An example from Star Trek:
The Enterprise D crew go to Earth where Data's head and a stopwatch are discovered in a cave. The story plays through, it's not really important, suffice to say they end up bringing Arthur Conan Doyle (I think, it's not really important) forward in time to the Enterprise. While there he picks up his stopwatch, assuming he'd dropped it before leaving.
But then when he goes back to his own time, he intentionally leaves his stopwatch in the cave to be discovered centuries later. But surely, when its discovered, it will be about 600 years older than it was 'last' time it was discovered.
In which case, doesn't it stand to reason that this watch is infinitely old, like eternal?
In the same way, it's always Jane and he-Jane that give birth to baby-Jane. It makes you wonder how it all got started. Thinking it from Jane's perspective her/his family is in fact immortal.
Oh no, here come the temporal investigators. I should have listened when you told me to back off.
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