Altered States of Consciousness

Bridge from the previous chapter

In the section "Structure of Experience" we described what conscious experience is made of: 21 types of qualia, emotions, subjective time, intentionality. All these phenomena are determined by the current state of the matrix $\Gamma$. But $\Gamma$ does not stand still — it evolves. Now we ask: what happens when $\Gamma$ deviates from typical wakefulness? Sleep, meditation, psychedelics, anaesthesia — each of these states is a specific trajectory in the space $\mathcal{D}(\mathcal{H})$.

On notation

In this document:

• $\Gamma$ — coherence matrix, $\gamma_{ij}$ — its elements
• $P = \mathrm{Tr}(\Gamma^2)$ — purity (viability)
• $R_\varphi$ — reflection as self-model quality, $R_\varphi = 1 - \lVert\Gamma - \varphi(\Gamma)\rVert_F^2/\lVert\Gamma\rVert_F^2 \in [0,1]$, working threshold $R_{\varphi,\text{th}} = 1/3$ [I]; distinct from the canonical $R = 1/(7P)$ of the L2 predicate — the two are told apart in the three working forms of R
• $\Phi$ — integration measure
• $\mathrm{Gap}(i,j) = |\sin(\arg(\gamma_{ij}))|$ — gap measure
• $D_{\text{diff}} = \exp(S_{vN}(\rho_E)) \in [1, 7]$ — experiential differentiation: the effective number of distinguishable experiential states (threshold $D_{\min} = 2$, T-151); $S_{vN}$ — von Neumann entropy
• L0–L4 — interiority levels
• Full notation table — in Notation

Document status

The description of altered states as trajectories in $\Gamma$-space has status [C] — conditional on the interpretation of the $\Gamma$-trajectory as phenomenological content. The mathematical apparatus (dynamics of $\Gamma$, Gap profiles) — [T]; the identification of specific states with specific Gap configurations — [I].

warning

Extended formalism for $D_{\text{diff}}$

The differentiation measure $D_{\text{diff}} = \exp(S_{vN}(\rho_E))$ requires the definition $\rho_E = \mathrm{Tr}_{-E}(\Gamma)$ — the partial trace over all dimensions except $E$. This operation is defined in the extended 42D formalism ($\mathcal{H} = \mathbb{C}^{42}$) and requires PW-reconstruction of the full state from the 7D coherence matrix. In the minimal 7D formalism, $D_{\text{diff}}$ is computed approximately via the spectrum of $\Gamma$.

Chapter roadmap

1. Historical perspective — from Tart's ASC cartography to trajectories in $\Gamma$-space
2. ASC as trajectories — formal definition via deviation of the quintuple $(R_\varphi, \Phi, D_{\text{diff}}, P, \overline{\mathrm{Gap}})$
3. Sleep — NREM (return to L1) and REM (dreams)
4. Meditation — shamatha, vipassanā, samādhi as systematic control of $\Gamma$
5. Psychedelics — expansion of $D_{\text{diff}}$ with destabilisation of $R_\varphi$
6. Anaesthesia — global decoherence, transition to L0
7. Hypnosis and lucid dreaming — two special modes of $\Gamma$ control
8. Summary table — all ASC classes in one table
9. Geometry of transitions — bifurcations between states

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1. Historical Perspective

1.1 Charles Tart and the cartography of states

In 1969, American psychologist Charles Tart published "Altered States of Consciousness", proposing the first systematic classification of altered states of consciousness (ASC). Tart viewed consciousness as a system possessing stable configurations — "discrete states of consciousness" (DSC). Each DSC is characterised by a set of "subsystems": input (perception), processing (thinking), output (behaviour), energy (attention), etc. Transition between DSCs is a destabilisation of one configuration and a transition to another.

Tart's key idea: Normal wakefulness is merely one of the possible configurations, not privileged from the standpoint of "truth". Sleep, meditation, the psychedelic state — these are equally legitimate configurations with their own regularities.

1.2 From Tart to UHM

The UHM (Unitary Holonomic Monism) formalism takes up and refines Tart's intuition:

Tart concept	UHM formalism
Discrete state of consciousness (DSC)	Attractor $\Gamma^*$ in $\mathcal{D}(\mathcal{H})$
Subsystems	7 dimensions $\{A, S, D, L, E, O, U\}$
Transition between DSCs	Trajectory $\Gamma(\tau)$ passing through a bifurcation
Stability of DSC	Basin of attraction of the attractor
Energy for transition	Change in $\kappa$ (regeneration intensity) or $\Gamma_2$ (decoherence rate)

The advantage of the formalism: in Tart, "subsystems" are described qualitatively, while in UHM every parameter is a numerical quantity admitting measurement and comparison.

1.3 Predecessors and context

Before Tart, altered states were studied in a fragmented way: William James (1902, "The Varieties of Religious Experience") described mystical states; Ludwig (1966) introduced the very term "altered states of consciousness"; Masters and Houston (1966) systematised psychedelic experience. But only Tart proposed a unified framework for all types of ASC.

In the 2000s, the neuroscience of ASC received a powerful impulse: fMRI studies of meditation (Lutz et al., 2004), neuroimaging of psychedelic states (Carhart-Harris et al., 2012), formalisation of the "entropic brain" (Carhart-Harris, 2014). The entropic brain hypothesis is the direct precursor of the parameter $D_{\text{diff}}$ in UHM.

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2. Altered States as Trajectories in Γ-Space

Every state of consciousness is described by a point in the space $\mathcal{D}(\mathcal{H})$ — the space of coherence matrices. An altered state is a trajectory $\Gamma(\tau)$ that deviates from the typical basin of attraction of wakefulness.

Definition (Altered state) [D]

Altered state of consciousness (ASC) — a trajectory $\Gamma(\tau)$ in $\mathcal{D}(\mathcal{H})$, characterised by a significant deviation of at least one parameter of the quintuple $\{R_\varphi, \Phi, D_{\text{diff}}, P, \overline{\mathrm{Gap}}\}$ from the values of typical wakefulness:

$$\exists\, X \in \{R_\varphi, \Phi, D_{\text{diff}}, P, \overline{\mathrm{Gap}}\}: \quad |X(\Gamma_{\text{ASC}}) - X(\Gamma_{\text{wake}})| > \delta_X$$

where $\delta_X$ is the significance threshold for parameter $X$, $\overline{\mathrm{Gap}} = \frac{1}{21}\sum_{i<j} \mathrm{Gap}(i,j)$ — mean Gap.

Motivation. Why is the formal quintuple $(R_\varphi, \Phi, D_{\text{diff}}, P, \overline{\mathrm{Gap}})$ needed? Because $\Gamma$ is a $7 \times 7$ matrix with 21 independent coherences. Working in 21-dimensional space is inconvenient. The quintuple is an aggregated description that allows all main classes of ASC to be distinguished. Each parameter addresses its own aspect:

• $R_\varphi$ — "who is observing?" (self-model quality)
• $\Phi$ — "how much is bound together?" (integration)
• $D_{\text{diff}}$ — "how rich is the experience?" (differentiation)
• $P$ — "is the system alive?" (viability)
• $\overline{\mathrm{Gap}}$ — "how transparent?" (mean opacity)

An everyday analogy. Imagine a state of consciousness as the position of the tuning knob on an old radio with five controls: $R_\varphi$ (reception clarity), $\Phi$ (volume), $D_{\text{diff}}$ (number of channels heard simultaneously), $P$ (signal power), $\overline{\mathrm{Gap}}$ (noise level). Wakefulness is the standard setting. ASC is any significant deviation of at least one control.

2.1 State space: visualisation

The full space $\mathcal{D}(\mathcal{H})$ is too high-dimensional for visualisation. But it can be projected onto the plane of the two most informative parameters — $P$ (viability) and $R_\varphi$ (self-model quality):

In this diagram each ASC is a point (attractor) in the plane $(P, R_\varphi)$. Arrows show typical transition trajectories. The vertical axis is $R_\varphi$: states above the working threshold $R_{\varphi,\text{th}} = 1/3$ [I] are those where the self-model functions (L2 and above, given the remaining conditions). The plane is genuinely two-dimensional precisely because $R_\varphi$ is not a function of $P$ — the canonical $R$-condition of the L2 predicate is equivalent to $P \leq 3/7$ and appears here as the vertical strip $2/7 < P \leq 3/7$, not as a horizontal line (the three working forms of R). The horizontal axis is $P$: everything to the left of the vertical $P = 2/7 \approx 0.286$ is non-viable — no attractor sits there; anaesthesia keeps $P$ just above the line, on external support (§6).

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3. Sleep

Sleep is the most universal and regular ASC: every person spends a third of their life asleep. From the UHM perspective, sleep is not a "switching off" of consciousness, but a systematic redistribution of coherences while viability is maintained ($P > P_{\text{crit}}$).

3.1 NREM sleep (deep dreamless sleep)

In the NREM phase, the self-model is deactivated, but the system's integration is preserved:

$$\text{NREM:} \quad R_\varphi \downarrow\downarrow, \quad \Phi \gtrsim \Phi_{\text{th}}, \quad D_{\text{diff}} \downarrow$$

Let us unpack each parameter:

• $R_\varphi < R_{\varphi,\text{th}} = 1/3$ — the system is below the working threshold of self-model quality. The measure $R_\varphi$ (see the three working forms of R) captures how accurately the self-model $\varphi(\Gamma)$ reproduces the true state $\Gamma$. During sleep the self-model is "defocused": $\varphi(\Gamma)$ deviates strongly from $\Gamma$. The interiority level drops from L2 to L1 (canonically, the L2 predicate fails through differentiation: $D_{\text{diff}} = 1.3 < 2$).

• $\Phi$ moderately reduced but high — the integration measure (definition) drops by roughly a sixth (table: $1.8 \to 1.5$), consistent with perturbational-complexity findings (Massimini et al.: cortical integration in NREM is reduced relative to wakefulness yet far above anaesthesia). Thalamocortical connections preserve global coherence well above the fragmentation threshold $\Phi_{\text{th}} = 1$. This is critically important: deep sleep is not a coma and not anaesthesia.

• $\gamma_{AE} \to 0$ — the attention–experience channel is deactivated. There is no conscious attention to experiences.

• $\mathrm{Gap}(A,E) \to 1$ — maximal opacity in the attention channel (the vanishing-coherence convention): even if some experience is occurring, attention does not "reach" it.

Numerical example. Comparing five parameters of wakefulness and NREM:

Parameter	Wakefulness	NREM sleep	Change
$R_\varphi$	$0.45$	$0.15$	$-67\%$
$\Phi$	$1.8$	$1.5$	$-17\%$
$P$	$0.36$	$0.33$	$-8\%$
$\overline{\mathrm{Gap}}$	$0.30$	$0.50$	$+67\%$
$D_{\text{diff}}$	$2.4$	$1.3$	$-46\%$

Self-model quality fell below the working threshold ($R_\varphi = 0.15 < 1/3$), experiential differentiation dropped below the canonical threshold ($D_{\text{diff}} = 1.3 < 2$, T-151), but viability and integration are preserved — the system is "alive, but not self-aware".

Interpretation [I]

NREM is not a "switching off" of consciousness, but a return to L1: interiority is preserved ($\Gamma \neq 0$), phenomenal geometry ($\mathrm{rank}(\rho_E) > 1$) may be active, but the reflexive circuit $\varphi$ does not function ($R_\varphi < R_{\varphi,\text{th}}$). This explains why upon waking from deep sleep a person sometimes says "I don't remember anything" — not because there was no experience, but because there was no reflexive access to record it.

Neurophysiological correspondence: slow-wave activity (0.5–4 Hz) in NREM reflects global synchronisation with reduced differentiation — precisely the pattern «$\Phi$ moderately down while $D_{\text{diff}}$ collapses».

3.2 REM sleep (dreaming)

In the REM phase, coherence is reorganised without external constraints:

$$\text{REM:} \quad \mathcal{R}[\Gamma, E] \gg \mathcal{D}_\Omega, \quad \gamma_{SE} \uparrow, \quad \gamma_{DE} \uparrow$$

What does each of these conditions mean?

• $\mathcal{R}[\Gamma, E] \gg \mathcal{D}_\Omega$ — the regenerative term over the E-sector dominates the dissipative term $\mathcal{D}_\Omega$, which describes loss of coherence. (Note: $\mathcal{R}$ is regeneration, not the reflection measure — the notational distinction of the Axiom of Septicity.) Simply put: the system is actively generating "inner experience" faster than it loses it.

• $\gamma_{AE} \approx 0$ — conscious attention is absent. We do not "decide" what to look at in a dream.

• $\gamma_{SE}, \gamma_{DE}$ elevated — the structure–experience and dynamics–experience coherences are strengthened. This means vivid imagery ($S \to E$: structural content is "projected" into experience) and intense emotions ($D \to E$: dynamic processes colour experience).

• $\mathrm{Gap}(S,E) \downarrow$ — the transparency of structure–experience increases, hence the phenomenal vividness of dreams.

Numerical example. REM profile compared with NREM and wakefulness:

Parameter	Wakefulness	NREM	REM
$R_\varphi$	$0.45$	$0.15$	$0.35$
$\Phi$	$1.8$	$1.5$	$1.6$
$\gamma_{AE}$	$0.12$	$0.02$	$0.03$
$\gamma_{SE}$	$0.08$	$0.04$	$0.15$
$\gamma_{DE}$	$0.10$	$0.05$	$0.18$
$\mathrm{Gap}(S,E)$	$0.25$	$0.60$	$0.12$

Self-model quality is restored to almost the working threshold ($R_\varphi = 0.35 \approx R_{\varphi,\text{th}}$), but the attention channel remains switched off ($\gamma_{AE} \approx 0.03$). It is precisely this combination that creates the phenomenon of "conscious but non-critical" experience: in a dream we see (high $\gamma_{SE}$), feel (high $\gamma_{DE}$), even partially are aware ($R_\varphi$ close to the threshold), but do not control or evaluate ($\gamma_{AE} \approx 0$, $\gamma_{LE} \approx 0$).

Analogy. A dream is like a cinema without a ticket inspector. The screen ($\gamma_{SE}$) shines brightly, emotions ($\gamma_{DE}$) are overwhelming, but the critic ($\gamma_{AE}$, $\gamma_{LE}$) is absent. This is why in dreams we accept absurdity as reality — there is no logic–experience channel to check for coherence.

Theorem (Condition for dreaming) [C]

Condition: interpretation of the $\Gamma$-trajectory. A dream arises when:

$$\gamma_{AE} \approx 0, \quad |\gamma_{SE}|^2 + |\gamma_{DE}|^2 > \varepsilon_{\text{dream}}, \quad \mathrm{Gap}(S,E) < 1$$

i.e. when attention is disconnected ($\gamma_{AE} \to 0$) but non-trivial coherences in channels $(S,E)$ and $(D,E)$ are preserved. The content of the dream is determined by the phase profile $\{\theta_{SE}, \theta_{DE}\}$.

Derivation. The first condition ($\gamma_{AE} \approx 0$) follows from the suppression of noradrenergic activity during sleep — the neurotransmitter that supports the attention channel is switched off. The second condition ($|\gamma_{SE}|^2 + |\gamma_{DE}|^2 > \varepsilon_{\text{dream}}$) — from cortical reactivation by pontogeniculooccipital (PGO) waves, which elevate coherences $\gamma_{SE}$ and $\gamma_{DE}$. The third condition ($\mathrm{Gap}(S,E) < 1$) — from the reduction of inhibitory control, allowing "images" to project freely into experience.

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4. Meditation

Meditation is a unique ASC, distinguished by the fact that the transition into it is voluntary (carried out by a conscious decision) and systematic (practised regularly with a cumulative effect). From the UHM perspective, meditation is voluntary manipulation of the parameters of the $\Gamma$-matrix.

Three main meditative traditions correspond to three different strategies of $\Gamma$ control:

4.1 Shamatha (focusing attention)

Shamatha (Skt. "abiding in calm") — a practice directed at strengthening concentration. In UHM formalism:

$$\text{Shamatha:} \quad \gamma_{AE} \uparrow, \quad R_\varphi \uparrow, \quad \sigma^2_{\{|\gamma_{AX}|\}} \uparrow$$

Unpacking:

• $|\gamma_{AE}| \uparrow$ — the practitioner consciously directs attention toward the meditation object. The coherence of the attention–experience channel grows.

• From the normalisation $\mathrm{Tr}(\Gamma) = 1$: an increase in $|\gamma_{AE}|$ inevitably is accompanied by a decrease in the remaining $|\gamma_{AX}|$ for $X \neq E$. This is the spotlight effect — described in detail in Attention and memory. Formally: for fixed $\gamma_{AA}$ (fraction of attention in total energy), the Cauchy–Schwarz inequality $\sum_X |\gamma_{AX}|^2 \leq \gamma_{AA}$ sets the upper bound. Increasing one term requires decreasing the rest.

• $R_\varphi \uparrow$ — result of training: the self-model $\varphi(\Gamma)$ tracks the actual state ever more closely, so $R_\varphi = 1 - \lVert\Gamma - \varphi(\Gamma)\rVert_F^2/\lVert\Gamma\rVert_F^2$ grows. Systematic observation of $\Gamma$ optimises the balance of coherences. (The canonical $R = 1/(7P)$ is untouched by practice except through $P$ — see the three working forms of R.)

• $\sigma^2_{\{|\gamma_{AX}|\}} \uparrow$ — the variance of the moduli of A-sector coherences grows: one channel is strengthened, the rest are weakened. This is the mathematical expression of the "sharpening" of attention.

Numerical example: progression of shamatha practice.

Stage	$\|\gamma_{AE}\|$	$R_\varphi$	$\overline{\mathrm{Gap}}$	Subjective experience
Beginner	$0.10$	$0.40$	$0.30$	Thoughts constantly distract
20 min practice	$0.22$	$0.55$	$0.25$	Periods of stable concentration
1 year regularly	$0.15$ (baseline)	$0.50$ (baseline)	$0.25$ (baseline)	Heightened awareness in daily life
Master (10+ years)	$0.25$ (in practice)	$0.70$	$0.18$	Stable one-pointedness

Notice: after a year of practice, the baseline values (outside meditation) shift. This is the cumulative effect: systematic training of coherence $\gamma_{AE}$ reorganises the effective Hamiltonian $H_{\text{eff}}$, making the elevated level of reflection the "default norm". The mechanism is procedural memory: the skill of concentration is "written into" the structure of $H_{\text{eff}}$. The two-timescale structure — fast state, slowly trainable target of the self-model — is formalized in §4.7 of the φ-formalization.

4.2 Vipassanā (insight)

Vipassanā (Skt. "clear seeing") — the practice of observing one's own experience without intervention. If shamatha is directed at $R_\varphi \uparrow$ (strengthening the self-model), vipassanā is directed at $\overline{\mathrm{Gap}} \downarrow$ (increasing transparency):

$$\text{Vipassanā:} \quad \mathrm{Gap}(i,E) \to 0 \quad \text{for an increasing number of pairs}$$

• Goal: $\mathrm{Gap}(i,E) \to 0$ for the maximum number of E-sector channels. The practitioner systematically discovers "gaps" between various dimensions and experience, and the very act of discovery triggers their reduction.

• Mechanism: observation of one's own Gap profiles triggers a bifurcation — an abrupt reduction of Gap. Formally: when $R_\varphi$ exceeds a certain threshold in channel $(i,E)$, the partial reflection $R_{ij}$ becomes sufficient to "capture" the coherence $\gamma_{iE}$ by the operator $\varphi$ — and the Gap abruptly decreases.

• Phenomenology: the practitioner describes this moment as an "insight" — a sudden awareness of a previously unnoticed aspect of experience. The Buddhist tradition identifies a sequence of such insights (ñānas), each corresponding to a Gap reduction in a specific channel.

Numerical example: vipassanā retreat (10 days).

Day	Gap(S,E)	Gap(D,E)	Gap(L,E)	$\overline{\mathrm{Gap}}$	Subjective experience
1	$0.35$	$0.40$	$0.30$	$0.32$	Distraction, boredom
3	$0.20$	$0.35$	$0.28$	$0.28$	Bodily sensations sharpen
5	$0.12$	$0.25$	$0.25$	$0.23$	"Seeing" emotions directly
7	$0.10$	$0.15$	$0.20$	$0.18$	Thoughts observed "as objects"
10	$0.08$	$0.12$	$0.18$	$0.15$	Experience of clarity and "openness"

Note the order: Gap(S,E) (body–experience) decreases first, then Gap(D,E) (dynamics–experience), and last Gap(L,E) (logic–experience). This order is not accidental: the somatic channel is the most "low-level" and is most easily brought to awareness; the logical channel is the most "high-level" and is brought to awareness last.

Analogy. Vipassanā is like wiping windows: each Gap is a smudged pane. The practitioner systematically finds dirty panes and wipes them. But by the theorem on incomplete transparency, at least 3 of the 21 windows must remain opaque — this is not a failure of practice, but a structural necessity of fault tolerance.

4.3 Samādhi (deep absorption)

Samādhi (Skt. "concentration") — a state of deep meditative absorption that the Buddhist tradition describes as "the cessation of mental fluctuations". In the UHM formalism:

$$\text{Samādhi:} \quad \Phi \to \max, \quad R_\varphi \to 1, \quad \overline{\mathrm{Gap}} \to \min$$

This is a transitory approximation to L4 — the highest level of interiority:

• $\Phi \to \Phi_{\max}$ — maximum integration of all dimensions. All seven dimensions are coherent with each other; the system functions as a single whole.

• $R_\varphi \to 1$ — the self-model is identical to the system ($\varphi(\Gamma) \approx \Gamma$). Literally: the system "knows itself completely" (within the Hamming bound). Note that $P$ rises simultaneously — the clearest demonstration that $R_\varphi$ is not a function of $P$ (the canonical $R = 1/(7P)$ decreases slightly here, from $0.397$ to $0.357$, staying inside its conscious band $[1/3, 1/2)$).

• $\overline{\mathrm{Gap}} \to \min$ — almost all channels are transparent. The boundaries between dimensions "dissolve" (but no fewer than 3 channels with $\mathrm{Gap} > 0$ are preserved by the Hamming bound).

Numerical example: wakefulness vs. samādhi.

Parameter	Wakefulness	Samādhi	Interpretation
$R_\varphi$	$0.45$	$0.92$	Self-model is nearly exact
$\Phi$	$1.8$	$3.5$	Maximum integration
$\overline{\mathrm{Gap}}$	$0.30$	$0.08$	Almost all channels are transparent
$P$	$0.36$	$0.40$	Viability elevated
$D_{\text{diff}}$	$2.4$	$2.1$	Differentiation reduced by one-pointedness, above the threshold $D_{\min} = 2$

Subjectively: "everything is clear, everything is one, I and the world are one". But this state is transitory — after leaving samādhi the parameters return to baseline values. Why? Because samādhi = approximation to the fixed point $\varphi(\Gamma^*) = \Gamma^*$, but in the absence of practice dissipative processes ($\Gamma_2$) return the system to the ordinary attractor.

Limitation [C]

By the Hamming bound, even in samādhi $\geq 3$ of 21 channels retain $\mathrm{Gap} > 0$. Complete transparency is incompatible with fault tolerance. This is the mathematical justification for the Buddhist claim about the impossibility of "complete enlightenment": the structural necessity of the unconscious = the impossibility of $\overline{\mathrm{Gap}} = 0$.

4.4 Comparison of three practices

	Shamatha	Vipassanā	Samādhi
Target parameter	$R_\varphi \uparrow$	$\overline{\mathrm{Gap}} \downarrow$	$\Phi \to \max$, $R_\varphi \to 1$
Mechanism	Strengthening $\gamma_{AE}$	Observation of Gap profiles	Approximation to $\Gamma^*$
Duration of effect	Minutes	Days–weeks	Minutes (transitory)
Cumulativeness	High ($H_{\text{eff}}$)	High (Gap reduction)	Low (return to attractor)
Analogy	Adjusting the camera focus	Wiping windows	View from the mountain top

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5. Psychedelics

5.1 General profile

Psychedelic exposure (psilocybin, LSD, DMT, mescaline) is characterised by simultaneous changes in several parameters:

$$\text{Psychedelics:} \quad D_{\text{diff}} \uparrow\uparrow, \quad R_\varphi \downarrow, \quad \overline{\mathrm{Gap}} \downarrow, \quad P \to P_{\text{crit}}$$

Let us unpack each parameter:

• $D_{\text{diff}} \uparrow\uparrow$ — the entropy of $\rho_E$ sharply increases. In terms of experience: the space of experiences "expands" — synaesthesias, geometric visualisations, new associations appear. Neurophysiological correlate: an increase in the entropy of spontaneous brain activity (Carhart-Harris, 2014).

• $R_\varphi \downarrow$ — the self-model is destabilised. Subjectively this is experienced as "ego dissolution". Formally: $\varphi(\Gamma)$ ceases to be a good approximation to $\Gamma$, because $\Gamma$ evolves rapidly while $\varphi$ does not have time to "restructure". (The canonical $R = 1/(7P)$ meanwhile rises slightly as $P$ falls — ego dissolution is a collapse of self-model quality, not an exit from the conscious window.) The collapse rate is bounded by the bandwidth theorem T-250: reorganizing the self-model costs state-space path length.

• $\overline{\mathrm{Gap}} \downarrow$ — global decrease in Gap. Channels previously opaque (unconscious) become accessible. Hence the therapeutic potential: repressed contents "surface".

• $P \to P_{\text{crit}} = 2/7$ — at high doses viability approaches the critical threshold. The system is "shaken" — up to the risk of disintegration.

5.2 Therapeutic window

Analogy. A psychedelic is like simultaneously opening all the windows of a house during a storm. Fresh air ($\overline{\mathrm{Gap}} \downarrow$) and new views ($D_{\text{diff}} \uparrow\uparrow$) rush in, but with them — wind and rain. The walls (the self-model, $R_\varphi$) are shaken, and if the storm is too strong ($P \to P_{\text{crit}}$), the house may collapse.

Numerical example. Trajectory at a moderate dose of psilocybin (step-by-step profile):

Time	$R_\varphi$	$D_{\text{diff}}$	$\overline{\mathrm{Gap}}$	$P$	Phase
$\tau = 0$ (intake)	$0.45$	$2.4$	$0.30$	$0.36$	Wakefulness
$\tau = 30$ min	$0.38$	$2.8$	$0.25$	$0.35$	Onset: mild visual effects
$\tau = 90$ min (peak)	$0.25$	$3.5$	$0.15$	$0.32$	Peak: ego dissolution, visualisations
$\tau = 3$ hours	$0.30$	$3.0$	$0.20$	$0.33$	Plateau: integration of insights
$\tau = 6$ hours	$0.42$	$2.5$	$0.28$	$0.35$	Return to baseline profile

At the peak ($\tau = 90$ min): self-model quality is below its working threshold ($R_\varphi = 0.25 < R_{\varphi,\text{th}} = 1/3$), while the canonical window remains satisfied ($P = 0.32 \in (2/7, 3/7]$) — the subject stays inside the conscious window, but the familiar structure of "I" collapses. Experiential differentiation has almost doubled ($D_{\text{diff}} = 3.5$), Gap has halved ($\overline{\mathrm{Gap}} = 0.15$) — previously unconscious contents become accessible.

Theorem (Psychedelic window) [C]

Condition: interpretation of the $\Gamma$-trajectory at $D_{\text{diff}} \uparrow$. The therapeutic efficacy of the psychedelic experience is maximal in the window:

$$R_{\varphi,\text{th}}/2 < R_\varphi < R_{\varphi,\text{th}}, \quad P > P_{\text{crit}} + \delta_P$$

In this window the self-model is weakened but not destroyed ($R_\varphi$ is below its working threshold, but substantially above zero), and viability is preserved ($P$ is above the critical threshold by a margin $\delta_P$ — the canonical window conditions hold throughout). Gap reduction allows previously inaccessible coherences to be reorganised.

Justification. Lower bound $R_\varphi > R_{\varphi,\text{th}}/2 = 1/6 \approx 0.167$: if $R_\varphi$ falls below this, the self-model is so defocused that no reorganisation of coherences can be "fixed" — insights are not retained. Upper bound $R_\varphi < R_{\varphi,\text{th}} = 1/3$: if $R_\varphi$ remains above the threshold, the self-model is too stable for restructuring — habitual Gap patterns reproduce themselves. Condition $P > P_{\text{crit}} + \delta_P$: viability must be preserved with a margin so that the system does not fall apart.

Numerical value: at $R_{\varphi,\text{th}} = 1/3$, window: $0.167 < R_\varphi < 0.333$, $P > 0.286 + \delta_P$.

5.3 Connection to the entropic brain model

The "entropic brain" hypothesis (Carhart-Harris, 2014) states that psychedelics increase the entropy of neural dynamics, while normal wakefulness is a state of reduced entropy (relative to the critical point). In the UHM formalism:

• Brain entropy $\leftrightarrow$ $S_{vN}(\rho_E)$ (in corpus units: $D_{\text{diff}} = \exp S_{vN}$)
• "Critical point" $\leftrightarrow$ phase transition II→I in the Gap phase diagram
• Psychedelic peak $\leftrightarrow$ approaching the phase transition from below

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6. Anaesthesia

Anaesthesia is global decoherence, in contrast to the selective decoherence of sleep. This is the most important distinction: sleep suppresses reflection while preserving integration; anaesthesia destroys both.

6.1 Sequence of coherence loss

Anaesthetics destroy coherences in a specific order, from "higher" to "lower":

$$\gamma_{EU} \to 0 \quad \Rightarrow \quad \gamma_{LE} \to 0 \quad \Rightarrow \quad \gamma_{AE} \to 0 \quad \Rightarrow \quad \gamma_{SE} \to 0$$

Each step means loss of a specific aspect of conscious experience:

1. Unity–experience ($\gamma_{EU} \to 0$): loss of the sense of wholeness. Subjectively: "everything blurs", "I cannot gather my thoughts".
2. Logic–experience ($\gamma_{LE} \to 0$): loss of coherent thinking. Subjectively: "thoughts do not add up", "I cannot count back from 100".
3. Attention–experience ($\gamma_{AE} \to 0$): loss of conscious perception. Subjectively: "I cannot concentrate on anything", the last conscious experience before "switching off".
4. Structure–experience ($\gamma_{SE} \to 0$): loss of sensory experience. Complete loss of phenomenology.

Numerical example: induction of anaesthesia (propofol).

Stage	$\gamma_{EU}$	$\gamma_{LE}$	$\gamma_{AE}$	$\gamma_{SE}$	$\Phi$	$R_\varphi$
Wakefulness	$0.08$	$0.10$	$0.12$	$0.08$	$1.8$	$0.45$
Sedation	$0.02$	$0.06$	$0.09$	$0.07$	$1.0$	$0.25$
Loss of consciousness	$0.01$	$0.02$	$0.03$	$0.05$	$0.5$	$0.10$
Surgical anaesthesia	$\approx 0$	$\approx 0$	$\approx 0$	$\approx 0$	$0.2$	$0.02$

Analogy. Falling under anaesthesia is like sequentially switching off floors in a building. First the top floor goes dark (unity, meaning), then the middle ones (logic, attention), and finally the ground floor (basic sensations). On awakening, the floors switch on in reverse order — first feelings, then thoughts, then understanding "who I am and where I am".

6.2 Distinction from sleep

Definition (Anaesthetic decoherence) [D]

Anaesthesia is characterised by a global loss of integration:

$$\Phi \to 0, \quad \text{all } |\gamma_{iE}| \to 0 \quad (i \neq E)$$

in contrast to sleep, where only $\gamma_{AE} \to 0$ while $\Phi$ is preserved. Anaesthesia is a transition from L2 to L0 (not to L1 as in sleep).

Numerical example: NREM sleep vs. anaesthesia.

Parameter	NREM sleep	Anaesthesia	Difference
$R_\varphi$	$0.15$	$0.02$	7 times lower
$\Phi$	$1.5$	$0.2$	7.5 times lower
$P$	$0.33$	$0.30$	Near $P_{\text{crit}} = 2/7 \approx 0.286$
Level	L1	L0	1 level lower
Self-maintenance	Yes	Only with support	Requires ventilation

The key distinction: in NREM, integration is preserved ($\Phi = 1.5$, level L1) and the system is viable with a margin ($P = 0.33$). In anaesthesia integration collapses ($\Phi \to 0$) while purity stays just above the threshold ($P = 0.30 > P_{\text{crit}} = 2/7 \approx 0.286$) — in agreement with the canonical criterion of Death and Continuity: anaesthesia is reversible precisely because $P > P_{\text{crit}}$ is maintained. The margin, however, is small, and regeneration $\mathcal{R}[\Gamma, E]$ is pharmacologically weakened — without external support (mechanical ventilation, monitoring) $P$ would drift below the threshold. This is precisely why general anaesthesia requires life support equipment.

6.3 Awareness during anaesthesia (intraoperative awareness)

A rare but clinically significant complication is awareness during surgical anaesthesia (1–2 cases per 1000). In UHM formalism this means incomplete decoherence:

$$\gamma_{AE} > \varepsilon_{\text{aware}}, \quad \mathrm{Gap}(A,E) < 1$$

Meanwhile $\gamma_{LE} \approx 0$: the patient feels (the channel $A \to E$ is partially working), but cannot make sense of or report the experience (channels $L \to E$ and $L \to D$ are blocked). This is a Gap profile analogous to the Jungian shadow, but pharmacologically induced.

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7. Hypnosis and Lucid Dreaming

7.1 Hypnosis

Hypnosis is a state of heightened suggestibility, achieved through directed relaxation and focusing of attention. In UHM formalism, hypnosis is a dissociation of the attention channel from the logic channel:

$$\text{Hypnosis:} \quad |\gamma_{AE}| \uparrow, \quad \mathrm{Gap}(L,E) \uparrow, \quad R_\varphi \downarrow \text{ (moderately)}$$

What is happening here?

• $|\gamma_{AE}| \uparrow$ — attention is intensely directed toward the hypnotist's voice (or an inner object). In this respect hypnosis resembles shamatha.
• $\mathrm{Gap}(L,E) \uparrow$ — but, unlike shamatha, logical control is switched off. The subject "hears" and "executes", but does not "evaluate critically".
• $R_\varphi \downarrow$ — self-model quality is moderately reduced, but remains above $R_{\varphi,\text{th}}/2$. Hypnosis is not a loss of consciousness, but its reorganisation.

Numerical example.

Parameter	Wakefulness	Hypnosis	Shamatha
$\|\gamma_{AE}\|$	$0.12$	$0.20$	$0.22$
$\mathrm{Gap}(L,E)$	$0.25$	$0.70$	$0.20$
$R_\varphi$	$0.45$	$0.30$	$0.55$
$\overline{\mathrm{Gap}}$	$0.30$	$0.35$	$0.25$

The critical difference from shamatha: in meditation Gap(L,E) decreases (logic becomes more transparent), while in hypnosis it increases (logical control weakens). This explains heightened suggestibility: commands pass directly through the channel $A \to E$, bypassing the critical check $L \to E$.

Analogy. Hypnosis is like an audio system with the equaliser switched off: the sound (command) goes directly to the speakers (experience) without processing (logical filtering).

7.2 Lucid dreaming

A lucid dream is REM sleep in which the sleeper is aware that they are dreaming and can partially control the content. In UHM formalism:

$$\text{Lucidity:} \quad \text{REM profile} + \gamma_{AE} > 0 + R_\varphi \geq R_{\varphi,\text{th}}$$

In other words, the typical REM profile (high $\gamma_{SE}$, $\gamma_{DE}$, low $\gamma_{LE}$) is supplemented by the restoration of the attention channel ($\gamma_{AE} > 0$) and of self-model quality ($R_\varphi \geq R_{\varphi,\text{th}}$). The sleeper rises from L1 (ordinary REM) to L2 (awareness).

Numerical example: ordinary REM vs. lucid dream.

Parameter	Ordinary REM	Lucid dream
$\gamma_{AE}$	$0.03$	$0.10$
$R_\varphi$	$0.35$	$0.48$
$\gamma_{SE}$	$0.15$	$0.14$
$\gamma_{DE}$	$0.18$	$0.16$
$\gamma_{LE}$	$0.02$	$0.06$
Level	L1–L2	L2

A lucid dream is an intermediate state between sleep and wakefulness: the vividness of imagery ($\gamma_{SE}$) is preserved from REM, but reflexive control ($R_\varphi > R_{\varphi,\text{th}}$, $\gamma_{AE} > 0$) is added. Training in lucid dreaming is, in essence, training the ability to restore $\gamma_{AE}$ and $R_\varphi$ from the REM state.

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8. Summary Table: All ASC Classes

Parameter	Wake	NREM	REM	Samādhi	Psyched.	Anaesth.	Hypnosis	Lucid sl.
$R_\varphi$	$\geq 1/3$	$< 1/3$	$\sim 1/3$	$\to 1$	$\downarrow$	$\to 0$	$\downarrow$	$\geq 1/3$
$\Phi$	$\geq 1$	$\approx \Phi_0$	$\approx \Phi_0$	$\to \max$	$\sim \Phi_0$	$\to 0$	$\sim \Phi_0$	$\approx \Phi_0$
$D_{\text{diff}}$	Moderate	$\downarrow$	$\uparrow$	Moderate	$\uparrow\uparrow$	$\to 1$	Moderate	$\uparrow$
$\overline{\mathrm{Gap}}$	$0.2$–$0.4$	$0.4$–$0.6$	$0.3$–$0.5$	$\to \min$	$\downarrow$	N/a	$0.3$–$0.4$	$0.2$–$0.4$
$P$	$> 2/7$	$> 2/7$	$> 2/7$	$> 2/7$	$\to 2/7$	$\approx 2/7^{+}$	$> 2/7$	$> 2/7$
Level	L2	L1	L1–L2	L3–L4	L1–L2	L0	L1–L2	L2
$\gamma_{AE}$	$+$	$\approx 0$	$\approx 0$	$+$	$\downarrow$	$\approx 0$	$\uparrow$	$+$
Gap(L,E)	Low	High	High	$\to 0$	Low	Max	$\uparrow$	Moderate

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9. Geometry of Transitions

Transitions between states are trajectories in $\mathcal{D}(\mathcal{H})$ passing through bifurcations. Each transition has a characteristic "profile" — a pattern of parameter changes over time.

9.1 Types of transitions

• Falling asleep (wakefulness $\to$ NREM): crossing the working threshold $R_\varphi = R_{\varphi,\text{th}}$ from above — a saddle-node bifurcation. The transition is gradual (5–15 minutes), characterised by a gradual decrease in $\gamma_{AE}$.

• Onset of dreaming (NREM $\to$ REM): reactivation of E-sector coherences without restoration of $\gamma_{AE}$. The transition is rapid (seconds), triggered by PGO waves.

• Entry into samādhi: approach to the fixed point $\varphi(\Gamma^*) = \Gamma^*$. The transition is gradual (minutes to hours), requires prior preparation (shamatha + vipassanā).

• Psychedelic peak: passage near the phase transition II $\to$ I. The transition is rapid (minutes), subjectively perceived as a "jump".

• Hypnotic induction (wakefulness $\to$ hypnosis): gradual increase in $\gamma_{AE}$ with simultaneous growth of $\mathrm{Gap}(L,E)$. The transition takes 5–20 minutes.

• Lucidity in sleep (REM $\to$ lucid REM): abrupt restoration of $\gamma_{AE}$ and $R_\varphi$ with preservation of the REM profile. The transition is instantaneous (the moment of "realising I am asleep").

9.2 Transition diagram

Analogy. Transitions between ASC are like phase transitions of water: falling asleep is the "freezing" of reflection (gradual passage of $R_\varphi$ through the working threshold), the psychedelic peak is the "boiling" of experience ($D_{\text{diff}}$ sharply increases), anaesthesia is "absolute zero" ($\Phi \to 0$). Each transition has its own "temperature" and "pressure" — the parameters $\Gamma_2$ (rate of decoherence) and $\kappa$ (intensity of regeneration) play this role.

For more on correction strategies for pathological transitions. The connection with the CC theorems — in the part on dynamic attractors.

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What we learned

1. Historical line: Tart (1969) introduced systematic ASC cartography; UHM transforms it into a quantitative theory with numerical parameters and predictions
2. ASC — a trajectory in $\mathcal{D}(\mathcal{H})$ with deviation of at least one parameter from the quintuple $(R_\varphi, \Phi, D_{\text{diff}}, P, \overline{\mathrm{Gap}})$
3. NREM — return to L1 ($R_\varphi < 1/3$), integration preserved; REM — L1–L2 without attention ($\gamma_{AE} \approx 0$), vivid imagery ($\gamma_{SE} \uparrow$)
4. Meditation — systematic control: shamatha ($R_\varphi \uparrow$), vipassanā ($\mathrm{Gap} \downarrow$), samādhi (approach to L4)
5. Psychedelics — $D_{\text{diff}} \uparrow\uparrow$, $R_\varphi \downarrow$, $\overline{\mathrm{Gap}} \downarrow$; therapeutic window: $R_{\varphi,\text{th}}/2 < R_\varphi < R_{\varphi,\text{th}}$
6. Anaesthesia — global decoherence, $\Phi \to 0$, transition to L0 (as opposed to L1 in sleep)
7. Hypnosis — dissociation of attention from logic: $\gamma_{AE} \uparrow$, $\mathrm{Gap}(L,E) \uparrow$
8. Lucid dreaming — REM + restoration of reflection: $R_\varphi \geq R_{\varphi,\text{th}}$, $\gamma_{AE} > 0$
9. Transitions — bifurcations of the Gap landscape; each type of ASC has a characteristic transition geometry

Bridge to the next chapter

ASC show how $\Gamma$ deviates from the norm. But some coherences always remain inaccessible to consciousness — this is the unconscious. In the next chapter — Unconscious — we will show that the unconscious = the set of channels with $\mathrm{Gap} \to 1$, and that complete transparency is impossible by the Hamming theorem.

Related Documents

• Dynamics of Γ: Evolution of Γ — equations of motion
• Viability: Viability measure — threshold $P_{\text{crit}} = 2/7$
• Level hierarchy: Interiority hierarchy — definitions of L0–L4
• Gap characterisation: Gap characterisation of levels — signatures
• Bifurcations: Gap dynamics — theory of transitions
• Unconscious: Unconscious — Gap structure of inaccessible sectors
• Pathology: Pathology of consciousness — deviations from the norm
• CC theorems: Coherence Cybernetics — applied consequences for dynamic attractors
• Entropic brain: Phase diagram — connection to Carhart-Harris's hypothesis