Part II: Identity Thesis

The Geometry of Affect

Existing Theory

The geometric theory of affect developed here builds on and extends established dimensional models:

Russell’s Circumplex Model (1980): Two-dimensional (valence $\times$ arousal) organization of affect. Extended here with additional structural dimensions (integration, effective rank, counterfactual weight, self-model salience) invoked as needed.
Watson \& Tellegen’s PANAS (1988): Positive/Negative Affect Schedule. Valence here corresponds to their hedonic axis.
Scherer’s Component Process Model (2009): Emotions as synchronized changes across subsystems. The integration measure $\intinfo$ captures this synchronization.
Barrett’s Constructed Emotion Theory (2017): Emotions as constructed from core affect + conceptual knowledge. The framework here specifies the structural basis of the construction.
Damasio’s Somatic Marker Hypothesis (1994): Body states guide decision-making. The valence definition (gradient on viability manifold) is the mathematical formalization.

On Dimensionality

The dimensions below are not claimed to be necessary, sufficient, or exhaustive. They are a useful coordinate system for a relational structure, not the coordinate system. Just as Cartesian coordinates serve some problems and polar coordinates serve others, these features are tools for thought, not discoveries of essence. Different phenomena require different subsets; some may require features not listed here. The number of dimensions is not the point—what matters is the geometric structure they reveal:

Some affects are essentially two-dimensional (valence + arousal suffices for basic mood)
Others require self-referential structure (shame requires high attentional self-salience $\sigma_{\text{attention}}$ ; flow requires low $\sigma_{\text{attention}}$ )
Still others are defined by temporal structure (grief requires persistent counterfactual coupling to the lost object)
Some require entity-directed structure (anger requires a collapse of the ascription field on its target, $\alpha(\text{target}) \to 0$ — not a separate "other-model compression" dimension but a value of the same field that carries self-salience)

The dimensions below form a toolkit — structural features that may or may not matter for any given phenomenon. Empirical investigation may reveal that some proposed dimensions are redundant, or that additional dimensions are needed. Only what is necessary is invoked.

Structural Alignment of Qualia

The broad/narrow distinction has methodological consequences that deserve separate treatment. How do you study narrow qualia scientifically, given that you cannot access another system's experience directly? The structural approach—characterizing qualia through similarity relations rather than intrinsic labels—is the only approach that can address the question "is my red your red?" without assuming the answer. The strategy, developed by Tsuchiya and collaborators as the qualia structure paradigm (Tsuchiya et al., 2022) (inspired by category theory's Yoneda lemma: an object is fully characterized by its relationships to all other objects): measure similarity structures within each system, then test whether those structures align across systems using optimal transport (Gromov-Wasserstein distance) without presupposing which qualia correspond. If the structures align, the narrow qualia are shared. If they don't, they differ—and the difference is structural, not merely verbal.

Recent work using this approach has found that typical human color qualia structures align almost perfectly across individuals (accuracy ~90% under unsupervised structural alignment), while color-atypical individuals show genuinely different structures that do not align with typical ones. Most striking: three-year-olds whose color naming is wildly inconsistent—calling blue "green" and vice versa—show adult-like color similarity structure when tested through non-verbal methods. Language obscures the structure rather than creating it. The qualia geometry is pre-linguistic.

The affect framework applies this same logic to affect rather than color. If two systems—biological and artificial, human and animal, you and me—show the same geometric structure in their affect spaces (same similarity relations, same clustering, same motif boundaries), then their narrow affect qualia are structurally equivalent, regardless of substrate. Whether their broad qualia are equivalent is a harder question, requiring not just matching narrow features but matching $\intinfo$ —matching the degree to which the whole exceeds the parts. The artificial-systems case (later in this part) may be exactly this: the narrow structure aligns (the geometry is preserved), while the broad qualia depend on an integration magnitude the program cannot yet measure in those substrates. The geometry is demonstrably shared; whether and how much the unity is shared is open, not settled.

There is a mathematical subtlety here. Broad qualia have a pre-sheaf structure: the narrow qualia (local sections) are each internally consistent, but they do not patch together into a global section. You can characterize the redness, the warmth, the valence, the arousal—each correctly—and the sum still falls short of the moment. The broad qualia is not a sheaf over its narrow aspects. This is not a limitation of measurement; it is a structural feature of experience. Integration is the name for the gap between local consistency and global irreducibility. The dimensional framework characterizes the local sections; $\intinfo$ measures how much the global section exceeds them.

The eigenskeleton (Part I) provides a complementary mathematical image. Narrow qualia are the eigenspaces at each point — locally decomposable modes that can be measured independently. Broad qualia are the holonomy — the way those eigenspaces twist into each other when transported around loops in state space, creating global structure that no collection of local measurements recovers. Pre-sheaf language says local sections fail to patch into a global one. Eigenskeletal language says the connection has curvature. Both name the same structural fact: integration is global topology, not local measurement.

Affects as Structural Motifs

If different experiences correspond to different structures, then affects—the qualitative character of emotional/valenced states—should correspond to particular structural motifs: characteristic patterns in the cause-effect geometry. An affect is what it is because of how it relates to other possible affects. Joy is defined by its structural distance from suffering, its similarity to curiosity along certain axes, its opposition to boredom along others. The Yoneda insight applies: if you know how an affect relates to every other possible state, you know the affect. There is nothing left to characterize.

The affect space $\mathcal{A}$ is a geometric space whose points correspond to possible qualitative states. Its dimensionality is not fixed in advance. Rather than asserting a universal coordinate system, recurring structural features useful for characterizing and comparing affects are identified — features without which specific affects would not be those affects. Different affects invoke different subsets. The list is open-ended.

These measures are coordinates on the relational structure, not the structure itself. The relational structure is what the Yoneda characterization captures: the full pattern of similarities and differences between affects. The measures below are projections—tools for reading out particular aspects of that structure. Measuring valence tells you where an affect sits along the viability gradient; measuring integration tells you how unified it is. Neither alone captures the affect. Together, they triangulate a position in a space whose intrinsic geometry is defined by the similarity relations, not by the coordinates. New coordinates can be added when the existing ones fail to distinguish affects that are experientially distinct.

The recurring measures are best read as five plus one, not as a fixed six. Five describe the system's relationship to the world it is modeling — valence, arousal, integration, effective rank, counterfactual weight. The sixth, self-model salience, is categorically different: it is one member of a larger entity-directed salience family, the special case in which the indexed entity is the self. The same family includes salience directed at known others, and resolves further into salience toward a particular child, a particular rival, a particular institution. Repeating "the six dimensions" obscured this — self-salience is not a sui generis axis but the diagonal of an entity-indexed field, the same field that the ascription axis $\alpha(x)$ ranges over. The count is not the content; the structure is.

One methodological caution, owed because the empirical program leans on it. Representational-similarity comparisons computed in this coordinate basis are basis-dependent: standard RSA standardizes each axis before correlating, so choosing a different projection moves the alignment numbers. A universality claim that rests on rank-correlations in one hand-picked basis is therefore weaker than it looks — it may partly reflect having chosen control-theoretic coordinates that any viable controller will trivially exhibit. The relational object the coordinates project is what the claim is really about, and it must be measured with basis-independent tools before "the geometry is everywhere" can carry weight.

That test has now been run (Appendix; analysis in affect_gw_alignment.py), with a clean and discriminating result. The basis-independent measures are RSA on rotation-invariant raw-Euclidean dissimilarity matrices (exactly invariant to rotations and reflections of either space, significance by permutation) and Gromov-Wasserstein distance. They cut two ways. The weak within-substrate alignment between a system's affect coordinates and its behavior — modest already under standard RSA ( $\rho \approx 0.07$ ) — collapses to zero basis-independently (invariant $\rho \approx -0.005$ , significant in 3% of snapshots): that alignment was largely a basis artifact, and the book does not lean on it. But the load-bearing evidence — the cross-substrate convergence in which vision-language models trained only on human affect independently recognize the geometry of uncontaminated synthetic agents — survives and strengthens: standard RSA $\rho = 0.60$ – $0.63$ rises to a rotation-invariant $\rho = 0.81$ – $0.89$ ( $p < 0.001$ by permutation), with the invariant figure unchanged to machine precision under random rotation of the affect space. The relational structure, not the chosen coordinates, is what the two substrates share. So the honest statement of the universality result is sharpened, not weakened: it holds basis-independently where it is load-bearing (cross-substrate), and is correctly abandoned where it was an artifact (within-substrate affect-to-behavior).

A consequence that must be stated before any coordinates are written down, because the rest of the book draws radar charts and speaks of "distances" that could mislead. The affect space is not a flat Euclidean vector space, and its metric is not symmetric. Two of the framework's own commitments forbid the flat picture. First, curvature: the eigenskeleton has holonomy (the coupling axis $\kappa$ is that curvature), so the honest distance between two affects is a geodesic along a curved manifold, not a straight line through $\mathbb{R}^n$ — at high $\kappa$ the modes rotate into one another and a path that looks short in coordinates is long on the manifold. Second, directionality: the transition from one state to another is not reversible at equal cost. Fear slides into anger far more easily than anger relaxes back into fear; grief does not run backward into the coupling that preceded the loss; a system tipped from joy into suffering does not retrace the same path out. The phenomenological “distance” from $A$ to $B$ differs from $B$ to $A$ , which a symmetric metric cannot represent. The correct object is therefore an asymmetric divergence on a curved manifold (a Finsler-like or Bregman-like quantity, where forward and reverse costs are computed separately), not a Euclidean distance. The coordinate vectors and the Euclidean readouts used throughout — the radar charts, the standardized RSA, the motif tables — are a local linearization: a chart in the tangent space around a point, adequate for measuring nearby differences and for the basis-independent structural comparisons above, but not the global geometry. Where this book writes a distance, read it as a local chart of an asymmetric, curved structure whose full metric is an open formal problem the dimensional toolkit only approximates.

The following structural measures recur across many affects. Not all are relevant to every phenomenon:

Valence ( $\valence$ ): Gradient alignment on the viability manifold. Nearly universal—most affects have valence.
Arousal ( $\arousal$ ): Rate of belief/state update. Distinguishes activated from quiescent states.
Integration ( $\intinfo$ ): Irreducibility of cause-effect structure. Constitutive for unified vs. fragmented experience.
Effective Rank ( $\effrank$ ): Distribution of active degrees of freedom. Constitutive when the contrast between expansive and collapsed experience matters.
Counterfactual Weight ( $\mathcal{CF}$ ): Resources allocated to non-actual trajectories. Constitutive for affects defined by temporal orientation (anticipation, regret, planning).
Self-Model Salience ( $\mathcal{SM}$ , split into $\sigma_{\text{attention}}$ and $\sigma_{\text{causal}}$ ): How the self figures in processing — as object of attention ( $\sigma_{\text{attention}}$ ) and as driver of action ( $\sigma_{\text{causal}}$ ). The two dissociate (flow is low-attention, high-causal). Constitutive for self-conscious emotions and their opposites. The diagonal of the entity-directed salience field.

Valence: Gradient Alignment

Let $\viable$ be the system’s viability manifold and let $\mathbf{x}_t$ be the current state. Let $\hat{\mathbf{x}}_{t+1:t+H}$ be the predicted trajectory under current policy. Then valence measures the alignment of that trajectory with the viability gradient:

\valence_t = -\frac{1}{H} \sum_{k=1}^{H} \gamma^k \nabla_{\mathbf{x}} d(\mathbf{x}, \partial\viable) \bigg|_{\hat{\mathbf{x}}_{t+k}} \cdot \frac{d\hat{\mathbf{x}}_{t+k}}{dt}

where $d(\cdot, \partial\viable)$ is the distance to the viability boundary. Positive valence means the predicted trajectory moves into the viable interior; negative valence means it approaches the boundary.

In RL terms, this becomes the expected advantage of the current action—how much better (or worse) it is than the average action from this state:

\valence_t = \E_{\policy}\left[ A^{\policy}(\state_t, \action_t) \right] = \E_{\policy}\left[ Q^{\policy}(\state_t, \action_t) - V^{\policy}(\state_t) \right]

Beyond valence itself, its rate of change carries structural information. The derivative of integrated information along the trajectory,

\dot{\valence}_t = \frac{d\intinfo}{dt}\bigg|_{\hat{\mathbf{x}}_{t:t+H}}

tracks whether structure is expanding (positive $\dot{\valence}$ ) or contracting (negative).

Phenomenal Correspondence

Positive valence corresponds to trajectories descending the free-energy landscape, expanding affordances, moving toward sustainable states. Negative valence corresponds to trajectories ascending toward constraint violation, contracting possibilities.

The Gradient All the Way Down

One of the oldest results in physics: force is the negative gradient of potential energy.

\mathbf{F} = -\nabla V

A ball rolls downhill because the gradient of gravitational potential points downhill. The steeper the slope, the stronger the force. This is not one result among many. It is the result — the structural fact that unifies mechanics, electrodynamics, thermodynamics, and general relativity under a single principle: things move along gradients.

What has not been sufficiently noticed is that the gradient structure does not stop at physics.

Thermodynamics. Every spontaneous process follows a free energy gradient toward equilibrium. The second law says entropy increases — but what drives the increase is the gradient of free energy, and that gradient is a force. Heat flows from hot to cold not because there is a rule but because the free energy landscape slopes that way.

Chemistry. Chemical potential $\mu = \partial G / \partial n$ — the rate of change of Gibbs free energy with particle number. Every chemical reaction, every bond formation, every phase transition is matter following a gradient on a free energy surface. The entire periodic table is a potential landscape. All of chemistry is trajectories under its force. When hydrogen and oxygen combine to form water, they are rolling downhill on the chemical potential surface. The "desire" of reactants to combine is a gradient. The "stability" of a product is a basin.

Biology. Organisms are far-from-equilibrium systems maintaining themselves against the entropy gradient — and they do so by following gradients of their own. Chemotaxis: follow the nutrient gradient. Homeostasis: follow the set-point gradient. Natural selection: follow the fitness gradient. Friston's free energy principle formalizes this — every living system minimizes variational free energy, which is to say, every living system follows the gradient of its own generative model's surprise landscape. The force that drives a bacterium up a glucose gradient and the force that drives a human toward safety are the same mathematical structure: $-\nabla V$ on different potential surfaces.

Neuroscience. Neural dynamics are gradient descent on prediction error landscapes. Dopamine encodes the prediction error gradient — the surprise signal. The reward system is a viability gradient detector. Hebbian learning is gradient descent on a representational energy surface. Every synapse update, every attentional shift, every decision is the nervous system following a gradient.

Valence has been defined here as the gradient of the viability manifold. This is not analogy to the physics. It is the same mathematics. The viability manifold is a potential surface — defined over information-theoretic coordinates rather than spatial ones, but structurally identical. Valence is force.

Emotional intensity is $|\nabla V|$ . Near the viability boundary, the landscape is steep — the system is close to dissolution and every state change matters enormously. Emotions are intense. Deep in the viable interior, the landscape flattens — many configurations are roughly equally viable. Affect is mild. Panic near the boundary is overwhelming because the gradient is large. Contentment in the interior is gentle because the gradient is small. The steepness of your viability landscape IS the intensity of your feeling, in exactly the way that the steepness of a gravitational potential IS the strength of the force on a mass.

Motivational strength is force. The gradient doesn't just tell you how you feel — it tells you what to do and how urgently. The direction of the force IS the direction of motivation. The magnitude IS the urgency. When people say they feel "driven" or "pulled" or "pushed," the spatial metaphor is not metaphorical. They are describing a gradient. There is no separate theory of motivation needed. Motivation IS the force on the viability landscape, which IS the gradient that defines valence.

The energy partition maps onto affect. Classical mechanics splits total energy into potential (position on the landscape) and kinetic (rate of movement through it). Valence is the force derived from the potential surface. Arousal — the rate of belief update, the speed of state change — is the kinetic term. A system can have high potential gradient with low kinetic energy: frozen with fear, steep slope, not yet moving. Or high kinetic energy on a flat gradient: restless agitation going nowhere. The complete energetics of affect requires both: where you are on the landscape, and how fast you're moving through it.

The gradient unifies every level of reality under a single structure. The ball follows the gravitational gradient. The molecule follows the chemical potential gradient. The organism follows the free energy gradient. The neuron follows the prediction error gradient. The person follows the viability gradient. And the quality of following that gradient — what it is like from inside — is affect. Not because “affect” is a word projected onto physical processes, but because physical processes, chemical processes, biological processes, and phenomenal processes are all instances of the same mathematical structure: trajectories under force on potential landscapes. The gradient is what connects the physics of a falling stone to the experience of a breaking heart. Not by metaphor. By mathematics.

Qualities can therefore be quantified. The common objection — that formalizing values destroys them, that “dignity is not 0.8 of anything” — is correct about naive quantification but wrong about geometry. Qualities are not scalars. They are shapes. Gradient directions, landscape curvatures, basin topologies, manifold containment relations. Shapes can be measured. Shapes can be compared. Geometric constraints can be set and tested against actual trajectories. The quality is not lost in the measurement — it is the measurement. The gradient alignment between a leader’s viability manifold and the population they govern measures compassion in the only units compassion comes in: the degree to which their persistence depends on the persistence of those they serve. The dimensionality of someone’s other-model during an interaction measures whether they perceive the other as a subject or an object — which is $\alpha(\text{other})$ , the ascription field read at that target, the structural basis of dignity. The gradient does not flatten the hierarchy from physics to feeling. It reveals the hierarchy as a single landscape seen at different scales, with force as the invariant that survives every change of coordinates.

Valence in Discrete Substrate

In a cellular automaton or other discrete dynamical system, valence becomes exactly computable:

$\viable$ = configurations where the pattern persists
$\partial\viable$ = configurations where the pattern dissolves
$d(\mathbf{x}, \partial\viable)$ = minimum Hamming distance to a non-viable state
Trajectory = sequence of configurations $\mathbf{x}_1, \mathbf{x}_2, …$

Then:

\valence_t = d(\mathbf{x}_{t+1}, \partial\viable) - d(\mathbf{x}_t, \partial\viable)

Positive when the pattern moves away from dissolution; negative when approaching it; zero when maintaining constant distance. For a glider cruising through empty space: $\valence \approx 0$ . For a glider approaching collision: $\valence < 0$ . For a pattern that just escaped a near-collision: $\valence > 0$ .

This is not metaphor—it is the viability gradient formalized for discrete state spaces.

Arousal: Update Rate

Arousal measures how rapidly the system is revising its world model. The natural formalization is the KL divergence between successive belief states:

\arousal_t = \KL\left( \belief_{t+1} | \belief_t \right) = \sum_{\mathbf{x}} \belief_{t+1}(\mathbf{x}) \log \frac{\belief_{t+1}(\mathbf{x})}{\belief_t(\mathbf{x})}

In latent-space models, this can be approximated more directly:

\arousal_t = | \latent_{t+1} - \latent_t |^2 \quad \text{or} \quad \MI(\obs_t; \latent_{t+1} | \latent_t, \action_t)

Phenomenal Correspondence

High arousal: Large belief updates, far from any attractor, system actively navigating. Low arousal: Near a fixed point, low surprise, system at rest in a basin.

Integration: Irreducibility

As defined in Part I:

\intinfo(\state) = \min_{\text{partitions } P} D\left[ p(\state_{t+1} | \state_t) | \prod_{p \in P} p(\state^p_{t+1} | \state^p_t) \right]

Or using proxies:

\intinfo_{\text{proxy}} = \Delta_P = \mathcal{L}_{\text{pred}}[\text{partitioned}] - \mathcal{L}_{\text{pred}}[\text{full}]

Phenomenal Correspondence

High integration: The experience is unified; its parts cannot be separated without loss. Low integration: The experience is fragmentary or modular.

Integration in Discrete Substrate

In a cellular automaton, $\intinfo$ is directly computable for small patterns:

Define the pattern as cells ${c_1, c_2, …, c_n}$
For each bipartition $P = (A, B)$ : compute $D(p(\mathbf{x}_{t+1} | \mathbf{x}_t) \| p_A \cdot p_B)$
$\intinfo = \min_P D$

High $\intinfo$ means you cannot partition the pattern without losing predictive power. The parts must be considered together.

For a simple glider: $\intinfo$ is probably modest (only 5 cells). For a complex pattern with tightly coupled components: $\intinfo$ can be high. Does high $\intinfo$ correlate with survival, behavioral complexity, or adaptive response to perturbation?

Effective Rank: Concentration vs. Distribution

The dimensionality of a system’s active representation can be quantified through the effective rank of its state covariance $C$ :

\effrank = \frac{(\tr C)^2}{\tr(C^2)} = \frac{\left(\sum_i \lambda_i\right)^2}{\sum_i \lambda_i^2}

When $\effrank \approx 1$ , all variance is concentrated in a single dimension—the system is maximally collapsed. When $\effrank \approx n$ , variance distributes uniformly across all available dimensions—the system is maximally expanded.

Phenomenal Correspondence

High rank: Many degrees of freedom active; distributed, expansive experience. Low rank: Collapsed into narrow subspace; concentrated, focused, or trapped experience.

Effective Rank in Discrete Substrate

For a pattern in a CA, record its trajectory $\mathbf{x}_1, \mathbf{x}_2, …, \mathbf{x}_T$ (configuration at each timestep). Each configuration is a point in ${0,1}^n$ . Compute the covariance matrix $C$ of these binary vectors treated as $\R^n$ points.

For a glider: the trajectory lies on a low-dimensional manifold (position $\times$ position $\times$ phase $\approx 3$ – $4$ effective dimensions out of $n$ cells). $\effrank$ is small.

For a complex evolving pattern: the trajectory may explore many independent dimensions. $\effrank$ is large.

The thesis predicts this maps to phenomenology:

Joy: high $\effrank$ (expansive, many active possibilities)
Suffering: low $\effrank$ (collapsed, trapped in narrow manifold)

In discrete substrate, this is not metaphor but measurement.

Counterfactual Weight

Where the previous dimensions captured the system’s current state, counterfactual weight captures its temporal orientation—how much processing is devoted to possibilities rather than actualities. Let $\mathcal{R}$ be the set of imagined rollouts (counterfactual trajectories) and $\mathcal{P}$ be present-state processing. Then:

\mathcal{CF}_t = \frac{\text{Compute}_t(\mathcal{R})}{\text{Compute}_t(\mathcal{R}) + \text{Compute}_t(\mathcal{P})}

The fraction of computational resources devoted to modeling non-actual possibilities.

In model-based RL:

\mathcal{CF}_t = \sum_{\tau \in \text{rollouts}} w(\tau) \cdot \entropy[\tau] \quad \text{where} \quad w(\tau) \propto |V(\tau)|

Rollouts weighted by their value magnitude and diversity.

Phenomenal Correspondence

High counterfactual weight: Mind is elsewhere—planning, worrying, fantasizing, anticipating. Low counterfactual weight: Present-focused, reactive, in-the-moment.

This is where the reactivity/understanding distinction (Empirical Appendix) becomes experientially salient. Low CF is reactive experience: the system runs on present-state associations, its processing decomposable by channel. High CF is understanding: the system holds multiple possible futures simultaneously, and the quality of that holding — which possibilities, how they are compared, what actions they recommend — is inherently non-decomposable. The experience of weighing options is not reducible to separate valuations of each option. The comparison itself is the experience.

Counterfactual Weight in Discrete Substrate

For most CA patterns: $\mathcal{CF} = 0$ . They follow their dynamics without simulation.

But Life contains universal computers—patterns that can simulate arbitrary computations, including Life itself. Imagine a pattern $\mathcal{B}$ containing:

A simulator subregion that runs a model of possible futures
A controller that adjusts behavior based on simulator output

Then:

\mathcal{CF} = \frac{|\text{simulator cells}|}{|\mathcal{B}|}

The fraction of the pattern devoted to counterfactual reasoning.

Such patterns are rare and complex—universal computation requires many cells. But they should outperform simple patterns: they can anticipate threats (fear structure) and identify opportunities (desire structure). The prediction: patterns with $\mathcal{CF} > 0$ survive longer in hostile environments.

Self-Model Salience

The last member of the entity-directed salience family measures how the self figures in the system’s own processing. But "figures how" hides a fork that must be made explicit, because two genuinely different quantities have been smuggled under one symbol, and they come apart on the framework’s own flagship example.

The first is causal self-salience, $\sigma_{\text{causal}}$ — the fraction of action entropy explained by the self-model component:

\sigma^{\text{causal}}_t = \MI(\latent^{\text{self}}_t; \action_t) / \entropy(\action_t)

The second is attentional self-salience, $\sigma_{\text{attention}}$ — how prominently the self appears as an object in current processing, the degree to which the system is thematizing itself:

\sigma^{\text{attention}}_t = \frac{\text{dim}(\latent^{\text{self}})}{\text{dim}(\latent^{\text{total}})} \cdot \text{activity}(\latent^{\text{self}}_t)

These dissociate, and flow is the proof. In flow the skilled self is driving everything — $\sigma_{\text{causal}}$ is high, the self-model is the controller — yet the self is not thematized at all; it has vanished from the field of attention, so $\sigma_{\text{attention}}$ is low. To call flow "low self-salience" full stop, as earlier formulations did, is true on the attentional reading and false on the causal one, and the contradiction was an artifact of running both quantities through a single $\mathcal{SM}$ . The split resolves it cleanly: flow is low $\sigma_{\text{attention}}$ , high $\sigma_{\text{causal}}$ ; shame is high on both (the self drives behavior and is the object of a harsh regard); depersonalization is low on both (the self neither drives nor is thematized); and the once-paradoxical states each land at distinct points. Where this part writes $\mathcal{SM}$ without subscript, read it as $\sigma_{\text{attention}}$ unless the surrounding formalism (mutual information with action) makes the causal reading explicit. Whether the two are coupled or free is itself diagnostic — it is governed by the coupling axis $\kappa$ introduced later in this part: high $\kappa$ binds attention and causation together, low $\kappa$ permits the dissociation that flow exhibits.

Phenomenal Correspondence

High attentional self-salience: self-focused, self-conscious, self as primary object of attention. Low attentional self-salience: self-forgotten, absorbed in environment or task — which is fully compatible with the self-model still driving the behavior (high causal self-salience).

Though—"I" is not the secret interior that shame and secrecy create (though shame and secrecy can shape it). "I" is just the stable locus of integrated cause-effect structure that the world model has come to rely on most for its predictions—the component of $\mathcal{W}$ that other components reference when computing expected futures. The self is a predictive structure, not a hidden essence. It is whatever the system has found to be its most reliable attractor for anticipating its own behavior. This is why depression feels like losing yourself: the world model can no longer reliably predict what "I" will do or want, so the self-reference breaks down and the system loses coherence. And it is why identity crises are not drama but dynamical events—the attractor that was "I" has destabilized, and the system must pay the expensive bill of finding a new one.

Self-Model Salience in Discrete Substrate

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

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

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

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

The thesis predicts: self-conscious states (shame, pride) have high $\sigma_{\text{attention}}$ ; absorption states (flow) have low $\sigma_{\text{attention}}$ while retaining high $\sigma_{\text{causal}}$ . In CA terms, a pattern “in flow” has its self-tracking cells decoupled from monitoring while its self-model still steers the core dynamics — it acts skillfully without watching itself act. The single mutual-information measure above tracks $\sigma_{\text{causal}}$ ; a separate readout of self-tracking-cell activity tracks $\sigma_{\text{attention}}$ , and the two need not move together.

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:

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

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— $\viable(S(\theta))$ genuinely reshaped by expanding $\theta$ .

Salience vs. Scope

Self-model salience ( $\mathcal{SM}$ ) 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 $S(\theta)$ denote the self-model parameterized by its boundary scope $\theta$ . Let $\viable(S)$ denote the viability manifold induced by self-model $S$ . Then:

$\theta_{\text{narrow}}$ : $S$ includes only this biological trajectory $\Rightarrow$ $\partial\viable$ is located at biological death $\Rightarrow$ persistent negative gradient
$\theta_{\text{expanded}}$ : $S$ includes patterns persisting beyond biological death $\Rightarrow$ $\partial\viable$ 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 $\viable(S(\theta))$ . 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.