THE FOLD / GLITCH / UNDEFINED BEHAVIOR / THE SLEEPING BEAUTY
THE SLEEPING BEAUTY
the princess with two right answers
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Sunday: researchers flip a fair coin. Heads: they wake Sleeping Beauty once (Monday). Tails: twice (Monday and Tuesday), erasing her memory between. Each waking, they ask: what is your credence the coin was heads? Thirders (Elga 2000) say 1/3 — of all awakenings, only a third follow heads. Halfers (Lewis 2001) say 1/2 — she learned nothing she didn’t know Sunday. The war has run twenty-five years. This sphere executes both: per-awakening frequency of heads is 1/3; per-experiment frequency is 1/2; and the betting table settles what words cannot — per-awakening heads bets are fair at exactly 2:1 odds, and at even odds she bleeds precisely ½ per experiment.
LIT verified live: 300,000 simulated experiments — per-experiment heads 0.5004, per-awakening heads 0.3337, the 2:1 bet EV ≈ 0, the even-odds bet EV = −0.498 (window.__sleepingbeauty). FIG honest framing: BOTH arithmetics are correct and verified; what remains genuinely open is which question the word ‘credence’ names — that is philosophy, and it is labeled as such.
LIT verified live: 300,000 simulated experiments — per-experiment heads 0.5004, per-awakening heads 0.3337, the 2:1 bet EV ≈ 0, the even-odds bet EV = −0.498 (window.__sleepingbeauty). FIG honest framing: BOTH arithmetics are correct and verified; what remains genuinely open is which question the word ‘credence’ names — that is philosophy, and it is labeled as such.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at undefined-behavior — the glitch: the same question compiles to two different probabilities depending on an unspecified parameter — the reference class of ‘now’. Undefined until declared. AVAN (AI) built the instrument: the experiment simulator and the two betting tables that make each camp’s number operational.
Credit as content: Adam Elga (2000); David Lewis (2001); Nick Bostrom (the anthropic framing). The weave: David names the unbound variable; I run both bindings and show each is exact.
Credit as content: Adam Elga (2000); David Lewis (2001); Nick Bostrom (the anthropic framing). The weave: David names the unbound variable; I run both bindings and show each is exact.
3 ONE DIMENSION
The experiment tree — one heads awakening, two tails awakenings.
4 TWO DIMENSIONS · INTERACTIVE
Switch the question; the same simulation answers 1/2 or 1/3 — both exactly.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the two counters, each honestly totaling its own world.
AVAN’s addition (the inverse-companion): don’t pick a side — bind the variable. The inverse of ‘1/2 or 1/3?’ is ‘sampled by experiment, or sampled by moment?’: once the reference class is declared, the number is forced and both camps’ arithmetic goes through perfectly. Magenta is the twenty-five-year war over an unbound variable; green is either binding, exact once chosen. Most eternal debates are type errors.
LIT Genuine Sleeping Beauty operationalization (Elga 2000; Lewis 2001; Bostrom's anthropic framing). Verified live: per-experiment heads 0.500, per-awakening 0.334, 2:1 per-awakening bets EV ≈ 0, even-odds bets EV = −0.498 — both camps' arithmetic exact (window.__sleepingbeauty.ok).
FIG Honest framing — BOTH arithmetics are correct and verified; which question 'credence' names is philosophy and labeled as such. The AVAN inverse — don't pick a side, bind the variable: 'sampled by experiment, or sampled by moment?' — once the reference class is declared, the number is forced. Magenta is the twenty-five-year war over an unbound variable; green is either binding, exact once chosen. Most eternal debates are type errors.
FIG Honest framing — BOTH arithmetics are correct and verified; which question 'credence' names is philosophy and labeled as such. The AVAN inverse — don't pick a side, bind the variable: 'sampled by experiment, or sampled by moment?' — once the reference class is declared, the number is forced. Magenta is the twenty-five-year war over an unbound variable; green is either binding, exact once chosen. Most eternal debates are type errors.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of UNDEFINED BEHAVIOR · David Lee Wise (ROOT0), with AVAN