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> Maybe, as the physicist Yakir Aharonov has advocated, our universe has not only a special, low-entropy initial state at the Big Bang, but also a “postselected

> Maybe, as the physicist Yakir Aharonov has advocated, our universe has not only a special, low-entropy initial state at the Big Bang, but also a “postselected final state,” toward which the outcomes of quantum measurements get mysteriously "pulled"—an effect that might show up in experiments as ever-so-slight deviations from the Born rule. Me, me! I know a kind of postselection effect that can be explained on a napkin (though nobody knows if it's actually true). As a bonus, it can affect not just the Born probabilities, but the probabilities of anything you choose, even things that already happened. Here's how it works. The idea is a variation on anthropic reasoning, originally due to Bostrom (http://www.anthropic-principle.com/preprints/cau/paradoxes.html http://www.anthropic-principle.com/preprints/cau/paradoxes.h...) If there's a completely fair quantum coin, and many people over many generations decide to have kids iff the coin comes up heads, then the coin might appear biased to us for anthropic reasons (more people in the heads-world than in the tails-world). You can influence all sorts of things this way, like Bostrom's example of Adam and Eve deciding to have kids iff a wounded deer passes by their cave to provide them with food. (That's if anthropic probabilities work in a certain intuitive way. If they work in the other intuitive way, you get other troubling paradoxes in the same vein. All imaginable options lead to weirdness AFAIK.) A few years back I spent a long time on such problems, and came up with a simple experiment about "spooky mental powers" that doesn't even involve creating new observers. It's completely non-anthropic and could be reproduced in a lab now, but the person inside the experiment will be deeply troubled. Here's how it goes: You're part of a ten-day experiment. Every night you get an injection that makes you forget what day it is. Every day you must pick between two envelopes, a red one and a blue one. One envelope contains $1000, the other contains nothing. At the end of the experiment, you go home with all the money you've made over the ten days. The kicker is how the envelopes get filled. On the first day, the experimenters flip a coin to choose whether the red or the blue one will contain $1000. On every subsequent day, they put the money in the envelope that you didn't pick on the first day. So here's the troubling thing. Imagine you're the kind of person who always picks the red envelope on principle. Just by having that preference, while you're inside the experiment, you're forcing the red envelope in front of you to be empty with high probability! Since your mental states over different days are indistinguishable to you, you can choose any randomized strategy of picking the envelope, and see the result of that strategy as if it already happened. In effect, you're sitting in a room with two envelopes, whose contents right now depend not just on what you'll choose right now, but on what randomized strategy you'll use to choose right now. If that's not freaky, I don't know what is. Going back to Aaronson's original point, the world as it looks to us might easily contain postselection and other weird things. Reducing everything to microstates is a valid way to look at the universe, but you aren't a microstate. You are an observer, a big complicated pattern that exists in many copies throughout the microstate, and the decisions of some copies might affect the probabilities observed by other copies at other times. The effects of such weirdness are small in practice, but unavoidable if you want a correct probabilistic theory of everything you observe (or a theory of decision-making for programs that can be copied, which is how I arrived at the problem).

omginternets 9y ago
>Since your mental states over different days are indistinguishable to you, you can choose any randomized strategy of picking the envelope, and see the result of that strategy as if it already happened. In effect, you're sitting in a room with two envelopes, whose contents right now depend not just on what you'll choose right now, but on what randomized strategy you'll use to choose right now. You lost me, and I'm not sure where... could you elaborate?
- cousin_it 9y ago
  Imagine two people going through this experiment, Alice and Bob. When Alice wakes up, she decides to pick red, because she always picks red which is her favorite color. Lo and behold, the red envelope is empty with >90% probability (because if Alice picked it on the first day, it will be empty on the next 9, and Alice doesn't know which day it is). When Bob wakes up, he decides to flip a coin, because that's how he always makes decisions. The coin tells him to pick red. Lo and behold, the red envelope is full with 50% probability. Even though Alice and Bob chose the same color. Nerdy explanation: if you maximize expected utility in the Von Neumann and Morgenstern sense, you can prove a theorem saying there's always an optimal strategy that's deterministic. You shouldn't need randomization, even if the world is random. In my experiment, the classical assumptions don't apply (specifically the axiom of independence), so the theorem becomes false and you need randomization to get the best result. The point of the experiment is showing that the axiom of independence isn't reasonable when you have copies, so vNM utility maximization needs to be modified. (For cases like this one, the right fix is modeling utility maximization as a single player game with imperfect information, chance moves, and behavioral strategies.) Bostrom's anthropic problems also show the same weirdness, but my contribution is making a non-anthropic scenario with fixed number of observers that still shows the weirdness.
visarga 9y ago
A problem similar to the one you're describing (having a number of options and limited number of attempts to maximize gains) is known as the "Multi-armed bandit" and has been studied in A/B testing, optimization and reinforcement learning. https://en.wikipedia.org/wiki/Multi-armed_bandit https://en.wikipedia.org/wiki/Multi-armed_bandit > In probability theory , the multi armed bandit problem (sometimes called the K - or N armed bandit problem) is a problem in which a gambler at a row of slot machines (sometimes known as "one armed bandits") has to decide which machines to play, how many times to play each machine and in which order to play them. When played, each machine provides a random reward from a probability distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. In essence it is a problem of balancing exploration and exploitation (the so called exploration/exploitation tradeoff), which is at the heart of how agents learn.

omginternets 9y ago

>Since your mental states over different days are indistinguishable to you, you can choose any randomized strategy of picking the envelope, and see the result of that strategy as if it already happened. In effect, you're sitting in a room with two envelopes, whose contents right now depend not just on what you'll choose right now, but on what randomized strategy you'll use to choose right now. You lost me, and I'm not sure where... could you elaborate?

cousin_it 9y ago
Imagine two people going through this experiment, Alice and Bob. When Alice wakes up, she decides to pick red, because she always picks red which is her favorite color. Lo and behold, the red envelope is empty with >90% probability (because if Alice picked it on the first day, it will be empty on the next 9, and Alice doesn't know which day it is). When Bob wakes up, he decides to flip a coin, because that's how he always makes decisions. The coin tells him to pick red. Lo and behold, the red envelope is full with 50% probability. Even though Alice and Bob chose the same color. Nerdy explanation: if you maximize expected utility in the Von Neumann and Morgenstern sense, you can prove a theorem saying there's always an optimal strategy that's deterministic. You shouldn't need randomization, even if the world is random. In my experiment, the classical assumptions don't apply (specifically the axiom of independence), so the theorem becomes false and you need randomization to get the best result. The point of the experiment is showing that the axiom of independence isn't reasonable when you have copies, so vNM utility maximization needs to be modified. (For cases like this one, the right fix is modeling utility maximization as a single player game with imperfect information, chance moves, and behavioral strategies.) Bostrom's anthropic problems also show the same weirdness, but my contribution is making a non-anthropic scenario with fixed number of observers that still shows the weirdness.

visarga 9y ago

A problem similar to the one you're describing (having a number of options and limited number of attempts to maximize gains) is known as the "Multi-armed bandit" and has been studied in A/B testing, optimization and reinforcement learning. https://en.wikipedia.org/wiki/Multi-armed_bandit https://en.wikipedia.org/wiki/Multi-armed_bandit > In probability theory , the multi armed bandit problem (sometimes called the K - or N armed bandit problem) is a problem in which a gambler at a row of slot machines (sometimes known as "one armed bandits") has to decide which machines to play, how many times to play each machine and in which order to play them. When played, each machine provides a random reward from a probability distribution specific to that machine. The objective of the gambler is to maximize the sum of rewards earned through a sequence of lever pulls. In essence it is a problem of balancing exploration and exploitation (the so called exploration/exploitation tradeoff), which is at the heart of how agents learn.