Part II: Identity Thesis

Summary: Defining Dimensions by Affect

Introduction

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Summary: Defining Dimensions by Affect

Each affect by its defining structure:

Affect	Constitutive Structure
Joy	$\valence{+}$ , $\intinfo{\uparrow}$ , $\effrank{\uparrow}$ , $\mathcal{SM}{\downarrow}$ (positive, unified, expansive, self-light)
Suffering	$\valence{-}$ , $\intinfo{\uparrow}$ , $\effrank{\downarrow}$ (negative, hyper-integrated, collapsed)
Fear	$\valence{-}$ , $\mathcal{CF}{\uparrow}$ (threat-focused), $\mathcal{SM}{\uparrow}$ (anticipatory self-threat)
Anger	$\valence{-}$ , $\arousal{\uparrow}$ , other-model compression (energized, externalized, simplified other)
Desire	$\valence{+}$ (anticipated), $\mathcal{CF}{\uparrow}$ (approach), goal-funneling (convergent anticipation)
Curiosity	$\valence{+}$ toward uncertainty, $\mathcal{CF}{\uparrow}$ with high branch entropy (welcomed unknown)
Grief	$\valence{-}$ , $\mathcal{CF}{\uparrow}$ (past-directed), persistent coupling to absent object
Shame	$\valence{-}$ , $\mathcal{SM}{\uparrow\uparrow}$ , integration of negative self-evaluation (self as seen by other)
Boredom	$\arousal{\downarrow}$ , $\intinfo{\downarrow}$ , $\effrank{\downarrow}$ (understimulated, fragmented, collapsed)
Awe	$\intinfo$ expanding, $\effrank{\uparrow}$ , $\mathcal{SM}{\downarrow}$ (self-dissolution through scale)

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.

Open Question

Is affect similarity symmetric? Work on the qualia structure of visual motion has found that perceptual similarity is asymmetric—similarity(A, B) $\neq$ similarity(B, A)—and that self-similarity is not always maximal (the same stimulus presented twice does not always feel identical). If affect similarity shares these properties, the Euclidean framework is insufficient. The transition from joy to grief is not the same experience as the transition from grief to joy; the "distance" between them is directional. Fear $\to$ anger (the moment threat becomes action) is phenomenologically different from anger $\to$ fear (the moment action reveals vulnerability). A quasimetric or enriched category structure may be needed—one where distances are not symmetric and the diagonal is not zero. The structural alignment methodology (optimal transport) can accommodate asymmetric similarity matrices. The question is whether affect similarity, when measured empirically through pairwise judgments, shows the same asymmetric structure that perceptual similarity does. If it does, the topology of affect space is richer than any fixed-dimensional Euclidean embedding can represent, and the framework needs to be honest about what the coordinate presentation misses.

Future Empirical Work

Quantifying the affect table: The qualitative descriptors (high, med, low) require empirical calibration:

Study 1: Affect induction with neural recording

Induce target affects via validated protocols (film clips, autobiographical recall, IAPS images)
Measure integration proxies (transfer entropy density, Lempel-Ziv complexity) from EEG/MEG
Measure effective rank from neural state covariance
Compare self-report (PANAS, SAM) with structural measures

Study 2: Real-time affect tracking

Continuous self-report (dial/slider) during naturalistic experience
Correlate with physiological proxies (HRV for arousal, pupil for $\mathcal{CF}$ , skin conductance)
Develop regression model: self-report $\sim f(\text{structural measures})$

Study 3: Cross-modal validation

Compare fMRI (spatial resolution) with MEG (temporal resolution)
Validate effective rank measure across modalities
Test whether integration predicts subjective intensity

Target outputs: Numerical ranges for each cell, confidence intervals, individual difference parameters.