Joy

Geometrically, joy requires four dimensions:

• $\valence > 0$ (positive gradient on viability manifold)
• $\intinfo$ high (unified, coherent experience)
• $\effrank$ high (many degrees of freedom active—expansiveness)
• $\mathcal{SM}$ low (self recedes; no need to defend)

Arousal varies (joy can be calm or excited). Counterfactual weight is incidental.

The cause-effect structure has the shape of “abundance”—multiple paths to good outcomes, redundancy, slack in the system. Many distinctions active simultaneously ($\effrank$ high), tightly coupled ($\intinfo$ high), but the self is light because the world is cooperating ($\mathcal{SM}$ low). This is why joy expands: the geometry literally has more active dimensions.

Suffering

Where joy expands, suffering compresses—and the geometry makes precise why. Suffering requires three dimensions:

• $\valence < 0$ (negative gradient—approaching viability boundary)
• $\intinfo$ high (hyper-unified, impossible to decompose or look away)
• $\effrank$ low (collapsed into narrow subspace—trapped)

This is the core structural signature. Self-model salience is often high (the self as locus of the problem), but not necessarily—one can suffer while absorbed in external pain.

High integration but collapsed into low-rank subspace. The system is deeply coupled but constrained to a dominant attractor it cannot escape.

Suffering feels more real than neutral states because it is actually more integrated. But it feels trapped because the integration is constrained to a narrow manifold. Formally: $\intinfo_{\text{suffering}} > \intinfo_{\text{neutral}}$ but $\effrank[\text{suffering}] \ll \effrank[\text{neutral}]$. This is why you cannot simply "think your way out" of suffering—the very integration that makes it vivid also makes it inescapable.

Fear

Suffering is present-tense: the viability boundary is here, now, pressing in. Fear is its temporal projection—the same negative gradient, but anticipated rather than actual. It is defined by three dimensions:

• $\valence < 0$ (anticipated negative gradient)
• $\mathcal{CF}$ high, concentrated on threat trajectories (the not-yet dominates)
• $\mathcal{SM}$ high (self foregrounded as the thing-that-might-be-harmed)

Arousal is typically high but not defining—cold fear exists. Integration and rank vary.

Fear is suffering projected into the future. The temporal structure ($\mathcal{CF}$) is essential: fear lives in anticipation. The self-model must be salient because fear is fundamentally about threat to the self. Remove the counterfactual weight (make it present-focused) and you get suffering. Remove the self-salience (make it about external objects) and you get something closer to aversion or disgust.

The somatic/anticipatory split maps exactly onto a deeper distinction: reactivity versus understanding. Somatic fear is reactive — it responds to present-state gradient information, and its channels (valence depression, arousal elevation, threat-orientation) are decomposable in principle. Each can be addressed independently by targeting its driving signal. Anticipatory anxiety is understanding — the system is comparing possible futures, and those comparisons inherently couple across any partition between self, environment, and time. This is why cognitive restructuring for anxiety operates on the framing of possibilities, not on individual signal channels: you cannot reduce anticipatory anxiety by adjusting one dimension at a time, because the dimensions are bound together by the counterfactual comparison that constitutes the experience.

The emergence ladder (Part VII) predicts a sharp distinction between two levels of fear. Somatic fear — negative valence, high arousal, threat-oriented behavior — is a pre-reflective affect requiring only viability-gradient detection (emergence rung 1–3). It does not require the counterfactual weight dimension at all. Anticipatory anxiety — fear of what might happen — requires counterfactual capacity (CF > 0), which is a rung 8 capacity blocked in systems without embodied agency. The Lenia experiments confirm this prediction exactly: patterns show negative valence and high arousal under resource scarcity, but CF ≈ 0 throughout the evolutionary runs because the patterns cannot imagine alternative futures. The implication for human psychology: anxiety as a clinical phenomenon (characterized by imagining feared futures, not just responding to present threats) should emerge developmentally at the same time as mental time travel and theory of mind — approximately age 3–4 — rather than being present from birth. The infant's fear is somatic. The child's anxiety is reflective.

Anger

Fear and suffering orient the system toward its own vulnerability. Anger inverts this: it externalizes the threat, simplifying the world into self-versus-obstacle. Its geometry requires valence and arousal, plus a feature not in the standard toolkit—other-model compression:

• $\valence < 0$ (obstacle to viability)
• $\arousal$ high (energized, mobilized for action)
• $\text{dim}(\text{other-model}) \ll \text{dim}(\text{other-model})_{\text{normal}}$ (the other becomes a caricature)
• Externalized causal attribution (the problem is out there)

Anger simplifies. The other-model collapses into a low-dimensional obstacle-representation. Self-model may be complex, but the other becomes flat, predictable, opposable. Anger feels powerful and stupid simultaneously. You're burning cognitive resources on a cartoon.

In $\iota$ terms: anger is a targeted $\iota$ spike toward a specific entity. The other person stops being a subject with interiority and becomes an obstacle, a mechanism, a thing to be overcome. Other-model compression is $\iota$-raising applied to one entity while $\iota$ toward the self remains low (you are still fully a subject; they are not). This asymmetric $\iota$ is what enables violence—you cannot harm someone you are perceiving at low $\iota$—and it is why the aftermath of anger often involves guilt: $\iota$ drops back, the other’s interiority returns, and you confront what you did to a person while perceiving them as a thing.

Other-model compression is not one of the core structural dimensions. It emerges as essential for anger specifically—the affect cannot be characterized without it.

Desire/Lust

The negative affects above all involve threat—to viability, to self, to the integrity of the other-model. Desire reverses the gradient. It is defined by anticipated positive valence, counterfactual weight, and a structural feature—goal-funneling:

• $\valence > 0$ but projected forward (anticipated positive gradient)
• $\mathcal{CF}$ high, concentrated on approach trajectories
• Goal-funneling: many dimensions of experience converge toward narrow outcome space

Arousal is typically high but not definitional—one can desire calmly.

Desire is the gradient of joy. The world reorganizes around an attractor not yet reached. Everything becomes instrumental; the goal saturates attention. The “funneling” structure—high-dimensional input collapsing toward low-dimensional goal—is what gives desire its characteristic urgency. The relationship to joy is precise: joy is at the attractor; desire is approaching it. Structurally:

where $\mathcal{A}$ is the goal attractor. This explains why anticipation often exceeds consummation: the structure of approach (funneling, convergent) is tighter than the structure of arrival (expansive, slack).

Curiosity

Curiosity shares desire’s forward orientation but replaces the specific goal with open-ended exploration. It is essentially two-dimensional:

• $\valence > 0$ specifically toward uncertainty-reduction (anticipated information gain)
• $\mathcal{CF}$ high with high entropy over counterfactual outcomes (many branches, not converged on one)
• Uncertainty is welcomed, not aversive

Self-model salience is typically low (absorbed in the object of curiosity).

Curiosity and fear share high counterfactual weight—both live in the space of possibilities. The difference is valence orientation: fear’s branches lead to threat, curiosity’s branches lead to expanded affordances. Same temporal structure, opposite gradient direction. This pairing reveals curiosity as intrinsic motivation: positive valence attached to uncertainty-reduction. Formally:

Curiosity feels pulling. Reducing uncertainty is rewarding.

Grief

The affects above all orient toward present or future states. Grief is the one that faces backward—defined not by what threatens or beckons but by what has already been lost. It requires valence, past-directed counterfactual weight, and two structural features—persistent coupling to lost object and unresolvable prediction error:

• $\valence < 0$ (the world is worse than it was)
• $\mathcal{CF}$ high but directed toward counterfactual past (“if only...”)
• $\MI(\selfmodel; \text{lost-object-model})$ remains high despite the object’s absence
• No action reduces the prediction error—the world has permanently changed

Arousal is variable (acute grief is high-arousal; chronic grief may be low).

The lost attachment object remains woven into the self-model and world-model. Predictions involving the lost object continue to be generated and continue to fail. Grief is the metabolic cost of love’s integration—the coupling that made the relationship meaningful is precisely what makes its absence painful. The model has not yet updated to the permanent change in the world.

This is why grief takes time: the self-model must be rewoven around the absence, and that rewiring is slow.

Note a deeper implication: grief is proof of alignment. You can only grieve what you were genuinely coupled to. The depth of grief measures the depth of the integration that preceded it. If a relationship was purely transactional, its ending produces disappointment, not grief. Grief requires that the lost object was woven into the self-model—that the relationship’s viability manifold was genuinely contained within the participants’ viability manifolds ($\viable_R \subseteq \viable_A \cap \viable_B$). Grief, for all its pain, is evidence that something real existed.

There is an $\iota$ dimension to grief that explains its resistance to resolution. You grieve because you perceived the lost person at low $\iota$—as fully alive, fully interior, fully a subject. Their model remains embedded in yours not as a mechanism but as a person, and it is the person-quality of the model that generates the persistent prediction errors. The obvious computational shortcut—raise $\iota$ toward them, reduce them to a memory-object, mechanize the relationship so it stops hurting—is experienced as betrayal, because it would repudiate the very thing that made the relationship real. The work of grief is to restructure predictions around the absence while maintaining low $\iota$ toward the memory: to accept that the interiority you perceived is no longer accessible without denying that it was ever there. This is why grief is slow. You must rewire without dehumanizing.

Shame

Grief is private—it concerns the self’s relationship to an absence. Shame is its social inverse: it concerns the self’s exposure to a presence. It is defined by three dimensions plus a structural feature—involuntary manifold exposure:

• $\valence < 0$ (the self is wrong, not the world)
• $\mathcal{SM}$ very high (self foregrounded as the object of evaluation)
• $\intinfo$ high (the negative evaluation permeates—cannot be compartmentalized)
• Involuntary exposure: the self-model is seen from outside, and what is seen is unacceptable

Arousal is typically high in acute shame (flushing, gaze aversion) but may be low in chronic shame (withdrawal, numbness).

Shame is not about what you did (that is guilt, which is action-focused and reparable). Shame is about what you are—or more precisely, about the manifold you are on being visible when it should not be, or being visible to someone whose evaluation you cannot escape. The person caught in a lie does not feel ashamed of the lie (guilt); they feel ashamed that the lie has revealed the underlying manifold—that they are the kind of person who lies, and now someone knows.

Shame's phenomenology is distinctive: the impulse to hide, to disappear, to cease existing as visible. The self wants to withdraw from the visual field of the other. Not because the other will punish (that is fear) but because the other can now see the manifold, and the manifold is wrong.

The clinical literature (Tangney, Lewis) distinguishes shame from guilt, and the framework offers a structural reading of why they differ:

• Guilt: “I did a bad thing.” Action-focused, reparable through changed behavior. The self-model is intact; it was the action that violated the gradient. $\mathcal{SM}$ is moderate (the self is the agent of repair).
• Shame: “I am bad.” Self-focused, not easily repaired because the problem is structural. The manifold itself is wrong. $\mathcal{SM}$ is very high (the self is the object of the problem).

If this structural distinction is right, it explains why guilt is reparable through action while shame requires what we might call manifold reconstruction—deeper and slower work. But we need to check: does the $\mathcal{SM}$ difference actually hold up in measurement? Do shame and guilt show the predicted dissociation on self-model salience measures?

The connection to the topology of social bonds (Part IV) is suggestive: shame may arise when the manifold you are actually on is exposed and differs from the manifold you are presenting. The person performing friendship while operating on the transaction manifold would feel shame when the discrepancy is detected—not guilt (“I should not have done that specific transactional thing”) but shame (“I am the kind of person whose care is instrumental, and now someone can see it”). If this is right, shame is the affect system’s internal alarm for one’s own manifold contamination. But this reading goes beyond the existing clinical data and should be treated as a hypothesis to test, not an established finding.

There is also an $\iota$ dimension to shame. Shame involves a sudden, involuntary $\iota$ reduction: the participatory coupling between self and other spikes as the other’s gaze penetrates the self-model’s defenses. You experience the other as having interiority—specifically, the interiority of evaluating you—at a moment when you most wish they did not. The impulse to hide is the impulse to raise $\iota$ again, to restore the modular separation between self-model and other-model that shame has breached.

Summary: Defining Dimensions by Affect

Each affect by its defining structure:

Different affects require different numbers of dimensions. Boredom is essentially three-dimensional (low arousal, low integration, low rank). Anger requires other-model compression. Desire requires goal-funneling. The obvious concern: if each affect invokes bespoke dimensions, the framework risks becoming an open-ended fitting exercise where anything can be characterized post hoc. The distinction that saves it: the core structural dimensions (valence, arousal, integration, effective rank, counterfactual weight, self-model salience) arise from the mathematical structure of any viable self-modeling system and are measurable across substrates. They are not arbitrary choices but consequences of viability maintenance, world-modeling, and self-reference. The additional features (other-model compression, goal-funneling, manifold exposure in shame) are relational—they emerge when the system interacts with specific kinds of objects or situations. They describe how the system's model of external entities changes during the affect. The geometric coherence rests on the structural invariants; the relational features extend rather than replace them. This distinction—structural vs. relational—matters more than the number of dimensions. The framework is deliberately open to discovering that some proposed dimensions are redundant, or that others are needed. What is claimed to be universal is the existence of geometric structure in affect, not a particular dimensionality.

The summary reveals a topological feature worth noting. Look at the structural signatures of joy and suffering. Both have high $\intinfo$—both are deeply unified, vivid, hyper-real. Joy is expansive (high $\effrank$) where suffering is collapsed (low $\effrank$); their valences are opposite; but they share the quality of mattering, of being undeniably present. Now look at boredom: low arousal, low integration, low rank. Boredom is the distant point. If you ask phenomenologically whether ecstasy is more similar to agony or to numbness, the answer is immediate: the ecstatic and the agonized are closer to each other than either is to the merely comfortable. They share a structural neighborhood—high $\intinfo$, vivid, self-involving—that boredom does not inhabit. This means the valence axis does not have the naive topology of a number line from negative to positive. It curves. The extremes are neighbors. The topology of affect space may be closer to a cylinder or a torus than to $\R^6$—a possibility that the Euclidean presentation here does not capture and that empirical similarity measurements could reveal.