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timtyler comments on Updating, part 1: When can you change your mind? The binary model - Less Wrong
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Before consuming the memory-loss drugs she knows her own temporal history. After consuming the drugs, she doesn't. She is more uncertain - because her memory has been meddled with, and important information has been deleted from it.
Information wasn't deleted. Conditions changed and she didn't receive enough information about the change. There is a type (with a single token) that is Beauty before the experiment and that type includes a property 'knows what day of the week it is', then the experiment begins and the day changes. During the experiment there is another type which is also Beauty, this type has two tokens. This type only has enough information to narrow down the date to one of two days. But she still knows what day of the week it was when the experiment began, it's just your usual indexical shift (instead of knowing the date now she knows the date then but it is the same thing).
Her memories were DELETED. That's the whole point of the amnesia-inducing drug.
Amnesia = memory LOSS: http://dictionary.reference.com/browse/Amnesia
Oh sure, the information contained in the memory of waking up is lost (though that information didn't contain what day of the week it was and you said "namely that she no longer knows which day of the week it is"). I still have zero idea of what you're trying to ask me.
If she had not ever been given the drug she would be likely to know which day of the week it was. She would know how many times she had been woken up, interviewed, etc. It is because all such information has been chemically deleted from her mind that she has the increased uncertainty that she does.
I might have some issues with that characterization but they aren't worth going into since I still don't know what this has to do with my discussion of the type-token ambiguity.
It is what was missing from this analysis:
"The type experience "waking up" has P=1 for heads and tails. So the prior never changes."
Your priors are a function of your existing knowledge. If that knowledge is deleted, your priors may change.
K.
Yes, counterfactually if she hadn't been given the drug on the second awakening she would have knowledge of the day. But she was given the drug. This meant a loss of the information and knowledge of the memory of the first awakening. But it doesn't mean a loss of the knowledge of what day it is, she obviously never had that. It is because all her new experiences keep getting deleted that she is incapable of updating her priors (which were set prior to the beginning of the experiment). In type-theoretic terms:
If the drugs had not been administered she would not have had type experience "waking up" a second time. She would have had type experience "waking up with the memory of waking up yesterday". If she had had that type experience then she would know what day it is.
Beauty probably knew what day it was before the experiment started. People often do know what day of the week it is.
You don't seem to respond to my: "Your priors are a function of your existing knowledge. If that knowledge is deleted, your priors may change."
In this case, that is exactly what happens. Had Beauty not been given the drug, her estimates of p(heads) would be: 0.5 on Monday and 0.0 on Tuesday. Since her knowledge of what day it is has been eliminated by a memory-erasing drug, her probability estimate is intermediate between those figures - reflecting her new uncertainty in the face of the chemical deletion of relevant evidence.
Yes. And throughout the experiment she knows what day it was before the experiment started. What she doesn't know is the new day. This is the second or third time I've said this. What don't you understand about an indexical shift?
The knowledge that Beauty has before the experiment is not deleted. Beauty has a single anticipated experience going into the experiment. That anticipated experience occurs. There is no new information to update on.
You don't seem to be following what I'm saying at all.