Part III: Affect Signatures

Quantitative Frameworks

Introduction

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Quantitative Frameworks

For any intervention $\mathcal{I}$ , the affect impact measures the shift in expected affect state:

\text{Impact}(\mathcal{I}) = \E_{p’}[\mathbf{a}] - \E_p[\mathbf{a}]

which can be decomposed component-wise:

\text{Impact}(\mathcal{I}) = (\Delta\bar{\valence}, \Delta\bar{\arousal}, \Delta\bar{\intinfo}, \Delta\bar{\effrank}, \Delta\overline{\mathcal{CF}}, \Delta\overline{\mathcal{SM}})

These component-wise impacts can be aggregated into a flourishing score—a weighted composite of affect dimensions aligned with human wellbeing:

\mathcal{F}(\mathbf{a}) = \alpha_1 \valence + \alpha_2 \intinfo + \alpha_3 \effrank - \alpha_4 (\mathcal{SM} - \mathcal{SM}_{\text{optimal}})^2 - \alpha_5 |\arousal - \arousal_{\text{optimal}}| + \alpha_6 \cdot \text{flex}(\iota)

where $\text{flex}(\iota) = \frac{1}{\tau}\int_0^\tau |\dot{\iota}(t)| , dt$ measures the time-averaged $\iota$ flexibility—the capacity to modulate the inhibition coefficient in response to context. The weights ${\alpha_i}$ encode normative commitments about what constitutes flourishing. The $\iota$ flexibility term deserves special emphasis: a system with positive valence, high integration, and high rank but rigid $\iota$ is fragile. The $\iota$ rigidity hypothesis (Psychopathology section) predicts that flexibility in perceptual configuration is itself a core component of wellbeing, independent of where on the $\iota$ spectrum one happens to be.

Comparative Analysis. Using standardized affect measurement, we can compare:

Meditation retreat vs.\ social media usage (expected: opposite affect signatures)
Different workplace designs (open office vs.\ private: integration differences)
Educational approaches (lecture vs.\ discussion: counterfactual weight differences)
Urban vs.\ rural environments (arousal and integration differences)