On 07 Sep 2015, at 19:05, Brent Meeker wrote:
On 9/7/2015 3:23 AM, Bruno Marchal wrote:
On 06 Sep 2015, at 22:27, Jason Resch wrote:
You will undergo the following experiment:
1. During the weekend you will be put to sleep with a drug and not
be woken up until Monday.
2. On monday you will be woken up and asked what day it is. How do
you answer?
3. You are then given a drug to put you to sleep again and also
given a drug that induces amnesia of being woken up at all on
Monday.
4. You are woken up on Tuesday, and asked what day it is. How do
you answer?
If asked to ascribe a probability to it being Monday when you are
woken up, how do you answer on either of the days you are awoken?
(I am particularly interested in John Clark's answer to the final
question)
I guess that the experiencer know the entire protocol, in this
case, without further reading, I would say it is equivalent with a
self-duplication. Nice thought experiment as it does not involve
self-duplication and illustrates also a probability in a
deterministic context. Not quite feasible, though, as it involves a
perfect one day amnesia, but it illustrates well the point.
And now reading further I see that we agree.
To Brent, I would add that we can use the frequentist probability
analysis, as that experience *can* be repeated, and if you asked me
the probability to have been woke up n times on Tuesday, (n less
than 52, the number of week in one year) when the experience is
repeated every week during one year, I would use the Gaussian
distribution, or the Pascal triangle, I mean the Newton binomial
(as 52 weeks is not very high to use Gauss function, perhaps).
If each time you woke up, you guessed the day and then someone told
you the correct day and you wrote it down (since otherwise you'd
never remember anything to use as statistics) then you'd be right
about half the time and you proportion correct would have a binomial
distribution. BUT suppose you just said "Monday" every time. Then
you would right exactly half the time, with no scatter; thus showing
that there's no randomness.
OK, good logical point. The iterated version of that experiment is
hard to do due to the fact that the protocol contains an amnesia. It
seems also that by predicting always "Monday", I will never been
correct in the long run, as this will always be deleted from the memory.
Bruno
Brent
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