The state of the lights tells me nothing about the color of the door. Whatever color room I happen to be in, the coin toss will turn my lights on or off with 50% probability.
I don’t see what you intend me to learn from this example...
That dead or alive you are still most likely behind a blue door. You can use the lights being on as evidence just as well as your being alive.
That in B through D you are already updating based on your continued existence.
Beforehand you would expect a 50% chance of dying.
Later, If you are alive, then the coin probably came up heads.
In E and F, You wake up, You know the coin flip is in your past, You know that most ‘survivors’ of situations like this come out of blue doors.
If you play Russian roulette and survive, you can have a much greater than 5⁄6 confidence that the chamber wasn’t loaded.
You can be very certain that you have great grandparents, given only your existence and basic knowledge about the world.
That dead or alive you are still most likely behind a blue door.
In A-D this is correct. I start out being probably behind a blue door (p=.99), and dying or not doesn’t influence that.
In E-F this is not correct. Your words “dead or alive” simply don’t apply: the dead observers never were alive (and conscious) in these scenarios. They were created and then destroyed without waking up. There is no possible sense in which “I” could be one of them; I am by definition alive now or at least were alive at some point in the past. Even under the assumptions of the SIA, a universe with potential observers that never actually materialize isn’t the same as one with actual observers.
I still think that in E-F, I’m equally likely to be behind a blue or a red door.
That in B through D you are already updating based on your continued existence.
Correct. The crucial difference is that in B-D I could have died but didn’t. In other Everett branches where the coin toss went the other way I did die. So I can talk about the probability of the branch where I survive, and update on the fact that I did survive.
But in E-F I could never have died! There is no branch of possibility where any conscious observer has died in E-F. That’s why no observer can update on being alive there; they are all alive with p=1.
You can be very certain that you have great grandparents, given only your existence and basic knowledge about the world.
Yes, because in our world there are people who fail to have grandchildren, and so there are potential grandchildren who don’t actually come to exist.
But in the world of scenarios E and F there is no one who fails to exist and to leave a “descendant” that is himself five minutes later...
I now understand that the argument in the article is correct (and p=.99 in all scenarios). The formulation of the scenarios caused me some kind of cognitive dissonance but now I no longer see a problem with the correct reading of the argument. Please ignore my comments below. (Should I delete in such cases?)
I now understand that the argument in the article is correct (and p=.99 in all scenarios). The formulation of the scenarios caused me some kind of cognitive dissonance but now I no longer see a problem with the correct reading of the argument.
The state of the lights tells me nothing about the color of the door. Whatever color room I happen to be in, the coin toss will turn my lights on or off with 50% probability.
I don’t see what you intend me to learn from this example...
That dead or alive you are still most likely behind a blue door. You can use the lights being on as evidence just as well as your being alive.
That in B through D you are already updating based on your continued existence.
Beforehand you would expect a 50% chance of dying. Later, If you are alive, then the coin probably came up heads. In E and F, You wake up, You know the coin flip is in your past, You know that most ‘survivors’ of situations like this come out of blue doors.
If you play Russian roulette and survive, you can have a much greater than 5⁄6 confidence that the chamber wasn’t loaded.
You can be very certain that you have great grandparents, given only your existence and basic knowledge about the world.
In E-F this is not correct. Your words “dead or alive” simply don’t apply: the dead observers never were alive (and conscious) in these scenarios. They were created and then destroyed without waking up. There is no possible sense in which “I” could be one of them; I am by definition alive now or at least were alive at some point in the past. Even under the assumptions of the SIA, a universe with potential observers that never actually materialize isn’t the same as one with actual observers.
I still think that in E-F, I’m equally likely to be behind a blue or a red door.
Correct. The crucial difference is that in B-D I could have died but didn’t. In other Everett branches where the coin toss went the other way I did die. So I can talk about the probability of the branch where I survive, and update on the fact that I did survive.
But in E-F I could never have died! There is no branch of possibility where any conscious observer has died in E-F. That’s why no observer can update on being alive there; they are all alive with p=1.
Yes, because in our world there are people who fail to have grandchildren, and so there are potential grandchildren who don’t actually come to exist.
But in the world of scenarios E and F there is no one who fails to exist and to leave a “descendant” that is himself five minutes later...
I now understand that the argument in the article is correct (and p=.99 in all scenarios). The formulation of the scenarios caused me some kind of cognitive dissonance but now I no longer see a problem with the correct reading of the argument. Please ignore my comments below. (Should I delete in such cases?)
I wouldn’t delete, if nothing else it serves as a good example of working through the dissonance.
edit It would also be helpful if you explained from your own perspective why you changed your mind.
Second James’s preference and note that I find it useful as a reader to see an edit note of some sort in comments that are no longer supported.
I now understand that the argument in the article is correct (and p=.99 in all scenarios). The formulation of the scenarios caused me some kind of cognitive dissonance but now I no longer see a problem with the correct reading of the argument.