What else does event “Monday” that has 2⁄3 probability means then?
It means “today is Monday”.
I do not I understand what you mean here. Beauty is part of simulation. Nothing prevents any person from running the same code and getting the same results.
I mean what will happen, if Beauty runs the same code? Like you said, “any person”—what if this person is Beauty during the experiment? If we then compare combined statistics, which model will be closer to reality?
Why would it?
My thinking is because then Beauty would experience more tails and simulation would have to reproduce that.
How is definition of knowledge relevant to probability theory? I suppose, if someone redefines “knowledge” as “being wrong” then yes, in such definition the Beauty should not accept the correct model, but why would we do it?
The point of using probability theory is to be right. That’s why your simulations have persuasive power. But different definition of knowledge may value average knowledge of awake moments of Beauty instead of knowledge of outside observer.
And Beauty is awakened, because all the outcomes represent Beauty’s awakened states. Which is “Beauty is awakened today which is Monday” or simply “Beauty is awakened on Monday” just as I was saying.
I mean what will happen, if Beauty runs the same code? Like you said, “any person”—what if this person is Beauty during the experiment? If we then compare combined statistics, which model will be closer to reality?
Nothing out of the ordinary. The Beauty will generate the list with the same statistical properties. Two lists if the coin is Tails.
My thinking is because then Beauty would experience more tails and simulation would have to reproduce that.
Simulation already reproduces that. Only 1⁄3 of the elements of the list are Heads&Monday. You should probably try running the code yourself to see how it works, because I have a feeling that you are missing something.
Oh, right, I missed that your simulation has 1⁄3 Heads. Thank you for your patient cooperation in finding mistakes in your arguments, by the way. So, why is it ok for a simulation of an outcome with 1⁄2 probability to have 1⁄3 frequency? That sounds like more serious failure of statistical test.
Nothing out of the ordinary. The Beauty will generate the list with the same statistical properties. Two lists if the coin is Tails.
I imagined that the Beauty would sample just once. And then if we combine all samples into list, we will see that if the Beauty uses your model, then the list will fail the “have the correct number of days” test.
Which is “Beauty is awakened today which is Monday” or simply “Beauty is awakened on Monday” just as I was saying.
They are not the same thing? The first one is false on Tuesday.
(I’m also interested in your thoughts about copies in another thread).
So, why is it ok for a simulation of an outcome with 1⁄2 probability to have 1⁄3 frequency?
There are only two outcomes and both of them have 1⁄2 probability and 1⁄2 frequency. The code saves awakenings in the list, not outcomes
People mistakenly assume that three awakenings mean three elementary outcomes. But as the simulation shows, there is order between awakenings and so they can’t be treated as individual outcomes. Tails&Monday and Tails&Tuesday awakenings are parts of the same outcome.
If this still doesn’t feel obvious, consider this. You have a list of Heads and Tails. And you need to distinguish between two hypothesis. Either the coin is unfair and P(Tails)=2/3, or the coin is fair but whenever it came Tails, the outcome was written twice in the list, while for Heads—only once. You check whether outcomes are randomly spread or pairs of Tails follow together. In the second case, even though the frequency of Tails in the list is twice as high as Heads, P(Tails)=P(Heads)=1/2.
It means “today is Monday”.
I mean what will happen, if Beauty runs the same code? Like you said, “any person”—what if this person is Beauty during the experiment? If we then compare combined statistics, which model will be closer to reality?
My thinking is because then Beauty would experience more tails and simulation would have to reproduce that.
The point of using probability theory is to be right. That’s why your simulations have persuasive power. But different definition of knowledge may value average knowledge of awake moments of Beauty instead of knowledge of outside observer.
And Beauty is awakened, because all the outcomes represent Beauty’s awakened states. Which is “Beauty is awakened today which is Monday” or simply “Beauty is awakened on Monday” just as I was saying.
Nothing out of the ordinary. The Beauty will generate the list with the same statistical properties. Two lists if the coin is Tails.
Simulation already reproduces that. Only 1⁄3 of the elements of the list are Heads&Monday. You should probably try running the code yourself to see how it works, because I have a feeling that you are missing something.
Oh, right, I missed that your simulation has 1⁄3 Heads. Thank you for your patient cooperation in finding mistakes in your arguments, by the way. So, why is it ok for a simulation of an outcome with 1⁄2 probability to have 1⁄3 frequency? That sounds like more serious failure of statistical test.
I imagined that the Beauty would sample just once. And then if we combine all samples into list, we will see that if the Beauty uses your model, then the list will fail the “have the correct number of days” test.
They are not the same thing? The first one is false on Tuesday.
(I’m also interested in your thoughts about copies in another thread).
There are only two outcomes and both of them have 1⁄2 probability and 1⁄2 frequency. The code saves awakenings in the list, not outcomes
People mistakenly assume that three awakenings mean three elementary outcomes. But as the simulation shows, there is order between awakenings and so they can’t be treated as individual outcomes. Tails&Monday and Tails&Tuesday awakenings are parts of the same outcome.
If this still doesn’t feel obvious, consider this. You have a list of Heads and Tails. And you need to distinguish between two hypothesis. Either the coin is unfair and P(Tails)=2/3, or the coin is fair but whenever it came Tails, the outcome was written twice in the list, while for Heads—only once. You check whether outcomes are randomly spread or pairs of Tails follow together. In the second case, even though the frequency of Tails in the list is twice as high as Heads, P(Tails)=P(Heads)=1/2.