However, in the Sleeping Beauty experiment, Beauty gains no new information from waking up at any time, in any outcome.
She gains the information that she is sleeping beauty waking up. This is actually very unlikely. Only a tiny fraction of life moments are sleeping beauty waking up.
There are twice as many such moments if she gets woken up twice, and presumably about the same number total. As such, this information doubles the odds that she woke up twice.
Of course, if sleeping beauty were the only person in the world ever, and only lived for this experiment, then the probability would be 50:50. If there were only a few other life moments, it would be somewhere in between.
In short, there is a difference between knowing that there exists a sleeping beauty waking up, and knowing you are a sleeping beauty waking up.
A good example of this is that a given planet has about a one in 5000 chance of having as little cosmic radiation as Earth. The fact that a planet like that has intelligent life just tells you that cosmic radiation isn’t necessary. The fact that it’s our planet tells us that it’s actively harmful.
However, in the Sleeping Beauty experiment, Beauty gains no new information from waking up at any time, in any outcome.
She gains the information that she is sleeping beauty waking up. This is actually very unlikely. Only a tiny fraction of life moments are sleeping beauty waking up.
But that does not constitute any new information relative to her state of knowledge before the experiment started. She already knew in advance what she’d be experiencing.
She didn’t know she was sleeping beauty waking up when she went to sleep. She did when she woke up. Thus, she had different information.
She knew she would become sleeping beauty waking up, but that’s entirely different information. The prior is orders of magnitude higher. She’d spend years being sleeping beauty going to wake up in that experiment, but only one or two days doing so.
In what way is “I will be Sleeping-Beauty-waking-up” different information than “I am Sleeping-Beauty-waking-up”? I cannot see any difference other than verb tense, and since one is spoken before the other, that only constitutes a difference in the frame of reference in which each one is spoken, not a difference in propositional content; they’re saying the same thing about the same event. (I think this is something like a variable question fallacy.)
The verb tense is important. One only works from a single frame of reference. The other works from several.
The probability of a given frame of reference is 1/number of frames of reference.
In my planet example, from any frame of reference you can say that there is a planet with intelligent life that has less cosmic radiation that all but 1⁄5000 of them, but only on planets like that can you say that that’s true of that planet.
The first is true unless cosmic radiation is necessary. The second is more likely to be true if cosmic radiation is harmful than if it isn’t.
Do we have enough information to deduce that cosmic radiation is harmful, or, for that matter, that planets are helpful? They use the same basic argument.
These make different predictions, so it isn’t the variable question fallacy.
She gains the information that she is sleeping beauty waking up. This is actually very unlikely. Only a tiny fraction of life moments are sleeping beauty waking up.
There are twice as many such moments if she gets woken up twice, and presumably about the same number total. As such, this information doubles the odds that she woke up twice.
Of course, if sleeping beauty were the only person in the world ever, and only lived for this experiment, then the probability would be 50:50. If there were only a few other life moments, it would be somewhere in between.
In short, there is a difference between knowing that there exists a sleeping beauty waking up, and knowing you are a sleeping beauty waking up.
A good example of this is that a given planet has about a one in 5000 chance of having as little cosmic radiation as Earth. The fact that a planet like that has intelligent life just tells you that cosmic radiation isn’t necessary. The fact that it’s our planet tells us that it’s actively harmful.
But that does not constitute any new information relative to her state of knowledge before the experiment started. She already knew in advance what she’d be experiencing.
She didn’t know she was sleeping beauty waking up when she went to sleep. She did when she woke up. Thus, she had different information.
She knew she would become sleeping beauty waking up, but that’s entirely different information. The prior is orders of magnitude higher. She’d spend years being sleeping beauty going to wake up in that experiment, but only one or two days doing so.
In what way is “I will be Sleeping-Beauty-waking-up” different information than “I am Sleeping-Beauty-waking-up”? I cannot see any difference other than verb tense, and since one is spoken before the other, that only constitutes a difference in the frame of reference in which each one is spoken, not a difference in propositional content; they’re saying the same thing about the same event. (I think this is something like a variable question fallacy.)
The verb tense is important. One only works from a single frame of reference. The other works from several.
The probability of a given frame of reference is 1/number of frames of reference.
In my planet example, from any frame of reference you can say that there is a planet with intelligent life that has less cosmic radiation that all but 1⁄5000 of them, but only on planets like that can you say that that’s true of that planet.
The first is true unless cosmic radiation is necessary. The second is more likely to be true if cosmic radiation is harmful than if it isn’t.
Do we have enough information to deduce that cosmic radiation is harmful, or, for that matter, that planets are helpful? They use the same basic argument.
These make different predictions, so it isn’t the variable question fallacy.