Stuff that might help from a “getting your head around it perspective” if you were ever going to try would be films like:
- Fight Club
- The Hobbit
- Lord of the Rings
- What happened to Monday
- Terminal
I would also recommend the TV series Travelers [which unfortunately bears no relationship whatsoever to Our Game]. This show uses the concept of time travel into the past via imprinting the personality/memory of an individual from the future into the mind of someone in the past. In most cases, the past mind is completely overwritten, but sometimes the intruding future mind can access fragmentary memories. Of course, everyone who knows the past person is quite confused when "their" personality changes (often quite radically).
NOTE: In the show, ethical time Travelers are careful to only overwrite the minds of those known history records as having died moments after the Traveler arrives in their mind. E.g. the Travelers are not hijacking bodies, only sidetracking them from their otherwise-final fate. And - yes - there are UNethical Travelers who don't follow this rule. Also, prepubescent children have minds flexible enough to be overwritten briefly - to deliver a message from the future - then recover without awareness that anything strange had occurred.
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