set {Oi } = {(Bi , Ai , Hi )} exists before configuration Operator Ôi (Ψ) = cj with probability P (cj | Oi ) R(t) = F [{Oi (t)}, S(t), I(C(t))] — reality as result dB/dt = γ · sgn ·d · B(1 − B) — influence on B Cycle R → B → R ensures self-replication

Environment is derivative (steps 1–3), but through feedback (step 4) begins influencing creators and reproduces itself (step 5). Derivative — but not passive.

1.6 5. FORMULA OF ENVIRONMENT IN ODTOE TERMS Formal definition of environment within ODTOE: DEFINITION. Environment is configuration C ∈ C, characterized by tuple: Environment = ⟨ C, I(C), U (C), S, N (t), Ô∗ ⟩ Component

Environmental Property

Formalization

Configuration

I(C)

Inertia

U (C)

Mode of organization

Density / Coherence

N (t)

Selective Pressure

Ô∗

Second Order

Point in C, realized by collective observation wj · Bj (C) — total belief in current state Potential determining landscape of permissible transitions ∑ ∥Bi − Bj ∥ — 1 − n(n−1) observer synchronization Number of observers + structure ∏ Pcoll = 1 − (1 − Bik ) Meta-operator: ability to generate new configurations

Environment is not “thing,” but six-dimensional “address” in space of all possible collective observation modes. Change to any of six parameters generates different environment.

1.7 6. CONCLUSION Alternative formulation: Configuration of accumulated and interconnected results of processes. In ODTOE terms — clarification: Environment is self-supporting configuration in space C, generated by collective observation, possessing inertia I(C), coherence S and potential U (C), ensuring its stability and replication. 1. Ontologies coincide: “environment = configuration, not entity” reproduces ODTOE ontology, where reality is point in C, lacking independent existence until observation. 2. All five properties derivable: inertia = I(C), density = N × S, selective pressure = Pcoll , self-replication = loop R ↔ B, second order = meta-operator Ô∗ . α 3. Environment as attractor: stable environment is attractor of dynamical system dC = − I(C) · ∇U (C) + η(t). Environment “attracts” observers to configuration and holds them.

4. Practical consequence: to create new environment, must change potential U (C) — restructure “landscape” of permissible configurations. Task of meta-environment (type 9) and cohort of influential (type 6). 5. Environment = managed reality: if environment is configuration, and configuration generated by observation, then environment design is reality design. ODTOE provides mathematical apparatus for this design.