A problem in anthropics with implications for the soundness of the simulation argument.

by philosophytorres1 min read19th Oct 201616 comments


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What are your intuitions about this? It has direct implications for whether the Simulation Argument is sound.


Imagine two rooms, A and B. Between times t1 and t2, 100 trillion people sojourn in room A while 100 billion sojourn in room B. At any given moment, though, exactly 1 person occupies room A while 1,000 people occupy room B. At t2, you find yourself in a room, but you don't know which one. If you have to place a bet on which room it is (at t2), what do you say? Do you consider the time-slice or the history of room occupants? How do you place your bet?


If you bet that you're in room B, then the Simulation Argument may be flawed: there could be a fourth disjunct that Bostrom misses, namely that we become a posthuman civilization that runs a huge number of simulations yet we don't have reason for believing that we're stimulants.



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Depends on information. If people retain memories, so that each person-moment follows from a previous one, then knowing only that I suddenly find myself in a room means I'm probably in room A. If people are memory-wiped at some interval, then this increases the probability I should assign to being in room B - probability of being in a specific room, given that your state of information is that you suddenly find yourself in a room, is proportional to the number of times "I have suddenly found myself in a room" is somebody's state of information.

The above is in fact true. So here's a fun puzzler for you: why is the following false?

"If you tell me the exact time, then my room must more likely be B, because there are 1000 times more people in room B at that time. Since this holds for all times you could tell me, it is always true that my room is probably B, so I'm probably in room B."

Hint: Assuming that room B residents "live" 1,000,000 times longer than room A residents, how does their probability of being in room B look throughout their life, assuming they retain their memories?

As for your first comment, imagine that everyone "wakes up" in a room with only the information provided and no prior memories. After 5 minutes, they're put back to sleep -- but before this occurs they're asked about which room they're in. (Does that make sense?)

I thought you might like to hear about some of the literature on this problem. Forgive me if you're already aware of this work and I've misunderstood you.

Manfred writes:

If people are memory-wiped at some interval, then this increases the probability I should assign to being in room B - probability of being in a specific room, given that your state of information is that you suddenly find yourself in a room, is proportional to the number of times "I have suddenly found myself in a room" is somebody's state of information.

In Anthropic Bias: Observation Selection Effects in Science and Philosophy, Nick Bostrom describes a thought experiment known as 'Mr. Amnesiac' to illustrate the desirability of a theory of observation selection effects that takes this kind of temporal uncertainty into account:

Mr. Amnesiac, the only observer ever to exist, is created in Room 1, where he stays for two hours. He is then transported into Room 2, where he spends one hour, whereupon he is terminated. His severe amnesia renders him incapable of retaining memories for any significant period of time. The details about the experimental situation he is in, however, are explained on posters in both rooms; so he is always aware of the relevant non-indexical features of his world.

Not unlike Manfred's arguments in favor of betting on room B under imperfect recall, Bostrom's solution here is to propose observer-moments, time intervals of observers' experiences of arbitrary length, and reason as though you are a randomly selected observer-moment from your reference class, as opposed to just a randomly selected observer (in philosophy, Strong Self-Sampling Assumption vs. Self-Sampling Assumption). With this assumption and imperfect recall, you would conclude in Mr. Amnesiac that the probability of your being in Room 1 = 2/3 and of being in Room 2 = 1/3, and that you should bet on Room 1.

But I don't think there's anything mysterious there. If I understand correctly, we are surreptitiously asking the room B people to bet 1000 more times per observer than the room A people. Yet again, the relevant consideration is "How many times is this experience occurring?"

Nitpick: If we do include imperfect recall, doesn't this actually just make us indifferent between room A and room B, as opposed to making us prefer room B? Room A people collectively possess 100 trillion observer-moments that belong to 100 trillion observers, room B people collectively possess 1000 observer-moments per observer times 100 billion observers = 100 trillion observer-moments that belong to 100 billion observers. Our credence should be 50/50 and we're indifferent between bets. Or am I confused?

Bostrom published that in 2002? Wow!

With amnesia, in room A there is 1 observer-moment per moment over the total occupied time T => T observer moments, while in room B there are 1000 observer-moments per moment over some other time T' => 1000 T' observer moments.

If the people in room B stick around long enough that T=T', then there are more total observer moments in room B. If each person gets the same amount of time (as suggested in the comment two above), then T'=T/1,000,000 and are more observer moments in room A.

(For more rigor, we might think of "observer-moment" as a density function rather than discrete occurrences).

Bostrom published that in 2002? Wow!

I always see you commenting on Stuart Armstrong's posts, so I actually just assumed you were alluding to that work in the great-great-grandparent. I wonder if I should start erring on the side of assuming that people do want pointers to the literature.

Yeah, my knowledge of the anthropics literature is pretty slim - thinking about anthropics has driven me to read about probability and causal models, rather than the object-level writings. Pointers to the literature are great :)

Here's a stab: If I understand you correctly, then every observer's experience is indistinguishable from every other's, so my credence in the proposition "I'm in room A" is 0.999 and my decision policy is "Bet that I'm in room A." If 100 trillion + 100 billion people choose room B, then 100 trillion will lose and 100 billion will win. If 100 trillion + 100 billion people choose room A, then 100 billion will lose and 100 trillion will win.

I don't understand how it could happen: do you mean that time in the room B is million times slower?

Not OP, but each single person could be in room A for 1/1,000,000 the time that they're in room B. The time doesn't run slower, but they're there less time, producing the same effect.

Yeah, to rephrase: do we update based on subjective or objective measure of time?

There are two groups of brains, x1 and x2. x1 exists for a million years but only experiences 1000 years of subjective time. x2 exists for 1000 years but experiences a million years of subjective time.

If you don't know which of the groups you are in you'll update differently depending on which rule you are following. If updating on objective time you'll update towards x1, if updating on subjective you'll update towards y1. What meta-rule we might propose that would generate differences between x1 and x2? I can't imagine what would.

Yes to both possibilities. But gbear605 is closer to what I was thinking.

Recommending an edit: The thousand instances of people in their respective instances of B rooms at time t are distinct situations, so it's confusing to say they're all in the same room. Say they're in red rooms while the others are in blue rooms, or something. A kind of room rather than a particular room.

It's sort of important to stress this because some patternists will genuinely try to erase the distinctions between the different rooms, you say, "you're talking about them like they're distinct, even if they encode exactly the same pattern you know they're conceptually distinct" but they just pretend they don't understand this and it's very annoying.

Phil of FB: (A more concrete example: 10,000 people are traveling to Mars. 1,000 board a large slow shuttle that takes a single trip to Mars between t1 and t3. Meanwhile, a really fast smaller shuttle takes 10 people at a time to Mars (going back and forth 900 times) during this same period. At time t3, all 10,000 people have safely arrived on Mars. If asked, at t3, whether one took the large slow shuttle or the fast small shuttle, one should say the latter. (Right?) But this is the opposite answer, I believe, that one should give if in the middle of the journey, at time t2, one is aroused from one's hibernation (let's say) and asked whether they are at that very moment on the slow or fast shuttle. Thus, it seems to matter whether the relevant event is ongoing or over. But I’m not exactly clear about why.)

My reply: Imagine there is a random person BOB. If Bob asked before flight to Mars, he will said that he will most likely fly small and quick spaceship. But if we ask a random person during the flight (And if it he is Bob - which is important point here) - than Bob is most likely on a large space plane. But the difference in both situation is that we must add probability that random person will be Bob. And this probability is rather small and will exactly compensate. The fact which is not represented is that there is third group of all travellers, which are already on Mars or wait start on earth, and when I am told that in the moment T3 I still flying, I get information, that I am not one of 8990 "waiters" and update my probabilities accordingly.

Now, about simulation. The fact that they will be run serially is very unlikely apriori, so any probability shift from it will be not high. And could not be known from inside a simulation, or it is not a simulation, or at least completely isolated simulation. But it is not the main objection. The main is that if I know that I am in the exact time moment in future, I also know that I am in simulation, as my time is not the same as outside time provided to me. There is also problems with many my copies in the infinite number of simulation and real worlds, which make total calculation even more difficult. The same me could appear in real world and in simulation, so saying that I am in one specific type of world is meaningless until I get some evidences. I am the same in many worlds. But after I get evidence that I am in a simulation, it is not a simulation.

In Bostrom's dissertation he says it's not clear if number of observers or the number of observer-moments is the appropriate reference class for anthropic reasoning.

I don't see how you are jumping to the fourth disjunct though. Like, maybe they run lots of simulations which are very short? But surely they would run enough to outweigh humanity's real history whichever way you measure it. Assuming they have posthuman levels of computational power.

How many seconds have you been in the room?

Let's say the time between t1 and t2 is 1 trillion seconds. Let us further assume that all people go through the rooms in the same amount of time (thus people spend 1 second each in room A, and 1 million seconds each in room B).

100 trillion of the 100.1 trillion observer moments between 0 and 1 seconds in a room occur in room A. All of the observer moments past 1 second occur in room B (this is somewhat flawed in that it is possible that the observers don't all spend the same amount of time in a given room, but even in the case where 100 million people stay in room A for 1 million seconds each, and the rest spend zero time, an observer who's been in a room for 1 million seconds is still overwhelmingly likely to be in room B. So basically the longer you've been in the room, the more probably you should consider it that you're in room B).

If an observer doesn't know how long they've been in a given room, I'm not sure how meaningful it is to call them "an" observer.