Didn’t check lesswrong for a month, almost missed this post. I have followed your work on anthropic for quite sometime. I want to ask a quick question:
An alternate characterisation of the SIA and SSA questions could be to ask, “If I said ‘I have X’, would I want most of my copies to be correct (SIA) or my copies to be correct in most universes (SSA)?”
What if I just want to be correct. Not giving any thought to other copies at all? Do you consider that response invalid?
For some context consider this example: Tonight during my sleep an alien Omega is going to toss a coin. If it land Tails it splits me in halves, and make two copies of me by molecular cloning the other half respectively. The process is accurate enought the resulting copies won’t be able to tell. If Heads Omega won’t do anything. After waking up Omega would ask one/both copies about the coin toss (guess the result or give a probabililty).
Now I wake up from the experiement, how should I guess the result? I think it can be answered without even care about what the other copy of me (if it exist) thinks. I can participate this experiment repeatedly and will experience about equal numbers of Heads vs Tails.
In the classical sleeping beauty problem, if I guess the coin was tails, I will be correct in 50% of the experiments, and in 67% of my guesses. Whether you score by “experiments” or by “guesses” gives a different optimal performance.
In the classical sleeping beauty problem, if I guess the coin was tails, I will be correct in 50% of the experiments, and in 67% of my guesses.
In this case, how do you define “my guesses”? Does that mean guesses made by the same physical person? That would lead to different answers in the sleeping beauty problem vs the above cloning/spliting problem.
To translate my position from the previous comment would be “my guesses” are primitively clear to me because I have the subjective experience of them. So when faced with the question “would I want most of my copies to be correct (SIA) or my copies to be correct in most universes (SSA)?”, I would simply say “I just want myself to be correct.” Do you think that is an invalid position?
Put it in the classical sleeping beauty problem, the exact duration of the experiment is inconsequential. The two awakenings can be one day apart (as the usual formulation), or a week apart, or an hour apart. It is still the same experiment/problem. I think we can all agree on that.
So imagine I wake up in the experiment. I can enter another iteration of the experiment right away. As long as the second experiment finishes before the potentially incoming memory wipe of the first experiment. For example, let the first experiment have awakenings 1 day apart, the second experiment with awakenings 1⁄2 day apart, the third experiment with awakenings 1⁄4 day apart, etc. Theoretically, the experiment can be repeated infinite times. (This is of course assuming the actual awakenings take insignificant time and the memory wipes happen just before the second awakening). When repeating the sleeping beauty problem this way, I have a clear track of how many iterations have I entered, what was my guesses in those iterations, and how many of them are right. And that number would approach 50% if I guess tails every time.
In this process, I never have to consider “this awakening” as a member of any reference class. Do you think “keeping the score” this way invalid?
Didn’t check lesswrong for a month, almost missed this post. I have followed your work on anthropic for quite sometime. I want to ask a quick question:
What if I just want to be correct. Not giving any thought to other copies at all? Do you consider that response invalid?
For some context consider this example: Tonight during my sleep an alien Omega is going to toss a coin. If it land Tails it splits me in halves, and make two copies of me by molecular cloning the other half respectively. The process is accurate enought the resulting copies won’t be able to tell. If Heads Omega won’t do anything. After waking up Omega would ask one/both copies about the coin toss (guess the result or give a probabililty).
Now I wake up from the experiement, how should I guess the result? I think it can be answered without even care about what the other copy of me (if it exist) thinks. I can participate this experiment repeatedly and will experience about equal numbers of Heads vs Tails.
In the classical sleeping beauty problem, if I guess the coin was tails, I will be correct in 50% of the experiments, and in 67% of my guesses. Whether you score by “experiments” or by “guesses” gives a different optimal performance.
In this case, how do you define “my guesses”? Does that mean guesses made by the same physical person? That would lead to different answers in the sleeping beauty problem vs the above cloning/spliting problem.
To translate my position from the previous comment would be “my guesses” are primitively clear to me because I have the subjective experience of them. So when faced with the question “would I want most of my copies to be correct (SIA) or my copies to be correct in most universes (SSA)?”, I would simply say “I just want myself to be correct.” Do you think that is an invalid position?
Put it in the classical sleeping beauty problem, the exact duration of the experiment is inconsequential. The two awakenings can be one day apart (as the usual formulation), or a week apart, or an hour apart. It is still the same experiment/problem. I think we can all agree on that.
So imagine I wake up in the experiment. I can enter another iteration of the experiment right away. As long as the second experiment finishes before the potentially incoming memory wipe of the first experiment. For example, let the first experiment have awakenings 1 day apart, the second experiment with awakenings 1⁄2 day apart, the third experiment with awakenings 1⁄4 day apart, etc. Theoretically, the experiment can be repeated infinite times. (This is of course assuming the actual awakenings take insignificant time and the memory wipes happen just before the second awakening). When repeating the sleeping beauty problem this way, I have a clear track of how many iterations have I entered, what was my guesses in those iterations, and how many of them are right. And that number would approach 50% if I guess tails every time.
In this process, I never have to consider “this awakening” as a member of any reference class. Do you think “keeping the score” this way invalid?
Different ways of keeping the score give different answers. So, no, I don’t think that’s invalid.