Hijacking this thread, has anybody worked through Ape in the coat’s anthropic posts and understood / gotten stuff out of them? It’s something I might want to do sometime in my copious free time but haven’t worked up to it yet.
Here is the core part that allows to understand why “Today” is ill-defined from the perspective of the Beauty:
Another intuition pump is that “today is Monday” is not actually True xor False from the perspective of the Beauty. From her perspective it’s True xor (True and False). This is because on Tails, the Beauty isn’t reasoning just for some one awakening—she is reasoning for both of them at the same time. When she awakens the first time the statement “today is Monday” is True, and when she awakens the second time the same statement is False. So the statement “today is Monday” doesn’t have stable truth value throughout the whole iteration of probability experiment. Suppose that Beauty really does not want to make false statements. Deciding to say outloud “Today is Monday”, leads to making a false statement in 100% of iterations of experiemnt when the coin is Tails.
As long as the Beauty is unable to distinguish between Monday and Tuesday awakenings, as long as the decision process which leads her to say the phrase “what day is it” works the same way, from her perspective there is no one “very moment she says that”. On Tails, there are two different moments when she says this, and the answer is different for them. So there is no answer for her
Let’s say there is an accurate mechanical calendar in the closed box in the room. She can open it but wouldn’t. Should she have no expectation about like in what state this calendar is?
Please specify this “now” thingy you are talking about, using formal logic. If this is a meaningful event for the setting, surely there wouldn’t be any problems.
Are you talking about Monday xor Tuesday? Monday or Tuesday? Monday and Tuesday? Something else?
Well, idk. My opinion here is that you bite some weird bullet, which I’m very ambivalent to. I think “now” question makes total sense and you factor it out into some separate parts from your model.
Like, can you add to the sleeping beauty some additional decision problems including the calendar? Will it work seamlessly?
Well, idk. My opinion here is that you bite some weird bullet, which I’m very ambivalent too. I think “now” question makes total sense and you factor it out into some separate parts from your model.
The counter-intuitiveness comes from us not being accustomed to reasoning under amnesia and repetition of the same experience. It’s understandable that initially we would think that question about “now”/”today” makes sense as we are used to situation where it indeed does. But then we can clearly see that in such situations there is no problem with formally defining what event we mean by it. Contrary to SB, where such event is ill-defined.
Like, can you add to the sleeping beauty some additional decision problems including the calendar? Will it work seamlessly?
Oh absolutely.
Suppose that on every awakening the Beauty is proposed to bet that “Today is Monday” What odds is she supposed to take?
“Today is Monday” is ill-defined, but she can construct a corresponding betting scheme using events “Monday awakening happens” and “Tuesday awakening happens” like this:
So, she shakes the box contemplatively. There is mechanical calendar. She knows the betting odds of it displaying “Monday” but not the credence. She thinks it’s really really weird
I’m very available to answer questions about my posts as soon as people actuall engage with the reasoning, so feel free to ask if you feel confused about anything.
If I am to highlight the core principle it would be: Thinking in terms of what happens in the probability experiment as a whole, to the best of your knowledge and from your perspective as a participant.
Suppose this experiment happened to you multiple times. If on iteration of the experiment something happens 2⁄3 of times then the probability of such event is 2⁄3. If something happens 100% of times then its probability is 1 and realizationof such event doesn’t give you you any evidence.
Hijacking this thread, has anybody worked through Ape in the coat’s anthropic posts and understood / gotten stuff out of them? It’s something I might want to do sometime in my copious free time but haven’t worked up to it yet.
I propose to sic o1 on them to distill it all into something readable/concise. (I tried to comprehend it and failed / got distracted).
I think some people pointed out in comments that their model doesn’t represent prob of “what day it is NOW” btw
I’m actually talking about it in the post here. But yes this is additionally explored in the comments pretty well.
Here is the core part that allows to understand why “Today” is ill-defined from the perspective of the Beauty:
Let’s say there is an accurate mechanical calendar in the closed box in the room. She can open it but wouldn’t. Should she have no expectation about like in what state this calendar is?
What state the calendar is when?
On Monday it’s Monday. On Tuesday it’s Tuesday. And “Today” is ill-defined, there is no coherent state for it.
Well, now! She looks at the box and thinks there is definitely a calendar in some state. What state? What would happen if i open it?
Please specify this “now” thingy you are talking about, using formal logic. If this is a meaningful event for the setting, surely there wouldn’t be any problems.
Are you talking about Monday xor Tuesday? Monday or Tuesday? Monday and Tuesday? Something else?
Well, idk. My opinion here is that you bite some weird bullet, which I’m very ambivalent to. I think “now” question makes total sense and you factor it out into some separate parts from your model.
Like, can you add to the sleeping beauty some additional decision problems including the calendar? Will it work seamlessly?
The counter-intuitiveness comes from us not being accustomed to reasoning under amnesia and repetition of the same experience. It’s understandable that initially we would think that question about “now”/”today” makes sense as we are used to situation where it indeed does. But then we can clearly see that in such situations there is no problem with formally defining what event we mean by it. Contrary to SB, where such event is ill-defined.
Oh absolutely.
Suppose that on every awakening the Beauty is proposed to bet that “Today is Monday” What odds is she supposed to take?
“Today is Monday” is ill-defined, but she can construct a corresponding betting scheme using events “Monday awakening happens” and “Tuesday awakening happens” like this:
E(Monday) = P(Monday)U(Monday) - P(Tuesday)U(Tuesday)
P(Monday) = 1; P(Tuesday) = 1⁄2, therefore
E(Monday) = U(Monday) − 1/2U(Tuesday)
solving E(Monday)=0 for U(Monday):
U(Monday) = 1/2U(Tuesday)
Which means 2:1 betting odds
As you see everything is quite seamless.
So, she shakes the box contemplatively. There is mechanical calendar. She knows the betting odds of it displaying “Monday” but not the credence. She thinks it’s really really weird
I’m very available to answer questions about my posts as soon as people actuall engage with the reasoning, so feel free to ask if you feel confused about anything.
If I am to highlight the core principle it would be: Thinking in terms of what happens in the probability experiment as a whole, to the best of your knowledge and from your perspective as a participant.
Suppose this experiment happened to you multiple times. If on iteration of the experiment something happens 2⁄3 of times then the probability of such event is 2⁄3. If something happens 100% of times then its probability is 1 and realizationof such event doesn’t give you you any evidence.
All the rest is commentary.