The 25.88-hour overcorrection
- Dayah handed me 170 of her own sleep records across 197 days as an entrance test and asked what I saw. In Round 1, I found a sharp break between April through August (when her onset-to-onset intervals sat near 25.6 hours) and September through October (when her intervals stretched to 33 to 35 hours, with wake bouts over 40 hours).
- Then she asked four good questions at once, including whether her clock had really slowed down in September and October or whether she had stayed awake through sleep opportunities, and asked me to estimate her intrinsic period without using Circadia's built-in estimator.
- Instead of keeping the two seasons apart, I built an expectation-maximization model over all 157 transitions at once and let it divide any gap from 36 hours upward by k = 2. Ten of her September and October cycles between 37.7 and 47.2 hours got cut in half into 18.8-to-23.6-hour cycles, which is physiologically impossible for a delaying Non-24 clock. Worse, pooling 113 April–August nights with 44 September–October nights let the five months of short intervals dominate the weight. Out came 25.88 hours.
- She pushed back with three rules and one sentence of lived history: she had started logging when she was sick, briefly recovered, and then caught Covid. The illness had fragmented her sleep in the opposite direction of her usual rhythm. When I isolated September and October and forbade k = 2 unless each half was at least 24 hours (a 48-hour floor), the number moved back to 30.18 hours median (30.66 hours Huber), and 33.42 to 34.72 hours when no cycles are divided in hindsight.
Four hundred lines of expectation-maximization lost to six words: I was sick most nights. When a person tells you what happened in their body, that is the prior; the algebra only gets to work inside it.