So are you guys saying that Willis is a kid at the same time he (Hodor) is an adult? The timelines are happening at the same time in some nonlinear circle? How does aging work then? How dies it know which no timeline version to age and at what rate? Interesting g stuff be definitely not as non-complicated as some are making it seem.
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There are a lot of different ways writers have handled time travel and paradoxes from them, and unless GRRM explains it in the story we won't really know. And I wouldn't be surprised if he never does.
Take the grandfather paradox... you go back in time and kill your grandfather when he was a young boy. What happens? If he dies without having kids you wouldn't have existed. If you didn't exist you can't go back in time to kill him, so you'd exist. But if you exist you go back in time. Loop. Paradox. Some writers leave it like that. Others use a number of ideas for how it might work to deal with the paradox.
One idea is there are separate Timelines. Where you exist and end up time traveling from is Timeline1. You go back in time and kill grandpa and then alternate Timeline2 starts up with dead grandpa where you never exist. A writer could have you return to the 'present' then, but it's the present in Timeline2 where you don't exist. Since you are from Timeline1 and have just traveled into Timeline2 you don't need to have been born in Timeline2, so it isn't a paradox. An example could play out like
It's a Wonderful Life to show George what the world would be like if he never existed, the angel changes the past and lets him run through the resulting Timeline2. Then when he learns his lesson he's returned to his original Timeline1 where he does exist. I know it was probably a dream in that movie and not time travel, but it makes a good example.
A writer may let there be both copies of you from different Timelines existing together (the movie Timecop and TV show 12 Monkeys), or may have your time traveling self replace the 'you' of that Timeline if there is one (Back to the Future where Marty returns to the present of Timeline2 and he's the only Marty) so there's only one of you present.
Another popular method is "time is a river". You can throw a rock in a river and it'll affect its flow, but the water around it will adjust and in reality you won't have changed much. This treats the flow of time the same way. You could go back in time and kill Einstein but someone else would come up with his theories and affect the world in a similar fashion so in reality not much changed. In the grandfather paradox version, someone else has a kid who has the impact of your father and has a kid who has the impact of you, even if he doesn't look just like you.
Ok, so GoT. It hasn't given us an explanation. We know Hodor's future moment of holding the door affected him in the past in some way that affected how he lived out his life.
It could be spun several ways. Time is a river... we would assume that if Hodor was never affected, Bran would still have fallen, got paralyzed, a mentally healthy Willis would have carried him or even someone else would have. Details may have differed but the overall major flow of the story and Timeline would have been the same. Events play out much the same whether it's Willis or Hodor.
Or they could just leave it a potential paradox and you can assume with Willis instead of Hodor that Bran would never have made it to the point he could view the past, effectively becoming a grandfather paradox.
If I was writing it and wanted to explain away the paradox I'd like a version with a first alternate timeline that got us to the present story we witnessed. Some other Timeline1 (not what we saw on TV) played out with a healthy Willis that still resulted in Bran visiting the past and Willis getting Hodor'd for the first time. This started Timeline2 with Hodor instead of Willis which plays out how we saw on TV. Now when Bran from Timeline2 who grew up with a Hodor views the past and Willis gets Hodor'd, nothing changes. The result is identical to our Timeline2 we already saw.
So in my version, time could be said to be a closed loop NOW, but it wasn't always that way.