Change a fictional sleep history, catch the moment two curves meet, and separate a local clock change from a biological clock. Then follow light information from eye to brain.
Enable JavaScript to change the conditions and run the interactive experiment.
How long you have been awake matters. So does circadian timing. These are different processes, and changing the numbers on a clock is different from changing either one.
Two histories have four hours awake and two asleep. Must their final model pressure match?
From S = 0.4, wake-then-sleep ends near 0.3220; sleep-then-wake ends near 0.3967. Each interval changes the state it starts with.
In the model, a quantity called sleep pressure rises during wake and falls during sleep. It changes smoothly; it does not become zero the instant sleep begins. Follow the solid gold curve and select one of its rising or falling sections.
Circadian rhythms are roughly daily biological patterns. Light and dark are major timing cues, and clocks exist across many tissues. Brain circuitry including the suprachiasmatic nucleus, or SCN, helps coordinate timing. A daily pattern can continue while you are asleep.
Our chosen two-process model switches from wake to sleep at an upper threshold and from sleep to wake at a lower one. The daily signal moves both thresholds. Select an intersection and ask which rule was active just before the switch.
Try four hours of modeled wake followed by two of sleep. Then reverse their order, starting at the same pressure. The totals match, but the final state differs. Each interval acts on the state left by the previous interval.
Freeze the display, then move its local clock label from 08:00 to 14:00. No extra six hours have passed inside the model. Real adaptation to a new daily light pattern involves biology; relabeling a dial does not calculate that adaptation.
Light is detected at the retina. Specialized photosensitive retinal ganglion cells contribute signals to clock-related pathways, including projections to the SCN region. The drawing’s relay is a neural message; it is not a ray shining through the skull into a brain clock.
We use the two-process presentation in Skeldon, Dijk & Derks (2014), Figure 1b. Wake: dS/dt = (1 − S)/18.2 h. Sleep: dS/dt = −S/4.2 h. C = sin[2π(t − α)/24 h]. The boundaries are U = 0.60 + 0.10C and L = 0.17 + 0.10C. S and the thresholds are dimensionless. The reset S = 0.17, awake at t = 0, is an authored initial condition.
Each branch uses its exact exponential solution. A bracketed first-crossing search switches states without resetting pressure. The plot and downloaded table sample that same trajectory. Removing circadian modulation is an intervention on this model’s structure; it is not a simulated treatment or brain lesion.
The quantitative circadian signal is prescribed. It has no light-response or entrainment equation. An assumed phase shift restarts a comparison; it is not the calculated result of turning on a lamp. The anatomy and light-experiment views explain separate biological evidence.
EEG slow-wave activity has been used to estimate homeostatic dynamics. Parameters can vary with individuals, normalization and modeling choices. Our S is not measured EEG voltage, blood adenosine concentration, subjective sleepiness, accumulated brain damage or a health score.
Human sleep includes REM and three NREM stages. A binary wake/sleep trace does not tell us those stages, dream content, learning performance or a person’s exact sleep requirement. Those questions need other observations and models.
Khalsa et al. studied a laboratory protocol with 6.7 hours of bright-light exposure and melatonin-phase measurements. Exposure centered before the critical phase produced delays; after it, advances. That biological phase convention is distinct from the arbitrary zero of our sine model. It is not a household-light schedule or a rule tied to one civil-clock hour.
The SCN region helps coordinate timing. Clock-related signaling also influences the pineal gland, which produces melatonin. The SCN is not itself the melatonin-producing gland. Added anatomical callouts are magnified teaching locations, not measured segmented nuclei.
An elegant curve needs a named variable, units, starting condition and rule. Keeping these visible helps distinguish a mechanism model from a sensor recording or a personal prediction.
Travel can change external time labels before biological rhythms adapt. The clock comparison isolates that first distinction; it does not calculate how long adaptation will take.
What was measured: behavior, EEG, melatonin phase or a subjective report? What changed: light protocol, history or only a plotted label? Separating those questions prevents one finding from being used to claim another.
Mark a 24-hour row. Draw one fictional 16-hour wake block and one 8-hour sleep block. These are model inputs, not recommended durations for a person.
Above the row, sketch a rising wake segment and falling sleep segment. Label it model pressure, not a measured chemical level. It should stay continuous at a switch.
Start a separate six-hour row at S=0.4. Compare four wake hours then two sleep hours with the reverse order. Use the calculated endpoints to check the difference; do not change your own sleep to test it.
Keep every block fixed. Use tracing paper or another row to move civil-clock labels by six hours. Explain why the interval lengths and elapsed waking time did not change.
If using ordinary observations, distinguish went to bed from estimated sleep began. Use a dotted mark for uncertainty and leave missing information blank. A diary does not directly measure the SCN’s phase.
Choose sleep stages, a personal need for sleep, or how a lamp changes phase. Explain why paper blocks and a fixed sine wave cannot answer that question. The light-study card uses a separate laboratory protocol.
Can you change clock labels without changing the length of an interval?
Use fictional cards, or record an ordinary routine afterward without changing it. No altered bedtime, alarms, caffeine, medication, light exposure or sleep duration. The record stays local and cannot diagnose a sleep condition.
Sleep pressure S The homeostatic branch changes with sleep/wake state; the prescribed circadian signal continues.
About 0.1472 One time constant leaves 1/e of the starting value. This does not establish an adequate sleep duration for a person.
No, the awake state uses U The upper boundary triggers onset while awake; the lower boundary triggers waking while asleep.
Potentially different final S The two six-hour trials end near 0.3220 and 0.3967 from the same initial S.
Neither follows from the label change Elapsed time and internal reference remain unchanged by this coordinate operation.
Yes, in the cited laboratory protocol Direction depended on phase in the cited experiment. The fixed-wave app has no light-dose response equation.
A dimensionless model state The app calculates a model variable and measures no bodily signal.
Neither is calculated here The engine tracks pressure and binary states against a prescribed circadian signal.
Unmodified PNGs by Servier Medical Art, CC BY 4.0. Separate schematic timing callouts are authored by Brytalearn; no exact SCN segmentation is claimed.
Servier Medical Art · BrainAnterior at right, optic-nerve exit at left; the retinal lining is distinct from the orange vitreous-body context. CC BY 4.0 with attribution.
Servier Medical Art · Eye structureInstitutional fact sheet. Its fruit-fly molecular example is not presented as a complete human clock.
NIH NIGMS · Circadian RhythmsInstitutional sleep/wake-cycle explanation. General physiology is not an individual calibration.
NIH NHLBI · Your Sleep/Wake CycleOriginal publication record. The accessible record verifies its 1982 origin; numerical parameters here are transcribed from the later explicit mathematical presentation.
Borbély · Human Neurobiology, 1982Original 1984 model abstract. Pressure need not be identified with one neurochemical substance.
Daan, Beersma & Borbély · 1984The two-process model section, equations 1–4 and Figure 1b. Other models and parameter sets in the paper are not mixed into this engine.
Skeldon, Dijk & Derks · PLOS ONE, 2014Original analysis in eight healthy young men, with EEG slow-wave activity and normalization choices. These results do not define defaults for all ages.
Rusterholz, Dürr & Achermann · Sleep, 2010Original study of 21 entrained participants under a 6.7-hour laboratory light protocol, using melatonin phase. Its protocol is not a household-lamp recommendation.
Khalsa et al. · Journal of Physiology, 2003Original rat/mouse melanopsin-cell study. Supports a neural retinal-to-SCN route, not direct light transmission through brain tissue.
Hattar et al. · Science, 2002Institutional explanation of sleep stages. No stage sequence or EEG signal is generated by the two-process model.
NIH NHLBI · Sleep Phases and StagesSection 2 distinguishes this limitation. Optimization schedules from the paper are not implemented.
Yin, Julius & Wen · PLOS ONE, 2021Brain-structure descriptions, pineal-gland item. The added output callout abbreviates intervening neural signals.
NIH NINDS · Understanding SleepIndependent subject review is pending.
Read the sources and model assumptions
Interactive explorationNudge a membrane, discover when a spike appears, test its recovery, and cross a chemical synapse. Then inspect a real potassium-channel structure.
Interactive explorationOpen a sourced 3D eye, move a target nearer, and catch the moment its light comes together. Then discover why a smaller pupil is different from better focus.
Interactive explorationStart with a vibration. Follow air, eardrum, tiny bones and hair cells, then see why the message reaching your brain is a different kind of signal.