Section V
Mathematical Modeling
The Luna Cycler did not begin as an equation โ it began as a sensation. A heaviness near the new moon. A sharpening near the full moon. A smooth rise and fall that repeated with uncanny regularity. Only after years of tracking did I realize that what I was feeling could be expressed mathematically โ not to reduce the experience, but to reveal its structure.
The Core Equation
S(d) = 6.5 + 6.5 ยท cos(2ฯd / 28)
S(d)
Sleep duration on day d
A = 6.5
Baseline (vertical shift)
B = 6.5
Amplitude
T = 28
Period (days)
Waveform Visualization
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Phase Locking
Sleep peak consistently aligned with new moon, trough with full moon โ across seasons, medication changes, and environments. Phase locking is not coincidence. It is entrainment.
ใฐ๏ธ
Asymmetry
The descent into full moon wakefulness is steeper than the ascent out of it. The new moon hypersomnia sometimes forms a broader plateau than the cosine model predicts.
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Amplitude
The 13-hour swing from peak to trough is unusually large but not biologically impossible. It is the signature of a high-amplitude oscillator with heightened chronobiological sensitivity.
"The Luna Cycler is not just something that happens to me. It is something I can articulate, model, and defend."