The rat can be explained. It's kind of crappy, but it can be explained. I'll assign times to events just to make it wasier to understand.
We're supposed to assume that, at say 12:00, the rat is sent 1 hour into the future where Dan will teach him how to run the maze. (I guess it's just coincidence that the rat is sent to exact point that Dan planned to teach it the maze.) We're also supposed to assume that the rat learns the entire maze in less than 15 minutes (1:00-1:10). The rat learns the maze and then returns to past time, in which the rat can now perform the maze. The rat dies within 75 minutes (sometime between 1:10-1:15).
First question that arises is if the rat already knows how to run the maze then when and how does Dan teach the rat.
Dan will still teach the rat in 1 hour from the present time (12:00). We have to remmeber that in 1 hour(1:00), a rat mind that doesn't know the maze will show up from the past and be put into body of the future later rat. In other words, the mind that knew the maze is replaced by the mind that hasn't learned it yet.
Once Dan finished teaching the rat the maze, the rat returns to the past (1:10 back to 12:00). The body of the rat has it's reg mind restored (1:10) and then dies within a few minutes (before 1:15), just in time for Desmond to wake up (1:15).
As far as I can tell that can explain away the paradox involving the rat, but I'm sure I missed something.
The Rat
4, 8, 15, 16, 23, ??
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