The Shore Keeps Two Clocks

Two clocks in the water

The shore keeps two clocks, and neither owns a minute hand.

One clock follows the Moon. The other follows the Sun. Their hands are waves. Twice a day they nearly agree, then slowly slip. When their crests arrive together, the water reaches farther up the stones. When one crest meets the other’s trough, the shore keeps more of itself.

Harmonic analysis represents local water level as a mean plus a set of cosines. Each constituent has an amplitude, frequency, and phase. The Moon, Sun, orbital geometry, basin shape, depth, friction, wind, and pressure all leave marks on the record.^1,2

The frequencies are close but not equal. Add two equal cosines and the fast oscillation acquires a slow envelope:

The fast term supplies the twice-daily rise and fall. The slow term produces the spring–neap modulation, returning from reinforcement to opposition and back in about 14.77 days.¹

The ocean has not gained or lost a clock. The clocks changed their angle.

The receiving shore

Spring tide does not mean the season. It names the larger tidal range when lunar and solar semidiurnal constituents reinforce. A neap tide brings the narrower range when they oppose.

A real tidal zone is less obedient than the blackboard. Continents interrupt the wave. Basins resonate. Shallow water distorts the curve and generates overtides. River discharge can change amplitude and phase. Wind and atmospheric pressure add residuals. Astronomical forcing is periodic; the local response need not remain stationary.³

A prediction table is therefore made for a place, not for the Moon in general. Harmonic constants fitted at one gauge cannot simply be carried down the coast like a bucket. Phase belongs to the system that receives the forcing.

Two processes in sleep

Sleep also arrives from two timekeepers. Homeostatic Process S rises with time awake and falls during sleep. Its simplest curves are exponential. Circadian Process C changes the biological tendency toward sleep and wake across roughly 24 hours. Sleep timing and intensity emerge through their interaction.⁴

Process S is not fatigue, although the two can travel together. Process C is not the clock on the wall, although light and schedule can shift it. The model is compact because it leaves much out: stages, local sleep pressure, age, medication, illness, light history, and social timing.

A strong sleep drive can meet a circadian wake signal. A stable circadian rhythm can meet too little accumulated sleep pressure. Identical component amplitudes can produce different nights when their phases change.

Three instruments, three objects

Fibromyalgia sleep research often begins with a complaint and then meets a measurement problem. A diary records experience. Actigraphy infers sleep and wake from movement. Polysomnography records brain, eye, muscle, breathing, and cardiac signals. These instruments do not measure the same object.

Okifuji and colleagues compared seven nights of diaries and actigraphy in 75 people with fibromyalgia. The two estimates differed by an average absolute 73 minutes per night; 19% of nights differed by more than two hours. Fibromyalgia symptoms correlated with subjective sleep reports but not with the actigraphic sleep variables.⁵ A motionless wrist and a restorative night are not synonyms.

Polysomnography adds detail without granting omniscience. Chervin and colleagues compared 15 women with fibromyalgia and 15 controls across sleep, arousal, cortisol, and HRV. On the second laboratory night, the fibromyalgia group showed more stage shifts, but no other conventional polysomnographic measure differed significantly.⁶ One defining sleep signature becomes difficult to defend.

Actigraphy can estimate the daily shape of activity. Neikrug and colleagues fitted 24-hour cosine models to six days of data from 292 people with fibromyalgia. Rhythm amplitude, peak timing, and their day-to-day variation were associated with clinical measures.⁷ Yet actigraphy records movement, not the molecular circadian pacemaker.

When the clocks push back

Pain and sleep also form feedback rather than a one-way arrow. A systematic review found associations in both directions across fibromyalgia studies: poorer sleep could precede worse pain, and pain could precede worse sleep. Measures, designs, and results were heterogeneous, and mood was entangled with both.⁸

Melatonin sits close to this story and invites overreach. It participates in circadian timing, and trials have examined supplementation in fibromyalgia.⁹ A treatment response would not prove that an endogenous melatonin defect caused the symptoms. A key can turn a lock without having built the door.

The tidal model offers a better question than “Is the rhythm broken?” Ask which property changed: amplitude, phase, period, damping, external forcing, coupling, or measurement window. In sleep, ask whether the record concerns timing, continuity, architecture, breathing, movement, or experience.

What the sum permits

The shared mathematics has a hard boundary. Ocean tides are fluid responses to astronomical and local forcing. Human sleep emerges from neural, endocrine, behavioural, and environmental systems. Process C is not M₂. Process S is not S₂. There is no spring tide of the spinal cord.

What transfers is the logic of interference. A level measured at noon cannot reveal the whole tide. One night cannot reveal a circadian rhythm. An average bedtime cannot establish circadian phase. A symptom score cannot identify which sleep process moved.

At low tide, the zone looks abandoned. Then the clocks align differently. Water enters channels, lifts weed from stone, and closes the bright gaps between pools. Nothing at the shore decided to return. The sum changed sign.