Sleeping Beauty (SB) volunteers for this experiment, and is told all these details by a Lab Assistant (LA):
I will put you to sleep tonight (Sunday) with a drug that lasts 12 hours. After you are asleep, I will flip two coins—a Dime and a Nickel. I will lock them in an opaque box that has a sensor which can tell if at least one coin inside is showing Tails.
I will then administer a drug to myself, that erases my memory of the last 12 hours, and go to sleep in the next room.
Until I am stopped (which will happen on Wednesday morning), when I wake up in the morning I will perform the following procedure:
If the box’s sensor says neither coin is showing Tails, I will administer a drug to you (in your sleep) that extends your sleep another 24 hours.
If the box’s sensor says that at least one coin is showing Tails, I will let you wake up. I will sa to you: “Before I looked at the box this morning, the probabilities the coins were showing HH, HT, TH, or TT were all 1⁄4. Now that we’ve proceeded to the awake portion of this procedure, what probability should each of us give that the Dime is currently showing Heads?” After receiving an answer, I will administer the amnesia drug to you, and then the 12-hour sleep drug.
In either case, after you are asleep I will open the box, turn the Nickel over to show its other face, administer the amnesia drug to myself, and go to sleep in the next room.
Questions:
1) Is the question “What side is the Dime currently showing?” functionally different, in any way and on either day, than the question “How did the Dime land on Sunday Night?”
2) Is LA’s probability distribution wrong in any way?
I think these answers are both “no.” So LA can answer the probability question (s)he asks. Since case HH is eliminated, in LA’s world the probability that the Dime is showing Heads is 1⁄3.
3) Is SB’s prior probability distribution for the two coins the same as LA’s?
4) Is SB’s information the same as LAX’s?
I think these answers are both “yes.” SB’s answer is the same as LAX’s. The probabiltiy is 1⁄3.
As far as I can tell, a halfer will say that the answer to #4 is a definite “no.” #3 is unclear to me, but how they address it seems to be how they justify saying her information is different.
I think Halfers use a Shcrodinger’s-Cat-like argument where HH and HT both true at the same time. HH cannot be eliminated because HT can’t. Literally, they seem to say that SB can’t consider the current state of the Nickel (which corresponds to the day in the original experiment) to be a random variable, since it shows both faces during the experiment. That’s an invalid argument here, since the sensor is based on what it is currently showing.
5) How is this question, in SB’s world, any different than the original SB problem?
I’d really like to hear a halfer’s answer. Because it isn’t.
Sleeping Beauty (SB) volunteers for this experiment, and is told all these details by a Lab Assistant (LA):
I will put you to sleep tonight (Sunday) with a drug that lasts 12 hours. After you are asleep, I will flip two coins—a Dime and a Nickel. I will lock them in an opaque box that has a sensor which can tell if at least one coin inside is showing Tails.
I will then administer a drug to myself, that erases my memory of the last 12 hours, and go to sleep in the next room.
Until I am stopped (which will happen on Wednesday morning), when I wake up in the morning I will perform the following procedure:
If the box’s sensor says neither coin is showing Tails, I will administer a drug to you (in your sleep) that extends your sleep another 24 hours.
If the box’s sensor says that at least one coin is showing Tails, I will let you wake up. I will sa to you: “Before I looked at the box this morning, the probabilities the coins were showing HH, HT, TH, or TT were all 1⁄4. Now that we’ve proceeded to the awake portion of this procedure, what probability should each of us give that the Dime is currently showing Heads?” After receiving an answer, I will administer the amnesia drug to you, and then the 12-hour sleep drug.
In either case, after you are asleep I will open the box, turn the Nickel over to show its other face, administer the amnesia drug to myself, and go to sleep in the next room.
Questions:
1) Is the question “What side is the Dime currently showing?” functionally different, in any way and on either day, than the question “How did the Dime land on Sunday Night?”
2) Is LA’s probability distribution wrong in any way?
I think these answers are both “no.” So LA can answer the probability question (s)he asks. Since case HH is eliminated, in LA’s world the probability that the Dime is showing Heads is 1⁄3.
3) Is SB’s prior probability distribution for the two coins the same as LA’s?
4) Is SB’s information the same as LAX’s?
I think these answers are both “yes.” SB’s answer is the same as LAX’s. The probabiltiy is 1⁄3.
As far as I can tell, a halfer will say that the answer to #4 is a definite “no.” #3 is unclear to me, but how they address it seems to be how they justify saying her information is different.
I think Halfers use a Shcrodinger’s-Cat-like argument where HH and HT both true at the same time. HH cannot be eliminated because HT can’t. Literally, they seem to say that SB can’t consider the current state of the Nickel (which corresponds to the day in the original experiment) to be a random variable, since it shows both faces during the experiment. That’s an invalid argument here, since the sensor is based on what it is currently showing.
5) How is this question, in SB’s world, any different than the original SB problem?
I’d really like to hear a halfer’s answer. Because it isn’t.