Theorem · Chain Position 99 of 346

HELL AS LOW-PHI ATTRACTOR

Matthew 25:41 - eternal fire; Revelation 20:14 - second death

** -1 states asymptote to minimal coherence (hell).

Scripture Bridge
Matthew 25:41 - eternal fire; Revelation 20:14 - second death: The theological grounding for this concept.

Connections

Objections & Responses
Objection: "Hell is a cruel divine punishment, not a natural consequence"
"You're just dressing up vindictive theology in scientific language. A loving God wouldn't create hell."
Response

This objection fundamentally misunderstands the axiom. [[099_T12.2_Hell-As-Low-Phi-Attractor|T12.2]] explicitly removes the "angry judge" model. Hell is not imposed by God; it is the natural attractor of a self-chosen trajectory. Consider: if you persistently fragment your consciousness through deception, self-deception, and anti-coherent behavior, you are constructing the low-Phi state yourself. God doesn't send you to minimal coherence; you asymptote there by your own dynamics. The attractor exists as a mathematical necessity of the phase space structure. Just as water flows downhill without being "punished" by gravity, sigma = -1 trajectories flow toward minimal Phi without being punished by God. The "cruelty" objection confuses consequences with punishments.

Objection: "Eternal suffering is disproportionate to finite sin"
"How can finite temporal actions warrant infinite consequences?"
Response

The objection assumes a ledger model of justice (finite sin = finite punishment). But [[099_T12.2_Hell-As-Low-Phi-Attractor|T12.2]] describes an asymptotic process, not a sentence. The low-Phi state is eternal because it is stable—once you reach the attractor basin's fixed point, there is no internal mechanism for escape. This is not punitive duration; it is dynamical stability. Consider: a ball at the bottom of a well stays there not because it's being held down as punishment, but because that's the stable equilibrium. Moreover, the "finite sin" framing is misleading—each moment of sustained sigma = -1 compounds the trajectory, much like compound interest. The integral of infinitesimal choices over time produces the asymptotic result. Finite causes can have infinite effects (consider a single initial condition determining an eternal trajectory in any dynamical system).

Objection: "Near-death experiences show universal love, not separation"
"NDEs consistently report unconditional acceptance, not judgment or hell."
Response

NDEs are valuable phenomenological data but must be interpreted carefully. First, NDE subjects return—by definition, they haven't reached the asymptotic limit. The trajectory hasn't completed. Second, the "unconditional love" experience may reflect initial conditions (the high-Phi Divine source), not final states. Third, hellish NDEs exist in the literature (Greyson, Ring) but are underreported due to social stigma. Fourth, the Theophysics model predicts that even hellish trajectories experience the Phi-gradient of the [[011_D2.2_Chi-Field-Properties|chi-field]] during transition—the "love" is the field itself, but the trajectory determines where you ultimately settle. The NDE is a snapshot of transition, not destination.

Objection: "Annihilationism is more coherent than eternal hell"
"If low-Phi means minimal consciousness, why not just cease to exist entirely?"
Response

This objection has genuine philosophical weight and represents one possible interpretation of "minimal coherence." However, [[099_T12.2_Hell-As-Low-Phi-Attractor|T12.2]] describes an attractor, not an annihilation point. The soul-field (psi_S) is conserved ([[083_A10.2_Soul-Conservation|A10.2]], [[084_D10.1_Soul-Field-Psi_S|D10.1]]), so total dissolution is not permitted by the conservation laws. What remains at the low-Phi attractor is a fragmented, decoherent state—not nothing, but almost nothing. The "second death" of Revelation may refer precisely to this: not non-existence, but existence stripped of integration, meaning, and coherence. Whether this constitutes "suffering" in any experiential sense depends on whether Phi = epsilon retains any qualia. The framework allows for a spectrum of interpretations, from conscious torment to mere informational persistence without integration.

Objection: "This determinism removes moral responsibility"
"If trajectories follow dynamical laws, where is free will?"
Response

The trajectory follows from the sign sigma, which is set by free moral choice ([[089_A11.2_Coherence-Morality-Identity|A11.2]], [[091_T11.1_Virtue-As-High-Phi|T11.1]], [[092_T11.2_Vice-As-Decoherence|T11.2]]). The dynamics are deterministic given the sign, but the sign itself is freely chosen at each moment. This is identical to standard physics: given initial conditions, trajectories are determined, but initial conditions can be set freely. The soul chooses sigma at each instant; the mathematics then unfolds. Moreover, the trajectory is not fixed until the asymptotic limit—repentance (sigma reversal) is always possible prior to the attractor. Free will operates within the dynamics, not outside them. The determinism objection confuses lawfulness with fatalism.

Physics Layer

Dynamical Systems Formalization

Phase space structure:

The soul exists in a phase space P with coordinates (Phi, sigma, t), where:

  • Phi in [0, Phi_max] is integrated information
  • sigma in {-1, +1} is moral sign (simplified from continuous [-1, +1])
  • t is proper time along the soul's worldline

Evolution equation:

\frac{d\Phi}{dt} = \sigma \cdot \Gamma(\Phi) - \lambda \cdot D(\Phi)

Where:

  • Gamma(Phi) is the coherence growth rate (positive, increasing in Phi)
  • D(Phi) is the natural decoherence rate (positive, decreasing in Phi)
  • sigma = -1 for vice-dominated trajectories

For sigma = -1:

\frac{d\Phi}{dt} = -\Gamma(\Phi) - \lambda D(\Phi) < 0 \quad \forall \Phi > 0

The trajectory is monotonically decreasing toward Phi = 0.

Fixed point analysis:

Setting dPhi/dt = 0 for sigma = -1:

-\Gamma(\Phi^) - \lambda D(\Phi^) = 0

Since both terms are negative, the only solution is Phi* = 0 (or epsilon, the minimal non-zero coherence).

Stability analysis:

Linearizing about Phi* = epsilon:

\frac{d(\delta\Phi)}{dt} = \left[-\Gamma'(\epsilon) - \lambda D'(\epsilon)\right] \delta\Phi

Since Gamma'(epsilon) > 0 and D'(epsilon) < 0, the coefficient is negative, confirming Phi* = epsilon is a stable attractor.

Mathematical Layer

Formal Attractor Definition

Definition (Attractor):

A set A in phase space P is an attractor if:

1. A is compact and invariant under the flow phi_t

2. There exists a neighborhood U of A such that for all x in U: d(phi_t(x), A) -> 0 as t -> infinity

3. A is minimal (no proper subset satisfies 1-2)

Theorem (Low-Phi Attractor Existence):

Given the evolution equation with sigma = -1, the set A = {(Phi, sigma, t) : Phi = epsilon, sigma = -1} is an attractor.

Proof sketch:

1. Show dPhi/dt < 0 for all Phi > epsilon when sigma = -1

2. Show Phi = epsilon is invariant (dPhi/dt = 0 at epsilon)

3. Show convergence: |Phi(t) - epsilon| -> 0 as t -> infinity

4. Minimality: A contains only the single fixed point

Defeat Conditions

To Falsify This

  1. **Demonstrate that negative moral trajectories do not decohere** - Show that sustained vice (sigma = -1) does not lead to decreased integrated information. This would require evidence that persistent deception, fragmentation, and anti-coherent behavior somehow maintains or increases Phi, contradicting both IIT predictions and the thermodynamic analogy of entropy increase in isolated systems.
  2. **Prove that low-Phi states are not stable attractors** - Show that minimal coherence configurations spontaneously self-organize into higher coherence without external input. This would contradict the second law of thermodynamics as applied to information systems and require demonstrating that fragmented states naturally re-integrate without coherent intervention.
  3. **Refute the bimodal outcome structure ([[094_A12.2_Bimodal-Outcome|A12.2]])** - Demonstrate that soul trajectories have a continuum of stable equilibria rather than two basins of attraction. This would require showing that intermediate coherence states are dynamically stable rather than transitional, contradicting the mathematical structure of the soul evolution equation.
  4. **Show that moral sign (sigma) does not couple to Phi dynamics** - Prove that ethical orientation has no effect on information integration. This would require severing the established connection between virtue/vice and coherence/decoherence, undermining the entire moral physics framework developed in prior axioms ([[091_T11.1_Virtue-As-High-Phi|T11.1]], [[092_T11.2_Vice-As-Decoherence|T11.2]]).
Cross-Domain Mappings
Domain Mapping
Physics Low-Phi attractor / entropy maximum
Theology Hell as separation / second death
Consciousness Fragmentation / disintegration
Quantum Decoherence basin
Scripture Matthew 25:41 - eternal fire; Revelation 20:14 - second death
Evidence IIT fragmentation states
Information Information dissolution

Bridge Count: 7