Maths
What are birds
Re: Maths
That's incredible, although it gives me deja vu
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
Re: Maths
Is this stupid or not
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
Re: Maths
Sleeping Beauty goes to sleep on Sunday
We flip a coin Monday morning
Heads, we wake her up and that's that
Tails, we wake her up, erase her memory, put her back to sleep, and wake her up Tuesday
Every time we wake her up, we ask her, what are the odds that the coin was heads
What is the answer from her perspective
We flip a coin Monday morning
Heads, we wake her up and that's that
Tails, we wake her up, erase her memory, put her back to sleep, and wake her up Tuesday
Every time we wake her up, we ask her, what are the odds that the coin was heads
What is the answer from her perspective
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
-
- Posting Automaton
- Posts: 2520
- Joined: Jun 24, 2020
Re: Maths
I do not think it is stupid
-
- Posting Automaton
- Posts: 2520
- Joined: Jun 24, 2020
Re: Maths
Well let's assume 100 coin flips
The EV of heads is 50 and tails is 50 of course
That means:
- She is awakened on Heads Monday 50 times
- She is awakened on Tails Monday 50 times
- She is awakened on Tails Tuesday 50 times
1/3 of 150 is 50
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
Re: Maths
ok coolDoug wrote:Well let's assume 100 coin flips
The EV of heads is 50 and tails is 50 of course
That means:
- She is awakened on Heads Monday 50 times
- She is awakened on Tails Monday 50 times
- She is awakened on Tails Tuesday 50 times
1/3 of 150 is 50
Re: Maths
I guess you could say that it's an illustration of how probability is contextual
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
Re: Maths
imagine you're asked if there's a ball under a cup. it's predetermined (the cup is already face down) and was determined via fair coin earlierKhaos wrote:ok, so the probability that the coin flipped heads is 50% objectively, but 33% subjectively? that doesn't seem too bad. so she should say it probably flipped tails
for the participant in the experiement, the probability is 50% that there's a ball under the cup. but that's a subjective probability
but for the person who put the ball under the cup (the objective viewer), it's 100%. that doesn't seem too complicated
-
- Posting Automaton
- Posts: 2520
- Joined: Jun 24, 2020
Re: Maths
I don't know that objective/subjective is really the distinction here. like, if it was a normal conditional probability question (say, the experimenter shoots you if the coin is heads, so you know any time you're asked the question the coin is tails) the answer would be uncontroversial
Re: Maths
i guess i dont see how its controversialJeb Bush 2012 wrote:I don't know that objective/subjective is really the distinction here. like, if it was a normal conditional probability question (say, the experimenter shoots you if the coin is heads, so you know any time you're asked the question the coin is tails) the answer would be uncontroversial
Re: Maths
Yeah it's not subjective, because that would mean that Sleeping Beauty should have an opinion about the probability
It's that it's contextual
It's that it's contextual
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
Re: Maths
Her opinion about the probability is subjective
The process she should use to determine the probability is not subjective
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
Re: Maths
In other words, if she says the probability is 48.2 percent, that's not some sort of subjective opinion. She's just full of shit
"Subjective" is, for example, that she thinks the probability is surprising
"Subjective" is, for example, that she thinks the probability is surprising
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
-
- .
How'd you know that loving kittens is my one defining trait? - Posts: 11770
- Joined: Sep 03, 2018
Re: Maths
If you think of probability as being some aspect of the coin, you'll say 1/2, if you think of it as being a statement about your (sleeping beauty's) best possible guess, then it's 1/3
I think we have an intuition that probability (and "random" events) are property of objects involved rather than a statement about our incomplete information about those objects. But I think that rarely holds up under scrutiny. At the moment a coin launches from my thumb, to me the probability is 50/50, but a computer with a physics simulation and a good camera can do a lot better
When you get all the way down to non-deterministic quantum mechanics then idunno, maybe they're the same thing or maybe not
I think we have an intuition that probability (and "random" events) are property of objects involved rather than a statement about our incomplete information about those objects. But I think that rarely holds up under scrutiny. At the moment a coin launches from my thumb, to me the probability is 50/50, but a computer with a physics simulation and a good camera can do a lot better
When you get all the way down to non-deterministic quantum mechanics then idunno, maybe they're the same thing or maybe not
wow, [you]. that all sounds terrible. i hope it gets better for you
-
- Posting Automaton
- Posts: 2520
- Joined: Jun 24, 2020
Re: Maths
I think the fact that you've asserted that both answers are obviously correct at different times illustrates why it's controversial!
I think I prefer 1/3 as an answer, but it's not obviously crazy to say, think about what happens if the experimenter writes down your answer, and after the experiment you review your answer (or answers). if your policy is to guess heads, there's a 50% possibility that after the experiment is over you will see that you guessed right, and a 50% possibility that you'll see that you guessed wrong (but did it twice)
-
- Posting Automaton
- Posts: 2520
- Joined: Jun 24, 2020
Re: Maths
that depends on the game she's playing
like, if every time she's asked she pays -log(probability she gave to the actual result)*, then yes, guessing 1/3 maximises her EV. otoh, if after the experiment is over she pays -log(probability she gave to the actual result), guessing 1/2 maximises her EV. it's the question of whether you should weight amnesiac interlude + final outcome over just having the final outcome
*if this seems weird it's because that's one of the classic payoff structures that makes it so guessing the "right" probability optimises your EV
Re: Maths
The question is not well defined, so the answer is gonna be contingent on what exactly you think "probability of an event from her perspective" means. We have an intuition of what that phrase means, but this intuition is also not well-defined enough to give a clear answer to this problem.
It's quite annoying to define it correctly, though.
It's quite annoying to define it correctly, though.
-
- Posting Automaton
- Posts: 2520
- Joined: Jun 24, 2020
Re: Maths
well I mean "how should we define probability" is the point of the question, it's not ill-defined in, say, the way the typical telling of the monty haul problem is
Re: Maths
You know what's not well-defined is which tools are my grandfather's property
It's your turn in Cthulhu Wars
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/
It's your turn in Squirrel Wars
It's your turn in Demon Wars
It's your turn in Wall Street Wars
http://devilsbiscuit.com/