The Four-Gradient Model of Human Timekeeping

A systems framework: T₁ planetary photothermal cycles, T₂ organism–environment interface, T₃ endogenous circadian & metabolic oscillators, and T₄ industrial temporal load as a coercive constraint field that acts through behavior.

Industrial temporal load = 4th zeitgeber ψ(T₄) modulates biological time R₄ = dominance ratio

Why a 4th gradient?

Classic chronobiology models entrainment mainly through T₁–T₃. Modern environments add something qualitatively different: a non-oscillatory, non-negotiable temporal force.

The Persistence Paradox:
People increasingly know circadian “best practices,” yet population-level circadian health keeps worsening. The model explains this as gradient dominance: when T₄ is high, it overrides behavior even with perfect knowledge.

Key idea

Behavior is the interface. It is where external gradients (T₁–T₂) meet internal clocks (T₃), and it’s also the lever that T₄ constrains.

What counts as T₄?

Work schedules (fixed, rotating, night shifts), gig/algorithmic scheduling
Economic precarity, time pressure, overtime dependency
Digital connectivity, notifications, boundaryless work
Artificial light at night (ALAN) and screen exposure
Climate control that flattens thermal cycles (HVAC monotony)
Institutional time structures (school start times, commuting, admin hours)

T₁–T₄ at a glance

A quick visual “feel” for each gradient: stability, modifiability, and coercion.

T₁

stable

Planetary photothermal cycles (light–dark, daily temperature, seasonal spectral shifts).

T₂

modifiable

Interface conditions (skin temp, humidity, convection, radiative exchange; architecture & clothing matter).

T₃

endogenous

SCN + peripheral clocks; hormonal and metabolic oscillators; needs anchoring and low-noise habits.

T₄

coercive

Industrial temporal load (non-oscillatory constraints that override timing behavior).

Dominance ratio

R₄ = w₄ / (w₁ + w₂)
When R₄ grows, behavior aligns with T₄ instead of T₁–T₂.

ψ(T₄): temporal load as a biological time modulator

The model formalizes “biological time acceleration” as a multiplicative factor acting on baseline oscillator scaling.

Core equations
Baseline scaling: τ₀ ∝ M^(1/4), with f₀ = 1/τ₀
Under load: f_bio = f₀ · ψ(T₄) and τ_bio = τ₀ / ψ(T₄)

ψ(T₄)	Meaning	Likely correlates (examples)
ψ < 1	Decelerated biological time more amplitude, deeper recovery	Higher HRV, stable sleep timing, strong dark window, regular feeding–fasting, strong thermal cycling, high autonomy over schedule.
ψ ≈ 1	Baseline scaling robust entrainment possible	Consistent routines with occasional disruption; natural cues still dominate most days.
ψ > 1	Accelerated biological time flattened rhythms, higher turnover	Reduced HRV, flattened endocrine rhythms, sleep fragmentation, irregular meals, persistent ALAN, high unpredictability and low autonomy.

Operationalizing ψ(T₄)

Physiology proxies: HRV (e.g., RMSSD), resting HR vs predicted, cortisol slope, sleep regularity index.
Exposure proxies: ALAN hours, variability of wake time, shift frequency, unpredictability indices, autonomy.
Composite index: ψ = 1 + β₁(ALAN) + β₂(irregularity) + β₃(stress) + β₄(autonomy⁻¹) + β₅(thermal monotony)

Three entrainment regimes

Regimes describe what happens as R₄ and ψ(T₄) increase.

Regime	Condition	Signature
I Rhythmic	R₄ ≪ 1 ψ ≤ 1.0	Natural gradients dominate. High circadian amplitude, stable phase relationships, strong thermoregulatory oscillations, deep recovery.
II Hybrid	R₄ ≈ 1 ψ ≈ 1.05–1.2	Weekday/weekend oscillation (“social jet lag”), partial misalignment, moderate HRV reduction, compensatory behaviors (caffeine, catch-up sleep).
III Override	R₄ ≫ 1 ψ ≥ 1.3	Industrial constraints dictate behavior regardless of biological signals. Flattened melatonin/cortisol rhythms, persistent sympathetic activation, fragmented sleep, higher chronic disease risk.

Historical escalation (approximate)

Era	ψ(T₄)	Primary drivers
Hunter–gatherer	0.9–1.0	Solar time, thermal cycling, autonomy
Early agriculture	~1.05	Seasonal labor constraints, hierarchy
Bronze Age urbanization	~1.1	Metallurgy, trade coordination
Medieval	1.1–1.15	Bells, monastic time discipline
Industrial Revolution	1.2–1.3	Fossil fuels, gas lighting, factory time
20th century	1.3–1.4	Electrification, shift work, global time
Digital age	1.4–1.6	24/7 connectivity, algorithmic time, ubiquitous ALAN

Clinical & practical implications

Stop treating non-compliance as moral failure. In high-ψ environments, behavior is constrained by T₄.
Assess temporal load. Autonomy, schedule predictability, ALAN exposure, commute/caregiving burden.
Stratify interventions by ψ. Low ψ: standard entrainment works; moderate ψ: buffering tactics; high ψ: damage mitigation + reducing T₄.

LifeCircuit translation:
If T₁–T₃ are “signals,” then T₄ is the “constraint field” that decides whether you can obey them. Your best protocol is often the one that reduces R₄ even slightly.

Figure placeholders (optional)

Your PDF references figures (schematics, regime trajectories, historical ψ timeline). If you later export those as images, drop them into this folder and update the src paths.

Figure	Description	File suggestion
Fig 1	Four-Gradient schematic: T₁–T₃ oscillatory, T₄ constraint field on behavior, ψ(T₄) modulation.	images/fig1-model.png
Fig 2	Behavioral entrainment under competing gradients: Regime I / II / III trajectories.	images/fig2-regimes.png
Fig 3	Historical escalation of ψ(T₄): timeline from pre-agricultural → digital.	images/fig3-timeline.png
Fig 4	Thermogenic–Photonic cascade: cold → UCP1 → ROS → ultra-weak photon emission (UPE).	images/fig4-upe.png
Fig 5	Predicted intervention efficacy vs ψ(T₄): declining returns at high ψ.	images/fig5-efficacy.png