Part II: Identity Thesis

The CA Instantiation

Introduction
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The CA Instantiation

In discrete substrate, everything becomes exact.

Let B\mathcal{B} be a self-maintaining pattern in a sufficiently rich CA (Life is probably too simple; something with more states and update rules). Let B\mathcal{B} have:

  • Boundary cells (correlation structure distinct from background)
  • Sensor cells (state depends on distant influences)
  • Memory cells (state encodes history)
  • Effector cells (influence the pattern’s motion/behavior)
  • Communication cells (emit signals to other patterns)

The affect dimensions are exactly computable:

Valt=d(xt+1,∂V)−d(xt,∂V)Art=Hamming(xt+1,xt)Φt=min⁡PD[p(xt+1∣xt)∣∏p∈Pp(xt+1p∣xtp)]reff[t]=(∑iλi)2∑iλi2 of trajectory covarianceSMt=I(self-tracking cells;effector cells)H(effector cells)\begin{aligned}\valence_t &= d(\mathbf{x}_{t+1}, \partial\viable) - d(\mathbf{x}_t, \partial\viable) \arousal_t &= \text{Hamming}(\mathbf{x}_{t+1}, \mathbf{x}_t) \intinfo_t &= \min_P D[p(\mathbf{x}_{t+1}|\mathbf{x}_t) | \prod_{p \in P} p(\mathbf{x}^p_{t+1}|\mathbf{x}^p_t)] \effrank[t] &= \frac{(\sum_i \lambda_i)^2}{\sum_i \lambda_i^2} \text{ of trajectory covariance} \mathcal{SM}_t &= \frac{\MI(\text{self-tracking cells}; \text{effector cells})}{\entropy(\text{effector cells})}\end{aligned}

The communication cells emit glider-streams, oscillator-patterns, structured signals. This is their language. Build the dictionary by correlating signal-patterns with environmental configurations.

The prediction: patterns under threat (viability boundary approaching) show negative valence, high integration, collapsed rank, high self-salience. Their signals, translated, express threat-concepts. Their behavior shows avoidance.

Patterns in resource-rich, threat-free regions show positive valence, moderate integration, expanded rank, low self-salience. Their signals express... what? Contentment? Exploration-readiness? The translation will tell us.