IMHO, depictions of time travel paradoxes reached their fictional literary zenith in the following dialog from David X. Cohen’s
“The Why of Fry”, episode #64 of the cartoon series “Futurama”:
Quote:
Nibblonian: "It's a genetic abnormality which resulted when you went back in time and performed certain actions which made you your own grandfather."
Fry: "I did do the nasty in the pasty!"
Nibbler: "Verily. And that past nastification is what shields you from the brains. You are the last hope of the universe."
Fry: "So, I really am important? How I feel when I'm drunk is correct?"
Nibblonian 1: "Yes. Except the Dave Matthews Band doesn't rock."
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Before, 2003, students of time travel science fiction could only refer to this scenario with uncatchy references to stories such as R. A. Heinlein’s 1959 short story
“All You Zombies-”, or thrown-off lines like “Temporal Parthenogenesis”. Now, thanks to Cohen, we can refer to the time travel paradox of
being, rather than
killing, one own grandfather by the catchy phrase “Past Nastification Paradox”.

(although RAH’s AYZ paradox is an notch more complex than DXC’s TWOF).
In all seriousness, time travel and its paradoxes can be seriously considered, yielding some interesting conclusions and implications, but it’s a technically demanding pursuit. On of my favorites approaches to a study of some fundamentals involves a hypothetical, frictionless pool table, with perfectly elastic balls where a ball entering one pocket emerges from another with the same momentum some amount of time after or before it enters. It’s possible to calculate the position of any system of balls at any time on the table, though the calculation needs to be done iteratively, as balls from one position in time jump back to interfere with themselves or others from at an earlier time.
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