Emotion Taxonomy from $\nabla P$

Bridge from the previous chapter

In Qualia structure we established that the 21 coherences $\gamma_{ij}$ exhaust all types of experience. Among them $\gamma_{DE}$ (Affection) — the connection between Dynamics and Interiority, the experience of "emotion" — plays a special role. We will now show that all emotions are derived from a single quantity — the rate of change of viability $dP/d\tau$ — and the sector signature $\sigma(\Gamma)$. Emotions are not postulated — they are computed.

On notation

• $P = \mathrm{Tr}(\Gamma^2)$ — purity (viability)
• $P_{\text{crit}} = 2/7$ — critical purity, status [T]
• $\Gamma$ — coherence matrix, $\gamma_{ij}$ — its elements
• $\tau$ — internal (emergent) time
• $R$ — reflection measure
• $\mathrm{Gap}(i,j)$ — gap measure
• Full notation table — in Notation

Chapter roadmap

1. History of the problem — from Darwin to Russell and Feldman Barrett
2. Motivation: why $dP/d\tau$ — evolutionary logic
3. Definition of emotion — the triple $(dP/d\tau,\; d^2P/d\tau^2,\; \sigma(\Gamma))$
4. Basic coordinates — valence and arousal as projections of $dP/d\tau$
5. Map of basic emotions — fear, joy, anger, surprise, sadness, disgust
6. Fear: formal analysis — divergence as $P \to P_{\text{crit}}$
7. Complex emotions — superpositions of basic patterns
8. Comparison with other taxonomies — Ekman, Russell, Plutchik
9. Conditions for reflexive access — threshold for awareness of one's own emotions
10. Evolutionary meaning — why $dP/d\tau$ is needed as an internal signal

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History of the problem: how emotions were understood before UHM

Darwin (1872): universality of expression

Charles Darwin in "The Expression of the Emotions in Man and Animals" (1872) first showed that emotions are not a cultural convention but a biological phenomenon: the smile of joy and the grimace of fear are recognisable in all peoples and even in primates. Darwin posed the question: if emotions are universal, they must serve some function for survival. Which one?

James–Lange (1884): the body is primary

William James (1884) and Carl Lange (independently) proposed a radical idea: we do not cry because we are sad — we are sad because we cry. An emotion is the perception of bodily changes. You see a bear, your body reacts (heartbeat, perspiration), and only then do you feel "fear".

Cannon–Bard (1927): the brain is primary

Walter Cannon objected: bodily reactions are too slow and non-specific to account for the speed and variety of emotions. The brain (thalamus) simultaneously generates both the bodily reaction and the subjective experience.

Schachter–Singer (1962): cognitive appraisal

Stanley Schachter and Jerome Singer showed that the same physiological arousal can be perceived as joy or anger — depending on the cognitive appraisal of the situation. Emotion = arousal + interpretation.

Ekman (1971): six basic emotions

Paul Ekman identified 6 basic emotions recognisable by facial expression across all cultures: joy, sadness, fear, anger, surprise, disgust. Each corresponds to a unique pattern of facial musculature.

Russell (1980): circumplex model

James Russell proposed the circumplex model: all emotions are arranged on a plane with two axes — valence (pleasant/unpleasant) and arousal (activation/deactivation). Joy — high valence, high arousal. Sadness — low valence, low arousal. Russell's model showed that Ekman's "basic emotions" are not fundamental building blocks but regions in a continuous two-dimensional space.

Feldman Barrett (2017): constructed emotions

Lisa Feldman Barrett in "How Emotions Are Made" (2017) argued that emotions are constructed by the brain, not "discovered" in the body. There are no fixed "fear centres" or "joy centres" — the brain actively creates emotional categories on the basis of past experience and current context.

UHM's position: emotions from $\nabla P$

UHM synthesises these approaches:

• Darwin is right: emotions are universal because they are linked to viability $P$ — the fundamental quantity for any coherent system
• James–Lange are partially right: emotion is indeed linked to bodily dynamics (the $\sigma(\Gamma)$ component)
• Russell is right: emotions form a continuous space (valence = $\mathrm{sign}(dP/d\tau)$, arousal = $|dP/d\tau|$)
• Feldman Barrett is partially right: the specific names of emotions are cultural constructs, but the underlying patterns of $dP/d\tau$ and $\sigma(\Gamma)$ are objective
• UHM adds: the full model is not 2D (Russell) but 30D (T-147 [T])

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Motivation: why emotions are linked to $dP/d\tau$

Emotions in UHM are neither primitives nor epiphenomena. They are derived from the dynamics of viability $P(\tau)$ and the sector structure of the coherence matrix $\Gamma(\tau)$.

Why $dP/d\tau$? Because $P$ is the only scalar quantity on which the system's survival depends. If $P > P_{\text{crit}} = 2/7$ — the system is alive (coherent). If $P < P_{\text{crit}}$ — the system irreversibly decoheres (dies). Consequently, any "survival sensor" must track precisely $P$.

But for effective navigation it is not enough to know the current value of $P$ — one needs the rate of change $dP/d\tau$:

• $dP/d\tau > 0$ — things are improving, current behaviour is working, continue
• $dP/d\tau < 0$ — things are worsening, something must change, act
• $dP/d\tau \approx 0$ — stability, one can relax (or is stuck and a change is needed)

This is valence — the sign of the viability derivative. Emotion is the "interior projection" of the change in the system's state.

Analogy from everyday life. Imagine a health thermometer. When temperature (viability $P$) rises — you feel better (positive emotions). When it falls — worse (negative). But an emotion is not merely "good/bad": what matters is which specific organ (sector) is changing and at what rate. A headache and a stomachache are both "bad" ($dP/d\tau < 0$), but experienced differently due to different sector signatures.

Definition of emotion (D.1)

Definition D.1 (Emotion) [D]

An emotion is a triple characterising the current dynamics of viability and the sector coherence profile:

$$\mathrm{Emotion}(\Gamma, \tau) := \left(\frac{dP}{d\tau},\; \frac{d^2P}{d\tau^2},\; \sigma(\Gamma)\right)$$

where:

• $\frac{dP}{d\tau} = \frac{d}{d\tau}\mathrm{Tr}(\Gamma^2)$ — rate of change of viability
• $\frac{d^2P}{d\tau^2}$ — acceleration of change of viability
• $\sigma(\Gamma) = \{\gamma_{ii}, |\gamma_{ij}|\}$ — sector Γ-signature (set of populations and moduli of coherences)

Let us examine each component:

1. $dP/d\tau$ — the first derivative. Determines valence (good/bad) and intensity (strong/weak). This is the "primary signal".

2. $d^2P/d\tau^2$ — the second derivative. Determines the trend: is the situation improving ($d^2P/d\tau^2 > 0$) or deteriorating ($d^2P/d\tau^2 < 0$)? It is precisely the second derivative that distinguishes "hope" ($dP/d\tau < 0$ but $d^2P/d\tau^2 > 0$: bad but improving) from "despair" ($dP/d\tau < 0$, $d^2P/d\tau^2 < 0$: bad and getting worse).

3. $\sigma(\Gamma)$ — the sector signature. Determines the qualitative character of the emotion: which dimensions are involved? Fear ($\gamma_{DD}$ high) and sadness ($\gamma_{DU}$ low) both have $dP/d\tau < 0$, but are experienced entirely differently.

Purity derivative: where does $dP/d\tau$ come from

The rate of change of purity is computed through the evolution equation:

$$\frac{dP}{d\tau} = 2\,\mathrm{Tr}\!\left(\Gamma \cdot \frac{d\Gamma}{d\tau}\right) = 2\,\mathrm{Tr}\!\left(\Gamma \cdot \mathcal{L}_\Omega[\Gamma]\right)$$

where $\mathcal{L}_\Omega[\Gamma] = -i[H_{\text{eff}}, \Gamma] + \mathcal{D}_\Omega[\Gamma] + \mathcal{R}[\Gamma, E]$ is the logical Liouvillian.

Let us examine the contribution of each term:

Contributions of the three terms:

Term	Contribution to $dP/d\tau$	Why?	Interpretation
$-i[H_{\text{eff}}, \Gamma]$	$0$ (unitary part)	$\mathrm{Tr}(\Gamma[H,\Gamma]) = 0$ for any Hermitian $H$	Coherent evolution does not change purity
$\mathcal{D}_\Omega[\Gamma]$	$\leq 0$ (decoherence)	Interaction with the environment destroys coherence	Loss of viability
$\mathcal{R}[\Gamma, E]$	$\geq 0$ (regeneration)	Recovery of coherence from the environment	Recovery of viability

Thus:

$$\frac{dP}{d\tau} = \underbrace{2\,\mathrm{Tr}(\Gamma \cdot \mathcal{D}_\Omega[\Gamma])}_{\leq 0,\;\text{decoherence}} + \underbrace{2\,\mathrm{Tr}(\Gamma \cdot \mathcal{R}[\Gamma, E])}_{\geq 0,\;\text{regeneration}}$$

Numerical example. Let the system be in the Goldilocks zone: $P = 0.35$ (above $P_{\text{crit}} = 2/7 \approx 0.286$). Decoherence contributes $-0.02$ per step, regeneration $+0.015$. Total $dP/d\tau = -0.005$ — a slow decline, experienced as mild anxiety. If regeneration increases to $+0.03$, then $dP/d\tau = +0.01$ — the experience of relief, improvement. The balance between these two terms is the system's "emotional wellbeing".

Basic affective coordinates (C.1)

Statement C.1 (Basic affective coordinates) [C]

Condition: Definition D.1 correctly defines the emotional profile; the interpretation of $dP/d\tau$ as a "viability signal" is a semantic postulate.

Valence and arousal are defined as:

$$\mathrm{Valence}(\tau) := \mathrm{sign}\!\left(\frac{dP}{d\tau}\right) \in \{-1, 0, +1\}$$$$\mathrm{Arousal}(\tau) := \left|\frac{dP}{d\tau}\right| \geq 0$$

Positive valence ($dP/d\tau > 0$) corresponds to "positive" emotions (viability rising). Negative — to "negative" (viability declining).

The coordinates $(V, A)$ determine the position in Russell's affective space (circumplex model), which in UHM receives a formal justification.

Analogy. Valence is a compass needle: it shows which direction the "wind" of viability is blowing (towards better or towards worse). Arousal is the strength of the wind. Calm ($A \approx 0$) — tranquillity or stagnation. Storm ($A \gg 0$) — intense experience (joy or terror). But a compass and wind strength do not yet fully describe the weather — the sector signature $\sigma(\Gamma)$ is needed to distinguish a thunderstorm from a blizzard.

Map of basic emotions

Basic emotions are characteristic regions in the space $\left(\frac{dP}{d\tau}, \frac{d^2P}{d\tau^2}, \sigma(\Gamma)\right)$.

Table of basic emotions

Epistemic separation

Mathematical layer [T]: 30D emotional space (T-147 [T]): $\mathbf{e}(\Gamma) \in \mathbb{R}^{30}$ — a formally defined vector of rates, accelerations, and stresses. Valence $\mathrm{sign}(dP/d\tau)$ is a computable quantity [T].

Semantic layer [I]: Identifying specific patterns of the 30D vector with emotion names (fear, joy, anger...) is an interpretation [I]. Real emotions are considerably more complex than the one-dimensional projection $dP/d\tau$. The table below is heuristic, not strictly derived.

Emotion	Condition on $dP/d\tau$	Condition on $d^2P/d\tau^2$	Sector signature	Interpretation
Fear	$< 0$, approaching $P_{\text{crit}}$	$< 0$ or $\approx 0$	$\gamma_{DD}$ ↑, $\gamma_{DE}$ ↑	Viability threat detected
Joy	$> 0$, moving away from $P_{\text{crit}}$	$\geq 0$	$\gamma_{EU}$ ↑, $\gamma_{SE}$ ↑	Viability rising
Anger	$< 0$	$\approx 0$	$\gamma_{DD}$ ↑↑, $\gamma_{LL}$ ↓	High dynamics without logical coherence
Surprise	any	$\left\lvert d^2P/d\tau^2\right\rvert \gg 0$	Abrupt $\delta\sigma$	Sudden change in rate
Sadness	$\approx 0$, $P$ low	$\approx 0$	$\gamma_{DU}$ ↓, $\gamma_{EO}$ ↓	Stagnation at low viability
Disgust	$< 0$	—	$\mathrm{Gap}(S,E)$ ↑↑	Sharp divergence of structure and experience

Detailed numerical examples for each basic emotion

For each emotion we give a concrete $\Gamma$-profile: a life situation, the values of key parameters, and interpretation.

Joy

Situation: a student learns that they passed a difficult exam.

Parameter	Value	Explanation
$P$	$0.38$	Above $P_{\text{crit}} = 0.286$, in the safe zone
$dP/d\tau$	$+0.025$	Viability rising rapidly
$d^2P/d\tau^2$	$+0.008$	Growth accelerating
$\gamma_{EU}$	$0.28$ (high)	Synthesis — sense of unity, "everything is coming together"
$\gamma_{SE}$	$0.22$ (high)	Representation — wholistic picture "I did it"
$\gamma_{DD}$	$0.12$ (normal)	Dynamics do not dominate — no need to act

Valence: $+1$. Arousal: $0.025$ (high). Sector signature indicates an integrative pattern (synthesis + representation).

Fear

Situation: a person walking through a dark alley hears footsteps behind them.

Parameter	Value	Explanation
$P$	$0.31$	Dangerously close to $P_{\text{crit}} = 0.286$
$dP/d\tau$	$-0.020$	Rapid fall in viability
$d^2P/d\tau^2$	$-0.008$	Fall accelerating
$\gamma_{DD}$	$0.22$ (high)	Dynamics dominate — body ready for action
$\gamma_{DE}$	$0.25$ (high)	Affection — the process strongly affects experience
$\gamma_{LE}$	$0.05$ (low)	Logic switched off — "no time to think"

Valence: $-1$. Arousal: $0.020$ (high). Sector signature indicates a dynamic/affective pattern.

Anger

Situation: a driver is cut off on the road.

Parameter	Value	Explanation
$P$	$0.34$	Not critical, but viability is declining
$dP/d\tau$	$-0.015$	Moderate decline
$d^2P/d\tau^2$	$\approx 0$	Stable decline without trend
$\gamma_{DD}$	$0.25$ (very high)	Dynamics maximal — energy for action
$\gamma_{LL}$	$0.05$ (low)	Logic suppressed — "no time for reasoning"
$\gamma_{DU}$	$0.18$ (high)	Teleology — directed action, "I want to respond"

Key difference from fear: in anger $\gamma_{DD}$ is even higher, and $\gamma_{LL}$ even lower. Energy is directed outward ($\gamma_{DU}$), not inward ($\gamma_{DE}$).

Surprise

Situation: an unexpected encounter with an old friend.

Parameter	Value	Explanation
$P$	$0.36$	Normal value
$dP/d\tau$	$+0.005$ (before) $\to +0.030$ (after)	Abrupt jump
$d^2P/d\tau^2$	$+0.050$ (very high)	It is precisely the acceleration that constitutes surprise
$\delta\sigma$	Abrupt change	Sector signature rearranges abruptly

Surprise is defined primarily by the second derivative: not so much "good" or "bad" as "sudden". It is the only basic emotion whose valence can be anything.

Sadness

Situation: a person recalls a lost friend.

Parameter	Value	Explanation
$P$	$0.30$	Low, but above $P_{\text{crit}}$
$dP/d\tau$	$\approx 0$	Viability unchanged — stagnation
$d^2P/d\tau^2$	$\approx 0$	No trend
$\gamma_{DU}$	$0.03$ (very low)	Teleology absent — "no goal, nowhere to go"
$\gamma_{EO}$	$0.04$ (low)	Immanence weakened — "emptiness inside"
$\gamma_{SE}$	$0.20$ (high)	Representation — "I remember them clearly"

Sadness differs from fear: with fear $P$ is actively falling, with sadness it is frozen at a low level. Neither threat nor hope — only quiet stagnation.

Disgust

Situation: a person sees spoiled food.

Parameter	Value	Explanation
$P$	$0.33$	Normal
$dP/d\tau$	$-0.010$	Moderate decline
$d^2P/d\tau^2$	$-0.003$	Weak negative trend
$\mathrm{Gap}(S,E)$	$0.85$ (very high)	Sharp divergence of structure and experience
$\gamma_{AD}$	$0.18$ (high)	Actualisation — "perception focused"

The key feature of disgust: high $\mathrm{Gap}(S,E)$. This means that the structure of the object (spoiled food as a physical form) sharply diverges from the experience (revulsion). Gap is a measure of "wrongness", "the mismatch between what one sees and what should be".

Phase diagram of emotions

Fear: formal analysis

Fear is the most "fundamental" emotion in UHM, since it is directly linked to the threat of existence. Let us examine it in detail.

Conditions for emergence

$$\text{Fear:} \quad \frac{dP}{d\tau} < 0, \quad P(\tau) \to P_{\text{crit}} = \frac{2}{7}$$

Fear intensity

Fear intensity is determined not only by the rate of fall $|dP/d\tau|$ but also by proximity to the threshold:

$$I_{\text{fear}} \propto \frac{|dP/d\tau|}{P - P_{\text{crit}}}$$

Why this formula? Because the same $dP/d\tau = -0.01$ is experienced entirely differently at $P = 0.40$ (far from the threshold, margin $0.114$) and at $P = 0.29$ (near the threshold, margin $0.004$). As $P \to P_{\text{crit}}$ intensity diverges — the system "experiences" an existential threat. If $P$ crosses $P_{\text{crit}}$ — irreversible decoherence (death of the system) begins.

Conditionality of quantitative estimates [C]

The specific formula $I_{\text{fear}} \propto |dP/d\tau| / (P - P_{\text{crit}})$ is a conditional statement. The form of the divergence as $P \to P_{\text{crit}}$ depends on the details of the regenerative term $\mathcal{R}[\Gamma, E]$ and the dissipator $\mathcal{D}_\Omega[\Gamma]$.

Numerical example: escalating fear

We show how intensity grows as the threshold is approached at a fixed rate $dP/d\tau = -0.01$:

$P$	$P - P_{\text{crit}}$	$I_{\text{fear}} \propto$	Subjective experience
$0.40$	$0.114$	$0.01/0.114 \approx 0.09$	Mild discomfort: "something is wrong"
$0.35$	$0.064$	$0.01/0.064 \approx 0.16$	Worry: "something needs to be done"
$0.32$	$0.034$	$0.01/0.034 \approx 0.29$	Anxiety: "the situation is worsening"
$0.30$	$0.014$	$0.01/0.014 \approx 0.71$	Pronounced fear: "the danger is real"
$0.29$	$0.004$	$0.01/0.004 \approx 2.50$	Panic: "I am on the edge"

The same rate of decline $dP/d\tau = -0.01$ is experienced with ever-greater intensity as the threshold is approached — an effect familiar to anyone who has ever awaited medical results: a week before — mild anxiety; an hour before — strong agitation; at the moment of opening the envelope — panic.

Complex emotions as superpositions

Basic emotions are regions in the 30D emotional space. But most real emotions are not "pure" basic ones but superpositions of several patterns. Just as in quantum mechanics a state can be a superposition of basis states, an emotion can combine several basic patterns simultaneously.

Complex emotion	Basic components	Sector characteristic	Life example
Anxiety	Fear + Surprise	$dP/d\tau < 0$, $\lvert d^2P/d\tau^2\rvert$ unstable	Waiting for test results
Awe	Joy + Surprise	$dP/d\tau > 0$, $\gamma_{EO}$ ↑, $\gamma_{OU}$ ↑	View from a mountain summit
Nostalgia	Joy + Sadness	$dP/d\tau \approx 0$, high $\gamma_{SE}$ with $\gamma_{SD}$ ↓	Memory of childhood
Inspiration	Joy + Surprise + Anger	$dP/d\tau > 0$, $\gamma_{DO}$ ↑, $\gamma_{AE}$ ↑, $\gamma_{DD}$ ↑	Beginning a creative project
Shame	Sadness + Fear + Anger (at oneself)	$dP/d\tau < 0$, $R$ high, $\gamma_{LE}$ ↑	Realising one's mistake
Tenderness	Joy + Sadness (mild)	$dP/d\tau > 0$, $\gamma_{EO}$ ↑, $\gamma_{SE}$ ↑	Watching a child

Numerical example: nostalgia. A person looks at photographs from their youth.

Parameter	Value	Component
$dP/d\tau$	$+0.002$	Weakly positive (pleasant memory)
$\gamma_{SE}$	$0.25$	High Representation — "I remember clearly"
$\gamma_{SD}$	$0.03$	Low Persistence — "this no longer exists"
$\gamma_{EU}$	$0.15$	Moderate Synthesis — "this was part of my life"

Nostalgia is simultaneously $dP/d\tau > 0$ (joy of memory) and $\gamma_{SD} \approx 0$ (awareness of irreversibility). Two opposing signals create the unique "bittersweet" taste.

Analogy. Basic emotions are like primary colours (red, blue, yellow). Complex emotions are mixed colours: nostalgia — mauve (joy + sadness), awe — gold (joy + surprise + depth). The 30D emotional space (T-147 [T]) makes it possible to describe the full "spectrum" of emotions, not just the named colours. Details — in CC theorems.

Comparison with other taxonomies

How does the UHM taxonomy relate to classical models of emotion?

Model	Number of basic	Structure	Mechanism	Status in UHM
Ekman (1971)	6	Discrete categories	Facial expression	6 regions in 30D space [I]
Russell (1980)	2 axes	Continuous circumplex	Valence + arousal	Projection onto $(V, A)$ = $(\mathrm{sign}(dP/d\tau),
Plutchik (1980)	8	Wheel with intensity	Evolutionary functions	8 regions, intensity = $
Feldman Barrett (2017)	0 (constructed)	No basic emotions	Predictive coding	$\sigma(\Gamma)$ — "construction", $(dP/d\tau)$ — "affective root" [C]
UHM	30D	Continuous space	$dP/d\tau + \sigma(\Gamma)$	Full model T-147 [T]

The main difference between UHM and all previous models: emotion is not a primitive (as in Ekman), not purely bodily (as in James), not purely cognitive (as in Schachter), but a derived quantity — it is computed from the dynamics of the single fundamental variable $P$, enriched by sector information $\sigma(\Gamma)$.

Conditions for reflexive access to emotions

Statement C.2 (Threshold of emotional reflection) [C]

Condition: The threshold $R_{\text{th}} = 1/3$ is a theorem [T] ($K = 3$ from the triadic decomposition).

Reflexive access to one's own emotions (the capacity to "notice that I feel fear") requires level L2:

$$R(\Gamma) \geq R_{\text{th}} = \frac{1}{3}$$

At $R < R_{\text{th}}$ emotions are experienced but not reflected upon. The system acts "emotionally" but has no model of its own emotions.

The difference between experiencing and knowing

This distinction is fundamental and is often confused in ordinary language:

	Experiencing emotion (L1)	Knowing the emotion (L2)
Condition	$\gamma_{DE} \neq 0$	$R \geq 1/3$, $\Phi \geq 1$
Example	A dog whimpers in fear	A person says "I am afraid"
Behaviour	Automatic reaction	Conscious choice of reaction
Verbal description	Impossible	Possible
Control	Only reflexive	Reflexive (in principle)

This explains the distinction between emotional behaviour (L1) and emotional self-awareness (L2). For further detail — see interiority hierarchy.

Analogy. A dog experiences fear ($dP/d\tau < 0$ as $P$ approaches $P_{\text{crit}}$) — this is L1, emotional behaviour: it runs away. A human also experiences fear, but additionally knows that they experience it ($R \geq 1/3$, level L2): "I am afraid, and I notice that I am afraid." This distinction has practical significance for pathologies of consciousness: in alexithymia ($\mathrm{Gap}(L,E) \to 1$) emotions are experienced but not perceived — formally L2, but with a "blocked" reflection channel.

Evolutionary meaning

The link between emotions and $dP/d\tau$ has a direct evolutionary meaning. Let us return to Darwin: emotions are universal because they serve a survival function. In UHM terms this function is the monitoring of viability:

Emotion	Signal	Function	Adaptive behaviour
Fear	$dP/d\tau < 0$, $P \to P_{\text{crit}}$	Threat detection	Flight, freezing
Anger	$dP/d\tau < 0$, $\gamma_{DD}$ ↑↑	Energy mobilisation	Fight, territory defence
Joy	$dP/d\tau > 0$	Reinforcement of successful behaviour	Continuation of current strategy
Sadness	$dP/d\tau \approx 0$, $P$ low	Signal to revise strategy	Social support, restructuring
Surprise	$	d^2P/d\tau^2	\gg 0$
Disgust	$\mathrm{Gap}(S,E)$ ↑↑	Avoidance of "toxic"	Rejection, gag reflex

• Negative emotions ($dP/d\tau < 0$) signal loss of coherence — motivate active countermeasures
• Positive emotions ($dP/d\tau > 0$) signal growth of coherence — reinforce current behaviour
• Surprise ($|d^2P/d\tau^2| \gg 0$) signals unpredictability — switches attention

In terms of the evolution equation, emotions are the "interior projection" of the balance between decoherence $\mathcal{D}_\Omega$ and regeneration $\mathcal{R}$. This balance is formalised in Coherence Cybernetics as the hedonic vector $V_{\text{hed}} = dP/d\tau$ (T-103 [T]).

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What we have learned

1. The history of emotions — from Darwin to Feldman Barrett — prepares the UHM position: emotions are not primitives, not illusions, but derivatives of viability dynamics
2. Emotion = triple $(dP/d\tau, d^2P/d\tau^2, \sigma(\Gamma))$ — fully determined by the dynamics of the coherence matrix
3. Valence = sign of $dP/d\tau$, arousal = modulus $|dP/d\tau|$ — reproduce Russell's model
4. 6 basic emotions (Ekman) receive a numerical description via $P$, $dP/d\tau$, $d^2P/d\tau^2$, and sector signature
5. Fear is the fundamental emotion: its intensity diverges as $P \to P_{\text{crit}} = 2/7$
6. Complex emotions are superpositions of basic sector patterns in 30D space (T-147 [T])
7. Reflection on emotions requires $R \geq 1/3$ (L2) — below this threshold emotions are experienced but not perceived

Bridge to the next chapter

Emotions unfold in time — the experience of "fear" takes time, "joy" lasts. But how does the subject experience time itself? Why does it sometimes "fly" and sometimes "drag"? In the next chapter — Subjective time — we will show that the subjective tempo is determined by the coherence $\gamma_{OE}$ between Foundation (internal clock) and Interiority (experience).

Related Documents

• Viability — canonical definition of $P$ and $P_{\text{crit}}$
• Evolution equation — dynamics of $\Gamma(\tau)$ and the logical Liouvillian $\mathcal{L}_\Omega$
• Interiority hierarchy — levels L0–L4, conditions for L2
• Qualia structure — 21-pair taxonomy and $\gamma_{DE}$ as "affection"
• Gap semantics — Gap(S,E) and phase diagnostics
• Coherence Cybernetics theorems — 30D emotional space, hedonic vector $V_{\text{hed}}$
• T-147 [T]: 30D emotional space — full model $\mathbf{e}(\Gamma) \in \mathbb{R}^{30}$, replacing the scalar $dP/d\tau$