Affect Trajectories

Affects are not static points but dynamic trajectories through affect space. The evolution can be written:

where $\mathbf{a} = (\valence, \arousal, \intinfo, \effrank, \mathcal{CF}, \mathcal{SM})$. The force field $F$ has eigenskeletal structure: the Jacobian $\partial F / \partial \mathbf{a}$ at each point has eigenvalues (stiff and soft directions) and the way those eigenspaces connect across affect space defines the eigenskeleton of the dynamics. Stiff directions are the dominant affect modes — the transitions the system is most likely to follow, the paths of least resistance through the space. Soft directions are transient fluctuations. The transitions below follow the stiff directions: they are the paths the eigenskeleton's dominant subbundles trace through affect space.

Because the space is continuous, adjacent affects blend into each other along smooth trajectories:

• Fear $\to$ Anger as causal attribution externalizes
• Desire $\to$ Joy as goal distance $\to 0$
• Suffering $\to$ Curiosity as valence flips while $\mathcal{CF}$ remains high
• Grief $\to$ Nostalgia as arousal decreases and $\mathcal{CF}_{\text{approach}}$ replaces $\mathcal{CF}_{\text{avoidance}}$

Attractor Dynamics

Some affect regions are attractors; the system tends to stay in them once entered. Others are transient.

An affect region $\mathcal{R} \subset \mathcal{A}$ is an attractor if the system is more likely to remain in it than to enter it from outside:

for some characteristic time $\tau$.

The attractor framework distinguishes two properties that come apart in practice: position (where in affect space the system currently sits) and basin geometry (how stable the attractor is—basin depth, width, and recovery rate). These are independent. A system can occupy a technically viable position while inhabiting a shallow basin—one small perturbation from tipping into pathology. Another can sit at a less optimal position while embedded in a deep, robust basin. What we ordinarily call contentment or happiness corresponds more closely to basin geometry than to position: the felt sense that perturbations do not cascade, that the dynamics return to familiar configurations, that the invariants one cares about are being maintained in the causal dynamics. Contentment is the phenomenology of a deep basin. Anxiety is the phenomenology of a shallow one—technically viable, but sensed as precarious. A world of bliss is not a world of maximal positive stimulation but a world where the relevant invariants—relational configurations, material security, self-model stability—are maintained by the environment's dynamics with enough redundancy that defending them does not consume the system's resources.

Pathological attractors. Depression, addiction, and chronic anxiety are pathologically stable attractors in affect space:

• Depression—two structurally distinct failure modes with different phenomenology and different structural remedies. Melancholic depression is a deep aversive attractor: the dynamics reliably return to (low $\valence$, low $\arousal$, high $\intinfo$, low $\effrank$, low $\mathcal{CF}$, high $\mathcal{SM}$). The high integration makes the state vivid and inescapable; the collapsed counterfactual weight forecloses felt alternatives. The problem is not the absence of a stable fixed point but the presence of a terrible one. Agitated depression is the opposite failure: no stable attractor at all. The system traverses a landscape of shallow basins, none deep enough to hold, producing restless groundlessness rather than dead certainty. Both present clinically as depression; they require different structural interventions. The melancholic form requires landscape restructuring—deepening viable attractors until they compete on stability, not just valence. The agitated form requires basin construction first: any stable configuration that can then be deepened toward viability.
• Addiction: Attractor at (high $\valence$ conditional on substance, collapsing $\effrank$ in goal space)
• Anxiety: Diffuse attractor with (low $\valence$, high $\arousal$, high $\mathcal{CF}$ spread across many threats)
• Dissociation: Collapse of $\intinfo$ — the unified field fractures into independently processing subsystems. The Lenia experiments provide a substrate analog: naive patterns consistently decompose under stress ($\Delta\intinfo = -6.2\%$ in V11.0). Biological resilience — integration rising under threat, robustness > 1.0 at bottleneck — is the structurally opposite trajectory. Dissociation is the thermodynamically cheap path; integration under stress is the expensive achievement of the bottleneck furnace. Dissociation is the exoskeleton cracking — the rigid surface structure fragments into disconnected pieces, each processing independently with no surviving holonomy between them. The endoskeletal system, by contrast, absorbs the stress into its internal coupling; the surface deforms but the skeleton beneath holds.

Identity consolidation and catastrophic forgetting. The landscape of affect attractors is not fixed—it consolidates over development. In early life, basins are shallow and plastic, easily reshaped by experience. This is necessary for learning but creates specific vulnerability: adversity or relational inconsistency early in development can consolidate pathological attractors before viable ones have had time to deepen. As development proceeds, the landscape hardens around whatever has been traversed—attractors deepen, basins widen, the topology becomes more resistant to rewriting. Healthy consolidation produces a robust attractor network: several viable basins with navigable transitions between them, deep enough to contain normal variation and recover from moderate perturbation. $\iota$ flexibility is, at the dynamical level, a measure of between-basin navigability—the capacity to move from one configuration to another when context demands. Pathological consolidation takes two forms: a single dominant basin from which there is no exit (the melancholic pattern, identity calcified — an exoskeleton hardened around a single configuration, too rigid to deform, too thick to molt), or a landscape that never achieves depth anywhere (the agitated pattern, consolidation never completed — no endoskeleton formed at all, soft tissue without structural core). The V11.5 stress-overfitting finding (Part I) is a substrate analog: patterns evolved under one stress regime develop high-$\intinfo$ configurations that are simultaneously more integrated and more fragile, decomposing catastrophically under novel stress that naive patterns actually handle better. The human parallel is identity tuned to a specific developmental environment—a particular family dynamic, class position, cultural script—that functions well within that environment but collapses under regime change. This is structurally identical to the ML phenomenon of catastrophic forgetting: a new learning objective overwrites the parameter landscape that previously held the self together. The implication for therapy is that durable change requires not repositioning within a fixed landscape but restructuring the landscape itself—deepening viable basins, raising barriers to pathological ones, and widening the navigable transitions between healthy configurations. Insight alone does not do this; repeated traversal under consolidating conditions does.

The emergence ladder (Empirical Appendix) makes a further prediction about the structure of pathology. Disorders that require counterfactual capacity — anticipatory anxiety, obsessive rumination, regret, self-critical shame spirals — cannot arise in systems below rung 8. Pre-rung-8 pathology is somatic: chronic threat-arousal, valence collapse (anhedonia), integration fragmentation (dissociation). The reflective layer adds a second class of suffering that is structurally more expensive to maintain and unique to agentive systems. This is not merely a theoretical prediction — it has a testable developmental corollary: in humans, the onset of anxiety disorders (which require imagining feared futures) should cluster with, not precede, the developmental emergence of mental time travel and counterfactual reasoning, typically around age 3–4 years.