Time travel into the past is logically possible, provided that your presence in the past only causes things to happen that have, in fact, already happened. In other words: if time travel is restricted to only one universe (as in general relativity), then there is only one version of the universe that actually happened -- it's never the case that one thing happens in the first "draft" and another in the second "draft". So, it's not possible to go back in time and kill your grandfather, thereby causing yourself not to have been born. If you try this, you will be stopped by freak accidents, such as tripping on a banana peel. In other words: if you look at all initial conditions, and time-evolve them forward, then the vast majority will lead to inconsistencies (blatant ones as in the grandfather case, or subtler ones such as a blade of grass being in the wrong place). The only ones left with time travel involve amazing coincidences. My question to all of you is: does this make time travel extremely improbable? The paper Bananas Enough for Time Travel argues it doesn't, but I'm not sure I'm convinced. I think to solve this question, you would have to know how to assign probabilities to various boundary conditions in General Relativity, which I don't. So, are there bananas enough for time travel?