Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake

#1

Post by foweltschmerz » Fri, Dec 13, 2024, 5:40 PM UTC

Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake
scientificamerican.com

Re: Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake

#2

Post by [deleted] » Fri, Dec 13, 2024, 6:33 PM UTC

[deleted]

Re: Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake

#3

Post by uberman » Fri, Dec 13, 2024, 6:56 PM UTC

This strikes me like the Monty Hall problem where people intuitively believe the answer to be 50/50.

Does this not simulate the problem in python?

    import random
    coin = ["heads", "tails"]
    guess = "heads"
    guesses_correct = 0
    wakings = 0

    n = 1_000_000
    for _ in range(n):
        actual = random.choice(coin)
        if actual == guess:
            wakings += 1
            guesses_correct += 1
        else:
            wakings += 2

    print(f"guessed correctly: {guesses_correct/wakings:0.2f}%")

Re: Why the 'Sleeping Beauty Problem' Is Keeping Mathematicians Awake

#4

Post by foweltschmerz » Sat, Dec 14, 2024, 3:21 AM UTC

uberman wrote: post #3

This strikes me like the Monty Hall problem where people intuitively believe the answer to be 50/50. Does this not simulate the problem in python? import random coin = ["heads", "tails"] guess = "heads" guesses_correct = 0 wakings = 0 n = 1_000_000 for _ in range(n): actual = random.choice(coin) if actual == guess: wakings += 1 guesses_correct += 1 else: wakings += 2 print(f"guessed correctly: {guesses_correct/waking…

Not really. Unlike the monty hall problem, sleeping beauty receives no additional information. The thought experiment was originally brought up to illustrate how a perfectly rational agent’s credence in the relevance of her temporal position to some proposition can change over time even though she receives no new information nor suffers from a cognitive mishap. This point is more evident in the original paper by Elga: https://swh.princeton.edu/~adame/papers/sleeping/sleeping.pd...