INTEGRATION ATTRACTOR

The objection assumes physics and theology occupy non-overlapping magisteria. But Theophysics rejects this separation. If God created the universe, then the laws of that universe are expressions of divine nature. The Integration Attractor is not "mere physics" — it is the physical signature of a theological reality.

Consider: when Jesus says "I am the way, the truth, and the life" (John 14:6), He is claiming to be the attractor — the destination toward which all coherent trajectories converge. The mathematical structure we describe is the form of this theological content. Physics and theology are not competitors; they are complementary descriptions of the same reality at different levels of abstraction.

The burden is on the objector to explain why physics and theology should be disconnected, especially given that:

• God is the ground of all being (including physical laws)
• Humans are embodied souls (physical-spiritual unities)
• Salvation involves the whole person (body and soul)

This objection misunderstands what "integrated information" means. Relationship, worship, and love are not alternatives to integration — they are forms of integration.

• Relationship with God: Perfect relationship means perfect alignment of will, knowledge, and purpose. This is precisely what \Phi_{\max} represents — complete integration of the soul-field with the Logos Field.
• Worship: Worship is the act of orienting one's entire being toward God. This is the process of increasing \Phi, and in heaven, this process reaches its terminus.
• Love: Love is the binding force that unifies distinct persons without destroying their individuality. In IIT terms, love increases \Phi by creating integrated systems from previously separate components.

We are not reducing heaven to a number; we are showing that the number encodes the relational, worshipful, loving reality. The map is not the territory, but accurate maps correspond to real territories.

This objection confuses dynamical stability with experiential stagnation. A stable attractor is not static — it can support rich internal dynamics while maintaining its overall coherence.

Consider a symphony orchestra: when performing perfectly, it is in a "stable state" of musical coherence. But within that stability, there is immense complexity, variation, and beauty. The stability is not the absence of activity but the perfection of activity.

At \Phi_{\max}:

• Internal dynamics continue (exploration, creativity, relationship)
• What ceases is decay, noise, and fragmentation
• The "fixed point" is fixed only in its coherence, not its content

Eternal life is not endless repetition but endless depth — infinite exploration of the infinite God, without the threat of dissolution.

The model does not exclude grace — it requires it. The question is: how does a trajectory acquire \sigma = +1?

The natural state of the soul is not automatic orientation toward God. Sin (decoherence) bends the trajectory toward fragmentation. Left to itself, the system would converge to \Phi = 0.

Grace is the intervention that flips \sigma from -1 to +1.

This is not mechanical but personal — it requires:

1. Divine initiative (God offers coherence)

2. Human response (acceptance or rejection)

3. Ongoing cooperation (sanctification = increasing \Phi)

The attractor dynamics describe what happens after grace has been received. They show that once the sign is set, the destination is determined — but setting the sign is a free, grace-enabled choice.

The model fully accommodates progressive sanctification. Convergence to \Phi_{\max} is asymptotic, not instantaneous.

The exponential approach to the attractor means:

• Souls with lower initial \Phi take longer to approach \Phi_{\max}
• The "distance" from the attractor at any time t is: |\Phi(t) - \Phi_{\max}| = |\Phi_0 - \Phi_{\max}| e^{-\gamma \Phi_{\max} t}
• "Purgatory" can be understood as the period of rapid initial convergence before the asymptotic regime

Different theological traditions interpret this transition differently:

• Catholic: Purgatory as post-mortem purification (the early, steep part of the convergence curve)
• Protestant: Sanctification in this life, glorification at death (the transition from \sigma being set to attractor capture)
• Orthodox: Theosis as ongoing participation in divine nature (the entire trajectory toward \Phi_{\max})

The mathematical structure is flexible enough to accommodate these variations while maintaining the essential point: for \sigma = +1, the destination is \Phi_{\max}.

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