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A113 comments on Causal Universes - Less Wrong
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Last time I tried reasoning on this one I came up against an annoying divide-by-infinity problem.
Suppose you have a CD with infinite storage space - if this is not possible in your universe, use a normal CD with N bits of storage, it just makes the maths more complicated. Do the following:
If nothing arrives in your timeline from the future, write a 0 on the CD and send it back in time.
If a CD arrives from the future, read the number on it. Call this number X. Write X+1 on your own CD and send it back in time.
What is the probability distribution of the number on your CD? What is the probability that you didn't receive a CD from the future?
Once you've worked that one out, consider this similar algorithm:
If nothing arrives in your timeline from the future, write a 0 on the CD and send it back in time.
If a CD arrives from the future, read the number on it. Call this number X. Write X on your own CD and send it back in time.
What is the probability distribution of the number on your CD? What is the probability that you didn't receive a CD from the future?
The Novikov Self-Consistency Principle can help answer that. It is one of my favorite things. I don't think it was named in the post, but the concept was there.
The idea is that contradictions have probability zero. So the first scenario, the one with the paradox, doesn't happen. It's like the Outcome Pump if you hit the Emergency Regret Button. Instead of saying "do the following," it should say "attempt the following." If it is one self-consistent timeline, then you will fail. I don't know why you'll fail, probably just whatever reason is least unlikely, but the probability of success is zero. The probability distribution is virtually all at "you send the same number you received." (With other probability mass for "you misread" and "transcription error" and stuff).
If your experiment succeeds, then you are not dealing with a single, self-consistent universe. The Novikov principle has been falsified. The distribution of X depends on how many "previous" iterations there were, which depends on the likelihood that you do this sequence given that you receive such a CD. I think it would be a geometric distribution?
The second one is also interesting. Any number is self-consistent. So (back to Novikov) none of them are vetoed. If a CD arrives, the distribution is whatever distribution you would get if you were asked "Write a number." More likely, you don't receive a CD from the future. That's what happened today. And yesterday. And the day before. If you resolve to send the CD to yourself the previous day, then you will fail if self-consistency applies
Have you read HPMoR yet? I also highly recommend this short story.
I wasn't reasoning under NSCP, just trying to pick holes in cousin_it's model.
Though I'm interested in knowing why you think that one outcome is "more likely" than any other. What determines that?
I said not receiving a CD from the future is the most likely because that's what usually happens. But I do have a pretty huge sampling bias of mainly talking to people who don't have time machines.
i would expect "no CD" to be the most common even if you do have one, just because I feel like a closed time loop should take some effort to start. But this is probably a generalization from fiction, since if they happen in the real universe they do "just happen" with no previous cause. So I guess I can't support it well enough to justify my intuition. I will say that if I'm wrong about this, any time traveller should be prepared for these to happen all the time on totally trivial things.