It would appear from this week's Lost that the show is about to offer its answer to the Grandfather Paradox. If Sayid's relationship with Ben resulted in Sayid being sent back in time, but then he shoots Ben dead whilst the latter is still a boy, what happens?
From what we've already seen it appears the answer is that present-day Ben falls into a coma, which makes precisely zero sense, but then this is time-travel and none of it makes any sense anyway. (Update: plus, Gooder reminds me in comments that it was a bad case of being hit with an oar that felled Ben, though of course there may be more going on there).
It did though remind me of a conversation I once had with a former girlfriend. Her theory, assuming time travel is possible, is that the Grandfather Paradox was actually irrelevant, because it would be impossible to cause sufficient change to the universe to obliterate oneself. Since you already exist, you can't have succeeded in destroying yourself. Something must have happened to prevent it. (Update: the ever-knowledgeable Pause tells me in comments that this is known as the Novikov Self-Consistency Principle; I can't remember if Rockgirl told me that at the time or not).
Because I'm a mathematician and I love having arguments, I started trying to work out the specifics of her theory. I asked whether it would be possible to find a time machine at location A at time B to go back in time, and send a letter to yourself telling you not go to location A at time B. Or, more plausibly, ask them to go to location C at time B instead. Possibly, in my case, by suggesting location C is a strip-bar with a sale on.
Her response was that the letter would be intercepted. I asked what would happen if I sent two letters, the first one and a second one, that either did suggest location A at time B, or was just totally irrelevant to anything. How would this "interception" work? How would it know which letter to block? It would be like playing Russian roulette with the laws of causality.
This was the point at which she got annoyed. Or at least, the point at which I noticed she was annoyed, which experience has taught me isn't often the same thing.
Once you get to this point, though, you're stuffed. You can't make any action that will potentially prevent you from going back in time, no matter how oblique the connection is. Absent the concept of God, then you also can't make any action that under other circumstances would potentially prevent you from going back in time. That means that either a) the universe is conscious in some sense, and prevents too much interference, or b) the universe would block any attempt at time travel whatsoever.
The latter option, of course, seems more likely. There's the other theory that each trip through time would create its own reality, which of course solves some questions and raises others, but I'm sticking with b) for now.
Anyway, that concludes this somewhat rambling post. Any other time-travel theories people want to share? Logical corollaries to my witterings? The phone lines are open...