Part II: Identity Thesis

Self-Model Salience

Introduction
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Self-Model Salience

The final dimension measures how prominently the self figures in the system’s own processing. Self-model salience is the fraction of action entropy explained by the self-model component:

SMt=I(ztself;at)/H(at)\mathcal{SM}_t = \MI(\latent^{\text{self}}_t; \action_t) / \entropy(\action_t)

Alternatively:

SMt=dim(zself)dim(ztotal)⋅activity(ztself)\mathcal{SM}_t = \frac{\text{dim}(\latent^{\text{self}})}{\text{dim}(\latent^{\text{total}})} \cdot \text{activity}(\latent^{\text{self}}_t)
Phenomenal Correspondence

High self-salience: Self-focused, self-conscious, self as primary object of attention. Low self-salience: Self-forgotten, absorbed in environment or task.

Self-Model Salience in Discrete Substrate

In a CA, a pattern’s “behavior” is its evolution. Let zself\latent^{\text{self}} denote cells that track the pattern’s own state (the self-model region). Then:

SM=I(ztself;st+1)H(st+1)\mathcal{SM} = \frac{\MI(\latent^{\text{self}}_t; \state_{t+1})}{\entropy(\state_{t+1})}

High SM\mathcal{SM}: the pattern’s evolution is dominated by self-monitoring. Changes in self-model strongly predict what happens.

Low SM\mathcal{SM}: external factors dominate; the self-model exists but doesn’t influence much.

The thesis predicts: self-conscious states (shame, pride) have high SM\mathcal{SM}; absorption states (flow) have low SM\mathcal{SM}. In CA terms, a pattern “in flow” has its self-tracking cells decoupled from its core dynamics—it acts without monitoring.

Self-Model Scope in Discrete Substrate

Beyond salience, there is scope: what does the self-model include?

In a CA, consider two gliders that have become “coupled”—their trajectories mutually dependent. Each glider’s self-model could have:

  • θnarrow\theta_{\text{narrow}}: Self-model includes only this glider. V=configs where THIS pattern persists\viable = {\text{configs where THIS pattern persists}}.
  • θexpanded\theta_{\text{expanded}}: Self-model includes both. V=configs where BOTH persist\viable = {\text{configs where BOTH persist}}.

Observable difference: with narrow scope, a glider might sacrifice the other to save itself. With expanded scope, it might sacrifice itself to save the pair.

Can scope expansion emerge dynamically? Can patterns that start with narrow scope “learn” to identify with larger structures? This would be the discrete-substrate analogue of the identification expansion discussed in the epilogue—V(S(θ))\viable(S(\theta)) genuinely reshaped by expanding θ\theta.

Salience vs. Scope

Self-model salience (SM\mathcal{SM}) measures how much attention the self-model receives—how prominent self-reference is in current processing. But there is another parameter: self-model scope—what the self-model includes.

Let S(θ)S(\theta) denote the self-model parameterized by its boundary scope θ\theta. Let V(S)\viable(S) denote the viability manifold induced by self-model SS. Then:

  • θnarrow\theta_{\text{narrow}}: SS includes only this biological trajectory ⇒\Rightarrow ∂V\partial\viable is located at biological death ⇒\Rightarrow persistent negative gradient
  • θexpanded\theta_{\text{expanded}}: SS includes patterns persisting beyond biological death ⇒\Rightarrow ∂V\partial\viable recedes ⇒\Rightarrow gradient can be positive even as death approaches

This is not metaphor. If the viability manifold is defined by what the system is trying to preserve, and if what the system is trying to preserve is determined by its self-model, then self-model scope directly shapes V(S(θ))\viable(S(\theta)). Expanding identification genuinely reshapes the existential gradient.

Salience and scope interact: high salience with narrow scope produces existential anxiety (trapped in awareness of bounded self approaching boundary). High salience with expanded scope produces something closer to what contemplatives describe as “witnessing”—self-aware but identified with something that doesn’t end where the body ends.