Maths

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Probably what *this* should be called.
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Re: Maths

Post by Khaos » Fri Nov 06, 2020 10:20 pm

maths are hards

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Re: Maths

Post by Ashenai » Tue Feb 16, 2021 3:47 pm


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Re: Maths

Post by Skeletor » Tue Feb 16, 2021 4:36 pm

All odd colors have an e in them
wow, [you]. that all sounds terrible. i hope it gets better for you

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Re: Maths

Post by Doug » Tue Feb 16, 2021 4:55 pm

That's incredible, although it gives me deja vu
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Re: Maths

Post by Doug » Tue Apr 13, 2021 6:55 pm

Is this stupid or not


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Re: Maths

Post by Khaos » Tue Apr 13, 2021 6:58 pm

pausing at 1:10 to say, hey, this question is ambiguous. so what's the actual question

edit: oh i see. there's only one coin. cool. question still seems dumb to me

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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:01 pm

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
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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:02 pm

i don't really understand how 1/3 could be an answer

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Re: Maths

Post by Jeb Bush 2012 » Tue Apr 13, 2021 7:02 pm

I do not think it is stupid

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Re: Maths

Post by Jeb Bush 2012 » Tue Apr 13, 2021 7:03 pm

Khaos wrote: Tue Apr 13, 2021 7:02 pm i don't really understand how 1/3 could be an answer
1/3 of the time you are asked the question, the coin will be heads (because you're asked it twice whenever it's tails, and don't remember because of the amnesia effect)

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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:05 pm

Khaos wrote: Tue Apr 13, 2021 7:02 pm i don't really understand how 1/3 could be an answer
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
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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:08 pm

Doug wrote:
Khaos wrote: Tue Apr 13, 2021 7:02 pm i don't really understand how 1/3 could be an answer
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
ok cool

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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:10 pm

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

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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:12 pm

I guess you could say that it's an illustration of how probability is contextual
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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:13 pm

Khaos 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
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 earlier

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

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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:14 pm

Doug wrote:I guess you could say that it's an illustration of how probability is contextual
yeah. kinda reminds me of calculating the probability of life forming on a planet

anyways, pretty cool

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Re: Maths

Post by Jeb Bush 2012 » Tue Apr 13, 2021 7:15 pm

Khaos wrote: Tue Apr 13, 2021 7:10 pm ok, so the probability that the coin flipped heads is 50% objectively, but 33% subjectively? that doesn't seem too bad
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

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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:16 pm

Jeb Bush 2012 wrote:
Khaos wrote: Tue Apr 13, 2021 7:10 pm ok, so the probability that the coin flipped heads is 50% objectively, but 33% subjectively? that doesn't seem too bad
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
i guess i dont see how its controversial

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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:17 pm

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
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Re: Maths

Post by Khaos » Tue Apr 13, 2021 7:17 pm

i guess i am still confused

i think she should have an opinion!

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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:19 pm

Khaos wrote: Tue Apr 13, 2021 7:17 pm i guess i am still confused

i think she should have an opinion!
Her opinion about the probability is subjective

The process she should use to determine the probability is not subjective
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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:20 pm

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
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Re: Maths

Post by Skeletor » Tue Apr 13, 2021 7:26 pm

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
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Re: Maths

Post by Crunchums » Tue Apr 13, 2021 7:28 pm

hey is that Julia Galef?
yes it is!
u gotta skate

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Re: Maths

Post by Jeb Bush 2012 » Tue Apr 13, 2021 7:33 pm

Khaos wrote: Tue Apr 13, 2021 7:16 pm i guess i dont see how its controversial
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)

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Re: Maths

Post by pterrus » Tue Apr 13, 2021 7:35 pm

For betting purposes, SB should consider P(H) to be 1/3. I see how it's kind of a philosophical question about what probability is, but really the 1/3 answer is the only one that matters from her perspective.

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Re: Maths

Post by Jeb Bush 2012 » Tue Apr 13, 2021 7:45 pm

pterrus wrote: Tue Apr 13, 2021 7:35 pm For betting purposes, SB should consider P(H) to be 1/3. I see how it's kind of a philosophical question about what probability is, but really the 1/3 answer is the only one that matters from her perspective.
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

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Re: Maths

Post by Ashenai » Tue Apr 13, 2021 7:46 pm

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.

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Re: Maths

Post by Jeb Bush 2012 » Tue Apr 13, 2021 7:47 pm

Ashenai wrote: Tue Apr 13, 2021 7:46 pm The question is not well defined, so the answer is gonna be contingent on what you think "probability of an event from her perspective" means.

It's quite annoying to define it correctly, though.
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

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Re: Maths

Post by Doug » Tue Apr 13, 2021 7:48 pm

You know what's not well-defined is which tools are my grandfather's property
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