Before tossing the coin, the Omega perfectly emulates my decision making process. In this emulation he tells me that I lost the coin toss, explains the deal and asks me to give him $100. If this emulated me gives up the $100 then he has a good chance of getting $10,000.
I have absolutely no way of knowing whether I am the ‘emulated me’ or the real me. Vladmir’s specification is quite unambiguous. I, me, the one doing the deciding right now in this real world, am the same me as the one inside the Omega’s head. If the emulation is in any way different to me then the Omega isn’t the Omega. The guy in the Omega’s head has been offered a deal that any rational man would accept, and I am that man.
So, it may sound stupid that I’m giving up $100 with no hope of getting anything back. But that’s because the counterfactual is stupid, not me.
So, it may sound stupid that I’m giving up $100 with no hope of getting anything back. But that’s because the counterfactual is stupid, not me.
(Disclaimer: I’m going to use the exact language you used, which means I will call you “stupid” in this post. I apologize if this comes off as trollish. I will admit that I am also quite torn about this decision, and I feel quite stupid too.)
No offense, but assuming free will, you are the one who is deciding to actually hand over the $100. The conterfactual isn’t the one making the decision. You are. You are in a situation, and there are two possible actions (lose $100 or don’t lose $100), and you are choosing to lose $100.
And now I try to calculate what you should treat as being the probability that you’re being emulated. Assume that Omega only emulates you if the coin comes up heads.
Suppose you decide beforehand that you are going to give Omega the $100, as you ought to. The expected value of this is $4950, as has been calculated.
Suppose that instead, you decide beforehand that E is the probability you’re being emulated assuming you hear that came up tails. You’ll still decide to give Omega the $100; therefore, your expected value if you hear that it came up heads is $10,000. Your expected value if you hear that the coin came up tails is -$100(1-E) + $10,000E.
The probability that you hear that the coin comes up tails should be given by P(H) + P(T and ~E) + P(T and E) = 0, P(H) = P(T and ~E), P(T and ~E) = P(T) - P(T and E), P(T and E) = P(E|T) * P(T). Solving these equations, I get P(E|T) = 2, which probably means I’ve made a mistake somewhere. If not, c’est l’Omega?
to REALLY evaluate that, we technically need to know how long omega runs the simulation for.
now, we have two options: one, assume omega keeps running the simulation indefinitely. two, assume that omega shuts the simulation down once he has the info he’s looking for (and before he has to worry about debugging the simulation.)
in # 1, what we are left with is p(S)=1/3, p(H)=1/3, p(t)=1/3, which means we’re moving 200$/3 from part of our possibility cloud to gain 10,000$/3 in another part. In #2, we’re moving a total of 100⁄2 $ to gain 10000⁄2. The 100$ in the simulation is quantum-virtual.
so, unless you have reason to suspect omega is running a LOT of simulations of you, AND not terminating them after a minute or so...(aka, is not inadvertently simulation-mugging you)...
You can generally treat Omega’s simulation capacity as a dashed causality arrow from one universe to another-sortof like the shadow produced by the simulation...
Here is one intuitive way of looking at it:
Before tossing the coin, the Omega perfectly emulates my decision making process. In this emulation he tells me that I lost the coin toss, explains the deal and asks me to give him $100. If this emulated me gives up the $100 then he has a good chance of getting $10,000.
I have absolutely no way of knowing whether I am the ‘emulated me’ or the real me. Vladmir’s specification is quite unambiguous. I, me, the one doing the deciding right now in this real world, am the same me as the one inside the Omega’s head. If the emulation is in any way different to me then the Omega isn’t the Omega. The guy in the Omega’s head has been offered a deal that any rational man would accept, and I am that man.
So, it may sound stupid that I’m giving up $100 with no hope of getting anything back. But that’s because the counterfactual is stupid, not me.
(Disclaimer: I’m going to use the exact language you used, which means I will call you “stupid” in this post. I apologize if this comes off as trollish. I will admit that I am also quite torn about this decision, and I feel quite stupid too.)
No offense, but assuming free will, you are the one who is deciding to actually hand over the $100. The conterfactual isn’t the one making the decision. You are. You are in a situation, and there are two possible actions (lose $100 or don’t lose $100), and you are choosing to lose $100.
So again, are you sure you are not stupid?
And now I try to calculate what you should treat as being the probability that you’re being emulated. Assume that Omega only emulates you if the coin comes up heads.
Suppose you decide beforehand that you are going to give Omega the $100, as you ought to. The expected value of this is $4950, as has been calculated.
Suppose that instead, you decide beforehand that E is the probability you’re being emulated assuming you hear that came up tails. You’ll still decide to give Omega the $100; therefore, your expected value if you hear that it came up heads is $10,000. Your expected value if you hear that the coin came up tails is -$100(1-E) + $10,000E.
The probability that you hear that the coin comes up tails should be given by P(H) + P(T and ~E) + P(T and E) = 0, P(H) = P(T and ~E), P(T and ~E) = P(T) - P(T and E), P(T and E) = P(E|T) * P(T). Solving these equations, I get P(E|T) = 2, which probably means I’ve made a mistake somewhere. If not, c’est l’Omega?
um… lets see....
to REALLY evaluate that, we technically need to know how long omega runs the simulation for.
now, we have two options: one, assume omega keeps running the simulation indefinitely. two, assume that omega shuts the simulation down once he has the info he’s looking for (and before he has to worry about debugging the simulation.)
in # 1, what we are left with is p(S)=1/3, p(H)=1/3, p(t)=1/3, which means we’re moving 200$/3 from part of our possibility cloud to gain 10,000$/3 in another part.
In #2, we’re moving a total of 100⁄2 $ to gain 10000⁄2. The 100$ in the simulation is quantum-virtual.
so, unless you have reason to suspect omega is running a LOT of simulations of you, AND not terminating them after a minute or so...(aka, is not inadvertently simulation-mugging you)...
You can generally treat Omega’s simulation capacity as a dashed causality arrow from one universe to another-sortof like the shadow produced by the simulation...