This isn't really relevant to the post but:
And you could stand outside time and look at the cycle, and ask, "Why is this cycle here?" The answer to that would presumably lie within the laws of physics, rather than Jane having written the laws of physics to create herself.
I'm always annoyed when fiction has stable time loops, but doesn't answer this question. The only time I've seen something resembling an answer is continuum, and they only answered it to the amount necessary to play the game.
The rules I find most obvious would be that each possibility is equally likely (for a deterministic universe), and that the probability is proportional to the probability of the loop causing itself (for an indeterministic universe). It would look pretty similar either way, and the upshot is that the difficulty of sending something back in time increases exponentially with both the length of the message and the time. This would mean that you could only send short text messages back, and not too far, otherwise you'd end up with something shorter and garbled that happens to be able to cause itself.
Of course, all that is for one timeline. Many Worlds doesn't really work for stable time loops, but you could get something similar: The probability of time travel arriving is the probability of it being sent from any possible future. If you wait for your future self to send you a bit, and then flip it and send it to your past self, you'd have a 50% chance of getting 1 and sending 0, and a 50% chance of getting 0 and sending 1. Basically, the information would leave through a different branch than it entered from.
The only time I've seen something resembling an answer is continuum
Would you mind outlining that answer, for those of us who aren't familiar with the game?
I've never played the game either. I know you can do stuff like declare that you will go back in time and put an item out of sight, then reach there and the item will be there. You can also declare that you will go back in time to help yourself out of this mess, and then your future self will appear to help you.
I guess the rule is that the stable time-loops must be decided before it gets noticed. It's not the kind of rule you'd expect from reality.
I'm not sure what happens if two people fight and try to use this tactic, even though only one can win. My guess is that the winner has to trick out time to prevent fragging. For example, give their enemy the tools they planned on giving themselves, or sending an actor back to pretend to be their future selves.
Today's post, The Ultimate Source was originally published on 15 June 2008. A summary (taken from the LW wiki):
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