Part II: Identity Thesis

Desire/Lust

Introduction

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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:

d(\state_{\text{joy}}, \mathcal{A}) \approx 0, \quad d(\state_{\text{desire}}, \mathcal{A}) > 0, \quad \frac{d}{dt}d(\state_{\text{desire}}, \mathcal{A}) < 0

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).