Rain comments on Open Thread: March 2010, part 3 - Less Wrong
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Here's a puzzle that involves time travel:
Suppose you have just built a machine that allows you to see one day into the future. Suppose also that you are firmly committed to realizing the particular future that the machine will show you. So if you see that the lights in your workshop are on tomorrow, you will make sure to leave them on; if they are off, you will make sure to leave them off. If you find the furniture rearranged, you will rearrange the furniture. If there is a cow in your workshop, you will spend the next 24 hours getting a cow into your workshop.
My question is this: What is your prior probability for any observation you can make with this machine? For example, what are the odds of the windows being open?
Can't answer until I know the laws of time travel.
No, seriously. Is the resulting universe randomly selected from all possible self-consistent ones? By what weighting? Does the resulting universe look like the result of iteration until a stable point is reached? And what about quantum branching?
Considering that all I know of causality and reality calls for non-circular causal graphs, I do feel a bit of justification in refusing to just hand out an answer.
Why is something like this an acceptable answer here, but not in Newcomb's Problem or Counterfactual Mugging?
Because it's clear what the intended clarification of these experiments is, but less so for time travel. When the thought experiments are posed, the goal is not to find the answer to some question, but to understand the described situation, which might as well involve additionally specifying it.
I can't imagine what you would want to know more about before giving an answer to Newcomb. Do you think Omega would have no choice but to use time travel?
No, but the mechanism Omega uses to predict my answer may be relevant to solving the problem. I have an old post about that. Also see the comment by Toby Ord there.
Because these don't involve time travel, but normal physics?
He did say "something like this", not "this".
I could tell you that time travel works by exploiting closed time-like curves in general relativity, and that quantum effects haven't been tested yet. But yes, that wouldn't be telling you how to handle probabilities.
So, it looks like this is a situation where the prior you were born with is as good as any other.