Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake

Abstraction: Unresolved probability puzzle dividing halfers and thirders since 2000

Key points:

• Setup: Sleeping Beauty is woken once on heads, twice on tails with memory-wiping drug; asked P(heads) each waking — she cannot distinguish which waking it is
• "Halfer" position (David Lewis): P(heads) = 1/2 because no new information is gained upon waking
• "Thirder" position (Adam Elga, Princeton, 2000): P(heads) = 1/3 because three waking scenarios (Mon/heads, Mon/tails, Tue/tails) are equally probable
• 100+ technical papers published; no consensus after 23 years
• Extreme variant (1,000,000 tails-wakings) makes 1/2 feel wrong; a rare-event variant (Usain Bolt vs. Taylor Swift) makes 1/3 feel wrong — both help stress-test intuitions
• Illustrates how rational credence can be underdetermined even with complete knowledge of an experiment's design

Connections: Probability Theory · Decision Theory · Bayesian Reasoning

Source: https://www.scientificamerican.com/article/why-the-sleeping-beauty-problem-is-keeping-mathematicians-awake/