I don’t understand what return ['Tails&Monday','Tails&Tuesday'] and ListC += outcome mean. Can you explain it more?
ListC += outcome is a list concatenation operation. Meaning, that both 'Tails&Monday' and 'Tails&Tuesday' are added to the list in one tick of a logical clock, thus preserving the order between them.
For example, if Sleeping Beauty is allowed to make bets every time she is woken up, I claim she should bet as though she believes the coin came up with probability 1⁄3 for Heads and 2⁄3 for Tails (≈because over many iterations she’ll find herself betting in situations where Tails is true twice as often as in situations where Heads is true).
I’ll be exploring betting odds in the next post in more details. But the short version is that she should bet according to 1⁄2 probability for Heads which naturally leads to 1:2 betting odds in the betting scheme that you’ve proposed. Probability for Heads and Tails are equal but successfully guessing Tails is rewarded twice as much as successfully guessing Heads.
I don’t understand what your solution means for Sleeping Beauty.
It means that during the experiment she can’t lawfully reason about such events as “This day is Monday” or “This day is Tuesday”, only “Monday awakening happens in this experiment” and “Tuesday awakening happens in this experiment”. Whether she will be able to reason about “this day” after the experiment is over is a separate question and depends on whichever circumstances she will be in.
During the experiment the Beauty tries to distinguish between two outcomes: “Heads, only Monday awakening” and “Tails, Monday and Tuesday awakenings” if she manages to find some evidence that Tuesday awakening is to happen in this iteration of the experiment she lawfully updates in favor of the second outcome. It doesn’t matter whether the evidence is about today or tomorrow.
For example, imagine that the Beauty awakens and finds in her room a timetable, that some of the scientists has left there by mistake. According to the timetable the Beauty is currently experiencing a Monday awakening but also has to be awakened tomorrow. The Beauty shouldn’t think like: “Oh, well, seems that today is Monday so both Heads and Tails are equally likely”. No! She should immediately conclude that the coin is Tails, even though she is not experiencing Tuesday awakening at this moment of physical time. Knowledge that it definitely happens in the future is enough.
You don’t have to reply, but FYI I don’t understand what ListC represents (a total ordering of events defined by a logical clock? A logical clock ordering Beauty’s thoughts, or a logical clock ordering what causally can affect what, or logically affect what allowing for Newcomb-like situations? Why is there a clock at all?), how ListC is used, what concatenating multiple entries to ListC means in terms of beliefs, etc. If it’s important for readers to understand this you might have to step us through (or point us to an earlier article where you stepped us through).
ListC represents the same thing as ListE, ListL and ListU. Its a list of ordered outcomes of multiple runs of a particular model, which than we can compare to ListSB—a list of ordered awakenings of the Beauty in multiple iterations of an experiment and see whether their statistical properties are the same. The nature of the test is described in Statistical Analysis part of the post. I provide an inner hyperlink to it here:
The correct model represents the only lawful way to reason about the Sleeping Beauty problem without smuggling unjustified assumptions that the current awakening is randomly sampled. It passes the statistical test with flying colors, as it essentially reimplements the sleepingBeauty() function
Right, I read all that. I still don’t understand what it means to append two things to the list.
Here’s how I understand modelLewis, modelElga, etc.
“This model represent the world as a probability distribution. To get a more concrete sense of the world model, here’s a function which generates a sample from that probability distribution”
Here’s how I understand your model.
“This model represents the world as a ????, which like a probability distribution but different. To get a concrete sense of the world model, here’s a function which generates a sample from that probability distribution JUST KIDDING here’s TWO samples”.
Why can you generate two samples at once? What does that even mean?? The world model isn’t quite just a stationary probability distribution, fine, what is it then? Your model isn’t structured like other models, fine, but how is it structured? I’m drowning in type errors.
EDIT and I’m suggesting be really concrete, if you can, if that will help. Like come up with some concrete situation where Beauty makes a bet, or says a thing, (“Beauty woke up on Monday and said ‘I think there’s a 50% chance the coin came up on heads, and refuse to say there’s a state of affairs about what day it presently is’”) and explain what in her model made her make that bet or say that thing. Or maybe draw a picture which what her brain looks like under that circumstance compared to other circumstances.
Here’s how I think of what the list is. Sleeping Beauty writes a diary entry each day she wakes up. (“Nice weather today. I wonder how the coin landed.”). She would like to add today’s date, but can’t due to amnesia. After the experiment ends, she goes back to annotate each diary entry with what day it was written, and also the coin flip result, which she also now knows.
The experiment is lots of fun, so she signs up for it many times. The Python list corresponds to the dates she wrote in her dairy.
ListC += outcomeis a list concatenation operation. Meaning, that both'Tails&Monday'and'Tails&Tuesday'are added to the list in one tick of a logical clock, thus preserving the order between them.I’ll be exploring betting odds in the next post in more details. But the short version is that she should bet according to 1⁄2 probability for Heads which naturally leads to 1:2 betting odds in the betting scheme that you’ve proposed. Probability for Heads and Tails are equal but successfully guessing Tails is rewarded twice as much as successfully guessing Heads.
It means that during the experiment she can’t lawfully reason about such events as “This day is Monday” or “This day is Tuesday”, only “Monday awakening happens in this experiment” and “Tuesday awakening happens in this experiment”. Whether she will be able to reason about “this day” after the experiment is over is a separate question and depends on whichever circumstances she will be in.
During the experiment the Beauty tries to distinguish between two outcomes: “Heads, only Monday awakening” and “Tails, Monday and Tuesday awakenings” if she manages to find some evidence that Tuesday awakening is to happen in this iteration of the experiment she lawfully updates in favor of the second outcome. It doesn’t matter whether the evidence is about today or tomorrow.
For example, imagine that the Beauty awakens and finds in her room a timetable, that some of the scientists has left there by mistake. According to the timetable the Beauty is currently experiencing a Monday awakening but also has to be awakened tomorrow. The Beauty shouldn’t think like: “Oh, well, seems that today is Monday so both Heads and Tails are equally likely”. No! She should immediately conclude that the coin is Tails, even though she is not experiencing Tuesday awakening at this moment of physical time. Knowledge that it definitely happens in the future is enough.
You don’t have to reply, but FYI I don’t understand what
ListCrepresents (a total ordering of events defined by a logical clock? A logical clock ordering Beauty’s thoughts, or a logical clock ordering what causally can affect what, or logically affect what allowing for Newcomb-like situations? Why is there a clock at all?), howListCis used, what concatenating multiple entries toListCmeans in terms of beliefs, etc. If it’s important for readers to understand this you might have to step us through (or point us to an earlier article where you stepped us through).ListC represents the same thing as ListE, ListL and ListU. Its a list of ordered outcomes of multiple runs of a particular model, which than we can compare to ListSB—a list of ordered awakenings of the Beauty in multiple iterations of an experiment and see whether their statistical properties are the same. The nature of the test is described in Statistical Analysis part of the post. I provide an inner hyperlink to it here:
Right, I read all that. I still don’t understand what it means to append two things to the list.
Here’s how I understand
modelLewis,modelElga, etc.“This model represent the world as a probability distribution. To get a more concrete sense of the world model, here’s a function which generates a sample from that probability distribution”
Here’s how I understand your model.
“This model represents the world as a ????, which like a probability distribution but different. To get a concrete sense of the world model, here’s a function which generates a sample from that probability distribution JUST KIDDING here’s TWO samples”.
Why can you generate two samples at once? What does that even mean?? The world model isn’t quite just a stationary probability distribution, fine, what is it then? Your model isn’t structured like other models, fine, but how is it structured? I’m drowning in type errors.
EDIT and I’m suggesting be really concrete, if you can, if that will help. Like come up with some concrete situation where Beauty makes a bet, or says a thing, (“Beauty woke up on Monday and said ‘I think there’s a 50% chance the coin came up on heads, and refuse to say there’s a state of affairs about what day it presently is’”) and explain what in her model made her make that bet or say that thing. Or maybe draw a picture which what her brain looks like under that circumstance compared to other circumstances.
Here’s how I think of what the list is. Sleeping Beauty writes a diary entry each day she wakes up. (“Nice weather today. I wonder how the coin landed.”). She would like to add today’s date, but can’t due to amnesia. After the experiment ends, she goes back to annotate each diary entry with what day it was written, and also the coin flip result, which she also now knows.
The experiment is lots of fun, so she signs up for it many times. The Python list corresponds to the dates she wrote in her dairy.