In fact, the probability goes up anyway in that fraction of a second, whether you blink or not.
Ah, sorry; I wasn’t clear. What I meant was that blinking increases your probability of being tortured beyond the normal “baseline” probability of torture. Obviously, even if you don’t blink, there’s still a probability of you being tortured. My claim is that blinking affects the probability of being tortured so that the probability is higher than it would be if you hadn’t blinked (since you can’t see for a fraction of a second while blinking, leaving you ever-so-slightly more vulnerable than you would be with your eyes open), and moreover that it would increase by more than 1/3^^^3. So basically what I’m saying is that P(torture|blink) > P(torture|~blink) + 1/3^^^3.
The choice comes down to dust specks at time T or dust specks at time T + dT, where the interval dT allows you time to blink. The argument is that in the interval dT, the probability of being captured and tortured increases by an amount greater than your odds in the lottery.
It seems to me that the blinking is immaterial. If the question were whether to hold the lottery today or put dust in everyone’s eyes tomorrow, the argument should be unchanged. It appears to hinge on the notion that as time increases, so do the odds of something bad happening, and therefore you’d prefer to be in the present instead of the future.
The problem I have is that the future is going to happen anyway. Once the interval dT passes, the odds of someone being captured in that time will go up regardless of whether you chose the lottery or not.
Ah, sorry; I wasn’t clear. What I meant was that blinking increases your probability of being tortured beyond the normal “baseline” probability of torture. Obviously, even if you don’t blink, there’s still a probability of you being tortured. My claim is that blinking affects the probability of being tortured so that the probability is higher than it would be if you hadn’t blinked (since you can’t see for a fraction of a second while blinking, leaving you ever-so-slightly more vulnerable than you would be with your eyes open), and moreover that it would increase by more than 1/3^^^3. So basically what I’m saying is that P(torture|blink) > P(torture|~blink) + 1/3^^^3.
Let me see if I get this straight:
The choice comes down to dust specks at time T or dust specks at time T + dT, where the interval dT allows you time to blink. The argument is that in the interval dT, the probability of being captured and tortured increases by an amount greater than your odds in the lottery.
It seems to me that the blinking is immaterial. If the question were whether to hold the lottery today or put dust in everyone’s eyes tomorrow, the argument should be unchanged. It appears to hinge on the notion that as time increases, so do the odds of something bad happening, and therefore you’d prefer to be in the present instead of the future.
The problem I have is that the future is going to happen anyway. Once the interval dT passes, the odds of someone being captured in that time will go up regardless of whether you chose the lottery or not.