Lesson 11 · Solution · Calibration seed: estimation & 90% intervals

Solution: The Bet a 90% Interval Makes

About 78%. (Oxygen is ~21%, and the remaining ~1% is mostly argon plus trace gases like CO₂.)

The number itself isn’t the point — how your interval did is. Three ways this could have gone:

  • Your interval contained 78%, and it wasn’t absurdly wide. Good — that’s what calibration looks like on a question you had solid but imperfect general knowledge about.
  • Your interval missed. Worth asking honestly: was your best guess just off, or was your interval too narrow around a guess that was reasonable but not exact? Those are different failures — the first is a knowledge gap, the second is overconfidence about how sure you were.
  • Your interval was enormous (say, 20% to 95%) and “won” by containing the truth. That’s not a win. An interval that wide is nearly unfalsifiable — it would have “succeeded” against almost any true value, which means it told you almost nothing. Calibration isn’t about avoiding misses at any cost; it’s about intervals that are exactly as wide as your actual uncertainty, checked against how often they should miss (about 1 in 10 times, no more, no less).

Why this belongs in a Bayesian-reasoning track and not a trivia track: a posterior distribution is a calibrated statement of belief — every credible interval you’ll compute from here on (Stage 2 onward) makes exactly this same kind of promise (“the true value falls in here with X% plausibility”), just built from data and a prior instead of general knowledge. Training the raw skill — stating honest uncertainty, then checking it against reality — on easy trivia now means you’ll trust the harder, math-backed intervals later precisely because you’ll have felt, firsthand, what a well-calibrated interval feels like versus an overconfident one.

Where this goes: every several lessons from here, an estimate puzzle will reappear to keep building your personal calibration log — watch it over time, not just puzzle by puzzle. Next up, Stage 2 opens with the machinery underneath every posterior you’ve computed so far: a distribution, formally, as an “answer sheet” assigning plausibility to every possible value at once.

How was this one? Any answer marks it complete and moves on — your rating shapes future lessons.