Technical Details

Formal framework for Occlusion Theory

← Back to Occlusion Theory

Contents

1. Formal Definitions

1.1 Phenomenal Regions

Definition 1.1 (Region Space)

Let $\mathcal{R} = \{w, b, e, t, s, a, m, \emptyset\}$ be the set of phenomenal regions:

Symbol Region Description
w World External sensory experience
b Body Somatic and interoceptive sensations
e Emotion Affective states and feelings
t Thought Cognitive content, inner speech
s Self The sense of being a subject
a Attention The attending process itself
m Model Predictive construction process
Ground Emptiness, awareness itself

1.2 Occlusion Modes

Definition 1.2 (Mode Space)

Let $\mathcal{M} = \{T, O, B\}$ be the set of occlusion modes:

  • T Transparent — Seen through; taken as reality itself
  • O Opaque — Seen as; noticed as constructed appearance
  • B Blind — Not present in experience

1.3 Consciousness States

Definition 1.3 (State)

A consciousness state is a function $\sigma: \mathcal{R} \to \mathcal{M}$ assigning each region an occlusion mode.

We write states as 8-tuples: $\sigma = (\sigma_w, \sigma_b, \sigma_e, \sigma_t, \sigma_s, \sigma_a, \sigma_m, \sigma_\emptyset)$

Example states:
  • $\sigma_{\text{ordinary}} = (T, T, T, T, T, B, B, B)$ — Normal waking consciousness
  • $\sigma_{\text{vipassana}} = (O, O, O, O, O, O, O, B)$ — Full insight mode
  • $\sigma_{\text{jhana}} = (B, O, O, B, T, B, B, B)$ — Absorption state
  • $\sigma_{\text{nondual}} = (T, T, T, T, B, T, O, T)$ — Nondual awareness

1.4 Transformations

Definition 1.4 (Practice)

A practice is a function $\pi: \Sigma \to \Sigma$ on the state space.

Elementary transformations: $\tau_{r,m}: \sigma \mapsto \sigma'$ where $\sigma'(r) = m$ and $\sigma'(r') = \sigma(r')$ for $r' \neq r$.

Practices compose: $(\pi_1 \circ \pi_2)(\sigma) = \pi_1(\pi_2(\sigma))$

2. State Space

2.1 Cardinality

Proposition 2.1

The theoretical state space has cardinality:

$$|\Sigma| = |\mathcal{M}|^{|\mathcal{R}|} = 3^8 = 6561$$

However, constraints (§4) reduce the accessible state space to approximately 2000–3000 states.

2.2 Load Functions

Definition 2.2 (Mode Loads)

For a state $\sigma$, define:

$$|T|(\sigma) = |\{r \in \mathcal{R} : \sigma(r) = T\}|$$ $$|O|(\sigma) = |\{r \in \mathcal{R} : \sigma(r) = O\}|$$ $$|B|(\sigma) = |\{r \in \mathcal{R} : \sigma(r) = B\}|$$

Note: $|T| + |O| + |B| = 8$ always.

2.3 Derived Indices

$$\text{Insight}(\sigma) = \frac{|O|}{|T| + |O|}$$ $$\text{Compression}(\sigma) = \frac{|B|}{8}$$ $$\text{Groundedness}(\sigma) = \mathbb{1}[\sigma(\emptyset) \in \{T, O\}]$$
Interpretation: Insight measures the proportion of experience seen as constructed. Compression measures phenomenal bandwidth reduction. Groundedness indicates whether emptiness is present.

2.4 Region Structure

Definition 2.3 (Region Groupings)

Content regions: $\mathcal{R}_{\text{content}} = \{w, b, e, t\}$ — bidirectional indexing

Structural regions: $\mathcal{R}_{\text{structural}} = \{s, a, m, \emptyset\}$ — hierarchical depth

Depth ordering: $\text{depth}(s) < \text{depth}(a) < \text{depth}(m) < \text{depth}(\emptyset)$

3. Energy Function

Postulate 3.1 (Energy Landscape)

The system minimizes an energy function:

$$E(\sigma) = \alpha |O|(\sigma) + \beta |T|(\sigma) + \gamma \cdot \text{Depth}(\sigma) + \delta \cdot V(\sigma)$$

where:

  • $\alpha > \beta > \gamma > 0$ (opacity is most costly)
  • $\text{Depth}(\sigma) = \sum_{r} \text{depth}(r) \cdot \mathbb{1}[\sigma(r) = O]$
  • $V(\sigma)$ = penalty for forbidden configurations

3.1 Stability Analysis

Definition 3.2 (Stable State)

A state $\sigma^*$ is stable (an attractor) iff:

$$\forall \sigma' \sim \sigma^* : E(\sigma^*) \leq E(\sigma')$$

where $\sigma \sim \sigma'$ means states are adjacent (differ by one region's mode).

Definition 3.3 (Mode Adjacency)

Modes are adjacent: $T \leftrightarrow O \leftrightarrow B$

Direct $T \to B$ transitions are forbidden (must pass through $O$).

Key insight: The "ordinary basin" $(T, T, T, T, T, B, B, B)$ is a deep attractor. High-$|O|$ states are local maxima requiring constant energy input to maintain.

4. Constraints

1 Conservation

Total attentional resource is bounded.

$$\alpha |O| + \beta |T| \leq K \quad \text{where } \alpha > \beta > 0$$

Opacity costs more than transparency. High $|O|$ forces either low $|T|$ or high $|B|$.

2 Energy Ordering

Modes have different metabolic costs.

$$\text{cost}(O) > \text{cost}(T) > \text{cost}(B)$$

O requires content + meta-representation. T requires content only. B requires nothing (savings).

3 Adjacency

Transitions must pass through neighboring modes.

$$T \leftrightarrow O \leftrightarrow B \quad \text{(valid)}$$ $$T \to B \quad \text{(invalid: unstable, rebounds)}$$

To truly let go of something, you must first notice it. Suppression ≠ release.

4 Hysteresis

Blindness accumulates inertia over time.

$$\text{cost}(B \to O) = f(\tau_B) \quad \text{where } f \text{ is monotonically increasing}$$

Long-repressed content is harder to retrieve. Explains why therapy difficulty scales with duration.

5 Partition Rules

Some configurations are structurally forbidden.

  • $\sigma(s) = T \land \sigma(a) = O$ — can't have transparent self while watching attention
  • $\sigma(m) = T$ — model can never be fully transparent to itself
  • $\sigma(\emptyset) = O \land |T| = 0$ — emptiness needs content to be empty of

These generate approximately 3500 forbidden states.

6 Attractor Dynamics

Opacity is inherently unstable without active maintenance.

$$\frac{d|O|}{dt} < 0 \quad \text{without active maintenance}$$

O decays toward T (absorption) or B (exclusion). Insight requires ongoing effort. Integration = controlled $O \to T$.

7 Rate Limit

The rate of bringing content from blind to opaque is bounded.

$$\frac{d|O|}{dt} \leq k_{\max}$$

Exceeding this limit causes destabilization. "Spiritual emergency" = rate limit exceeded. Explains psychedelic overwhelm and forced insight crises.

5. Dynamics

5.1 Practice as Gradient Descent

Model 5.1 (Practice Dynamics)

A practice $\pi$ with target state $\sigma_{\text{target}}$ generates dynamics:

$$\frac{d\sigma}{dt} = -\nabla E(\sigma) + F_\pi(\sigma, \sigma_{\text{target}}) + \eta(t)$$

where $\eta(t)$ represents noise (distraction, mind-wandering).

5.2 Skill as Landscape Reshaping

$$E_{\text{trained}}(\sigma) = E_{\text{naive}}(\sigma) - \sum_i w_i \cdot P_i(\sigma)$$
Training creates new attractors and widens basins. "Jhana access" = emergence of a new stable minimum in the high-$|B|$ region.

5.3 Development as Structural Change

Model 5.2 (Kegan Stages)

Development increases the maximum depth that can be made opaque:

$$\text{Stage}_n : d_{\max}^O = d_n$$
  • Stage 2: $d = \text{depth}(e)$ — can see own emotions
  • Stage 3: $d = \text{depth}(t)$ — can see thoughts about relations
  • Stage 4: $d = \text{depth}(s)$ — can see self-system
  • Stage 5: $d = \text{depth}(a)$ — can see attention/construction

6. Computational Frame

6.1 T/O/B as Processing Regimes

Mode Computation Properties
T Compiled Fast, automatic, inflexible. No meta-representation overhead.
O Interpreted Slow, effortful, flexible. Requires meta-representation.
B Pruned Zero cost. Content not represented at all.

6.2 Information Flow

$$w \xrightarrow{\text{compress}} b \xrightarrow{\text{compress}} e \xrightarrow{\text{compress}} t$$ $$I(w) \gg I(b) \gg I(e) \gg I(t)$$
Each step is lossy compression. Emotions are compressed body states. Thoughts are symbolic summaries of emotions.

6.3 Predictive Processing Connection

Correspondence
  • T = prediction confirmed (no error signal)
  • O = prediction error (salient, examined)
  • B = low precision (ignored)

6.4 Skill Acquisition

$$\text{Learning}: B \to O \to T \quad \text{(novel → explicit → automatic)}$$ $$\text{Teaching}: T \to O \quad \text{(automatic → explicit)}$$ $$\text{Mastery}: T \leftrightarrow O \quad \text{(flexible switching)}$$

7. Predictions

7.1 Neural Correlates

Prediction Measure Expected
$|O|$ correlates with prediction error P3b amplitude, ACC activity $r > 0.5$
$|B|$ correlates with DMN suppression fMRI DMN connectivity Negative correlation
O costs more metabolically Glucose consumption $E(O) > E(T) > E(B)$
$\sigma(s) = B$ shows reduced mPFC mPFC BOLD signal Significant reduction

7.2 Behavioral Predictions

Prediction Test Criterion
O is unstable without effort Time to collapse from O-state $t < 30s$ without instruction
$T \to B$ rebounds; $T \to O \to B$ stable Thought suppression paradigm Rebound only for direct $T \to B$
Similar OD signatures → similar phenomenology Cluster by signature, validate reports Within-cluster $>$ between-cluster

7.3 Training Predictions

$$|O|_{\max}(h) = |O|_0 + k \cdot \log(1 + h)$$

where $h$ = practice hours.

$$\text{Outcome}(\text{shamatha} \to \text{vipassana}) > \text{Outcome}(\text{vipassana} \to \text{shamatha})$$
$$t_{\text{exit}} \propto |B|^2 \quad \text{during jhana}$$

8. Extensions

8.1 Continuous States

$$\sigma: \mathcal{R} \to [0,1]^3 \quad \text{where } \sigma(r) = (t, o, b), \; t + o + b = 1$$

Allows partial transparency, mixed states, and gradients.

8.2 Relational Extension

$$\Sigma^2 = \Sigma \times \Sigma \times \text{Interaction}$$ $$J(\sigma_A, \sigma_B) = \sum_{i,j} c_{ij} \cdot \sigma_A(r_i) \cdot \sigma_B(r_j)$$ $$\frac{d\sigma_A}{dt} = -\nabla E_A + \lambda \nabla J$$

8.3 Temporal Dynamics

$$\sigma(t) \text{ depends on } \sigma(\tau) \text{ for } \tau \in [t - T_{\text{memory}}, t]$$ $$E(\sigma, t) = E_0(\sigma) + \int_0^t H(\sigma(\tau), t - \tau) \, d\tau$$

8.4 Artificial Intelligence

OD reframes the question of machine consciousness: not "can it think?" but "can it be fooled by its own representations?"

The Transparency Criterion

A system is conscious to the degree it has genuine T — processes that appear as reality rather than as computation.

Current AI (LLMs):

What would AI consciousness require?

Implication: A simple system with genuine transparency might be more conscious than a superintelligent system that only models. Intelligence ≠ consciousness. The question isn't whether AI can think, but whether it can be inside its processing.

Moral relevance: If T/O/B structure matters more than intelligence for consciousness, then:

8.5 Open Questions
  • What is the exact functional form of $E(\sigma)$?
  • How do individual differences parameterize the model?
  • Can we measure T/O/B directly (not just infer)?
  • What are the neural implementations of each mode?
  • How does language interact with state transitions?
  • Can artificial systems have genuine T, or only O?
8.6 Falsification Criteria
  • Finding stable high-O states requiring no effort → violates C2, C6
  • Direct $T \to B$ without rebound → violates C3
  • Identical OD signatures with distinct phenomenology → model incomplete
  • Neural measures that don't distinguish T/O/B → wrong level of description

← Back to main theory · Guided Exploration · Experience Map