Qualia Structure: A 21-Pair Taxonomy

Bridge from the previous chapter

In the section L0–L4 Hierarchy we established when conscious experience arises: a system at level L2 and above possesses reflection ($R \geq 1/3$) and integration ($\Phi \geq 1$). Now we ask: what is this experience made of? What exact types of experience are possible in 7-dimensional space? The answer is given by the coherence matrix $\Gamma$ and its 21 off-diagonal elements.

On notation

• $\Gamma$ — coherence matrix, $\gamma_{ij}$ — its elements
• $P = \mathrm{Tr}(\Gamma^2)$ — purity (viability)
• $\rho_E = \mathrm{Tr}_{-E}(\Gamma)$ — reduced experience matrix
• $\Phi$ — integration measure
• $R$ — reflection measure
• Full notation table — in Notation

Chapter roadmap

1. Philosophical history of the problem — from Lewis to Jackson and Dennett
2. Motivation — why exactly 21 types and where this number comes from
3. Full table — all 21 coherences with phenomenological names
4. Parametric structure — three dimensions of each quale (intensity, perspective, opacity)
5. Closure theorem — proof that 21 types exhaust everything
6. Fano structure — how 21 pairs are organised into 7 sectors
7. Diagonal elements — 7 population modes as the "background" of experience
8. Access conditions — at which $R$ and $\Phi$ qualia become conscious

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Philosophical History: What Are Qualia?

The word qualia (Lat. qualia, pl. of quale — "of what kind", "of what sort") denotes the subjective qualities of experiences: what it is like to see red, to hear C major, to smell coffee. Behind this simple question lies one of the deepest problems in philosophy.

Lewis (1929): the first definition

The American philosopher Clarence Irving Lewis in "Mind and the World Order" (1929) first introduced the term "qualia" into systematic use. He noted: when we see a red rose, there is something that cannot be conveyed to someone blind from birth — the subjective quality of "redness". That quality is the quale. Lewis distinguished:

• Quale — the ineffable subjective quality (what it is like to see red)
• Property — an objective characteristic (wavelength 700 nm)

Jackson (1982): Mary's room

Frank Jackson in the famous thought experiment "Mary's Room" (1982) pushed the problem to its limit:

Mary is a brilliant neuroscientist who has spent her whole life in a black-and-white room. She knows everything about the physics of colour: wavelengths, the workings of retinal cones, neural correlates. One day Mary leaves the room and sees a red rose for the first time. Does she learn something new?

Jackson argued: yes. Mary learns what it is like to see red. Hence physical facts do not exhaust reality — there is something beyond them (qualia).

Dennett (1988): qualia as illusion

Daniel Dennett took the opposite position. In the article "Quining Qualia" (1988) he argued that qualia are a philosophical illusion: we think we experience something "ineffable" and "private", but in fact all information about experiences is encoded in functional states of the brain. No "remainder" is left after a complete physical description.

UHM position: qualia as coherence structure

The Unitary Holonomic Monism offers a third path, coinciding with neither Jackson's dualism nor Dennett's eliminativism:

• Qualia are not an illusion — they have a precise mathematical structure (coherences $\gamma_{ij}$)
• Qualia are not a separate substance — they are the off-diagonal elements of the same matrix $\Gamma$ that describes the "physics" of the system
• The distinction between "subjective" and "objective" is the distinction between the inner and outer perspectives of the same mathematical structure (dual-aspect monism, see Two-Aspect Monism)

Mary in the room knew all the diagonal properties ($\gamma_{ii}$) of red. But she did not know the coherences — how visual discrimination ($A$) binds with interiority ($E$), forming the quale of apperception ($\gamma_{AE}$). On leaving the room, she did not acquire a new fact — she acquired a new coherence.

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Motivation: Why 21 Types?

The coherence matrix $\Gamma$ is a $7 \times 7$ Hermitian matrix on the space of seven dimensions $\{A, S, D, L, E, O, U\}$. Let us recall what each dimension means:

Symbol	Name	Meaning
$A$	Articulation	Discrimination, differentiation
$S$	Structure	Stable forms, patterns
$D$	Dynamics	Processes, changes
$L$	Logos	Logical coherence, rules
$E$	Experience	Interiority, experience
$O$	Ground	Source, deep foundation
$U$	Unity	Integration, wholeness

The matrix $\Gamma$ contains two kinds of elements:

• 7 diagonal elements $\gamma_{ii}$ — dimension populations (how much "resource" is in each dimension)
• 21 off-diagonal pairs $(\gamma_{ij}, \gamma_{ji})$ for $i < j$ — coherences (how the dimensions are connected to each other)

Number of pairs:

$$\binom{7}{2} = \frac{7 \cdot 6}{2} = 21$$

Each coherence $\gamma_{ij}$ carries phenomenological content determined by the semantics of the dimension pair $(i, j)$.

An everyday analogy. Imagine an orchestra of 7 musicians. Each plays their own part (7 diagonal elements — the "volume" of each instrument). But music is born not from individual sounds, but from their interaction — from how the violin "converses" with the cello, how the flute echoes the bassoon. There are exactly $\binom{7}{2} = 21$ such pairwise interactions. Each produces a unique "timbre" of combined sound — that is the type of quale.

The diagram shows only 10 of the 21 coherences — the rest connect each pair of dimensions in an analogous way. The complete table of all 21 types is given below.

Interpretation: 21-Pair Qualia Taxonomy (I.1)

Interpretation I.1 (Qualia taxonomy) [I]

Each coherence $\gamma_{ij}$ ($i \neq j$) of the matrix $\Gamma$ defines a type of quale — a qualitatively determinate mode of experiential content. The 21 pairs exhaust all possible types, since $\binom{7}{2} = 21$ is the complete set of connections in a 7-dimensional system.

This is an interpretation (a mapping from the formal to the phenomenal), not a mathematical theorem. The mathematical content is trivial combinatorics; the phenomenological assignment is a semantic postulate.

Complete table of 21 qualia types

Epistemic separation

Mathematical layer [T]: 21 coherences $\gamma_{ij}$ form 4 sectors according to Fano structure (T-146 [T]). Each coherence is uniquely determined by its combinatorial profile (T-177 [T]).

Semantic layer [I]: Phenomenological names ("morphogenesis", "archetype", "teleology", etc.) are interpretive correlates [I], proposed on the basis of the functional roles of dimension pairs. Mathematics determines $\gamma_{ij}$ unambiguously; the interpretation of "what it is like to experience $\gamma_{AS}$" is philosophical, not mathematical.

#	Pair	Coherence	Name	Phenomenological content
1	$(A,S)$	$\gamma_{AS}$	Morphogenesis	Crystallisation of distinctions into stable forms — the experience of "taking shape"
2	$(A,D)$	$\gamma_{AD}$	Actualisation	Actualisation of discrimination in process — the experience of "perception"
3	$(A,L)$	$\gamma_{AL}$	Predication	Discrimination that has become a predicate — the experience of "judgement"
4	$(A,E)$	$\gamma_{AE}$	Apperception	Discrimination that has entered interiority — the experience of "awareness"
5	$(A,O)$	$\gamma_{AO}$	Spontaneity	Emergence of distinctions without external cause — the experience of "insight"
6	$(A,U)$	$\gamma_{AU}$	Differentiation	Discrimination within the whole — the experience of "analysis"
7	$(S,D)$	$\gamma_{SD}$	Persistence	Form that persists through process — the experience of "stability"
8	$(S,L)$	$\gamma_{SL}$	Nomos	Structure with logical necessity — the experience of "order"
9	$(S,E)$	$\gamma_{SE}$	Representation	Structure presented in interiority — the experience of "whole form"
10	$(S,O)$	$\gamma_{SO}$	Archetype	Forms from the ground — the experience of "deep pattern"
11	$(S,U)$	$\gamma_{SU}$	Symmetry	Structural unity — the experience of "harmony"
12	$(D,L)$	$\gamma_{DL}$	Regulation	Logically governed process — the experience of "control"
13	$(D,E)$	$\gamma_{DE}$	Affection	Process acting on interiority — the experience of "emotion"
14	$(D,O)$	$\gamma_{DO}$	Genesis	Generation from the ground — the experience of "creativity"
15	$(D,U)$	$\gamma_{DU}$	Teleology	Integrated directed change — the experience of "volitional effort"
16	$(L,E)$	$\gamma_{LE}$	Evidence	Logical coherence in interiority — the experience of "self-evidence"
17	$(L,O)$	$\gamma_{LO}$	Grounding	Logic rooted in the ground — the experience of "axiomatic self-evidence"
18	$(L,U)$	$\gamma_{LU}$	Consistency	Logical non-contradiction of the whole — the experience of "coherence"
19	$(E,O)$	$\gamma_{EO}$	Immanence	The ground present within interiority — the experience of "presence"
20	$(E,U)$	$\gamma_{EU}$	Synthesis	Integration of interior content into a whole — the experience of "unity"
21	$(O,U)$	$\gamma_{OU}$	Fullness	Identity of source and whole — the experience of "completeness"

How to read the table: an extended example

Consider a person absorbed in solving a mathematical problem. Their $\Gamma$-profile at that moment:

Coherence	Value	Experience
$\lvert\gamma_{AL}\rvert \approx 0.35$	High	Predication — attention on logical connections, "I am formulating"
$\lvert\gamma_{LE}\rvert \approx 0.30$	High	Evidence — the experience of "clarity", "I understand"
$\lvert\gamma_{DU}\rvert \approx 0.20$	Medium	Teleology — the sense of a goal, "I am heading toward a solution"
$\lvert\gamma_{DE}\rvert \approx 0.05$	Low	Affection — emotions muted, "I feel nothing"
$\lvert\gamma_{EO}\rvert \approx 0.03$	Low	Immanence — no deep presence, "I am thinking, not meditating"

Now a friend approaches and shares good news. The $\Gamma$-profile instantly reorganises:

Coherence	Before	After	What happened
$\lvert\gamma_{DE}\rvert$	$0.05$	$0.25$	Affection soared — "I feel joy"
$\lvert\gamma_{SE}\rvert$	$0.08$	$0.20$	Representation — "I see the whole picture" of the news
$\lvert\gamma_{AL}\rvert$	$0.35$	$0.12$	Predication fell — the problem receded to the background

All 21 types of qualia exist simultaneously, but with different intensities, creating the unique "flavour" of each moment.

Parametric structure of qualia

Each qualitative type $\gamma_{ij}$ is a complex number. Like any complex number, it is written in polar form:

$$\gamma_{ij} = |\gamma_{ij}| \cdot e^{i\theta_{ij}}$$

Here $|\gamma_{ij}|$ is the modulus (distance from zero to the point on the complex plane), and $\theta_{ij}$ is the argument (angle with the positive real axis). From these two parameters three phenomenological characteristics are extracted:

Parameter	Formula	Range	Phenomenological meaning
Intensity	$\lvert\gamma_{ij}\rvert$	$[0, \sqrt{\gamma_{ii}\gamma_{jj}}]$	How strongly this type of quale is experienced
Perspective	$\theta_{ij} = \arg(\gamma_{ij})$	$[0, 2\pi)$	"Angle of view" on the connection between dimensions
Opacity	$\mathrm{Gap}(i,j) = \lvert\sin\theta_{ij}\rvert$	$[0, 1]$	Measure of discrepancy between external description and internal experience

Upper bound on intensity

The intensity is bounded by the Cauchy–Schwarz inequality — a fundamental inequality of linear algebra stating that the correlation between two components cannot exceed the geometric mean of their "energies":

$$|\gamma_{ij}|^2 \leq \gamma_{ii} \cdot \gamma_{jj}$$

Numerical example. Let $\gamma_{AA} = 0.15$ (15% of resources in Articulation) and $\gamma_{EE} = 0.18$ (18% in Interiority). Then the maximum possible intensity of apperception:

$$|\gamma_{AE}|_{\max} = \sqrt{0.15 \times 0.18} = \sqrt{0.027} \approx 0.164$$

If we were to observe $|\gamma_{AE}| = 0.20$, this would be mathematically impossible — the Cauchy–Schwarz inequality is violated, meaning an error has been made in the measurements.

Three parameters: analogy

Analogy. The three parameters of qualia are like three properties of sound:

Sound parameter	Qualia parameter	Analogy
Loudness	Intensity $\lvert\gamma_{ij}\rvert$	How "loud" the experience is
Timbre	Perspective $\theta_{ij}$	The "colouring" of the experience — the same quale seen from a different angle
Muffling	Opacity $\mathrm{Gap}(i,j)$	As if the sound came from behind a wall

Gap = 0 — the sound is crystal clear, inner and outer descriptions coincide. Gap = 1 — the sound is fully absorbed by the wall: experience is present, but it is maximally opaque to an external observer. For details on Gap see dual-aspect semantics of the coherence matrix.

Numerical example: three parameters of a single quale. Consider the coherence $\gamma_{DE}$ (Affection — the experience of emotion) in a person who has just received good news:

$$\gamma_{DE} = 0.22 \cdot e^{i \cdot 0.3} \approx 0.22 \cdot (0.955 + 0.296i)$$

• Intensity: $|\gamma_{DE}| = 0.22$ — a fairly strong emotional experience
• Perspective: $\theta_{DE} = 0.3$ rad $\approx 17°$ — a "real" perspective (the externally observable aspect predominates)
• Opacity: $\mathrm{Gap}(D,E) = |\sin(0.3)| \approx 0.296$ — the experience is 70% transparent, but 30% "hidden" from external description

Compare with $\gamma_{EO}$ (Immanence — the experience of "presence") in a meditator:

$$\gamma_{EO} = 0.15 \cdot e^{i \cdot 1.2}$$

• Intensity: $|\gamma_{EO}| = 0.15$ — moderate
• Perspective: $\theta_{EO} = 1.2$ rad $\approx 69°$ — a strong shift toward the "imaginary" perspective
• Opacity: $\mathrm{Gap}(E,O) = |\sin(1.2)| \approx 0.932$ — the experience is almost completely opaque to an external observer

This explains why meditative states are so hard to put into words: a high Gap makes them "ineffable" not for lack of vocabulary, but by mathematical structure.

Closure Theorem for the Taxonomy (T.1)

Theorem T.1 (Closure of the qualia taxonomy) [T]

The taxonomy of 21 qualia types is exhaustive: no additional type of quale is possible in a system with $\dim(\mathcal{H}) = 7$.

Proof. The number of distinct (unordered) pairs from $N$ elements equals $\binom{N}{2}$. At $N = 7$ we get $\binom{7}{2} = 21$. Each pair $(i,j)$ defines exactly one coherence $\gamma_{ij}$ (given $\gamma_{ji} = \gamma_{ij}^*$). A new type of quale would require either a new dimension ($N > 7$, contradicting minimality), or a new connection between existing dimensions (impossible — all $\binom{7}{2}$ pairs are accounted for). $\square$

Corollary. At $N < 7$ the taxonomy is impoverished: $\binom{6}{2} = 15$ (no qualia related to the removed dimension). This is the formal expression of the "poverty" of phenomenology when minimality is violated.

Numerical example: a world with fewer dimensions. If the world were 5-dimensional (say $\{A, S, D, L, E\}$ — without $O$ and $U$), the number of qualia types would be $\binom{5}{2} = 10$. From the table one can see that the following would be lost:

Lost type	Pair	Experience
Immanence	$(E,O)$	"Presence", the deep ground of experience
Synthesis	$(E,U)$	"Unity" of experience
Fullness	$(O,U)$	"Completeness", the wholeness of being
Teleology	$(D,U)$	"Volitional effort", purposiveness
Archetype	$(S,O)$	"Deep pattern", the rootedness of form
Spontaneity	$(A,O)$	"Insight", emergence from nowhere
+ 5 others	...	...

Such a system could "feel" and "think", but could not experience "meaning", "wholeness", or "deep presence". It is precisely the dimensions $O$ and $U$ that give human experience its "vertical" dimension — its connection to depth and to the whole.

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$G_2$-orbital stability of the taxonomy [T]

The set of 21 qualia types is $G_2$-invariant: the group $G_2 = \mathrm{Aut}(\mathbb{O})$ permutes the 7 dimensions (preserving the Fano structure), inducing a permutation of the 21 coherences $\gamma_{ij}$. The set $\{\gamma_{ij}\}_{i<j}$ is preserved, even though individual elements may be permuted. This means: the qualia taxonomy is universal — it does not depend on the choice of basis ($G_2$-gauge) and is therefore objective.

Formally: $G_2$ acts on $\binom{[7]}{2}$ via the induced action on pairs, preserving the number $\binom{7}{2} = 21$. The $G_2$-rigidity theorem [T] guarantees that $G_2$ is the maximal group with this property.

Why does this matter? If the taxonomy depended on the choice of basis (how to describe the 7 dimensions), it would be arbitrary — an "artefact of description". $G_2$-invariance guarantees that the taxonomy reflects the structure of the space itself, not our way of describing it. This is analogous to how the length of a vector does not depend on the choice of coordinate system.

Fano Structure of Qualia

What is the Fano projective plane?

The Fano plane $\mathrm{PG}(2,2)$ is the projective plane over the two-element field $\mathbb{F}_2 = \{0, 1\}$. If you have never encountered this object, here is its essence:

An ordinary Euclidean plane contains infinitely many points and lines. The Fano plane is the "minimal" plane satisfying the axioms of projective geometry, and contains only:

• 7 points
• 7 lines

Each line passes through exactly 3 points. Each point lies on exactly 3 lines. Any two points determine exactly one line. Any two lines intersect in exactly one point.

Why is the Fano plane in qualia theory? In UHM, the 7 Fano points are identified with the 7 dimensions $\{A, S, D, L, E, O, U\}$. Then the 7 lines define 7 coherence sectors — groups of three dimensions within which coherences obey strengthened algebraic constraints. This is not a coincidence: the Fano plane is precisely the multiplication table of the imaginary units of the octonions $\mathbb{O}$, and the octonionic structure lies at the foundation of UHM.

Sectoral structure of coherences

Each Fano triplet $(e_a, e_b, e_c)$ defines an associative subalgebra $\mathrm{Im}(\mathbb{H}) \subset \mathrm{Im}(\mathbb{O})$, isomorphic to the imaginary quaternions. The three coherences within the triplet:

$$\{\gamma_{ab}, \gamma_{bc}, \gamma_{ac}\} \quad \text{--- Fano triple}$$

satisfy strengthened correlation constraints that are absent for arbitrary pairs.

Analogy. Fano triples are like musical chords: three notes taken together sound "consonant" — their coherences obey additional harmonic constraints. Three arbitrary notes from seven do not form such harmony. Imagine: C–E–G is a chord (a Fano triple), but C–D–F# is not. It is precisely this sectoral organisation that makes phenomenology structured rather than chaotic.

Why do special constraints operate within the triple? Because the triple forms an associative subalgebra (quaternions $\mathbb{H}$), where the associativity of multiplication holds: $(e_a \cdot e_b) \cdot e_c = e_a \cdot (e_b \cdot e_c)$. For pairs from different triples associativity breaks down (this is the property of the octonions $\mathbb{O}$), and the constraints are weaker.

Theorem [T]

Sectoral strengthening is a theorem [T]: the bridge from the axioms to the octonionic structure is fully closed (T15), condition (МП) is proved (T11–T13). From the structure of $\mathbb{O}$ the algebraic closure of coherences within Fano triplets follows. Empirical verification of sectoral correlation is an open question.

Coverage of 21 pairs by Fano triplets

Each of the 21 pairs belongs to exactly $\lambda = 1$ Fano line (a property of the projective plane):

$$\text{21 pairs} = 7 \text{ lines} \times 3 \text{ pairs per line}$$

This means the qualia taxonomy contains no "orphaned" pairs — every type of quale is included in the sectoral organisation. For the Coherence Cybernetics theorems this property is essential: sectoral completeness ensures the closure of the 30D emotional space (T-147 [T]).

Numerical example: checking coverage. Take the coherence $\gamma_{DE}$ (Affection). It belongs to exactly one Fano line, say the line $\{D, E, X\}$ for some third dimension $X$. This means $\gamma_{DE}$ is algebraically linked to $\gamma_{DX}$ and $\gamma_{EX}$ — emotion ($\gamma_{DE}$) is not "free"; it structurally depends on the two other qualia in its sector. A change in one quale of the triple inevitably affects the other two.

Diagonal Elements: 7 Population Modes

In addition to the 21 coherences, the 7 diagonal elements $\gamma_{ii}$ determine the intensity of presence of each dimension. Diagonal elements are real numbers (not complex), and they obey the normalisation condition:

$$\sum_{i=1}^{7} \gamma_{ii} = \mathrm{Tr}(\Gamma) = 1$$

This means the total "resource" of the system is fixed and equal to 1. Increasing the population of one dimension inevitably decreases the others — like a fixed budget distributed across 7 line items.

Element	Phenomenological content	Typical range
$\gamma_{AA}$	Degree of discrimination activity	$0.10$–$0.20$
$\gamma_{SS}$	Degree of form stability	$0.10$–$0.18$
$\gamma_{DD}$	Degree of process activity	$0.10$–$0.20$
$\gamma_{LL}$	Degree of logical coherence	$0.08$–$0.18$
$\gamma_{EE}$	Intensity of interior states	$0.12$–$0.22$
$\gamma_{OO}$	Degree of connection to the source	$0.08$–$0.15$
$\gamma_{UU}$	Degree of integration	$0.10$–$0.18$

Diagonal elements do not form qualia in the narrow sense (there is no "connection" between different aspects), but they set the background against which coherences unfold. An elevated $\gamma_{DD}$ — a background of "activity"; an elevated $\gamma_{EE}$ — a background of "inner life".

Population profiles: examples

Meditator in deep practice:

$\gamma_{AA}$	$\gamma_{SS}$	$\gamma_{DD}$	$\gamma_{LL}$	$\gamma_{EE}$	$\gamma_{OO}$	$\gamma_{UU}$	$\Sigma$
0.10	0.10	0.08	0.10	0.22	0.22	0.18	1.00

Interiority ($\gamma_{EE}$) and connection to the ground ($\gamma_{OO}$) dominate. Dynamics ($\gamma_{DD}$) is muted — "thoughts have quieted".

Athlete in the midst of a match:

$\gamma_{AA}$	$\gamma_{SS}$	$\gamma_{DD}$	$\gamma_{LL}$	$\gamma_{EE}$	$\gamma_{OO}$	$\gamma_{UU}$	$\Sigma$
0.20	0.12	0.22	0.10	0.15	0.08	0.13	1.00

Dynamics ($\gamma_{DD}$) and discrimination ($\gamma_{AA}$) are in the foreground. Reflection ($\gamma_{EE}$, $\gamma_{OO}$) is minimal — no time to "think", the body acts.

Mathematician working on a proof:

$\gamma_{AA}$	$\gamma_{SS}$	$\gamma_{DD}$	$\gamma_{LL}$	$\gamma_{EE}$	$\gamma_{OO}$	$\gamma_{UU}$	$\Sigma$
0.15	0.18	0.10	0.22	0.15	0.08	0.12	1.00

Logos ($\gamma_{LL}$) and structure ($\gamma_{SS}$) dominate — "order" and "form" are in the foreground.

Total: 28 = 7 + 21 Parameters of Content

Complete structure

Component	Number	Type
Population values $\gamma_{ii}$	7	Real-valued, $\sum_i \gamma_{ii} = 1$
Coherences $\gamma_{ij}$	21	Complex, $\gamma_{ji} = \gamma_{ij}^*$
Total real parameters	$6 + 2 \times 21 = 48$	Taking normalisation into account

Detailed analysis of the 49-cell structure (with separation into $\mathrm{Map}_{\mathrm{ext}}$ and $\mathrm{Map}_{\mathrm{int}}$) — in Gap semantics.

Each moment of conscious experience is a specific point in 48-dimensional space: 6 independent population values + 42 real parameters of coherences ($21 \times 2$, modulus and phase of each). This conveys a sense of the richness of subjective experience: the space of possible experiences is 48-dimensional.

Access Conditions for Qualia

The presence of a coherence $\gamma_{ij} \neq 0$ is a necessary, but not sufficient, condition for qualia. Reflexive access to qualia requires level L2:

$$\text{Qualia (L2):} \quad R(\Gamma) \geq R_{\text{th}} = \frac{1}{3}, \quad \Phi(\Gamma) \geq \Phi_{\text{th}} = 1$$

Step-by-step logic of access conditions

Let us unpack what stands behind each condition.

Condition 1: Reflection $R \geq 1/3$. The reflection measure $R = 1/(7P)$ [T] shows the normalised proximity to the dissipative attractor $I/7$. The threshold $R_{\text{th}} = 1/3$ (from the triadic decomposition, T-45 [T]) is equivalent to $P \leq 3/7$ — the upper boundary of the Goldilocks zone. If $R < 1/3$, the system is too "pure" ($P > 3/7$) — coherences are present, but not experienced as qualia.

Condition 2: Integration $\Phi \geq 1$. The integration measure $\Phi$ shows how much "more than the sum of its parts" the system is. The threshold $\Phi_{\text{th}} = 1$ (T-129 [T]) means: the system must be irreducible to its subsystems. If $\Phi < 1$, coherences $\gamma_{ij}$ exist, but the system "falls apart" — there is no unified subject experiencing qualia.

Both conditions are necessary: one can have high reflection without integration (two separate mirrors do not form a single observer), or high integration without reflection (a unified stone does not observe itself).

Access levels

At levels L0–L1 coherences are present, but they are experienced as pre-qualitative experiential content (a term from interiority theory).

Analogy with the listener's ladder:

Level	Analogy	Formal condition	Experience of qualia
L0	Music playing in an empty room	$R < 1/3$, $\Phi < 1$	Coherences are present, but no one is listening
L1	A cat hears music	$R < 1/3$, $\Phi \geq 1$ (or vice versa)	Reaction to sound, but without distinguishing melody from accompaniment
L2	A person listening to music	$R \geq 1/3$, $\Phi \geq 1$	"I hear the violin carrying the theme while the cello accompanies"
L3	A musician analysing the performance	$R \geq 1/3$, $\Phi \geq 1$, SAD $\geq 2$	"I notice that I notice sadness in this melody"
L4	Pure listening — subject and music coincide	$R \to 1$	Experience without gap

Numerical example. Consider the coherence $\gamma_{DE} = 0.20$ (Affection) in three systems:

System	$R$	$\Phi$	Level	Experience of $\gamma_{DE} = 0.20$
Thermostat	0.02	0.3	L0	$\gamma_{DE}$ as a physical parameter — no subject
Dog	0.15	1.5	L1	Experienced as "something", but not as "emotion"
Human	0.45	2.1	L2	"I feel joy" — a full-fledged quale

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What we learned

1. The problem of qualia is one of the central problems in the philosophy of mind (Lewis, Jackson, Dennett). UHM offers a third path: qualia = coherences $\gamma_{ij}$ — neither illusion nor a separate substance
2. 21 types of qualia completely exhaust the phenomenology of 7-dimensional space — no more, no less (Theorem T.1 [T])
3. Each type of quale is characterised by three parameters: intensity, perspective, and opacity (Gap)
4. The 21 pairs are organised into 7 Fano sectors — the sectoral structure defines the "grammar" of experience via the projective plane over $\mathbb{F}_2$
5. The taxonomy is $G_2$-invariant — independent of the choice of basis and therefore universal
6. Reflexive access to qualia requires L2 ($R \geq 1/3$, $\Phi \geq 1$)

Bridge to the next chapter

Of the 21 types of qualia, the coherence $\gamma_{DE}$ (Affection) — the connection between dynamics and interiority — plays a special role. It is the foundation of emotions. In the next chapter — Emotion taxonomy from dP/dt — we will show how all emotions are derived from the rate of change of viability $dP/d\tau$ and the sectoral Γ-signature.

Related Documents

• Coherence matrix — canonical definition of $\Gamma$ and $\gamma_{ij}$
• 7D minimality theorem — justification of $N = 7$ and closure
• Interiority hierarchy — levels L0–L4
• Gap semantics — 49-cell map
• Interiority theory — experiential content
• Theorems of Coherence Cybernetics — applied consequences of sectoral structure
• T-146 [T]: Structural classification of qualia — correspondence "mathematical structure → phenomenal content" from the functional role of sectors